Finite Group Databasebeta

← #14920997

Subgroups — #14920997

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623053C211yesmaximal, characteristic
3#13074541C212yesmaximal, complemented
4#13074538C212yesmaximal, complemented
5#13074497C212yesmaximal, complemented
6#13074489C212yesmaximal, complemented
7#13074440C211yesmaximal, characteristic, complemented
8#13074437C211yesmaximal, characteristic, complemented
9#13074416C212yesmaximal, complemented
10#13074383C211yesmaximal, characteristic, complemented
11#13074346C212yesmaximal
12#13071908C212yesmaximal, complemented
13#13071901C212yesmaximal, complemented
14#13071880C212yesmaximal, complemented
15#13071878C212yesmaximal, complemented
16#13071154C212yesmaximal, complemented
17C22⋊Q8×Dic11C212yesmaximal, complemented
18#13071009C211yesmaximal, characteristic, complemented
19C11×#2621C211yesmaximal, characteristic, complemented
20C22×#4339C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2212yes—
23C2×C11×#117C2211yescharacteristic
24C2×#66999C2212yes—
25C2×#66999C2212yes—
26C2×Q8×Dic11C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28#10623259—28no—
29#10623053—28no—
30C2×#66950C2212yes—
31C2×#66946C2211yescharacteristic
32C2×#66946C2211yescharacteristic
33C2×#66945C2212yes—
34C2×#66943C2212yes—
35C2×#66940C2212yes—
36C2×#66940C2211yescharacteristic
37C2×#66940C2211yescharacteristic
38C2×(C22⋊D11)⋊C4C2211yescharacteristic
39C2×(C22⋊D11)⋊C4C2211yescharacteristic
40C2×(C22⋊D11)⋊C4C2211yescharacteristic
41C2×(C22⋊D11)⋊C4C2211yescharacteristic
42C2×#66925C2211yescharacteristic
43C2×#66925C2211yescharacteristic
44C2×C42×D11C2211yescharacteristic
45C2×C42×D11C2211yescharacteristic
46C2×#66922C2211yescharacteristic
47C11×#398C2212yes—
48C11×#398C2212yes—
49C11×#397C2212yes—
50C11×#397C2212yes—
51C11×#391C2212yes—
52C11×#382C2211yescharacteristic
53#10622843C2212yes—
54#10622825C2212yes—
55#10622606C2212yes—
56#10622606C2212yes—
57#10622604C2214yes—
58#10622600C2212yes—
59#10622600C2212yes—
60#10622599C2212yes—
61#10622598C2212yes—
62#10622594C2214yes—
63#10622593C2212yes—
64#10622593C2212yes—
65#10622592C2212yes—
66#10622592C2214yes—
67C4⋊C4×Dic11C2214yes—
68C4⋊C4×Dic11C2212yes—
69#10622572C2214yes—
70#10622572C2214yes—
71#10622563C2214yes—
72#10622562C2212yes—
73#10622560C2212yes—
74C22⋊C4×Dic11C2214yes—
75#10622549C2211yescharacteristic
76#10622541C2212yes—
77#10622290C2212yes—
78#10622288C2214yes—
79#10622287C2214yes—
80#10622286C2212yes—
81#10622281C2214yes—
82#10622279C2212yes—
83#10622279C2214yes—
84#10622277C2212yes—
85#10622272C2212yes—
86#10622271C2214yes—
87#10622270C2214yes—
88#10622269C2212yes—
89#10622268C2214yes—
90#10622264C2212yes—
91#10622262C2214yes—
92#10622261C2212yes—
93C22×Q8×C11C2312yes—
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11C2311yescharacteristic
96C22×C22⋊D11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C2×#4339—24no—
100C2×#4339—24no—
101C2×#4339—24no—
102C22×D44C2311yescharacteristic
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2311yescharacteristic
108C22×C4×D11C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C22×Dic22C2312yes—
111C11×C4⋊Q8—24no—
112C11×C22⋊Q8—28no—
113C11×#117—24no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C4⋊C4C2314yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C22⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4C2314yes—
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C2×C22⋊Dic11C2314yes—
126#66999—28no—
127#66999—28no—
128Q8×Dic11—28no—
129C2×(C2×D11)⋊C4C2311yescharacteristic
130C2×(C2×D11)⋊C4C2311yescharacteristic
131C2×(C2×D11)⋊C4C2311yescharacteristic
132C2×(C2×D11)⋊C4C2311yescharacteristic
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×C4⋊Dic11C2312yes—
138C2×C4⋊Dic11C2312yes—
139C2×C4⋊Dic11C2314yes—
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4C2311yescharacteristic
143C2×Dic11⋊C4C2311yescharacteristic
144C2×Dic11⋊C4C2311yescharacteristic
145C2×Dic11⋊C4C2311yescharacteristic
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×C4×Dic11—24no—
150C2×C4×Dic11C2311yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2311yescharacteristic
155C2×C4×Dic11C2311yescharacteristic
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2311yescharacteristic
158C2×C4×Dic11C2311yescharacteristic
159C2×C4×Dic11C2311yescharacteristic
160#66950—28no—
161#66946—24no—
162#66946—24no—
163#66945—28no—
164#66943—28no—
165#66940—28no—
166#66940—24no—
167#66940—24no—
168(C22⋊D11)⋊C4—24no—
169(C22⋊D11)⋊C4—24no—
170(C22⋊D11)⋊C4—24no—
171(C22⋊D11)⋊C4—24no—
172#66925—24no—
173#66925—24no—
174C42×D11—24no—
175C42×D11D418yes—
176#66922—24no—
177C11×#95C2312yes—
178C11×#95C2314yes—
179C11×#95C2312yes—
180C11×#95C2314yes—
181C11⋊#95C2314yes—
182C11⋊#95C2312yes—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185C11⋊#95C2312yes—
186C11⋊#95C2314yes—
187C11⋊#95C2314yes—
188C11⋊#95C2314yes—
189C11⋊#95C2314yes—
190C11⋊#95C2314yes—
191#34627—111nomaximal, Sylow
192C24×C11C2411yescharacteristic
193C23×D11C2411yescharacteristic
194C23×D11C2411yescharacteristic
195C2×Q8×C11—24no—
196C2×Q8×C11—24no—
197C2×Q8×C11—24no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11#4114yes—
201C22×C4×C11C2411yescharacteristic
202C22×C4×C11C2414yes—
203C22×C4×C11C2414yes—
204C22×C4×C11C2411yescharacteristic
205C22×C4×C11C2411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—22no—
210C2×C22⋊D11—22no—
211C2×C22⋊D11—22no—
212C2×C22⋊D11—22no—
213C2×C22⋊D11—22no—
214C2×C22⋊D11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—24no—
218C22×Dic11—42no—
219C22×Dic11C2411yescharacteristic
220C22×Dic11C2414yes—
221C22×Dic11C2411yescharacteristic
222C22×Dic11C2414yes—
223C22×Dic11C2411yescharacteristic
224C22×Dic11C2411yescharacteristic
225C22×Dic11C2411yescharacteristic
226C22×Dic11C2411yescharacteristic
227#4339—232no—
228C2×D44—22no—
229C2×D44—22no—
230C2×D44—22no—
231C2×C4×D11—24no—
232C2×C4×D11—22no—
233C2×C4×D11—22no—
234C2×C4×D11—24no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—22no—
239C2×C4×D11—42no—
240C2×C4×D11—42no—
241C2×C4×D11C2×D414yes—
242C2×C4×D11C2×D414yes—
243C2×C4×D11C2×D414yes—
244C2×C4×D11#4114yes—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22—24no—
248C2×Dic22—22no—
249C2×Dic22—44no—
250C11×C4⋊C4—22no—
251C11×C4⋊C4—22no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—28no—
256C11×C22⋊C4—28no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—22no—
259C42×C11—22no—
260C42×C11C2×D414yes—
261C22⋊Dic11—44no—
262(C2×D11)⋊C4—22no—
263(C2×D11)⋊C4—22no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—22no—
267(C2×D11)⋊C4—22no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270C4⋊Dic11—28no—
271C4⋊Dic11—24no—
272C4⋊Dic11—24no—
273C4⋊Dic11—24no—
274C4⋊Dic11—44no—
275Dic11⋊C4—22no—
276Dic11⋊C4—22no—
277Dic11⋊C4—28no—
278Dic11⋊C4—28no—
279Dic11⋊C4—22no—
280Dic11⋊C4—22no—
281Dic11⋊C4—44no—
282C4×Dic11—22no—
283C4×Dic11—22no—
284C4×Dic11—28no—
285C4×Dic11—22no—
286C4×Dic11—22no—
287C4×Dic11—28no—
288C4×Dic11—22no—
289C4×Dic11C2×D414yes—
290C4×Dic11C2×D414yes—
291C4×Dic11C2×D414yes—
292C2×#533—111no—
293C2×C4×#41—111no—
294#2638—112no—
295#2638—112no—
296#2634—112no—
297#2633—112no—
298#2628—111no—
299#2628—111no—
300#2625—112no—
301#2621—111no—
302#2621D1111yescharacteristic, complemented
303#2616—112no—
304#2399—112no—
305#2398—112no—
306#2395—112no—
307#2395—112no—
308C4×C22⋊Q8—112no—
309C4×C22⋊Q8—112no—
310#2283—111no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11C2×#4112yes—
316C23×C11C2511yescharacteristic
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—21no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11C22×D412yes—
326C22×D11C2×#4112yes—
327Q8×C11—48no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—28no—
333C2×C4×C11—24no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—24no—
337C2×C4×C11—24no—
338C2×C4×C11—24no—
339C2×C4×C11—24no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C2×#4112yes—
347C2×C4×C11C2×#4112yes—
348C2×C4×C11C2×#4112yes—
349C22⋊D11—28no—
350C22⋊D11—28no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—21no—
355C2×Dic11—22no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—24no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—22no—
365C2×Dic11—24no—
366C2×Dic11—44no—
367C2×Dic11—44no—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371C2×Dic11C2×#4112yes—
372C2×Dic112−1+414yes—
373D44—28no—
374C4×D11—28no—
375C4×D11—28no—
376C4×D11—28no—
377C4×D11—44no—
378C4×D11—44no—
379C4×D11—44no—
380Dic22—28no—
381Dic22—48no—
382C22×#41—111no—
383#533—228no—
384C2×C4⋊Q8—111no—
385C2×C4⋊Q8C2×D1111yescharacteristic
386C2×#125—112no—
387C2×C22⋊Q8—112no—
388C2×C22⋊Q8—112no—
389C2×C22⋊Q8—112no—
390C2×C22⋊Q8C2×D1112yes—
391C4×#41—228no—
392C2×C4×Q8—112no—
393C2×C4×Q8—111no—
394C2×C4×Q8—112no—
395C2×C4×Q8—111no—
396C2×C4×D4—111no—
397C2×C4×D4—111no—
398C2×C4×D4—111no—
399C2×C4×D4—111no—
400C2×C4×D4—111no—
401C2×C4×D4—111no—
402C2×#117—112no—
403C2×#117—111no—
404C2×#117—111no—
405C2×#117C2×D1111yescharacteristic
406C22×C42—111no—
407C22×C42—111no—
408C22×C42—111no—
409#400—112no—
410#400—114no—
411#400—112no—
412#399—112no—
413#399—112no—
414#398—112no—
415#398—112no—
416#398—114no—
417#398C2×D1112yes—
418#398C2×D1112yes—
419#397—112no—
420#397—112no—
421#397—114no—
422#397—114no—
423#397C2×D1112yes—
424#397C2×D1112yes—
425#395—114no—
426#395—112no—
427#395—112no—
428#394—114no—
429#394—114no—
430#394—114no—
431#393—112no—
432#393—112no—
433#391—112no—
434#391C2×D1112yes—
435#389—112no—
436#389—112no—
437#387—114no—
438#387—114no—
439#385—114no—
440#385—114no—
441#383—112no—
442#382—111no—
443#382C2×D1111yescharacteristic
444#381—112no—
445#380—112no—
446#380—112no—
447#380—112no—
448C4×C4⋊C4—114no—
449C4×C4⋊C4—112no—
450C4×C4⋊C4—114no—
451C4×C22⋊C4—114no—
452C4×C22⋊C4—112no—
453C4×C22⋊C4—114no—
454#376—112no—
455C22×C11—22no—
456C22×C11—24no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—42no—
460C22×C11C23×D411yescharacteristic
461C22×C11C22×#4111yescharacteristic
462C22×C11C22×#4111yescharacteristic
463C22×C11C2×2−1+412yes—
464C22×C11#58512yes—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—24no—
470C2×D11—41no—
471C2×D11—41no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—44no—
479C4×C11—41no—
480C4×C11—41no—
481C4×C11—44no—
482C4×C11#52514yes—
483Dic11—22no—
484Dic11—22no—
485Dic11—22no—
486Dic11—41no—
487Dic11—44no—
488Dic11—41no—
489Dic11—44no—
490Dic11#53614yes—
491C2×#41—224no—
492C2×#41—224no—
493C2×#41—224no—
494C22×Q8—111no—
495C22×Q8—112no—
496C22×Q8C22×D1112yes—
497C22×D4—111no—
498C22×D4—111no—
499C22×D4—111no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—111no—
508C23×C4C22×D1111yescharacteristic
509C4⋊Q8—24no—
510C4⋊Q8—224no—
511#125—228no—
512C22⋊Q8—28no—
513C22⋊Q8—228no—
514C22⋊Q8—228no—
515C22⋊Q8—228no—
516C4×Q8—224no—
517C4×Q8—224no—
518C4×Q8—228no—
519C4×Q8—228no—
520C4×D4—224no—
521C4×D4—224no—
522C4×D4—224no—
523C4×D4—224no—
524C4×D4—224no—
525C4×D4—224no—
526#117—24no—
527#117—224no—
528#117—228no—
529#117—224no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—112no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—112no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4C22×D1112yes—
543C2×C4⋊C4C22×D1111yescharacteristic
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C4⋊C4C22×D1112yes—
546C2×C4⋊C4C22×D1112yes—
547C2×C4⋊C4C22×D1114yes—
548C2×C22⋊C4—111no—
549C2×C22⋊C4—111no—
550C2×C22⋊C4—111no—
551C2×C22⋊C4—111no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4C22×D1111yescharacteristic
559C2×C22⋊C4C22×D1114yes—
560C2×C42—111no—
561C2×C42—111no—
562C2×C42—111no—
563C2×C42—118no—
564C2×C42—111no—
565C2×C42—114no—
566C2×C42—111no—
567C2×C42—111no—
568C2×C42—111no—
569C2×C42—111no—
570C2×C42—114no—
571C2×C42—224no—
572C2×C42—224no—
573C2×C42C22×D1111yescharacteristic
574C2×C42C22×D1111yescharacteristic
575#95—114no—
576#95—112no—
577#95—112no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95—114no—
584#95—114no—
585#95C22×D1112yes—
586#95C22×D1112yes—
587#95C22×D1114yes—
588#95C22×D1114yes—
589C2×C11—42no—
590C2×C11C2×#52511yescharacteristic
591C2×C11C2×#53611yescharacteristic
592C2×C11#344911yescharacteristic
593C2×C11#346112yes—
594C2×C11#346112yes—
595D11—42no—
596D11—42no—
597C24—111no—
598C24—111no—
599C24C23×D1111yescharacteristic
600#41—2232no—
601C2×Q8—24no—
602C2×Q8—24no—
603C2×Q8—24no—
604C2×Q8—222no—
605C2×Q8—222no—
606C2×Q8—224no—
607C2×Q8—222no—
608C2×Q8—444no—
609C2×D4—222no—
610C2×D4—222no—
611C2×D4—222no—
612C2×D4—222no—
613C2×D4—222no—
614C2×D4—222no—
615C2×D4—222no—
616C2×D4—222no—
617C2×D4—222no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—111no—
621C22×C4—111no—
622C22×C4—111no—
623C22×C4—111no—
624C22×C4—114no—
625C22×C4—114no—
626C22×C4—114no—
627C22×C4—114no—
628C22×C4—111no—
629C22×C4—114no—
630C22×C4—111no—
631C22×C4—114no—
632C22×C4—224no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—224no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—224no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—442no—
644C22×C4—442no—
645C22×C4—442no—
646C22×C4#434114yes—
647C22×C4C23×D1111yescharacteristic
648C22×C4C23×D1114yes—
649C22×C4C23×D1114yes—
650C22×C4C23×D1111yescharacteristic
651C22×C4C23×D1111yescharacteristic
652C22×C4C23×D1111yescharacteristic
653C22×C4C23×D1111yescharacteristic
654C22×C4C23×D1111yescharacteristic
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—28no—
661C4⋊C4—222no—
662C4⋊C4—222no—
663C4⋊C4—228no—
664C4⋊C4—228no—
665C4⋊C4—228no—
666C4⋊C4—222no—
667C4⋊C4—222no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—224no—
671C4⋊C4—444no—
672C4⋊C4—444no—
673C22⋊C4—28no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—222no—
677C22⋊C4—222no—
678C22⋊C4—228no—
679C22⋊C4—228no—
680C22⋊C4—222no—
681C22⋊C4—222no—
682C22⋊C4—444no—
683C22⋊C4—444no—
684C22⋊C4—444no—
685C42—22no—
686C42—114no—
687C42—114no—
688C42—114no—
689C42—222no—
690C42—222no—
691C42—222no—
692C42—222no—
693C42—228no—
694C42—228no—
695C42—222no—
696C42D4×D1114yes—
697C11#3462711yescharacteristic, complemented, Sylow
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—112no—
703C23—112no—
704C23—221no—
705C23—221no—
706C23—221no—
707C23—221no—
708C23—222no—
709C23—222no—
710C23—222no—
711C23—222no—
712C23C2×#434112yes—
713C23C24×D1111yescharacteristic
714Q8—48no—
715Q8—228no—
716Q8—448no—
717D4—228no—
718D4—228no—
719D4—228no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—28no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—112no—
736C2×C4—114no—
737C2×C4—112no—
738C2×C4—112no—
739C2×C4—112no—
740C2×C4—228no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—222no—
746C2×C4—228no—
747C2×C4—228no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—224no—
751C2×C4—224no—
752C2×C4—224no—
753C2×C4—222no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—222no—
757C2×C4—224no—
758C2×C4—444no—
759C2×C4—444no—
760C2×C4—444no—
761C2×C4—444no—
762C2×C4—444no—
763C2×C4C2×D4×D1112yes—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1112yes—
766C2×C4C2×#434112yes—
767C2×C4C2×#434112yes—
768C2×C4#41×D1112yes—
769C22—22no—
770C22—24no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—222no—
775C22—222no—
776C22—222no—
777C22—222no—
778C22—224no—
779C22—441no—
780C22—441no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22C22×D4×D1111yescharacteristic
785C22C22×#434111yescharacteristic
786C22C2×#41×D1111yescharacteristic
787C22D11×2−1+412yes—
788C22#1062345712yes—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—44no—
793C4—41no—
794C4—41no—
795C4—44no—
796C4—114no—
797C4—222no—
798C4—222no—
799C4—222no—
800C4—441no—
801C4—441no—
802C4—444no—
803C4—444no—
804C4#1062313714yes—
805C2—42no—
806C2—442no—
807C2—442no—
808C2C2×#1062313711yescharacteristic
809C2D11×#53611yescharacteristic
810C2#1308194811yescharacteristic
811C2#1308204012yes—
812C2#1308204812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2621C2
prime radicalC22×#4339C22
hypercenter#2621D11
hypocenterC11#34627
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2621

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13074541C2semidirect
4. #13074538C2semidirect
5. #13074497C2semidirect
6. #13074489C2semidirect
7. #13074440C2semidirect
8. #13074437C2semidirect
9. #13074416C2semidirect
10. #13074383C2semidirect
12. #13071908C2semidirect
13. #13071901C2semidirect
14. #13071880C2semidirect
15. #13071878C2semidirect
16. #13071154C2semidirect
17. C22⋊Q8×Dic11C2semidirect
18. #13071009C2semidirect
19. C11×#2621C2semidirect
302. #2621D11semidirect
697. C11#34627semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106230532
#130745412
#130745382
#130744972
#130744892
#130744402
#130744372
#130744162
#130743832
#130743462
#130719082
#130719012
#130718802
#130718782
#130711542
C22⋊Q8×Dic112
#130710092
C11×#26212
#3462711