Finite Group Databasebeta

← #14960565

Subgroups — #14960565

Order 2816.

3038 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623025C211yesmaximal, characteristic, complemented
2#13076903C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic, complemented
4#13075093C214yesmaximal, complemented
5#13074917C214yesmaximal, complemented
6#13074906C214yesmaximal, complemented
7#13074847C214yesmaximal, complemented
8#13074421C211yesmaximal, characteristic, complemented
9#13074350C211yesmaximal, characteristic, complemented
10#13073963C212yesmaximal, complemented
11#13071990C212yesmaximal, complemented
12#13071990C212yesmaximal, complemented
13#13071966C212yesmaximal, complemented
14#13071230C211yesmaximal, characteristic, complemented
15C22×C11×#121C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C2×C11×#121—28no—
21C2×C11×#121C2214yes—
22C2×C11×#121C2214yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C2×#67006C2212yes—
27C2×#67006C2212yes—
28C2×#67006C2212yes—
29C22×C22⋊Dic11C2212yes—
30C2×#66992C2214yescomplemented
31C2×#66992C2214yescomplemented
32C2×#66991C2214yescomplemented
33C2×#66983C2211yescharacteristic
34C2×#66983C2212yescomplemented
35C2×C4×C22⋊D11C2212yes—
36C2×#66977C2211yescharacteristic
37C2×#66977C2212yescomplemented
38#10623025—28no—
39C2×#66938C2212yescomplemented
40C2×#66937C2212yescomplemented
41C2×#66936C2212yescomplemented
42C2×#66932C2212yescomplemented
43#10622860C2212yes—
44#10622860C2212yes—
45#10622836C2214yescomplemented
46#10622836C2214yescomplemented
47#10622836C2214yescomplemented
48#10622835C2214yescomplemented
49#10622835C2214yescomplemented
50#10622835C2214yescomplemented
51#10622834C2214yescomplemented
52#10622833C2214yescomplemented
53#10622833C2214yescomplemented
54#10622826C2212yes—
55#10622826C2212yes—
56#10622826C2214yescomplemented
57#10622825C2212yes—
58#10622825C2211yescharacteristic
59#10622825C2211yescharacteristic
60#10622825C2212yescomplemented
61#10622825C2212yescomplemented
62#10622823C2212yes—
63#10622823C2212yes—
64#10622823C2214yescomplemented
65#10622607C2214yescomplemented
66#10622602C2214yescomplemented
67#10622597C2214yescomplemented
68#10622591C2214yescomplemented
69#10622574C2214yescomplemented
70#10622573C2212yescomplemented
71#10622566C2212yescomplemented
72#10622563C2214yescomplemented
73#10622563C2214yescomplemented
74#10622562C2212yescomplemented
75#10622561C2214yescomplemented
76#10622560C2212yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C25×C11C2311yescharacteristic
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11—44no—
84C22×D4×C11—44no—
85C22×D4×C11—44no—
86C22×D4×C11C2314yes—
87C22×D4×C11C2314yes—
88C22×D4×C11C2314yes—
89C23×C4×C11—24no—
90C23×C4×C11—44no—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2312yes—
93C23×C4×C11C2312yes—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2312yes—
99C22×C22⋊D11C2312yes—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C23×Dic11C2314yes—
103C22×D44C2311yescharacteristic
104C22×C4×D11C2312yes—
105C22×Dic22C2311yescharacteristic
106C11×#121—216no—
107C11×#121—216no—
108C2×C11×C4⋊C4—24no—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4D418yescomplemented
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116#67006—28no—
117#67006—44no—
118#67006—44no—
119C2×C22⋊Dic11—44no—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132#66992—48no—
133#66992—48no—
134#66991—48no—
135#66983—24no—
136#66983—44no—
137C4×C22⋊D11—28no—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2312yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2312yes—
146C2×C4⋊Dic11C2314yes—
147#66977—24no—
148#66977—44no—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×C4×Dic11C2312yes—
154#66938—28no—
155#66937—28no—
156#66936—28no—
157#66932—28no—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2312yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165#36706—111nomaximal, Sylow
166C24×C11—22no—
167C24×C11—24no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—42no—
176C24×C11—42no—
177C24×C11—42no—
178C24×C11—42no—
179C24×C11—42no—
180C24×C11C2×D414yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2412yes—
184C24×C11C2411yescharacteristic
185C23×D11C2412yes—
186C2×D4×C11—28no—
187C2×D4×C11—28no—
188C2×D4×C11—28no—
189C2×D4×C11—28no—
190C2×D4×C11—28no—
191C2×D4×C11—28no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—416no—
196C2×D4×C11—416no—
197C2×D4×C11—416no—
198C22×C4×C11—22no—
199C22×C4×C11—24no—
200C22×C4×C11—22no—
201C22×C4×C11—24no—
202C22×C4×C11—24no—
203C22×C4×C11—24no—
204C22×C4×C11—24no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11—42no—
210C22×C4×C11—416no—
211C22×C4×C11C2×D414yes—
212C22×C4×C11C2×D414yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2411yescharacteristic
216C22×C4×C11C2411yescharacteristic
217C22×C4×C11C2412yes—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C22×Dic11—44no—
232C22×Dic11—44no—
233C22×Dic11—44no—
234C22×Dic11C2412yes—
235C22×Dic11C2414yes—
236C22×Dic11C2414yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C2×D44—22no—
240C2×D44—42no—
241C2×C4×D11—24no—
242C2×C4×D11—44no—
243C2×Dic22—22no—
244C2×Dic22—42no—
245C11×C4⋊C4—28no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4C2×D418yes—
249C11×C22⋊C4C2×D418yes—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—28no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—44no—
257C22⋊Dic11—44no—
258C22⋊Dic11—44no—
259C22⋊Dic11—44no—
260C22⋊Dic11—44no—
261C22⋊Dic11—44no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—44no—
266C4⋊Dic11—22no—
267C4⋊Dic11—22no—
268C4⋊Dic11—42no—
269C4⋊Dic11—42no—
270C4⋊Dic11—44no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—28no—
274Dic11⋊C4—44no—
275C4×Dic11—24no—
276C2×#538—111no—
277C22×#121D1111yescharacteristic, complemented
278#2848—111no—
279#2847—111no—
280#2691—114no—
281#2676—114no—
282#2675—114no—
283#2671—114no—
284#2626—111no—
285#2617—111no—
286#2579—112no—
287#2410—112no—
288#2410—112no—
289#2408—112no—
290#2315—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—28no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—24no—
299C23×C11—24no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—28no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—24no—
308C23×C11—24no—
309C23×C11—22no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—48no—
313C23×C11—48no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—84no—
320C23×C11—84no—
321C23×C11—84no—
322C23×C11—84no—
323C23×C11C22×D414yes—
324C23×C11C22×D412yes—
325C23×C11H(5,𝔽2)14yes—
326C23×C11H(5,𝔽2)12yes—
327C23×C112−1+412yes—
328C23×C11C2511yescharacteristic
329C22×D11—22no—
330C22×D11—24no—
331C22×D11—24no—
332C22×D11—22no—
333C22×D11—22no—
334D4×C11—416no—
335D4×C11—416no—
336D4×C11—416no—
337C2×C4×C11—28no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—44no—
346C2×C4×C11—44no—
347C2×C4×C11—48no—
348C2×C4×C11—48no—
349C2×C4×C11—44no—
350C2×C4×C11C22×D414yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11H(5,𝔽2)14yes—
354C22⋊D11—48no—
355C22⋊D11—84no—
356C22⋊D11—84no—
357C22⋊D11—88no—
358C22⋊D11—88no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—24no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—24no—
368C2×Dic11—24no—
369C2×Dic11—24no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—88no—
373D44—82no—
374C4×D11—84no—
375Dic22—82no—
376C23×D4C2×D1111yescharacteristic
377C23×D4C2×D1111yescharacteristic
378C23×D4C2×D1111yescharacteristic
379C24×C4C2×D1111yescharacteristic
380#538—228no—
381C2×#126—112no—
382C2×#124—112no—
383C2×#123—112no—
384C2×C22⋊Q8—111no—
385C2×C22⋊Q8—112no—
386C2×#121—28no—
387C2×#121—111no—
388C2×#121—114no—
389C2×#121—114no—
390C2×#121—114no—
391C2×#121—112no—
392C2×#121—112no—
393C2×#121C2×D1114yes—
394C2×#121C2×D1114yes—
395C2×#120—112no—
396C2×#120—112no—
397C2×#120—112no—
398C2×C4×D4—112no—
399C22×C4⋊C4C2×D1111yescharacteristic
400C22×C22⋊C4—112no—
401C22×C22⋊C4C2×D1111yescharacteristic
402C22×C22⋊C4C2×D1111yescharacteristic
403#399—112no—
404#398—114no—
405#397—112no—
406#396—114no—
407#396—114no—
408#394—114no—
409#394—114no—
410#394—114no—
411#394—114no—
412#393—112no—
413#392—114no—
414#392—114no—
415#392—114no—
416#392—112no—
417#390—114no—
418#387—114no—
419#386—114no—
420#386—114no—
421#386—112no—
422#386—112no—
423#386—114no—
424#385—112no—
425#385—112no—
426#385—114no—
427#385—114no—
428#385—114no—
429#385—114no—
430#380—112no—
431#380—111no—
432#380—111no—
433#380—112no—
434#380—112no—
435#379—112no—
436#379—112no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—24no—
440C22×C11—24no—
441C22×C11—24no—
442C22×C11—24no—
443C22×C11—24no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—416no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—44no—
452C22×C11—42no—
453C22×C11—44no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—44no—
458C22×C11—44no—
459C22×C11—88no—
460C22×C11—88no—
461C22×C11#53714yes—
462C22×C11C23×D411yescharacteristic
463C22×C11C2×H(5,𝔽2)12yes—
464C22×C11C2×H(5,𝔽2)12yes—
465C22×C11C2×H(5,𝔽2)11yescharacteristic
466C22×C11C2×2−1+411yescharacteristic
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—44no—
471C2×D11—44no—
472C4×C11—24no—
473C4×C11—22no—
474C4×C11—22no—
475C4×C11—24no—
476C4×C11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480Dic11—44no—
481Dic11—44no—
482C25C22×D1111yescharacteristic
483C25C22×D1111yescharacteristic
484C25C22×D1111yescharacteristic
485C22×Q8—111no—
486C22×D4—24no—
487C22×D4—24no—
488C22×D4—24no—
489C22×D4—44no—
490C22×D4—44no—
491C22×D4—44no—
492C22×D4—112no—
493C22×D4—112no—
494C22×D4—112no—
495C22×D4—114no—
496C22×D4—114no—
497C22×D4—111no—
498C22×D4C22×D1114yes—
499C22×D4C22×D1114yes—
500C22×D4C22×D1114yes—
501C23×C4—24no—
502C23×C4—44no—
503C23×C4—114no—
504C23×C4—112no—
505C23×C4C22×D1111yescharacteristic
506C23×C4C22×D1112yes—
507C23×C4C22×D1112yes—
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511#126—228no—
512#124—228no—
513#123—228no—
514C22⋊Q8—224no—
515C22⋊Q8—444no—
516#121—216no—
517#121—216no—
518#121—224no—
519#121—228no—
520#121—444no—
521#121—448no—
522#121—448no—
523#121—448no—
524#120—228no—
525#120—444no—
526#120—444no—
527C4×D4—228no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—112no—
531C2×C4⋊C4—114no—
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⋊C4C22×D1114yes—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4—112no—
544C2×C22⋊C4—112no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—112no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—112no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—444no—
557C2×C22⋊C4C22⋊D1118yescomplemented
558C2×C22⋊C4C22×D1112yes—
559C2×C22⋊C4C22×D1112yes—
560C2×C22⋊C4C22×D1112yes—
561C2×C22⋊C4C22×D1112yes—
562C2×C42—112no—
563#95—112no—
564#95—114no—
565#95—114no—
566#95—112no—
567#95—114no—
568#95—114no—
569#95—114no—
570C2×C11—24no—
571C2×C11—44no—
572C2×C11—44no—
573C2×C11—82no—
574C2×C11C2×#53711yescharacteristic
575C2×C11#348411yescharacteristic
576C2×C11#348411yescharacteristic
577C2×C11#353612yes—
578C2×C11#353712yes—
579D11—82no—
580C24—24no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—42no—
590C24—42no—
591C24—42no—
592C24—42no—
593C24—42no—
594C24—112no—
595C24C2×C22⋊D1114yes—
596C24C23×D1112yes—
597C24C23×D1112yes—
598C24C23×D1112yes—
599C24C23×D1111yescharacteristic
600C2×Q8—222no—
601C2×Q8—442no—
602C2×D4—28no—
603C2×D4—28no—
604C2×D4—28no—
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—416no—
612C2×D4—416no—
613C2×D4—416no—
614C2×D4—224no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—228no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—222no—
621C2×D4—442no—
622C2×D4—444no—
623C2×D4—444no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—444no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—22no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—416no—
642C22×C4—112no—
643C22×C4—114no—
644C22×C4—114no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—224no—
648C22×C4—444no—
649C22×C4—444no—
650C22×C4—444no—
651C22×C4—444no—
652C22×C4C2×C22⋊D1114yes—
653C22×C4C2×C22⋊D1114yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1111yescharacteristic
658C22×C4C23×D1111yescharacteristic
659C4⋊C4—28no—
660C4⋊C4—228no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—222no—
664C4⋊C4—222no—
665C4⋊C4—444no—
666C4⋊C4—442no—
667C4⋊C4—444no—
668C4⋊C4—442no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—228no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—228no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—444no—
681C22⋊C4—444no—
682C22⋊C4—444no—
683C22⋊C4—444no—
684C22⋊C4—444no—
685C22⋊C4—444no—
686C22⋊C4—444no—
687C22⋊C4C2×C22⋊D1118yes—
688C22⋊C4C2×C22⋊D1118yes—
689C42—224no—
690C11#3670611yescharacteristic, complemented, Sylow
691C23—22no—
692C23—22no—
693C23—28no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—28no—
705C23—24no—
706C23—24no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—44no—
711C23—44no—
712C23—48no—
713C23—48no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—84no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—224no—
724C23—224no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23#6703714yes—
729C23#6704212yes—
730C23#6704312yes—
731C23C22×C22⋊D1114yes—
732C23C22×C22⋊D1112yes—
733C23C24×D1111yescharacteristic
734Q8—882no—
735D4—416no—
736D4—416no—
737D4—416no—
738D4—448no—
739D4—882no—
740D4—884no—
741D4—884no—
742D4—888no—
743D4—888no—
744C2×C4—28no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—48no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—224no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—224no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—884no—
771C2×C4—888no—
772C2×C4#6703714yes—
773C2×C4C22×C22⋊D1114yes—
774C2×C4C22×C22⋊D1112yes—
775C2×C4C22×C22⋊D1112yes—
776C22—22no—
777C22—22no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—416no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—44no—
798C22—88no—
799C22—88no—
800C22—442no—
801C22—442no—
802C22—442no—
803C22—444no—
804C22—444no—
805C22#1062336414yes—
806C22C2×#6703712yes—
807C22C2×#6703712yes—
808C22C2×#6704211yescharacteristic
809C22C2×#6704311yescharacteristic
810C22C23×C22⋊D1111yescharacteristic
811C4—24no—
812C4—22no—
813C4—22no—
814C4—24no—
815C4—42no—
816C4—442no—
817C4—442no—
818C4—442no—
819C4—444no—
820C4—444no—
821C2—24no—
822C2—44no—
823C2—44no—
824C2—82no—
825C2—882no—
826C2C2×#1062336411yescharacteristic
827C2#1308225111yescharacteristic
828C2#1308225111yescharacteristic
829C2#1308283812yes—
830C2#1308285112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×#121C2
hypercenterC22×#121D11
hypocenterC11#36706
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623025C2semidirect
2. #13076903C2semidirect
3. #13076898C2semidirect
4. #13075093C2semidirect
5. #13074917C2semidirect
6. #13074906C2semidirect
7. #13074847C2semidirect
8. #13074421C2semidirect
9. #13074350C2semidirect
10. #13073963C2semidirect
11. #13071990C2semidirect
12. #13071990C2semidirect
13. #13071966C2semidirect
14. #13071230C2semidirect
15. C22×C11×#121C2semidirect
30. C2×#66992C22semidirect
31. C2×#66992C22semidirect
32. C2×#66991C22semidirect
34. C2×#66983C22semidirect
37. C2×#66977C22semidirect
39. C2×#66938C22semidirect
40. C2×#66937C22semidirect
41. C2×#66936C22semidirect
42. C2×#66932C22semidirect
45. #10622836C22semidirect
46. #10622836C22semidirect
47. #10622836C22semidirect
48. #10622835C22semidirect
49. #10622835C22semidirect
50. #10622835C22semidirect
51. #10622834C22semidirect
52. #10622833C22semidirect
53. #10622833C22semidirect
56. #10622826C22semidirect
60. #10622825C22semidirect
61. #10622825C22semidirect
64. #10622823C22semidirect
65. #10622607C22semidirect
66. #10622602C22semidirect
67. #10622597C22semidirect
68. #10622591C22semidirect
69. #10622574C22semidirect
70. #10622573C22semidirect
71. #10622566C22semidirect
72. #10622563C22semidirect
73. #10622563C22semidirect
74. #10622562C22semidirect
75. #10622561C22semidirect
76. #10622560C22semidirect
111. C2×C11×C22⋊C4D4semidirect
277. C22×#121D11semidirect
557. C2×C22⋊C4C22⋊D11semidirect
690. C11#36706semidirect

Maximal subgroups

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

subgroupindex
C2×#106230252
#130769032
#130768982
#130750932
#130749172
#130749062
#130748472
#130744212
#130743502
#130739632
#130719902
#130719662
#130712302
C22×C11×#1212
#3670611