Finite Group Databasebeta

← #35570202

Subgroups — #35570202

Order 21248.

2544 conjugacy classes of subgroups.

The subgroup lattice has 1656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128441C211yesmaximal, characteristic
2#24910603C211yesmaximal, characteristic, complemented
3#24910603C211yesmaximal, characteristic, complemented
4#24910600C211yesmaximal, characteristic, complemented
5#24910591C211yesmaximal, characteristic, complemented
6#24910586C211yesmaximal, characteristic, complemented
7#24910577C211yesmaximal, characteristic, complemented
8#24910524C211yesmaximal, characteristic, complemented
9#24910513C211yesmaximal, characteristic, complemented
10#24910507C211yesmaximal, characteristic, complemented
11#24910500C211yesmaximal, characteristic, complemented
12#24910499C211yesmaximal, characteristic, complemented
13#24910481C211yesmaximal, characteristic, complemented
14#24910476C211yesmaximal, characteristic, complemented
15#24910459C211yesmaximal, characteristic, complemented
16#24910454C211yesmaximal, characteristic, complemented
17#24910255C211yesmaximal, characteristic, complemented
18#24910244C211yesmaximal, characteristic, complemented
19#24910243C211yesmaximal, characteristic, complemented
20#24910227C211yesmaximal, characteristic, complemented
21#24910226C211yesmaximal, characteristic, complemented
22#24910184C211yesmaximal, characteristic, complemented
23#24910163C211yesmaximal, characteristic, complemented
24#24910162C211yesmaximal, characteristic, complemented
25#24910152C211yesmaximal, characteristic, complemented
26#24910151C211yesmaximal, characteristic, complemented
27#24910130C211yesmaximal, characteristic, complemented
28#24909968C211yesmaximal, characteristic, complemented
29C4×#14581762C211yesmaximal, characteristic, complemented
30#24909964C211yesmaximal, characteristic, complemented
31C83×#2335C211yesmaximal, characteristic, complemented
32C23×C4×D83C2211yescharacteristic
33#19128441C4116yescomplemented
34C2×#14581788C2211yescharacteristic
35C2×#14581787C2211yescharacteristic
36C2×#14581787C2211yescharacteristic
37C2×#14581774C2211yescharacteristic
38C2×#14581774C2211yescharacteristic
39C2×#14581767C2211yescharacteristic
40C2×#14581767C2211yescharacteristic
41C2×#14581766C2211yescharacteristic
42C2×#14581766C2211yescharacteristic
43C2×#14581765C2211yescharacteristic
44C2×#14581765C2211yescharacteristic
45C2×#14581762C2211yescharacteristic
46C2×#14581762C2211yescharacteristic
47C2×#14581760C2211yescharacteristic
48C2×C4×D332C2211yescharacteristic
49C2×C4×D332C2211yescharacteristic
50C2×C4×D332C2211yescharacteristic, complemented
51C2×D4×Dic83C2211yescharacteristic
52C2×#14581754C2211yescharacteristic
53C2×#14581754C2211yescharacteristic
54C2×C4×C22⋊D83C2211yescharacteristic
55C2×(C22⋊D83)⋊C4C2211yescharacteristic
56C2×(C22⋊D83)⋊C4C2211yescharacteristic
57C2×(C22⋊D83)⋊C4C2211yescharacteristic
58C2×(C22⋊D83)⋊C4C2211yescharacteristic, complemented
59C2×(C22⋊D83)⋊C4C2211yescharacteristic, complemented
60C2×#14581751C2211yescharacteristic, complemented
61C2×#14581750C2211yescharacteristic, complemented
62C2×C4⋊C4×D83C2211yescharacteristic, complemented
63#19127603C2211yescharacteristic
64#19127603C2211yescharacteristic
65#19127602C2211yescharacteristic
66#19127602C2211yescharacteristic
67#19127602C2211yescharacteristic, complemented
68#19127601C2211yescharacteristic
69#19127601C2211yescharacteristic
70#19127601C2211yescharacteristic
71#19127601C2211yescharacteristic
72#19127601C2211yescharacteristic, complemented
73#19127601C2211yescharacteristic, complemented
74#19127600C2211yescharacteristic, complemented
75#19127599C2211yescharacteristic, complemented
76#19127598C2211yescharacteristic, complemented
77#19127598C2211yescharacteristic, complemented
78#19127597C2211yescharacteristic, complemented
79#19127594C2211yescharacteristic
80#19127594C2211yescharacteristic
81#19127593C2211yescharacteristic
82#19127593C2211yescharacteristic
83#19127593C2211yescharacteristic, complemented
84#19127592C2211yescharacteristic
85#19127592C2211yescharacteristic
86#19127592C2211yescharacteristic
87#19127592C2211yescharacteristic
88#19127592C2211yescharacteristic, complemented
89#19127591C2211yescharacteristic
90#19127591C2211yescharacteristic
91#19127591C2211yescharacteristic
92#19127591C2211yescharacteristic
93#19127591C2211yescharacteristic, complemented
94#19127590C2211yescharacteristic
95#19127590C2211yescharacteristic
96#19127590C2211yescharacteristic, complemented
97#19127589C2211yescharacteristic
98#19127589C2211yescharacteristic
99#19127587C2211yescharacteristic, complemented
100#19127587C2211yescharacteristic, complemented
101#19127586C2211yescharacteristic, complemented
102#19127586C2211yescharacteristic, complemented
103#19127584C2211yescharacteristic, complemented
104#19127584C2211yescharacteristic, complemented
105#19127583C2211yescharacteristic, complemented
106#19127583C2211yescharacteristic, complemented
107#19127582C2211yescharacteristic, complemented
108#19127582C2211yescharacteristic, complemented
109#19127581C2211yescharacteristic
110#19127580C2211yescharacteristic
111#19127579C2211yescharacteristic
112#19127579C2211yescharacteristic
113#19127579C2211yescharacteristic
114#19127579C2211yescharacteristic
115#19127579C2211yescharacteristic
116#19127579C2211yescharacteristic
117#19127579C2211yescharacteristic
118#19127579C2211yescharacteristic
119#19127579C2211yescharacteristic, complemented
120#19127579C2211yescharacteristic, complemented
121#19127578C2211yescharacteristic
122#19127578C2211yescharacteristic
123#19127578C2211yescharacteristic
124#19127578C2211yescharacteristic, complemented
125#19127578C2211yescharacteristic, complemented
126#19127577C2211yescharacteristic
127#19127577C2211yescharacteristic
128#19127577C2211yescharacteristic
129#19127577C2211yescharacteristic
130#19127577C2211yescharacteristic, complemented
131#19127577C2211yescharacteristic, complemented
132#19127576C2211yescharacteristic
133#19127576C2211yescharacteristic, complemented
134#19127575C2211yescharacteristic
135#19127575C2211yescharacteristic
136#19127575C2211yescharacteristic
137#19127575C2211yescharacteristic
138#19127575C2211yescharacteristic, complemented
139#19127574C2211yescharacteristic
140#19127572C2211yescharacteristic
141#19127572C2211yescharacteristic
142#19127572C2211yescharacteristic, complemented
143#19127565C2211yescharacteristic, complemented
144#19127563C2211yescharacteristic, complemented
145#19127560C2211yescharacteristic, complemented
146#19127556C2211yescharacteristic
147#19127556C2211yescharacteristic
148#19127556C2211yescharacteristic
149C4⋊C4×Dic83C2211yescharacteristic, complemented
150C4⋊C4×Dic83C2211yescharacteristic, complemented
151C4⋊C4×Dic83C2211yescharacteristic, complemented
152C4×Dic83⋊C4C2211yescharacteristic, complemented
153C4×Dic83⋊C4C2211yescharacteristic, complemented
154C4×Dic83⋊C4C2211yescharacteristic, complemented
155C4×C4⋊Dic83C2211yescharacteristic, complemented
156C22⋊C4×Dic83C2211yescharacteristic
157C22⋊C4×Dic83C2211yescharacteristic
158C22⋊C4×Dic83C2211yescharacteristic, complemented
159C4×(C2×D83)⋊C4C2211yescharacteristic
160C4×(C2×D83)⋊C4C2211yescharacteristic
161C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
162C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
163C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
164#19127548C2211yescharacteristic
165#19127548C2211yescharacteristic
166#19127548C2211yescharacteristic
167#19127548C2211yescharacteristic
168#19127548C2211yescharacteristic, complemented
169#19127548C2211yescharacteristic, complemented
170#19127546C2211yescharacteristic, complemented
171C2×C83⋊#95C2211yescharacteristic, complemented
172#95×D83C2211yescharacteristic, complemented
173C2×#123×C83C2211yescharacteristic
174#390×C83C2211yescharacteristic
175#389×C83C2211yescharacteristic, complemented
176#388×C83C2211yescharacteristic
177#388×C83C2211yescharacteristic
178#388×C83C2211yescharacteristic, complemented
179#388×C83C2211yescharacteristic, complemented
180#387×C83C2211yescharacteristic, complemented
181#387×C83C2211yescharacteristic, complemented
182#386×C83C2211yescharacteristic
183#385×C83C2211yescharacteristic
184#380×C83C2211yescharacteristic, complemented
185C4×C4⋊C4×C83C2211yescharacteristic, complemented
186C4×C22⋊C4×C83C2211yescharacteristic
187C4×C22⋊C4×C83C2211yescharacteristic, complemented
188C24×D83C2311yescharacteristic
189C22×D332C2311yescharacteristic
190C22×D332C2311yescharacteristic
191C22×D332C2311yescharacteristic
192C22×D332C2311yescharacteristic
193C22×D332C2311yescharacteristic
194C22×C22⋊D83C2311yescharacteristic
195C22×C22⋊D83C2311yescharacteristic
196C22×C22⋊D83C2311yescharacteristic
197C22×C22⋊D83C2311yescharacteristic
198C22×C22⋊D83C2311yescharacteristic
199C22×C22⋊D83C2311yescharacteristic
200C23×Dic83C2311yescharacteristic
201C23×Dic83C2311yescharacteristic
202C23×Dic83C2311yescharacteristic
203C22×C4×D83—42no—
204C22×C4×D83—42no—
205C22×C4×D83—42no—
206C22×C4×D83C2311yescharacteristic
207C22×C4×D83C2311yescharacteristic
208C22×C4×D83C2311yescharacteristic
209C22×C4×D83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212C22×C4×D83C2311yescharacteristic
213C22×C4×D83C2311yescharacteristic
214C22×C4×D83C2311yescharacteristic
215C22×C4×D83C2311yescharacteristic
216#14581788C2×C418yescomplemented
217#14581787C2×C418yescomplemented
218#14581787C2×C418yescomplemented
219#14581774C2×C418yescomplemented
220#14581774C2×C418yescomplemented
221#14581767C2×C418yescomplemented
222#14581767C2×C418yescomplemented
223#14581766C2×C418yescomplemented
224#14581766C2×C418yescomplemented
225#14581765C2×C418yescomplemented
226#14581765C2×C418yescomplemented
227#14581762C2×C418yescomplemented
228#14581762C2×C418yescomplemented
229#14581760C2×C418yescomplemented
230C4×D332—42no—
231C4×D332—42no—
232C4×D332—42no—
233D4×Dic83—42no—
234#14581754—42no—
235#14581754—42no—
236C4×C22⋊D83—42no—
237(C22⋊D83)⋊C4—42no—
238(C22⋊D83)⋊C4—42no—
239(C22⋊D83)⋊C4—42no—
240(C22⋊D83)⋊C4—42no—
241(C22⋊D83)⋊C4—42no—
242#14581751—42no—
243#14581750—42no—
244C2×C4⋊Dic83C2311yescharacteristic
245C2×C4⋊Dic83C2311yescharacteristic
246C2×C4⋊Dic83C2311yescharacteristic
247C2×C4⋊Dic83C2311yescharacteristic
248C2×C4⋊Dic83C2311yescharacteristic
249C2×C4⋊Dic83C2311yescharacteristic
250C2×C4⋊Dic83C2311yescharacteristic
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
261C4⋊C4×D83—42no—
262C2×C22⋊Dic83C2311yescharacteristic
263C2×C22⋊Dic83C2311yescharacteristic
264C2×C22⋊Dic83C2311yescharacteristic
265C2×C22⋊Dic83C2311yescharacteristic
266C2×C22⋊Dic83C2311yescharacteristic
267C2×C22⋊Dic83C2311yescharacteristic
268C2×(C2×D83)⋊C4C2311yescharacteristic
269C2×(C2×D83)⋊C4C2311yescharacteristic
270C2×(C2×D83)⋊C4C2311yescharacteristic
271C2×(C2×D83)⋊C4C2311yescharacteristic
272C2×(C2×D83)⋊C4C2311yescharacteristic
273C2×(C2×D83)⋊C4C2311yescharacteristic
274C2×(C2×D83)⋊C4C2311yescharacteristic
275C2×(C2×D83)⋊C4C2311yescharacteristic
276C2×(C2×D83)⋊C4C2311yescharacteristic
277C2×(C2×D83)⋊C4C2311yescharacteristic
278C2×(C2×D83)⋊C4C2311yescharacteristic
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×C4×Dic83C2311yescharacteristic
301C2×C4×Dic83C2311yescharacteristic
302C2×C4×Dic83C2311yescharacteristic
303C2×C4×Dic83C2311yescharacteristic
304C2×C4×Dic83C2311yescharacteristic
305C2×C4×Dic83C2311yescharacteristic
306C2×C4×Dic83C2311yescharacteristic
307C2×C4×Dic83C2311yescharacteristic
308C2×C4×Dic83C2311yescharacteristic
309C2×C4×Dic83C2311yescharacteristic
310C2×C4×Dic83C2311yescharacteristic
311C2×C4×Dic83C2311yescharacteristic
312C2×C4×Dic83C2311yescharacteristic
313C2×C4×Dic83C2311yescharacteristic
314C83⋊#95C2311yescharacteristic
315C83⋊#95C2311yescharacteristic
316C83⋊#95C2311yescharacteristic
317C83⋊#95C2311yescharacteristic
318C83⋊#95C2311yescharacteristic
319C83⋊#95C2311yescharacteristic
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
340C22×D4×C83C2311yescharacteristic
341C23×C4×C83C2311yescharacteristic
342C23×C4×C83C2311yescharacteristic
343#123×C83C2×C418yescomplemented
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C4⋊C4×C83C2311yescharacteristic
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C4⋊C4×C83C2311yescharacteristic
349C2×C4⋊C4×C83C2311yescharacteristic
350C2×C4⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83C2311yescharacteristic
355C2×C22⋊C4×C83C2311yescharacteristic
356C2×C22⋊C4×C83C2311yescharacteristic
357C2×C22⋊C4×C83C2311yescharacteristic
358C2×C22⋊C4×C83C2311yescharacteristic
359C2×C22⋊C4×C83C2311yescharacteristic
360C2×C22⋊C4×C83C2311yescharacteristic
361C2×C42×C83C2311yescharacteristic
362C2×C42×C83C2311yescharacteristic
363C2×C42×C83C2311yescharacteristic
364C2×C42×C83C2311yescharacteristic
365C2×C42×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370#95×C83C2311yescharacteristic
371#95×C83C2311yescharacteristic
372#95×C83C2311yescharacteristic
373#95×C83C2311yescharacteristic
374#95×C83C2311yescharacteristic
375#95×C83C2311yescharacteristic
376C23×D83—41no—
377C23×D83—41no—
378C23×D83—41no—
379C23×D83—41no—
380C23×D83—41no—
381C23×D83—41no—
382C23×D83C22×C414yes—
383C23×D83C2411yescharacteristic
384C23×D83C2411yescharacteristic
385C23×D83C2411yescharacteristic
386C23×D83C2411yescharacteristic
387C2×D332—41no—
388C2×D332—41no—
389C2×D332—41no—
390C2×D332—41no—
391C2×D332—41no—
392C2×D332—41no—
393C2×D332—41no—
394C2×D332—41no—
395C2×D332—41no—
396C2×D332—41no—
397C2×D332C22×C414yes—
398C2×D332C22×C414yes—
399C2×D332C22×C414yes—
400C2×D332C22×C414yes—
401C2×D332C22×C414yescomplemented
402C2×C22⋊D83—41no—
403C2×C22⋊D83—41no—
404C2×C22⋊D83—41no—
405C2×C22⋊D83—41no—
406C2×C22⋊D83—41no—
407C2×C22⋊D83—41no—
408C2×C22⋊D83—41no—
409C2×C22⋊D83—41no—
410C2×C22⋊D83—41no—
411C2×C22⋊D83—41no—
412C2×C22⋊D83—41no—
413C2×C22⋊D83—41no—
414C2×C22⋊D83C22×C414yes—
415C2×C22⋊D83C22×C414yes—
416C2×C22⋊D83C22×C414yes—
417C2×C22⋊D83C22×C414yes—
418C2×C22⋊D83C22×C414yescomplemented
419C2×C22⋊D83C22×C414yescomplemented
420C22×Dic83—22no—
421C22×Dic83—22no—
422C22×Dic83—22no—
423C22×Dic83—41no—
424C22×Dic83—41no—
425C22×Dic83—41no—
426C22×Dic83—41no—
427C22×Dic83—41no—
428C22×Dic83—41no—
429C22×Dic83C2411yescharacteristic
430C22×Dic83C2411yescharacteristic
431C22×Dic83C2411yescharacteristic
432C22×Dic83C2411yescharacteristic
433C22×Dic83C2411yescharacteristic
434C22×Dic83C2411yescharacteristic
435C22×Dic83C2411yescharacteristic
436C22×Dic83C2411yescharacteristic
437C22×Dic83C2411yescharacteristic
438C22×Dic83C2411yescharacteristic
439C22×Dic83C2411yescharacteristic
440C22×Dic83C2411yescharacteristic
441C2×C4×D83—22no—
442C2×C4×D83—22no—
443C2×C4×D83—22no—
444C2×C4×D83—22no—
445C2×C4×D83—22no—
446C2×C4×D83—22no—
447C2×C4×D83—22no—
448C2×C4×D83—22no—
449C2×C4×D83—41no—
450C2×C4×D83—41no—
451C2×C4×D83—41no—
452C2×C4×D83—41no—
453C2×C4×D83—41no—
454C2×C4×D83—41no—
455C2×C4×D83—41no—
456C2×C4×D83—41no—
457C2×C4×D83—41no—
458C2×C4×D83—41no—
459C2×C4×D83—416no—
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×C414yescomplemented
471C2×C4×D83C22×C414yescomplemented
472C4⋊Dic83—22no—
473C4⋊Dic83—22no—
474C4⋊Dic83—22no—
475C4⋊Dic83—41no—
476C4⋊Dic83—41no—
477C4⋊Dic83C22×C414yescomplemented
478C4⋊Dic83C22×C414yescomplemented
479Dic83⋊C4—22no—
480Dic83⋊C4—22no—
481Dic83⋊C4—41no—
482Dic83⋊C4—41no—
483Dic83⋊C4—41no—
484Dic83⋊C4—41no—
485Dic83⋊C4—41no—
486Dic83⋊C4—41no—
487Dic83⋊C4C22×C414yescomplemented
488Dic83⋊C4C22×C414yescomplemented
489C22⋊Dic83—22no—
490C22⋊Dic83—41no—
491C22⋊Dic83—41no—
492C22⋊Dic83—41no—
493C22⋊Dic83—41no—
494C22⋊Dic83C22×C414yes—
495(C2×D83)⋊C4—22no—
496(C2×D83)⋊C4—22no—
497(C2×D83)⋊C4—22no—
498(C2×D83)⋊C4—22no—
499(C2×D83)⋊C4—41no—
500(C2×D83)⋊C4—41no—
501(C2×D83)⋊C4—41no—
502(C2×D83)⋊C4—41no—
503(C2×D83)⋊C4—41no—
504(C2×D83)⋊C4—41no—
505(C2×D83)⋊C4—41no—
506(C2×D83)⋊C4—41no—
507(C2×D83)⋊C4—41no—
508(C2×D83)⋊C4—41no—
509(C2×D83)⋊C4—41no—
510(C2×D83)⋊C4—41no—
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)⋊C4C22×C414yes—
520(C2×D83)⋊C4C22×C414yes—
521(C2×D83)⋊C4C22×C414yes—
522(C2×D83)⋊C4C22×C414yes—
523(C2×D83)⋊C4C22×C414yes—
524(C2×D83)⋊C4C22×C414yes—
525(C2×D83)⋊C4C22×C414yescomplemented
526(C2×D83)⋊C4C22×C414yescomplemented
527C4×Dic83—22no—
528C4×Dic83—22no—
529C4×Dic83—22no—
530C4×Dic83—41no—
531C4×Dic83—41no—
532C4×Dic83—41no—
533C4×Dic83—41no—
534C4×Dic83—41no—
535C4×Dic83—41no—
536C4×Dic83—41no—
537C4×Dic83—41no—
538C4×Dic83—41no—
539C4×Dic83—41no—
540C4×Dic83C22×C414yescomplemented
541C24×C83C2411yescharacteristic
542C24×C83C2411yescharacteristic
543C2×D4×C83—41no—
544C2×D4×C83—41no—
545C2×D4×C83C22×C414yes—
546C22×C4×C83—22no—
547C22×C4×C83—41no—
548C22×C4×C83—41no—
549C22×C4×C83—41no—
550C22×C4×C83—41no—
551C22×C4×C83C22×C414yescomplemented
552C22×C4×C83C2411yescharacteristic
553C22×C4×C83C2411yescharacteristic
554C22×C4×C83C2411yescharacteristic
555C22×C4×C83C2411yescharacteristic
556C22×C4×C83C2411yescharacteristic
557C22×C4×C83C2411yescharacteristic
558C22×C4×C83C2411yescharacteristic
559C22×C4×C83C2411yescharacteristic
560C22×C4×C83C2411yescharacteristic
561C22×C4×C83C2411yescharacteristic
562C22×C4×C83C2411yescharacteristic
563C22×C4×C83C2411yescharacteristic
564C22×C4×C83C2411yescharacteristic
565C4⋊C4×C83—22no—
566C4⋊C4×C83—41no—
567C4⋊C4×C83—41no—
568C4⋊C4×C83—41no—
569C4⋊C4×C83—41no—
570C4⋊C4×C83C22×C414yescomplemented
571C4⋊C4×C83C22×C414yescomplemented
572C22⋊C4×C83—22no—
573C22⋊C4×C83—41no—
574C22⋊C4×C83—41no—
575C22⋊C4×C83—41no—
576C22⋊C4×C83—41no—
577C22⋊C4×C83—41no—
578C22⋊C4×C83—41no—
579C22⋊C4×C83C22×C414yes—
580C22⋊C4×C83C22×C414yes—
581C22⋊C4×C83C22×C414yescomplemented
582C42×C83—41no—
583C42×C83—41no—
584C42×C83—41no—
585C42×C83—41no—
586C42×C83—41no—
587C23×C83—21no—
588C23×C83—21no—
589C23×C83—21no—
590C23×C83—21no—
591C23×C83—21no—
592C23×C83—21no—
593C23×C83—21no—
594C23×C83—21no—
595C23×C83—21no—
596C23×C83—21no—
597C23×C83—21no—
598C23×C83—21no—
599C23×C83C23×C412yes—
600C23×C83C23×C412yes—
601C23×C83C2511yescharacteristic
602C22×D83—21no—
603C22×D83—21no—
604C22×D83—21no—
605C22×D83—21no—
606C22×D83—21no—
607C22×D83—21no—
608C22×D83—21no—
609C22×D83—21no—
610C22×D83—21no—
611C22×D83—21no—
612C22×D83—21no—
613C22×D83—21no—
614C22×D83—21no—
615C22×D83—21no—
616C22×D83—21no—
617C22×D83—21no—
618C22×D83—21no—
619C22×D83—21no—
620C22×D83—21no—
621C22×D83—21no—
622C22×D83—21no—
623C22×D83—21no—
624C22×D83—21no—
625C22×D83—21no—
626C22×D83—44no—
627C22×D83—44no—
628C22×D83—44no—
629C22×D83—44no—
630C22×D83—44no—
631C22×D83—44no—
632C22×D83—44no—
633C22×D83C23×C412yes—
634C22×D83C23×C412yes—
635C22×D83C23×C412yes—
636C22×D83C23×C412yes—
637D4×C83—44no—
638C2×C4×C83—21no—
639C2×C4×C83—21no—
640C2×C4×C83—21no—
641C2×C4×C83—21no—
642C2×C4×C83—21no—
643C2×C4×C83—21no—
644C2×C4×C83—21no—
645C2×C4×C83—21no—
646C2×C4×C83—21no—
647C2×C4×C83—21no—
648C2×C4×C83—21no—
649C2×C4×C83—21no—
650C2×C4×C83—21no—
651C2×C4×C83—21no—
652C2×C4×C83—21no—
653C2×C4×C83—21no—
654C2×C4×C83—21no—
655C2×C4×C83—21no—
656C2×C4×C83—21no—
657C2×C4×C83—21no—
658C2×C4×C83—21no—
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—44no—
672C2×C4×C83—44no—
673C2×C4×C83C23×C412yes—
674C2×C4×C83C23×C412yes—
675C2×C4×C83C23×C412yes—
676C2×C4×C83C23×C412yes—
677C2×C4×C83C23×C412yes—
678C2×C4×C83H(5,𝔽2)12yes—
679C22⋊D83—44no—
680C22⋊D83—44no—
681C22⋊D83—44no—
682C22⋊D83—44no—
683C22⋊D83—44no—
684C22⋊D83—44no—
685C2×Dic83—21no—
686C2×Dic83—21no—
687C2×Dic83—21no—
688C2×Dic83—21no—
689C2×Dic83—21no—
690C2×Dic83—21no—
691C2×Dic83—21no—
692C2×Dic83—21no—
693C2×Dic83—21no—
694C2×Dic83—21no—
695C2×Dic83—21no—
696C2×Dic83—21no—
697C2×Dic83—21no—
698C2×Dic83—21no—
699C2×Dic83—21no—
700C2×Dic83—21no—
701C2×Dic83—21no—
702C2×Dic83—21no—
703C2×Dic83—21no—
704C2×Dic83—21no—
705C2×Dic83—21no—
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—21no—
715C2×Dic83—44no—
716C2×Dic83—82no—
717C2×Dic83—82no—
718C2×Dic83C23×C412yes—
719C2×Dic83C23×C412yes—
720C2×Dic83C23×C412yes—
721C2×Dic83C23×C412yes—
722C2×Dic83H(5,𝔽2)12yes—
723C2×Dic83H(5,𝔽2)12yes—
724D332—44no—
725D332—44no—
726D332—44no—
727D332—44no—
728D332—44no—
729C4×D83—44no—
730C4×D83—44no—
731C4×D83—44no—
732C4×D83—44no—
733C4×D83—44no—
734C4×D83—44no—
735C4×D83—82no—
736C4×D83—82no—
737C4×D83—82no—
738C4×D83—82no—
739C22×C83—22no—
740C22×C83—22no—
741C22×C83—22no—
742C22×C83—22no—
743C22×C83—22no—
744C22×C83—22no—
745C22×C83—41no—
746C22×C83—41no—
747C22×C83—41no—
748C22×C83—41no—
749C22×C83—41no—
750C22×C83—41no—
751C22×C83—41no—
752C22×C83—41no—
753C22×C83C24×C411yescharacteristic
754C22×C83C2×H(5,𝔽2)11yescharacteristic
755C22×C83C2×H(5,𝔽2)11yescharacteristic
756C22×C83C2×H(5,𝔽2)11yescharacteristic
757C22×C83#58511yescharacteristic
758C22×C83#58511yescharacteristic
759C22×C83#58511yescharacteristic
760C2×D83—22no—
761C2×D83—22no—
762C2×D83—22no—
763C2×D83—22no—
764C2×D83—22no—
765C2×D83—22no—
766C2×D83—22no—
767C2×D83—22no—
768C2×D83—22no—
769C2×D83—22no—
770C2×D83—22no—
771C2×D83—22no—
772C2×D83—416no—
773C2×D83—41no—
774C2×D83—41no—
775C2×D83—41no—
776C2×D83—41no—
777C2×D83—41no—
778C2×D83—41no—
779C2×D83—41no—
780C2×D83—41no—
781C2×D83—41no—
782C2×D83—41no—
783C2×D83—41no—
784C2×D83—41no—
785C2×D83—41no—
786C2×D83—41no—
787C2×D83—41no—
788C2×D83—41no—
789C4×C83—22no—
790C4×C83—22no—
791C4×C83—22no—
792C4×C83—22no—
793C4×C83—22no—
794C4×C83—22no—
795C4×C83—41no—
796C4×C83—41no—
797C4×C83—41no—
798C4×C83—41no—
799C4×C83—41no—
800C4×C83—41no—
801C4×C83—41no—
802Dic83—22no—
803Dic83—22no—
804Dic83—22no—
805Dic83—22no—
806Dic83—22no—
807Dic83—22no—
808Dic83—41no—
809Dic83—41no—
810Dic83—41no—
811Dic83—41no—
812Dic83—41no—
813Dic83—41no—
814#34511—831nomaximal, Sylow
815C2×C83—42no—
816C2×C83—42no—
817C2×C83C4×H(5,𝔽2)11yescharacteristic
818C2×C83C4×H(5,𝔽2)11yescharacteristic
819C2×C83C4×H(5,𝔽2)11yescharacteristic
820C2×C83#353211yescharacteristic
821C2×C83#353911yescharacteristic
822C2×C83#353911yescharacteristic
823C2×C83#354011yescharacteristic
824D83—42no—
825D83—42no—
826D83—42no—
827D83—42no—
828C2×#560—831no—
829#2375—831no—
830#2375—831no—
831#2375—831no—
832#2374—831no—
833#2373—831no—
834#2373—831no—
835#2366—831no—
836#2364—831no—
837#2364—831no—
838#2363—831no—
839#2363—831no—
840#2361—831no—
841#2361—831no—
842#2359—831no—
843#2359—831no—
844#2335—831no—
845#2335D8311yescharacteristic, complemented
846#2334—831no—
847#2334—831no—
848#2333—831no—
849#2333—831no—
850#2328—831no—
851#2325—831no—
852#2325—831no—
853#2324—831no—
854#2324—831no—
855#2322—831no—
856C4×#120—831no—
857C4×#120—831no—
858C4×#120—831no—
859C83#3451111yescharacteristic, complemented, Sylow
860C24×C4—831no—
861#560—8316no—
862C2×#127—831no—
863C2×#126—831no—
864C2×#126—831no—
865C2×#123—831no—
866C2×#123—831no—
867C2×#123C2×D8311yescharacteristic
868C2×#121—831no—
869C2×#121—831no—
870C2×#121—831no—
871C2×#121—831no—
872C2×#121—831no—
873C2×#121—831no—
874C2×#120—831no—
875C2×#120—831no—
876C2×#120—831no—
877C2×C4×D4—831no—
878C2×C4×D4—831no—
879C2×C4×D4—831no—
880C2×C4×D4—831no—
881C2×C4×D4—831no—
882C2×C4×D4—831no—
883C2×C4×D4—831no—
884C2×C4×D4—831no—
885C2×C4×D4—831no—
886C2×C4×D4—831no—
887C2×C4×D4—831no—
888C2×C4×D4—831no—
889C2×#117—831no—
890C2×#117—831no—
891C22×C4⋊C4—831no—
892#390—831no—
893#390—831no—
894#390—831no—
895#390—831no—
896#390—831no—
897#390—831no—
898#390—831no—
899#390—831no—
900#390—831no—
901#390—831no—
902#390—831no—
903#390C2×D8311yescharacteristic
904#389—831no—
905#389—831no—
906#389—831no—
907#389—831no—
908#389—831no—
909#389C2×D8311yescharacteristic, complemented
910#388—831no—
911#388—831no—
912#388—831no—
913#388—831no—
914#388—831no—
915#388—831no—
916#388—831no—
917#388—831no—
918#388—831no—
919#388—831no—
920#388—831no—
921#388—831no—
922#388—831no—
923#388—831no—
924#388—831no—
925#388—831no—
926#388—831no—
927#388—831no—
928#388—831no—
929#388—831no—
930#388C2×D8311yescharacteristic
931#388C2×D8311yescharacteristic
932#388C2×D8311yescharacteristic, complemented
933#388C2×D8311yescharacteristic, complemented
934#387—831no—
935#387—831no—
936#387—831no—
937#387—831no—
938#387—831no—
939#387—831no—
940#387—831no—
941#387—831no—
942#387—831no—
943#387—831no—
944#387C2×D8311yescharacteristic, complemented
945#387C2×D8311yescharacteristic, complemented
946#386—831no—
947#386—831no—
948#386—831no—
949#386—831no—
950#386—831no—
951#386—831no—
952#386—831no—
953#386—831no—
954#386—831no—
955#386—831no—
956#386—831no—
957#386—831no—
958#386—831no—
959#386—831no—
960#386—831no—
961#386—831no—
962#386—831no—
963#386—831no—
964#386—831no—
965#386—831no—
966#386—831no—
967#386—831no—
968#386—831no—
969#386C2×D8311yescharacteristic
970#385—831no—
971#385—831no—
972#385—831no—
973#385—831no—
974#385—831no—
975#385—831no—
976#385—831no—
977#385—831no—
978#385—831no—
979#385—831no—
980#385—831no—
981#385C2×D8311yescharacteristic
982#382—831no—
983#381—831no—
984#380—831no—
985#380C2×D8311yescharacteristic, complemented
986#379—831no—
987#379—831no—
988#379—831no—
989C4×C4⋊C4—831no—
990C4×C4⋊C4—831no—
991C4×C4⋊C4—831no—
992C4×C4⋊C4—831no—
993C4×C4⋊C4—831no—
994C4×C4⋊C4—831no—
995C4×C4⋊C4—831no—
996C4×C4⋊C4C2×D8311yescharacteristic, complemented
997C4×C22⋊C4—831no—
998C4×C22⋊C4—831no—
999C4×C22⋊C4—831no—
1000C4×C22⋊C4—831no—
1001C4×C22⋊C4—831no—
1002C4×C22⋊C4—831no—
1003C4×C22⋊C4—831no—
1004C4×C22⋊C4—831no—
1005C4×C22⋊C4—831no—
1006C4×C22⋊C4—831no—
1007C4×C22⋊C4—831no—
1008C4×C22⋊C4—831no—
1009C4×C22⋊C4—831no—
1010C4×C22⋊C4—831no—
1011C4×C22⋊C4C2×D8311yescharacteristic
1012C4×C22⋊C4C2×D8311yescharacteristic, complemented
1013#376—831no—
1014C2×#95—831no—
1015C2×#95—831no—
1016C25—831no—
1017C22×D4—831no—
1018C22×D4—831no—
1019C22×D4—831no—
1020C22×D4—831no—
1021C22×D4—831no—
1022C22×D4—831no—
1023C22×D4—831no—
1024C22×D4—831no—
1025C22×D4—831no—
1026C22×D4—831no—
1027C22×D4—831no—
1028C22×D4C22×D8311yescharacteristic
1029C23×C4—3322no—
1030C23×C4—3322no—
1031C23×C4—3322no—
1032C23×C4—831no—
1033C23×C4—831no—
1034C23×C4—831no—
1035C23×C4—831no—
1036C23×C4—831no—
1037C23×C4—831no—
1038C23×C4—831no—
1039C23×C4—831no—
1040C23×C4—831no—
1041C23×C4—831no—
1042C23×C4—831no—
1043C23×C4—831no—
1044C23×C4—831no—
1045C23×C4C22×D8311yescharacteristic
1046C23×C4C22×D8311yescharacteristic
1047#127—838no—
1048#126—838no—
1049#126—838no—
1050#123—838no—
1051#123—838no—
1052#123C4×D8318yescomplemented
1053#121—838no—
1054#121—838no—
1055#121—838no—
1056#121—838no—
1057#121—838no—
1058#121—838no—
1059#120—838no—
1060#120—838no—
1061#120—838no—
1062C4×D4—3322no—
1063C4×D4—3322no—
1064C4×D4—3322no—
1065C4×D4—3322no—
1066C4×D4—3322no—
1067C4×D4—3322no—
1068C4×D4—3322no—
1069C4×D4—3322no—
1070C4×D4—3322no—
1071C4×D4—3322no—
1072C4×D4—3322no—
1073C4×D4—3322no—
1074#117—3322no—
1075#117—3322no—
1076C2×C4⋊C4—3322no—
1077C2×C4⋊C4—831no—
1078C2×C4⋊C4—831no—
1079C2×C4⋊C4—831no—
1080C2×C4⋊C4—831no—
1081C2×C4⋊C4—831no—
1082C2×C4⋊C4—831no—
1083C2×C4⋊C4—831no—
1084C2×C4⋊C4—831no—
1085C2×C4⋊C4—831no—
1086C2×C4⋊C4—831no—
1087C2×C4⋊C4—831no—
1088C2×C4⋊C4—831no—
1089C2×C4⋊C4—831no—
1090C2×C4⋊C4—831no—
1091C2×C4⋊C4—831no—
1092C2×C4⋊C4—831no—
1093C2×C4⋊C4—831no—
1094C2×C4⋊C4C22×D8311yescharacteristic
1095C2×C4⋊C4C22×D8311yescharacteristic
1096C2×C4⋊C4C22×D8311yescharacteristic
1097C2×C4⋊C4C22×D8311yescharacteristic
1098C2×C4⋊C4C22×D8311yescharacteristic
1099C2×C4⋊C4C22×D8311yescharacteristic
1100C2×C4⋊C4C22×D8311yescharacteristic
1101C2×C22⋊C4—831no—
1102C2×C22⋊C4—831no—
1103C2×C22⋊C4—831no—
1104C2×C22⋊C4—831no—
1105C2×C22⋊C4—831no—
1106C2×C22⋊C4—831no—
1107C2×C22⋊C4—831no—
1108C2×C22⋊C4—831no—
1109C2×C22⋊C4—831no—
1110C2×C22⋊C4—831no—
1111C2×C22⋊C4—831no—
1112C2×C22⋊C4—831no—
1113C2×C22⋊C4—831no—
1114C2×C22⋊C4—831no—
1115C2×C22⋊C4—831no—
1116C2×C22⋊C4—831no—
1117C2×C22⋊C4—831no—
1118C2×C22⋊C4—831no—
1119C2×C22⋊C4—831no—
1120C2×C22⋊C4—831no—
1121C2×C22⋊C4—831no—
1122C2×C22⋊C4—831no—
1123C2×C22⋊C4—831no—
1124C2×C22⋊C4—831no—
1125C2×C22⋊C4—831no—
1126C2×C22⋊C4—831no—
1127C2×C22⋊C4—831no—
1128C2×C22⋊C4—831no—
1129C2×C22⋊C4—831no—
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⋊C4C22×D8311yescharacteristic
1140C2×C22⋊C4C22×D8311yescharacteristic
1141C2×C22⋊C4C22×D8311yescharacteristic
1142C2×C22⋊C4C22×D8311yescharacteristic
1143C2×C22⋊C4C22×D8311yescharacteristic
1144C2×C22⋊C4C22×D8311yescharacteristic
1145C2×C22⋊C4C22×D8311yescharacteristic
1146C2×C22⋊C4C22×D8311yescharacteristic
1147C2×C22⋊C4C22×D8311yescharacteristic
1148C2×C22⋊C4C22×D8311yescharacteristic
1149C2×C42—831no—
1150C2×C42—831no—
1151C2×C42—831no—
1152C2×C42—831no—
1153C2×C42—831no—
1154C2×C42—831no—
1155C2×C42—831no—
1156C2×C42—831no—
1157C2×C42—831no—
1158C2×C42—831no—
1159C2×C42—831no—
1160C2×C42—831no—
1161C2×C42—831no—
1162C2×C42—831no—
1163C2×C42C22×D8311yescharacteristic
1164C2×C42C22×D8311yescharacteristic
1165C2×C42C22×D8311yescharacteristic
1166C2×C42C22×D8311yescharacteristic
1167C2×C42C22×D8311yescharacteristic
1168#95—831no—
1169#95—831no—
1170#95—831no—
1171#95—831no—
1172#95—831no—
1173#95—831no—
1174#95—831no—
1175#95—831no—
1176#95—831no—
1177#95—831no—
1178#95—831no—
1179#95—831no—
1180#95—831no—
1181#95—831no—
1182#95—831no—
1183#95—831no—
1184#95—831no—
1185#95—831no—
1186#95—831no—
1187#95—831no—
1188#95—831no—
1189#95—831no—
1190#95—831no—
1191#95—831no—
1192#95—831no—
1193#95—831no—
1194#95C22×D8311yescharacteristic
1195#95C22×D8311yescharacteristic
1196#95C22×D8311yescharacteristic
1197#95C22×D8311yescharacteristic
1198#95C22×D8311yescharacteristic
1199#95C22×D8311yescharacteristic
1200#95C22×D8311yescharacteristic
1201#95C22×D8311yescharacteristic
1202#95C22×D8311yescharacteristic
1203#95C22×D8311yescharacteristic
1204C24—3321no—
1205C24—3321no—
1206C24—3321no—
1207C24—3321no—
1208C24—3321no—
1209C24—3321no—
1210C24—834no—
1211C24—831no—
1212C24—831no—
1213C24—831no—
1214C24—831no—
1215C24C23×D8311yescharacteristic
1216C24C23×D8311yescharacteristic
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—3321no—
1220C2×D4—3321no—
1221C2×D4—3321no—
1222C2×D4—3321no—
1223C2×D4—3321no—
1224C2×D4—3321no—
1225C2×D4—3321no—
1226C2×D4—3321no—
1227C2×D4—3321no—
1228C2×D4—3321no—
1229C2×D4—3321no—
1230C2×D4—3321no—
1231C2×D4—3321no—
1232C2×D4—3321no—
1233C2×D4—3321no—
1234C2×D4—3321no—
1235C2×D4—3321no—
1236C2×D4—3321no—
1237C2×D4—3321no—
1238C2×D4—3321no—
1239C2×D4—3321no—
1240C2×D4—3321no—
1241C2×D4—834no—
1242C2×D4—834no—
1243C2×D4—834no—
1244C2×D4—834no—
1245C2×D4—834no—
1246C2×D4—834no—
1247C2×D4—834no—
1248C2×D4—834no—
1249C2×D4—834no—
1250C2×D4—834no—
1251C2×D4—834no—
1252C2×D4C2×C4×D8314yes—
1253C22×C4—22no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—3321no—
1259C22×C4—3321no—
1260C22×C4—3321no—
1261C22×C4—3321no—
1262C22×C4—3321no—
1263C22×C4—3321no—
1264C22×C4—3321no—
1265C22×C4—3321no—
1266C22×C4—3321no—
1267C22×C4—3321no—
1268C22×C4—3321no—
1269C22×C4—3321no—
1270C22×C4—3321no—
1271C22×C4—3321no—
1272C22×C4—3321no—
1273C22×C4—3321no—
1274C22×C4—3321no—
1275C22×C4—3321no—
1276C22×C4—3321no—
1277C22×C4—3321no—
1278C22×C4—33216no—
1279C22×C4—3321no—
1280C22×C4—3321no—
1281C22×C4—3321no—
1282C22×C4—3321no—
1283C22×C4—3321no—
1284C22×C4—3321no—
1285C22×C4—834no—
1286C22×C4—834no—
1287C22×C4—831no—
1288C22×C4—831no—
1289C22×C4—831no—
1290C22×C4—831no—
1291C22×C4—831no—
1292C22×C4—831no—
1293C22×C4—831no—
1294C22×C4—831no—
1295C22×C4—831no—
1296C22×C4—831no—
1297C22×C4—831no—
1298C22×C4—831no—
1299C22×C4—1662no—
1300C22×C4—1662no—
1301C22×C4—1662no—
1302C22×C4—1662no—
1303C22×C4—1662no—
1304C22×C4—1662no—
1305C22×C4—1662no—
1306C22×C4—1662no—
1307C22×C4—1662no—
1308C22×C4—1662no—
1309C22×C4—1662no—
1310C22×C4C2×C4×D8314yescomplemented
1311C22×C4C23×D8311yescharacteristic
1312C22×C4C23×D8311yescharacteristic
1313C22×C4C23×D8311yescharacteristic
1314C22×C4C23×D8311yescharacteristic
1315C22×C4C23×D8311yescharacteristic
1316C22×C4C23×D8311yescharacteristic
1317C22×C4C23×D8311yescharacteristic
1318C22×C4C23×D8311yescharacteristic
1319C22×C4C23×D8311yescharacteristic
1320C22×C4C23×D8311yescharacteristic
1321C22×C4C23×D8311yescharacteristic
1322C22×C4C23×D8311yescharacteristic
1323C22×C4C23×D8311yescharacteristic
1324C4⋊C4—22no—
1325C4⋊C4—41no—
1326C4⋊C4—41no—
1327C4⋊C4—41no—
1328C4⋊C4—41no—
1329C4⋊C4—3321no—
1330C4⋊C4—3321no—
1331C4⋊C4—3321no—
1332C4⋊C4—3321no—
1333C4⋊C4—3321no—
1334C4⋊C4—3321no—
1335C4⋊C4—3321no—
1336C4⋊C4—3321no—
1337C4⋊C4—834no—
1338C4⋊C4—834no—
1339C4⋊C4—834no—
1340C4⋊C4—834no—
1341C4⋊C4—1662no—
1342C4⋊C4—1662no—
1343C4⋊C4—1662no—
1344C4⋊C4—1662no—
1345C4⋊C4—1662no—
1346C4⋊C4C2×C4×D8314yescomplemented
1347C4⋊C4C2×C4×D8314yescomplemented
1348C22⋊C4—22no—
1349C22⋊C4—41no—
1350C22⋊C4—41no—
1351C22⋊C4—41no—
1352C22⋊C4—41no—
1353C22⋊C4—41no—
1354C22⋊C4—41no—
1355C22⋊C4—3321no—
1356C22⋊C4—3321no—
1357C22⋊C4—3321no—
1358C22⋊C4—3321no—
1359C22⋊C4—3321no—
1360C22⋊C4—3321no—
1361C22⋊C4—3321no—
1362C22⋊C4—3321no—
1363C22⋊C4—3321no—
1364C22⋊C4—3321no—
1365C22⋊C4—3321no—
1366C22⋊C4—3321no—
1367C22⋊C4—3321no—
1368C22⋊C4—3321no—
1369C22⋊C4—3321no—
1370C22⋊C4—3321no—
1371C22⋊C4—3321no—
1372C22⋊C4—3321no—
1373C22⋊C4—3321no—
1374C22⋊C4—3321no—
1375C22⋊C4—3321no—
1376C22⋊C4—3321no—
1377C22⋊C4—3321no—
1378C22⋊C4—3321no—
1379C22⋊C4—834no—
1380C22⋊C4—834no—
1381C22⋊C4—834no—
1382C22⋊C4—834no—
1383C22⋊C4—834no—
1384C22⋊C4—834no—
1385C22⋊C4—834no—
1386C22⋊C4—834no—
1387C22⋊C4—834no—
1388C22⋊C4—1662no—
1389C22⋊C4—1662no—
1390C22⋊C4—1662no—
1391C22⋊C4—1662no—
1392C22⋊C4—1662no—
1393C22⋊C4C2×C4×D8314yes—
1394C22⋊C4C2×C4×D8314yes—
1395C22⋊C4C2×C4×D8314yescomplemented
1396C42—41no—
1397C42—41no—
1398C42—41no—
1399C42—41no—
1400C42—41no—
1401C42—3321no—
1402C42—3321no—
1403C42—3321no—
1404C42—3321no—
1405C42—3321no—
1406C42—3321no—
1407C42—3321no—
1408C42—3321no—
1409C42—3321no—
1410C42—3321no—
1411C42—834no—
1412C42—1662no—
1413C42—1662no—
1414C42—1662no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—3324no—
1428C23—3324no—
1429C23—3324no—
1430C23—3324no—
1431C23—3324no—
1432C23—3324no—
1433C23—3324no—
1434C23—832no—
1435C23—832no—
1436C23—832no—
1437C23—832no—
1438C23—1661no—
1439C23—1661no—
1440C23—1661no—
1441C23—1661no—
1442C23—1661no—
1443C23—1661no—
1444C23—1661no—
1445C23—1661no—
1446C23—1661no—
1447C23—1661no—
1448C23—1661no—
1449C23—1661no—
1450C23—1661no—
1451C23—1661no—
1452C23—1661no—
1453C23—1661no—
1454C23—1661no—
1455C23—1661no—
1456C23—1661no—
1457C23—1661no—
1458C23—1661no—
1459C23—1661no—
1460C23—1661no—
1461C23—1661no—
1462C23C22×C4×D8312yes—
1463C23C22×C4×D8312yes—
1464C23C24×D8311yescharacteristic
1465D4—44no—
1466D4—3324no—
1467D4—3324no—
1468D4—3324no—
1469D4—3324no—
1470D4—3324no—
1471D4—3324no—
1472D4—3324no—
1473D4—3324no—
1474D4—3324no—
1475D4—3324no—
1476D4—3324no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—44no—
1511C2×C4—44no—
1512C2×C4—3324no—
1513C2×C4—3324no—
1514C2×C4—3324no—
1515C2×C4—3324no—
1516C2×C4—3324no—
1517C2×C4—3324no—
1518C2×C4—3324no—
1519C2×C4—832no—
1520C2×C4—832no—
1521C2×C4—832no—
1522C2×C4—832no—
1523C2×C4—832no—
1524C2×C4—832no—
1525C2×C4—6642no—
1526C2×C4—6642no—
1527C2×C4—6642no—
1528C2×C4—6642no—
1529C2×C4—6642no—
1530C2×C4—6642no—
1531C2×C4—1661no—
1532C2×C4—1661no—
1533C2×C4—1661no—
1534C2×C4—1661no—
1535C2×C4—1661no—
1536C2×C4—1661no—
1537C2×C4—1661no—
1538C2×C4—1661no—
1539C2×C4—1661no—
1540C2×C4—1661no—
1541C2×C4—1661no—
1542C2×C4—1661no—
1543C2×C4—1661no—
1544C2×C4—1661no—
1545C2×C4—1661no—
1546C2×C4—1661no—
1547C2×C4—1661no—
1548C2×C4—1661no—
1549C2×C4—1661no—
1550C2×C4—1661no—
1551C2×C4—1661no—
1552C2×C4—1661no—
1553C2×C4—1661no—
1554C2×C4—1661no—
1555C2×C4—1661no—
1556C2×C4—1661no—
1557C2×C4—1661no—
1558C2×C4—1661no—
1559C2×C4—1661no—
1560C2×C4—1661no—
1561C2×C4C22×C4×D8312yes—
1562C2×C4C22×C4×D8312yes—
1563C2×C4C22×C4×D8312yes—
1564C2×C4C22×C4×D8312yes—
1565C2×C4C22×C4×D8312yes—
1566C2×C4#1458183812yes—
1567C22—22no—
1568C22—22no—
1569C22—22no—
1570C22—22no—
1571C22—22no—
1572C22—22no—
1573C22—41no—
1574C22—41no—
1575C22—41no—
1576C22—41no—
1577C22—41no—
1578C22—41no—
1579C22—41no—
1580C22—41no—
1581C22—33216no—
1582C22—3321no—
1583C22—3321no—
1584C22—3321no—
1585C22—3321no—
1586C22—3321no—
1587C22—3321no—
1588C22—3321no—
1589C22—3321no—
1590C22—3321no—
1591C22—3321no—
1592C22—3321no—
1593C22—3321no—
1594C22—3321no—
1595C22—3321no—
1596C22—3321no—
1597C22—3321no—
1598C22—1662no—
1599C22—1662no—
1600C22—1662no—
1601C22—1662no—
1602C22—1662no—
1603C22—1662no—
1604C22—1662no—
1605C22—1662no—
1606C22—1662no—
1607C22—1662no—
1608C22—1662no—
1609C22—1662no—
1610C22C23×C4×D8311yescharacteristic
1611C22H(5,𝔽2)×D8311yescharacteristic
1612C22H(5,𝔽2)×D8311yescharacteristic
1613C22C2×#1458183811yescharacteristic
1614C22#1912853611yescharacteristic
1615C22#1912853711yescharacteristic
1616C22#1912853811yescharacteristic
1617C4—22no—
1618C4—22no—
1619C4—22no—
1620C4—22no—
1621C4—22no—
1622C4—22no—
1623C4—41no—
1624C4—41no—
1625C4—41no—
1626C4—41no—
1627C4—41no—
1628C4—41no—
1629C4—41no—
1630C4—3321no—
1631C4—3321no—
1632C4—3321no—
1633C4—3321no—
1634C4—3321no—
1635C4—3321no—
1636C4—1662no—
1637C4—1662no—
1638C4—1662no—
1639C4—1662no—
1640C4—1662no—
1641C4—1662no—
1642C2—42no—
1643C2—42no—
1644C2—3322no—
1645C2—3322no—
1646C2—3322no—
1647C2—3322no—
1648C2#2492066711yescharacteristic
1649C2#2492066911yescharacteristic
1650C2C4×#1458183811yescharacteristic
1651C2#2492161411yescharacteristic
1652C2#2492171511yescharacteristic
1653C2#2492172111yescharacteristic
1654C2#2492173511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2335C2
socle, cosocleC23×C83C25
prime radicalC2×#19128441C2
hypercenter#2335D83
hypocenterC83#34511
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2335

Complements

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

NH ≅ G/Ntype
2. #24910603C2semidirect
3. #24910603C2semidirect
4. #24910600C2semidirect
5. #24910591C2semidirect
6. #24910586C2semidirect
7. #24910577C2semidirect
8. #24910524C2semidirect
9. #24910513C2semidirect
10. #24910507C2semidirect
11. #24910500C2semidirect
12. #24910499C2semidirect
13. #24910481C2semidirect
14. #24910476C2semidirect
15. #24910459C2semidirect
16. #24910454C2semidirect
17. #24910255C2semidirect
18. #24910244C2semidirect
19. #24910243C2semidirect
20. #24910227C2semidirect
21. #24910226C2semidirect
22. #24910184C2semidirect
23. #24910163C2semidirect
24. #24910162C2semidirect
25. #24910152C2semidirect
26. #24910151C2semidirect
27. #24910130C2semidirect
28. #24909968C2semidirect
29. C4×#14581762C2semidirect
30. #24909964C2semidirect
31. C83×#2335C2semidirect
33. #19128441C4semidirect
50. C2×C4×D332C22semidirect
58. C2×(C22⋊D83)⋊C4C22semidirect
59. C2×(C22⋊D83)⋊C4C22semidirect
60. C2×#14581751C22semidirect
61. C2×#14581750C22semidirect
62. C2×C4⋊C4×D83C22semidirect
67. #19127602C22semidirect
72. #19127601C22semidirect
73. #19127601C22semidirect
74. #19127600C22semidirect
75. #19127599C22semidirect
76. #19127598C22semidirect
77. #19127598C22semidirect
78. #19127597C22semidirect
83. #19127593C22semidirect
88. #19127592C22semidirect
93. #19127591C22semidirect
96. #19127590C22semidirect
99. #19127587C22semidirect
100. #19127587C22semidirect
101. #19127586C22semidirect
102. #19127586C22semidirect
103. #19127584C22semidirect
104. #19127584C22semidirect
105. #19127583C22semidirect
106. #19127583C22semidirect
107. #19127582C22semidirect
108. #19127582C22semidirect
119. #19127579C22semidirect
120. #19127579C22semidirect
124. #19127578C22semidirect
125. #19127578C22semidirect
130. #19127577C22semidirect
131. #19127577C22semidirect
133. #19127576C22semidirect
138. #19127575C22semidirect
142. #19127572C22semidirect
143. #19127565C22semidirect
144. #19127563C22semidirect
145. #19127560C22semidirect
149. C4⋊C4×Dic83C22semidirect
150. C4⋊C4×Dic83C22semidirect
151. C4⋊C4×Dic83C22semidirect
152. C4×Dic83⋊C4C22semidirect
153. C4×Dic83⋊C4C22semidirect
154. C4×Dic83⋊C4C22semidirect
155. C4×C4⋊Dic83C22semidirect
158. C22⋊C4×Dic83C22semidirect
161. C4×(C2×D83)⋊C4C22semidirect
162. C4×(C2×D83)⋊C4C22semidirect
163. C4×(C2×D83)⋊C4C22semidirect
168. #19127548C22semidirect
169. #19127548C22semidirect
170. #19127546C22semidirect
171. C2×C83⋊#95C22semidirect
172. #95×D83C22semidirect
175. #389×C83C22semidirect
178. #388×C83C22semidirect
179. #388×C83C22semidirect
180. #387×C83C22semidirect
181. #387×C83C22semidirect
184. #380×C83C22semidirect
185. C4×C4⋊C4×C83C22semidirect
187. C4×C22⋊C4×C83C22semidirect
216. #14581788C2×C4semidirect
217. #14581787C2×C4semidirect
218. #14581787C2×C4semidirect
219. #14581774C2×C4semidirect
220. #14581774C2×C4semidirect
221. #14581767C2×C4semidirect
222. #14581767C2×C4semidirect
223. #14581766C2×C4semidirect
224. #14581766C2×C4semidirect
225. #14581765C2×C4semidirect
226. #14581765C2×C4semidirect
227. #14581762C2×C4semidirect
228. #14581762C2×C4semidirect
229. #14581760C2×C4semidirect
343. #123×C83C2×C4semidirect
401. C2×D332C22×C4semidirect
418. C2×C22⋊D83C22×C4semidirect
419. C2×C22⋊D83C22×C4semidirect
470. C2×C4×D83C22×C4semidirect
471. C2×C4×D83C22×C4semidirect
477. C4⋊Dic83C22×C4semidirect
478. C4⋊Dic83C22×C4semidirect
487. Dic83⋊C4C22×C4semidirect
488. Dic83⋊C4C22×C4semidirect
525. (C2×D83)⋊C4C22×C4semidirect
526. (C2×D83)⋊C4C22×C4semidirect
540. C4×Dic83C22×C4semidirect
551. C22×C4×C83C22×C4semidirect
570. C4⋊C4×C83C22×C4semidirect
571. C4⋊C4×C83C22×C4semidirect
581. C22⋊C4×C83C22×C4semidirect
845. #2335D83semidirect
859. C83#34511semidirect
909. #389C2×D83semidirect
932. #388C2×D83semidirect
933. #388C2×D83semidirect
944. #387C2×D83semidirect
945. #387C2×D83semidirect
985. #380C2×D83semidirect
996. C4×C4⋊C4C2×D83semidirect
1012. C4×C22⋊C4C2×D83semidirect
1052. #123C4×D83semidirect
1310. C22×C4C2×C4×D83semidirect
1346. C4⋊C4C2×C4×D83semidirect
1347. C4⋊C4C2×C4×D83semidirect
1395. C22⋊C4C2×C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191284412
#249106032
#249106002
#249105912
#249105862
#249105772
#249105242
#249105132
#249105072
#249105002
#249104992
#249104812
#249104762
#249104592
#249104542
#249102552
#249102442
#249102432
#249102272
#249102262
#249101842
#249101632
#249101622
#249101522
#249101512
#249101302
#249099682
C4×#145817622
#249099642
C83×#23352
#3451183