Finite Group Databasebeta

← #35569501

Subgroups — #35569501

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
1#24910655C211yesmaximal, characteristic, complemented
2#24910637C211yesmaximal, characteristic, complemented
3#24910629C211yesmaximal, characteristic, complemented
4#24910611C211yesmaximal, characteristic, complemented
5#24910587C211yesmaximal, characteristic, complemented
6#24910548C211yesmaximal, characteristic, complemented
7#24910459C211yesmaximal, characteristic, complemented
8#24910459C211yesmaximal, characteristic, complemented
9#24910447C211yesmaximal, characteristic
10#24910412C211yesmaximal, characteristic, complemented
11#24910373C211yesmaximal, characteristic, complemented
12#24910348C211yesmaximal, characteristic, complemented
13#24910323C211yesmaximal, characteristic, complemented
14#24910312C211yesmaximal, characteristic, complemented
15#24910312C211yesmaximal, characteristic, complemented
16#24910257C211yesmaximal, characteristic, complemented
17#24910257C211yesmaximal, characteristic, complemented
18#24910242C211yesmaximal, characteristic, complemented
19#24910242C211yesmaximal, characteristic, complemented
20#24910176C211yesmaximal, characteristic, complemented
21#24910147C211yesmaximal, characteristic, complemented
22#24910135C211yesmaximal, characteristic, complemented
23#24910124C211yesmaximal, characteristic
24#24910096C211yesmaximal, characteristic, complemented
25#24910086C211yesmaximal, characteristic, complemented
26#24910077C211yesmaximal, characteristic, complemented
27#24910072C211yesmaximal, characteristic, complemented
28C22⋊Q8×Dic83C211yesmaximal, characteristic, complemented
29#24909908C211yesmaximal, characteristic, complemented
30C2×#19127594C211yesmaximal, characteristic, complemented
31C2×#551×C83C211yesmaximal, characteristic
32C2×Q8×Dic83C2211yescharacteristic, complemented
33C2×D4×Dic83C2211yescharacteristic
34C2×D4×Dic83C2211yescharacteristic
35C2×D4×Dic83C2211yescharacteristic
36C2×#14581751C2211yescharacteristic
37C2×#14581751C2211yescharacteristic
38C2×#14581751C2211yescharacteristic, complemented
39C22×C4⋊Dic83C2211yescharacteristic
40C22×C22⋊Dic83C2211yescharacteristic
41C22×C22⋊Dic83C2211yescharacteristic
42C22×C22⋊Dic83C2211yescharacteristic
43C22×C4×Dic83C2211yescharacteristic
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#19127600C2211yescharacteristic, complemented
55#19127600C2211yescharacteristic, complemented
56#19127600C2211yescharacteristic, complemented
57#19127600C2211yescharacteristic, complemented
58#19127600C2211yescharacteristic, complemented
59#19127600C2211yescharacteristic, complemented
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
77#19127594C2211yescharacteristic
78#19127594C2211yescharacteristic
79#19127594C2211yescharacteristic
80#19127594C2211yescharacteristic
81#19127594C2211yescharacteristic
82#19127594C2211yescharacteristic, complemented
83#19127594C2211yescharacteristic, complemented
84#19127594C2211yescharacteristic, complemented
85#19127594C2211yescharacteristic, complemented
86#19127594C2211yescharacteristic, complemented
87#19127594C2211yescharacteristic, 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#19127587C2211yescharacteristic, complemented
99#19127587C2211yescharacteristic, complemented
100#19127587C2211yescharacteristic, complemented
101#19127587C2211yescharacteristic, complemented
102#19127587C2211yescharacteristic, complemented
103#19127587C2211yescharacteristic, complemented
104#19127581C2211yescharacteristic
105#19127581C2211yescharacteristic
106#19127581C2211yescharacteristic
107#19127581C2211yescharacteristic
108#19127581C2211yescharacteristic
109#19127581C2211yescharacteristic
110#19127576C2211yescharacteristic
111#19127576C2211yescharacteristic
112#19127576C2211yescharacteristic
113#19127576C2211yescharacteristic
114#19127576C2211yescharacteristic
115#19127576C2211yescharacteristic
116#19127576C2211yescharacteristic
117#19127576C2211yescharacteristic
118#19127576C2211yescharacteristic
119#19127576C2211yescharacteristic
120#19127576C2211yescharacteristic
121#19127576C2211yescharacteristic
122#19127576C2211yescharacteristic
123#19127576C2211yescharacteristic
124#19127576C2211yescharacteristic
125#19127576C2211yescharacteristic, complemented
126#19127576C2211yescharacteristic, complemented
127#19127576C2211yescharacteristic, complemented
128#19127576C2211yescharacteristic, complemented
129#19127576C2211yescharacteristic, complemented
130#19127571C2211yescharacteristic, complemented
131#19127571C2211yescharacteristic, complemented
132#19127569C2211yescharacteristic, complemented
133#19127567C2211yescharacteristic, complemented
134#19127567C2211yescharacteristic, complemented
135#19127567C2211yescharacteristic, complemented
136#19127567C2211yescharacteristic, complemented
137#19127564C2211yescharacteristic
138#19127564C2211yescharacteristic
139#19127561C2211yescharacteristic
140#19127561C2211yescharacteristic
141#19127561C2211yescharacteristic
142#19127561C2211yescharacteristic
143#19127561C2211yescharacteristic
144#19127561C2211yescharacteristic
145#19127561C2211yescharacteristic, complemented
146#19127557C2211yescharacteristic
147C4⋊C4×Dic83C2211yescharacteristic, complemented
148C4⋊C4×Dic83C2211yescharacteristic, complemented
149C4⋊C4×Dic83C2211yescharacteristic, complemented
150C4⋊C4×Dic83C2211yescharacteristic, complemented
151C4⋊C4×Dic83C2211yescharacteristic, complemented
152C4⋊C4×Dic83C2211yescharacteristic, complemented
153C4×C4⋊Dic83C2211yescharacteristic, complemented
154C4×C4⋊Dic83C2211yescharacteristic, complemented
155C4×C4⋊Dic83C2211yescharacteristic, complemented
156C22⋊C4×Dic83C2211yescharacteristic
157C22⋊C4×Dic83C2211yescharacteristic
158C22⋊C4×Dic83C2211yescharacteristic
159C22⋊C4×Dic83C2211yescharacteristic
160C22⋊C4×Dic83C2211yescharacteristic
161C22⋊C4×Dic83C2211yescharacteristic
162C22⋊C4×Dic83C2211yescharacteristic
163C22⋊C4×Dic83C2211yescharacteristic, complemented
164C4×C22⋊Dic83C2211yescharacteristic
165C4×C22⋊Dic83C2211yescharacteristic
166C4×C22⋊Dic83C2211yescharacteristic, complemented
167#19127547C2211yescharacteristic, complemented
168#19127547C2211yescharacteristic, complemented
169C2×C83⋊#95C2211yescharacteristic
170C2×C83⋊#95C2211yescharacteristic
171C2×C83⋊#95C2211yescharacteristic, 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—42no—
198D4×Dic83—42no—
199D4×Dic83—42no—
200#14581751—42no—
201#14581751—42no—
202#14581751—42no—
203C2×C4⋊Dic83—42no—
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×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×C22⋊Dic83—42no—
231C2×C22⋊Dic83—42no—
232C2×C22⋊Dic83—42no—
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×C22⋊Dic83C2311yescharacteristic
249C2×C22⋊Dic83C2311yescharacteristic
250C2×C22⋊Dic83C2311yescharacteristic
251C2×C22⋊Dic83C2311yescharacteristic
252C2×C22⋊Dic83C2311yescharacteristic
253C2×C22⋊Dic83C2311yescharacteristic
254C2×C22⋊Dic83C2311yescharacteristic
255C2×C22⋊Dic83C2311yescharacteristic
256C2×C22⋊Dic83C2311yescharacteristic
257C2×C4×Dic83—42no—
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—41no—
376C22×Dic83—41no—
377C22×Dic83—41no—
378C22×Dic83—41no—
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—41no—
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—41no—
412C4⋊Dic83—41no—
413C4⋊Dic83—41no—
414C4⋊Dic83—41no—
415C4⋊Dic83—41no—
416C4⋊Dic83—41no—
417C4⋊Dic83—41no—
418C4⋊Dic83—41no—
419C4⋊Dic83—41no—
420C4⋊Dic83—41no—
421C4⋊Dic83—41no—
422C4⋊Dic83—41no—
423C4⋊Dic83—41no—
424C4⋊Dic83—41no—
425C4⋊Dic83—41no—
426C4⋊Dic83—41no—
427C4⋊Dic83—41no—
428C4⋊Dic83—41no—
429C4⋊Dic83—41no—
430C4⋊Dic83—41no—
431C4⋊Dic83—41no—
432C4⋊Dic83—41no—
433C4⋊Dic83—41no—
434C4⋊Dic83—41no—
435C4⋊Dic83—41no—
436C22⋊Dic83—22no—
437C22⋊Dic83—22no—
438C22⋊Dic83—22no—
439C22⋊Dic83—22no—
440C22⋊Dic83—22no—
441C22⋊Dic83—22no—
442C22⋊Dic83—22no—
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—41no—
452C22⋊Dic83—41no—
453C22⋊Dic83—41no—
454C22⋊Dic83—41no—
455C22⋊Dic83—41no—
456C22⋊Dic83—41no—
457C22⋊Dic83—41no—
458C22⋊Dic83—41no—
459C22⋊Dic83—41no—
460C4×Dic83—22no—
461C4×Dic83—22no—
462C4×Dic83—22no—
463C4×Dic83—22no—
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×C83H(5,𝔽2)12yes—
586C23×C832−1+412yes—
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—21no—
674C2×Dic83—21no—
675C2×Dic83—21no—
676C2×Dic83—21no—
677C2×Dic83—44no—
678C2×Dic83—44no—
679C2×Dic83—82no—
680C2×Dic83—82no—
681C2×Dic83—82no—
682C2×Dic83—82no—
683C2×Dic83—82no—
684C2×Dic83—82no—
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×C83#52014yes—
715C22×C83C24×C411yescharacteristic
716C22×C83C2×H(5,𝔽2)11yescharacteristic
717C22×C83C2×H(5,𝔽2)11yescharacteristic
718C22×C83C2×2−1+411yescharacteristic
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—41no—
735Dic83—41no—
736Dic83—41no—
737Dic83—41no—
738Dic83—41no—
739Dic83—41no—
740Dic83—41no—
741Dic83—41no—
742Dic83—41no—
743Dic83—41no—
744Dic83—41no—
745Dic83—41no—
746Dic83—41no—
747Dic83—41no—
748Dic83—41no—
749#34479—831nomaximal, Sylow
750C2×C83—24no—
751C2×C83—42no—
752C2×C83—42no—
753C2×C83—42no—
754C2×C83C2×#52011yescharacteristic
755C2×C83#342811yescharacteristic
756C2×C83C4×H(5,𝔽2)11yescharacteristic
757C2×C83#353511yescharacteristic
758C2×C83#354211yescharacteristic
759C2×C83#354511yescharacteristic
760C2×C83#356411yescharacteristic
761C2×#551D8311yescharacteristic
762#2383—831no—
763#2379—831no—
764#2378—831no—
765#2376—831no—
766#2373—831no—
767#2368—831no—
768#2359—831no—
769#2359—831no—
770#2358—831no—
771#2354—831no—
772#2349—831no—
773#2346—831no—
774#2343—831no—
775#2342—831no—
776#2342—831no—
777#2335—831no—
778#2335—831no—
779#2334—831no—
780#2334—831no—
781#2326—831no—
782#2323—831no—
783#2322—831no—
784#2321—831no—
785#2318—831no—
786#2317—831no—
787#2315—831no—
788#2314—831no—
789C4×C22⋊Q8—831no—
790#2290—831no—
791C2×#388—831no—
792C83#3447911yescharacteristic, 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×#117—831no—
812C2×#117C2×D8311yescharacteristic
813C2×#117C2×D8311yescharacteristic
814C22×C4⋊C4—831no—
815C22×C22⋊C4—831no—
816C22×C22⋊C4—831no—
817C22×C22⋊C4—831no—
818C22×C22⋊C4C2×D8311yescharacteristic
819C22×C22⋊C4C2×D8311yescharacteristic
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#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#388—831no—
860#388—831no—
861#388—831no—
862#388—831no—
863#388—831no—
864#388—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#387—831no—
876#387—831no—
877#387—831no—
878#387—831no—
879#387—831no—
880#387—831no—
881#386—831no—
882#386—831no—
883#386—831no—
884#386—831no—
885#386—831no—
886#386—831no—
887#385—831no—
888#385—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#385—831no—
906#385—831no—
907#384—831no—
908#384—831no—
909#383—831no—
910#382—831no—
911#382—831no—
912#382—831no—
913#382—831no—
914#381—831no—
915#381—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×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—
948C2×#95—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—3322no—
979C4×D4—3322no—
980C4×D4C2×Dic8318yescomplemented
981C4×D4C2×Dic8318yescomplemented
982#117—3322no—
983#117—3322no—
984#117—3322no—
985#117C2×Dic8318yescomplemented
986#117C2×Dic8318yescomplemented
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⋊C4C22×D8311yescharacteristic
1015C2×C4⋊C4C22×D8311yescharacteristic
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—831no—
1045C2×C22⋊C4—831no—
1046C2×C22⋊C4—831no—
1047C2×C22⋊C4—831no—
1048C2×C22⋊C4—831no—
1049C2×C22⋊C4C2×Dic8318yescomplemented
1050C2×C22⋊C4C2×Dic8318yescomplemented
1051C2×C22⋊C4C22×D8311yescharacteristic
1052C2×C22⋊C4C22×D8311yescharacteristic
1053C2×C22⋊C4C22×D8311yescharacteristic
1054C2×C22⋊C4C22×D8311yescharacteristic
1055C2×C22⋊C4C22×D8311yescharacteristic
1056C2×C22⋊C4C22×D8311yescharacteristic
1057C2×C22⋊C4C22×D8311yescharacteristic
1058C2×C22⋊C4C22×D8311yescharacteristic
1059C2×C22⋊C4C22×D8311yescharacteristic
1060C2×C22⋊C4C22×D8311yescharacteristic
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×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—3321no—
1179C22×C4—3321no—
1180C22×C4—3321no—
1181C22×C4—3321no—
1182C22×C4—3321no—
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—831no—
1196C22×C4—831no—
1197C22×C4—831no—
1198C22×C4—831no—
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—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—3321no—
1243C4⋊C4—3321no—
1244C4⋊C4—3321no—
1245C4⋊C4—1662no—
1246C4⋊C4C22×Dic8314yes—
1247C4⋊C4C22×Dic8314yes—
1248C4⋊C4C22×Dic8314yes—
1249C4⋊C4C22×Dic8314yes—
1250C4⋊C4C22×Dic8314yes—
1251C4⋊C4C22×Dic8314yes—
1252C4⋊C4C22×Dic8314yes—
1253C4⋊C4C22×Dic8314yes—
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—3321no—
1264C22⋊C4—3321no—
1265C22⋊C4—3321no—
1266C22⋊C4—3321no—
1267C22⋊C4—3321no—
1268C22⋊C4—3321no—
1269C22⋊C4—3321no—
1270C22⋊C4—3321no—
1271C22⋊C4—1662no—
1272C22⋊C4—1662no—
1273C22⋊C4—1662no—
1274C22⋊C4—1662no—
1275C22⋊C4—1662no—
1276C22⋊C4—1662no—
1277C22⋊C4—1662no—
1278C22⋊C4C22×Dic8314yes—
1279C22⋊C4C22×Dic8314yes—
1280C22⋊C4C22×Dic8314yes—
1281C22⋊C4C22×Dic8314yes—
1282C22⋊C4C22×Dic8314yes—
1283C22⋊C4C22×Dic8314yes—
1284C22⋊C4C22×Dic8314yes—
1285C22⋊C4C22×Dic8314yes—
1286C22⋊C4C22×Dic8314yes—
1287C22⋊C4C22×Dic8314yes—
1288C22⋊C4C22×Dic8314yes—
1289C22⋊C4C22×Dic8314yes—
1290C22⋊C4C22×Dic8314yes—
1291C22⋊C4C22×Dic8314yes—
1292C42—3321no—
1293C42—3321no—
1294C42—3321no—
1295C42—3321no—
1296C42—3321no—
1297C42—3321no—
1298C42—3321no—
1299C42—3321no—
1300C42—3321no—
1301C42—3321no—
1302C42—3321no—
1303C42—3321no—
1304C42—3321no—
1305C42—3321no—
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#1458183812yes—
1347C23#1458183912yes—
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—832no—
1383C2×C4—6642no—
1384C2×C4—6642no—
1385C2×C4—6642no—
1386C2×C4—6642no—
1387C2×C4—6642no—
1388C2×C4—6642no—
1389C2×C4—1661no—
1390C2×C4—1661no—
1391C2×C4—1661no—
1392C2×C4—1661no—
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#1912818414yes—
1476C22C24×Dic8311yescharacteristic
1477C22H(5,𝔽2)×D8311yescharacteristic
1478C22C2×#1458183811yescharacteristic
1479C22C2×#1458183911yescharacteristic
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—3321no—
1506C4—3321no—
1507C4—3321no—
1508C4—3321no—
1509C4—1662no—
1510C2—24no—
1511C2—42no—
1512C2—42no—
1513C2—42no—
1514C2C2×#1912818411yescharacteristic
1515C2#2492066611yescharacteristic
1516C2H(5,𝔽2)×Dic8311yescharacteristic
1517C2#2492165911yescharacteristic
1518C2#2492177211yescharacteristic
1519C2#2492181911yescharacteristic
1520C2#2492207911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC2×#551×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#120×C83C22
hypercenterC2×#551D83
hypocenterC83#34479
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #24910655C2semidirect
2. #24910637C2semidirect
3. #24910629C2semidirect
4. #24910611C2semidirect
5. #24910587C2semidirect
6. #24910548C2semidirect
7. #24910459C2semidirect
8. #24910459C2semidirect
10. #24910412C2semidirect
11. #24910373C2semidirect
12. #24910348C2semidirect
13. #24910323C2semidirect
14. #24910312C2semidirect
15. #24910312C2semidirect
16. #24910257C2semidirect
17. #24910257C2semidirect
18. #24910242C2semidirect
19. #24910242C2semidirect
20. #24910176C2semidirect
21. #24910147C2semidirect
22. #24910135C2semidirect
24. #24910096C2semidirect
25. #24910086C2semidirect
26. #24910077C2semidirect
27. #24910072C2semidirect
28. C22⋊Q8×Dic83C2semidirect
29. #24909908C2semidirect
30. C2×#19127594C2semidirect
32. C2×Q8×Dic83C22semidirect
38. C2×#14581751C22semidirect
44. #19127608C22semidirect
45. #19127608C22semidirect
46. #19127608C22semidirect
50. #19127600C22semidirect
51. #19127600C22semidirect
52. #19127600C22semidirect
53. #19127600C22semidirect
54. #19127600C22semidirect
55. #19127600C22semidirect
56. #19127600C22semidirect
57. #19127600C22semidirect
58. #19127600C22semidirect
59. #19127600C22semidirect
82. #19127594C22semidirect
83. #19127594C22semidirect
84. #19127594C22semidirect
85. #19127594C22semidirect
86. #19127594C22semidirect
87. #19127594C22semidirect
88. #19127587C22semidirect
89. #19127587C22semidirect
90. #19127587C22semidirect
91. #19127587C22semidirect
92. #19127587C22semidirect
93. #19127587C22semidirect
94. #19127587C22semidirect
95. #19127587C22semidirect
96. #19127587C22semidirect
97. #19127587C22semidirect
98. #19127587C22semidirect
99. #19127587C22semidirect
100. #19127587C22semidirect
101. #19127587C22semidirect
102. #19127587C22semidirect
103. #19127587C22semidirect
125. #19127576C22semidirect
126. #19127576C22semidirect
127. #19127576C22semidirect
128. #19127576C22semidirect
129. #19127576C22semidirect
130. #19127571C22semidirect
131. #19127571C22semidirect
132. #19127569C22semidirect
133. #19127567C22semidirect
134. #19127567C22semidirect
135. #19127567C22semidirect
136. #19127567C22semidirect
145. #19127561C22semidirect
147. C4⋊C4×Dic83C22semidirect
148. C4⋊C4×Dic83C22semidirect
149. C4⋊C4×Dic83C22semidirect
150. C4⋊C4×Dic83C22semidirect
151. C4⋊C4×Dic83C22semidirect
152. C4⋊C4×Dic83C22semidirect
153. C4×C4⋊Dic83C22semidirect
154. C4×C4⋊Dic83C22semidirect
155. C4×C4⋊Dic83C22semidirect
163. C22⋊C4×Dic83C22semidirect
166. C4×C22⋊Dic83C22semidirect
167. #19127547C22semidirect
168. #19127547C22semidirect
171. C2×C83⋊#95C22semidirect
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#34479semidirect
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
985. #117C2×Dic83semidirect
986. #117C2×Dic83semidirect
1049. C2×C22⋊C4C2×Dic83semidirect
1050. C2×C22⋊C4C2×Dic83semidirect

Maximal subgroups

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

subgroupindex
#249106552
#249106372
#249106292
#249106112
#249105872
#249105482
#249104592
#249104472
#249104122
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#249102572
#249102422
#249101762
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