Finite Group Databasebeta

← #14926035

Subgroups — #14926035

Order 2816.

3270 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074185C212yesmaximal, complemented
4#13074177C212yesmaximal, complemented
5#13073969C212yesmaximal, complemented
6#13073514C212yesmaximal, complemented
7#13072928C212yesmaximal, complemented
8#13072885C212yesmaximal, complemented
9#13071967C212yesmaximal, complemented
10#13071936C212yesmaximal, complemented
11#13071899C211yesmaximal, characteristic, complemented
12#13071897C211yesmaximal, characteristic, complemented
13#13071895C211yesmaximal, characteristic, complemented
14C4×#66937C214yesmaximal, complemented
15C4×#66935C214yesmaximal, complemented
16#13071008C211yesmaximal, characteristic, complemented
17C11×#2398C211yesmaximal, characteristic, complemented
18C22×#4343C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C23×C4×D11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic, complemented
22C2×C4×D4×C11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic, complemented
24C2×D4×Dic11C2211yescharacteristic
25C2×C4×C22⋊D11C2212yes—
26C2×C4×C22⋊D11C2214yescomplemented
27C4×#4343—28no—
28C4×D4×D11—28no—
29C2×#66946C2211yescharacteristic
30C2×#66946C2212yes—
31C2×#66946C2211yescharacteristic, complemented
32C2×#66945C2211yescharacteristic
33C2×#66945C2212yescomplemented
34C2×C4⋊C4×D11C2211yescharacteristic
35C2×#66937C2214yes—
36C2×#66935C2214yes—
37C2×(C22⋊D11)⋊C4C2212yes—
38C2×C22⋊C4×D11C2212yes—
39C2×C4×D44C2212yes—
40C2×C4×D44C2211yescharacteristic
41C2×C4×D44C2211yescharacteristic, complemented
42C2×C4×D44C2214yescomplemented
43C2×C42×D11C2211yescharacteristic
44C2×C42×D11C2212yescomplemented
45C11×#400C2212yescomplemented
46C11×#397C2212yescomplemented
47C11×#394C2212yes—
48C11×#393C2212yescomplemented
49C4×C11×C22⋊C4C2214yescomplemented
50C11×#376C2211yescharacteristic, complemented
51#10622844C2212yescomplemented
52#10622836C2212yes—
53#10622606C2212yescomplemented
54#10622605C2212yescomplemented
55#10622604C2212yes—
56#10622599C2212yescomplemented
57#10622573C2212yescomplemented
58#10622571C2214yescomplemented
59#10622570C2214yes—
60#10622569C2214yescomplemented
61#10622568C2214yes—
62#10622564C2214yescomplemented
63#10622563C2214yescomplemented
64#10622562C2212yescomplemented
65C4×(C2×D11)⋊C4C2212yes—
66C4×(C2×D11)⋊C4C2214yescomplemented
67#10622545C2211yescharacteristic, complemented
68C4×Dic11⋊C4C2212yescomplemented
69#10622290C2212yescomplemented
70#10622290C2212yescomplemented
71#10622284C2212yes—
72#10622284C2212yescomplemented
73#10622282C2214yescomplemented
74#10622281C2214yes—
75#10622281C2214yescomplemented
76#10622280C2212yes—
77#10622280C2214yescomplemented
78#10622278C2214yes—
79#10622278C2214yescomplemented
80#10622278C2214yescomplemented
81#10622277C2212yes—
82#10622264C2212yescomplemented
83#10622263C2212yescomplemented
84#10622260C2214yescomplemented
85C24×D11C2312yes—
86C22×Q8×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11C2312yes—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2312yes—
91C23×Dic11C2312yes—
92C2×#4343—28no—
93C2×#4343—24no—
94C2×D4×D11—28no—
95C2×D4×D11—24no—
96C22×D44C2311yescharacteristic
97C22×D44C2311yescharacteristic
98C22×D44C2314yes—
99C22×D44C2312yes—
100C22×C4×D11—28no—
101C22×C4×D11—48no—
102C22×C4×D11C2312yes—
103C22×C4×D11C2312yes—
104C22×C4×D11C2312yes—
105C22×C4×D11C2312yes—
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2311yescharacteristic
108C22×C4×D11C2311yescharacteristic
109C22×C4×D11C2312yes—
110C22×C4×D11C2312yes—
111C4×Q8×C11—24no—
112C4×D4×C11—24no—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C42×C11C2312yes—
120C2×C42×C11C2312yes—
121C2×C42×C11C2311yescharacteristic
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2314yes—
124Q8×Dic11—24no—
125D4×Dic11—24no—
126C4×C22⋊D11—28no—
127C4×C22⋊D11—48no—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2314yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11C2312yes—
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2311yescharacteristic
150C2×C4×Dic11C2311yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152#66946—28no—
153#66946—24no—
154#66946—24no—
155#66945—24no—
156#66945—28no—
157C4⋊C4×D11—24no—
158#66937—216no—
159#66935—216no—
160(C22⋊D11)⋊C4—28no—
161C22⋊C4×D11—28no—
162C4×D44—28no—
163C4×D44—24no—
164C4×D44—24no—
165C4×D44—48no—
166C42×D11—28no—
167C42×D11D418yescomplemented
168C11×#95C2314yes—
169C11×#95C2312yes—
170C11×#95C2312yes—
171C11×#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2312yes—
175C11⋊#95C2314yes—
176C11⋊#95C2312yes—
177C11⋊#95C2314yes—
178#34963—111nomaximal, Sylow
179C24×C11C2412yes—
180C23×D11—24no—
181C23×D11—24no—
182C23×D11—24no—
183C23×D11—28no—
184C23×D11—44no—
185C23×D11C2412yes—
186C23×D11C2412yes—
187C23×D11C2411yescharacteristic
188C2×Q8×C11—22no—
189C2×Q8×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—22no—
192C22×C4×C11—24no—
193C22×C4×C11—28no—
194C22×C4×C11C2414yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2412yes—
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—28no—
204C2×C22⋊D11—28no—
205C2×C22⋊D11—44no—
206C2×C22⋊D11#4118yescomplemented
207C22×Dic11—24no—
208C22×Dic11—44no—
209C22×Dic11C2414yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C22×Dic11C2411yescharacteristic
213C22×Dic11C2411yescharacteristic
214C22×Dic11C2411yescharacteristic
215#4343—232no—
216D4×D11—232no—
217C2×D44—24no—
218C2×D44—24no—
219C2×D44—24no—
220C2×D44—24no—
221C2×D44—28no—
222C2×D44—28no—
223C2×D44—22no—
224C2×D44—22no—
225C2×D44—44no—
226C2×D44#4118yes—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—28no—
232C2×C4×D11—24no—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—24no—
239C2×C4×D11—28no—
240C2×C4×D11—28no—
241C2×C4×D11—44no—
242C2×C4×D11—44no—
243C2×C4×D11—432no—
244C2×C4×D11C2×D414yes—
245C2×C4×D11C2×D414yes—
246C2×C4×D11C2×D414yes—
247C11×C4⋊C4—22no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—22no—
250C11×C22⋊C4—28no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—28no—
253C42×C11—24no—
254C42×C11—24no—
255C42×C11C2×D414yes—
256C22⋊Dic11—24no—
257C22⋊Dic11—44no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269C4⋊Dic11—24no—
270C4⋊Dic11—22no—
271C4⋊Dic11—22no—
272C4⋊Dic11—44no—
273Dic11⋊C4—24no—
274Dic11⋊C4—28no—
275Dic11⋊C4—44no—
276C4×Dic11—24no—
277C4×Dic11—24no—
278C4×Dic11—24no—
279C4×Dic11C2×D414yes—
280C4×Dic11C2×D414yes—
281C4×Dic11C2×D414yes—
282C2×C4×#41—111no—
283C22×C4×D4—111no—
284#2598—112no—
285#2598—112no—
286#2580—112no—
287#2535—112no—
288#2487—112no—
289#2482—112no—
290#2408—112no—
291#2404—112no—
292#2398—111no—
293#2398D1111yescharacteristic, complemented
294#2397—111no—
295#2397—111no—
296C4×#121—114no—
297C4×#120—114no—
298#2283—111no—
299C23×C11—22no—
300C23×C11—24no—
301C23×C11—22no—
302C23×C11—24no—
303C23×C11C2×#4114yes—
304C23×C11C2511yescharacteristic
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—216no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—24no—
311C22×D11—22no—
312C22×D11—24no—
313C22×D11—22no—
314C22×D11—24no—
315C22×D11—24no—
316C22×D11—416no—
317C22×D11—416no—
318C22×D11—48no—
319C22×D11—48no—
320C22×D11C22×D412yes—
321C22×D11C2×#4114yes—
322C22×D11C2×#4114yes—
323C22×D11C2×#4114yes—
324Q8×C11—28no—
325D4×C11—28no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—24no—
333C2×C4×C11—24no—
334C2×C4×C11—24no—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—48no—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C2×#4114yes—
342C2×C4×C11H(5,𝔽2)14yes—
343C22⋊D11—216no—
344C22⋊D11—416no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—24no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—24no—
353C2×Dic11—24no—
354C2×Dic11—48no—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358C2×Dic11C2×#4114yes—
359D44—28no—
360D44—28no—
361D44—216no—
362D44—416no—
363C4×D11—216no—
364C4×D11—28no—
365C4×D11—28no—
366C4×D11—28no—
367C4×D11—48no—
368C4×D11—48no—
369C4×D11—48no—
370C4×D11—48no—
371C4×D11—48no—
372C22×#41—111no—
373C23×D4—111no—
374C24×C4—112no—
375C2×#121—114no—
376C2×#120—114no—
377C4×#41—228no—
378C2×C4×Q8—111no—
379C2×C4×Q8C2×D1111yescharacteristic, complemented
380C2×C4×D4—111no—
381C2×C4×D4—112no—
382C2×C4×D4—114no—
383C2×C4×D4—111no—
384C2×C4×D4—112no—
385C2×C4×D4—111no—
386C2×C4×D4—112no—
387C2×C4×D4—111no—
388C2×C4×D4—112no—
389C2×C4×D4—111no—
390C2×C4×D4—114no—
391C2×C4×D4—228no—
392C2×C4×D4C2×D1111yescharacteristic
393C2×#117—112no—
394C2×#117—111no—
395C22×C4⋊C4—111no—
396C22×C22⋊C4—112no—
397C22×C42—111no—
398C22×C42—112no—
399#400—112no—
400#400C2×D1112yescomplemented
401#399—112no—
402#399—112no—
403#399—112no—
404#399—112no—
405#397—112no—
406#397C2×D1112yescomplemented
407#394—112no—
408#394C2×D1112yes—
409#393—112no—
410#393C2×D1112yescomplemented
411#392—112no—
412#392—112no—
413#392—112no—
414#392—112no—
415#390—114no—
416#389—114no—
417#388—114no—
418#388—114no—
419#386—114no—
420#386—114no—
421#386—114no—
422#386—114no—
423#386—114no—
424#385—114no—
425#385—114no—
426#385—114no—
427#383—112no—
428#382—112no—
429#381—112no—
430#380—112no—
431#380—114no—
432#379—114no—
433C4×C4⋊C4—112no—
434C4×C22⋊C4—112no—
435C4×C22⋊C4—114no—
436C4×C22⋊C4C2×D1114yescomplemented
437#376—111no—
438#376C2×D1111yescharacteristic, complemented
439C22×C11—24no—
440C22×C11—28no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—44no—
444C22×C11C23×D411yescharacteristic
445C22×C11C22×#4112yes—
446C22×C11C22×#4112yes—
447C22×C11C2×H(5,𝔽2)12yes—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—28no—
451C2×D11—24no—
452C2×D11—24no—
453C2×D11—28no—
454C2×D11—28no—
455C2×D11—432no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—44no—
461C2×D11—44no—
462C2×D11#52514yes—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—24no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11—44no—
469C4×C11#53514yes—
470Dic11—22no—
471Dic11—22no—
472Dic11—42no—
473Dic11—42no—
474Dic11—44no—
475Dic11#52514yes—
476C25—112no—
477C2×#41—224no—
478C2×#41—228no—
479C22×Q8C22×D1111yescharacteristic
480C22×D4—112no—
481C22×D4—114no—
482C22×D4—112no—
483C22×D4—111no—
484C22×D4—111no—
485C22×D4—114no—
486C22×D4—224no—
487C22×D4—228no—
488C22×D4C22×D1111yescharacteristic
489C23×C4—111no—
490C23×C4—111no—
491C23×C4—111no—
492C23×C4—112no—
493C23×C4—112no—
494C23×C4—112no—
495C23×C4—112no—
496C23×C4—112no—
497C23×C4—112no—
498C23×C4—112no—
499C23×C4—228no—
500C23×C4—448no—
501C23×C4C22×D1112yes—
502#121—2216no—
503#120—2216no—
504C4×Q8—24no—
505C4×Q8—224no—
506C4×D4—24no—
507C4×D4—228no—
508C4×D4—228no—
509C4×D4—224no—
510C4×D4—224no—
511C4×D4—228no—
512C4×D4—224no—
513C4×D4—228no—
514C4×D4—224no—
515C4×D4—224no—
516C4×D4—448no—
517C4×D4—448no—
518#117—228no—
519#117—224no—
520C2×C4⋊C4—112no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—112no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—114no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—224no—
528C2×C4⋊C4C22×D1111yescharacteristic
529C2×C4⋊C4C22×D1112yes—
530C2×C4⋊C4C22×D1111yescharacteristic
531C2×C22⋊C4—112no—
532C2×C22⋊C4—112no—
533C2×C22⋊C4—112no—
534C2×C22⋊C4—112no—
535C2×C22⋊C4—112no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—228no—
545C2×C22⋊C4C22×D1112yes—
546C2×C22⋊C4C22×D1114yes—
547C2×C22⋊C4C22×D1114yes—
548C2×C42—111no—
549C2×C42—111no—
550C2×C42—111no—
551C2×C42—118no—
552C2×C42—112no—
553C2×C42—112no—
554C2×C42—112no—
555C2×C42—228no—
556C2×C42C22×D1112yes—
557C2×C42C22×D1112yes—
558C2×C42C22×D1111yescharacteristic
559#95—112no—
560#95—112no—
561#95—114no—
562#95—114no—
563#95—114no—
564#95—114no—
565#95C22×D1112yes—
566#95C22×D1112yes—
567#95C22×D1114yes—
568#95C22×D1114yes—
569C2×C11—44no—
570C2×C11C2×#52511yescharacteristic
571C2×C11C2×#52511yescharacteristic
572C2×C11C2×#53511yescharacteristic
573C2×C11#348114yes—
574D11—24no—
575D11—44no—
576D11—44no—
577C24—111no—
578C24—112no—
579C24—112no—
580C24—224no—
581C24—224no—
582C24—228no—
583C24—224no—
584C24—444no—
585C24C23×D1112yes—
586#41—2232no—
587C2×Q8—22no—
588C2×Q8—24no—
589C2×D4—24no—
590C2×D4—22no—
591C2×D4—118no—
592C2×D4—118no—
593C2×D4—224no—
594C2×D4—224no—
595C2×D4—224no—
596C2×D4—224no—
597C2×D4—228no—
598C2×D4—228no—
599C2×D4—224no—
600C2×D4—224no—
601C2×D4—2232no—
602C2×D4—228no—
603C2×D4—228no—
604C2×D4—222no—
605C2×D4—222no—
606C2×D4—444no—
607C2×D4—444no—
608C22×C4—24no—
609C22×C4—28no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—114no—
614C22×C4—114no—
615C22×C4—114no—
616C22×C4—114no—
617C22×C4—112no—
618C22×C4—112no—
619C22×C4—224no—
620C22×C4—224no—
621C22×C4—224no—
622C22×C4—224no—
623C22×C4—228no—
624C22×C4—224no—
625C22×C4—224no—
626C22×C4—224no—
627C22×C4—224no—
628C22×C4—224no—
629C22×C4—224no—
630C22×C4—224no—
631C22×C4—224no—
632C22×C4—228no—
633C22×C4—228no—
634C22×C4—444no—
635C22×C4—444no—
636C22×C4—4432no—
637C22×C4—444no—
638C22×C4C23×D1114yes—
639C22×C4C23×D1112yes—
640C22×C4C23×D1112yes—
641C22×C4C23×D1111yescharacteristic
642C22×C4C23×D1111yescharacteristic
643C22×C4C23×D1112yes—
644C22×C4C23×D1111yescharacteristic
645C4⋊C4—22no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—228no—
651C4⋊C4—222no—
652C4⋊C4—222no—
653C4⋊C4—444no—
654C4⋊C4—444no—
655C22⋊C4—28no—
656C22⋊C4—24no—
657C22⋊C4—28no—
658C22⋊C4—224no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—228no—
662C22⋊C4—228no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C22⋊C4—224no—
666C22⋊C4—228no—
667C22⋊C4—444no—
668C22⋊C4—444no—
669C22⋊C4—444no—
670C22⋊C4—444no—
671C42—24no—
672C42—24no—
673C42—114no—
674C42—114no—
675C42—114no—
676C42—224no—
677C42—224no—
678C42—224no—
679C42D4×D1114yes—
680C11#3496311yescharacteristic, complemented, Sylow
681C23—22no—
682C23—24no—
683C23—22no—
684C23—24no—
685C23—112no—
686C23—114no—
687C23—114no—
688C23—114no—
689C23—2216no—
690C23—222no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23—224no—
695C23—224no—
696C23—222no—
697C23—222no—
698C23—224no—
699C23—224no—
700C23—4416no—
701C23—448no—
702C23—4416no—
703C23—448no—
704C23#41×D1114yes—
705C23C24×D1111yescharacteristic
706Q8—28no—
707D4—28no—
708D4—2216no—
709D4—228no—
710D4—228no—
711D4—2216no—
712D4—4416no—
713D4—4416no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—48no—
726C2×C4—112no—
727C2×C4—114no—
728C2×C4—112no—
729C2×C4—112no—
730C2×C4—228no—
731C2×C4—228no—
732C2×C4—2216no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—228no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—224no—
742C2×C4—224no—
743C2×C4—448no—
744C2×C4—448no—
745C2×C4—448no—
746C2×C4—448no—
747C2×C4—448no—
748C2×C4—448no—
749C2×C4C2×D4×D1112yes—
750C2×C4C2×D4×D1112yes—
751C2×C4C2×D4×D1112yes—
752C2×C4#41×D1114yes—
753C2×C4#6704214yes—
754C22—28no—
755C22—24no—
756C22—42no—
757C22—44no—
758C22—42no—
759C22—114no—
760C22—222no—
761C22—228no—
762C22—222no—
763C22—228no—
764C22—228no—
765C22—224no—
766C22—224no—
767C22—4432no—
768C22—442no—
769C22—442no—
770C22—444no—
771C22—444no—
772C22—442no—
773C22—442no—
774C22C22×D4×D1111yescharacteristic
775C22C2×#41×D1112yes—
776C22C2×#41×D1112yes—
777C22C2×#6704212yes—
778C4—22no—
779C4—22no—
780C4—24no—
781C4—42no—
782C4—44no—
783C4—42no—
784C4—114no—
785C4—222no—
786C4—222no—
787C4—442no—
788C4—442no—
789C4—444no—
790C4#1062320514yes—
791C2—44no—
792C2—224no—
793C2—444no—
794C2—444no—
795C2D11×#52511yescharacteristic
796C2D11×#52511yescharacteristic
797C2C2×#1062320511yescharacteristic
798C2#1308222214yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2398C2
hypercenter#2398D11
hypocenterC11#34963
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. C2×C4×#4343C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074185C2semidirect
4. #13074177C2semidirect
5. #13073969C2semidirect
6. #13073514C2semidirect
7. #13072928C2semidirect
8. #13072885C2semidirect
9. #13071967C2semidirect
10. #13071936C2semidirect
11. #13071899C2semidirect
12. #13071897C2semidirect
13. #13071895C2semidirect
14. C4×#66937C2semidirect
15. C4×#66935C2semidirect
16. #13071008C2semidirect
17. C11×#2398C2semidirect
21. C2×C4×Q8×C11C22semidirect
23. C2×Q8×Dic11C22semidirect
26. C2×C4×C22⋊D11C22semidirect
31. C2×#66946C22semidirect
33. C2×#66945C22semidirect
41. C2×C4×D44C22semidirect
42. C2×C4×D44C22semidirect
44. C2×C42×D11C22semidirect
45. C11×#400C22semidirect
46. C11×#397C22semidirect
48. C11×#393C22semidirect
49. C4×C11×C22⋊C4C22semidirect
50. C11×#376C22semidirect
51. #10622844C22semidirect
53. #10622606C22semidirect
54. #10622605C22semidirect
56. #10622599C22semidirect
57. #10622573C22semidirect
58. #10622571C22semidirect
60. #10622569C22semidirect
62. #10622564C22semidirect
63. #10622563C22semidirect
64. #10622562C22semidirect
66. C4×(C2×D11)⋊C4C22semidirect
67. #10622545C22semidirect
68. C4×Dic11⋊C4C22semidirect
69. #10622290C22semidirect
70. #10622290C22semidirect
72. #10622284C22semidirect
73. #10622282C22semidirect
75. #10622281C22semidirect
77. #10622280C22semidirect
79. #10622278C22semidirect
80. #10622278C22semidirect
82. #10622264C22semidirect
83. #10622263C22semidirect
84. #10622260C22semidirect
167. C42×D11D4semidirect
206. C2×C22⋊D11#41semidirect
293. #2398D11semidirect
379. C2×C4×Q8C2×D11semidirect
400. #400C2×D11semidirect
406. #397C2×D11semidirect
410. #393C2×D11semidirect
436. C4×C22⋊C4C2×D11semidirect
438. #376C2×D11semidirect
680. C11#34963semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43432
C2×C4×D4×D112
#130741852
#130741772
#130739692
#130735142
#130729282
#130728852
#130719672
#130719362
#130718992
#130718972
#130718952
C4×#669372
C4×#669352
#130710082
C11×#23982
#3496311