Finite Group Databasebeta

← #35569415

Subgroups — #35569415

Order 21248.

2736 conjugacy classes of subgroups.

The subgroup lattice has 1700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128341C211yesmaximal, characteristic
2#24910622C211yesmaximal, characteristic, complemented
3#24910616C211yesmaximal, characteristic, complemented
4#24910607C211yesmaximal, characteristic, complemented
5#24910605C211yesmaximal, characteristic, complemented
6#24910537C211yesmaximal, characteristic, complemented
7#24910476C211yesmaximal, characteristic, complemented
8#24910469C211yesmaximal, characteristic, complemented
9#24910445C211yesmaximal, characteristic, complemented
10#24910442C211yesmaximal, characteristic, complemented
11#24910413C211yesmaximal, characteristic, complemented
12#24910361C211yesmaximal, characteristic, complemented
13#24910310C211yesmaximal, characteristic, complemented
14#24910303C211yesmaximal, characteristic, complemented
15#24910279C211yesmaximal, characteristic, complemented
16#24910260C211yesmaximal, characteristic, complemented
17#24910253C211yesmaximal, characteristic, complemented
18#24910172C211yesmaximal, characteristic, complemented
19#24910156C211yesmaximal, characteristic, complemented
20#24910151C211yesmaximal, characteristic, complemented
21#24910151C211yesmaximal, characteristic, complemented
22#24910123C211yesmaximal, characteristic, complemented
23#24910118C211yesmaximal, characteristic, complemented
24#24910103C211yesmaximal, characteristic, complemented
25#24910077C211yesmaximal, characteristic, complemented
26#24910074C211yesmaximal, characteristic, complemented
27#24910052C211yesmaximal, characteristic, complemented
28C4×#14581769C211yesmaximal, characteristic, complemented
29C2×#19127601C211yesmaximal, characteristic, complemented
30#24909899C211yesmaximal, characteristic, complemented
31C83×#2342C211yesmaximal, characteristic, complemented
32C22×#13050590C2211yescharacteristic
33C23×C22⋊D83C2211yescharacteristic
34#19128341C4116yescomplemented
35C2×#14581778C2211yescharacteristic
36C2×#14581775C2211yescharacteristic
37C2×#14581774C2211yescharacteristic
38C2×#14581769C2211yescharacteristic
39C2×#14581766C2211yescharacteristic
40C2×#14581765C2211yescharacteristic
41C2×#14581765C2211yescharacteristic
42C2×#14581762C2211yescharacteristic
43C2×#14581761C2211yescharacteristic
44C2×C4×Dic166C2211yescharacteristic, complemented
45C2×C4×Dic166C2211yescharacteristic, complemented
46C2×C4×D332C2211yescharacteristic, complemented
47C2×C4×C22⋊D83C2211yescharacteristic
48C2×C4×C22⋊D83C2211yescharacteristic
49C2×(C22⋊D83)⋊C4C2211yescharacteristic
50C2×(C22⋊D83)⋊C4C2211yescharacteristic
51C2×(C22⋊D83)⋊C4C2211yescharacteristic
52C2×(C22⋊D83)⋊C4C2211yescharacteristic
53C2×(C22⋊D83)⋊C4C2211yescharacteristic, complemented
54C2×#14581750C2211yescharacteristic, complemented
55C2×#14581750C2211yescharacteristic, complemented
56C22×Dic83⋊C4C2211yescharacteristic
57C2×C4⋊C4×D83C2211yescharacteristic, complemented
58C22×C22⋊Dic83C2211yescharacteristic
59C22×C22⋊Dic83C2211yescharacteristic
60C22×(C2×D83)⋊C4C2211yescharacteristic
61C22×(C2×D83)⋊C4C2211yescharacteristic
62C2×C22⋊C4×D83C2211yescharacteristic
63C2×C22⋊C4×D83C2211yescharacteristic
64C22×C4×Dic83C2211yescharacteristic
65#19127605C2211yescharacteristic, complemented
66#19127605C2211yescharacteristic, complemented
67#19127603C2211yescharacteristic, complemented
68#19127603C2211yescharacteristic, complemented
69#19127603C2211yescharacteristic, complemented
70#19127601C2211yescharacteristic
71#19127601C2211yescharacteristic
72#19127601C2211yescharacteristic
73#19127601C2211yescharacteristic
74#19127601C2211yescharacteristic
75#19127601C2211yescharacteristic
76#19127601C2211yescharacteristic
77#19127601C2211yescharacteristic
78#19127601C2211yescharacteristic
79#19127601C2211yescharacteristic
80#19127601C2211yescharacteristic, complemented
81#19127601C2211yescharacteristic, complemented
82#19127601C2211yescharacteristic, complemented
83#19127599C2211yescharacteristic, complemented
84#19127598C2211yescharacteristic, complemented
85#19127598C2211yescharacteristic, complemented
86#19127598C2211yescharacteristic, complemented
87#19127598C2211yescharacteristic, complemented
88#19127596C2211yescharacteristic, complemented
89#19127595C2211yescharacteristic, complemented
90#19127595C2211yescharacteristic, complemented
91#19127595C2211yescharacteristic, complemented
92#19127593C2211yescharacteristic, complemented
93#19127593C2211yescharacteristic, complemented
94#19127593C2211yescharacteristic, complemented
95#19127593C2211yescharacteristic, complemented
96#19127593C2211yescharacteristic, complemented
97#19127593C2211yescharacteristic, complemented
98#19127592C2211yescharacteristic, complemented
99#19127592C2211yescharacteristic, complemented
100#19127592C2211yescharacteristic, complemented
101#19127591C2211yescharacteristic, complemented
102#19127591C2211yescharacteristic, complemented
103#19127591C2211yescharacteristic, complemented
104#19127589C2211yescharacteristic, complemented
105#19127589C2211yescharacteristic, complemented
106#19127589C2211yescharacteristic, complemented
107#19127588C2211yescharacteristic, complemented
108#19127588C2211yescharacteristic, complemented
109#19127585C2211yescharacteristic, complemented
110#19127584C2211yescharacteristic, complemented
111#19127584C2211yescharacteristic, complemented
112#19127582C2211yescharacteristic, complemented
113#19127580C2211yescharacteristic
114#19127579C2211yescharacteristic, complemented
115#19127579C2211yescharacteristic, complemented
116#19127579C2211yescharacteristic, complemented
117#19127579C2211yescharacteristic, complemented
118#19127578C2211yescharacteristic
119#19127578C2211yescharacteristic
120#19127578C2211yescharacteristic
121#19127578C2211yescharacteristic, complemented
122#19127577C2211yescharacteristic
123#19127577C2211yescharacteristic
124#19127577C2211yescharacteristic, complemented
125#19127577C2211yescharacteristic, complemented
126#19127577C2211yescharacteristic, complemented
127#19127576C2211yescharacteristic
128#19127576C2211yescharacteristic
129#19127576C2211yescharacteristic
130#19127576C2211yescharacteristic
131#19127576C2211yescharacteristic, complemented
132#19127576C2211yescharacteristic, complemented
133#19127576C2211yescharacteristic, complemented
134#19127576C2211yescharacteristic, complemented
135#19127575C2211yescharacteristic, complemented
136#19127575C2211yescharacteristic, complemented
137#19127575C2211yescharacteristic, complemented
138#19127575C2211yescharacteristic, complemented
139#19127574C2211yescharacteristic
140#19127573C2211yescharacteristic
141#19127573C2211yescharacteristic, complemented
142#19127572C2211yescharacteristic, complemented
143#19127572C2211yescharacteristic, complemented
144#19127572C2211yescharacteristic, complemented
145#19127570C2211yescharacteristic, complemented
146#19127563C2211yescharacteristic, complemented
147#19127561C2211yescharacteristic, complemented
148#19127561C2211yescharacteristic, complemented
149#19127561C2211yescharacteristic, complemented
150#19127561C2211yescharacteristic, complemented
151#19127560C2211yescharacteristic, complemented
152#19127560C2211yescharacteristic, complemented
153#19127560C2211yescharacteristic, complemented
154#19127559C2211yescharacteristic
155#19127558C2211yescharacteristic, complemented
156#19127558C2211yescharacteristic, complemented
157#19127558C2211yescharacteristic, complemented
158#19127556C2211yescharacteristic
159C4⋊C4×Dic83C2211yescharacteristic, complemented
160C4×Dic83⋊C4C2211yescharacteristic, complemented
161C4×Dic83⋊C4C2211yescharacteristic, complemented
162C4×Dic83⋊C4C2211yescharacteristic, complemented
163C4×C4⋊Dic83C2211yescharacteristic, complemented
164#19127552C2211yescharacteristic, complemented
165C22⋊C4×Dic83C2211yescharacteristic
166C22⋊C4×Dic83C2211yescharacteristic
167C22⋊C4×Dic83C2211yescharacteristic, complemented
168C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
169C4×C22⋊Dic83C2211yescharacteristic
170#19127548C2211yescharacteristic, complemented
171#19127548C2211yescharacteristic, complemented
172#19127546C2211yescharacteristic, complemented
173C2×#117×C83C2211yescharacteristic, complemented
174C22×C22⋊C4×C83C2211yescharacteristic
175C22×C22⋊C4×C83C2211yescharacteristic
176#388×C83C2211yescharacteristic, complemented
177#388×C83C2211yescharacteristic, complemented
178#388×C83C2211yescharacteristic, complemented
179#388×C83C2211yescharacteristic, complemented
180#385×C83C2211yescharacteristic
181#385×C83C2211yescharacteristic
182#381×C83C2211yescharacteristic, complemented
183#380×C83C2211yescharacteristic, complemented
184#379×C83C2211yescharacteristic
185C4×C22⋊C4×C83C2211yescharacteristic
186C4×C22⋊C4×C83C2211yescharacteristic
187C4×C22⋊C4×C83C2211yescharacteristic, complemented
188C24×D83C2311yescharacteristic
189C2×#13050590—42no—
190C2×#13050590—42no—
191C2×#13050590C2×C418yescomplemented
192C22×Dic166C2311yescharacteristic
193C22×D332C2311yescharacteristic
194C22×D332C2311yescharacteristic
195C22×C22⋊D83—42no—
196C22×C22⋊D83—42no—
197C22×C22⋊D83C2×C418yescomplemented
198C22×C22⋊D83C2311yescharacteristic
199C22×C22⋊D83C2311yescharacteristic
200C22×C22⋊D83C2311yescharacteristic
201C22×C22⋊D83C2311yescharacteristic
202C22×C22⋊D83C2311yescharacteristic
203C22×C22⋊D83C2311yescharacteristic
204C22×C22⋊D83C2311yescharacteristic
205C23×Dic83C2311yescharacteristic
206C23×Dic83C2311yescharacteristic
207C23×Dic83C2311yescharacteristic
208C23×Dic83C2311yescharacteristic
209C23×Dic83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212C22×C4×D83C2311yescharacteristic
213C22×C4×D83C2311yescharacteristic
214C22×C4×D83C2311yescharacteristic
215C22×C4×D83C2311yescharacteristic
216C22×C4×D83C2311yescharacteristic
217#14581778C2×C418yescomplemented
218#14581775C2×C418yescomplemented
219#14581774C2×C418yescomplemented
220#14581769C2×C418yescomplemented
221#14581766C2×C418yescomplemented
222#14581765C2×C418yescomplemented
223#14581765C2×C418yescomplemented
224#14581762C2×C418yescomplemented
225#14581761C2×C418yescomplemented
226C4×Dic166—42no—
227C4×Dic166—42no—
228C4×D332—42no—
229C4×C22⋊D83—42no—
230C4×C22⋊D83C2×C418yescomplemented
231(C22⋊D83)⋊C4—42no—
232(C22⋊D83)⋊C4—42no—
233(C22⋊D83)⋊C4—42no—
234(C22⋊D83)⋊C4—42no—
235(C22⋊D83)⋊C4C2×C418yescomplemented
236#14581750—42no—
237#14581750—42no—
238C2×C4⋊Dic83C2311yescharacteristic
239C2×C4⋊Dic83C2311yescharacteristic
240C2×C4⋊Dic83C2311yescharacteristic
241C2×C4⋊Dic83C2311yescharacteristic
242C2×C4⋊Dic83C2311yescharacteristic
243C2×C4⋊Dic83C2311yescharacteristic
244C2×C4⋊Dic83C2311yescharacteristic
245C2×C4⋊Dic83C2311yescharacteristic
246C2×C4⋊Dic83C2311yescharacteristic
247C2×Dic83⋊C4—42no—
248C2×Dic83⋊C4C2311yescharacteristic
249C2×Dic83⋊C4C2311yescharacteristic
250C2×Dic83⋊C4C2311yescharacteristic
251C2×Dic83⋊C4C2311yescharacteristic
252C2×Dic83⋊C4C2311yescharacteristic
253C2×Dic83⋊C4C2311yescharacteristic
254C2×Dic83⋊C4C2311yescharacteristic
255C2×Dic83⋊C4C2311yescharacteristic
256C2×Dic83⋊C4C2311yescharacteristic
257C2×Dic83⋊C4C2311yescharacteristic
258C2×Dic83⋊C4C2311yescharacteristic
259C2×Dic83⋊C4C2311yescharacteristic
260C2×Dic83⋊C4C2311yescharacteristic
261C2×Dic83⋊C4C2311yescharacteristic
262C2×Dic83⋊C4C2311yescharacteristic
263C4⋊C4×D83—42no—
264C2×C22⋊Dic83—42no—
265C2×C22⋊Dic83—42no—
266C2×C22⋊Dic83C2311yescharacteristic
267C2×C22⋊Dic83C2311yescharacteristic
268C2×C22⋊Dic83C2311yescharacteristic
269C2×C22⋊Dic83C2311yescharacteristic
270C2×C22⋊Dic83C2311yescharacteristic
271C2×C22⋊Dic83C2311yescharacteristic
272C2×C22⋊Dic83C2311yescharacteristic
273C2×C22⋊Dic83C2311yescharacteristic
274C2×C22⋊Dic83C2311yescharacteristic
275C2×C22⋊Dic83C2311yescharacteristic
276C2×C22⋊Dic83C2311yescharacteristic
277C2×(C2×D83)⋊C4—42no—
278C2×(C2×D83)⋊C4—42no—
279C2×(C2×D83)⋊C4C2311yescharacteristic
280C2×(C2×D83)⋊C4C2311yescharacteristic
281C2×(C2×D83)⋊C4C2311yescharacteristic
282C2×(C2×D83)⋊C4C2311yescharacteristic
283C2×(C2×D83)⋊C4C2311yescharacteristic
284C2×(C2×D83)⋊C4C2311yescharacteristic
285C2×(C2×D83)⋊C4C2311yescharacteristic
286C2×(C2×D83)⋊C4C2311yescharacteristic
287C2×(C2×D83)⋊C4C2311yescharacteristic
288C2×(C2×D83)⋊C4C2311yescharacteristic
289C2×(C2×D83)⋊C4C2311yescharacteristic
290C2×(C2×D83)⋊C4C2311yescharacteristic
291C2×(C2×D83)⋊C4C2311yescharacteristic
292C2×(C2×D83)⋊C4C2311yescharacteristic
293C2×(C2×D83)⋊C4C2311yescharacteristic
294C2×(C2×D83)⋊C4C2311yescharacteristic
295C2×(C2×D83)⋊C4C2311yescharacteristic
296C2×(C2×D83)⋊C4C2311yescharacteristic
297C2×(C2×D83)⋊C4C2311yescharacteristic
298C2×(C2×D83)⋊C4C2311yescharacteristic
299C2×(C2×D83)⋊C4C2311yescharacteristic
300C2×(C2×D83)⋊C4C2311yescharacteristic
301C2×(C2×D83)⋊C4C2311yescharacteristic
302C2×(C2×D83)⋊C4C2311yescharacteristic
303C2×(C2×D83)⋊C4C2311yescharacteristic
304C22⋊C4×D83—42no—
305C22⋊C4×D83C2×C418yescomplemented
306C2×C4×Dic83—42no—
307C2×C4×Dic83C2311yescharacteristic
308C2×C4×Dic83C2311yescharacteristic
309C2×C4×Dic83C2311yescharacteristic
310C2×C4×Dic83C2311yescharacteristic
311C2×C4×Dic83C2311yescharacteristic
312C2×C4×Dic83C2311yescharacteristic
313C2×C4×Dic83C2311yescharacteristic
314C2×C4×Dic83C2311yescharacteristic
315C2×C4×Dic83C2311yescharacteristic
316C2×C4×Dic83C2311yescharacteristic
317C2×C4×Dic83C2311yescharacteristic
318C2×C4×Dic83C2311yescharacteristic
319C2×C4×Dic83C2311yescharacteristic
320C83⋊#95C2311yescharacteristic
321C83⋊#95C2311yescharacteristic
322C83⋊#95C2311yescharacteristic
323C83⋊#95C2311yescharacteristic
324C83⋊#95C2311yescharacteristic
325C83⋊#95C2311yescharacteristic
326C83⋊#95C2311yescharacteristic
327C83⋊#95C2311yescharacteristic
328C83⋊#95C2311yescharacteristic
329C83⋊#95C2311yescharacteristic
330C83⋊#95C2311yescharacteristic
331C83⋊#95C2311yescharacteristic
332C83⋊#95C2311yescharacteristic
333C83⋊#95C2311yescharacteristic
334C83⋊#95C2311yescharacteristic
335C83⋊#95C2311yescharacteristic
336C83⋊#95C2311yescharacteristic
337C83⋊#95C2311yescharacteristic
338C83⋊#95C2311yescharacteristic
339C83⋊#95C2311yescharacteristic
340C83⋊#95C2311yescharacteristic
341C83⋊#95C2311yescharacteristic
342C83⋊#95C2311yescharacteristic
343C83⋊#95C2311yescharacteristic
344C25×C83C2311yescharacteristic
345C23×C4×C83C2311yescharacteristic
346C23×C4×C83C2311yescharacteristic
347C23×C4×C83C2311yescharacteristic
348C23×C4×C83C2311yescharacteristic
349#117×C83—42no—
350C2×C4⋊C4×C83C2311yescharacteristic
351C2×C4⋊C4×C83C2311yescharacteristic
352C2×C4⋊C4×C83C2311yescharacteristic
353C2×C4⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83—42no—
355C2×C22⋊C4×C83C2×C418yescomplemented
356C2×C22⋊C4×C83C2311yescharacteristic
357C2×C22⋊C4×C83C2311yescharacteristic
358C2×C22⋊C4×C83C2311yescharacteristic
359C2×C22⋊C4×C83C2311yescharacteristic
360C2×C22⋊C4×C83C2311yescharacteristic
361C2×C22⋊C4×C83C2311yescharacteristic
362C2×C22⋊C4×C83C2311yescharacteristic
363C2×C22⋊C4×C83C2311yescharacteristic
364C2×C22⋊C4×C83C2311yescharacteristic
365C2×C22⋊C4×C83C2311yescharacteristic
366C2×C22⋊C4×C83C2311yescharacteristic
367C2×C22⋊C4×C83C2311yescharacteristic
368C2×C22⋊C4×C83C2311yescharacteristic
369C2×C22⋊C4×C83C2311yescharacteristic
370C2×C42×C83C2311yescharacteristic
371C2×C42×C83C2311yescharacteristic
372C2×C42×C83C2311yescharacteristic
373C2×C42×C83C2311yescharacteristic
374#95×C83C2311yescharacteristic
375#95×C83C2311yescharacteristic
376#95×C83C2311yescharacteristic
377#95×C83C2311yescharacteristic
378#95×C83C2311yescharacteristic
379#95×C83C2311yescharacteristic
380#95×C83C2311yescharacteristic
381#95×C83C2311yescharacteristic
382C23×D83—22no—
383C23×D83—22no—
384C23×D83—41no—
385C23×D83—41no—
386C23×D83—41no—
387C23×D83—41no—
388C23×D83C22×C414yes—
389C23×D83C2411yescharacteristic
390C23×D83C2411yescharacteristic
391C23×D83C2411yescharacteristic
392#13050590—416no—
393C2×Dic166—22no—
394C2×Dic166—22no—
395C2×Dic166C22×C414yes—
396C2×D332—41no—
397C2×D332—41no—
398C2×D332—41no—
399C2×D332—41no—
400C2×D332C22×C414yes—
401C2×D332C22×C414yes—
402C2×C22⋊D83—22no—
403C2×C22⋊D83—22no—
404C2×C22⋊D83—22no—
405C2×C22⋊D83—22no—
406C2×C22⋊D83—22no—
407C2×C22⋊D83—22no—
408C2×C22⋊D83—416no—
409C2×C22⋊D83—41no—
410C2×C22⋊D83—41no—
411C2×C22⋊D83—41no—
412C2×C22⋊D83—41no—
413C2×C22⋊D83—41no—
414C2×C22⋊D83—41no—
415C2×C22⋊D83—41no—
416C2×C22⋊D83—41no—
417C2×C22⋊D83C22×C414yes—
418C2×C22⋊D83C22×C414yes—
419C2×C22⋊D83C22×C414yes—
420C2×C22⋊D83C22×C414yes—
421C2×C22⋊D83C22×C414yes—
422C2×C22⋊D83C22×C414yes—
423C2×C22⋊D83C22×C414yes—
424C22×Dic83—22no—
425C22×Dic83—22no—
426C22×Dic83—22no—
427C22×Dic83—22no—
428C22×Dic83—41no—
429C22×Dic83—41no—
430C22×Dic83—41no—
431C22×Dic83—41no—
432C22×Dic83—41no—
433C22×Dic83—41no—
434C22×Dic83—41no—
435C22×Dic83—41no—
436C22×Dic83—41no—
437C22×Dic83—41no—
438C22×Dic83C22×C414yes—
439C22×Dic83C2411yescharacteristic
440C22×Dic83C2411yescharacteristic
441C22×Dic83C2411yescharacteristic
442C22×Dic83C2411yescharacteristic
443C22×Dic83C2411yescharacteristic
444C22×Dic83C2411yescharacteristic
445C22×Dic83C2411yescharacteristic
446C22×Dic83C2411yescharacteristic
447C22×Dic83C2411yescharacteristic
448C22×Dic83C2411yescharacteristic
449C22×Dic83C2411yescharacteristic
450C22×Dic83C2411yescharacteristic
451C22×Dic83C2411yescharacteristic
452C2×C4×D83—22no—
453C2×C4×D83—22no—
454C2×C4×D83—41no—
455C2×C4×D83—41no—
456C2×C4×D83—41no—
457C2×C4×D83—41no—
458C2×C4×D83—41no—
459C2×C4×D83—41no—
460C2×C4×D83—41no—
461C2×C4×D83—41no—
462C2×C4×D83—41no—
463C2×C4×D83—41no—
464C2×C4×D83—41no—
465C2×C4×D83—41no—
466C2×C4×D83—41no—
467C2×C4×D83—41no—
468C2×C4×D83—41no—
469C2×C4×D83—41no—
470C2×C4×D83C22×C414yes—
471C2×C4×D83C22×C414yes—
472C2×C4×D83C22×C414yes—
473C4⋊Dic83—41no—
474C4⋊Dic83—41no—
475C4⋊Dic83—41no—
476C4⋊Dic83—41no—
477C4⋊Dic83—41no—
478C4⋊Dic83—41no—
479C4⋊Dic83—41no—
480C4⋊Dic83—41no—
481C4⋊Dic83C22×C414yes—
482Dic83⋊C4—22no—
483Dic83⋊C4—22no—
484Dic83⋊C4—22no—
485Dic83⋊C4—22no—
486Dic83⋊C4—41no—
487Dic83⋊C4—41no—
488Dic83⋊C4—41no—
489Dic83⋊C4—41no—
490Dic83⋊C4—41no—
491Dic83⋊C4—41no—
492Dic83⋊C4—41no—
493Dic83⋊C4—41no—
494Dic83⋊C4C22×C414yes—
495Dic83⋊C4C22×C414yes—
496Dic83⋊C4C22×C414yes—
497C22⋊Dic83—22no—
498C22⋊Dic83—22no—
499C22⋊Dic83—41no—
500C22⋊Dic83—41no—
501C22⋊Dic83—41no—
502C22⋊Dic83—41no—
503C22⋊Dic83—41no—
504C22⋊Dic83—41no—
505C22⋊Dic83C22×C414yes—
506C22⋊Dic83C22×C414yes—
507C22⋊Dic83C22×C414yes—
508(C2×D83)⋊C4—22no—
509(C2×D83)⋊C4—22no—
510(C2×D83)⋊C4—22no—
511(C2×D83)⋊C4—41no—
512(C2×D83)⋊C4—41no—
513(C2×D83)⋊C4—41no—
514(C2×D83)⋊C4—41no—
515(C2×D83)⋊C4—41no—
516(C2×D83)⋊C4—41no—
517(C2×D83)⋊C4—41no—
518(C2×D83)⋊C4—41no—
519(C2×D83)⋊C4—41no—
520(C2×D83)⋊C4—41no—
521(C2×D83)⋊C4—41no—
522(C2×D83)⋊C4—41no—
523(C2×D83)⋊C4—41no—
524(C2×D83)⋊C4—41no—
525(C2×D83)⋊C4—41no—
526(C2×D83)⋊C4—41no—
527(C2×D83)⋊C4—41no—
528(C2×D83)⋊C4C22×C414yes—
529(C2×D83)⋊C4C22×C414yes—
530(C2×D83)⋊C4C22×C414yes—
531(C2×D83)⋊C4C22×C414yes—
532(C2×D83)⋊C4C22×C414yes—
533C4×Dic83—22no—
534C4×Dic83—22no—
535C4×Dic83—22no—
536C4×Dic83—22no—
537C4×Dic83—22no—
538C4×Dic83—41no—
539C4×Dic83—41no—
540C4×Dic83—41no—
541C4×Dic83—41no—
542C4×Dic83—41no—
543C4×Dic83—41no—
544C4×Dic83—41no—
545C4×Dic83C22×C414yes—
546C24×C83—22no—
547C24×C83—22no—
548C24×C83—41no—
549C24×C83—41no—
550C24×C83—41no—
551C24×C83—41no—
552C24×C83C22×C414yes—
553C24×C83C2411yescharacteristic
554C24×C83C2411yescharacteristic
555C24×C83C2411yescharacteristic
556C22×C4×C83—22no—
557C22×C4×C83—22no—
558C22×C4×C83—22no—
559C22×C4×C83—41no—
560C22×C4×C83—41no—
561C22×C4×C83—41no—
562C22×C4×C83—41no—
563C22×C4×C83—41no—
564C22×C4×C83—41no—
565C22×C4×C83—41no—
566C22×C4×C83C22×C414yes—
567C22×C4×C83C22×C414yes—
568C22×C4×C83C2411yescharacteristic
569C22×C4×C83C2411yescharacteristic
570C22×C4×C83C2411yescharacteristic
571C22×C4×C83C2411yescharacteristic
572C22×C4×C83C2411yescharacteristic
573C22×C4×C83C2411yescharacteristic
574C22×C4×C83C2411yescharacteristic
575C22×C4×C83C2411yescharacteristic
576C22×C4×C83C2411yescharacteristic
577C22×C4×C83C2411yescharacteristic
578C22×C4×C83C2411yescharacteristic
579C22×C4×C83C2411yescharacteristic
580C4⋊C4×C83—22no—
581C4⋊C4×C83—41no—
582C4⋊C4×C83—41no—
583C4⋊C4×C83—41no—
584C22⋊C4×C83—22no—
585C22⋊C4×C83—22no—
586C22⋊C4×C83—22no—
587C22⋊C4×C83—22no—
588C22⋊C4×C83—41no—
589C22⋊C4×C83—41no—
590C22⋊C4×C83—41no—
591C22⋊C4×C83—41no—
592C22⋊C4×C83—41no—
593C22⋊C4×C83—41no—
594C22⋊C4×C83C22×C414yes—
595C22⋊C4×C83C22×C414yes—
596C22⋊C4×C83C22×C414yes—
597C22⋊C4×C83C22×C414yes—
598C42×C83—22no—
599C42×C83—41no—
600C42×C83—41no—
601C42×C83—41no—
602C23×C83—21no—
603C23×C83—21no—
604C23×C83—21no—
605C23×C83—21no—
606C23×C83—21no—
607C23×C83—21no—
608C23×C83—21no—
609C23×C83—21no—
610C23×C83—21no—
611C23×C83—21no—
612C23×C83—21no—
613C23×C83—21no—
614C23×C83—21no—
615C23×C83—21no—
616C23×C83—21no—
617C23×C83—21no—
618C23×C83—28no—
619C23×C83—44no—
620C23×C83—44no—
621C23×C83—82no—
622C23×C83—82no—
623C23×C83—82no—
624C23×C83—82no—
625C23×C83C23×C412yes—
626C23×C83C23×C412yes—
627C23×C83C23×C412yes—
628C23×C83H(5,𝔽2)12yes—
629C23×C832−1+412yes—
630C23×C83C2511yescharacteristic
631C22×D83—21no—
632C22×D83—21no—
633C22×D83—21no—
634C22×D83—21no—
635C22×D83—21no—
636C22×D83—21no—
637C22×D83—21no—
638C22×D83—21no—
639C22×D83—21no—
640C22×D83—21no—
641C22×D83—21no—
642C22×D83—21no—
643C22×D83—21no—
644C22×D83—21no—
645C22×D83—21no—
646C22×D83—21no—
647C22×D83—21no—
648C22×D83—21no—
649C22×D83—28no—
650C22×D83—44no—
651C22×D83—44no—
652C22×D83—82no—
653C22×D83—82no—
654C22×D83—82no—
655C22×D83—82no—
656C22×D83C23×C412yes—
657C22×D83C23×C412yes—
658C22×D83C23×C412yes—
659C2×C4×C83—21no—
660C2×C4×C83—21no—
661C2×C4×C83—21no—
662C2×C4×C83—21no—
663C2×C4×C83—21no—
664C2×C4×C83—21no—
665C2×C4×C83—21no—
666C2×C4×C83—21no—
667C2×C4×C83—21no—
668C2×C4×C83—21no—
669C2×C4×C83—21no—
670C2×C4×C83—21no—
671C2×C4×C83—21no—
672C2×C4×C83—21no—
673C2×C4×C83—21no—
674C2×C4×C83—21no—
675C2×C4×C83—21no—
676C2×C4×C83—21no—
677C2×C4×C83—21no—
678C2×C4×C83—21no—
679C2×C4×C83—21no—
680C2×C4×C83—21no—
681C2×C4×C83—21no—
682C2×C4×C83—21no—
683C2×C4×C83—21no—
684C2×C4×C83—21no—
685C2×C4×C83—21no—
686C2×C4×C83—21no—
687C2×C4×C83—21no—
688C2×C4×C83—21no—
689C2×C4×C83—21no—
690C2×C4×C83—44no—
691C2×C4×C83—44no—
692C2×C4×C83—44no—
693C2×C4×C83—82no—
694C2×C4×C83C23×C412yes—
695C2×C4×C83C23×C412yes—
696C2×C4×C83C23×C412yes—
697C2×C4×C83C23×C412yes—
698C2×C4×C83H(5,𝔽2)12yes—
699C22⋊D83—28no—
700C22⋊D83—28no—
701C22⋊D83—28no—
702C22⋊D83—44no—
703C22⋊D83—44no—
704C22⋊D83—44no—
705C22⋊D83—44no—
706C2×Dic83—21no—
707C2×Dic83—21no—
708C2×Dic83—21no—
709C2×Dic83—21no—
710C2×Dic83—21no—
711C2×Dic83—21no—
712C2×Dic83—21no—
713C2×Dic83—21no—
714C2×Dic83—28no—
715C2×Dic83—21no—
716C2×Dic83—21no—
717C2×Dic83—21no—
718C2×Dic83—21no—
719C2×Dic83—21no—
720C2×Dic83—21no—
721C2×Dic83—21no—
722C2×Dic83—21no—
723C2×Dic83—21no—
724C2×Dic83—21no—
725C2×Dic83—21no—
726C2×Dic83—21no—
727C2×Dic83—21no—
728C2×Dic83—21no—
729C2×Dic83—21no—
730C2×Dic83—21no—
731C2×Dic83—21no—
732C2×Dic83—21no—
733C2×Dic83—21no—
734C2×Dic83—21no—
735C2×Dic83—21no—
736C2×Dic83—21no—
737C2×Dic83—21no—
738C2×Dic83—21no—
739C2×Dic83—44no—
740C2×Dic83—82no—
741C2×Dic83—82no—
742C2×Dic83—82no—
743C2×Dic83C23×C412yes—
744C2×Dic83C23×C412yes—
745C2×Dic83C23×C412yes—
746C2×Dic83C23×C412yes—
747C2×Dic83C23×C412yes—
748C2×Dic83H(5,𝔽2)12yes—
749C2×Dic83H(5,𝔽2)12yes—
750D332—44no—
751D332—44no—
752C4×D83—28no—
753C4×D83—44no—
754C4×D83—44no—
755C4×D83—82no—
756C4×D83—82no—
757C4×D83—82no—
758C4×D83—82no—
759Dic166—28no—
760C22×C83—22no—
761C22×C83—22no—
762C22×C83—22no—
763C22×C83—22no—
764C22×C83—22no—
765C22×C83—22no—
766C22×C83—22no—
767C22×C83—22no—
768C22×C83—22no—
769C22×C83—22no—
770C22×C83—22no—
771C22×C83—22no—
772C22×C83—41no—
773C22×C83—41no—
774C22×C83—41no—
775C22×C83—41no—
776C22×C83—41no—
777C22×C83—41no—
778C22×C83—41no—
779C22×C83—41no—
780C22×C83—88no—
781C22×C83#52014yes—
782C22×C83C24×C411yescharacteristic
783C22×C83C2×H(5,𝔽2)11yescharacteristic
784C22×C83C2×H(5,𝔽2)11yescharacteristic
785C22×C83C2×H(5,𝔽2)11yescharacteristic
786C22×C83C2×H(5,𝔽2)11yescharacteristic
787C22×C83C2×2−1+411yescharacteristic
788C22×C83#58511yescharacteristic
789C2×D83—22no—
790C2×D83—22no—
791C2×D83—22no—
792C2×D83—22no—
793C2×D83—22no—
794C2×D83—22no—
795C2×D83—22no—
796C2×D83—22no—
797C2×D83—22no—
798C2×D83—41no—
799C2×D83—41no—
800C2×D83—41no—
801C2×D83—41no—
802C2×D83—41no—
803C2×D83—41no—
804C2×D83—41no—
805C2×D83—41no—
806C2×D83—41no—
807C2×D83—41no—
808C2×D83—41no—
809C2×D83—41no—
810C2×D83—88no—
811C4×C83—22no—
812C4×C83—22no—
813C4×C83—22no—
814C4×C83—22no—
815C4×C83—22no—
816C4×C83—41no—
817C4×C83—41no—
818C4×C83—41no—
819C4×C83—41no—
820C4×C83—41no—
821C4×C83—41no—
822C4×C83—41no—
823Dic83—22no—
824Dic83—22no—
825Dic83—22no—
826Dic83—22no—
827Dic83—41no—
828Dic83—41no—
829Dic83—41no—
830Dic83—41no—
831Dic83—41no—
832Dic83—41no—
833Dic83—41no—
834Dic83—41no—
835Dic83#51814yes—
836#34476—831nomaximal, Sylow
837C2×C83—24no—
838C2×C83—42no—
839C2×C83—42no—
840C2×C83C2×#51811yescharacteristic
841C2×C83C2×#52011yescharacteristic
842C2×C83C4×H(5,𝔽2)11yescharacteristic
843C2×C83#353611yescharacteristic
844C2×C83#354211yescharacteristic
845C2×C83#354311yescharacteristic
846C2×C83#356111yescharacteristic
847D83—42no—
848D83—42no—
849D83—42no—
850C2×#546—831no—
851#2377—831no—
852#2377—831no—
853#2376—831no—
854#2376—831no—
855#2367—831no—
856#2361—831no—
857#2360—831no—
858#2358—831no—
859#2358—831no—
860#2354—831no—
861D4×C4⋊C4—831no—
862#2342—831no—
863#2342D8311yescharacteristic, complemented
864#2341—831no—
865D4×C22⋊C4—831no—
866#2335—831no—
867#2335—831no—
868#2326—831no—
869#2324—831no—
870#2324—831no—
871#2324—831no—
872#2321—831no—
873#2321—831no—
874#2319—831no—
875#2315—831no—
876#2315—831no—
877#2311—831no—
878C4×C22⋊Q8—831no—
879C2×#390—831no—
880#2290—831no—
881C83#3447611yescharacteristic, complemented, Sylow
882C22×#41—831no—
883C23×D4—831no—
884#546—8316no—
885C2×#124—831no—
886C2×#123—831no—
887C2×#123—831no—
888C2×C22⋊Q8—831no—
889C2×#121—831no—
890C2×#121—831no—
891C2×#121—831no—
892C2×#120—831no—
893C2×#120—831no—
894C2×C4×Q8—831no—
895C2×C4×Q8—831no—
896C2×C4×D4—831no—
897C2×C4×D4—831no—
898C2×C4×D4—831no—
899C2×C4×D4—831no—
900C2×C4×D4—831no—
901C2×C4×D4—831no—
902C2×C4×D4—831no—
903C2×C4×D4—831no—
904C2×#117—831no—
905C2×#117—831no—
906C2×#117C2×D8311yescharacteristic, complemented
907C22×C4⋊C4—831no—
908C22×C4⋊C4—831no—
909C22×C22⋊C4—831no—
910C22×C22⋊C4—831no—
911C22×C22⋊C4—831no—
912C22×C22⋊C4—831no—
913C22×C22⋊C4—831no—
914C22×C22⋊C4—831no—
915C22×C22⋊C4C2×D8311yescharacteristic
916C22×C22⋊C4C2×D8311yescharacteristic
917C22×C42—831no—
918#391—831no—
919#391—831no—
920#390—831no—
921#390—831no—
922#390—831no—
923#390—831no—
924#390—831no—
925#390—831no—
926#390—831no—
927#390—831no—
928#390—831no—
929#390—831no—
930#390—831no—
931#390—831no—
932#390—831no—
933#390—831no—
934#390—831no—
935#390—831no—
936#389—831no—
937#389—831no—
938#389—831no—
939#389—831no—
940#389—831no—
941#389—831no—
942#388—831no—
943#388—831no—
944#388—831no—
945#388—831no—
946#388—831no—
947#388—831no—
948#388—831no—
949#388—831no—
950#388—831no—
951#388—831no—
952#388—831no—
953#388—831no—
954#388—831no—
955#388—831no—
956#388—831no—
957#388—831no—
958#388—831no—
959#388—831no—
960#388C2×D8311yescharacteristic, complemented
961#388C2×D8311yescharacteristic, complemented
962#388C2×D8311yescharacteristic, complemented
963#388C2×D8311yescharacteristic, complemented
964#387—831no—
965#387—831no—
966#387—831no—
967#387—831no—
968#387—831no—
969#387—831no—
970#386—831no—
971#386—831no—
972#386—831no—
973#386—831no—
974#386—831no—
975#386—831no—
976#386—831no—
977#386—831no—
978#386—831no—
979#386—831no—
980#386—831no—
981#386—831no—
982#386—831no—
983#386—831no—
984#385—831no—
985#385—831no—
986#385—831no—
987#385—831no—
988#385—831no—
989#385—831no—
990#385—831no—
991#385—831no—
992#385—831no—
993#385—831no—
994#385—831no—
995#385—831no—
996#385—831no—
997#385—831no—
998#385—831no—
999#385—831no—
1000#385—831no—
1001#385—831no—
1002#385C2×D8311yescharacteristic
1003#385C2×D8311yescharacteristic
1004#384—831no—
1005#381—831no—
1006#381C2×D8311yescharacteristic, complemented
1007#380—831no—
1008#380—831no—
1009#380—831no—
1010#380—831no—
1011#380—831no—
1012#380—831no—
1013#380—831no—
1014#380—831no—
1015#380—831no—
1016#380—831no—
1017#380—831no—
1018#380C2×D8311yescharacteristic, complemented
1019#379—831no—
1020#379C2×D8311yescharacteristic
1021C4×C4⋊C4—831no—
1022C4×C4⋊C4—831no—
1023C4×C4⋊C4—831no—
1024C4×C4⋊C4—831no—
1025C4×C4⋊C4—831no—
1026C4×C4⋊C4—831no—
1027C4×C22⋊C4—831no—
1028C4×C22⋊C4—831no—
1029C4×C22⋊C4—831no—
1030C4×C22⋊C4—831no—
1031C4×C22⋊C4—831no—
1032C4×C22⋊C4—831no—
1033C4×C22⋊C4—831no—
1034C4×C22⋊C4C2×D8311yescharacteristic
1035C4×C22⋊C4C2×D8311yescharacteristic
1036C4×C22⋊C4C2×D8311yescharacteristic, complemented
1037#376—831no—
1038C25—831no—
1039C25C22×D8311yescharacteristic
1040C2×#41—3322no—
1041C2×#41—3322no—
1042C2×#41—838no—
1043C22×Q8—831no—
1044C22×D4—3322no—
1045C22×D4—3322no—
1046C22×D4—838no—
1047C22×D4—831no—
1048C22×D4—831no—
1049C22×D4—831no—
1050C22×D4—831no—
1051C22×D4—831no—
1052C22×D4—831no—
1053C22×D4—831no—
1054C22×D4—831no—
1055C22×D4—831no—
1056C23×C4—831no—
1057C23×C4—831no—
1058C23×C4—831no—
1059C23×C4—831no—
1060C23×C4—831no—
1061C23×C4—831no—
1062C23×C4—831no—
1063C23×C4—831no—
1064C23×C4—831no—
1065C23×C4—831no—
1066C23×C4—831no—
1067C23×C4—831no—
1068C23×C4C22×D8311yescharacteristic
1069C23×C4C22×D8311yescharacteristic
1070C23×C4C22×D8311yescharacteristic
1071C23×C4C22×D8311yescharacteristic
1072#124—838no—
1073#123—838no—
1074#123—838no—
1075C22⋊Q8—838no—
1076#121—838no—
1077#121—838no—
1078#121—838no—
1079#120—838no—
1080#120—838no—
1081C4×Q8—3322no—
1082C4×Q8—3322no—
1083C4×D4—3322no—
1084C4×D4—3322no—
1085C4×D4—3322no—
1086C4×D4—3322no—
1087C4×D4—3322no—
1088C4×D4—3322no—
1089C4×D4—838no—
1090C4×D4—838no—
1091#117—42no—
1092#117—3322no—
1093#117—3322no—
1094C2×C4⋊C4—3322no—
1095C2×C4⋊C4—3322no—
1096C2×C4⋊C4—831no—
1097C2×C4⋊C4—831no—
1098C2×C4⋊C4—831no—
1099C2×C4⋊C4—831no—
1100C2×C4⋊C4—831no—
1101C2×C4⋊C4—831no—
1102C2×C4⋊C4—831no—
1103C2×C4⋊C4—831no—
1104C2×C4⋊C4—831no—
1105C2×C4⋊C4—831no—
1106C2×C4⋊C4—831no—
1107C2×C4⋊C4—831no—
1108C2×C4⋊C4—831no—
1109C2×C4⋊C4—831no—
1110C2×C4⋊C4—831no—
1111C2×C4⋊C4—831no—
1112C2×C4⋊C4—831no—
1113C2×C4⋊C4—831no—
1114C2×C4⋊C4—831no—
1115C2×C4⋊C4—831no—
1116C2×C4⋊C4—831no—
1117C2×C4⋊C4—831no—
1118C2×C4⋊C4—831no—
1119C2×C4⋊C4—831no—
1120C2×C4⋊C4C22×D8311yescharacteristic
1121C2×C4⋊C4C22×D8311yescharacteristic
1122C2×C4⋊C4C22×D8311yescharacteristic
1123C2×C4⋊C4C22×D8311yescharacteristic
1124C2×C22⋊C4—42no—
1125C2×C22⋊C4—3322no—
1126C2×C22⋊C4—3322no—
1127C2×C22⋊C4—3322no—
1128C2×C22⋊C4—3322no—
1129C2×C22⋊C4—3322no—
1130C2×C22⋊C4—831no—
1131C2×C22⋊C4—831no—
1132C2×C22⋊C4—831no—
1133C2×C22⋊C4—831no—
1134C2×C22⋊C4—831no—
1135C2×C22⋊C4—831no—
1136C2×C22⋊C4—831no—
1137C2×C22⋊C4—831no—
1138C2×C22⋊C4—831no—
1139C2×C22⋊C4—831no—
1140C2×C22⋊C4—831no—
1141C2×C22⋊C4—831no—
1142C2×C22⋊C4—831no—
1143C2×C22⋊C4—831no—
1144C2×C22⋊C4—831no—
1145C2×C22⋊C4—831no—
1146C2×C22⋊C4—831no—
1147C2×C22⋊C4—831no—
1148C2×C22⋊C4—831no—
1149C2×C22⋊C4—831no—
1150C2×C22⋊C4—831no—
1151C2×C22⋊C4—831no—
1152C2×C22⋊C4—831no—
1153C2×C22⋊C4—831no—
1154C2×C22⋊C4—831no—
1155C2×C22⋊C4—831no—
1156C2×C22⋊C4—831no—
1157C2×C22⋊C4—831no—
1158C2×C22⋊C4—831no—
1159C2×C22⋊C4—831no—
1160C2×C22⋊C4—831no—
1161C2×C22⋊C4—838no—
1162C2×C22⋊C4—831no—
1163C2×C22⋊C4—831no—
1164C2×C22⋊C4—831no—
1165C2×C22⋊C4—831no—
1166C2×C22⋊C4—831no—
1167C2×C22⋊C4C4×D8318yescomplemented
1168C2×C22⋊C4C22×D8311yescharacteristic
1169C2×C22⋊C4C22×D8311yescharacteristic
1170C2×C22⋊C4C22×D8311yescharacteristic
1171C2×C22⋊C4C22×D8311yescharacteristic
1172C2×C22⋊C4C22×D8311yescharacteristic
1173C2×C22⋊C4C22×D8311yescharacteristic
1174C2×C22⋊C4C22×D8311yescharacteristic
1175C2×C22⋊C4C22×D8311yescharacteristic
1176C2×C22⋊C4C22×D8311yescharacteristic
1177C2×C22⋊C4C22×D8311yescharacteristic
1178C2×C22⋊C4C22×D8311yescharacteristic
1179C2×C22⋊C4C22×D8311yescharacteristic
1180C2×C22⋊C4C22×D8311yescharacteristic
1181C2×C22⋊C4C22×D8311yescharacteristic
1182C2×C42—3322no—
1183C2×C42—831no—
1184C2×C42—831no—
1185C2×C42—831no—
1186C2×C42—831no—
1187C2×C42—831no—
1188C2×C42—831no—
1189C2×C42—831no—
1190C2×C42—831no—
1191C2×C42—831no—
1192C2×C42—831no—
1193C2×C42—831no—
1194C2×C42—831no—
1195C2×C42—831no—
1196C2×C42C22×D8311yescharacteristic
1197C2×C42C22×D8311yescharacteristic
1198C2×C42C22×D8311yescharacteristic
1199C2×C42C22×D8311yescharacteristic
1200#95—831no—
1201#95—831no—
1202#95—831no—
1203#95—831no—
1204#95—831no—
1205#95—831no—
1206#95—831no—
1207#95—831no—
1208#95—831no—
1209#95—831no—
1210#95—831no—
1211#95—831no—
1212#95—831no—
1213#95—831no—
1214#95—831no—
1215#95—831no—
1216#95—831no—
1217#95—831no—
1218#95—831no—
1219#95—831no—
1220#95—831no—
1221#95—831no—
1222#95—831no—
1223#95—831no—
1224#95C22×D8311yescharacteristic
1225#95C22×D8311yescharacteristic
1226#95C22×D8311yescharacteristic
1227#95C22×D8311yescharacteristic
1228#95C22×D8311yescharacteristic
1229#95C22×D8311yescharacteristic
1230#95C22×D8311yescharacteristic
1231#95C22×D8311yescharacteristic
1232C24—22no—
1233C24—22no—
1234C24—41no—
1235C24—41no—
1236C24—41no—
1237C24—41no—
1238C24—3321no—
1239C24—3321no—
1240C24—3321no—
1241C24—3321no—
1242C24—834no—
1243C24—831no—
1244C24—831no—
1245C24—831no—
1246C24—1662no—
1247C24—1662no—
1248C24C2×C4×D8314yes—
1249C24C23×D8311yescharacteristic
1250C24C23×D8311yescharacteristic
1251C24C23×D8311yescharacteristic
1252#41—33216no—
1253C2×Q8—834no—
1254C2×Q8—1662no—
1255C2×Q8—1662no—
1256C2×D4—3321no—
1257C2×D4—3321no—
1258C2×D4—3321no—
1259C2×D4—3321no—
1260C2×D4—3321no—
1261C2×D4—3321no—
1262C2×D4—3321no—
1263C2×D4—3321no—
1264C2×D4—3321no—
1265C2×D4—3321no—
1266C2×D4—3321no—
1267C2×D4—3321no—
1268C2×D4—33216no—
1269C2×D4—834no—
1270C2×D4—834no—
1271C2×D4—834no—
1272C2×D4—834no—
1273C2×D4—834no—
1274C2×D4—834no—
1275C2×D4—834no—
1276C2×D4—834no—
1277C2×D4—834no—
1278C2×D4—1662no—
1279C2×D4—1662no—
1280C2×D4—1662no—
1281C2×D4—1662no—
1282C2×D4—1662no—
1283C2×D4—1662no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—3321no—
1295C22×C4—3321no—
1296C22×C4—3321no—
1297C22×C4—3321no—
1298C22×C4—3321no—
1299C22×C4—3321no—
1300C22×C4—3321no—
1301C22×C4—3321no—
1302C22×C4—3321no—
1303C22×C4—3321no—
1304C22×C4—3321no—
1305C22×C4—3321no—
1306C22×C4—3321no—
1307C22×C4—3321no—
1308C22×C4—3321no—
1309C22×C4—3321no—
1310C22×C4—3321no—
1311C22×C4—3321no—
1312C22×C4—3321no—
1313C22×C4—3321no—
1314C22×C4—3321no—
1315C22×C4—3321no—
1316C22×C4—3321no—
1317C22×C4—3321no—
1318C22×C4—3321no—
1319C22×C4—3321no—
1320C22×C4—834no—
1321C22×C4—834no—
1322C22×C4—831no—
1323C22×C4—834no—
1324C22×C4—831no—
1325C22×C4—831no—
1326C22×C4—831no—
1327C22×C4—831no—
1328C22×C4—834no—
1329C22×C4—831no—
1330C22×C4—831no—
1331C22×C4—831no—
1332C22×C4—831no—
1333C22×C4—831no—
1334C22×C4—831no—
1335C22×C4—831no—
1336C22×C4—831no—
1337C22×C4—1662no—
1338C22×C4—1662no—
1339C22×C4—1662no—
1340C22×C4—1662no—
1341C22×C4—1662no—
1342C22×C4—1662no—
1343C22×C4C2×C4×D8314yes—
1344C22×C4C2×C4×D8314yes—
1345C22×C4C23×D8311yescharacteristic
1346C22×C4C23×D8311yescharacteristic
1347C22×C4C23×D8311yescharacteristic
1348C22×C4C23×D8311yescharacteristic
1349C22×C4C23×D8311yescharacteristic
1350C22×C4C23×D8311yescharacteristic
1351C22×C4C23×D8311yescharacteristic
1352C22×C4C23×D8311yescharacteristic
1353C22×C4C23×D8311yescharacteristic
1354C22×C4C23×D8311yescharacteristic
1355C22×C4C23×D8311yescharacteristic
1356C22×C4C23×D8311yescharacteristic
1357C4⋊C4—22no—
1358C4⋊C4—41no—
1359C4⋊C4—41no—
1360C4⋊C4—41no—
1361C4⋊C4—3321no—
1362C4⋊C4—3321no—
1363C4⋊C4—3321no—
1364C4⋊C4—3321no—
1365C4⋊C4—3321no—
1366C4⋊C4—3321no—
1367C4⋊C4—3321no—
1368C4⋊C4—3321no—
1369C4⋊C4—3321no—
1370C4⋊C4—3321no—
1371C4⋊C4—3321no—
1372C4⋊C4—3321no—
1373C4⋊C4—3321no—
1374C4⋊C4—3321no—
1375C4⋊C4—3321no—
1376C4⋊C4—3321no—
1377C4⋊C4—834no—
1378C4⋊C4—834no—
1379C4⋊C4—834no—
1380C4⋊C4—834no—
1381C4⋊C4—1662no—
1382C4⋊C4—1662no—
1383C4⋊C4—1662no—
1384C4⋊C4—1662no—
1385C22⋊C4—22no—
1386C22⋊C4—22no—
1387C22⋊C4—22no—
1388C22⋊C4—22no—
1389C22⋊C4—41no—
1390C22⋊C4—41no—
1391C22⋊C4—41no—
1392C22⋊C4—41no—
1393C22⋊C4—41no—
1394C22⋊C4—41no—
1395C22⋊C4—3321no—
1396C22⋊C4—3321no—
1397C22⋊C4—3321no—
1398C22⋊C4—3321no—
1399C22⋊C4—3321no—
1400C22⋊C4—3321no—
1401C22⋊C4—3321no—
1402C22⋊C4—3321no—
1403C22⋊C4—3321no—
1404C22⋊C4—3321no—
1405C22⋊C4—3321no—
1406C22⋊C4—3321no—
1407C22⋊C4—3321no—
1408C22⋊C4—3321no—
1409C22⋊C4—3321no—
1410C22⋊C4—3321no—
1411C22⋊C4—3321no—
1412C22⋊C4—3321no—
1413C22⋊C4—3321no—
1414C22⋊C4—3321no—
1415C22⋊C4—3321no—
1416C22⋊C4—3321no—
1417C22⋊C4—3321no—
1418C22⋊C4—834no—
1419C22⋊C4—834no—
1420C22⋊C4—834no—
1421C22⋊C4—834no—
1422C22⋊C4—834no—
1423C22⋊C4—834no—
1424C22⋊C4—834no—
1425C22⋊C4—834no—
1426C22⋊C4—1662no—
1427C22⋊C4—1662no—
1428C22⋊C4—1662no—
1429C22⋊C4—1662no—
1430C22⋊C4—1662no—
1431C22⋊C4C2×C4×D8314yes—
1432C22⋊C4C2×C4×D8314yes—
1433C22⋊C4C2×C4×D8314yes—
1434C22⋊C4C2×C4×D8314yes—
1435C42—22no—
1436C42—41no—
1437C42—41no—
1438C42—41no—
1439C42—3321no—
1440C42—3321no—
1441C42—3321no—
1442C42—3321no—
1443C42—3321no—
1444C42—3321no—
1445C42—3321no—
1446C42—834no—
1447C42—1662no—
1448C42—1662no—
1449C42—1662no—
1450C42—1662no—
1451C42—1662no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—21no—
1464C23—21no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—28no—
1469C23—44no—
1470C23—44no—
1471C23—82no—
1472C23—82no—
1473C23—82no—
1474C23—82no—
1475C23—3324no—
1476C23—3324no—
1477C23—832no—
1478C23—832no—
1479C23—832no—
1480C23—6642no—
1481C23—6642no—
1482C23—6642no—
1483C23—6642no—
1484C23—1661no—
1485C23—1661no—
1486C23—1661no—
1487C23—1661no—
1488C23—1661no—
1489C23—1661no—
1490C23—1661no—
1491C23—1661no—
1492C23—1661no—
1493C23—1661no—
1494C23—1661no—
1495C23—1661no—
1496C23—1661no—
1497C23—1661no—
1498C23—1661no—
1499C23—1661no—
1500C23—1661no—
1501C23—1661no—
1502C23—1668no—
1503C23C22×C4×D8312yes—
1504C23C22×C4×D8312yes—
1505C23C22×C4×D8312yes—
1506C23#1458183812yes—
1507C23#1458183912yes—
1508C23C24×D8311yescharacteristic
1509Q8—1668no—
1510D4—3324no—
1511D4—3324no—
1512D4—3324no—
1513D4—3324no—
1514D4—3324no—
1515D4—3324no—
1516D4—1668no—
1517D4—1668no—
1518D4—1668no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—44no—
1551C2×C4—44no—
1552C2×C4—44no—
1553C2×C4—82no—
1554C2×C4—3324no—
1555C2×C4—3324no—
1556C2×C4—3324no—
1557C2×C4—832no—
1558C2×C4—832no—
1559C2×C4—832no—
1560C2×C4—832no—
1561C2×C4—832no—
1562C2×C4—832no—
1563C2×C4—832no—
1564C2×C4—6642no—
1565C2×C4—6642no—
1566C2×C4—6642no—
1567C2×C4—6642no—
1568C2×C4—6642no—
1569C2×C4—6642no—
1570C2×C4—6642no—
1571C2×C4—1668no—
1572C2×C4—1661no—
1573C2×C4—1661no—
1574C2×C4—1661no—
1575C2×C4—1661no—
1576C2×C4—1661no—
1577C2×C4—1661no—
1578C2×C4—1661no—
1579C2×C4—1661no—
1580C2×C4—1661no—
1581C2×C4—1661no—
1582C2×C4—1661no—
1583C2×C4—1661no—
1584C2×C4—1661no—
1585C2×C4—1661no—
1586C2×C4—1661no—
1587C2×C4—1661no—
1588C2×C4—1661no—
1589C2×C4—1661no—
1590C2×C4—1661no—
1591C2×C4—1661no—
1592C2×C4—1661no—
1593C2×C4—1661no—
1594C2×C4—1661no—
1595C2×C4—1661no—
1596C2×C4—1668no—
1597C2×C4—1661no—
1598C2×C4—1661no—
1599C2×C4—1661no—
1600C2×C4—1661no—
1601C2×C4—1661no—
1602C2×C4—1661no—
1603C2×C4—1661no—
1604C2×C4—1661no—
1605C2×C4C22×C4×D8312yes—
1606C2×C4C22×C4×D8312yes—
1607C2×C4C22×C4×D8312yes—
1608C2×C4C22×C4×D8312yes—
1609C2×C4#1458183712yes—
1610C22—22no—
1611C22—22no—
1612C22—22no—
1613C22—22no—
1614C22—22no—
1615C22—22no—
1616C22—22no—
1617C22—22no—
1618C22—22no—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—41no—
1623C22—41no—
1624C22—41no—
1625C22—41no—
1626C22—41no—
1627C22—41no—
1628C22—41no—
1629C22—41no—
1630C22—88no—
1631C22—3321no—
1632C22—3321no—
1633C22—3321no—
1634C22—3321no—
1635C22—3321no—
1636C22—3321no—
1637C22—3321no—
1638C22—3321no—
1639C22—3321no—
1640C22—3321no—
1641C22—3321no—
1642C22—3321no—
1643C22—6648no—
1644C22—1662no—
1645C22—1662no—
1646C22—1662no—
1647C22—1662no—
1648C22—1662no—
1649C22—1662no—
1650C22—1662no—
1651C22—1662no—
1652C22—1662no—
1653C22#1912818114yes—
1654C22C23×C4×D8311yescharacteristic
1655C22H(5,𝔽2)×D8311yescharacteristic
1656C22H(5,𝔽2)×D8311yescharacteristic
1657C22C2×#1458183711yescharacteristic
1658C22C2×#1458183811yescharacteristic
1659C22C2×#1458183911yescharacteristic
1660C22#1912853711yescharacteristic
1661C4—22no—
1662C4—22no—
1663C4—22no—
1664C4—22no—
1665C4—22no—
1666C4—41no—
1667C4—41no—
1668C4—41no—
1669C4—41no—
1670C4—41no—
1671C4—41no—
1672C4—41no—
1673C4—3321no—
1674C4—3321no—
1675C4—3321no—
1676C4—3321no—
1677C4—3321no—
1678C4—3321no—
1679C4—3321no—
1680C4—3321no—
1681C4—834no—
1682C4—1662no—
1683C4—1662no—
1684C4—1662no—
1685C4—1662no—
1686C2—24no—
1687C2—42no—
1688C2—42no—
1689C2—3322no—
1690C2—3322no—
1691C2—3322no—
1692C2#518×D8311yescharacteristic
1693C2C2×#1912818111yescharacteristic
1694C2C4×#1458183711yescharacteristic
1695C2#2492167811yescharacteristic
1696C2#2492177211yescharacteristic
1697C2#2492179511yescharacteristic
1698C2#2492202111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2342C2
socle, cosocleC23×C83C25
prime radicalC2×#19128341C2
hypercenter#2342D83
hypocenterC83#34476
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2342

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #24910622C2semidirect
3. #24910616C2semidirect
4. #24910607C2semidirect
5. #24910605C2semidirect
6. #24910537C2semidirect
7. #24910476C2semidirect
8. #24910469C2semidirect
9. #24910445C2semidirect
10. #24910442C2semidirect
11. #24910413C2semidirect
12. #24910361C2semidirect
13. #24910310C2semidirect
14. #24910303C2semidirect
15. #24910279C2semidirect
16. #24910260C2semidirect
17. #24910253C2semidirect
18. #24910172C2semidirect
19. #24910156C2semidirect
20. #24910151C2semidirect
21. #24910151C2semidirect
22. #24910123C2semidirect
23. #24910118C2semidirect
24. #24910103C2semidirect
25. #24910077C2semidirect
26. #24910074C2semidirect
27. #24910052C2semidirect
28. C4×#14581769C2semidirect
29. C2×#19127601C2semidirect
30. #24909899C2semidirect
31. C83×#2342C2semidirect
34. #19128341C4semidirect
44. C2×C4×Dic166C22semidirect
45. C2×C4×Dic166C22semidirect
46. C2×C4×D332C22semidirect
53. C2×(C22⋊D83)⋊C4C22semidirect
54. C2×#14581750C22semidirect
55. C2×#14581750C22semidirect
57. C2×C4⋊C4×D83C22semidirect
65. #19127605C22semidirect
66. #19127605C22semidirect
67. #19127603C22semidirect
68. #19127603C22semidirect
69. #19127603C22semidirect
80. #19127601C22semidirect
81. #19127601C22semidirect
82. #19127601C22semidirect
83. #19127599C22semidirect
84. #19127598C22semidirect
85. #19127598C22semidirect
86. #19127598C22semidirect
87. #19127598C22semidirect
88. #19127596C22semidirect
89. #19127595C22semidirect
90. #19127595C22semidirect
91. #19127595C22semidirect
92. #19127593C22semidirect
93. #19127593C22semidirect
94. #19127593C22semidirect
95. #19127593C22semidirect
96. #19127593C22semidirect
97. #19127593C22semidirect
98. #19127592C22semidirect
99. #19127592C22semidirect
100. #19127592C22semidirect
101. #19127591C22semidirect
102. #19127591C22semidirect
103. #19127591C22semidirect
104. #19127589C22semidirect
105. #19127589C22semidirect
106. #19127589C22semidirect
107. #19127588C22semidirect
108. #19127588C22semidirect
109. #19127585C22semidirect
110. #19127584C22semidirect
111. #19127584C22semidirect
112. #19127582C22semidirect
114. #19127579C22semidirect
115. #19127579C22semidirect
116. #19127579C22semidirect
117. #19127579C22semidirect
121. #19127578C22semidirect
124. #19127577C22semidirect
125. #19127577C22semidirect
126. #19127577C22semidirect
131. #19127576C22semidirect
132. #19127576C22semidirect
133. #19127576C22semidirect
134. #19127576C22semidirect
135. #19127575C22semidirect
136. #19127575C22semidirect
137. #19127575C22semidirect
138. #19127575C22semidirect
141. #19127573C22semidirect
142. #19127572C22semidirect
143. #19127572C22semidirect
144. #19127572C22semidirect
145. #19127570C22semidirect
146. #19127563C22semidirect
147. #19127561C22semidirect
148. #19127561C22semidirect
149. #19127561C22semidirect
150. #19127561C22semidirect
151. #19127560C22semidirect
152. #19127560C22semidirect
153. #19127560C22semidirect
155. #19127558C22semidirect
156. #19127558C22semidirect
157. #19127558C22semidirect
159. C4⋊C4×Dic83C22semidirect
160. C4×Dic83⋊C4C22semidirect
161. C4×Dic83⋊C4C22semidirect
162. C4×Dic83⋊C4C22semidirect
163. C4×C4⋊Dic83C22semidirect
164. #19127552C22semidirect
167. C22⋊C4×Dic83C22semidirect
168. C4×(C2×D83)⋊C4C22semidirect
170. #19127548C22semidirect
171. #19127548C22semidirect
172. #19127546C22semidirect
173. C2×#117×C83C22semidirect
176. #388×C83C22semidirect
177. #388×C83C22semidirect
178. #388×C83C22semidirect
179. #388×C83C22semidirect
182. #381×C83C22semidirect
183. #380×C83C22semidirect
187. C4×C22⋊C4×C83C22semidirect
191. C2×#13050590C2×C4semidirect
197. C22×C22⋊D83C2×C4semidirect
217. #14581778C2×C4semidirect
218. #14581775C2×C4semidirect
219. #14581774C2×C4semidirect
220. #14581769C2×C4semidirect
221. #14581766C2×C4semidirect
222. #14581765C2×C4semidirect
223. #14581765C2×C4semidirect
224. #14581762C2×C4semidirect
225. #14581761C2×C4semidirect
230. C4×C22⋊D83C2×C4semidirect
235. (C22⋊D83)⋊C4C2×C4semidirect
305. C22⋊C4×D83C2×C4semidirect
355. C2×C22⋊C4×C83C2×C4semidirect
863. #2342D83semidirect
881. C83#34476semidirect
906. C2×#117C2×D83semidirect
960. #388C2×D83semidirect
961. #388C2×D83semidirect
962. #388C2×D83semidirect
963. #388C2×D83semidirect
1006. #381C2×D83semidirect
1018. #380C2×D83semidirect
1036. C4×C22⋊C4C2×D83semidirect
1167. C2×C22⋊C4C4×D83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191283412
#249106222
#249106162
#249106072
#249106052
#249105372
#249104762
#249104692
#249104452
#249104422
#249104132
#249103612
#249103102
#249103032
#249102792
#249102602
#249102532
#249101722
#249101562
#249101512
#249101232
#249101182
#249101032
#249100772
#249100742
#249100522
C4×#145817692
C2×#191276012
#249098992
C83×#23422
#3447683