Finite Group Databasebeta

← #15618809

Subgroups — #15618809

Order 2816.

1658 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077722C214yesmaximal, complemented
2#13077718C212yesmaximal, complemented
3#13077711C212yesmaximal, complemented
4#13077711C214yesmaximal, complemented
5#13077705C212yesmaximal, complemented
6#13077701C212yesmaximal, complemented
7Q8×#4318C211yesmaximal, characteristic, complemented
8#13077565C211yesmaximal, characteristic, complemented
9#13077565C212yesmaximal, complemented
10#13077557C212yesmaximal, complemented
11#13077551C211yesmaximal, characteristic, complemented
12C2×#10622637C211yesmaximal, characteristic, complemented
13#13077282C211yesmaximal, characteristic
14#13077282C212yesmaximal
15#13077267C212yesmaximal
16#13077260C211yesmaximal, characteristic
17Q8×C11×#41C211yesmaximal, characteristic
18Q82×C11C411yescharacteristic
19C11×#557C411yescharacteristic
20C11×#557C412yes—
21C11×#554C412yes—
22C11×#554C411yescharacteristic
23C11×#554C414yes—
24C11×#554C412yes—
25D4×Q8×C11C411yescharacteristic
26D4×Q8×C11C412yes—
27C11×#533C2211yescharacteristic
28C11×#533C2212yes—
29C11×#533C2212yes—
30C11×#533C2214yes—
31C4×C11×#41C2211yescharacteristic
32C4×C11×#41C2212yes—
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C4×Q8×C11C2212yes—
35#10622847C2211yescharacteristic
36#10622847C2211yescharacteristic
37#10622847C2212yes—
38#10622637C2211yescharacteristic
39#10622637C2211yescharacteristic
40#10622637C2211yescharacteristic
41#10622637C2212yes—
42#10622637C2211yescharacteristic
43#10622637C2212yes—
44#10622637C2212yes—
45#10622637C2212yes—
46#10622637C2214yes—
47#10622637C2214yes—
48#10622637C2214yes—
49#10622637C2214yes—
50#10622637C2212yes—
51#10622637C2214yes—
52#10622637C2214yes—
53#10622637C2214yes—
54#10622637C2214yes—
55#10622637C2212yes—
56#10622637C2214yes—
57Q8×C11⋊C8C2212yes—
58Q8×C11⋊C8C2212yes—
59Q8×C11⋊C8C2212yes—
60Q8×C11⋊C8C2214yes—
61Q8×C11⋊C8C2212yes—
62#10622613C2212yes—
63#10622613C2212yes—
64#10622613C2214yes—
65#10622613C2214yes—
66#10622613C2214yes—
67#10622613C2214yes—
68#10622613C2214yes—
69#10622612C2211yescharacteristic
70#10622612C2211yescharacteristic
71#10622612C2212yes—
72#10622612C2212yes—
73#10622610C2212yes—
74#10622610C2212yes—
75#10622610C2212yes—
76#10622539C2214yes—
77#10622539C2214yes—
78#10622539C2214yes—
79#10622539C2212yes—
80#10622538C2212yes—
81#10622538C2212yes—
82#10622538C2212yes—
83#10622538C2214yes—
84#10622537C2211yescharacteristic
85#10622537C2212yes—
86C2×C4⋊(C11⋊C8)C2211yescharacteristic
87C2×C4⋊(C11⋊C8)C2212yes—
88C4×#4318C2211yescharacteristic
89C4×#4318C2212yes—
90C2×#66867C2212yes—
91C2×C4×C11⋊C8C2211yescharacteristic
92C2×C11×#41C2311yescharacteristic
93C22×Q8×C11C2×C411yescharacteristic
94C22×Q8×C11C2×C412yes—
95C11×C4⋊Q8C2×C411yescharacteristic
96C11×C4⋊Q8C2×C412yes—
97C11×C4⋊Q8C2×C412yes—
98C11×C4⋊Q8C2×C414yes—
99C11×C4⋊Q8C2×C411yescharacteristic
100C11×C4⋊Q8C2×C412yes—
101C11×C4⋊Q8C2×C412yes—
102C11×C4⋊Q8C2×C414yes—
103C11×#125C2×C412yes—
104C11×#125C2×C412yes—
105C11×#125C2×C412yes—
106C11×#125C2×C414yes—
107C11×#125C2×C414yes—
108C11×#125C2×C414yes—
109C11×C22⋊Q8C2×C412yes—
110C11×C22⋊Q8C2×C412yes—
111C11×C22⋊Q8C2×C412yes—
112C11×C22⋊Q8C2×C414yes—
113C11×C22⋊Q8C2×C414yes—
114C11×C22⋊Q8C2×C414yes—
115C11×C22⋊Q8C2×C412yes—
116C11×C22⋊Q8C2×C414yes—
117C11×C22⋊Q8C2×C414yes—
118C11×C22⋊Q8C2×C414yes—
119C11×C22⋊Q8C2×C414yes—
120C4×Q8×C11C2×C411yescharacteristic
121C4×Q8×C11C2×C412yes—
122C4×Q8×C11C2×C411yescharacteristic
123C4×Q8×C11C2×C412yes—
124C4×Q8×C11C2×C412yes—
125C4×Q8×C11C2×C414yes—
126C4×Q8×C11C2×C411yescharacteristic
127C4×Q8×C11C2×C412yes—
128C4×Q8×C11C2×C411yescharacteristic
129C4×Q8×C11C2×C412yes—
130C4×Q8×C11C2311yescharacteristic
131C4×Q8×C11C2311yescharacteristic
132C4×Q8×C11C2312yes—
133C4×Q8×C11C2312yes—
134C4×Q8×C11C2314yes—
135C4×Q8×C11C2312yes—
136C4×Q8×C11C2314yes—
137C4×D4×C11C2×C412yes—
138C4×D4×C11C2×C411yescharacteristic
139C4×D4×C11C2×C414yes—
140C4×D4×C11C2×C412yes—
141C4×D4×C11C2×C412yes—
142C4×D4×C11C2×C411yescharacteristic
143C4×D4×C11C2×C414yes—
144C4×D4×C11C2×C412yes—
145C11×#117C2312yes—
146C11×#117C2311yescharacteristic
147C11×#117C2312yes—
148C11×#117C2314yes—
149C2×C11×C4⋊C4C2×C411yescharacteristic
150C2×C11×C4⋊C4C2×C412yes—
151C2×C11×C4⋊C4C2×C412yes—
152C2×C11×C4⋊C4C2×C414yes—
153C2×C42×C11C2311yescharacteristic
154C2×C42×C11C2312yes—
155C2×C42×C11C2312yes—
156C2×C42×C11C2314yes—
157C2×#4318C2311yescharacteristic
158C2×#4318C2311yescharacteristic
159C2×#4318C2312yes—
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162C22×C11⋊C8C2312yes—
163C22⋊(C11⋊C8)C2312yes—
164C22⋊(C11⋊C8)C2312yes—
165C22⋊(C11⋊C8)C2312yes—
166C22⋊(C11⋊C8)C2312yes—
167C22⋊(C11⋊C8)C2314yes—
168C22⋊(C11⋊C8)C2314yes—
169C4⋊(C11⋊C8)C2312yes—
170C4⋊(C11⋊C8)C2311yescharacteristic
171C4⋊(C11⋊C8)C2311yescharacteristic
172C4⋊(C11⋊C8)C2312yes—
173C4⋊(C11⋊C8)C2312yes—
174C4⋊(C11⋊C8)C2312yes—
175C4⋊(C11⋊C8)C2312yes—
176C4⋊(C11⋊C8)C2312yes—
177C4⋊(C11⋊C8)C2314yes—
178C4⋊(C11⋊C8)C2312yes—
179C4⋊(C11⋊C8)C2314yes—
180C4⋊(C11⋊C8)C2312yes—
181C4⋊(C11⋊C8)C2312yes—
182C4⋊(C11⋊C8)C2312yes—
183C4⋊(C11⋊C8)C2312yes—
184C4⋊(C11⋊C8)C2314yes—
185C4⋊(C11⋊C8)C2314yes—
186C4⋊(C11⋊C8)C2314yes—
187C4⋊(C11⋊C8)C2314yes—
188#66867C2312yes—
189#66867C2312yes—
190#66867C2312yes—
191#66867C2312yes—
192#66867C2314yes—
193#66867C2312yes—
194#66867C2314yes—
195#66867C2314yes—
196#66867C2314yes—
197C4×C11⋊C8C2311yescharacteristic
198C4×C11⋊C8C2311yescharacteristic
199C4×C11⋊C8C2311yescharacteristic
200C4×C11⋊C8C2311yescharacteristic
201C4×C11⋊C8C2312yes—
202C4×C11⋊C8C2314yes—
203C4×C11⋊C8C2314yes—
204C4×C11⋊C8C2314yes—
205C4×C11⋊C8C2314yes—
206#60254—111nomaximal, Sylow
207C11×#41—22no—
208C11×#41—22no—
209C2×Q8×C11—42no—
210C2×Q8×C11—44no—
211C2×Q8×C11C22×C411yescharacteristic
212C2×Q8×C11C22×C411yescharacteristic
213C2×Q8×C11C22×C411yescharacteristic
214C2×Q8×C11C22×C412yes—
215C2×Q8×C11C22×C412yes—
216C2×Q8×C11C22×C414yes—
217C2×Q8×C11C22×C412yes—
218C2×Q8×C11C22×C414yes—
219C2×D4×C11C22×C412yes—
220C2×D4×C11C22×C411yescharacteristic
221C22×C4×C11C22×C412yes—
222C22×C4×C11C22×C411yescharacteristic
223C22×C4×C11C22×C412yes—
224C22×C4×C11C22×C414yes—
225C22×C4×C11C22×C411yescharacteristic
226C22×C4×C11C22×C412yes—
227C22×C4×C11C22×C414yes—
228C22×C4×C11C22×C412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2411yescharacteristic
231C11×C4⋊C4C22×C412yes—
232C11×C4⋊C4C22×C411yescharacteristic
233C11×C4⋊C4C22×C412yes—
234C11×C4⋊C4C22×C414yes—
235C11×C4⋊C4C22×C412yes—
236C11×C4⋊C4C22×C414yes—
237C11×C4⋊C4C22×C412yes—
238C11×C4⋊C4C22×C414yes—
239C11×C4⋊C4C22×C412yes—
240C11×C4⋊C4C22×C414yes—
241C11×C4⋊C4C22×C411yescharacteristic
242C11×C4⋊C4C22×C412yes—
243C11×C4⋊C4C22×C412yes—
244C11×C4⋊C4C22×C414yes—
245C11×C4⋊C4C22×C412yes—
246C11×C4⋊C4C22×C414yes—
247C11×C4⋊C4C22×C411yescharacteristic
248C11×C4⋊C4C22×C412yes—
249C11×C4⋊C4C22×C412yes—
250C11×C4⋊C4C22×C411yescharacteristic
251C11×C4⋊C4C22×C414yes—
252C11×C4⋊C4C22×C414yes—
253C11×C4⋊C4C22×C414yes—
254C11×C4⋊C4C22×C412yes—
255C11×C4⋊C4C22×C414yes—
256C11×C22⋊C4C22×C412yes—
257C11×C22⋊C4C22×C412yes—
258C11×C22⋊C4C22×C414yes—
259C11×C22⋊C4C22×C414yes—
260C11×C22⋊C4C22×C412yes—
261C11×C22⋊C4C22×C414yes—
262C42×C11C22×C412yes—
263C42×C11C22×C414yes—
264C42×C11C22×C411yescharacteristic
265C42×C11C22×C412yes—
266C42×C11C22×C414yes—
267C42×C11C22×C412yes—
268C42×C11C22×C412yes—
269C42×C11C22×C411yescharacteristic
270C42×C11C2411yescharacteristic
271C42×C11C2411yescharacteristic
272C42×C11C2412yes—
273C42×C11C2414yes—
274C42×C11C2412yes—
275C42×C11C2412yes—
276#4318—22no—
277#4318—22no—
278#4318—24no—
279C2×C11⋊C8—22no—
280C2×C11⋊C8—24no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8C2411yescharacteristic
283C2×C11⋊C8C2412yes—
284C2×C11⋊C8C2412yes—
285C2×C11⋊C8C2414yes—
286C2×C11⋊C8C2411yescharacteristic
287C2×C11⋊C8C2411yescharacteristic
288C2×C11⋊C8C2411yescharacteristic
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291Q8×#41D1111yescharacteristic
292#2987—114no—
293#2986—112no—
294#2985—112no—
295#2985—114no—
296#2984—112no—
297#2983—112no—
298Q8×M16—111no—
299#2962—111no—
300#2962—112no—
301#2961—112no—
302#2960—111no—
303C2×#446—111no—
304#2925—111no—
305#2925—112no—
306#2923—112no—
307#2922—111no—
308C23×C11C23×C412yes—
309C23×C11C23×C411yescharacteristic
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—22no—
313Q8×C11—24no—
314Q8×C11—42no—
315Q8×C11—44no—
316Q8×C11—42no—
317Q8×C11—44no—
318D4×C11—24no—
319D4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—41no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—44no—
328C2×C4×C11—42no—
329C2×C4×C11—44no—
330C2×C4×C11C23×C412yes—
331C2×C4×C11C23×C411yescharacteristic
332C2×C4×C11C23×C412yes—
333C2×C4×C11C23×C412yes—
334C2×C4×C11C23×C412yes—
335C2×C4×C11C23×C411yescharacteristic
336C2×C4×C11C23×C414yes—
337C2×C4×C11C23×C412yes—
338C2×C4×C11C23×C414yes—
339C2×C4×C11C23×C412yes—
340C2×C4×C11C23×C412yes—
341C2×C4×C11C23×C411yescharacteristic
342C2×C4×C11C23×C411yescharacteristic
343C2×C4×C11C23×C411yescharacteristic
344C2×C4×C112−1+412yes—
345C2×C4×C112−1+412yes—
346C2×C4×C11C2511yescharacteristic
347C11⋊C8—21no—
348C11⋊C8—21no—
349C11⋊C8—22no—
350C11⋊C8—22no—
351C11⋊C8—21no—
352C11⋊C8—21no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C11⋊C8—24no—
356Q82Dic1111yescharacteristic
357#557Dic1111yescharacteristic
358#557Dic1112yes—
359#554Dic1112yes—
360#554Dic1111yescharacteristic
361#554Dic1114yes—
362#554Dic1112yes—
363D4×Q8Dic1111yescharacteristic
364D4×Q8Dic1112yes—
365#533C2×D1111yescharacteristic
366#533C2×D1112yes—
367#533C2×D1112yes—
368#533C2×D1114yes—
369C4×#41C2×D1111yescharacteristic
370C4×#41C2×D1112yes—
371C2×C4×Q8C2×D1111yescharacteristic
372C2×C4×Q8C2×D1112yes—
373#446—111no—
374#446—111no—
375#446—111no—
376#446—112no—
377#446—111no—
378#446—112no—
379#446—112no—
380#446—112no—
381#446—114no—
382#446—114no—
383#446—114no—
384#446—114no—
385#446—112no—
386#446—114no—
387#446—114no—
388#446—114no—
389#446—114no—
390#446—112no—
391#446—114no—
392C8×Q8—112no—
393C8×Q8—112no—
394C8×Q8—112no—
395C8×Q8—114no—
396C8×Q8—112no—
397#433—112no—
398#433—112no—
399#433—114no—
400#433—114no—
401#433—114no—
402#433—114no—
403#433—114no—
404#432—114no—
405#432—114no—
406#432—114no—
407#432—112no—
408#431—112no—
409#431—112no—
410#431—112no—
411#431—114no—
412#424—111no—
413#424—111no—
414#424—112no—
415#424—112no—
416#423—111no—
417#423—112no—
418C2×C4⋊C8—111no—
419C2×C4⋊C8—112no—
420#408—111no—
421#408—111no—
422#408—112no—
423#405—112no—
424#405—112no—
425#405—112no—
426C4×M16—111no—
427C4×M16—112no—
428C2×#97—112no—
429C2×C4×C8—111no—
430C22×C11—21no—
431C22×C11—21no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11#51912yes—
436C22×C11C24×C411yescharacteristic
437C4×C11—22no—
438C4×C11—21no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—24no—
443C4×C11—21no—
444C4×C11—22no—
445C4×C11—21no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—24no—
449C4×C11#51912yes—
450C4×C11#56812yes—
451C4×C11C2×2−1+411yescharacteristic
452C4×C11C2×2−1+411yescharacteristic
453C2×#41C22×D1111yescharacteristic
454C22×Q8C2×Dic1111yescharacteristic
455C22×Q8C2×Dic1112yes—
456C2×M16—111no—
457C2×M16—111no—
458C2×M16—112no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8—112no—
462C4⋊Q8C2×Dic1111yescharacteristic
463C4⋊Q8C2×Dic1112yes—
464C4⋊Q8C2×Dic1112yes—
465C4⋊Q8C2×Dic1114yes—
466C4⋊Q8C2×Dic1111yescharacteristic
467C4⋊Q8C2×Dic1112yes—
468C4⋊Q8C2×Dic1112yes—
469C4⋊Q8C2×Dic1114yes—
470#125C2×Dic1112yes—
471#125C2×Dic1112yes—
472#125C2×Dic1112yes—
473#125C2×Dic1114yes—
474#125C2×Dic1114yes—
475#125C2×Dic1114yes—
476C22⋊Q8C2×Dic1112yes—
477C22⋊Q8C2×Dic1112yes—
478C22⋊Q8C2×Dic1112yes—
479C22⋊Q8C2×Dic1114yes—
480C22⋊Q8C2×Dic1114yes—
481C22⋊Q8C2×Dic1114yes—
482C22⋊Q8C2×Dic1112yes—
483C22⋊Q8C2×Dic1114yes—
484C22⋊Q8C2×Dic1114yes—
485C22⋊Q8C2×Dic1114yes—
486C22⋊Q8C2×Dic1114yes—
487C4×Q8C2×Dic1111yescharacteristic
488C4×Q8C2×Dic1112yes—
489C4×Q8C2×Dic1111yescharacteristic
490C4×Q8C2×Dic1112yes—
491C4×Q8C2×Dic1112yes—
492C4×Q8C2×Dic1114yes—
493C4×Q8C2×Dic1111yescharacteristic
494C4×Q8C2×Dic1112yes—
495C4×Q8C2×Dic1111yescharacteristic
496C4×Q8C2×Dic1112yes—
497C4×Q8C22×D1111yescharacteristic
498C4×Q8C22×D1111yescharacteristic
499C4×Q8C22×D1112yes—
500C4×Q8C22×D1112yes—
501C4×Q8C22×D1114yes—
502C4×Q8C22×D1112yes—
503C4×Q8C22×D1114yes—
504C4×D4C2×Dic1112yes—
505C4×D4C2×Dic1111yescharacteristic
506C4×D4C2×Dic1114yes—
507C4×D4C2×Dic1112yes—
508C4×D4C2×Dic1112yes—
509C4×D4C2×Dic1111yescharacteristic
510C4×D4C2×Dic1114yes—
511C4×D4C2×Dic1112yes—
512#117C22×D1111yescharacteristic
513#117C22×D1112yes—
514#117C22×D1112yes—
515#117C22×D1114yes—
516C2×C4⋊C4C2×Dic1111yescharacteristic
517C2×C4⋊C4C2×Dic1112yes—
518C2×C4⋊C4C2×Dic1112yes—
519C2×C4⋊C4C2×Dic1114yes—
520C2×C42C22×D1111yescharacteristic
521C2×C42C22×D1112yes—
522C2×C42C22×D1112yes—
523C2×C42C22×D1114yes—
524C4⋊C8—111no—
525C4⋊C8—112no—
526C4⋊C8—111no—
527C4⋊C8—112no—
528C4⋊C8—112no—
529C4⋊C8—112no—
530C4⋊C8—112no—
531C4⋊C8—112no—
532C4⋊C8—114no—
533C4⋊C8—112no—
534C4⋊C8—114no—
535C4⋊C8—112no—
536C4⋊C8—112no—
537C4⋊C8—112no—
538C4⋊C8—112no—
539C4⋊C8—114no—
540C4⋊C8—114no—
541C4⋊C8—114no—
542C4⋊C8—114no—
543C22⋊C8—112no—
544C22⋊C8—112no—
545C22⋊C8—112no—
546C22⋊C8—112no—
547C22⋊C8—114no—
548C22⋊C8—114no—
549#97—112no—
550#97—112no—
551#97—112no—
552#97—112no—
553#97—114no—
554#97—112no—
555#97—114no—
556#97—114no—
557#97—114no—
558C4×C8—111no—
559C4×C8—111no—
560C4×C8—111no—
561C4×C8—111no—
562C4×C8—112no—
563C4×C8—114no—
564C4×C8—114no—
565C4×C8—114no—
566C4×C8—114no—
567C2×C11—22no—
568C2×C11—42no—
569C2×C11C2×#51911yescharacteristic
570C2×C11C2×#56811yescharacteristic
571C2×C11#357311yescharacteristic
572#41—22no—
573#41—22no—
574C2×Q8—42no—
575C2×Q8—44no—
576C2×Q8C22×Dic1111yescharacteristic
577C2×Q8C22×Dic1111yescharacteristic
578C2×Q8C22×Dic1112yes—
579C2×Q8C22×Dic1111yescharacteristic
580C2×Q8C22×Dic1112yes—
581C2×Q8C22×Dic1114yes—
582C2×Q8C22×Dic1112yes—
583C2×Q8C22×Dic1114yes—
584C2×D4C22×Dic1112yes—
585C2×D4C22×Dic1111yescharacteristic
586C22×C4C22×Dic1112yes—
587C22×C4C22×Dic1111yescharacteristic
588C22×C4C22×Dic1112yes—
589C22×C4C22×Dic1114yes—
590C22×C4C22×Dic1111yescharacteristic
591C22×C4C22×Dic1112yes—
592C22×C4C22×Dic1114yes—
593C22×C4C22×Dic1112yes—
594C22×C4C23×D1112yes—
595C22×C4C23×D1111yescharacteristic
596M16—222no—
597M16—222no—
598M16—224no—
599C2×C8—111no—
600C2×C8—112no—
601C2×C8—112no—
602C2×C8—114no—
603C2×C8—111no—
604C2×C8—111no—
605C2×C8—111no—
606C2×C8—112no—
607C2×C8—112no—
608C2×C8—222no—
609C2×C8—224no—
610C2×C8—222no—
611C4⋊C4C22×Dic1112yes—
612C4⋊C4C22×Dic1111yescharacteristic
613C4⋊C4C22×Dic1112yes—
614C4⋊C4C22×Dic1114yes—
615C4⋊C4C22×Dic1112yes—
616C4⋊C4C22×Dic1114yes—
617C4⋊C4C22×Dic1112yes—
618C4⋊C4C22×Dic1114yes—
619C4⋊C4C22×Dic1112yes—
620C4⋊C4C22×Dic1114yes—
621C4⋊C4C22×Dic1111yescharacteristic
622C4⋊C4C22×Dic1112yes—
623C4⋊C4C22×Dic1112yes—
624C4⋊C4C22×Dic1114yes—
625C4⋊C4C22×Dic1112yes—
626C4⋊C4C22×Dic1114yes—
627C4⋊C4C22×Dic1111yescharacteristic
628C4⋊C4C22×Dic1112yes—
629C4⋊C4C22×Dic1111yescharacteristic
630C4⋊C4C22×Dic1112yes—
631C4⋊C4C22×Dic1114yes—
632C4⋊C4C22×Dic1114yes—
633C4⋊C4C22×Dic1114yes—
634C4⋊C4C22×Dic1112yes—
635C4⋊C4C22×Dic1114yes—
636C22⋊C4C22×Dic1112yes—
637C22⋊C4C22×Dic1112yes—
638C22⋊C4C22×Dic1114yes—
639C22⋊C4C22×Dic1114yes—
640C22⋊C4C22×Dic1112yes—
641C22⋊C4C22×Dic1114yes—
642C42C22×Dic1112yes—
643C42C22×Dic1114yes—
644C42C22×Dic1111yescharacteristic
645C42C22×Dic1112yes—
646C42C22×Dic1114yes—
647C42C22×Dic1112yes—
648C42C22×Dic1112yes—
649C42C22×Dic1111yescharacteristic
650C42C23×D1111yescharacteristic
651C42C23×D1111yescharacteristic
652C42C23×D1112yes—
653C42C23×D1114yes—
654C42C23×D1112yes—
655C42C23×D1112yes—
656C11#6025411yescharacteristic, complemented, Sylow
657C23C23×Dic1112yes—
658C23C23×Dic1111yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—24no—
663Q8—42no—
664Q8—44no—
665Q8—42no—
666Q8—44no—
667D4—24no—
668D4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4#6704012yes—
680C2×C4#6704012yes—
681C2×C4C23×Dic1112yes—
682C2×C4C23×Dic1111yescharacteristic
683C2×C4C23×Dic1112yes—
684C2×C4C23×Dic1112yes—
685C2×C4C23×Dic1112yes—
686C2×C4C23×Dic1111yescharacteristic
687C2×C4C23×Dic1114yes—
688C2×C4C23×Dic1112yes—
689C2×C4C23×Dic1114yes—
690C2×C4C23×Dic1112yes—
691C2×C4C23×Dic1112yes—
692C2×C4C23×Dic1111yescharacteristic
693C2×C4C23×Dic1111yescharacteristic
694C2×C4C23×Dic1111yescharacteristic
695C2×C4C24×D1111yescharacteristic
696C8—221no—
697C8—221no—
698C8—222no—
699C8—222no—
700C8—221no—
701C8—221no—
702C8—222no—
703C8—222no—
704C8—224no—
705C22—21no—
706C22—21no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22#1062334312yes—
711C22C24×Dic1111yescharacteristic
712C4—21no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—24no—
717C4—21no—
718C4—22no—
719C4—21no—
720C4—22no—
721C4—22no—
722C4—24no—
723C4—22no—
724C4#1062334312yes—
725C4#1062335012yes—
726C4C2×#6704011yescharacteristic
727C4C2×#6704011yescharacteristic
728C2—22no—
729C2—42no—
730C2C2×#1062334311yescharacteristic
731C2C2×#1062335011yescharacteristic
732C2#1308332811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingQ8×C11×#41C2
prime radicalC2×C11×#41C23
cosocleC2×C4×C11C25
hypercenterQ8×#41D11
hypocenterC11#60254
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #13077722C2semidirect
2. #13077718C2semidirect
3. #13077711C2semidirect
4. #13077711C2semidirect
5. #13077705C2semidirect
6. #13077701C2semidirect
7. Q8×#4318C2semidirect
8. #13077565C2semidirect
9. #13077565C2semidirect
10. #13077557C2semidirect
11. #13077551C2semidirect
12. C2×#10622637C2semidirect
656. C11#60254semidirect

Maximal subgroups

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

subgroupindex
#130777222
#130777182
#130777112
#130777052
#130777012
Q8×#43182
#130775652
#130775572
#130775512
C2×#106226372
#130772822
#130772672
#130772602
Q8×C11×#412
#6025411