Finite Group Databasebeta

← #14926100

Subgroups — #14926100

Order 2816.

1940 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073368C212yesmaximal, complemented
2#13073320C212yesmaximal, complemented
3#13073299C212yesmaximal, complemented
4#13073236C212yesmaximal, complemented
5#13072677C212yesmaximal, complemented
6#13072638C212yesmaximal, complemented
7#13072578C212yesmaximal
8#13072539C212yesmaximal, complemented
9#13071910C211yesmaximal, characteristic, complemented
10#13071900C211yesmaximal, characteristic, complemented
11#13071884C211yesmaximal, characteristic, complemented
12C4×#66932C212yesmaximal, complemented
13C4×#66989C212yesmaximal, complemented
14C4×#66931C212yesmaximal, complemented
15C4×#66988C212yesmaximal, complemented
16#13071114C211yesmaximal, characteristic, complemented
17C4×#66940C211yesmaximal, characteristic, complemented
18C4×D4×Dic11C211yesmaximal, characteristic, complemented
19C11×#2392C211yesmaximal, characteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2212yes—
22C2×C11×#117C2211yescharacteristic
23C2×#66989C2212yes—
24C2×#66988C2212yes—
25C2×D4×Dic11C2212yes—
26C22×C4×Dic11C2212yes—
27C2×#66940C2212yes—
28C2×#66932C2212yes—
29C2×#66931C2212yes—
30C2×C4×Dic22C2211yescharacteristic
31C2×C4×Dic22C2212yes—
32C11×#398C2211yescharacteristic
33C11×#397C2211yescharacteristic
34C11×#396C2212yes—
35C11×#394C2211yescharacteristic
36C11×#394C2212yes—
37C11×#392C2211yescharacteristic
38C4×C11×C4⋊C4C2211yescharacteristic
39C4×C11×C22⋊C4C2212yes—
40#10622835C2212yes—
41#10622834C2212yes—
42#10622833C2212yes—
43C4×C22⋊Dic11C2211yescharacteristic
44C4×C22⋊Dic11C2211yescharacteristic
45C4×C22⋊Dic11C2212yes—
46C4×C22⋊Dic11C2212yes—
47C4×C22⋊Dic11C2212yes—
48C4×C22⋊Dic11C2212yes—
49#10622599C2211yescharacteristic
50#10622597C2212yes—
51#10622597C2212yes—
52#10622595C2212yes—
53#10622594C2212yes—
54#10622594C2212yes—
55#10622592C2211yescharacteristic
56#10622592C2212yes—
57#10622591C2212yes—
58#10622591C2212yes—
59#10622590C2212yes—
60C4⋊C4×Dic11C2212yes—
61C4⋊C4×Dic11C2212yes—
62#10622587C2212yes—
63#10622566C2212yes—
64#10622564C2212yes—
65#10622564C2212yes—
66#10622564C2212yes—
67#10622563C2212yes—
68#10622562C2211yescharacteristic
69#10622561C2212yes—
70#10622560C2211yescharacteristic
71#10622560C2212yes—
72#10622559C2212yes—
73#10622559C2212yes—
74#10622558C2212yes—
75#10622558C2212yes—
76#10622558C2212yes—
77#10622558C2212yes—
78#10622558C2212yes—
79#10622557C2212yes—
80#10622557C2212yes—
81#10622557C2212yes—
82#10622556C2212yes—
83#10622555C2212yes—
84C22⋊C4×Dic11C2212yes—
85C22⋊C4×Dic11C2212yes—
86C4×C4⋊Dic11C2211yescharacteristic
87C4×C4⋊Dic11C2211yescharacteristic
88C4×C4⋊Dic11C2211yescharacteristic
89#10622545C2211yescharacteristic
90C4×Dic11⋊C4C2212yes—
91C4×Dic11⋊C4C2212yes—
92C4×Dic11⋊C4C2212yes—
93C42×Dic11C2211yescharacteristic
94C42×Dic11C2212yes—
95#10622270C2212yes—
96#10622269C2212yes—
97#10622268C2212yes—
98#10622268C2212yes—
99#10622267C2212yes—
100#10622266C2212yes—
101#10622265C2212yes—
102#10622264C2212yes—
103#10622262C2212yes—
104#10622262C2212yes—
105#10622260C2212yes—
106#10622259C2212yes—
107C22×D4×C11C2311yescharacteristic
108C22×D4×C11C2312yes—
109C23×C4×C11C2312yes—
110C23×C4×C11C2311yescharacteristic
111C23×Dic11C2312yes—
112C23×Dic11C2312yes—
113C22×Dic22C2311yescharacteristic
114C22×Dic22C2312yes—
115C4×D4×C11—24no—
116C4×D4×C11—44no—
117C11×#117—24no—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2312yes—
123C2×C11×C22⋊C4C2312yes—
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4C2311yescharacteristic
128C2×C11×C22⋊C4C2312yes—
129C2×C11×C22⋊C4C2312yes—
130C2×C42×C11C2312yes—
131C2×C42×C11C2311yescharacteristic
132C2×C42×C11C2311yescharacteristic
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×C22⋊Dic11C2312yes—
138C2×C22⋊Dic11C2312yes—
139C2×C22⋊Dic11C2312yes—
140C2×C22⋊Dic11C2312yes—
141C2×C22⋊Dic11C2312yes—
142C2×C22⋊Dic11C2312yes—
143#66989—28no—
144#66988—28no—
145D4×Dic11—28no—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2312yes—
148C2×C4⋊Dic11C2312yes—
149C2×C4⋊Dic11C2312yes—
150C2×C4⋊Dic11C2312yes—
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2312yes—
156C2×Dic11⋊C4C2312yes—
157C2×Dic11⋊C4C2312yes—
158C2×Dic11⋊C4C2312yes—
159C2×Dic11⋊C4C2312yes—
160C2×C4×Dic11—44no—
161C2×C4×Dic11C2311yescharacteristic
162C2×C4×Dic11C2312yes—
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2312yes—
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2312yes—
168C2×C4×Dic11C2312yes—
169C2×C4×Dic11C2312yes—
170C2×C4×Dic11C2311yescharacteristic
171C2×C4×Dic11C2311yescharacteristic
172C2×C4×Dic11C2311yescharacteristic
173C2×C4×Dic11C2312yes—
174C2×C4×Dic11C2312yes—
175#66940—28no—
176#66932—28no—
177#66931—28no—
178C4×Dic22—24no—
179C4×Dic22—44no—
180C11×#95C2312yes—
181C11×#95C2312yes—
182C11×#95C2311yescharacteristic
183C11×#95C2311yescharacteristic
184C11⋊#95C2312yes—
185C11⋊#95C2312yes—
186C11⋊#95C2312yes—
187C11⋊#95C2312yes—
188C11⋊#95C2312yes—
189C11⋊#95C2312yes—
190C11⋊#95C2312yes—
191C11⋊#95C2312yes—
192C11⋊#95C2312yes—
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2311yescharacteristic
201C11⋊#95C2311yescharacteristic
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206#34968—111nomaximal, Sylow
207C24×C11C2411yescharacteristic
208C24×C11C2412yes—
209C2×D4×C11—24no—
210C2×D4×C11—24no—
211C2×D4×C11—22no—
212C2×D4×C11—24no—
213C2×D4×C11—42no—
214C22×C4×C11—22no—
215C22×C4×C11—24no—
216C22×C4×C11—24no—
217C22×C4×C11—22no—
218C22×C4×C11—24no—
219C22×C4×C11—22no—
220C22×C4×C11C2411yescharacteristic
221C22×C4×C11C2412yes—
222C22×C4×C11C2411yescharacteristic
223C22×C4×C11C2411yescharacteristic
224C22×C4×C11C2412yes—
225C22×C4×C11C2411yescharacteristic
226C22×C4×C11C2411yescharacteristic
227C22×C4×C11C2412yes—
228C22×C4×C11C2411yescharacteristic
229C22×Dic11—24no—
230C22×Dic11—24no—
231C22×Dic11—24no—
232C22×Dic11—24no—
233C22×Dic11—42no—
234C22×Dic11—42no—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C2×Dic22—24no—
244C2×Dic22—24no—
245C2×Dic22—22no—
246C2×Dic22—24no—
247C2×Dic22—42no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—22no—
250C11×C4⋊C4—22no—
251C11×C4⋊C4—22no—
252C11×C4⋊C4—42no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—22no—
256C11×C22⋊C4—22no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—42no—
259C11×C22⋊C4—42no—
260C42×C11—22no—
261C42×C11—24no—
262C42×C11#4114yes—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
272C22⋊Dic11#4118yes—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276C4⋊Dic11—22no—
277C4⋊Dic11—42no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—42no—
285Dic11⋊C4—42no—
286Dic11⋊C4#4118yes—
287C4×Dic11—24no—
288C4×Dic11—24no—
289C4×Dic11—24no—
290C4×Dic11—24no—
291C4×Dic11—24no—
292C4×Dic11—24no—
293C4×Dic11—24no—
294C4×Dic11—22no—
295C4×Dic11—24no—
296C4×Dic11—22no—
297C4×Dic11—22no—
298C4×Dic11—22no—
299C4×Dic11—42no—
300C4×Dic11—42no—
301#2525—112no—
302#2521—112no—
303#2520—112no—
304#2515—112no—
305#2468—112no—
306#2465—112no—
307#2461—112no—
308#2458—112no—
309#2399—111no—
310#2398—111no—
311#2396—111no—
312#2392D1111yescharacteristic
313C4×#126—112no—
314C4×#124—112no—
315C4×C22⋊Q8—112no—
316C4×#123—112no—
317#2298—111no—
318C42×Q8—111no—
319C42×D4—111no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11C2×#4114yes—
332C23×C11C2511yescharacteristic
333D4×C11—28no—
334D4×C11—48no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—21no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—48no—
353C2×C4×C11—44no—
354C2×C4×C11C2×#4112yes—
355C2×C4×C11C2×#4112yes—
356C2×C4×C11C2×#4112yes—
357C2×C4×C11C2×#4114yes—
358C2×C4×C11H(5,𝔽2)12yes—
359C2×C4×C112−1+412yes—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—48no—
381C2×Dic11—48no—
382C2×Dic11C2×#4114yes—
383C2×Dic11C2×#4114yes—
384C2×Dic11C2×#4114yes—
385C2×Dic11C2×#4114yes—
386Dic22—28no—
387Dic22—48no—
388C2×#126—112no—
389C2×#124—112no—
390C2×#123—112no—
391C2×C22⋊Q8—112no—
392C2×C4×Q8—112no—
393C2×C4×Q8—111no—
394C2×C4×Q8—112no—
395C2×C4×D4—112no—
396C2×C4×D4C2×D1111yescharacteristic
397C2×C4×D4C2×D1112yes—
398C2×#117C2×D1111yescharacteristic
399C22×C42—112no—
400#400—111no—
401#400—112no—
402#399—111no—
403#398—112no—
404#398—112no—
405#398—112no—
406#398C2×D1111yescharacteristic
407#397—112no—
408#397C2×D1111yescharacteristic
409#396—112no—
410#396C2×D1112yes—
411#395—111no—
412#395—112no—
413#395—112no—
414#394—112no—
415#394C2×D1112yes—
416#394C2×D1111yescharacteristic
417#393—111no—
418#393—112no—
419#392C2×D1111yescharacteristic
420#391—112no—
421#391—112no—
422#390—112no—
423#389—112no—
424#388—112no—
425#388—112no—
426#388—112no—
427#388—112no—
428#388—112no—
429#388—112no—
430#388—112no—
431#388—112no—
432#388—112no—
433#388—112no—
434#388—112no—
435#387—112no—
436#387—112no—
437#387—112no—
438#387—112no—
439#387—112no—
440#387—112no—
441#387—112no—
442#387—112no—
443#387—112no—
444#386—112no—
445#385—112no—
446#385—112no—
447#385—112no—
448#383—112no—
449#382—112no—
450#381—112no—
451#380—112no—
452C4×C4⋊C4—112no—
453C4×C4⋊C4—112no—
454C4×C4⋊C4—111no—
455C4×C4⋊C4—112no—
456C4×C4⋊C4—112no—
457C4×C4⋊C4—112no—
458C4×C4⋊C4—111no—
459C4×C4⋊C4—111no—
460C4×C4⋊C4—112no—
461C4×C4⋊C4—112no—
462C4×C4⋊C4C2×D1111yescharacteristic
463C4×C22⋊C4—112no—
464C4×C22⋊C4—112no—
465C4×C22⋊C4—112no—
466C4×C22⋊C4—112no—
467C4×C22⋊C4—111no—
468C4×C22⋊C4—111no—
469C4×C22⋊C4—112no—
470C4×C22⋊C4—112no—
471C4×C22⋊C4C2×D1112yes—
472#376—111no—
473C43—112no—
474C43—111no—
475C22×C11—24no—
476C22×C11—24no—
477C22×C11—24no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11C22×#4111yescharacteristic
488C22×C11C22×#4112yes—
489C22×C11C22×#4112yes—
490C22×C11C2×H(5,𝔽2)11yescharacteristic
491C22×C11C2×2−1+411yescharacteristic
492C4×C11—22no—
493C4×C11—22no—
494C4×C11—24no—
495C4×C11—41no—
496C4×C11—41no—
497C4×C11—42no—
498C4×C11—41no—
499C4×C11—42no—
500C4×C11#54214yes—
501Dic11—24no—
502Dic11—24no—
503Dic11—24no—
504Dic11—24no—
505Dic11—42no—
506Dic11—42no—
507Dic11—42no—
508Dic11—42no—
509C22×Q8—111no—
510C22×Q8—112no—
511C22×D4C22×D1111yescharacteristic
512C22×D4C22×D1112yes—
513C23×C4—112no—
514C23×C4—112no—
515C23×C4C22×D1111yescharacteristic
516C23×C4C22×D1112yes—
517#126—228no—
518#124—228no—
519#123—228no—
520C22⋊Q8—228no—
521C4×Q8—228no—
522C4×Q8—224no—
523C4×Q8—444no—
524C4×D4—24no—
525C4×D4—44no—
526C4×D4—228no—
527#117—24no—
528C2×C4⋊C4—112no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—112no—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—112no—
535C2×C4⋊C4—112no—
536C2×C4⋊C4—112no—
537C2×C4⋊C4—112no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—112no—
540C2×C4⋊C4—112no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4C22×D1111yescharacteristic
543C2×C4⋊C4C22×D1111yescharacteristic
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C4⋊C4C22×D1112yes—
546C2×C4⋊C4C22×D1112yes—
547C2×C22⋊C4—112no—
548C2×C22⋊C4—112no—
549C2×C22⋊C4—112no—
550C2×C22⋊C4—112no—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4C22×D1111yescharacteristic
559C2×C22⋊C4C22×D1112yes—
560C2×C22⋊C4C22×D1112yes—
561C2×C22⋊C4C22×D1112yes—
562C2×C22⋊C4C22×D1112yes—
563C2×C22⋊C4C22×D1112yes—
564C2×C42—112no—
565C2×C42—112no—
566C2×C42—112no—
567C2×C42—112no—
568C2×C42—112no—
569C2×C42—112no—
570C2×C42—111no—
571C2×C42—112no—
572C2×C42—112no—
573C2×C42—111no—
574C2×C42—111no—
575C2×C42—111no—
576C2×C42—112no—
577C2×C42—112no—
578C2×C42—444no—
579C2×C42C22×D1111yescharacteristic
580C2×C42C22×D1112yes—
581C2×C42C22×D1111yescharacteristic
582#95—112no—
583#95—112no—
584#95—112no—
585#95—112no—
586#95—111no—
587#95—111no—
588#95—112no—
589#95—112no—
590#95—112no—
591#95—112no—
592#95—112no—
593#95—112no—
594#95—112no—
595#95—112no—
596#95—112no—
597#95—112no—
598#95—112no—
599#95—112no—
600#95—112no—
601#95—112no—
602#95—112no—
603#95—112no—
604#95C22×D1112yes—
605#95C22×D1112yes—
606#95C22×D1111yescharacteristic
607#95C22×D1111yescharacteristic
608C2×C11—44no—
609C2×C11—81no—
610C2×C11#344411yescharacteristic
611C2×C11#344411yescharacteristic
612C2×C11C2×#54211yescharacteristic
613C2×C11#348112yes—
614C2×C11#348212yes—
615C24C23×D1111yescharacteristic
616C24C23×D1112yes—
617C2×Q8—224no—
618C2×Q8—224no—
619C2×Q8—222no—
620C2×Q8—224no—
621C2×Q8—442no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—42no—
627C22×C4—22no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—22no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—224no—
645C22×C4—442no—
646C22×C4—442no—
647C22×C4C23×D1111yescharacteristic
648C22×C4C23×D1112yes—
649C22×C4C23×D1111yescharacteristic
650C22×C4C23×D1111yescharacteristic
651C22×C4C23×D1112yes—
652C22×C4C23×D1111yescharacteristic
653C22×C4C23×D1111yescharacteristic
654C22×C4C23×D1112yes—
655C22×C4C23×D1111yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—24no—
660C4⋊C4—42no—
661C4⋊C4—118no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—222no—
671C4⋊C4—224no—
672C4⋊C4—442no—
673C4⋊C4—442no—
674C4⋊C4—442no—
675C22⋊C4—24no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—118no—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C42—22no—
693C42—24no—
694C42—224no—
695C42—224no—
696C42—224no—
697C42—224no—
698C42—224no—
699C42—224no—
700C42—222no—
701C42—224no—
702C42—222no—
703C42—224no—
704C42—222no—
705C42—222no—
706C42—442no—
707C42—442no—
708C42#434114yes—
709C11#3496811yescharacteristic, complemented, Sylow
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—22no—
720C23—21no—
721C23#41×D1114yes—
722C23C24×D1111yescharacteristic
723Q8—228no—
724Q8—448no—
725D4—28no—
726D4—48no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—114no—
747C2×C4—114no—
748C2×C4—114no—
749C2×C4—114no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—448no—
771C2×C4—448no—
772C2×C4C2×#434112yes—
773C2×C4C2×#434112yes—
774C2×C4C2×#434112yes—
775C2×C4#6703712yes—
776C2×C4#41×D1114yes—
777C2×C4#6704312yes—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—41no—
790C22C22×#434111yescharacteristic
791C22C2×#6703711yescharacteristic
792C22C2×#41×D1112yes—
793C22C2×#41×D1112yes—
794C22C2×#6704311yescharacteristic
795C4—22no—
796C4—22no—
797C4—24no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—41no—
803C4—224no—
804C4—224no—
805C4—224no—
806C4—224no—
807C4—442no—
808C4—442no—
809C4—442no—
810C4—442no—
811C4#1062313414yes—
812C2—44no—
813C2—81no—
814C2#1308190811yescharacteristic
815C2#1308191111yescharacteristic
816C2C2×#1062313411yescharacteristic
817C2#1308221812yes—
818C2#1308222912yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2392C2
prime radicalC11×#392C22
hypercenter#2392D11
hypocenterC11#34968
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. #13073368C2semidirect
2. #13073320C2semidirect
3. #13073299C2semidirect
4. #13073236C2semidirect
5. #13072677C2semidirect
6. #13072638C2semidirect
8. #13072539C2semidirect
9. #13071910C2semidirect
10. #13071900C2semidirect
11. #13071884C2semidirect
12. C4×#66932C2semidirect
13. C4×#66989C2semidirect
14. C4×#66931C2semidirect
15. C4×#66988C2semidirect
16. #13071114C2semidirect
17. C4×#66940C2semidirect
18. C4×D4×Dic11C2semidirect
709. C11#34968semidirect

Maximal subgroups

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

subgroupindex
#130733682
#130733202
#130732992
#130732362
#130726772
#130726382
#130725782
#130725392
#130719102
#130719002
#130718842
C4×#669322
C4×#669892
C4×#669312
C4×#669882
#130711142
C4×#669402
C4×D4×Dic112
C11×#23922
#3496811