Finite Group Databasebeta

← #14926562

Subgroups — #14926562

Order 2816.

2378 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076908C212yesmaximal, complemented
2#13076903C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic
4#13074586C211yesmaximal, characteristic, complemented
5#13074569C212yesmaximal, complemented
6#13074544C211yesmaximal, characteristic, complemented
7#13073176C212yesmaximal, complemented
8#13073117C212yesmaximal, complemented
9#13073001C212yesmaximal, complemented
10#13072942C212yesmaximal, complemented
11#13072440C212yesmaximal, complemented
12#13072366C212yesmaximal, complemented
13#13072167C212yesmaximal, complemented
14#13072093C212yesmaximal, complemented
15#13071349C211yesmaximal, characteristic, complemented
16#13071319C211yesmaximal, characteristic, complemented
17#13071250C212yesmaximal, complemented
18C4×#67006C212yesmaximal, complemented
19C22×C11×#95C211yesmaximal, characteristic, complemented
20C24×C4×C11C2211yescharacteristic
21C24×C4×C11C2211yescharacteristic
22C24×C4×C11C2211yescharacteristic
23C2×#67006C2212yes—
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66983C2211yescharacteristic
27C2×#66982C2212yes—
28C2×#66982C2212yes—
29C2×C4×C22⋊D11C2212yes—
30C2×C4×C22⋊D11C2212yes—
31C2×C4×C22⋊D11C2212yes—
32C2×#66977C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×C11×#95C2212yes—
36C2×C11×#95C2212yes—
37C2×C11×#95C2212yes—
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2212yes—
43#10622860C2212yes—
44#10622826C2212yes—
45#10622826C2212yes—
46#10622826C2212yes—
47#10622826C2212yes—
48#10622826C2212yes—
49#10622826C2212yes—
50#10622826C2212yes—
51#10622826C2212yes—
52#10622826C2212yes—
53#10622826C2212yes—
54#10622825C2211yescharacteristic
55#10622825C2211yescharacteristic
56#10622825C2211yescharacteristic
57#10622825C2211yescharacteristic
58#10622825C2211yescharacteristic
59#10622825C2211yescharacteristic
60#10622824C2212yes—
61#10622824C2212yes—
62#10622823C2212yes—
63#10622823C2212yes—
64#10622823C2212yes—
65#10622823C2212yes—
66#10622823C2212yes—
67#10622823C2212yes—
68#10622823C2212yes—
69#10622823C2212yes—
70#10622823C2212yes—
71#10622823C2212yes—
72C4×C22⋊Dic11C2212yes—
73C4×C22⋊Dic11C2212yes—
74C4×C22⋊Dic11C2212yes—
75#10622289C2212yescomplemented
76#10622288C2212yescomplemented
77#10622288C2212yescomplemented
78#10622288C2212yescomplemented
79#10622287C2212yescomplemented
80#10622286C2212yescomplemented
81#10622285C2212yescomplemented
82#10622283C2212yescomplemented
83#10622282C2212yescomplemented
84#10622282C2212yescomplemented
85#10622281C2212yescomplemented
86#10622280C2212yescomplemented
87#10622278C2212yescomplemented
88#10622277C2212yescomplemented
89C11⋊#401C2212yescomplemented
90#10622273C2212yescomplemented
91#10622273C2212yescomplemented
92#10622272C2212yescomplemented
93#10622271C2212yescomplemented
94#10622271C2212yescomplemented
95#10622271C2212yescomplemented
96#10622270C2212yescomplemented
97#10622270C2212yescomplemented
98#10622268C2212yescomplemented
99#10622267C2212yescomplemented
100#10622266C2212yescomplemented
101#10622265C2212yescomplemented
102#10622265C2212yescomplemented
103#10622264C2212yescomplemented
104#10622263C2212yescomplemented
105#10622260C2212yescomplemented
106#10622259C2212yescomplemented
107C25×C11C2311yescharacteristic
108C23×C4×C11—24no—
109C23×C4×C11—24no—
110C23×C4×C11—24no—
111C23×C4×C11—42no—
112C23×C4×C11—42no—
113C23×C4×C11—42no—
114C23×C4×C11—42no—
115C23×C4×C11—42no—
116C23×C4×C11—42no—
117C23×C4×C11C2312yes—
118C23×C4×C11C2311yescharacteristic
119C23×C4×C11C2311yescharacteristic
120C23×C4×C11C2312yes—
121C23×C4×C11C2312yes—
122C23×C4×C11C2311yescharacteristic
123C23×C4×C11C2311yescharacteristic
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×D44C2311yescharacteristic
135C22×C4×D11C2312yes—
136C22×Dic22C2311yescharacteristic
137#67006—28no—
138C2×C22⋊Dic11C2312yes—
139C2×C22⋊Dic11C2312yes—
140C2×C22⋊Dic11C2312yes—
141C2×C22⋊Dic11C2312yes—
142C2×C22⋊Dic11C2312yes—
143C2×C22⋊Dic11C2312yes—
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2312yes—
147#66983—24no—
148#66983—42no—
149#66983—42no—
150#66982—44no—
151#66982—44no—
152C4×C22⋊D11—28no—
153C4×C22⋊D11—44no—
154C4×C22⋊D11—44no—
155C2×(C2×D11)⋊C4C2312yes—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2311yescharacteristic
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171#66977—24no—
172#66977—42no—
173#66977—42no—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2312yes—
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⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206C11⋊#95C2312yes—
207C11⋊#95C2312yes—
208C11⋊#95C2312yes—
209C11⋊#95C2312yes—
210C11⋊#95C2312yes—
211C11⋊#95C2312yes—
212C11⋊#95C2312yes—
213C11⋊#95C2312yes—
214C11⋊#95C2312yes—
215#34997—111nomaximal, Sylow
216C24×C11—22no—
217C24×C11—22no—
218C24×C11—22no—
219C24×C11—22no—
220C24×C11—22no—
221C24×C11—22no—
222C24×C11#4114yes—
223C24×C11C2411yescharacteristic
224C24×C11C2411yescharacteristic
225C24×C11C2411yescharacteristic
226C23×D11C2412yes—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—24no—
232C22×C4×C11—24no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—24no—
236C22×C4×C11—24no—
237C22×C4×C11—24no—
238C22×C4×C11—24no—
239C22×C4×C11—22no—
240C22×C4×C11—22no—
241C22×C4×C11—24no—
242C22×C4×C11—24no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—41no—
248C22×C4×C11—41no—
249C22×C4×C11—42no—
250C22×C4×C11—42no—
251C22×C4×C11—41no—
252C22×C4×C11—41no—
253C22×C4×C11—41no—
254C22×C4×C11—41no—
255C22×C4×C11—41no—
256C22×C4×C11—41no—
257C22×C4×C11—41no—
258C22×C4×C11—41no—
259C22×C4×C11—41no—
260C22×C4×C11—41no—
261C22×C4×C11—41no—
262C22×C4×C11—41no—
263C22×C4×C11—42no—
264C22×C4×C11—42no—
265C22×C4×C11—41no—
266C22×C4×C11—41no—
267C22×C4×C11—416no—
268C22×C4×C11—416no—
269C22×C4×C11—416no—
270C22×C4×C11#4114yes—
271C22×C4×C11#4114yes—
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2412yes—
275C22×C4×C11C2412yes—
276C22×C4×C11C2412yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C2×C22⋊D11—24no—
281C2×C22⋊D11—24no—
282C2×C22⋊D11—24no—
283C2×C22⋊D11—24no—
284C2×C22⋊D11—24no—
285C2×C22⋊D11—24no—
286C2×C22⋊D11—24no—
287C2×C22⋊D11—24no—
288C2×C22⋊D11—24no—
289C22×Dic11C2412yes—
290C22×Dic11C2412yes—
291C22×Dic11C2412yes—
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2412yes—
295C22×Dic11C2412yes—
296C2×D44—22no—
297C2×D44—41no—
298C2×D44—41no—
299C2×C4×D11—24no—
300C2×C4×D11—42no—
301C2×C4×D11—42no—
302C2×Dic22—22no—
303C2×Dic22—41no—
304C2×Dic22—41no—
305C22⋊Dic11—24no—
306C22⋊Dic11—24no—
307C22⋊Dic11—24no—
308C22⋊Dic11—24no—
309C22⋊Dic11—24no—
310C22⋊Dic11—24no—
311C22⋊Dic11—24no—
312C22⋊Dic11—24no—
313C22⋊Dic11—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—24no—
316(C2×D11)⋊C4—42no—
317(C2×D11)⋊C4—42no—
318(C2×D11)⋊C4—42no—
319(C2×D11)⋊C4—42no—
320(C2×D11)⋊C4—42no—
321(C2×D11)⋊C4—42no—
322(C2×D11)⋊C4—42no—
323(C2×D11)⋊C4—42no—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11—41no—
327C4⋊Dic11—41no—
328C4⋊Dic11—41no—
329C4⋊Dic11—41no—
330Dic11⋊C4—24no—
331Dic11⋊C4—24no—
332Dic11⋊C4—42no—
333Dic11⋊C4—42no—
334Dic11⋊C4—42no—
335Dic11⋊C4—42no—
336Dic11⋊C4—42no—
337Dic11⋊C4—42no—
338Dic11⋊C4—42no—
339Dic11⋊C4—42no—
340C4×Dic11—24no—
341C4×Dic11—42no—
342C4×Dic11—42no—
343#2849—112no—
344#2848—111no—
345#2847—111no—
346#2646—111no—
347#2643—112no—
348#2639—111no—
349#2510—112no—
350#2505—112no—
351#2493—112no—
352#2488—112no—
353#2450—112no—
354#2444—112no—
355#2425—112no—
356#2419—112no—
357#2329—111no—
358#2325—111no—
359#2318—112no—
360C4×#120—112no—
361C22×#95D1111yescharacteristic, complemented
362C23×C11—28no—
363C23×C11—28no—
364C23×C11—28no—
365C23×C11—28no—
366C23×C11—28no—
367C23×C11—28no—
368C23×C11—28no—
369C23×C11—21no—
370C23×C11—21no—
371C23×C11—21no—
372C23×C11—21no—
373C23×C11—21no—
374C23×C11—21no—
375C23×C11—21no—
376C23×C11—21no—
377C23×C11—21no—
378C23×C11—21no—
379C23×C11—21no—
380C23×C11—21no—
381C23×C11C2×#4112yes—
382C23×C11C2×#4112yes—
383C23×C11C2×#4112yes—
384C23×C11C2×#4112yes—
385C23×C11C2×#4112yes—
386C23×C11H(5,𝔽2)12yes—
387C23×C11H(5,𝔽2)12yes—
388C23×C11H(5,𝔽2)12yes—
389C23×C112−1+412yes—
390C23×C11C2511yescharacteristic
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—22no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—44no—
420C2×C4×C11—44no—
421C2×C4×C11—44no—
422C2×C4×C11—44no—
423C2×C4×C11—48no—
424C2×C4×C11—48no—
425C2×C4×C11—44no—
426C2×C4×C11—44no—
427C2×C4×C11—44no—
428C2×C4×C11—44no—
429C2×C4×C11—48no—
430C2×C4×C11—44no—
431C2×C4×C11—44no—
432C2×C4×C11—48no—
433C2×C4×C11C2×#4114yes—
434C2×C4×C11C2×#4112yes—
435C2×C4×C11C2×#4112yes—
436C22⋊D11—48no—
437C22⋊D11—48no—
438C22⋊D11—48no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460D44—82no—
461C4×D11—84no—
462Dic22—82no—
463C24×C4C2×D1111yescharacteristic
464C24×C4C2×D1111yescharacteristic
465C24×C4C2×D1111yescharacteristic
466C2×#123—112no—
467C2×#123—112no—
468C2×C22⋊Q8—111no—
469C2×C22⋊Q8—111no—
470C2×C22⋊Q8—111no—
471C2×#121—111no—
472C2×#121—111no—
473C2×#121—111no—
474C2×#120—112no—
475C2×C4×D4—112no—
476C2×C4×D4—112no—
477C2×C4×D4—112no—
478#401—112no—
479#400—112no—
480#400—112no—
481#400—112no—
482#400—112no—
483#400—112no—
484#400—112no—
485#398—112no—
486#398—112no—
487#397—112no—
488#397—112no—
489#397—112no—
490#397—112no—
491#396—112no—
492#394—112no—
493#393—112no—
494#391—112no—
495#389—112no—
496#388—112no—
497#388—112no—
498#388—112no—
499#387—112no—
500#387—112no—
501#387—112no—
502#387—112no—
503#387—112no—
504#386—112no—
505#386—112no—
506#386—112no—
507#386—112no—
508#386—112no—
509#386—112no—
510#386—112no—
511#386—112no—
512#386—112no—
513#386—112no—
514#386—112no—
515#385—112no—
516#385—112no—
517#385—112no—
518#385—112no—
519#385—112no—
520#385—112no—
521#385—112no—
522#385—112no—
523#385—112no—
524#385—112no—
525#385—112no—
526#383—112no—
527#382—112no—
528#381—112no—
529#381—112no—
530#381—112no—
531#380—111no—
532#380—111no—
533#380—111no—
534#380—111no—
535#380—111no—
536#380—111no—
537#380—112no—
538#379—112no—
539C4×C22⋊C4—112no—
540C4×C22⋊C4—112no—
541C4×C22⋊C4—112no—
542C2×#95C2×D1111yescharacteristic
543C2×#95C2×D1111yescharacteristic
544C2×#95C2×D1111yescharacteristic
545C2×#95C2×D1111yescharacteristic
546C2×#95C2×D1112yes—
547C2×#95C2×D1112yes—
548C2×#95C2×D1112yes—
549C2×#95C2×D1112yes—
550C22×C11—232no—
551C22×C11—22no—
552C22×C11—22no—
553C22×C11—22no—
554C22×C11—22no—
555C22×C11—22no—
556C22×C11—22no—
557C22×C11—22no—
558C22×C11—22no—
559C22×C11—22no—
560C22×C11—22no—
561C22×C11—22no—
562C22×C11—22no—
563C22×C11—22no—
564C22×C11—22no—
565C22×C11—22no—
566C22×C11—22no—
567C22×C11—22no—
568C22×C11—22no—
569C22×C11#52914yes—
570C22×C11#53814yes—
571C22×C11#53914yes—
572C22×C11C22×#4111yescharacteristic
573C22×C11C22×#4111yescharacteristic
574C22×C11C22×#4111yescharacteristic
575C22×C11C2×H(5,𝔽2)11yescharacteristic
576C22×C11C2×H(5,𝔽2)11yescharacteristic
577C22×C11C2×H(5,𝔽2)11yescharacteristic
578C22×C11C2×2−1+411yescharacteristic
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C2×D11—42no—
585C2×D11—42no—
586C4×C11—22no—
587C4×C11—24no—
588C4×C11—22no—
589C4×C11—42no—
590C4×C11—42no—
591C4×C11—41no—
592C4×C11—41no—
593C4×C11—42no—
594Dic11—42no—
595Dic11—42no—
596Dic11—42no—
597Dic11—42no—
598Dic11—42no—
599Dic11—42no—
600Dic11—42no—
601C25C22×D1111yescharacteristic
602C22×Q8—111no—
603C22×D4—112no—
604C22×D4—112no—
605C22×D4—112no—
606C22×D4—111no—
607C23×C4—24no—
608C23×C4—24no—
609C23×C4—24no—
610C23×C4—42no—
611C23×C4—42no—
612C23×C4—42no—
613C23×C4—42no—
614C23×C4—42no—
615C23×C4—42no—
616C23×C4—112no—
617C23×C4C22×D1112yes—
618C23×C4C22×D1112yes—
619C23×C4C22×D1112yes—
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623C23×C4C22×D1111yescharacteristic
624C23×C4C22×D1111yescharacteristic
625C23×C4C22×D1111yescharacteristic
626C23×C4C22×D1111yescharacteristic
627C23×C4C22×D1111yescharacteristic
628C23×C4C22×D1112yes—
629C23×C4C22×D1111yescharacteristic
630C23×C4C22×D1111yescharacteristic
631#123—444no—
632#123—444no—
633C22⋊Q8—224no—
634C22⋊Q8—442no—
635C22⋊Q8—442no—
636#121—224no—
637#121—442no—
638#121—442no—
639#120—228no—
640C4×D4—228no—
641C4×D4—444no—
642C4×D4—444no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—112no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—112no—
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—112no—
671C2×C22⋊C4—112no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4—112no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4—112no—
677C2×C22⋊C4—112no—
678C2×C42—112no—
679C2×C42—112no—
680C2×C42—112no—
681#95—112no—
682#95—112no—
683#95—112no—
684#95—112no—
685#95—112no—
686#95—112no—
687#95—112no—
688#95—112no—
689#95—112no—
690#95—112no—
691#95—112no—
692#95—112no—
693#95—112no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—112no—
698#95—112no—
699#95—112no—
700#95—112no—
701#95C22×D1112yes—
702#95C22×D1112yes—
703#95C22×D1112yes—
704#95C22×D1112yes—
705#95C22×D1112yes—
706#95C22×D1112yes—
707#95C22×D1112yes—
708#95C22×D1112yes—
709C2×C11—24no—
710C2×C11—24no—
711C2×C11—24no—
712C2×C11C2×#52911yescharacteristic
713C2×C11C2×#53811yescharacteristic
714C2×C11C2×#53911yescharacteristic
715C2×C11#349011yescharacteristic
716C2×C11#349011yescharacteristic
717C2×C11#349211yescharacteristic
718C2×C11#349211yescharacteristic
719D11—82no—
720C24—22no—
721C24—22no—
722C24—22no—
723C24—22no—
724C24—22no—
725C24—22no—
726C24—112no—
727C24#433914yes—
728C24C23×D1111yescharacteristic
729C24C23×D1111yescharacteristic
730C24C23×D1111yescharacteristic
731C2×Q8—222no—
732C2×Q8—441no—
733C2×Q8—441no—
734C2×D4—224no—
735C2×D4—224no—
736C2×D4—224no—
737C2×D4—224no—
738C2×D4—224no—
739C2×D4—224no—
740C2×D4—224no—
741C2×D4—224no—
742C2×D4—224no—
743C2×D4—222no—
744C2×D4—441no—
745C2×D4—441no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—41no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—41no—
776C22×C4—41no—
777C22×C4—41no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—416no—
787C22×C4—416no—
788C22×C4—416no—
789C22×C4—112no—
790C22×C4—112no—
791C22×C4—112no—
792C22×C4—112no—
793C22×C4—112no—
794C22×C4—112no—
795C22×C4—112no—
796C22×C4—224no—
797C22×C4—442no—
798C22×C4—442no—
799C22×C4#433914yes—
800C22×C4#433914yes—
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1111yescharacteristic
803C22×C4C23×D1112yes—
804C22×C4C23×D1112yes—
805C22×C4C23×D1112yes—
806C22×C4C23×D1112yes—
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1111yescharacteristic
809C4⋊C4—224no—
810C4⋊C4—222no—
811C4⋊C4—224no—
812C4⋊C4—222no—
813C4⋊C4—442no—
814C4⋊C4—442no—
815C4⋊C4—441no—
816C4⋊C4—441no—
817C4⋊C4—442no—
818C4⋊C4—442no—
819C4⋊C4—441no—
820C4⋊C4—441no—
821C4⋊C4—442no—
822C4⋊C4—442no—
823C4⋊C4—442no—
824C4⋊C4—442no—
825C22⋊C4—224no—
826C22⋊C4—224no—
827C22⋊C4—224no—
828C22⋊C4—224no—
829C22⋊C4—224no—
830C22⋊C4—224no—
831C22⋊C4—224no—
832C22⋊C4—224no—
833C22⋊C4—224no—
834C22⋊C4—224no—
835C22⋊C4—224no—
836C22⋊C4—442no—
837C22⋊C4—442no—
838C22⋊C4—442no—
839C22⋊C4—442no—
840C22⋊C4—442no—
841C22⋊C4—442no—
842C22⋊C4—442no—
843C22⋊C4—442no—
844C42—224no—
845C42—442no—
846C42—442no—
847C11#3499711yescharacteristic, complemented, Sylow
848C23—28no—
849C23—28no—
850C23—28no—
851C23—28no—
852C23—28no—
853C23—28no—
854C23—28no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23C2×#433912yes—
875C23C2×#433912yes—
876C23C2×#433912yes—
877C23C2×#433912yes—
878C23C2×#433912yes—
879C23#6703712yes—
880C23#6703712yes—
881C23#6703712yes—
882C23#6704012yes—
883C23C24×D1111yescharacteristic
884Q8—882no—
885D4—448no—
886D4—448no—
887D4—448no—
888D4—882no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—44no—
911C2×C4—44no—
912C2×C4—48no—
913C2×C4—48no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—44no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—48no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—48no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—884no—
946C2×C4C2×#433914yes—
947C2×C4C2×#433912yes—
948C2×C4C2×#433912yes—
949C22—232no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—22no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22—442no—
973C22—442no—
974C22—442no—
975C22#1062301014yes—
976C22#1062302514yes—
977C22#1062304614yes—
978C22C22×#433911yescharacteristic
979C22C22×#433911yescharacteristic
980C22C22×#433911yescharacteristic
981C22C2×#6703711yescharacteristic
982C22C2×#6703711yescharacteristic
983C22C2×#6703711yescharacteristic
984C22C2×#6704011yescharacteristic
985C4—24no—
986C4—22no—
987C4—22no—
988C4—42no—
989C4—42no—
990C4—41no—
991C4—41no—
992C4—42no—
993C4—442no—
994C4—442no—
995C4—442no—
996C4—442no—
997C4—442no—
998C4—442no—
999C4—442no—
1000C2—24no—
1001C2—24no—
1002C2—24no—
1003C2—882no—
1004C2C2×#1062301011yescharacteristic
1005C2C2×#1062302511yescharacteristic
1006C2C2×#1062304611yescharacteristic
1007C2#1308230511yescharacteristic
1008C2#1308230511yescharacteristic
1009C2#1308232511yescharacteristic
1010C2#1308232511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×#95C2
prime radical#13076898C2
hypercenterC22×#95D11
hypocenterC11#34997
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. #13076908C2semidirect
2. #13076903C2semidirect
4. #13074586C2semidirect
5. #13074569C2semidirect
6. #13074544C2semidirect
7. #13073176C2semidirect
8. #13073117C2semidirect
9. #13073001C2semidirect
10. #13072942C2semidirect
11. #13072440C2semidirect
12. #13072366C2semidirect
13. #13072167C2semidirect
14. #13072093C2semidirect
15. #13071349C2semidirect
16. #13071319C2semidirect
17. #13071250C2semidirect
18. C4×#67006C2semidirect
19. C22×C11×#95C2semidirect
75. #10622289C22semidirect
76. #10622288C22semidirect
77. #10622288C22semidirect
78. #10622288C22semidirect
79. #10622287C22semidirect
80. #10622286C22semidirect
81. #10622285C22semidirect
82. #10622283C22semidirect
83. #10622282C22semidirect
84. #10622282C22semidirect
85. #10622281C22semidirect
86. #10622280C22semidirect
87. #10622278C22semidirect
88. #10622277C22semidirect
89. C11⋊#401C22semidirect
90. #10622273C22semidirect
91. #10622273C22semidirect
92. #10622272C22semidirect
93. #10622271C22semidirect
94. #10622271C22semidirect
95. #10622271C22semidirect
96. #10622270C22semidirect
97. #10622270C22semidirect
98. #10622268C22semidirect
99. #10622267C22semidirect
100. #10622266C22semidirect
101. #10622265C22semidirect
102. #10622265C22semidirect
103. #10622264C22semidirect
104. #10622263C22semidirect
105. #10622260C22semidirect
106. #10622259C22semidirect
361. C22×#95D11semidirect
847. C11#34997semidirect

Maximal subgroups

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

subgroupindex
#130769082
#130769032
#130768982
#130745862
#130745692
#130745442
#130731762
#130731172
#130730012
#130729422
#130724402
#130723662
#130721672
#130720932
#130713492
#130713192
#130712502
C4×#670062
C22×C11×#952
#3499711