Finite Group Databasebeta

← #35566541

Subgroups — #35566541

Order 21248.

2396 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
1#24910599C211yesmaximal, characteristic, complemented
2#24910599C211yesmaximal, characteristic, complemented
3#24910587C211yesmaximal, characteristic, complemented
4#24910587C211yesmaximal, characteristic, complemented
5#24910548C211yesmaximal, characteristic, complemented
6#24910538C211yesmaximal, characteristic, complemented
7#24910494C211yesmaximal, characteristic, complemented
8#24910459C211yesmaximal, characteristic, complemented
9#24910447C211yesmaximal, characteristic
10#24910436C211yesmaximal, characteristic, complemented
11#24910403C211yesmaximal, characteristic, complemented
12#24910356C211yesmaximal, characteristic, complemented
13#24910323C211yesmaximal, characteristic, complemented
14#24910312C211yesmaximal, characteristic, complemented
15#24910312C211yesmaximal, characteristic, complemented
16#24910278C211yesmaximal, characteristic, complemented
17#24910257C211yesmaximal, characteristic, complemented
18#24910242C211yesmaximal, characteristic, complemented
19#24910221C211yesmaximal, characteristic, complemented
20#24910135C211yesmaximal, characteristic, complemented
21#24910124C211yesmaximal, characteristic
22#126×Dic83C211yesmaximal, characteristic, complemented
23C22⋊Q8×Dic83C211yesmaximal, characteristic, complemented
24#123×Dic83C211yesmaximal, characteristic, complemented
25#24909961C211yesmaximal, characteristic, complemented
26#24909908C211yesmaximal, characteristic, complemented
27C2×#19127594C211yesmaximal, characteristic, complemented
28#24909819C211yesmaximal, characteristic, complemented
29#24909816C211yesmaximal, characteristic, complemented
30C4×D4×Dic83C211yesmaximal, characteristic, complemented
31C2×#551×C83C211yesmaximal, characteristic
32C2×Q8×Dic83C2211yescharacteristic, complemented
33C2×D4×Dic83C2211yescharacteristic
34C2×D4×Dic83C2211yescharacteristic
35C2×D4×Dic83C2211yescharacteristic
36C2×#14581751C2211yescharacteristic
37C2×#14581751C2211yescharacteristic
38C22×C4⋊Dic83C2211yescharacteristic
39C22×C22⋊Dic83C2211yescharacteristic
40C22×C22⋊Dic83C2211yescharacteristic
41C22×C22⋊Dic83C2211yescharacteristic
42C22×C4×Dic83C2211yescharacteristic
43C22×C4×Dic83C2211yescharacteristic, complemented
44#19127608C2211yescharacteristic, complemented
45#19127608C2211yescharacteristic, complemented
46#19127608C2211yescharacteristic, complemented
47#19127604C2211yescharacteristic
48#19127604C2211yescharacteristic
49#19127604C2211yescharacteristic
50#19127600C2211yescharacteristic, complemented
51#19127600C2211yescharacteristic, complemented
52#19127600C2211yescharacteristic, complemented
53#19127600C2211yescharacteristic, complemented
54#19127594C2211yescharacteristic
55#19127594C2211yescharacteristic
56#19127594C2211yescharacteristic
57#19127594C2211yescharacteristic
58#19127594C2211yescharacteristic
59#19127594C2211yescharacteristic
60#19127594C2211yescharacteristic
61#19127594C2211yescharacteristic
62#19127594C2211yescharacteristic
63#19127594C2211yescharacteristic
64#19127594C2211yescharacteristic
65#19127594C2211yescharacteristic
66#19127594C2211yescharacteristic
67#19127594C2211yescharacteristic
68#19127594C2211yescharacteristic
69#19127594C2211yescharacteristic
70#19127594C2211yescharacteristic
71#19127594C2211yescharacteristic
72#19127594C2211yescharacteristic
73#19127594C2211yescharacteristic
74#19127594C2211yescharacteristic
75#19127594C2211yescharacteristic
76#19127594C2211yescharacteristic, complemented
77#19127594C2211yescharacteristic, complemented
78#19127594C2211yescharacteristic, complemented
79#19127594C2211yescharacteristic, complemented
80#19127594C2211yescharacteristic, complemented
81#19127594C2211yescharacteristic, complemented
82#19127587C2211yescharacteristic, complemented
83#19127587C2211yescharacteristic, complemented
84#19127587C2211yescharacteristic, complemented
85#19127587C2211yescharacteristic, complemented
86#19127587C2211yescharacteristic, complemented
87#19127587C2211yescharacteristic, complemented
88#19127587C2211yescharacteristic, complemented
89#19127587C2211yescharacteristic, complemented
90#19127587C2211yescharacteristic, complemented
91#19127587C2211yescharacteristic, complemented
92#19127587C2211yescharacteristic, complemented
93#19127587C2211yescharacteristic, complemented
94#19127587C2211yescharacteristic, complemented
95#19127587C2211yescharacteristic, complemented
96#19127587C2211yescharacteristic, complemented
97#19127587C2211yescharacteristic, complemented
98#19127581C2211yescharacteristic
99#19127581C2211yescharacteristic
100#19127581C2211yescharacteristic
101#19127581C2211yescharacteristic
102#19127581C2211yescharacteristic
103#19127581C2211yescharacteristic
104#19127576C2211yescharacteristic
105#19127576C2211yescharacteristic
106#19127576C2211yescharacteristic
107#19127576C2211yescharacteristic
108#19127576C2211yescharacteristic
109#19127576C2211yescharacteristic
110#19127576C2211yescharacteristic
111#19127576C2211yescharacteristic, complemented
112#19127576C2211yescharacteristic, complemented
113#19127576C2211yescharacteristic, complemented
114#19127569C2211yescharacteristic, complemented
115#19127569C2211yescharacteristic, complemented
116#19127567C2211yescharacteristic, complemented
117#19127564C2211yescharacteristic
118#19127564C2211yescharacteristic
119#19127564C2211yescharacteristic, complemented
120#19127561C2211yescharacteristic
121#19127561C2211yescharacteristic
122#19127557C2211yescharacteristic
123C4⋊C4×Dic83C2211yescharacteristic, complemented
124C4⋊C4×Dic83C2211yescharacteristic, complemented
125C4⋊C4×Dic83C2211yescharacteristic, complemented
126C4⋊C4×Dic83C2211yescharacteristic, complemented
127C4⋊C4×Dic83C2211yescharacteristic, complemented
128C4⋊C4×Dic83C2211yescharacteristic, complemented
129C4⋊C4×Dic83C2211yescharacteristic, complemented
130C4⋊C4×Dic83C2211yescharacteristic, complemented
131C4⋊C4×Dic83C2211yescharacteristic, complemented
132C4⋊C4×Dic83C2211yescharacteristic, complemented
133C4⋊C4×Dic83C2211yescharacteristic, complemented
134C4⋊C4×Dic83C2211yescharacteristic, complemented
135C4×C4⋊Dic83C2211yescharacteristic, complemented
136C4×C4⋊Dic83C2211yescharacteristic, complemented
137C4×C4⋊Dic83C2211yescharacteristic, complemented
138C4×C4⋊Dic83C2211yescharacteristic, complemented
139C4×C4⋊Dic83C2211yescharacteristic, complemented
140C4×C4⋊Dic83C2211yescharacteristic, complemented
141C22⋊C4×Dic83C2211yescharacteristic
142C22⋊C4×Dic83C2211yescharacteristic
143C22⋊C4×Dic83C2211yescharacteristic
144C22⋊C4×Dic83C2211yescharacteristic
145C22⋊C4×Dic83C2211yescharacteristic
146C22⋊C4×Dic83C2211yescharacteristic
147C22⋊C4×Dic83C2211yescharacteristic
148C22⋊C4×Dic83C2211yescharacteristic
149C22⋊C4×Dic83C2211yescharacteristic
150C22⋊C4×Dic83C2211yescharacteristic
151C22⋊C4×Dic83C2211yescharacteristic
152C22⋊C4×Dic83C2211yescharacteristic
153C22⋊C4×Dic83C2211yescharacteristic
154C22⋊C4×Dic83C2211yescharacteristic
155C22⋊C4×Dic83C2211yescharacteristic
156C22⋊C4×Dic83C2211yescharacteristic, complemented
157C22⋊C4×Dic83C2211yescharacteristic, complemented
158C22⋊C4×Dic83C2211yescharacteristic, complemented
159C4×C22⋊Dic83C2211yescharacteristic
160C4×C22⋊Dic83C2211yescharacteristic
161C4×C22⋊Dic83C2211yescharacteristic
162C4×C22⋊Dic83C2211yescharacteristic
163C4×C22⋊Dic83C2211yescharacteristic
164C4×C22⋊Dic83C2211yescharacteristic
165C4×C22⋊Dic83C2211yescharacteristic, complemented
166C4×C22⋊Dic83C2211yescharacteristic, complemented
167#19127547C2211yescharacteristic, complemented
168#19127547C2211yescharacteristic, complemented
169C2×C83⋊#95C2211yescharacteristic
170C2×C83⋊#95C2211yescharacteristic
171C42×Dic83C2211yescharacteristic, complemented
172#551×C83C4116yescomplemented
173C2×#126×C83C2211yescharacteristic
174C2×#126×C83C2211yescharacteristic
175C2×#124×C83C2211yescharacteristic
176C2×#123×C83C2211yescharacteristic
177C2×#123×C83C2211yescharacteristic
178C2×#123×C83C2211yescharacteristic
179C2×C22⋊Q8×C83C2211yescharacteristic
180C2×C22⋊Q8×C83C2211yescharacteristic
181C2×#120×C83C2211yescharacteristic
182C2×C4×D4×C83C2211yescharacteristic
183C2×C4×D4×C83C2211yescharacteristic
184C2×#117×C83C2211yescharacteristic
185C2×#117×C83C2211yescharacteristic
186C22×C22⋊C4×C83C2211yescharacteristic
187C22×C22⋊C4×C83C2211yescharacteristic
188C23×Dic83C2311yescharacteristic
189C23×Dic83C2311yescharacteristic
190C23×Dic83C2311yescharacteristic
191C23×Dic83C2311yescharacteristic
192C23×Dic83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C23×Dic83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196Q8×Dic83—42no—
197D4×Dic83—24no—
198D4×Dic83—24no—
199D4×Dic83—42no—
200#14581751—24no—
201#14581751—42no—
202C2×C4⋊Dic83—24no—
203C2×C4⋊Dic83C2311yescharacteristic
204C2×C4⋊Dic83C2311yescharacteristic
205C2×C4⋊Dic83C2311yescharacteristic
206C2×C4⋊Dic83C2311yescharacteristic
207C2×C4⋊Dic83C2311yescharacteristic
208C2×C4⋊Dic83C2311yescharacteristic
209C2×C4⋊Dic83C2311yescharacteristic
210C2×C4⋊Dic83C2311yescharacteristic
211C2×C4⋊Dic83C2311yescharacteristic
212C2×C4⋊Dic83C2311yescharacteristic
213C2×C4⋊Dic83C2311yescharacteristic
214C2×C4⋊Dic83C2311yescharacteristic
215C2×C4⋊Dic83C2311yescharacteristic
216C2×C4⋊Dic83C2311yescharacteristic
217C2×C4⋊Dic83C2311yescharacteristic
218C2×C4⋊Dic83C2311yescharacteristic
219C2×C4⋊Dic83C2311yescharacteristic
220C2×C4⋊Dic83C2311yescharacteristic
221C2×C22⋊Dic83—24no—
222C2×C22⋊Dic83—24no—
223C2×C22⋊Dic83—42no—
224C2×C22⋊Dic83C2311yescharacteristic
225C2×C22⋊Dic83C2311yescharacteristic
226C2×C22⋊Dic83C2311yescharacteristic
227C2×C22⋊Dic83C2311yescharacteristic
228C2×C22⋊Dic83C2311yescharacteristic
229C2×C22⋊Dic83C2311yescharacteristic
230C2×C22⋊Dic83C2311yescharacteristic
231C2×C22⋊Dic83C2311yescharacteristic
232C2×C22⋊Dic83C2311yescharacteristic
233C2×C22⋊Dic83C2311yescharacteristic
234C2×C22⋊Dic83C2311yescharacteristic
235C2×C22⋊Dic83C2311yescharacteristic
236C2×C22⋊Dic83C2311yescharacteristic
237C2×C22⋊Dic83C2311yescharacteristic
238C2×C22⋊Dic83C2311yescharacteristic
239C2×C22⋊Dic83C2311yescharacteristic
240C2×C22⋊Dic83C2311yescharacteristic
241C2×C22⋊Dic83C2311yescharacteristic
242C2×C22⋊Dic83C2311yescharacteristic
243C2×C22⋊Dic83C2311yescharacteristic
244C2×C22⋊Dic83C2311yescharacteristic
245C2×C22⋊Dic83C2311yescharacteristic
246C2×C22⋊Dic83C2311yescharacteristic
247C2×C22⋊Dic83C2311yescharacteristic
248C2×C4×Dic83—42no—
249C2×C4×Dic83—42no—
250C2×C4×Dic83C2311yescharacteristic
251C2×C4×Dic83C2311yescharacteristic
252C2×C4×Dic83C2311yescharacteristic
253C2×C4×Dic83C2311yescharacteristic
254C2×C4×Dic83C2311yescharacteristic
255C2×C4×Dic83C2311yescharacteristic
256C2×C4×Dic83C2311yescharacteristic
257C2×C4×Dic83C2311yescharacteristic
258C2×C4×Dic83C2311yescharacteristic
259C2×C4×Dic83C2311yescharacteristic
260C2×C4×Dic83C2311yescharacteristic
261C2×C4×Dic83C2311yescharacteristic
262C2×C4×Dic83C2311yescharacteristic
263C2×C4×Dic83C2311yescharacteristic
264C2×C4×Dic83C2311yescharacteristic
265C2×C4×Dic83C2311yescharacteristic
266C2×C4×Dic83C2311yescharacteristic
267C2×C4×Dic83C2311yescharacteristic
268C2×C4×Dic83C2311yescharacteristic
269C2×C4×Dic83C2311yescharacteristic
270C2×C4×Dic83C2311yescharacteristic
271C2×C4×Dic83C2311yescharacteristic
272C2×C4×Dic83C2311yescharacteristic
273C2×C4×Dic83C2311yescharacteristic
274C2×C4×Dic83C2311yescharacteristic
275C2×C4×Dic83C2311yescharacteristic
276C83⋊#95C2311yescharacteristic
277C83⋊#95C2311yescharacteristic
278C83⋊#95C2311yescharacteristic
279C83⋊#95C2311yescharacteristic
280C83⋊#95C2311yescharacteristic
281C83⋊#95C2311yescharacteristic
282C83⋊#95C2311yescharacteristic
283C83⋊#95C2311yescharacteristic
284C83⋊#95C2311yescharacteristic
285C83⋊#95C2311yescharacteristic
286C83⋊#95C2311yescharacteristic
287C83⋊#95C2311yescharacteristic
288C83⋊#95C2311yescharacteristic
289C83⋊#95C2311yescharacteristic
290C83⋊#95C2311yescharacteristic
291C83⋊#95C2311yescharacteristic
292C83⋊#95C2311yescharacteristic
293C83⋊#95C2311yescharacteristic
294C83⋊#95C2311yescharacteristic
295C83⋊#95C2311yescharacteristic
296C83⋊#95C2311yescharacteristic
297C83⋊#95C2311yescharacteristic
298C83⋊#95C2311yescharacteristic
299C83⋊#95C2311yescharacteristic
300C83⋊#95C2311yescharacteristic
301C83⋊#95C2311yescharacteristic
302C83⋊#95C2311yescharacteristic
303C83⋊#95C2311yescharacteristic
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
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
320C25×C83C2311yescharacteristic
321C22×Q8×C83C2311yescharacteristic
322C22×D4×C83C2311yescharacteristic
323C22×D4×C83C2311yescharacteristic
324C22×D4×C83C2311yescharacteristic
325C23×C4×C83C2311yescharacteristic
326C23×C4×C83C2311yescharacteristic
327C23×C4×C83C2311yescharacteristic
328C23×C4×C83C2311yescharacteristic
329C23×C4×C83C2311yescharacteristic
330#126×C83C2×C418yescomplemented
331#126×C83C2×C418yescomplemented
332#124×C83C2×C418yescomplemented
333#123×C83C2×C418yescomplemented
334#123×C83C2×C418yescomplemented
335#123×C83C2×C418yescomplemented
336C22⋊Q8×C83C2×C418yescomplemented
337C22⋊Q8×C83C2×C418yescomplemented
338#120×C83C2×C418yes—
339C4×D4×C83C2×C418yescomplemented
340C4×D4×C83C2×C418yescomplemented
341#117×C83C2×C418yescomplemented
342#117×C83C2×C418yescomplemented
343C2×C4⋊C4×C83C2311yescharacteristic
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×C83C2×C418yescomplemented
352C2×C22⋊C4×C83C2×C418yescomplemented
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×C22⋊C4×C83C2311yescharacteristic
362C2×C22⋊C4×C83C2311yescharacteristic
363C2×C22⋊C4×C83C2311yescharacteristic
364C2×C22⋊C4×C83C2311yescharacteristic
365C2×C22⋊C4×C83C2311yescharacteristic
366C2×C22⋊C4×C83C2311yescharacteristic
367C2×C42×C83C2311yescharacteristic
368C2×C42×C83C2311yescharacteristic
369C2×C42×C83C2311yescharacteristic
370C22×Dic83—22no—
371C22×Dic83—22no—
372C22×Dic83—22no—
373C22×Dic83—22no—
374C22×Dic83—22no—
375C22×Dic83—22no—
376C22×Dic83—22no—
377C22×Dic83—22no—
378C22×Dic83—22no—
379C22×Dic83—41no—
380C22×Dic83—41no—
381C22×Dic83—41no—
382C22×Dic83—41no—
383C22×Dic83—41no—
384C22×Dic83—41no—
385C22×Dic83—41no—
386C22×Dic83—41no—
387C22×Dic83—41no—
388C22×Dic83—41no—
389C22×Dic83—41no—
390C22×Dic83—41no—
391C22×Dic83—41no—
392C22×Dic83—41no—
393C22×Dic83#4114yes—
394C22×Dic83C2411yescharacteristic
395C22×Dic83C2411yescharacteristic
396C22×Dic83C2411yescharacteristic
397C22×Dic83C2411yescharacteristic
398C22×Dic83C2411yescharacteristic
399C22×Dic83C2411yescharacteristic
400C22×Dic83C2411yescharacteristic
401C22×Dic83C2411yescharacteristic
402C22×Dic83C2411yescharacteristic
403C22×Dic83C2411yescharacteristic
404C22×Dic83C2411yescharacteristic
405C22×Dic83C2411yescharacteristic
406C22×Dic83C2411yescharacteristic
407C22×Dic83C2411yescharacteristic
408C22×Dic83C2411yescharacteristic
409C22×Dic83C2411yescharacteristic
410C4⋊Dic83—22no—
411C4⋊Dic83—22no—
412C4⋊Dic83—22no—
413C4⋊Dic83—22no—
414C4⋊Dic83—22no—
415C4⋊Dic83—22no—
416C4⋊Dic83—22no—
417C4⋊Dic83—22no—
418C4⋊Dic83—22no—
419C4⋊Dic83—22no—
420C4⋊Dic83—41no—
421C4⋊Dic83—41no—
422C4⋊Dic83—41no—
423C4⋊Dic83—41no—
424C4⋊Dic83—41no—
425C4⋊Dic83—41no—
426C4⋊Dic83—41no—
427C4⋊Dic83—41no—
428C22⋊Dic83—22no—
429C22⋊Dic83—22no—
430C22⋊Dic83—22no—
431C22⋊Dic83—22no—
432C22⋊Dic83—22no—
433C22⋊Dic83—22no—
434C22⋊Dic83—22no—
435C22⋊Dic83—22no—
436C22⋊Dic83—22no—
437C22⋊Dic83—22no—
438C22⋊Dic83—22no—
439C22⋊Dic83—22no—
440C22⋊Dic83—22no—
441C22⋊Dic83—41no—
442C22⋊Dic83—41no—
443C22⋊Dic83—41no—
444C22⋊Dic83—41no—
445C22⋊Dic83—41no—
446C22⋊Dic83—41no—
447C22⋊Dic83—41no—
448C22⋊Dic83—41no—
449C22⋊Dic83—41no—
450C22⋊Dic83—41no—
451C22⋊Dic83#4114yes—
452C4×Dic83—22no—
453C4×Dic83—22no—
454C4×Dic83—22no—
455C4×Dic83—22no—
456C4×Dic83—22no—
457C4×Dic83—22no—
458C4×Dic83—22no—
459C4×Dic83—41no—
460C4×Dic83—41no—
461C4×Dic83—41no—
462C4×Dic83—41no—
463C4×Dic83—41no—
464C4×Dic83—41no—
465C4×Dic83—41no—
466C4×Dic83—41no—
467C4×Dic83—41no—
468C4×Dic83—41no—
469C4×Dic83—41no—
470C4×Dic83—41no—
471C4×Dic83—41no—
472C4×Dic83—41no—
473C4×Dic83—41no—
474C4×Dic83—41no—
475C4×Dic83—41no—
476C4×Dic83—41no—
477C4×Dic83—41no—
478C24×C83—22no—
479C24×C83—22no—
480C24×C83—41no—
481C24×C83—41no—
482C24×C83—41no—
483C24×C83—41no—
484C24×C83C22×C414yes—
485C24×C83C2411yescharacteristic
486C24×C83C2411yescharacteristic
487C24×C83C2411yescharacteristic
488C24×C83C2411yescharacteristic
489C2×Q8×C83—41no—
490C2×Q8×C83—41no—
491C2×Q8×C83C22×C414yes—
492C2×D4×C83—22no—
493C2×D4×C83—22no—
494C2×D4×C83—41no—
495C2×D4×C83—41no—
496C2×D4×C83—41no—
497C2×D4×C83—41no—
498C2×D4×C83C22×C414yes—
499C2×D4×C83C22×C414yes—
500C2×D4×C83C22×C414yes—
501C22×C4×C83—22no—
502C22×C4×C83—22no—
503C22×C4×C83—41no—
504C22×C4×C83—41no—
505C22×C4×C83—41no—
506C22×C4×C83—41no—
507C22×C4×C83—41no—
508C22×C4×C83—41no—
509C22×C4×C83—41no—
510C22×C4×C83—41no—
511C22×C4×C83C22×C414yes—
512C22×C4×C83C22×C414yes—
513C22×C4×C83C22×C414yes—
514C22×C4×C83C22×C414yes—
515C22×C4×C83C22×C414yes—
516C22×C4×C83C2411yescharacteristic
517C22×C4×C83C2411yescharacteristic
518C22×C4×C83C2411yescharacteristic
519C22×C4×C83C2411yescharacteristic
520C22×C4×C83C2411yescharacteristic
521C22×C4×C83C2411yescharacteristic
522C22×C4×C83C2411yescharacteristic
523C22×C4×C83C2411yescharacteristic
524C22×C4×C83C2411yescharacteristic
525C22×C4×C83C2411yescharacteristic
526C22×C4×C83C2411yescharacteristic
527C4⋊C4×C83C22×C414yes—
528C4⋊C4×C83C22×C414yes—
529C4⋊C4×C83C22×C414yes—
530C4⋊C4×C83C22×C414yes—
531C4⋊C4×C83C22×C414yes—
532C4⋊C4×C83C22×C414yes—
533C4⋊C4×C83C22×C414yes—
534C4⋊C4×C83C22×C414yes—
535C22⋊C4×C83C22×C414yes—
536C22⋊C4×C83C22×C414yes—
537C22⋊C4×C83C22×C414yes—
538C22⋊C4×C83C22×C414yes—
539C22⋊C4×C83C22×C414yes—
540C22⋊C4×C83C22×C414yes—
541C22⋊C4×C83C22×C414yes—
542C22⋊C4×C83C22×C414yes—
543C22⋊C4×C83C22×C414yes—
544C22⋊C4×C83C22×C414yes—
545C22⋊C4×C83C22×C414yes—
546C22⋊C4×C83C22×C414yes—
547C22⋊C4×C83C22×C414yes—
548C22⋊C4×C83C22×C414yes—
549C42×C83C22×C414yes—
550C42×C83C22×C414yes—
551C42×C83C22×C414yes—
552C23×C83—21no—
553C23×C83—21no—
554C23×C83—21no—
555C23×C83—21no—
556C23×C83—21no—
557C23×C83—21no—
558C23×C83—21no—
559C23×C83—21no—
560C23×C83—21no—
561C23×C83—21no—
562C23×C83—21no—
563C23×C83—21no—
564C23×C83—21no—
565C23×C83—21no—
566C23×C83—21no—
567C23×C83—21no—
568C23×C83—21no—
569C23×C83—21no—
570C23×C83—21no—
571C23×C83—21no—
572C23×C83—21no—
573C23×C83—21no—
574C23×C83—28no—
575C23×C83—44no—
576C23×C83—44no—
577C23×C83—82no—
578C23×C83—82no—
579C23×C83—82no—
580C23×C83—82no—
581C23×C83C23×C412yes—
582C23×C83C23×C412yes—
583C23×C83C23×C412yes—
584C23×C83C23×C412yes—
585C23×C83C2×#4112yes—
586C23×C83C2×#4112yes—
587C23×C83C2511yescharacteristic
588Q8×C83—44no—
589D4×C83—28no—
590D4×C83—44no—
591D4×C83—44no—
592C2×C4×C83—28no—
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—44no—
616C2×C4×C83—44no—
617C2×C4×C83—44no—
618C2×C4×C83—44no—
619C2×C4×C83C23×C412yes—
620C2×C4×C83C23×C412yes—
621C2×C4×C83C23×C412yes—
622C2×C4×C83C23×C412yes—
623C2×C4×C83C23×C412yes—
624C2×C4×C83C23×C412yes—
625C2×C4×C83C23×C412yes—
626C2×C4×C83C23×C412yes—
627C2×C4×C83C23×C412yes—
628C2×C4×C83C23×C412yes—
629C2×C4×C83C23×C412yes—
630C2×Dic83—21no—
631C2×Dic83—21no—
632C2×Dic83—21no—
633C2×Dic83—21no—
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—21no—
668C2×Dic83—21no—
669C2×Dic83—21no—
670C2×Dic83—21no—
671C2×Dic83—21no—
672C2×Dic83—21no—
673C2×Dic83—44no—
674C2×Dic83—44no—
675C2×Dic83—44no—
676C2×Dic83—44no—
677C2×Dic83—82no—
678C2×Dic83—82no—
679C2×Dic83—82no—
680C2×Dic83—82no—
681C2×Dic83C2×#4112yes—
682C2×Dic83C2×#4112yes—
683C2×Dic83C2×#4112yes—
684C2×Dic83C2×#4112yes—
685C2×Dic83H(5,𝔽2)12yes—
686C22×C83—22no—
687C22×C83—22no—
688C22×C83—22no—
689C22×C83—22no—
690C22×C83—22no—
691C22×C83—22no—
692C22×C83—22no—
693C22×C83—22no—
694C22×C83—22no—
695C22×C83—22no—
696C22×C83—22no—
697C22×C83—22no—
698C22×C83—22no—
699C22×C83—22no—
700C22×C83—22no—
701C22×C83—41no—
702C22×C83—41no—
703C22×C83—41no—
704C22×C83—41no—
705C22×C83—41no—
706C22×C83—41no—
707C22×C83—41no—
708C22×C83—41no—
709C22×C83—41no—
710C22×C83—41no—
711C22×C83—41no—
712C22×C83—41no—
713C22×C83—88no—
714C22×C83C4×#4114yes—
715C22×C83C24×C411yescharacteristic
716C22×C83C22×#4111yescharacteristic
717C22×C83C22×#4111yescharacteristic
718C22×C83C2×H(5,𝔽2)11yescharacteristic
719C22×C83#58511yescharacteristic
720C22×C83#58511yescharacteristic
721C22×C83#58511yescharacteristic
722C4×C83—22no—
723C4×C83—22no—
724C4×C83—22no—
725C4×C83—22no—
726C4×C83—22no—
727C4×C83—22no—
728C4×C83—22no—
729C4×C83—22no—
730C4×C83—22no—
731C4×C83—22no—
732C4×C83—22no—
733Dic83—22no—
734Dic83—22no—
735Dic83—22no—
736Dic83—22no—
737Dic83—22no—
738Dic83—41no—
739Dic83—41no—
740Dic83—41no—
741Dic83—41no—
742Dic83—41no—
743Dic83—41no—
744Dic83—41no—
745Dic83—41no—
746Dic83—41no—
747Dic83—41no—
748Dic83—41no—
749#34315—831nomaximal, Sylow
750C2×C83—24no—
751C2×C83—42no—
752C2×C83—42no—
753C2×C83—42no—
754C2×C83C2×C4×#4111yescharacteristic
755C2×C83#342811yescharacteristic
756C2×C83C4×H(5,𝔽2)11yescharacteristic
757C2×C83#350511yescharacteristic
758C2×C83#351011yescharacteristic
759C2×C83#351311yescharacteristic
760C2×C83#352111yescharacteristic
761C2×#551D8311yescharacteristic
762#2374—831no—
763#2374—831no—
764#2373—831no—
765#2373—831no—
766#2368—831no—
767#2367—831no—
768#2362—831no—
769#2359—831no—
770#2358—831no—
771#2357—831no—
772#2353—831no—
773#2347—831no—
774#2343—831no—
775#2342—831no—
776#2342—831no—
777#2337—831no—
778#2335—831no—
779#2334—831no—
780#2332—831no—
781#2322—831no—
782#2321—831no—
783C4×#126—831no—
784C4×C22⋊Q8—831no—
785C4×#123—831no—
786#2298—831no—
787#2290—831no—
788C2×#388—831no—
789#2274—831no—
790#2273—831no—
791C42×D4—831no—
792C83#3431511yescharacteristic, complemented, Sylow
793#551Dic83116yescomplemented
794C2×#126C2×D8311yescharacteristic
795C2×#126C2×D8311yescharacteristic
796C2×#124C2×D8311yescharacteristic
797C2×#123C2×D8311yescharacteristic
798C2×#123C2×D8311yescharacteristic
799C2×#123C2×D8311yescharacteristic
800C2×C22⋊Q8C2×D8311yescharacteristic
801C2×C22⋊Q8C2×D8311yescharacteristic
802C2×#120C2×D8311yescharacteristic
803C2×C4×Q8—831no—
804C2×C4×D4—831no—
805C2×C4×D4—831no—
806C2×C4×D4—831no—
807C2×C4×D4C2×D8311yescharacteristic
808C2×C4×D4C2×D8311yescharacteristic
809C2×#117—831no—
810C2×#117—831no—
811C2×#117C2×D8311yescharacteristic
812C2×#117C2×D8311yescharacteristic
813C22×C4⋊C4—831no—
814C22×C22⋊C4—831no—
815C22×C22⋊C4—831no—
816C22×C22⋊C4—831no—
817C22×C22⋊C4C2×D8311yescharacteristic
818C22×C22⋊C4C2×D8311yescharacteristic
819C22×C42—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#388—831no—
832#388—831no—
833#388—831no—
834#388—831no—
835#388—831no—
836#388—831no—
837#388—831no—
838#388—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#387—831no—
860#387—831no—
861#387—831no—
862#387—831no—
863#387—831no—
864#387—831no—
865#387—831no—
866#387—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#386—831no—
876#386—831no—
877#386—831no—
878#386—831no—
879#386—831no—
880#386—831no—
881#385—831no—
882#385—831no—
883#385—831no—
884#385—831no—
885#385—831no—
886#385—831no—
887#385—831no—
888#385—831no—
889#385—831no—
890#385—831no—
891#383—831no—
892#383—831no—
893#382—831no—
894#381—831no—
895#381—831no—
896#381—831no—
897#380—831no—
898#380—831no—
899#379—831no—
900C4×C4⋊C4—831no—
901C4×C4⋊C4—831no—
902C4×C4⋊C4—831no—
903C4×C4⋊C4—831no—
904C4×C4⋊C4—831no—
905C4×C4⋊C4—831no—
906C4×C4⋊C4—831no—
907C4×C4⋊C4—831no—
908C4×C4⋊C4—831no—
909C4×C4⋊C4—831no—
910C4×C4⋊C4—831no—
911C4×C4⋊C4—831no—
912C4×C4⋊C4—831no—
913C4×C4⋊C4—831no—
914C4×C4⋊C4—831no—
915C4×C4⋊C4—831no—
916C4×C4⋊C4—831no—
917C4×C4⋊C4—831no—
918C4×C22⋊C4—831no—
919C4×C22⋊C4—831no—
920C4×C22⋊C4—831no—
921C4×C22⋊C4—831no—
922C4×C22⋊C4—831no—
923C4×C22⋊C4—831no—
924C4×C22⋊C4—831no—
925C4×C22⋊C4—831no—
926C4×C22⋊C4—831no—
927C4×C22⋊C4—831no—
928C4×C22⋊C4—831no—
929C4×C22⋊C4—831no—
930C4×C22⋊C4—831no—
931C4×C22⋊C4—831no—
932C4×C22⋊C4—831no—
933C4×C22⋊C4—831no—
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—
944#376—831no—
945#376—831no—
946C2×#95—831no—
947C2×#95—831no—
948C43—831no—
949C25C22×D8311yescharacteristic
950C22×Q8C22×D8311yescharacteristic
951C22×D4C22×D8311yescharacteristic
952C22×D4C22×D8311yescharacteristic
953C22×D4C22×D8311yescharacteristic
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×C4C22×D8311yescharacteristic
963C23×C4C22×D8311yescharacteristic
964C23×C4C22×D8311yescharacteristic
965C23×C4C22×D8311yescharacteristic
966C23×C4C22×D8311yescharacteristic
967#126C2×Dic8318yescomplemented
968#126C2×Dic8318yescomplemented
969#124C2×Dic8318yescomplemented
970#123C2×Dic8318yescomplemented
971#123C2×Dic8318yescomplemented
972#123C2×Dic8318yescomplemented
973C22⋊Q8C2×Dic8318yescomplemented
974C22⋊Q8C2×Dic8318yescomplemented
975#120C2×Dic8318yes—
976C4×Q8—3322no—
977C4×D4—3322no—
978C4×D4—1664no—
979C4×D4—1664no—
980C4×D4C2×Dic8318yescomplemented
981C4×D4C2×Dic8318yescomplemented
982#117—3322no—
983#117—1664no—
984#117C2×Dic8318yescomplemented
985#117C2×Dic8318yescomplemented
986C2×C4⋊C4—831no—
987C2×C4⋊C4—831no—
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—1664no—
1005C2×C4⋊C4C22×D8311yescharacteristic
1006C2×C4⋊C4C22×D8311yescharacteristic
1007C2×C4⋊C4C22×D8311yescharacteristic
1008C2×C4⋊C4C22×D8311yescharacteristic
1009C2×C4⋊C4C22×D8311yescharacteristic
1010C2×C4⋊C4C22×D8311yescharacteristic
1011C2×C4⋊C4C22×D8311yescharacteristic
1012C2×C4⋊C4C22×D8311yescharacteristic
1013C2×C22⋊C4—3322no—
1014C2×C22⋊C4—831no—
1015C2×C22⋊C4—831no—
1016C2×C22⋊C4—831no—
1017C2×C22⋊C4—831no—
1018C2×C22⋊C4—831no—
1019C2×C22⋊C4—831no—
1020C2×C22⋊C4—831no—
1021C2×C22⋊C4—831no—
1022C2×C22⋊C4—831no—
1023C2×C22⋊C4—831no—
1024C2×C22⋊C4—831no—
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—1664no—
1039C2×C22⋊C4—1664no—
1040C2×C22⋊C4C2×Dic8318yescomplemented
1041C2×C22⋊C4C2×Dic8318yescomplemented
1042C2×C22⋊C4C22×D8311yescharacteristic
1043C2×C22⋊C4C22×D8311yescharacteristic
1044C2×C22⋊C4C22×D8311yescharacteristic
1045C2×C22⋊C4C22×D8311yescharacteristic
1046C2×C22⋊C4C22×D8311yescharacteristic
1047C2×C22⋊C4C22×D8311yescharacteristic
1048C2×C22⋊C4C22×D8311yescharacteristic
1049C2×C22⋊C4C22×D8311yescharacteristic
1050C2×C22⋊C4C22×D8311yescharacteristic
1051C2×C22⋊C4C22×D8311yescharacteristic
1052C2×C22⋊C4C22×D8311yescharacteristic
1053C2×C22⋊C4C22×D8311yescharacteristic
1054C2×C22⋊C4C22×D8311yescharacteristic
1055C2×C22⋊C4C22×D8311yescharacteristic
1056C2×C42—3322no—
1057C2×C42—3322no—
1058C2×C42—831no—
1059C2×C42—831no—
1060C2×C42—831no—
1061C2×C42—831no—
1062C2×C42—831no—
1063C2×C42—831no—
1064C2×C42—831no—
1065C2×C42—831no—
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×C42—831no—
1082C2×C42—831no—
1083C2×C42—831no—
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#95—831no—
1116#95—831no—
1117#95—831no—
1118#95—831no—
1119#95—831no—
1120#95—831no—
1121#95—831no—
1122#95—831no—
1123#95—831no—
1124#95—831no—
1125#95—831no—
1126#95—831no—
1127#95—831no—
1128#95—831no—
1129#95—831no—
1130#95—831no—
1131C24—22no—
1132C24—22no—
1133C24—41no—
1134C24—41no—
1135C24—41no—
1136C24—41no—
1137C24C22×Dic8314yes—
1138C24C23×D8311yescharacteristic
1139C24C23×D8311yescharacteristic
1140C24C23×D8311yescharacteristic
1141C24C23×D8311yescharacteristic
1142C2×Q8—41no—
1143C2×Q8—41no—
1144C2×Q8C22×Dic8314yes—
1145C2×D4—22no—
1146C2×D4—22no—
1147C2×D4—41no—
1148C2×D4—41no—
1149C2×D4—41no—
1150C2×D4—41no—
1151C2×D4C22×Dic8314yes—
1152C2×D4C22×Dic8314yes—
1153C2×D4C22×Dic8314yes—
1154C22×C4—22no—
1155C22×C4—22no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—41no—
1163C22×C4—41no—
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—834no—
1179C22×C4—831no—
1180C22×C4—831no—
1181C22×C4—831no—
1182C22×C4—831no—
1183C22×C4—831no—
1184C22×C4—831no—
1185C22×C4—831no—
1186C22×C4—831no—
1187C22×C4—831no—
1188C22×C4—831no—
1189C22×C4—831no—
1190C22×C4—831no—
1191C22×C4—831no—
1192C22×C4—831no—
1193C22×C4—831no—
1194C22×C4—831no—
1195C22×C4—1662no—
1196C22×C4—1662no—
1197C22×C4—1662no—
1198C22×C4—1662no—
1199C22×C4—1662no—
1200C22×C4—1662no—
1201C22×C4—1662no—
1202C22×C4—1662no—
1203C22×C4—1662no—
1204C22×C4C22×Dic8314yes—
1205C22×C4C22×Dic8314yes—
1206C22×C4C22×Dic8314yes—
1207C22×C4C22×Dic8314yes—
1208C22×C4C22×Dic8314yes—
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—3321no—
1221C4⋊C4—3321no—
1222C4⋊C4—3321no—
1223C4⋊C4—3321no—
1224C4⋊C4—3321no—
1225C4⋊C4—3321no—
1226C4⋊C4—3321no—
1227C4⋊C4—3321no—
1228C4⋊C4—1662no—
1229C4⋊C4—1662no—
1230C4⋊C4—1662no—
1231C4⋊C4—1662no—
1232C4⋊C4—1662no—
1233C4⋊C4—1662no—
1234C4⋊C4—1662no—
1235C4⋊C4—1662no—
1236C4⋊C4—1662no—
1237C4⋊C4—1662no—
1238C4⋊C4C22×Dic8314yes—
1239C4⋊C4C22×Dic8314yes—
1240C4⋊C4C22×Dic8314yes—
1241C4⋊C4C22×Dic8314yes—
1242C4⋊C4C22×Dic8314yes—
1243C4⋊C4C22×Dic8314yes—
1244C4⋊C4C22×Dic8314yes—
1245C4⋊C4C22×Dic8314yes—
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—834no—
1257C22⋊C4—1662no—
1258C22⋊C4—1662no—
1259C22⋊C4—1662no—
1260C22⋊C4—1662no—
1261C22⋊C4—1662no—
1262C22⋊C4—1662no—
1263C22⋊C4—1662no—
1264C22⋊C4—1662no—
1265C22⋊C4—1662no—
1266C22⋊C4—1662no—
1267C22⋊C4—1662no—
1268C22⋊C4—1662no—
1269C22⋊C4—1662no—
1270C22⋊C4C22×Dic8314yes—
1271C22⋊C4C22×Dic8314yes—
1272C22⋊C4C22×Dic8314yes—
1273C22⋊C4C22×Dic8314yes—
1274C22⋊C4C22×Dic8314yes—
1275C22⋊C4C22×Dic8314yes—
1276C22⋊C4C22×Dic8314yes—
1277C22⋊C4C22×Dic8314yes—
1278C22⋊C4C22×Dic8314yes—
1279C22⋊C4C22×Dic8314yes—
1280C22⋊C4C22×Dic8314yes—
1281C22⋊C4C22×Dic8314yes—
1282C22⋊C4C22×Dic8314yes—
1283C22⋊C4C22×Dic8314yes—
1284C42—3321no—
1285C42—3321no—
1286C42—3321no—
1287C42—3321no—
1288C42—3321no—
1289C42—3321no—
1290C42—3321no—
1291C42—3321no—
1292C42—3321no—
1293C42—3321no—
1294C42—3321no—
1295C42—3321no—
1296C42—3321no—
1297C42—3321no—
1298C42—3321no—
1299C42—3321no—
1300C42—3321no—
1301C42—3321no—
1302C42—3321no—
1303C42—1662no—
1304C42—1662no—
1305C42—1662no—
1306C42—1662no—
1307C42—1662no—
1308C42—1662no—
1309C42—1662no—
1310C42C22×Dic8314yes—
1311C42C22×Dic8314yes—
1312C42C22×Dic8314yes—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—21no—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—21no—
1330C23—21no—
1331C23—21no—
1332C23—21no—
1333C23—21no—
1334C23—21no—
1335C23—28no—
1336C23—44no—
1337C23—44no—
1338C23—82no—
1339C23—82no—
1340C23—82no—
1341C23—82no—
1342C23C23×Dic8312yes—
1343C23C23×Dic8312yes—
1344C23C23×Dic8312yes—
1345C23C23×Dic8312yes—
1346C23#41×D8312yes—
1347C23#41×D8312yes—
1348C23C24×D8311yescharacteristic
1349Q8—44no—
1350D4—28no—
1351D4—44no—
1352D4—44no—
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—44no—
1377C2×C4—44no—
1378C2×C4—44no—
1379C2×C4—44no—
1380C2×C4—3324no—
1381C2×C4—3324no—
1382C2×C4—3324no—
1383C2×C4—3324no—
1384C2×C4—832no—
1385C2×C4—832no—
1386C2×C4—832no—
1387C2×C4—832no—
1388C2×C4—832no—
1389C2×C4—6642no—
1390C2×C4—6642no—
1391C2×C4—6642no—
1392C2×C4—6642no—
1393C2×C4—1661no—
1394C2×C4—1661no—
1395C2×C4—1661no—
1396C2×C4—1661no—
1397C2×C4—1661no—
1398C2×C4—1661no—
1399C2×C4—1661no—
1400C2×C4—1661no—
1401C2×C4—1661no—
1402C2×C4—1661no—
1403C2×C4—1661no—
1404C2×C4—1661no—
1405C2×C4—1661no—
1406C2×C4—1661no—
1407C2×C4—1661no—
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×C4C23×Dic8312yes—
1437C2×C4C23×Dic8312yes—
1438C2×C4C23×Dic8312yes—
1439C2×C4C23×Dic8312yes—
1440C2×C4C23×Dic8312yes—
1441C2×C4C23×Dic8312yes—
1442C2×C4C23×Dic8312yes—
1443C2×C4C23×Dic8312yes—
1444C2×C4C23×Dic8312yes—
1445C2×C4C23×Dic8312yes—
1446C2×C4C23×Dic8312yes—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—22no—
1451C22—22no—
1452C22—22no—
1453C22—22no—
1454C22—22no—
1455C22—22no—
1456C22—22no—
1457C22—22no—
1458C22—22no—
1459C22—22no—
1460C22—22no—
1461C22—22no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—41no—
1466C22—41no—
1467C22—41no—
1468C22—41no—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22—88no—
1475C22#41×Dic8314yes—
1476C22C24×Dic8311yescharacteristic
1477C22C2×#41×D8311yescharacteristic
1478C22C2×#41×D8311yescharacteristic
1479C22H(5,𝔽2)×D8311yescharacteristic
1480C22#1912853611yescharacteristic
1481C22#1912853711yescharacteristic
1482C22#1912853711yescharacteristic
1483C4—22no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—22no—
1488C4—22no—
1489C4—22no—
1490C4—22no—
1491C4—22no—
1492C4—22no—
1493C4—22no—
1494C4—3321no—
1495C4—3321no—
1496C4—3321no—
1497C4—3321no—
1498C4—3321no—
1499C4—3321no—
1500C4—3321no—
1501C4—3321no—
1502C4—3321no—
1503C4—3321no—
1504C4—3321no—
1505C4—1662no—
1506C4—1662no—
1507C4—1662no—
1508C4—1662no—
1509C4—1662no—
1510C2—24no—
1511C2—42no—
1512C2—42no—
1513C2—42no—
1514C2C2×#41×Dic8311yescharacteristic
1515C2#2492066611yescharacteristic
1516C2H(5,𝔽2)×Dic8311yescharacteristic
1517C2#2492129411yescharacteristic
1518C2#2492135111yescharacteristic
1519C2#2492140011yescharacteristic
1520C2#2492152811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC2×#551×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#120×C83C22
hypercenterC2×#551D83
hypocenterC83#34315
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #24910599C2semidirect
2. #24910599C2semidirect
3. #24910587C2semidirect
4. #24910587C2semidirect
5. #24910548C2semidirect
6. #24910538C2semidirect
7. #24910494C2semidirect
8. #24910459C2semidirect
10. #24910436C2semidirect
11. #24910403C2semidirect
12. #24910356C2semidirect
13. #24910323C2semidirect
14. #24910312C2semidirect
15. #24910312C2semidirect
16. #24910278C2semidirect
17. #24910257C2semidirect
18. #24910242C2semidirect
19. #24910221C2semidirect
20. #24910135C2semidirect
22. #126×Dic83C2semidirect
23. C22⋊Q8×Dic83C2semidirect
24. #123×Dic83C2semidirect
25. #24909961C2semidirect
26. #24909908C2semidirect
27. C2×#19127594C2semidirect
28. #24909819C2semidirect
29. #24909816C2semidirect
30. C4×D4×Dic83C2semidirect
32. C2×Q8×Dic83C22semidirect
43. C22×C4×Dic83C22semidirect
44. #19127608C22semidirect
45. #19127608C22semidirect
46. #19127608C22semidirect
50. #19127600C22semidirect
51. #19127600C22semidirect
52. #19127600C22semidirect
53. #19127600C22semidirect
76. #19127594C22semidirect
77. #19127594C22semidirect
78. #19127594C22semidirect
79. #19127594C22semidirect
80. #19127594C22semidirect
81. #19127594C22semidirect
82. #19127587C22semidirect
83. #19127587C22semidirect
84. #19127587C22semidirect
85. #19127587C22semidirect
86. #19127587C22semidirect
87. #19127587C22semidirect
88. #19127587C22semidirect
89. #19127587C22semidirect
90. #19127587C22semidirect
91. #19127587C22semidirect
92. #19127587C22semidirect
93. #19127587C22semidirect
94. #19127587C22semidirect
95. #19127587C22semidirect
96. #19127587C22semidirect
97. #19127587C22semidirect
111. #19127576C22semidirect
112. #19127576C22semidirect
113. #19127576C22semidirect
114. #19127569C22semidirect
115. #19127569C22semidirect
116. #19127567C22semidirect
119. #19127564C22semidirect
123. C4⋊C4×Dic83C22semidirect
124. C4⋊C4×Dic83C22semidirect
125. C4⋊C4×Dic83C22semidirect
126. C4⋊C4×Dic83C22semidirect
127. C4⋊C4×Dic83C22semidirect
128. C4⋊C4×Dic83C22semidirect
129. C4⋊C4×Dic83C22semidirect
130. C4⋊C4×Dic83C22semidirect
131. C4⋊C4×Dic83C22semidirect
132. C4⋊C4×Dic83C22semidirect
133. C4⋊C4×Dic83C22semidirect
134. C4⋊C4×Dic83C22semidirect
135. C4×C4⋊Dic83C22semidirect
136. C4×C4⋊Dic83C22semidirect
137. C4×C4⋊Dic83C22semidirect
138. C4×C4⋊Dic83C22semidirect
139. C4×C4⋊Dic83C22semidirect
140. C4×C4⋊Dic83C22semidirect
156. C22⋊C4×Dic83C22semidirect
157. C22⋊C4×Dic83C22semidirect
158. C22⋊C4×Dic83C22semidirect
165. C4×C22⋊Dic83C22semidirect
166. C4×C22⋊Dic83C22semidirect
167. #19127547C22semidirect
168. #19127547C22semidirect
171. C42×Dic83C22semidirect
172. #551×C83C4semidirect
330. #126×C83C2×C4semidirect
331. #126×C83C2×C4semidirect
332. #124×C83C2×C4semidirect
333. #123×C83C2×C4semidirect
334. #123×C83C2×C4semidirect
335. #123×C83C2×C4semidirect
336. C22⋊Q8×C83C2×C4semidirect
337. C22⋊Q8×C83C2×C4semidirect
339. C4×D4×C83C2×C4semidirect
340. C4×D4×C83C2×C4semidirect
341. #117×C83C2×C4semidirect
342. #117×C83C2×C4semidirect
351. C2×C22⋊C4×C83C2×C4semidirect
352. C2×C22⋊C4×C83C2×C4semidirect
792. C83#34315semidirect
793. #551Dic83semidirect
967. #126C2×Dic83semidirect
968. #126C2×Dic83semidirect
969. #124C2×Dic83semidirect
970. #123C2×Dic83semidirect
971. #123C2×Dic83semidirect
972. #123C2×Dic83semidirect
973. C22⋊Q8C2×Dic83semidirect
974. C22⋊Q8C2×Dic83semidirect
980. C4×D4C2×Dic83semidirect
981. C4×D4C2×Dic83semidirect
984. #117C2×Dic83semidirect
985. #117C2×Dic83semidirect
1040. C2×C22⋊C4C2×Dic83semidirect
1041. C2×C22⋊C4C2×Dic83semidirect

Maximal subgroups

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

subgroupindex
#249105992
#249105872
#249105482
#249105382
#249104942
#249104592
#249104472
#249104362
#249104032
#249103562
#249103232
#249103122
#249102782
#249102572
#249102422
#249102212
#249101352
#249101242
#126×Dic832
C22⋊Q8×Dic832
#123×Dic832
#249099612
#249099082
C2×#191275942
#249098192
#249098162
C4×D4×Dic832
C2×#551×C832
#3431583