Finite Group Databasebeta

← #35568982

Subgroups — #35568982

Order 21248.

2292 conjugacy classes of subgroups.

The subgroup lattice has 1522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128375C211yesmaximal, characteristic
2#24910653C211yesmaximal, characteristic, complemented
3#24910628C211yesmaximal, characteristic, complemented
4#24910610C211yesmaximal, characteristic, complemented
5#24910610C211yesmaximal, characteristic, complemented
6#24910583C211yesmaximal, characteristic, complemented
7#24910532C211yesmaximal, characteristic, complemented
8#24910469C211yesmaximal, characteristic, complemented
9#24910451C211yesmaximal, characteristic, complemented
10#24910445C211yesmaximal, characteristic
11#24910389C211yesmaximal, characteristic, complemented
12#24910361C211yesmaximal, characteristic, complemented
13#24910351C211yesmaximal, characteristic, complemented
14#24910310C211yesmaximal, characteristic, complemented
15#24910305C211yesmaximal, characteristic, complemented
16#24910273C211yesmaximal, characteristic, complemented
17#24910252C211yesmaximal, characteristic, complemented
18#24910241C211yesmaximal, characteristic, complemented
19#24910234C211yesmaximal, characteristic, complemented
20#24910191C211yesmaximal, characteristic, complemented
21#24910144C211yesmaximal, characteristic, complemented
22#24910136C211yesmaximal, characteristic, complemented
23#24910123C211yesmaximal, characteristic
24#24910107C211yesmaximal, characteristic, complemented
25#24910091C211yesmaximal, characteristic, complemented
26#24910074C211yesmaximal, characteristic, complemented
27#24910068C211yesmaximal, characteristic, complemented
28#24909980C211yesmaximal, characteristic, complemented
29#24909947C211yesmaximal, characteristic, complemented
30C2×#19127590C211yesmaximal, characteristic, complemented
31C83×#2343C211yesmaximal, characteristic, complemented
32#19128375C4116yescomplemented
33C2×#14581787C2211yescharacteristic
34C2×#14581786C2211yescharacteristic
35C2×#14581780C2211yescharacteristic
36C2×#14581777C2211yescharacteristic
37C2×#14581777C2211yescharacteristic
38C2×#14581775C2211yescharacteristic
39C2×#14581770C2211yescharacteristic
40C2×#14581769C2211yescharacteristic
41C2×#14581762C2211yescharacteristic
42C2×C4×Dic166C2211yescharacteristic, complemented
43C2×C4×D332C2211yescharacteristic
44C2×C4×D332C2211yescharacteristic
45C2×C4×C22⋊D83C2211yescharacteristic
46C2×(C22⋊D83)⋊C4C2211yescharacteristic
47C2×(C22⋊D83)⋊C4C2211yescharacteristic
48C2×#14581751C2211yescharacteristic
49C2×#14581750C2211yescharacteristic
50C2×#14581749C2211yescharacteristic
51C22×Dic83⋊C4C2211yescharacteristic
52C2×C4⋊C4×D83C2211yescharacteristic, complemented
53C22×(C2×D83)⋊C4C2211yescharacteristic
54C22×(C2×D83)⋊C4C2211yescharacteristic
55C22×(C2×D83)⋊C4C2211yescharacteristic
56C2×C22⋊C4×D83C2211yescharacteristic
57C2×C22⋊C4×D83C2211yescharacteristic
58C22×C4×Dic83C2211yescharacteristic
59#19127607C2211yescharacteristic, complemented
60#19127605C2211yescharacteristic, complemented
61#19127605C2211yescharacteristic, complemented
62#19127603C2211yescharacteristic
63#19127603C2211yescharacteristic
64#19127603C2211yescharacteristic
65#19127600C2211yescharacteristic, complemented
66#19127600C2211yescharacteristic, complemented
67#19127600C2211yescharacteristic, complemented
68#19127600C2211yescharacteristic, complemented
69#19127599C2211yescharacteristic, complemented
70#19127599C2211yescharacteristic, complemented
71#19127598C2211yescharacteristic, complemented
72#19127598C2211yescharacteristic, complemented
73#19127598C2211yescharacteristic, complemented
74#19127598C2211yescharacteristic, complemented
75#19127598C2211yescharacteristic, complemented
76#19127596C2211yescharacteristic, complemented
77#19127593C2211yescharacteristic
78#19127593C2211yescharacteristic
79#19127593C2211yescharacteristic
80#19127593C2211yescharacteristic
81#19127593C2211yescharacteristic
82#19127593C2211yescharacteristic
83#19127593C2211yescharacteristic
84#19127593C2211yescharacteristic, complemented
85#19127593C2211yescharacteristic, complemented
86#19127592C2211yescharacteristic
87#19127592C2211yescharacteristic
88#19127592C2211yescharacteristic
89#19127591C2211yescharacteristic
90#19127591C2211yescharacteristic
91#19127591C2211yescharacteristic, complemented
92#19127590C2211yescharacteristic
93#19127590C2211yescharacteristic
94#19127590C2211yescharacteristic
95#19127590C2211yescharacteristic
96#19127590C2211yescharacteristic
97#19127590C2211yescharacteristic
98#19127590C2211yescharacteristic
99#19127590C2211yescharacteristic
100#19127590C2211yescharacteristic
101#19127590C2211yescharacteristic
102#19127590C2211yescharacteristic, complemented
103#19127590C2211yescharacteristic, complemented
104#19127590C2211yescharacteristic, complemented
105#19127588C2211yescharacteristic, complemented
106#19127588C2211yescharacteristic, complemented
107#19127588C2211yescharacteristic, complemented
108#19127585C2211yescharacteristic, complemented
109#19127585C2211yescharacteristic, complemented
110#19127585C2211yescharacteristic, complemented
111#19127584C2211yescharacteristic, complemented
112#19127584C2211yescharacteristic, complemented
113#19127583C2211yescharacteristic, complemented
114#19127583C2211yescharacteristic, complemented
115#19127583C2211yescharacteristic, complemented
116#19127582C2211yescharacteristic, complemented
117#19127580C2211yescharacteristic
118#19127579C2211yescharacteristic
119#19127579C2211yescharacteristic
120#19127579C2211yescharacteristic
121#19127579C2211yescharacteristic
122#19127578C2211yescharacteristic
123#19127576C2211yescharacteristic
124#19127576C2211yescharacteristic
125#19127576C2211yescharacteristic
126#19127576C2211yescharacteristic
127#19127575C2211yescharacteristic
128#19127575C2211yescharacteristic
129#19127575C2211yescharacteristic
130#19127575C2211yescharacteristic
131#19127575C2211yescharacteristic
132#19127575C2211yescharacteristic, complemented
133#19127575C2211yescharacteristic, complemented
134#19127574C2211yescharacteristic
135#19127573C2211yescharacteristic
136#19127572C2211yescharacteristic
137#19127572C2211yescharacteristic
138#19127572C2211yescharacteristic, complemented
139#19127570C2211yescharacteristic, complemented
140#19127568C2211yescharacteristic, complemented
141#19127566C2211yescharacteristic, complemented
142#19127563C2211yescharacteristic
143#19127563C2211yescharacteristic, complemented
144#19127560C2211yescharacteristic
145#19127560C2211yescharacteristic
146#19127560C2211yescharacteristic, complemented
147#19127559C2211yescharacteristic
148#19127558C2211yescharacteristic
149#19127558C2211yescharacteristic
150#19127558C2211yescharacteristic
151#19127558C2211yescharacteristic, complemented
152#19127556C2211yescharacteristic
153C4×Dic83⋊C4C2211yescharacteristic, complemented
154C4×C4⋊Dic83C2211yescharacteristic, complemented
155C4×C4⋊Dic83C2211yescharacteristic, complemented
156C4×C4⋊Dic83C2211yescharacteristic, complemented
157C4×C4⋊Dic83C2211yescharacteristic, complemented
158#19127552C2211yescharacteristic, complemented
159#19127552C2211yescharacteristic, complemented
160#19127552C2211yescharacteristic, complemented
161#19127552C2211yescharacteristic, complemented
162C22⋊C4×Dic83C2211yescharacteristic
163C22⋊C4×Dic83C2211yescharacteristic
164C4×(C2×D83)⋊C4C2211yescharacteristic
165C4×C22⋊Dic83C2211yescharacteristic
166#19127548C2211yescharacteristic
167#19127548C2211yescharacteristic
168#19127548C2211yescharacteristic
169#19127548C2211yescharacteristic, complemented
170#19127548C2211yescharacteristic, complemented
171#19127548C2211yescharacteristic, complemented
172C2×C83⋊#95C2211yescharacteristic
173C2×#117×C83C2211yescharacteristic
174#387×C83C2211yescharacteristic, complemented
175#387×C83C2211yescharacteristic, complemented
176#387×C83C2211yescharacteristic, complemented
177#387×C83C2211yescharacteristic, complemented
178#385×C83C2211yescharacteristic
179#385×C83C2211yescharacteristic
180#383×C83C2211yescharacteristic, complemented
181#382×C83C2211yescharacteristic, complemented
182#381×C83C2211yescharacteristic
183C4×C4⋊C4×C83C2211yescharacteristic, complemented
184C4×C22⋊C4×C83C2211yescharacteristic
185C4×C22⋊C4×C83C2211yescharacteristic
186#376×C83C2211yescharacteristic, complemented
187C2×#95×C83C2211yescharacteristic
188C24×D83C2311yescharacteristic
189C22×Dic166C2311yescharacteristic
190C22×D332C2311yescharacteristic
191C22×D332C2311yescharacteristic
192C22×C22⋊D83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C23×Dic83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C22×C4×D83C2311yescharacteristic
197C22×C4×D83C2311yescharacteristic
198C22×C4×D83C2311yescharacteristic
199C22×C4×D83C2311yescharacteristic
200C22×C4×D83C2311yescharacteristic
201C22×C4×D83C2311yescharacteristic
202C22×C4×D83C2311yescharacteristic
203#14581787C2×C418yescomplemented
204#14581786C2×C418yescomplemented
205#14581780C2×C418yescomplemented
206#14581777C2×C418yescomplemented
207#14581777C2×C418yescomplemented
208#14581775C2×C418yescomplemented
209#14581770C2×C418yescomplemented
210#14581769C2×C418yescomplemented
211#14581762C2×C418yes—
212C4×Dic166—42no—
213C4×D332—42no—
214C4×D332C2×C418yescomplemented
215C4×C22⋊D83—42no—
216(C22⋊D83)⋊C4—42no—
217(C22⋊D83)⋊C4C2×C418yescomplemented
218#14581751—42no—
219#14581750—42no—
220#14581749C2×C418yescomplemented
221C2×C4⋊Dic83C2311yescharacteristic
222C2×C4⋊Dic83C2311yescharacteristic
223C2×C4⋊Dic83C2311yescharacteristic
224C2×C4⋊Dic83C2311yescharacteristic
225C2×C4⋊Dic83C2311yescharacteristic
226C2×C4⋊Dic83C2311yescharacteristic
227C2×C4⋊Dic83C2311yescharacteristic
228C2×C4⋊Dic83C2311yescharacteristic
229C2×C4⋊Dic83C2311yescharacteristic
230C2×C4⋊Dic83C2311yescharacteristic
231C2×C4⋊Dic83C2311yescharacteristic
232C2×Dic83⋊C4—42no—
233C2×Dic83⋊C4C2311yescharacteristic
234C2×Dic83⋊C4C2311yescharacteristic
235C2×Dic83⋊C4C2311yescharacteristic
236C2×Dic83⋊C4C2311yescharacteristic
237C2×Dic83⋊C4C2311yescharacteristic
238C2×Dic83⋊C4C2311yescharacteristic
239C2×Dic83⋊C4C2311yescharacteristic
240C2×Dic83⋊C4C2311yescharacteristic
241C2×Dic83⋊C4C2311yescharacteristic
242C2×Dic83⋊C4C2311yescharacteristic
243C2×Dic83⋊C4C2311yescharacteristic
244C2×Dic83⋊C4C2311yescharacteristic
245C2×Dic83⋊C4C2311yescharacteristic
246C2×Dic83⋊C4C2311yescharacteristic
247C2×Dic83⋊C4C2311yescharacteristic
248C2×Dic83⋊C4C2311yescharacteristic
249C2×Dic83⋊C4C2311yescharacteristic
250C4⋊C4×D83—42no—
251C2×C22⋊Dic83C2311yescharacteristic
252C2×C22⋊Dic83C2311yescharacteristic
253C2×C22⋊Dic83C2311yescharacteristic
254C2×(C2×D83)⋊C4—42no—
255C2×(C2×D83)⋊C4—42no—
256C2×(C2×D83)⋊C4C2×C418yescomplemented
257C2×(C2×D83)⋊C4C2311yescharacteristic
258C2×(C2×D83)⋊C4C2311yescharacteristic
259C2×(C2×D83)⋊C4C2311yescharacteristic
260C2×(C2×D83)⋊C4C2311yescharacteristic
261C2×(C2×D83)⋊C4C2311yescharacteristic
262C2×(C2×D83)⋊C4C2311yescharacteristic
263C2×(C2×D83)⋊C4C2311yescharacteristic
264C2×(C2×D83)⋊C4C2311yescharacteristic
265C2×(C2×D83)⋊C4C2311yescharacteristic
266C2×(C2×D83)⋊C4C2311yescharacteristic
267C2×(C2×D83)⋊C4C2311yescharacteristic
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
288C22⋊C4×D83—42no—
289C22⋊C4×D83C2×C418yescomplemented
290C2×C4×Dic83—42no—
291C2×C4×Dic83C2311yescharacteristic
292C2×C4×Dic83C2311yescharacteristic
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
296C2×C4×Dic83C2311yescharacteristic
297C2×C4×Dic83C2311yescharacteristic
298C2×C4×Dic83C2311yescharacteristic
299C2×C4×Dic83C2311yescharacteristic
300C2×C4×Dic83C2311yescharacteristic
301C2×C4×Dic83C2311yescharacteristic
302C2×C4×Dic83C2311yescharacteristic
303C2×C4×Dic83C2311yescharacteristic
304C2×C4×Dic83C2311yescharacteristic
305C2×C4×Dic83C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
310C83⋊#95C2311yescharacteristic
311C83⋊#95C2311yescharacteristic
312C83⋊#95C2311yescharacteristic
313C83⋊#95C2311yescharacteristic
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
334C23×C4×C83C2311yescharacteristic
335C23×C4×C83C2311yescharacteristic
336C23×C4×C83C2311yescharacteristic
337#117×C83C2×C418yescomplemented
338C2×C4⋊C4×C83C2311yescharacteristic
339C2×C4⋊C4×C83C2311yescharacteristic
340C2×C4⋊C4×C83C2311yescharacteristic
341C2×C4⋊C4×C83C2311yescharacteristic
342C2×C4⋊C4×C83C2311yescharacteristic
343C2×C4⋊C4×C83C2311yescharacteristic
344C2×C22⋊C4×C83C2311yescharacteristic
345C2×C22⋊C4×C83C2311yescharacteristic
346C2×C22⋊C4×C83C2311yescharacteristic
347C2×C22⋊C4×C83C2311yescharacteristic
348C2×C42×C83C2311yescharacteristic
349C2×C42×C83C2311yescharacteristic
350C2×C42×C83C2311yescharacteristic
351C2×C42×C83C2311yescharacteristic
352C2×C42×C83C2311yescharacteristic
353C2×C42×C83C2311yescharacteristic
354#95×C83C2311yescharacteristic
355#95×C83C2311yescharacteristic
356#95×C83C2311yescharacteristic
357#95×C83C2311yescharacteristic
358#95×C83C2311yescharacteristic
359#95×C83C2311yescharacteristic
360#95×C83C2311yescharacteristic
361#95×C83C2311yescharacteristic
362#95×C83C2311yescharacteristic
363#95×C83C2311yescharacteristic
364#95×C83C2311yescharacteristic
365#95×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370C23×D83—22no—
371C23×D83—22no—
372C23×D83—41no—
373C23×D83—41no—
374C23×D83—41no—
375C23×D83—41no—
376C23×D83C22×C414yes—
377C23×D83C2411yescharacteristic
378C23×D83C2411yescharacteristic
379C23×D83C2411yescharacteristic
380C2×Dic166—41no—
381C2×Dic166—41no—
382C2×Dic166C22×C414yes—
383C2×D332—41no—
384C2×D332—41no—
385C2×D332—41no—
386C2×D332—41no—
387C2×D332C22×C414yes—
388C2×D332C22×C414yes—
389C2×C22⋊D83—22no—
390C2×C22⋊D83—22no—
391C2×C22⋊D83C22×C414yes—
392C22×Dic83—22no—
393C22×Dic83—22no—
394C22×Dic83—22no—
395C22×Dic83—41no—
396C22×Dic83—41no—
397C22×Dic83—41no—
398C22×Dic83—41no—
399C22×Dic83—41no—
400C22×Dic83C22×C414yes—
401C22×Dic83C2411yescharacteristic
402C22×Dic83C2411yescharacteristic
403C22×Dic83C2411yescharacteristic
404C22×Dic83C2411yescharacteristic
405C22×Dic83C2411yescharacteristic
406C22×Dic83C2411yescharacteristic
407C22×Dic83C2411yescharacteristic
408C22×Dic83C2411yescharacteristic
409C22×Dic83C2411yescharacteristic
410C22×Dic83C2411yescharacteristic
411C22×Dic83C2411yescharacteristic
412C22×Dic83C2411yescharacteristic
413C22×Dic83C2411yescharacteristic
414C2×C4×D83—22no—
415C2×C4×D83—41no—
416C2×C4×D83—41no—
417C2×C4×D83—41no—
418C2×C4×D83—41no—
419C2×C4×D83—41no—
420C2×C4×D83—41no—
421C2×C4×D83—41no—
422C2×C4×D83—41no—
423C2×C4×D83—41no—
424C2×C4×D83—41no—
425C2×C4×D83—41no—
426C2×C4×D83—41no—
427C2×C4×D83—41no—
428C2×C4×D83—41no—
429C2×C4×D83—41no—
430C2×C4×D83—41no—
431C2×C4×D83—41no—
432C2×C4×D83C22×C414yes—
433C2×C4×D83C22×C414yes—
434C2×C4×D83C22×C414yes—
435C4⋊Dic83—22no—
436C4⋊Dic83—22no—
437C4⋊Dic83—41no—
438C4⋊Dic83—41no—
439C4⋊Dic83—41no—
440C4⋊Dic83—41no—
441C4⋊Dic83—41no—
442C4⋊Dic83—41no—
443C4⋊Dic83—41no—
444C4⋊Dic83—41no—
445C4⋊Dic83C22×C414yes—
446Dic83⋊C4—22no—
447Dic83⋊C4—22no—
448Dic83⋊C4—41no—
449Dic83⋊C4—41no—
450Dic83⋊C4—41no—
451Dic83⋊C4—41no—
452Dic83⋊C4—41no—
453Dic83⋊C4—41no—
454Dic83⋊C4—41no—
455Dic83⋊C4—41no—
456Dic83⋊C4—41no—
457Dic83⋊C4—41no—
458Dic83⋊C4C22×C414yes—
459Dic83⋊C4C22×C414yes—
460Dic83⋊C4C22×C414yes—
461Dic83⋊C4C22×C414yes—
462Dic83⋊C4C22×C414yes—
463C22⋊Dic83—22no—
464C22⋊Dic83—22no—
465C22⋊Dic83C22×C414yes—
466(C2×D83)⋊C4—22no—
467(C2×D83)⋊C4—22no—
468(C2×D83)⋊C4—41no—
469(C2×D83)⋊C4—41no—
470(C2×D83)⋊C4—41no—
471(C2×D83)⋊C4—41no—
472(C2×D83)⋊C4—41no—
473(C2×D83)⋊C4—41no—
474(C2×D83)⋊C4—41no—
475(C2×D83)⋊C4—41no—
476(C2×D83)⋊C4—41no—
477(C2×D83)⋊C4—41no—
478(C2×D83)⋊C4—41no—
479(C2×D83)⋊C4—41no—
480(C2×D83)⋊C4—41no—
481(C2×D83)⋊C4—41no—
482(C2×D83)⋊C4—41no—
483(C2×D83)⋊C4—41no—
484(C2×D83)⋊C4—41no—
485(C2×D83)⋊C4—41no—
486(C2×D83)⋊C4C22×C414yes—
487(C2×D83)⋊C4C22×C414yes—
488(C2×D83)⋊C4C22×C414yes—
489(C2×D83)⋊C4C22×C414yes—
490(C2×D83)⋊C4C22×C414yes—
491(C2×D83)⋊C4C22×C414yes—
492(C2×D83)⋊C4C22×C414yes—
493(C2×D83)⋊C4C22×C414yes—
494(C2×D83)⋊C4C22×C414yes—
495(C2×D83)⋊C4C22×C414yes—
496(C2×D83)⋊C4C22×C414yes—
497C4×Dic83—22no—
498C4×Dic83—41no—
499C4×Dic83—41no—
500C4×Dic83—41no—
501C4×Dic83—41no—
502C4×Dic83—41no—
503C4×Dic83—41no—
504C4×Dic83—41no—
505C4×Dic83—41no—
506C4×Dic83—41no—
507C4×Dic83—41no—
508C4×Dic83—41no—
509C4×Dic83—41no—
510C4×Dic83—41no—
511C4×Dic83C22×C414yes—
512C24×C83C2411yescharacteristic
513C22×C4×C83—22no—
514C22×C4×C83—22no—
515C22×C4×C83—22no—
516C22×C4×C83—22no—
517C22×C4×C83—41no—
518C22×C4×C83—41no—
519C22×C4×C83—41no—
520C22×C4×C83—41no—
521C22×C4×C83C22×C414yes—
522C22×C4×C83C2411yescharacteristic
523C22×C4×C83C2411yescharacteristic
524C22×C4×C83C2411yescharacteristic
525C22×C4×C83C2411yescharacteristic
526C22×C4×C83C2411yescharacteristic
527C22×C4×C83C2411yescharacteristic
528C22×C4×C83C2411yescharacteristic
529C22×C4×C83C2411yescharacteristic
530C22×C4×C83C2411yescharacteristic
531C22×C4×C83C2411yescharacteristic
532C22×C4×C83C2411yescharacteristic
533C22×C4×C83C2411yescharacteristic
534C22×C4×C83C2411yescharacteristic
535C22×C4×C83C2411yescharacteristic
536C4⋊C4×C83—41no—
537C4⋊C4×C83—41no—
538C4⋊C4×C83—41no—
539C4⋊C4×C83—41no—
540C4⋊C4×C83C22×C414yes—
541C4⋊C4×C83C22×C414yes—
542C22⋊C4×C83—22no—
543C22⋊C4×C83—22no—
544C22⋊C4×C83C22×C414yes—
545C22⋊C4×C83C22×C414yes—
546C42×C83—41no—
547C42×C83—41no—
548C42×C83—41no—
549C42×C83—41no—
550C42×C83C22×C414yes—
551C42×C83C22×C414yes—
552C23×C83—21no—
553C23×C83—21no—
554C23×C83—21no—
555C23×C83—21no—
556C23×C83C23×C412yes—
557C23×C83H(5,𝔽2)12yes—
558C23×C832−1+412yes—
559C23×C83C2511yescharacteristic
560C22×D83—21no—
561C22×D83—21no—
562C22×D83—21no—
563C22×D83—21no—
564C22×D83—21no—
565C22×D83—21no—
566C22×D83—21no—
567C22×D83—21no—
568C22×D83—21no—
569C22×D83—21no—
570C22×D83—21no—
571C22×D83—21no—
572C22×D83—21no—
573C22×D83—21no—
574C22×D83—21no—
575C22×D83—21no—
576C22×D83—21no—
577C22×D83—21no—
578C22×D83—28no—
579C22×D83—44no—
580C22×D83—44no—
581C22×D83—82no—
582C22×D83—82no—
583C22×D83—82no—
584C22×D83—82no—
585C22×D83C23×C412yes—
586C22×D83C23×C412yes—
587C22×D83C23×C412yes—
588C2×C4×C83—28no—
589C2×C4×C83—21no—
590C2×C4×C83—21no—
591C2×C4×C83—21no—
592C2×C4×C83—21no—
593C2×C4×C83—21no—
594C2×C4×C83—21no—
595C2×C4×C83—21no—
596C2×C4×C83—21no—
597C2×C4×C83—21no—
598C2×C4×C83—21no—
599C2×C4×C83—21no—
600C2×C4×C83—21no—
601C2×C4×C83—21no—
602C2×C4×C83—21no—
603C2×C4×C83—21no—
604C2×C4×C83—21no—
605C2×C4×C83—21no—
606C2×C4×C83—21no—
607C2×C4×C83—21no—
608C2×C4×C83—21no—
609C2×C4×C83—21no—
610C2×C4×C83—21no—
611C2×C4×C83—21no—
612C2×C4×C83—21no—
613C2×C4×C83—21no—
614C2×C4×C83—21no—
615C2×C4×C83—21no—
616C2×C4×C83—21no—
617C2×C4×C83—21no—
618C2×C4×C83—21no—
619C2×C4×C83—21no—
620C2×C4×C83—21no—
621C2×C4×C83—21no—
622C2×C4×C83—21no—
623C2×C4×C83—21no—
624C2×C4×C83—21no—
625C2×C4×C83—82no—
626C2×C4×C83—82no—
627C2×C4×C83C23×C412yes—
628C2×C4×C83C23×C412yes—
629C2×C4×C83C23×C412yes—
630C2×C4×C83C23×C412yes—
631C2×C4×C83C23×C412yes—
632C2×C4×C83C23×C412yes—
633C22⋊D83—28no—
634C2×Dic83—21no—
635C2×Dic83—21no—
636C2×Dic83—21no—
637C2×Dic83—21no—
638C2×Dic83—21no—
639C2×Dic83—21no—
640C2×Dic83—21no—
641C2×Dic83—21no—
642C2×Dic83—21no—
643C2×Dic83—21no—
644C2×Dic83—21no—
645C2×Dic83—21no—
646C2×Dic83—21no—
647C2×Dic83—21no—
648C2×Dic83—21no—
649C2×Dic83—21no—
650C2×Dic83—21no—
651C2×Dic83—21no—
652C2×Dic83—21no—
653C2×Dic83—21no—
654C2×Dic83—21no—
655C2×Dic83—21no—
656C2×Dic83—21no—
657C2×Dic83—21no—
658C2×Dic83—21no—
659C2×Dic83—21no—
660C2×Dic83—21no—
661C2×Dic83—21no—
662C2×Dic83—21no—
663C2×Dic83—21no—
664C2×Dic83—21no—
665C2×Dic83—21no—
666C2×Dic83—21no—
667C2×Dic83—44no—
668C2×Dic83—44no—
669C2×Dic83—44no—
670C2×Dic83C23×C412yes—
671C2×Dic83C23×C412yes—
672C2×Dic83C23×C412yes—
673C2×Dic83C23×C412yes—
674C2×Dic83C23×C412yes—
675C2×Dic83H(5,𝔽2)12yes—
676D332—44no—
677D332—44no—
678C4×D83—44no—
679C4×D83—44no—
680C4×D83—44no—
681C4×D83—82no—
682C4×D83—82no—
683C4×D83—82no—
684C4×D83—82no—
685Dic166—44no—
686C22×C83—22no—
687C22×C83—22no—
688C22×C83—22no—
689C22×C83—22no—
690C22×C83—22no—
691C22×C83—22no—
692C22×C83#52014yes—
693C22×C83C24×C411yescharacteristic
694C22×C83C2×H(5,𝔽2)11yescharacteristic
695C22×C83C2×H(5,𝔽2)11yescharacteristic
696C22×C83C2×2−1+411yescharacteristic
697C22×C83#58511yescharacteristic
698C22×C83#58511yescharacteristic
699C22×C83#58511yescharacteristic
700C2×D83—22no—
701C2×D83—22no—
702C2×D83—22no—
703C2×D83—22no—
704C2×D83—22no—
705C2×D83—22no—
706C2×D83—22no—
707C2×D83—22no—
708C2×D83—22no—
709C2×D83—41no—
710C2×D83—41no—
711C2×D83—41no—
712C2×D83—41no—
713C2×D83—41no—
714C2×D83—41no—
715C2×D83—41no—
716C2×D83—41no—
717C2×D83—41no—
718C2×D83—41no—
719C2×D83—41no—
720C2×D83—41no—
721C2×D83—88no—
722C4×C83—22no—
723C4×C83—22no—
724C4×C83—22no—
725C4×C83—22no—
726C4×C83—22no—
727C4×C83—22no—
728C4×C83—41no—
729C4×C83—41no—
730C4×C83—41no—
731C4×C83—41no—
732C4×C83—41no—
733C4×C83—41no—
734C4×C83—41no—
735C4×C83—41no—
736Dic83—22no—
737Dic83—22no—
738Dic83—22no—
739Dic83—22no—
740Dic83—22no—
741Dic83—22no—
742Dic83—41no—
743Dic83—41no—
744Dic83—41no—
745Dic83—41no—
746Dic83—41no—
747Dic83—41no—
748Dic83—41no—
749#34458—831nomaximal, Sylow
750C2×C83—24no—
751C2×C83C2×#52011yescharacteristic
752C2×C83#342811yescharacteristic
753C2×C83C4×H(5,𝔽2)11yescharacteristic
754C2×C83#353311yescharacteristic
755C2×C83#353411yescharacteristic
756C2×C83#356111yescharacteristic
757C2×C83#356411yescharacteristic
758D83—42no—
759D83—42no—
760D83—42no—
761C2×#551—831no—
762#2383—831no—
763#2378—831no—
764#2376—831no—
765#2376—831no—
766#2373—831no—
767#2367—831no—
768#2360—831no—
769#2359—831no—
770#2358—831no—
771#2352—831no—
772D4×C4⋊C4—831no—
773#2347—831no—
774#2343D8311yescharacteristic, complemented
775#2342—831no—
776#2342—831no—
777#2337—831no—
778#2335—831no—
779#2334—831no—
780#2334—831no—
781#2329—831no—
782#2323—831no—
783#2322—831no—
784#2321—831no—
785#2319—831no—
786#2318—831no—
787#2315—831no—
788#2314—831no—
789C4×#123—831no—
790#2296—831no—
791C2×#388—831no—
792C83#3445811yescharacteristic, complemented, Sylow
793#551—8316no—
794C2×#126—831no—
795C2×#126—831no—
796C2×#124—831no—
797C2×#123—831no—
798C2×#123—831no—
799C2×#123—831no—
800C2×C22⋊Q8—831no—
801C2×C22⋊Q8—831no—
802C2×#120—831no—
803C2×C4×Q8—831no—
804C2×C4×D4—831no—
805C2×C4×D4—831no—
806C2×C4×D4—831no—
807C2×C4×D4—831no—
808C2×C4×D4—831no—
809C2×#117—831no—
810C2×#117—831no—
811C2×#117—831no—
812C2×#117C2×D8311yescharacteristic
813C22×C4⋊C4—831no—
814C22×C4⋊C4—831no—
815C22×C22⋊C4—831no—
816C22×C22⋊C4—831no—
817C22×C22⋊C4—831no—
818C22×C22⋊C4—831no—
819C22×C22⋊C4—831no—
820C22×C42—831no—
821#391—831no—
822#391—831no—
823#391—831no—
824#390—831no—
825#390—831no—
826#390—831no—
827#389—831no—
828#389—831no—
829#389—831no—
830#389—831no—
831#389—831no—
832#389—831no—
833#389—831no—
834#389—831no—
835#389—831no—
836#389—831no—
837#389—831no—
838#389—831no—
839#388—831no—
840#388—831no—
841#388—831no—
842#388—831no—
843#388—831no—
844#388—831no—
845#388—831no—
846#388—831no—
847#388—831no—
848#388—831no—
849#388—831no—
850#388—831no—
851#388—831no—
852#388—831no—
853#388—831no—
854#388—831no—
855#388—831no—
856#388—831no—
857#388—831no—
858#388—831no—
859#388—831no—
860#388—831no—
861#388—831no—
862#388—831no—
863#388—831no—
864#388—831no—
865#388—831no—
866#388—831no—
867#387—831no—
868#387—831no—
869#387—831no—
870#387—831no—
871#387—831no—
872#387—831no—
873#387—831no—
874#387—831no—
875#387—831no—
876#387—831no—
877#387—831no—
878#387—831no—
879#387C2×D8311yescharacteristic, complemented
880#387C2×D8311yescharacteristic, complemented
881#387C2×D8311yescharacteristic, complemented
882#387C2×D8311yescharacteristic, complemented
883#386—831no—
884#386—831no—
885#386—831no—
886#386—831no—
887#386—831no—
888#386—831no—
889#385—831no—
890#385—831no—
891#385—831no—
892#385—831no—
893#385—831no—
894#385—831no—
895#385—831no—
896#385—831no—
897#385—831no—
898#385—831no—
899#385—831no—
900#385—831no—
901#385—831no—
902#385—831no—
903#385—831no—
904#385—831no—
905#385C2×D8311yescharacteristic
906#385C2×D8311yescharacteristic
907#384—831no—
908#383—831no—
909#383C2×D8311yescharacteristic, complemented
910#382—831no—
911#382C2×D8311yescharacteristic, complemented
912#381—831no—
913#381—831no—
914#381C2×D8311yescharacteristic
915#380—831no—
916#380—831no—
917#380—831no—
918#380—831no—
919#380—831no—
920#380—831no—
921#380—831no—
922#380—831no—
923#379—831no—
924C4×C4⋊C4—831no—
925C4×C4⋊C4—831no—
926C4×C4⋊C4—831no—
927C4×C4⋊C4—831no—
928C4×C4⋊C4—831no—
929C4×C4⋊C4—831no—
930C4×C4⋊C4—831no—
931C4×C4⋊C4—831no—
932C4×C4⋊C4—831no—
933C4×C4⋊C4C2×D8311yescharacteristic, complemented
934C4×C22⋊C4—831no—
935C4×C22⋊C4—831no—
936C4×C22⋊C4—831no—
937C4×C22⋊C4—831no—
938C4×C22⋊C4—831no—
939C4×C22⋊C4—831no—
940C4×C22⋊C4—831no—
941C4×C22⋊C4—831no—
942C4×C22⋊C4—831no—
943C4×C22⋊C4—831no—
944C4×C22⋊C4C2×D8311yescharacteristic
945C4×C22⋊C4C2×D8311yescharacteristic
946#376C2×D8311yescharacteristic, complemented
947C2×#95—831no—
948C2×#95C2×D8311yescharacteristic
949C25—831no—
950C22×Q8—831no—
951C22×D4—831no—
952C22×D4—831no—
953C22×D4—831no—
954C23×C4—831no—
955C23×C4—831no—
956C23×C4—831no—
957C23×C4—831no—
958C23×C4—831no—
959C23×C4—831no—
960C23×C4—831no—
961C23×C4—831no—
962C23×C4—831no—
963C23×C4—831no—
964C23×C4C22×D8311yescharacteristic
965C23×C4C22×D8311yescharacteristic
966C23×C4C22×D8311yescharacteristic
967#126—838no—
968#126—838no—
969#124—838no—
970#123—838no—
971#123—838no—
972#123—838no—
973C22⋊Q8—838no—
974C22⋊Q8—838no—
975#120—838no—
976C4×Q8—3322no—
977C4×D4—3322no—
978C4×D4—3322no—
979C4×D4—3322no—
980C4×D4—838no—
981C4×D4—838no—
982#117—3322no—
983#117—3322no—
984#117—838no—
985#117C4×D8318yescomplemented
986C2×C4⋊C4—3322no—
987C2×C4⋊C4—3322no—
988C2×C4⋊C4—831no—
989C2×C4⋊C4—831no—
990C2×C4⋊C4—831no—
991C2×C4⋊C4—831no—
992C2×C4⋊C4—831no—
993C2×C4⋊C4—831no—
994C2×C4⋊C4—831no—
995C2×C4⋊C4—831no—
996C2×C4⋊C4—831no—
997C2×C4⋊C4—831no—
998C2×C4⋊C4—831no—
999C2×C4⋊C4—831no—
1000C2×C4⋊C4—831no—
1001C2×C4⋊C4—831no—
1002C2×C4⋊C4—831no—
1003C2×C4⋊C4—831no—
1004C2×C4⋊C4—831no—
1005C2×C4⋊C4—831no—
1006C2×C4⋊C4—831no—
1007C2×C4⋊C4—831no—
1008C2×C4⋊C4—831no—
1009C2×C4⋊C4—831no—
1010C2×C4⋊C4—831no—
1011C2×C4⋊C4—831no—
1012C2×C4⋊C4—831no—
1013C2×C4⋊C4—831no—
1014C2×C4⋊C4—831no—
1015C2×C4⋊C4—831no—
1016C2×C4⋊C4C22×D8311yescharacteristic
1017C2×C4⋊C4C22×D8311yescharacteristic
1018C2×C4⋊C4C22×D8311yescharacteristic
1019C2×C4⋊C4C22×D8311yescharacteristic
1020C2×C4⋊C4C22×D8311yescharacteristic
1021C2×C4⋊C4C22×D8311yescharacteristic
1022C2×C22⋊C4—3322no—
1023C2×C22⋊C4—3322no—
1024C2×C22⋊C4—3322no—
1025C2×C22⋊C4—831no—
1026C2×C22⋊C4—831no—
1027C2×C22⋊C4—831no—
1028C2×C22⋊C4—831no—
1029C2×C22⋊C4—831no—
1030C2×C22⋊C4—831no—
1031C2×C22⋊C4—831no—
1032C2×C22⋊C4—831no—
1033C2×C22⋊C4—831no—
1034C2×C22⋊C4—831no—
1035C2×C22⋊C4—831no—
1036C2×C22⋊C4—831no—
1037C2×C22⋊C4—831no—
1038C2×C22⋊C4—831no—
1039C2×C22⋊C4—831no—
1040C2×C22⋊C4—831no—
1041C2×C22⋊C4—831no—
1042C2×C22⋊C4—831no—
1043C2×C22⋊C4—831no—
1044C2×C22⋊C4—838no—
1045C2×C22⋊C4—831no—
1046C2×C22⋊C4—831no—
1047C2×C22⋊C4—831no—
1048C2×C22⋊C4—831no—
1049C2×C22⋊C4—831no—
1050C2×C22⋊C4—831no—
1051C2×C22⋊C4—831no—
1052C2×C22⋊C4—831no—
1053C2×C22⋊C4—831no—
1054C2×C22⋊C4—831no—
1055C2×C22⋊C4—831no—
1056C2×C22⋊C4—838no—
1057C2×C22⋊C4—831no—
1058C2×C22⋊C4—831no—
1059C2×C22⋊C4—831no—
1060C2×C22⋊C4—831no—
1061C2×C22⋊C4C22×D8311yescharacteristic
1062C2×C22⋊C4C22×D8311yescharacteristic
1063C2×C22⋊C4C22×D8311yescharacteristic
1064C2×C22⋊C4C22×D8311yescharacteristic
1065C2×C42—3322no—
1066C2×C42—831no—
1067C2×C42—831no—
1068C2×C42—831no—
1069C2×C42—831no—
1070C2×C42—831no—
1071C2×C42—831no—
1072C2×C42—831no—
1073C2×C42—831no—
1074C2×C42—831no—
1075C2×C42—831no—
1076C2×C42—831no—
1077C2×C42—831no—
1078C2×C42—831no—
1079C2×C42—831no—
1080C2×C42—831no—
1081C2×C42C22×D8311yescharacteristic
1082C2×C42C22×D8311yescharacteristic
1083C2×C42C22×D8311yescharacteristic
1084C2×C42C22×D8311yescharacteristic
1085C2×C42C22×D8311yescharacteristic
1086C2×C42C22×D8311yescharacteristic
1087#95—831no—
1088#95—831no—
1089#95—831no—
1090#95—831no—
1091#95—831no—
1092#95—831no—
1093#95—831no—
1094#95—831no—
1095#95—831no—
1096#95—831no—
1097#95—831no—
1098#95—831no—
1099#95—831no—
1100#95—831no—
1101#95—831no—
1102#95—831no—
1103#95—831no—
1104#95—831no—
1105#95—831no—
1106#95—831no—
1107#95—831no—
1108#95—831no—
1109#95—831no—
1110#95—831no—
1111#95—831no—
1112#95—831no—
1113#95—831no—
1114#95—831no—
1115#95C22×D8311yescharacteristic
1116#95C22×D8311yescharacteristic
1117#95C22×D8311yescharacteristic
1118#95C22×D8311yescharacteristic
1119#95C22×D8311yescharacteristic
1120#95C22×D8311yescharacteristic
1121#95C22×D8311yescharacteristic
1122#95C22×D8311yescharacteristic
1123#95C22×D8311yescharacteristic
1124#95C22×D8311yescharacteristic
1125#95C22×D8311yescharacteristic
1126#95C22×D8311yescharacteristic
1127#95C22×D8311yescharacteristic
1128#95C22×D8311yescharacteristic
1129#95C22×D8311yescharacteristic
1130#95C22×D8311yescharacteristic
1131C24—3321no—
1132C24—3321no—
1133C24—3321no—
1134C24—3321no—
1135C24—834no—
1136C24—831no—
1137C24—831no—
1138C24—831no—
1139C24—1662no—
1140C24—1662no—
1141C24C23×D8311yescharacteristic
1142C2×Q8—3321no—
1143C2×Q8—3321no—
1144C2×Q8—834no—
1145C2×D4—3321no—
1146C2×D4—3321no—
1147C2×D4—3321no—
1148C2×D4—3321no—
1149C2×D4—834no—
1150C2×D4—834no—
1151C2×D4—834no—
1152C2×D4—1662no—
1153C2×D4—1662no—
1154C22×C4—22no—
1155C22×C4—22no—
1156C22×C4—22no—
1157C22×C4—22no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—3321no—
1163C22×C4—3321no—
1164C22×C4—3321no—
1165C22×C4—3321no—
1166C22×C4—3321no—
1167C22×C4—3321no—
1168C22×C4—3321no—
1169C22×C4—3321no—
1170C22×C4—3321no—
1171C22×C4—3321no—
1172C22×C4—3321no—
1173C22×C4—3321no—
1174C22×C4—3321no—
1175C22×C4—3321no—
1176C22×C4—3321no—
1177C22×C4—3321no—
1178C22×C4—3321no—
1179C22×C4—3321no—
1180C22×C4—3321no—
1181C22×C4—3321no—
1182C22×C4—3321no—
1183C22×C4—3321no—
1184C22×C4—834no—
1185C22×C4—834no—
1186C22×C4—834no—
1187C22×C4—834no—
1188C22×C4—831no—
1189C22×C4—831no—
1190C22×C4—831no—
1191C22×C4—831no—
1192C22×C4—831no—
1193C22×C4—831no—
1194C22×C4—831no—
1195C22×C4—831no—
1196C22×C4—831no—
1197C22×C4—831no—
1198C22×C4—831no—
1199C22×C4—831no—
1200C22×C4—831no—
1201C22×C4—1662no—
1202C22×C4—1662no—
1203C22×C4—1662no—
1204C22×C4—1662no—
1205C22×C4C2×C4×D8314yes—
1206C22×C4C23×D8311yescharacteristic
1207C22×C4C23×D8311yescharacteristic
1208C22×C4C23×D8311yescharacteristic
1209C22×C4C23×D8311yescharacteristic
1210C22×C4C23×D8311yescharacteristic
1211C22×C4C23×D8311yescharacteristic
1212C22×C4C23×D8311yescharacteristic
1213C22×C4C23×D8311yescharacteristic
1214C22×C4C23×D8311yescharacteristic
1215C22×C4C23×D8311yescharacteristic
1216C22×C4C23×D8311yescharacteristic
1217C22×C4C23×D8311yescharacteristic
1218C22×C4C23×D8311yescharacteristic
1219C22×C4C23×D8311yescharacteristic
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—3321no—
1225C4⋊C4—3321no—
1226C4⋊C4—3321no—
1227C4⋊C4—3321no—
1228C4⋊C4—3321no—
1229C4⋊C4—3321no—
1230C4⋊C4—3321no—
1231C4⋊C4—3321no—
1232C4⋊C4—3321no—
1233C4⋊C4—3321no—
1234C4⋊C4—3321no—
1235C4⋊C4—3321no—
1236C4⋊C4—3321no—
1237C4⋊C4—3321no—
1238C4⋊C4—3321no—
1239C4⋊C4—3321no—
1240C4⋊C4—3321no—
1241C4⋊C4—3321no—
1242C4⋊C4—834no—
1243C4⋊C4—834no—
1244C4⋊C4—834no—
1245C4⋊C4—834no—
1246C4⋊C4—834no—
1247C4⋊C4—834no—
1248C4⋊C4—1662no—
1249C4⋊C4—1662no—
1250C4⋊C4—1662no—
1251C4⋊C4—1662no—
1252C4⋊C4C2×C4×D8314yes—
1253C4⋊C4C2×C4×D8314yes—
1254C22⋊C4—22no—
1255C22⋊C4—22no—
1256C22⋊C4—3321no—
1257C22⋊C4—3321no—
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—834no—
1275C22⋊C4—834no—
1276C22⋊C4—834no—
1277C22⋊C4—834no—
1278C22⋊C4—834no—
1279C22⋊C4—834no—
1280C22⋊C4—834no—
1281C22⋊C4—834no—
1282C22⋊C4—834no—
1283C22⋊C4—834no—
1284C22⋊C4—834no—
1285C22⋊C4—834no—
1286C22⋊C4—1662no—
1287C22⋊C4—1662no—
1288C22⋊C4—1662no—
1289C22⋊C4—1662no—
1290C22⋊C4C2×C4×D8314yes—
1291C22⋊C4C2×C4×D8314yes—
1292C42—41no—
1293C42—41no—
1294C42—41no—
1295C42—41no—
1296C42—3321no—
1297C42—3321no—
1298C42—3321no—
1299C42—3321no—
1300C42—3321no—
1301C42—3321no—
1302C42—3321no—
1303C42—3321no—
1304C42—3321no—
1305C42—3321no—
1306C42—3321no—
1307C42—3321no—
1308C42—3321no—
1309C42—834no—
1310C42—1662no—
1311C42C2×C4×D8314yes—
1312C42C2×C4×D8314yes—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—3324no—
1318C23—3324no—
1319C23—832no—
1320C23—832no—
1321C23—832no—
1322C23—6642no—
1323C23—6642no—
1324C23—6642no—
1325C23—6642no—
1326C23—1661no—
1327C23—1661no—
1328C23—1661no—
1329C23—1661no—
1330C23—1661no—
1331C23—1661no—
1332C23—1661no—
1333C23—1661no—
1334C23—1661no—
1335C23—1661no—
1336C23—1661no—
1337C23—1661no—
1338C23—1661no—
1339C23—1661no—
1340C23—1661no—
1341C23—1661no—
1342C23—1661no—
1343C23—1661no—
1344C23—1668no—
1345C23C22×C4×D8312yes—
1346C23#1458183812yes—
1347C23#1458183912yes—
1348C23C24×D8311yescharacteristic
1349Q8—3324no—
1350D4—3324no—
1351D4—3324no—
1352D4—1668no—
1353C2×C4—28no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—82no—
1391C2×C4—82no—
1392C2×C4—3324no—
1393C2×C4—3324no—
1394C2×C4—3324no—
1395C2×C4—3324no—
1396C2×C4—3324no—
1397C2×C4—3324no—
1398C2×C4—832no—
1399C2×C4—832no—
1400C2×C4—832no—
1401C2×C4—832no—
1402C2×C4—832no—
1403C2×C4—832no—
1404C2×C4—6642no—
1405C2×C4—6642no—
1406C2×C4—6642no—
1407C2×C4—6642no—
1408C2×C4—1661no—
1409C2×C4—1661no—
1410C2×C4—1661no—
1411C2×C4—1661no—
1412C2×C4—1661no—
1413C2×C4—1661no—
1414C2×C4—1661no—
1415C2×C4—1661no—
1416C2×C4—1661no—
1417C2×C4—1661no—
1418C2×C4—1661no—
1419C2×C4—1661no—
1420C2×C4—1661no—
1421C2×C4—1661no—
1422C2×C4—1661no—
1423C2×C4—1661no—
1424C2×C4—1661no—
1425C2×C4—1661no—
1426C2×C4—1661no—
1427C2×C4—1661no—
1428C2×C4—1661no—
1429C2×C4—1661no—
1430C2×C4—1661no—
1431C2×C4—1661no—
1432C2×C4—1661no—
1433C2×C4—1661no—
1434C2×C4—1661no—
1435C2×C4—1661no—
1436C2×C4—1661no—
1437C2×C4—1661no—
1438C2×C4—1661no—
1439C2×C4—1661no—
1440C2×C4—1661no—
1441C2×C4C22×C4×D8312yes—
1442C2×C4C22×C4×D8312yes—
1443C2×C4C22×C4×D8312yes—
1444C2×C4C22×C4×D8312yes—
1445C2×C4C22×C4×D8312yes—
1446C2×C4C22×C4×D8312yes—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—22no—
1451C22—22no—
1452C22—22no—
1453C22—3321no—
1454C22—3321no—
1455C22—3321no—
1456C22—3321no—
1457C22—3321no—
1458C22—3321no—
1459C22—3321no—
1460C22—3321no—
1461C22—3321no—
1462C22—3321no—
1463C22—3321no—
1464C22—3321no—
1465C22—6648no—
1466C22—1662no—
1467C22—1662no—
1468C22—1662no—
1469C22—1662no—
1470C22—1662no—
1471C22—1662no—
1472C22—1662no—
1473C22—1662no—
1474C22—1662no—
1475C22#1912818114yes—
1476C22C23×C4×D8311yescharacteristic
1477C22H(5,𝔽2)×D8311yescharacteristic
1478C22C2×#1458183811yescharacteristic
1479C22C2×#1458183911yescharacteristic
1480C22#1912853711yescharacteristic
1481C22#1912853711yescharacteristic
1482C22#1912853811yescharacteristic
1483C4—22no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—22no—
1488C4—22no—
1489C4—41no—
1490C4—41no—
1491C4—41no—
1492C4—41no—
1493C4—41no—
1494C4—41no—
1495C4—41no—
1496C4—41no—
1497C4—3321no—
1498C4—3321no—
1499C4—3321no—
1500C4—3321no—
1501C4—3321no—
1502C4—3321no—
1503C4—3321no—
1504C4—1662no—
1505C4—1662no—
1506C4—1662no—
1507C4—1662no—
1508C4—1662no—
1509C4—1662no—
1510C2—24no—
1511C2—3322no—
1512C2—3322no—
1513C2—3322no—
1514C2C2×#1912818111yescharacteristic
1515C2#2492066211yescharacteristic
1516C2#2492066911yescharacteristic
1517C2#2492162911yescharacteristic
1518C2#2492165611yescharacteristic
1519C2#2492202111yescharacteristic
1520C2#2492208311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2343C2
socle, cosocleC23×C83C25
prime radicalC2×#14581762C22
hypercenter#2343D83
hypocenterC83#34458
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2343

Complements

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

NH ≅ G/Ntype
2. #24910653C2semidirect
3. #24910628C2semidirect
4. #24910610C2semidirect
5. #24910610C2semidirect
6. #24910583C2semidirect
7. #24910532C2semidirect
8. #24910469C2semidirect
9. #24910451C2semidirect
11. #24910389C2semidirect
12. #24910361C2semidirect
13. #24910351C2semidirect
14. #24910310C2semidirect
15. #24910305C2semidirect
16. #24910273C2semidirect
17. #24910252C2semidirect
18. #24910241C2semidirect
19. #24910234C2semidirect
20. #24910191C2semidirect
21. #24910144C2semidirect
22. #24910136C2semidirect
24. #24910107C2semidirect
25. #24910091C2semidirect
26. #24910074C2semidirect
27. #24910068C2semidirect
28. #24909980C2semidirect
29. #24909947C2semidirect
30. C2×#19127590C2semidirect
31. C83×#2343C2semidirect
32. #19128375C4semidirect
42. C2×C4×Dic166C22semidirect
52. C2×C4⋊C4×D83C22semidirect
59. #19127607C22semidirect
60. #19127605C22semidirect
61. #19127605C22semidirect
65. #19127600C22semidirect
66. #19127600C22semidirect
67. #19127600C22semidirect
68. #19127600C22semidirect
69. #19127599C22semidirect
70. #19127599C22semidirect
71. #19127598C22semidirect
72. #19127598C22semidirect
73. #19127598C22semidirect
74. #19127598C22semidirect
75. #19127598C22semidirect
76. #19127596C22semidirect
84. #19127593C22semidirect
85. #19127593C22semidirect
91. #19127591C22semidirect
102. #19127590C22semidirect
103. #19127590C22semidirect
104. #19127590C22semidirect
105. #19127588C22semidirect
106. #19127588C22semidirect
107. #19127588C22semidirect
108. #19127585C22semidirect
109. #19127585C22semidirect
110. #19127585C22semidirect
111. #19127584C22semidirect
112. #19127584C22semidirect
113. #19127583C22semidirect
114. #19127583C22semidirect
115. #19127583C22semidirect
116. #19127582C22semidirect
132. #19127575C22semidirect
133. #19127575C22semidirect
138. #19127572C22semidirect
139. #19127570C22semidirect
140. #19127568C22semidirect
141. #19127566C22semidirect
143. #19127563C22semidirect
146. #19127560C22semidirect
151. #19127558C22semidirect
153. C4×Dic83⋊C4C22semidirect
154. C4×C4⋊Dic83C22semidirect
155. C4×C4⋊Dic83C22semidirect
156. C4×C4⋊Dic83C22semidirect
157. C4×C4⋊Dic83C22semidirect
158. #19127552C22semidirect
159. #19127552C22semidirect
160. #19127552C22semidirect
161. #19127552C22semidirect
169. #19127548C22semidirect
170. #19127548C22semidirect
171. #19127548C22semidirect
174. #387×C83C22semidirect
175. #387×C83C22semidirect
176. #387×C83C22semidirect
177. #387×C83C22semidirect
180. #383×C83C22semidirect
181. #382×C83C22semidirect
183. C4×C4⋊C4×C83C22semidirect
186. #376×C83C22semidirect
203. #14581787C2×C4semidirect
204. #14581786C2×C4semidirect
205. #14581780C2×C4semidirect
206. #14581777C2×C4semidirect
207. #14581777C2×C4semidirect
208. #14581775C2×C4semidirect
209. #14581770C2×C4semidirect
210. #14581769C2×C4semidirect
214. C4×D332C2×C4semidirect
217. (C22⋊D83)⋊C4C2×C4semidirect
220. #14581749C2×C4semidirect
256. C2×(C2×D83)⋊C4C2×C4semidirect
289. C22⋊C4×D83C2×C4semidirect
337. #117×C83C2×C4semidirect
774. #2343D83semidirect
792. C83#34458semidirect
879. #387C2×D83semidirect
880. #387C2×D83semidirect
881. #387C2×D83semidirect
882. #387C2×D83semidirect
909. #383C2×D83semidirect
911. #382C2×D83semidirect
933. C4×C4⋊C4C2×D83semidirect
946. #376C2×D83semidirect
985. #117C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283752
#249106532
#249106282
#249106102
#249105832
#249105322
#249104692
#249104512
#249104452
#249103892
#249103612
#249103512
#249103102
#249103052
#249102732
#249102522
#249102412
#249102342
#249101912
#249101442
#249101362
#249101232
#249101072
#249100912
#249100742
#249100682
#249099802
#249099472
C2×#191275902
C83×#23432
#3445883