Finite Group Databasebeta

← #35613213

Subgroups — #35613213

Order 21248.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915756C211yesmaximal, characteristic, complemented
2#24915746C211yesmaximal, characteristic, complemented
3#24915407C211yesmaximal, characteristic, complemented
4#24915321C211yesmaximal, characteristic, complemented
5#24915215C211yesmaximal, characteristic, complemented
6#24915159C211yesmaximal, characteristic, complemented
7#24915110C211yesmaximal, characteristic, complemented
8#24915088C211yesmaximal, characteristic, complemented
9#24914722C211yesmaximal, characteristic, complemented
10#24914699C211yesmaximal, characteristic, complemented
11#24914257C211yesmaximal, characteristic, complemented
12#24914203C211yesmaximal, characteristic, complemented
13#24914187C211yesmaximal, characteristic, complemented
14#24914186C211yesmaximal, characteristic, complemented
15#24913998C211yesmaximal, characteristic, complemented
16#24913869C211yesmaximal, characteristic, complemented
17#24913829C211yesmaximal, characteristic, complemented
18#24913421C211yesmaximal, characteristic, complemented
19#24913395C211yesmaximal, characteristic, complemented
20#24911727C211yesmaximal, characteristic, complemented
21#24911582C211yesmaximal, characteristic, complemented
22#24911203C211yesmaximal, characteristic, complemented
23#24911138C211yesmaximal, characteristic, complemented
24#24911074C211yesmaximal, characteristic, complemented
25#24911004C211yesmaximal, characteristic, complemented
26#24910847C211yesmaximal, characteristic, complemented
27#24910783C211yesmaximal, characteristic, complemented
28#24910136C211yesmaximal, characteristic, complemented
29#24910054C211yesmaximal, characteristic, complemented
30#385×D83C211yesmaximal, characteristic, complemented
31C83×#2745C211yesmaximal, characteristic, complemented
32C22×#13050591C2211yescharacteristic
33C23×C4×D83C2211yescharacteristic
34C2×#14581787C2211yescharacteristic, complemented
35C2×#14581778C2211yescharacteristic
36C2×#14581777C2211yescharacteristic
37C2×#14581777C2211yescharacteristic, complemented
38C2×#14581776C2211yescharacteristic
39C2×#14581775C2211yescharacteristic
40C2×#14581770C2211yescharacteristic
41C2×#14581767C2211yescharacteristic
42C2×#14581767C2211yescharacteristic
43C2×#14581767C2211yescharacteristic
44C2×#14581766C2211yescharacteristic
45C2×#14581765C2211yescharacteristic
46C2×#14581762C2211yescharacteristic
47C2×#14581762C2211yescharacteristic
48C2×#14581762C2211yescharacteristic
49C2×C4×D332C2211yescharacteristic
50C2×#14581749C2211yescharacteristic
51C2×C4⋊C4×D83C2211yescharacteristic
52C2×C4⋊C4×D83C2211yescharacteristic
53C2×C22⋊C4×D83C2211yescharacteristic
54C2×C22⋊C4×D83C2211yescharacteristic
55#19127643C2211yescharacteristic, complemented
56#19127643C2211yescharacteristic, complemented
57#19127643C2211yescharacteristic, complemented
58#19127643C2211yescharacteristic, complemented
59#19127642C2211yescharacteristic, complemented
60#19127639C2211yescharacteristic, complemented
61#19127638C2211yescharacteristic, complemented
62#19127634C2211yescharacteristic, complemented
63#19127632C2211yescharacteristic, complemented
64#19127631C2211yescharacteristic, complemented
65#19127630C2211yescharacteristic, complemented
66#19127630C2211yescharacteristic, complemented
67#19127630C2211yescharacteristic, complemented
68#19127628C2211yescharacteristic, complemented
69#19127628C2211yescharacteristic, complemented
70#19127628C2211yescharacteristic, complemented
71#19127628C2211yescharacteristic, complemented
72#19127625C2211yescharacteristic
73#19127625C2211yescharacteristic, complemented
74#19127624C2211yescharacteristic
75#19127623C2211yescharacteristic
76#19127623C2211yescharacteristic, complemented
77#19127622C2211yescharacteristic, complemented
78#19127619C2211yescharacteristic
79#19127619C2211yescharacteristic
80#19127619C2211yescharacteristic, complemented
81#19127619C2211yescharacteristic, complemented
82#19127618C2211yescharacteristic, complemented
83#19127618C2211yescharacteristic, complemented
84#19127617C2211yescharacteristic
85#19127617C2211yescharacteristic
86#19127616C2211yescharacteristic
87#19127616C2211yescharacteristic
88#19127614C2211yescharacteristic
89#19127614C2211yescharacteristic, complemented
90#19127614C2211yescharacteristic, complemented
91#19127612C2211yescharacteristic
92#19127612C2211yescharacteristic, complemented
93#19127611C2211yescharacteristic
94#19127611C2211yescharacteristic
95#19127611C2211yescharacteristic, complemented
96#19127610C2211yescharacteristic
97#19127608C2211yescharacteristic, complemented
98#19127607C2211yescharacteristic, complemented
99#19127603C2211yescharacteristic
100#19127603C2211yescharacteristic
101#19127603C2211yescharacteristic, complemented
102#19127602C2211yescharacteristic
103#19127602C2211yescharacteristic, complemented
104#19127601C2211yescharacteristic
105#19127600C2211yescharacteristic, complemented
106#19127598C2211yescharacteristic, complemented
107#19127598C2211yescharacteristic, complemented
108#19127595C2211yescharacteristic
109#19127593C2211yescharacteristic, complemented
110#19127593C2211yescharacteristic, complemented
111#19127592C2211yescharacteristic, complemented
112#19127591C2211yescharacteristic
113#19127590C2211yescharacteristic
114#19127590C2211yescharacteristic, complemented
115#19127588C2211yescharacteristic, complemented
116#19127588C2211yescharacteristic, complemented
117#19127585C2211yescharacteristic, complemented
118#19127584C2211yescharacteristic, complemented
119#19127579C2211yescharacteristic
120#19127579C2211yescharacteristic
121#19127579C2211yescharacteristic
122#19127579C2211yescharacteristic
123#19127579C2211yescharacteristic
124#19127579C2211yescharacteristic
125#19127579C2211yescharacteristic
126#19127579C2211yescharacteristic
127#19127579C2211yescharacteristic
128#19127579C2211yescharacteristic
129#19127579C2211yescharacteristic
130#19127579C2211yescharacteristic
131#19127579C2211yescharacteristic
132#19127579C2211yescharacteristic
133#19127579C2211yescharacteristic
134#19127579C2211yescharacteristic
135#19127579C2211yescharacteristic
136#19127579C2211yescharacteristic, complemented
137#19127579C2211yescharacteristic, complemented
138#19127578C2211yescharacteristic
139#19127578C2211yescharacteristic
140#19127577C2211yescharacteristic
141#19127577C2211yescharacteristic
142#19127576C2211yescharacteristic
143#19127575C2211yescharacteristic
144#19127575C2211yescharacteristic
145#19127575C2211yescharacteristic
146#19127575C2211yescharacteristic
147#19127575C2211yescharacteristic
148#19127575C2211yescharacteristic
149#19127575C2211yescharacteristic
150#19127575C2211yescharacteristic
151#19127575C2211yescharacteristic, complemented
152#19127575C2211yescharacteristic, complemented
153#19127574C2211yescharacteristic
154#19127573C2211yescharacteristic
155#19127572C2211yescharacteristic
156#19127572C2211yescharacteristic
157#19127572C2211yescharacteristic, complemented
158#19127572C2211yescharacteristic, complemented
159#19127572C2211yescharacteristic, complemented
160#19127563C2211yescharacteristic
161#19127562C2211yescharacteristic
162#19127560C2211yescharacteristic, complemented
163#19127560C2211yescharacteristic, complemented
164#19127560C2211yescharacteristic, complemented
165#19127560C2211yescharacteristic, complemented
166#19127558C2211yescharacteristic
167#19127558C2211yescharacteristic
168#19127556C2211yescharacteristic
169#19127548C2211yescharacteristic
170#95×D83C2211yescharacteristic
171#95×D83C2211yescharacteristic
172#401×C83C2211yescharacteristic, complemented
173#400×C83C2211yescharacteristic, complemented
174#400×C83C2211yescharacteristic, complemented
175#397×C83C2211yescharacteristic
176#395×C83C2211yescharacteristic, complemented
177#393×C83C2211yescharacteristic
178#391×C83C2211yescharacteristic, complemented
179#388×C83C2211yescharacteristic
180#388×C83C2211yescharacteristic
181#387×C83C2211yescharacteristic, complemented
182#387×C83C2211yescharacteristic, complemented
183#387×C83C2211yescharacteristic, complemented
184#385×C83C2211yescharacteristic
185#381×C83C2211yescharacteristic
186#380×C83C2211yescharacteristic
187C24×D83C2311yescharacteristic
188C2×#13050591—24no—
189C2×#13050591—42no—
190C2×#13050591—42no—
191C22×Dic166C2311yescharacteristic
192C22×D332C2311yescharacteristic
193C22×D332C2311yescharacteristic
194C22×D332C2311yescharacteristic
195C22×D332C2311yescharacteristic
196C22×D332C2311yescharacteristic
197C22×D332C2311yescharacteristic
198C22×D332C2311yescharacteristic
199C22×D332C2311yescharacteristic
200C22×D332C2311yescharacteristic
201C22×C22⋊D83C2311yescharacteristic
202C22×C22⋊D83C2311yescharacteristic
203C22×C22⋊D83C2311yescharacteristic
204C23×Dic83C2311yescharacteristic
205C22×C4×D83—42no—
206C22×C4×D83—42no—
207C22×C4×D83—42no—
208C22×C4×D83C2311yescharacteristic
209C22×C4×D83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212C22×C4×D83C2311yescharacteristic
213C22×C4×D83C2311yescharacteristic
214C22×C4×D83C2311yescharacteristic
215C22×C4×D83C2311yescharacteristic
216C22×C4×D83C2311yescharacteristic
217C22×C4×D83C2311yescharacteristic
218C22×C4×D83C2311yescharacteristic
219#14581787—42no—
220#14581778—42no—
221#14581777—24no—
222#14581777—42no—
223#14581776—42no—
224#14581775—42no—
225#14581770—42no—
226#14581767—42no—
227#14581767—42no—
228#14581767—42no—
229#14581766—42no—
230#14581765—42no—
231#14581762—42no—
232#14581762—42no—
233#14581762—42no—
234C4×D332—42no—
235#14581749—42no—
236C2×C4⋊Dic83C2311yescharacteristic
237C2×C4⋊Dic83C2311yescharacteristic
238C2×C4⋊Dic83C2311yescharacteristic
239C2×C4⋊Dic83C2311yescharacteristic
240C2×C4⋊Dic83C2311yescharacteristic
241C2×C4⋊Dic83C2311yescharacteristic
242C2×C4⋊Dic83C2311yescharacteristic
243C2×C4⋊Dic83C2311yescharacteristic
244C2×Dic83⋊C4C2311yescharacteristic
245C2×Dic83⋊C4C2311yescharacteristic
246C2×Dic83⋊C4C2311yescharacteristic
247C2×Dic83⋊C4C2311yescharacteristic
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
257C4⋊C4×D83—42no—
258C4⋊C4×D83—42no—
259C2×C22⋊Dic83C2311yescharacteristic
260C2×C22⋊Dic83C2311yescharacteristic
261C2×C22⋊Dic83C2311yescharacteristic
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
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
303C22⋊C4×D83—24no—
304C22⋊C4×D83—42no—
305C2×C4×Dic83C2311yescharacteristic
306C2×C4×Dic83C2311yescharacteristic
307C2×C4×Dic83C2311yescharacteristic
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
334C22×Q8×C83C2311yescharacteristic
335C23×C4×C83C2311yescharacteristic
336C2×C4⋊C4×C83C2311yescharacteristic
337C2×C4⋊C4×C83C2311yescharacteristic
338C2×C4⋊C4×C83C2311yescharacteristic
339C2×C4⋊C4×C83C2311yescharacteristic
340C2×C4⋊C4×C83C2311yescharacteristic
341C2×C4⋊C4×C83C2311yescharacteristic
342C2×C4⋊C4×C83C2311yescharacteristic
343C2×C22⋊C4×C83C2311yescharacteristic
344C2×C22⋊C4×C83C2311yescharacteristic
345C2×C22⋊C4×C83C2311yescharacteristic
346C2×C22⋊C4×C83C2311yescharacteristic
347C2×C22⋊C4×C83C2311yescharacteristic
348C2×C22⋊C4×C83C2311yescharacteristic
349C2×C42×C83C2311yescharacteristic
350C2×C42×C83C2311yescharacteristic
351#95×C83C2311yescharacteristic
352#95×C83C2311yescharacteristic
353#95×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
369C23×D83—22no—
370C23×D83—22no—
371C23×D83—22no—
372C23×D83—22no—
373C23×D83—22no—
374C23×D83—41no—
375C23×D83—41no—
376C23×D83C2411yescharacteristic
377C23×D83C2411yescharacteristic
378C23×D83C2411yescharacteristic
379C23×D83C2411yescharacteristic
380C23×D83C2411yescharacteristic
381#13050591—416no—
382C2×Dic166—41no—
383C2×Dic166—41no—
384C2×Dic166—41no—
385C2×D332—22no—
386C2×D332—22no—
387C2×D332—22no—
388C2×D332—22no—
389C2×D332—22no—
390C2×D332—22no—
391C2×D332—22no—
392C2×D332—22no—
393C2×D332—22no—
394C2×D332—22no—
395C2×D332—22no—
396C2×D332—22no—
397C2×D332—22no—
398C2×D332—22no—
399C2×D332—41no—
400C2×D332—41no—
401C2×D332—41no—
402C2×D332—41no—
403C2×D332—41no—
404C2×D332—41no—
405C2×D332—41no—
406C2×D332—41no—
407C2×D332—41no—
408C2×D332—41no—
409C2×D332—41no—
410C2×D332—41no—
411C2×D332—41no—
412C2×C22⋊D83—22no—
413C2×C22⋊D83—22no—
414C2×C22⋊D83—22no—
415C2×C22⋊D83—41no—
416C2×C22⋊D83—41no—
417C2×C22⋊D83—41no—
418C2×C22⋊D83—41no—
419C2×C22⋊D83—41no—
420C2×C22⋊D83—41no—
421C22×Dic83—22no—
422C22×Dic83—41no—
423C22×Dic83—41no—
424C22×Dic83C2411yescharacteristic
425C22×Dic83C2411yescharacteristic
426C22×Dic83C2411yescharacteristic
427C22×Dic83C2411yescharacteristic
428C22×Dic83C2411yescharacteristic
429C22×Dic83C2411yescharacteristic
430C22×Dic83C2411yescharacteristic
431C22×Dic83C2411yescharacteristic
432C22×Dic83C2411yescharacteristic
433C22×Dic83C2411yescharacteristic
434C22×Dic83C2411yescharacteristic
435C2×C4×D83—22no—
436C2×C4×D83—22no—
437C2×C4×D83—22no—
438C2×C4×D83—22no—
439C2×C4×D83—22no—
440C2×C4×D83—22no—
441C2×C4×D83—22no—
442C2×C4×D83—22no—
443C2×C4×D83—22no—
444C2×C4×D83—22no—
445C2×C4×D83—22no—
446C2×C4×D83—41no—
447C2×C4×D83—41no—
448C2×C4×D83—41no—
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—41no—
460C2×C4×D83—416no—
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#4114yes—
469C4⋊Dic83—41no—
470C4⋊Dic83—41no—
471C4⋊Dic83—41no—
472C4⋊Dic83—41no—
473C4⋊Dic83—41no—
474C4⋊Dic83—41no—
475C4⋊Dic83—41no—
476C4⋊Dic83—41no—
477Dic83⋊C4—22no—
478Dic83⋊C4—22no—
479Dic83⋊C4—22no—
480Dic83⋊C4—41no—
481Dic83⋊C4—41no—
482Dic83⋊C4—41no—
483Dic83⋊C4—41no—
484Dic83⋊C4—41no—
485Dic83⋊C4—41no—
486Dic83⋊C4—41no—
487Dic83⋊C4—41no—
488Dic83⋊C4—41no—
489Dic83⋊C4—41no—
490C22⋊Dic83—22no—
491C22⋊Dic83—22no—
492C22⋊Dic83—41no—
493(C2×D83)⋊C4—22no—
494(C2×D83)⋊C4—22no—
495(C2×D83)⋊C4—22no—
496(C2×D83)⋊C4—22no—
497(C2×D83)⋊C4—22no—
498(C2×D83)⋊C4—22no—
499(C2×D83)⋊C4—22no—
500(C2×D83)⋊C4—22no—
501(C2×D83)⋊C4—22no—
502(C2×D83)⋊C4—22no—
503(C2×D83)⋊C4—22no—
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)⋊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)⋊C4—41no—
529(C2×D83)⋊C4—41no—
530(C2×D83)⋊C4—41no—
531(C2×D83)⋊C4—41no—
532(C2×D83)⋊C4—41no—
533(C2×D83)⋊C4—41no—
534C4×Dic83—41no—
535C4×Dic83—41no—
536C4×Dic83—41no—
537C24×C83C2411yescharacteristic
538C2×Q8×C83—22no—
539C2×Q8×C83—41no—
540C2×Q8×C83—41no—
541C22×C4×C83—22no—
542C22×C4×C83—22no—
543C22×C4×C83—41no—
544C22×C4×C83C2411yescharacteristic
545C22×C4×C83C2411yescharacteristic
546C22×C4×C83C2411yescharacteristic
547C22×C4×C83C2411yescharacteristic
548C22×C4×C83C2411yescharacteristic
549C22×C4×C83C2411yescharacteristic
550C22×C4×C83C2411yescharacteristic
551C22×C4×C83C2411yescharacteristic
552C22×C4×C83C2411yescharacteristic
553C22×C4×C83C2411yescharacteristic
554C22×C4×C83C2411yescharacteristic
555C22×C4×C83C2411yescharacteristic
556C22×C4×C83C2411yescharacteristic
557C22×C4×C83C2411yescharacteristic
558C4⋊C4×C83—22no—
559C4⋊C4×C83—22no—
560C4⋊C4×C83—22no—
561C4⋊C4×C83—41no—
562C4⋊C4×C83—41no—
563C4⋊C4×C83—41no—
564C4⋊C4×C83—41no—
565C22⋊C4×C83—22no—
566C22⋊C4×C83—22no—
567C22⋊C4×C83—22no—
568C22⋊C4×C83—41no—
569C22⋊C4×C83—41no—
570C22⋊C4×C83—41no—
571C42×C83—41no—
572C42×C83—41no—
573C23×C83—21no—
574C23×C83—21no—
575C23×C83—21no—
576C23×C83—21no—
577C23×C83—21no—
578C23×C83—21no—
579C23×C83H(5,𝔽2)12yes—
580C23×C83C2511yescharacteristic
581C22×D83—21no—
582C22×D83—21no—
583C22×D83—21no—
584C22×D83—21no—
585C22×D83—28no—
586C22×D83—21no—
587C22×D83—21no—
588C22×D83—21no—
589C22×D83—21no—
590C22×D83—21no—
591C22×D83—21no—
592C22×D83—21no—
593C22×D83—21no—
594C22×D83—21no—
595C22×D83—21no—
596C22×D83—21no—
597C22×D83—21no—
598C22×D83—21no—
599C22×D83—21no—
600C22×D83—21no—
601C22×D83—21no—
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—44no—
614C22×D83—44no—
615C22×D83—44no—
616C22×D83—44no—
617C22×D83—44no—
618C22×D83—44no—
619C22×D83C2×#4112yes—
620C22×D83H(5,𝔽2)12yes—
621C22×D83H(5,𝔽2)12yes—
622C22×D832−1+412yes—
623Q8×C83—44no—
624C2×C4×C83—21no—
625C2×C4×C83—21no—
626C2×C4×C83—21no—
627C2×C4×C83—21no—
628C2×C4×C83—21no—
629C2×C4×C83—21no—
630C2×C4×C83—21no—
631C2×C4×C83—21no—
632C2×C4×C83—21no—
633C2×C4×C83—21no—
634C2×C4×C83—21no—
635C2×C4×C83—21no—
636C2×C4×C83—21no—
637C2×C4×C83—21no—
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—44no—
665C2×C4×C83C2×#4112yes—
666C2×C4×C83H(5,𝔽2)12yes—
667C22⋊D83—82no—
668C22⋊D83—82no—
669C22⋊D83—82no—
670C2×Dic83—21no—
671C2×Dic83—21no—
672C2×Dic83—21no—
673C2×Dic83—21no—
674C2×Dic83—21no—
675C2×Dic83—21no—
676C2×Dic83—21no—
677C2×Dic83—21no—
678C2×Dic83—21no—
679C2×Dic83—21no—
680C2×Dic83—21no—
681C2×Dic83—21no—
682C2×Dic83—21no—
683C2×Dic83—21no—
684C2×Dic83—21no—
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—44no—
703C2×Dic83C2×#4112yes—
704D332—44no—
705D332—44no—
706D332—44no—
707D332—44no—
708D332—82no—
709D332—82no—
710D332—82no—
711D332—82no—
712D332—82no—
713C4×D83—28no—
714C4×D83—44no—
715C4×D83—44no—
716C4×D83—44no—
717C4×D83—44no—
718C4×D83—44no—
719C4×D83—44no—
720C4×D83—44no—
721C4×D83—82no—
722C4×D83—82no—
723C4×D83—82no—
724Dic166—82no—
725C22×C83—22no—
726C22×C83—22no—
727C22×C83—22no—
728C22×C83—41no—
729C22×C83—41no—
730C22×C83—41no—
731C22×C83—41no—
732C22×C83C22×#4111yescharacteristic
733C22×C83C2×H(5,𝔽2)11yescharacteristic
734C22×C83C2×H(5,𝔽2)11yescharacteristic
735C22×C83C2×H(5,𝔽2)11yescharacteristic
736C22×C83C2×H(5,𝔽2)11yescharacteristic
737C22×C83C2×2−1+411yescharacteristic
738C22×C83#58511yescharacteristic
739C2×D83—22no—
740C2×D83—22no—
741C2×D83—22no—
742C2×D83—22no—
743C2×D83—22no—
744C2×D83—22no—
745C2×D83—22no—
746C2×D83—22no—
747C2×D83—22no—
748C2×D83—416no—
749C2×D83—41no—
750C2×D83—41no—
751C2×D83—41no—
752C2×D83—41no—
753C2×D83—41no—
754C2×D83—41no—
755C2×D83—41no—
756C2×D83—41no—
757C2×D83—41no—
758C2×D83—41no—
759C2×D83—41no—
760C2×D83—41no—
761C2×D83—41no—
762C2×D83—41no—
763C2×D83—41no—
764C2×D83—41no—
765C2×D83—41no—
766C2×D83—41no—
767C2×D83—41no—
768C2×D83—41no—
769C2×D83—41no—
770C2×D83—41no—
771C2×D83—41no—
772C2×D83—41no—
773C2×D83—41no—
774C2×D83#53814yes—
775C4×C83—22no—
776C4×C83—22no—
777C4×C83—41no—
778C4×C83—41no—
779C4×C83—41no—
780C4×C83—41no—
781C4×C83—41no—
782C4×C83—41no—
783C4×C83—41no—
784C4×C83—41no—
785C4×C83—41no—
786C4×C83—41no—
787C4×C83—41no—
788C4×C83—41no—
789Dic83—22no—
790Dic83—41no—
791Dic83—41no—
792Dic83—41no—
793Dic83—41no—
794Dic83—41no—
795Dic83—41no—
796Dic83—41no—
797Dic83—41no—
798Dic83—41no—
799Dic83—41no—
800#36791—831nomaximal, Sylow
801C2×C83—42no—
802C2×C83C2×#53811yescharacteristic
803C2×C83#349211yescharacteristic
804C2×C83#350611yescharacteristic
805C2×C83#353211yescharacteristic
806C2×C83#353411yescharacteristic
807C2×C83#353511yescharacteristic
808C2×C83#353611yescharacteristic
809D83—24no—
810D83—42no—
811D83—81no—
812D83—81no—
813D83—81no—
814#2849—831no—
815#2847—831no—
816#2804—831no—
817#2797—831no—
818#2788—831no—
819#2784—831no—
820#2780—831no—
821#2778—831no—
822#2751—831no—
823#2750—831no—
824#2745D8311yescharacteristic, complemented
825#2714—831no—
826#2710—831no—
827#2708—831no—
828#2708—831no—
829#2695—831no—
830#2686—831no—
831#2682—831no—
832#2643—831no—
833#2639—831no—
834#2481—831no—
835#2472—831no—
836#2443—831no—
837#2438—831no—
838#2430—831no—
839#2424—831no—
840#2411—831no—
841#2404—831no—
842#2322—831no—
843#2311—831no—
844C2×#385—831no—
845C83#3679111yescharacteristic, complemented, Sylow
846C22×#41—831no—
847C24×C4—831no—
848C2×#126—831no—
849C2×#124—831no—
850C2×#123—831no—
851C2×#123—831no—
852C2×#123—831no—
853C2×#123—831no—
854C2×C22⋊Q8—831no—
855C2×#121—831no—
856C2×#121—831no—
857C2×#121—831no—
858C2×#121—831no—
859C2×#121—831no—
860C2×#120—831no—
861C2×#120—831no—
862C2×#120—831no—
863C2×C4×D4—831no—
864C2×#117—831no—
865C22×C4⋊C4—831no—
866C22×C4⋊C4—831no—
867C22×C22⋊C4—831no—
868C22×C22⋊C4—831no—
869#401C2×D8311yescharacteristic, complemented
870#400—831no—
871#400—831no—
872#400—831no—
873#400—831no—
874#400—831no—
875#400—831no—
876#400C2×D8311yescharacteristic, complemented
877#400C2×D8311yescharacteristic, complemented
878#399—831no—
879#398—831no—
880#398—831no—
881#398—831no—
882#397—831no—
883#397—831no—
884#397—831no—
885#397—831no—
886#397—831no—
887#397—831no—
888#397—831no—
889#397C2×D8311yescharacteristic
890#396—831no—
891#396—831no—
892#396—831no—
893#396—831no—
894#396—831no—
895#395—831no—
896#395C2×D8311yescharacteristic, complemented
897#394—831no—
898#394—831no—
899#394—831no—
900#394—831no—
901#394—831no—
902#394—831no—
903#394—831no—
904#394—831no—
905#394—831no—
906#394—831no—
907#393—831no—
908#393—831no—
909#393—831no—
910#393—831no—
911#393—831no—
912#393C2×D8311yescharacteristic
913#392—831no—
914#392—831no—
915#392—831no—
916#392—831no—
917#391—831no—
918#391—831no—
919#391C2×D8311yescharacteristic, complemented
920#390—831no—
921#390—831no—
922#390—831no—
923#390—831no—
924#390—831no—
925#390—831no—
926#389—831no—
927#389—831no—
928#389—831no—
929#388—831no—
930#388—831no—
931#388—831no—
932#388—831no—
933#388—831no—
934#388—831no—
935#388—831no—
936#388C2×D8311yescharacteristic
937#388C2×D8311yescharacteristic
938#387—831no—
939#387—831no—
940#387—831no—
941#387—831no—
942#387C2×D8311yescharacteristic, complemented
943#387C2×D8311yescharacteristic, complemented
944#387C2×D8311yescharacteristic, complemented
945#386—831no—
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#385—831no—
969#385—831no—
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#385—831no—
982#385—831no—
983#385—831no—
984#385—831no—
985#385—831no—
986#385C2×D8311yescharacteristic
987#381—831no—
988#381—831no—
989#381C2×D8311yescharacteristic
990#380—831no—
991#380—831no—
992#380—831no—
993#380—831no—
994#380—831no—
995#380—831no—
996#380C2×D8311yescharacteristic
997#379—831no—
998C4×C22⋊C4—831no—
999C2×#95—831no—
1000C2×#95—831no—
1001C25—831no—
1002C2×#41—3322no—
1003C2×#41—3322no—
1004C2×#41—1664no—
1005C22×Q8—831no—
1006C22×Q8C22×D8311yescharacteristic
1007C22×D4—831no—
1008C22×D4—831no—
1009C22×D4—831no—
1010C22×D4—831no—
1011C22×D4—831no—
1012C22×D4—831no—
1013C22×D4—831no—
1014C22×D4—831no—
1015C22×D4—831no—
1016C22×D4—831no—
1017C22×D4—831no—
1018C22×D4—831no—
1019C23×C4—3322no—
1020C23×C4—3322no—
1021C23×C4—3322no—
1022C23×C4—831no—
1023C23×C4—831no—
1024C23×C4—831no—
1025C23×C4—831no—
1026C23×C4—831no—
1027C23×C4—831no—
1028C23×C4—831no—
1029C23×C4—831no—
1030C23×C4—831no—
1031C23×C4—831no—
1032C23×C4—831no—
1033C23×C4—831no—
1034C23×C4C22×D8311yescharacteristic
1035#126—3322no—
1036#124—3322no—
1037#123—3322no—
1038#123—3322no—
1039#123—3322no—
1040#123—1664no—
1041C22⋊Q8—3322no—
1042#121—3322no—
1043#121—3322no—
1044#121—3322no—
1045#121—3322no—
1046#121—3322no—
1047#120—3322no—
1048#120—3322no—
1049#120—3322no—
1050C4×D4—3322no—
1051#117—3322no—
1052C2×C4⋊C4—3322no—
1053C2×C4⋊C4—3322no—
1054C2×C4⋊C4—831no—
1055C2×C4⋊C4—831no—
1056C2×C4⋊C4—831no—
1057C2×C4⋊C4—831no—
1058C2×C4⋊C4—831no—
1059C2×C4⋊C4—831no—
1060C2×C4⋊C4—831no—
1061C2×C4⋊C4—831no—
1062C2×C4⋊C4—831no—
1063C2×C4⋊C4—831no—
1064C2×C4⋊C4—831no—
1065C2×C4⋊C4—831no—
1066C2×C4⋊C4—831no—
1067C2×C4⋊C4—831no—
1068C2×C4⋊C4—831no—
1069C2×C4⋊C4—831no—
1070C2×C4⋊C4—831no—
1071C2×C4⋊C4—831no—
1072C2×C4⋊C4—831no—
1073C2×C4⋊C4—831no—
1074C2×C4⋊C4—831no—
1075C2×C4⋊C4C22×D8311yescharacteristic
1076C2×C4⋊C4C22×D8311yescharacteristic
1077C2×C4⋊C4C22×D8311yescharacteristic
1078C2×C4⋊C4C22×D8311yescharacteristic
1079C2×C4⋊C4C22×D8311yescharacteristic
1080C2×C4⋊C4C22×D8311yescharacteristic
1081C2×C4⋊C4C22×D8311yescharacteristic
1082C2×C22⋊C4—3322no—
1083C2×C22⋊C4—831no—
1084C2×C22⋊C4—831no—
1085C2×C22⋊C4—831no—
1086C2×C22⋊C4—831no—
1087C2×C22⋊C4—831no—
1088C2×C22⋊C4—831no—
1089C2×C22⋊C4—831no—
1090C2×C22⋊C4—831no—
1091C2×C22⋊C4—831no—
1092C2×C22⋊C4—831no—
1093C2×C22⋊C4—831no—
1094C2×C22⋊C4—831no—
1095C2×C22⋊C4—831no—
1096C2×C22⋊C4—831no—
1097C2×C22⋊C4—831no—
1098C2×C22⋊C4—831no—
1099C2×C22⋊C4—831no—
1100C2×C22⋊C4—831no—
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—1664no—
1128C2×C22⋊C4C22×D8311yescharacteristic
1129C2×C22⋊C4C22×D8311yescharacteristic
1130C2×C22⋊C4C22×D8311yescharacteristic
1131C2×C22⋊C4C22×D8311yescharacteristic
1132C2×C22⋊C4C22×D8311yescharacteristic
1133C2×C22⋊C4C22×D8311yescharacteristic
1134C2×C42—831no—
1135C2×C42—831no—
1136C2×C42—831no—
1137C2×C42C22×D8311yescharacteristic
1138C2×C42C22×D8311yescharacteristic
1139#95—831no—
1140#95—831no—
1141#95—831no—
1142#95—831no—
1143#95—831no—
1144#95—831no—
1145#95—831no—
1146#95—831no—
1147#95—831no—
1148#95—831no—
1149#95—831no—
1150#95—831no—
1151#95—831no—
1152#95—831no—
1153#95—831no—
1154#95—831no—
1155#95—831no—
1156#95—831no—
1157#95—831no—
1158#95—831no—
1159#95—831no—
1160#95—831no—
1161#95—831no—
1162#95—831no—
1163#95—831no—
1164#95—831no—
1165#95C22×D8311yescharacteristic
1166#95C22×D8311yescharacteristic
1167#95C22×D8311yescharacteristic
1168#95C22×D8311yescharacteristic
1169#95C22×D8311yescharacteristic
1170#95C22×D8311yescharacteristic
1171#95C22×D8311yescharacteristic
1172#95C22×D8311yescharacteristic
1173#95C22×D8311yescharacteristic
1174#95C22×D8311yescharacteristic
1175#95C22×D8311yescharacteristic
1176#95C22×D8311yescharacteristic
1177#95C22×D8311yescharacteristic
1178#95C22×D8311yescharacteristic
1179#95C22×D8311yescharacteristic
1180#95C22×D8311yescharacteristic
1181#95C22×D8311yescharacteristic
1182#95C22×D8311yescharacteristic
1183C24—3321no—
1184C24—3321no—
1185C24—831no—
1186C24—831no—
1187C24—831no—
1188C24—831no—
1189C24—831no—
1190C24—1662no—
1191C24—1662no—
1192C24—1662no—
1193C24—1662no—
1194C24—1662no—
1195C24C23×D8311yescharacteristic
1196#41—33216no—
1197C2×Q8—22no—
1198C2×Q8—41no—
1199C2×Q8—41no—
1200C2×Q8—3321no—
1201C2×Q8—3321no—
1202C2×Q8—3321no—
1203C2×D4—3321no—
1204C2×D4—3321no—
1205C2×D4—3321no—
1206C2×D4—3321no—
1207C2×D4—3321no—
1208C2×D4—3321no—
1209C2×D4—3321no—
1210C2×D4—3321no—
1211C2×D4—3321no—
1212C2×D4—3321no—
1213C2×D4—3321no—
1214C2×D4—3321no—
1215C2×D4—3321no—
1216C2×D4—3321no—
1217C2×D4—3321no—
1218C2×D4—3321no—
1219C2×D4—3321no—
1220C2×D4—3321no—
1221C2×D4—3321no—
1222C2×D4—1662no—
1223C2×D4—1662no—
1224C2×D4—1662no—
1225C2×D4—1662no—
1226C2×D4—1662no—
1227C2×D4—1662no—
1228C2×D4—1662no—
1229C2×D4—1662no—
1230C2×D4—1662no—
1231C2×D4—1662no—
1232C2×D4—1662no—
1233C2×D4—1662no—
1234C2×D4—1662no—
1235C2×D4—1662no—
1236C2×D4—1662no—
1237C2×D4—1662no—
1238C2×D4—1662no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—41no—
1242C22×C4—3321no—
1243C22×C4—3321no—
1244C22×C4—3321no—
1245C22×C4—3321no—
1246C22×C4—3321no—
1247C22×C4—3321no—
1248C22×C4—3321no—
1249C22×C4—3321no—
1250C22×C4—3321no—
1251C22×C4—3321no—
1252C22×C4—3321no—
1253C22×C4—3321no—
1254C22×C4—3321no—
1255C22×C4—3321no—
1256C22×C4—3321no—
1257C22×C4—3321no—
1258C22×C4—3321no—
1259C22×C4—3321no—
1260C22×C4—3321no—
1261C22×C4—3321no—
1262C22×C4—3321no—
1263C22×C4—33216no—
1264C22×C4—3321no—
1265C22×C4—3321no—
1266C22×C4—831no—
1267C22×C4—834no—
1268C22×C4—831no—
1269C22×C4—831no—
1270C22×C4—831no—
1271C22×C4—831no—
1272C22×C4—831no—
1273C22×C4—831no—
1274C22×C4—831no—
1275C22×C4—831no—
1276C22×C4—831no—
1277C22×C4—831no—
1278C22×C4—1662no—
1279C22×C4—1662no—
1280C22×C4—1662no—
1281C22×C4—1662no—
1282C22×C4—1662no—
1283C22×C4—1662no—
1284C22×C4—1662no—
1285C22×C4—1662no—
1286C22×C4—1662no—
1287C22×C4—1662no—
1288C22×C4—1662no—
1289C22×C4—1662no—
1290C22×C4C23×D8311yescharacteristic
1291C22×C4C23×D8311yescharacteristic
1292C22×C4C23×D8311yescharacteristic
1293C22×C4C23×D8311yescharacteristic
1294C22×C4C23×D8311yescharacteristic
1295C22×C4C23×D8311yescharacteristic
1296C22×C4C23×D8311yescharacteristic
1297C22×C4C23×D8311yescharacteristic
1298C22×C4C23×D8311yescharacteristic
1299C22×C4C23×D8311yescharacteristic
1300C22×C4C23×D8311yescharacteristic
1301C22×C4C23×D8311yescharacteristic
1302C22×C4C23×D8311yescharacteristic
1303C22×C4C23×D8311yescharacteristic
1304C4⋊C4—22no—
1305C4⋊C4—22no—
1306C4⋊C4—22no—
1307C4⋊C4—41no—
1308C4⋊C4—41no—
1309C4⋊C4—41no—
1310C4⋊C4—41no—
1311C4⋊C4—3321no—
1312C4⋊C4—3321no—
1313C4⋊C4—3321no—
1314C4⋊C4—3321no—
1315C4⋊C4—3321no—
1316C4⋊C4—3321no—
1317C4⋊C4—3321no—
1318C4⋊C4—3321no—
1319C4⋊C4—3321no—
1320C4⋊C4—3321no—
1321C4⋊C4—3321no—
1322C4⋊C4—3321no—
1323C4⋊C4—3321no—
1324C4⋊C4—3321no—
1325C4⋊C4—3321no—
1326C4⋊C4—3321no—
1327C4⋊C4—3321no—
1328C4⋊C4—3321no—
1329C4⋊C4—1662no—
1330C4⋊C4—1662no—
1331C4⋊C4—1662no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—3321no—
1339C22⋊C4—3321no—
1340C22⋊C4—3321no—
1341C22⋊C4—3321no—
1342C22⋊C4—3321no—
1343C22⋊C4—3321no—
1344C22⋊C4—3321no—
1345C22⋊C4—3321no—
1346C22⋊C4—3321no—
1347C22⋊C4—3321no—
1348C22⋊C4—3321no—
1349C22⋊C4—3321no—
1350C22⋊C4—3321no—
1351C22⋊C4—3321no—
1352C22⋊C4—3321no—
1353C22⋊C4—3321no—
1354C22⋊C4—3321no—
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—1662no—
1370C22⋊C4—1662no—
1371C22⋊C4—1662no—
1372C22⋊C4—1662no—
1373C22⋊C4—1662no—
1374C22⋊C4—1662no—
1375C22⋊C4—1662no—
1376C22⋊C4—1662no—
1377C22⋊C4—1662no—
1378C22⋊C4—1662no—
1379C22⋊C4—1662no—
1380C22⋊C4—1662no—
1381C22⋊C4—1662no—
1382C42—41no—
1383C42—41no—
1384C42—3321no—
1385C42—3321no—
1386C42—3321no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—3324no—
1394C23—3324no—
1395C23—3324no—
1396C23—3324no—
1397C23—3324no—
1398C23—3324no—
1399C23—832no—
1400C23—832no—
1401C23—832no—
1402C23—832no—
1403C23—1668no—
1404C23—1661no—
1405C23—1661no—
1406C23—1661no—
1407C23—1661no—
1408C23—1661no—
1409C23—1661no—
1410C23—1661no—
1411C23—1661no—
1412C23—1661no—
1413C23—1661no—
1414C23—1661no—
1415C23—1661no—
1416C23—1661no—
1417C23—1661no—
1418C23—1661no—
1419C23—1661no—
1420C23—1661no—
1421C23—1661no—
1422C23—1661no—
1423C23—1661no—
1424C23—1661no—
1425C23—1661no—
1426C23—1661no—
1427C23—1661no—
1428C23—1661no—
1429C23—1661no—
1430C23—1661no—
1431C23—1661no—
1432C23—1661no—
1433C23—1661no—
1434C23—1661no—
1435C23#1458183812yes—
1436C23C24×D8311yescharacteristic
1437Q8—44no—
1438Q8—6642no—
1439D4—3324no—
1440D4—3324no—
1441D4—3324no—
1442D4—3324no—
1443D4—6642no—
1444D4—6642no—
1445D4—6642no—
1446D4—6642no—
1447D4—6642no—
1448D4—6642no—
1449D4—6642no—
1450D4—6642no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
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—44no—
1492C2×C4—3324no—
1493C2×C4—3324no—
1494C2×C4—3324no—
1495C2×C4—3324no—
1496C2×C4—3324no—
1497C2×C4—3324no—
1498C2×C4—3324no—
1499C2×C4—3324no—
1500C2×C4—832no—
1501C2×C4—6642no—
1502C2×C4—6642no—
1503C2×C4—6642no—
1504C2×C4—1668no—
1505C2×C4—1661no—
1506C2×C4—1661no—
1507C2×C4—1661no—
1508C2×C4—1661no—
1509C2×C4—1661no—
1510C2×C4—1661no—
1511C2×C4—1661no—
1512C2×C4—1661no—
1513C2×C4—1661no—
1514C2×C4—1661no—
1515C2×C4—1661no—
1516C2×C4—1661no—
1517C2×C4—1661no—
1518C2×C4—1661no—
1519C2×C4—1661no—
1520C2×C4—1661no—
1521C2×C4—1661no—
1522C2×C4—1661no—
1523C2×C4—1661no—
1524C2×C4—1661no—
1525C2×C4—1661no—
1526C2×C4—1661no—
1527C2×C4—1661no—
1528C2×C4—1661no—
1529C2×C4—1661no—
1530C2×C4—1661no—
1531C2×C4—1661no—
1532C2×C4—1661no—
1533C2×C4—1661no—
1534C2×C4—1661no—
1535C2×C4—1661no—
1536C2×C4—1661no—
1537C2×C4#41×D8312yes—
1538C2×C4#1458183812yes—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—33216no—
1547C22—3321no—
1548C22—3321no—
1549C22—3321no—
1550C22—3321no—
1551C22—3321no—
1552C22—3321no—
1553C22—3321no—
1554C22—3321no—
1555C22—3321no—
1556C22—3321no—
1557C22—3321no—
1558C22—3321no—
1559C22—3321no—
1560C22—3321no—
1561C22—3321no—
1562C22—3321no—
1563C22—3321no—
1564C22—3321no—
1565C22—3321no—
1566C22—3321no—
1567C22—3321no—
1568C22—3321no—
1569C22—3321no—
1570C22—3321no—
1571C22—3321no—
1572C22—834no—
1573C22—1662no—
1574C22—1662no—
1575C22—1662no—
1576C22—1662no—
1577C22—1662no—
1578C22—1662no—
1579C22—1662no—
1580C22—1662no—
1581C22—1662no—
1582C22C2×#41×D8311yescharacteristic
1583C22H(5,𝔽2)×D8311yescharacteristic
1584C22H(5,𝔽2)×D8311yescharacteristic
1585C22C2×#1458183811yescharacteristic
1586C22C2×#1458183811yescharacteristic
1587C222−1+4×D8311yescharacteristic
1588C22#1912853811yescharacteristic
1589C4—22no—
1590C4—22no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—3321no—
1604C4—3321no—
1605C4—3321no—
1606C4—3321no—
1607C4—3321no—
1608C4—3321no—
1609C4—3321no—
1610C4—3321no—
1611C4—3321no—
1612C4—3321no—
1613C4—1662no—
1614C2—42no—
1615C2—3322no—
1616C2—6641no—
1617C2—6641no—
1618C2—6641no—
1619C2—1664no—
1620C2#538×D8311yescharacteristic
1621C2#2492116311yescharacteristic
1622C2#2492131611yescharacteristic
1623C2#2492161911yescharacteristic
1624C2#2492165111yescharacteristic
1625C2#2492167411yescharacteristic
1626C2#2492168811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2745C2
hypercenter#2745D83
hypocenterC83#36791
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2745

Complements

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

NH ≅ G/Ntype
1. #24915756C2semidirect
2. #24915746C2semidirect
3. #24915407C2semidirect
4. #24915321C2semidirect
5. #24915215C2semidirect
6. #24915159C2semidirect
7. #24915110C2semidirect
8. #24915088C2semidirect
9. #24914722C2semidirect
10. #24914699C2semidirect
11. #24914257C2semidirect
12. #24914203C2semidirect
13. #24914187C2semidirect
14. #24914186C2semidirect
15. #24913998C2semidirect
16. #24913869C2semidirect
17. #24913829C2semidirect
18. #24913421C2semidirect
19. #24913395C2semidirect
20. #24911727C2semidirect
21. #24911582C2semidirect
22. #24911203C2semidirect
23. #24911138C2semidirect
24. #24911074C2semidirect
25. #24911004C2semidirect
26. #24910847C2semidirect
27. #24910783C2semidirect
28. #24910136C2semidirect
29. #24910054C2semidirect
30. #385×D83C2semidirect
31. C83×#2745C2semidirect
34. C2×#14581787C22semidirect
37. C2×#14581777C22semidirect
55. #19127643C22semidirect
56. #19127643C22semidirect
57. #19127643C22semidirect
58. #19127643C22semidirect
59. #19127642C22semidirect
60. #19127639C22semidirect
61. #19127638C22semidirect
62. #19127634C22semidirect
63. #19127632C22semidirect
64. #19127631C22semidirect
65. #19127630C22semidirect
66. #19127630C22semidirect
67. #19127630C22semidirect
68. #19127628C22semidirect
69. #19127628C22semidirect
70. #19127628C22semidirect
71. #19127628C22semidirect
73. #19127625C22semidirect
76. #19127623C22semidirect
77. #19127622C22semidirect
80. #19127619C22semidirect
81. #19127619C22semidirect
82. #19127618C22semidirect
83. #19127618C22semidirect
89. #19127614C22semidirect
90. #19127614C22semidirect
92. #19127612C22semidirect
95. #19127611C22semidirect
97. #19127608C22semidirect
98. #19127607C22semidirect
101. #19127603C22semidirect
103. #19127602C22semidirect
105. #19127600C22semidirect
106. #19127598C22semidirect
107. #19127598C22semidirect
109. #19127593C22semidirect
110. #19127593C22semidirect
111. #19127592C22semidirect
114. #19127590C22semidirect
115. #19127588C22semidirect
116. #19127588C22semidirect
117. #19127585C22semidirect
118. #19127584C22semidirect
136. #19127579C22semidirect
137. #19127579C22semidirect
151. #19127575C22semidirect
152. #19127575C22semidirect
157. #19127572C22semidirect
158. #19127572C22semidirect
159. #19127572C22semidirect
162. #19127560C22semidirect
163. #19127560C22semidirect
164. #19127560C22semidirect
165. #19127560C22semidirect
172. #401×C83C22semidirect
173. #400×C83C22semidirect
174. #400×C83C22semidirect
176. #395×C83C22semidirect
178. #391×C83C22semidirect
181. #387×C83C22semidirect
182. #387×C83C22semidirect
183. #387×C83C22semidirect
824. #2745D83semidirect
845. C83#36791semidirect
869. #401C2×D83semidirect
876. #400C2×D83semidirect
877. #400C2×D83semidirect
896. #395C2×D83semidirect
919. #391C2×D83semidirect
942. #387C2×D83semidirect
943. #387C2×D83semidirect
944. #387C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249157562
#249157462
#249154072
#249153212
#249152152
#249151592
#249151102
#249150882
#249147222
#249146992
#249142572
#249142032
#249141872
#249141862
#249139982
#249138692
#249138292
#249134212
#249133952
#249117272
#249115822
#249112032
#249111382
#249110742
#249110042
#249108472
#249107832
#249101362
#249100542
#385×D832
C83×#27452
#3679183