Finite Group Databasebeta

← #14925989

Subgroups — #14925989

Order 2816.

1954 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074010C212yesmaximal, complemented
2#13073879C212yesmaximal, complemented
3#13073699C212yesmaximal, complemented
4#13073657C212yesmaximal, complemented
5#13073348C211yesmaximal, characteristic, complemented
6#13073265C211yesmaximal, characteristic, complemented
7#13072646C212yesmaximal, complemented
8#13072606C211yesmaximal, characteristic
9#13072563C212yesmaximal, complemented
10#13071885C211yesmaximal, characteristic, complemented
11#13071872C212yesmaximal, complemented
12#13071851C211yesmaximal, characteristic
13#13071175C212yesmaximal, complemented
14#13071170C212yesmaximal, complemented
15#13071148C212yesmaximal, complemented
16#123×Dic11C212yesmaximal, complemented
17#13071095C211yesmaximal, characteristic, complemented
18C4×D4×Dic11C212yesmaximal, complemented
19C11×#2455C211yesmaximal, characteristic
20C2×C11×#123C2212yes—
21C2×C4×D4×C11C2212yes—
22C2×D4×Dic11C2212yes—
23C2×D4×Dic11C2212yes—
24C2×D4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C2×#66943C2212yes—
28C2×#66940C2211yescharacteristic
29C2×#66932C2212yes—
30C2×#66931C2212yes—
31C2×#66930C2211yescharacteristic
32C2×#66930C2211yescharacteristic
33C11×#399C2211yescharacteristic
34C11×#394C2212yes—
35C11×#392C2211yescharacteristic
36C11×#389C2212yes—
37C11×#388C2212yes—
38C11×#385C2212yes—
39C11×#385C2211yescharacteristic
40#10622835C2212yes—
41#10622835C2212yes—
42#10622835C2211yescharacteristic
43#10622833C2212yes—
44#10622824C2212yes—
45#10622823C2211yescharacteristic
46#10622823C2212yes—
47C4×C22⋊Dic11C2212yes—
48C4×C22⋊Dic11C2212yes—
49#10622597C2212yes—
50#10622595C2211yescharacteristic
51#10622594C2212yes—
52#10622594C2212yes—
53#10622593C2212yes—
54#10622591C2212yes—
55#10622591C2212yes—
56#10622591C2212yes—
57#10622591C2212yes—
58#10622590C2212yes—
59C4⋊C4×Dic11C2212yes—
60C4⋊C4×Dic11C2212yes—
61C4⋊C4×Dic11C2212yes—
62C4⋊C4×Dic11C2212yes—
63C4⋊C4×Dic11C2212yes—
64#10622585C2212yes—
65#10622585C2212yes—
66#10622566C2212yes—
67#10622566C2211yescharacteristic
68#10622565C2212yes—
69#10622565C2212yes—
70#10622564C2212yes—
71#10622564C2212yes—
72#10622563C2212yes—
73#10622563C2211yescharacteristic
74#10622562C2212yes—
75#10622561C2212yes—
76#10622561C2212yes—
77#10622560C2211yescharacteristic
78#10622559C2211yescharacteristic
79#10622558C2212yes—
80#10622557C2212yes—
81#10622555C2212yes—
82C22⋊C4×Dic11C2212yes—
83C22⋊C4×Dic11C2212yes—
84C22⋊C4×Dic11C2212yes—
85C22⋊C4×Dic11C2212yes—
86C22⋊C4×Dic11C2212yes—
87C22⋊C4×Dic11C2212yes—
88C22⋊C4×Dic11C2212yes—
89C4×C4⋊Dic11C2212yes—
90#10622546C2212yes—
91C42×Dic11C2212yes—
92#10622541C2212yes—
93#10622274C2211yescharacteristic
94#10622273C2212yes—
95#10622269C2211yescharacteristic
96#10622267C2212yes—
97#10622266C2212yes—
98#10622266C2212yes—
99#10622266C2212yes—
100#10622264C2212yes—
101#10622262C2212yes—
102#10622262C2211yescharacteristic
103#10622262C2212yes—
104#10622262C2211yescharacteristic
105#10622260C2212yes—
106#10622259C2212yes—
107C22×D4×C11C2312yes—
108C22×D4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2312yes—
111C23×Dic11C2312yes—
112C23×Dic11C2312yes—
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2311yescharacteristic
115C22×Dic22C2311yescharacteristic
116C11×#123—28no—
117C4×D4×C11—28no—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C11×C22⋊C4C2311yescharacteristic
129C2×C11×C22⋊C4C2312yes—
130C2×C42×C11C2312yes—
131C2×C22⋊Dic11C2311yescharacteristic
132C2×C22⋊Dic11C2312yes—
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×C22⋊Dic11C2312yes—
138C2×C22⋊Dic11C2312yes—
139C2×C22⋊Dic11C2311yescharacteristic
140C2×C22⋊Dic11C2312yes—
141D4×Dic11—28no—
142D4×Dic11—28no—
143D4×Dic11—42no—
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2312yes—
146C2×C4⋊Dic11C2312yes—
147C2×C4⋊Dic11C2312yes—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2312yes—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2312yes—
156C2×Dic11⋊C4C2312yes—
157C2×Dic11⋊C4C2311yescharacteristic
158C2×Dic11⋊C4C2311yescharacteristic
159C2×Dic11⋊C4C2312yes—
160C2×C4×Dic11—44no—
161C2×C4×Dic11—42no—
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2311yescharacteristic
165C2×C4×Dic11C2312yes—
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2312yes—
168C2×C4×Dic11C2312yes—
169C2×C4×Dic11C2312yes—
170C2×C4×Dic11C2312yes—
171C2×C4×Dic11C2312yes—
172C2×C4×Dic11C2312yes—
173C2×C4×Dic11C2312yes—
174C2×C4×Dic11C2312yes—
175#66943—28no—
176#66940—42no—
177#66932—28no—
178#66931—28no—
179#66930—24no—
180#66930—42no—
181C11×#95C2312yes—
182C11×#95C2312yes—
183C11×#95C2311yescharacteristic
184C11×#95C2311yescharacteristic
185C11⋊#95C2312yes—
186C11⋊#95C2312yes—
187C11⋊#95C2312yes—
188C11⋊#95C2312yes—
189C11⋊#95C2311yescharacteristic
190C11⋊#95C2312yes—
191C11⋊#95C2312yes—
192C11⋊#95C2311yescharacteristic
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206C11⋊#95C2312yes—
207#34961—111nomaximal, Sylow
208C24×C11C2412yes—
209C24×C11C2411yescharacteristic
210C2×D4×C11—24no—
211C2×D4×C11—24no—
212C2×D4×C11—24no—
213C2×D4×C11—24no—
214C2×D4×C11—41no—
215C22×C4×C11—24no—
216C22×C4×C11—24no—
217C22×C4×C11—24no—
218C22×C4×C11—41no—
219C22×C4×C11—42no—
220C22×C4×C11C2412yes—
221C22×C4×C11C2411yescharacteristic
222C22×C4×C11C2412yes—
223C22×C4×C11C2411yescharacteristic
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—24no—
230C22×Dic11—24no—
231C22×Dic11—24no—
232C22×Dic11—24no—
233C22×Dic11—24no—
234C22×Dic11—24no—
235C22×Dic11—41no—
236C22×Dic11—42no—
237C22×Dic11#4114yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2411yescharacteristic
243C22×Dic11C2411yescharacteristic
244C22×Dic11C2412yes—
245C22×Dic11C2411yescharacteristic
246C22×Dic11C2412yes—
247C22×Dic11C2411yescharacteristic
248C2×Dic22—24no—
249C2×Dic22—41no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—41no—
255C11×C22⋊C4—22no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—41no—
261C11×C22⋊C4#4118yes—
262C42×C11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267C22⋊Dic11—22no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270C22⋊Dic11—24no—
271C22⋊Dic11—41no—
272C22⋊Dic11—42no—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276C4⋊Dic11—24no—
277C4⋊Dic11—41no—
278C4⋊Dic11#4118yes—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—41no—
287Dic11⋊C4—41no—
288Dic11⋊C4—42no—
289C4×Dic11—24no—
290C4×Dic11—24no—
291C4×Dic11—24no—
292C4×Dic11—22no—
293C4×Dic11—22no—
294C4×Dic11—24no—
295C4×Dic11—24no—
296C4×Dic11—24no—
297C4×Dic11—24no—
298C4×Dic11—24no—
299C4×Dic11—42no—
300C4×Dic11—42no—
301C4×Dic11—42no—
302#2585—112no—
303#2573—112no—
304#2556—112no—
305#2553—112no—
306#2523—111no—
307#2517—111no—
308#2466—112no—
309#2463—111no—
310#2460—112no—
311#2455D1111yescharacteristic
312#2396—111no—
313#2395—112no—
314#2392—111no—
315C4×#125—112no—
316C4×#126—112no—
317C4×C22⋊Q8—112no—
318C4×#123—112no—
319#2296—111no—
320C42×D4—112no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—21no—
328C23×C11—22no—
329C23×C11—21no—
330C23×C11—22no—
331C23×C11C2×#4114yes—
332C23×C11C2×#4112yes—
333C23×C11C2511yescharacteristic
334D4×C11—216no—
335D4×C11—44no—
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—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—44no—
353C2×C4×C11—48no—
354C2×C4×C11C2×#4114yes—
355C2×C4×C11C2×#4114yes—
356C2×C4×C11C2×#4114yes—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—28no—
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—21no—
376C2×Dic11—21no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—48no—
381C2×Dic11—44no—
382C2×Dic11—48no—
383C2×Dic11C2×#4114yes—
384C2×Dic11C2×#4112yes—
385C2×Dic11C2×#4114yes—
386C2×Dic11C2×#4112yes—
387C2×Dic11H(5,𝔽2)12yes—
388C2×Dic112−1+412yes—
389Dic22—44no—
390C2×#126—112no—
391C2×#125—112no—
392C2×#123C2×D1112yes—
393C2×C22⋊Q8—112no—
394C2×C4×Q8—111no—
395C2×C4×D4—112no—
396C2×C4×D4—112no—
397C2×C4×D4—111no—
398C2×C4×D4C2×D1112yes—
399C2×#117—111no—
400C2×#117—111no—
401C22×C42—111no—
402C22×C42—112no—
403#400—111no—
404#400—112no—
405#399—112no—
406#399C2×D1111yescharacteristic
407#398—112no—
408#398—112no—
409#398—111no—
410#397—112no—
411#397—111no—
412#397—112no—
413#397—112no—
414#396—112no—
415#396—112no—
416#395—111no—
417#394—112no—
418#394—111no—
419#394—112no—
420#394C2×D1112yes—
421#393—111no—
422#392C2×D1111yescharacteristic
423#391—112no—
424#389—112no—
425#389—112no—
426#389—112no—
427#389—112no—
428#389C2×D1112yes—
429#388—112no—
430#388—112no—
431#388—112no—
432#388—112no—
433#388C2×D1112yes—
434#387—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#387—112no—
445#386—112no—
446#385—111no—
447#385—112no—
448#385—111no—
449#385—111no—
450#385—112no—
451#385C2×D1112yes—
452#385C2×D1111yescharacteristic
453#383—112no—
454#382—112no—
455#381—112no—
456#380—112no—
457C4×C4⋊C4—112no—
458C4×C4⋊C4—112no—
459C4×C4⋊C4—112no—
460C4×C4⋊C4—112no—
461C4×C4⋊C4—112no—
462C4×C4⋊C4—112no—
463C4×C4⋊C4—111no—
464C4×C4⋊C4—112no—
465C4×C4⋊C4—111no—
466C4×C4⋊C4—112no—
467C4×C22⋊C4—112no—
468C4×C22⋊C4—112no—
469C4×C22⋊C4—112no—
470C4×C22⋊C4—112no—
471C4×C22⋊C4—112no—
472C4×C22⋊C4—112no—
473C4×C22⋊C4—112no—
474C4×C22⋊C4—112no—
475C4×C22⋊C4—112no—
476C43—112no—
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—22no—
480C22×C11—24no—
481C22×C11—24no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—41no—
485C22×C11—42no—
486C22×C11—41no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11C22×#4112yes—
490C22×C11C22×#4111yescharacteristic
491C22×C11C22×#4112yes—
492C22×C11C2×H(5,𝔽2)11yescharacteristic
493C22×C11C2×2−1+411yescharacteristic
494C4×C11—24no—
495C4×C11—24no—
496C4×C11—24no—
497C4×C11—42no—
498C4×C11—42no—
499C4×C11—41no—
500C4×C11—41no—
501Dic11—22no—
502Dic11—24no—
503Dic11—24no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507Dic11—41no—
508Dic11—41no—
509Dic11—42no—
510Dic11#53914yes—
511C22×Q8—111no—
512C22×D4C22×D1112yes—
513C22×D4C22×D1111yescharacteristic
514C23×C4—111no—
515C23×C4—112no—
516C23×C4—111no—
517C23×C4—112no—
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1112yes—
520#126—228no—
521#125—228no—
522#123—28no—
523C22⋊Q8—228no—
524C4×Q8—442no—
525C4×D4—28no—
526C4×D4—228no—
527C4×D4—228no—
528C4×D4—442no—
529#117—224no—
530#117—442no—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—112no—
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⋊C4—112no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4C22×D1112yes—
548C2×C4⋊C4C22×D1112yes—
549C2×C4⋊C4C22×D1112yes—
550C2×C4⋊C4C22×D1112yes—
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C22⋊C4—111no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—112no—
559C2×C22⋊C4—112no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—112no—
562C2×C22⋊C4C22×D1111yescharacteristic
563C2×C22⋊C4C22×D1112yes—
564C2×C22⋊C4C22×D1112yes—
565C2×C22⋊C4C22×D1112yes—
566C2×C22⋊C4C22×D1112yes—
567C2×C22⋊C4C22×D1111yescharacteristic
568C2×C22⋊C4C22×D1112yes—
569C2×C42—111no—
570C2×C42—111no—
571C2×C42—112no—
572C2×C42—112no—
573C2×C42—112no—
574C2×C42—112no—
575C2×C42—112no—
576C2×C42—112no—
577C2×C42—112no—
578C2×C42—112no—
579C2×C42—112no—
580C2×C42—112no—
581C2×C42—112no—
582C2×C42—442no—
583C2×C42—444no—
584C2×C42C22×D1112yes—
585#95—112no—
586#95—112no—
587#95—112no—
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—111no—
601#95—112no—
602#95—112no—
603#95—111no—
604#95—112no—
605#95—112no—
606#95—112no—
607#95C22×D1112yes—
608#95C22×D1112yes—
609#95C22×D1111yescharacteristic
610#95C22×D1111yescharacteristic
611C2×C11—42no—
612C2×C11—44no—
613C2×C11#344412yes—
614C2×C11C2×#53911yescharacteristic
615C2×C11#348111yescharacteristic
616C2×C11#348111yescharacteristic
617C2×C11#348212yes—
618C24C23×D1112yes—
619C24C23×D1111yescharacteristic
620C2×Q8—224no—
621C2×Q8—441no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—24no—
626C2×D4—41no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—41no—
631C22×C4—42no—
632C22×C4—111no—
633C22×C4—114no—
634C22×C4—112no—
635C22×C4—111no—
636C22×C4—112no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—111no—
642C22×C4—111no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—224no—
646C22×C4—224no—
647C22×C4—224no—
648C22×C4—224no—
649C22×C4—224no—
650C22×C4—224no—
651C22×C4—441no—
652C22×C4—442no—
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655C22×C4C23×D1112yes—
656C22×C4C23×D1111yescharacteristic
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—41no—
665C4⋊C4—118no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—224no—
671C4⋊C4—224no—
672C4⋊C4—224no—
673C4⋊C4—224no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—441no—
678C4⋊C4—441no—
679C4⋊C4—441no—
680C4⋊C4—442no—
681C22⋊C4—24no—
682C22⋊C4—22no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—41no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4—222no—
694C22⋊C4—224no—
695C22⋊C4—441no—
696C22⋊C4—442no—
697C22⋊C4#434118yes—
698C42—24no—
699C42—224no—
700C42—224no—
701C42—224no—
702C42—222no—
703C42—222no—
704C42—224no—
705C42—224no—
706C42—224no—
707C42—224no—
708C42—224no—
709C42—442no—
710C42—442no—
711C42—442no—
712C11#3496111yescharacteristic, complemented, Sylow
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—21no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23C2×#434114yes—
724C23#41×D1112yes—
725C23C24×D1111yescharacteristic
726Q8—444no—
727D4—216no—
728D4—44no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—48no—
747C2×C4—112no—
748C2×C4—112no—
749C2×C4—112no—
750C2×C4—114no—
751C2×C4—114no—
752C2×C4—112no—
753C2×C4—228no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—221no—
759C2×C4—221no—
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—222no—
771C2×C4—221no—
772C2×C4—221no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—448no—
777C2×C4—444no—
778C2×C4—448no—
779C2×C4C2×#434114yes—
780C2×C4C2×#434114yes—
781C2×C4#41×D1114yes—
782C22—24no—
783C22—24no—
784C22—22no—
785C22—24no—
786C22—24no—
787C22—42no—
788C22—42no—
789C22—41no—
790C22—42no—
791C22—41no—
792C22—42no—
793C22—42no—
794C22C22×#434112yes—
795C22C2×#41×D1111yescharacteristic
796C22C2×#41×D1112yes—
797C22D11×H(5,𝔽2)11yescharacteristic
798C22D11×2−1+411yescharacteristic
799C4—24no—
800C4—24no—
801C4—24no—
802C4—42no—
803C4—42no—
804C4—41no—
805C4—41no—
806C4—114no—
807C4—222no—
808C4—224no—
809C4—224no—
810C4—442no—
811C4—442no—
812C4—442no—
813C4—441no—
814C4—441no—
815C4—442no—
816C2—44no—
817C2—42no—
818C2#1308190812yes—
819C2D11×#53911yescharacteristic
820C2#1308221711yescharacteristic
821C2#1308222511yescharacteristic
822C2#1308222812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2455C2
prime radicalC11×#392C22
hypercenter#2455D11
hypocenterC11#34961
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2455

Complements

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

NH ≅ G/Ntype
1. #13074010C2semidirect
2. #13073879C2semidirect
3. #13073699C2semidirect
4. #13073657C2semidirect
5. #13073348C2semidirect
6. #13073265C2semidirect
7. #13072646C2semidirect
9. #13072563C2semidirect
10. #13071885C2semidirect
11. #13071872C2semidirect
13. #13071175C2semidirect
14. #13071170C2semidirect
15. #13071148C2semidirect
16. #123×Dic11C2semidirect
17. #13071095C2semidirect
18. C4×D4×Dic11C2semidirect
712. C11#34961semidirect

Maximal subgroups

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

subgroupindex
#130740102
#130738792
#130736992
#130736572
#130733482
#130732652
#130726462
#130726062
#130725632
#130718852
#130718722
#130718512
#130711752
#130711702
#130711482
#123×Dic112
#130710952
C4×D4×Dic112
C11×#24552
#3496111