Finite Group Databasebeta

← #14806831

Subgroups — #14806831

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic
2C2×#10622657C211yesmaximal, characteristic, complemented
3C2×#10622665C211yesmaximal, characteristic, complemented
4#13069954C211yesmaximal, characteristic, complemented
5#13069819C211yesmaximal, characteristic, complemented
6#13069767C211yesmaximal, characteristic, complemented
7#13069624C211yesmaximal, characteristic, complemented
8#13068960C211yesmaximal, characteristic, complemented
9#13068929C211yesmaximal, characteristic, complemented
10#13068928C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic
12#13068869C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14#13068337C211yesmaximal, characteristic, complemented
15C11×#2415C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66988—21no—
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27#10623072—24no—
28#10623072—24no—
29C2×#66942—21no—
30C2×#66932—21no—
31C2×#66930—21no—
32C2×#66923C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#397—21no—
35C11×#394—21no—
36C11×#391C2211yescharacteristic
37C11×#389—21no—
38C11×#389C2211yescharacteristic
39C11×#388—21no—
40C11×#380C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47#10622665—24no—
48#10622657—24no—
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11—21no—
68C22×Dic22C2311yescharacteristic
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—41no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C11×#117—22no—
76C11×#117—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×#4326—22no—
96C2×#4326—22no—
97C2×#4326—41no—
98#66988—28no—
99#66979—22no—
100#66979—22no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11D414yes—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107#66977—22no—
108#66977—22no—
109#66977—22no—
110#66977D414yes—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C2×#4318—22no—
119C2×#4318—22no—
120C2×#4318—41no—
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125#66942—28no—
126#66932—28no—
127#66930—28no—
128#66923—22no—
129#66923—22no—
130C4×Dic22—22no—
131C4×Dic22—22no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136#66899—22no—
137#66899—22no—
138#66899—22no—
139C22⋊(C11⋊C8)—22no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—41no—
142#66874—22no—
143#66874—22no—
144#66874—41no—
145#66872—22no—
146#66871—22no—
147#66871—22no—
148#25557—111nomaximal, Sylow
149C24×C11C2×D411yescharacteristic
150C24×C11C2×D411yescharacteristic
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×D4×C11—22no—
158C2×D4×C11—41no—
159C2×D4×C11—41no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2411yescharacteristic
181C22×Dic11—24no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—42no—
187C22×Dic11—42no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22C2×D412yes—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4—42no—
202C11×C4⋊C4—42no—
203C11×C4⋊C4#4112yes—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—42no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—42no—
213C22⋊Dic11—24no—
214C22⋊Dic11—24no—
215C22⋊Dic11—24no—
216#4326—44no—
217C4⋊Dic11—24no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11C2×D412yes—
222C4⋊Dic11C2×D412yes—
223C4⋊Dic11C2×D412yes—
224Dic11⋊C4—24no—
225Dic11⋊C4—24no—
226Dic11⋊C4—24no—
227Dic11⋊C4—24no—
228Dic11⋊C4—24no—
229C4×Dic11—24no—
230C4×Dic11—24no—
231#4318—44no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8#4112yes—
244C2×#552—111no—
245C2×#484—111no—
246C2×#470—111no—
247#2415D1111yescharacteristic
248#2059—111no—
249#2036—111no—
250#2026—111no—
251#2001—111no—
252#1878—111no—
253#1873—111no—
254#1873—111no—
255#1870—111no—
256#1863—111no—
257#1854—111no—
258#1736—111no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11#12012yes—
273C23×C11C22×D411yescharacteristic
274Q8×C11—41no—
275Q8×C11—41no—
276Q8×C11—41no—
277Q8×C11—41no—
278D4×C11—44no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11#12012yes—
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C112−1+411yescharacteristic
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—48no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330Dic22—22no—
331Dic22—22no—
332Dic22—41no—
333Dic22—41no—
334C11⋊C8—22no—
335C11⋊C8—41no—
336C11⋊C8—41no—
337C11⋊C8—41no—
338C22×Q16—111no—
339C22×M16—111no—
340#552—224no—
341#552—224no—
342C2×#126—221no—
343C2×#125—111no—
344C2×#125—221no—
345C2×#123—221no—
346C2×C22⋊Q8—111no—
347C2×C22⋊Q8—111no—
348C2×C22⋊Q8C2×D1111yescharacteristic
349C2×C22⋊Q8C2×D1111yescharacteristic
350C2×C4×Q8—111no—
351C2×C4×D4C2×D1111yescharacteristic
352C2×#117—111no—
353C2×#117—221no—
354C2×#117C2×D1111yescharacteristic
355C22×C4⋊C4—111no—
356#484—224no—
357#470—224no—
358C2×#107—111no—
359C2×#107—111no—
360C2×#106—111no—
361C2×#103—111no—
362C2×#103—111no—
363C2×#103—111no—
364C2×#103—111no—
365C2×#103—111no—
366C2×#103—111no—
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370#397—21no—
371#394—21no—
372#391C2×D1111yescharacteristic
373#389—21no—
374#389C2×D1111yescharacteristic
375#388—21no—
376#380C2×D1111yescharacteristic
377#340—111no—
378#340—111no—
379#340—111no—
380#340—111no—
381#340—111no—
382#340—111no—
383#336—111no—
384#336—111no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11C2×#12011yescharacteristic
400C22×C11#54611yescharacteristic
401C22×C11#54711yescharacteristic
402C22×C11#57511yescharacteristic
403C22×C11#57511yescharacteristic
404C22×C11#57811yescharacteristic
405C22×C11#57811yescharacteristic
406C4×C11—22no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11—41no—
410C4×C11—42no—
411C4×C11—81no—
412C4×C11—81no—
413C4×C11—81no—
414C4×C11#53211yescharacteristic
415C4×C11#53711yescharacteristic
416C4×C11#54611yescharacteristic
417C4×C11#54711yescharacteristic
418Dic11—42no—
419Dic11—42no—
420Dic11—42no—
421Dic11—42no—
422C22×Q8—111no—
423C22×Q8C22×D1111yescharacteristic
424C22×D4C22⋊D1111yescharacteristic
425C23×C4—221no—
426C23×C4C22×D1111yescharacteristic
427C23×C4C22×D1111yescharacteristic
428C2×Q16—222no—
429C2×Q16—222no—
430C2×Q16—441no—
431C2×M16—222no—
432C2×M16—222no—
433C2×M16—441no—
434C22×C8—111no—
435C22×C8—111no—
436C22×C8—111no—
437C22×C8—111no—
438#126—228no—
439#125—222no—
440#125—222no—
441#125—228no—
442#123—228no—
443C22⋊Q8—22no—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—41no—
447C22⋊Q8—114no—
448C22⋊Q8—222no—
449C22⋊Q8—222no—
450C22⋊Q8—222no—
451C4×Q8—222no—
452C4×Q8—222no—
453C4×D4—22no—
454C4×D4—22no—
455#117—22no—
456#117—41no—
457#117—228no—
458#117—222no—
459#117—222no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—114no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—222no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4C22⋊D1111yescharacteristic
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4C22⋊D1111yescharacteristic
486C2×C22⋊C4C22⋊D1111yescharacteristic
487C2×C42—21no—
488C2×C42—221no—
489C2×C42—221no—
490C2×C42C22×D1111yescharacteristic
491#107—222no—
492#107—222no—
493#106—222no—
494#103—222no—
495#103—222no—
496#103—222no—
497#103—222no—
498#103—222no—
499#103—441no—
500C22⋊C8—222no—
501C22⋊C8—222no—
502C22⋊C8—441no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507C2×C11—42no—
508C2×C11—81no—
509C2×C11#243011yescharacteristic
510C2×C11#300511yescharacteristic
511C2×C11#301111yescharacteristic
512C2×C11#331511yescharacteristic
513C2×C11#332711yescharacteristic
514C2×C11#334911yescharacteristic
515C2×C11#335211yescharacteristic
516C24C2×C22⋊D1111yescharacteristic
517C24C2×C22⋊D1111yescharacteristic
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—112no—
525C2×Q8—221no—
526C2×Q8—221no—
527C2×Q8—221no—
528C2×Q8—221no—
529C2×Q8—221no—
530C2×D4—22no—
531C2×D4—41no—
532C2×D4—41no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—224no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—442no—
553C22×C4—442no—
554C22×C4D4×D1112yes—
555C22×C4D4×D1112yes—
556C22×C4C2×C22⋊D1111yescharacteristic
557C22×C4C2×C22⋊D1111yescharacteristic
558C22×C4C2×C22⋊D1111yescharacteristic
559C22×C4C2×C22⋊D1111yescharacteristic
560C22×C4C23×D1111yescharacteristic
561Q16—444no—
562M16—444no—
563C2×C8—112no—
564C2×C8—221no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—112no—
585C4⋊C4—112no—
586C4⋊C4—112no—
587C4⋊C4—224no—
588C4⋊C4—224no—
589C4⋊C4—224no—
590C4⋊C4—224no—
591C4⋊C4—224no—
592C4⋊C4—224no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4#434112yes—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—224no—
604C22⋊C4—224no—
605C22⋊C4—224no—
606C42—21no—
607C42—21no—
608C42—42no—
609C42—224no—
610C42—224no—
611C11#2555711yescharacteristic, complemented, Sylow
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23#6699012yes—
626C23C22×C22⋊D1111yescharacteristic
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—222no—
632Q8—222no—
633Q8—441no—
634Q8—441no—
635D4—44no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—448no—
672C2×C4—441no—
673C2×C4—441no—
674C2×C4—441no—
675C2×C4—441no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4#6699012yes—
681C2×C4C2×D4×D1111yescharacteristic
682C2×C4C2×D4×D1111yescharacteristic
683C2×C4C2×#434111yescharacteristic
684C2×C4#6703711yescharacteristic
685C2×C4#41×D1111yescharacteristic
686C2×C4#6704311yescharacteristic
687C8—222no—
688C8—441no—
689C8—441no—
690C8—441no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22C2×#6699011yescharacteristic
706C22#1062333711yescharacteristic
707C22#1062335311yescharacteristic
708C22#1062335311yescharacteristic
709C22#1062335511yescharacteristic
710C22#1062336911yescharacteristic
711C22#1062336911yescharacteristic
712C4—22no—
713C4—41no—
714C4—41no—
715C4—42no—
716C4—41no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—442no—
721C4—442no—
722C4—442no—
723C4—442no—
724C4#1062312711yescharacteristic
725C4#1062312811yescharacteristic
726C4#1062314111yescharacteristic
727C4#1062314211yescharacteristic
728C2—42no—
729C2—81no—
730C2#1307222211yescharacteristic
731C2#1307785611yescharacteristic
732C2#1307790911yescharacteristic
733C2#1308071211yescharacteristic
734C2#1308088411yescharacteristic
735C2#1308114011yescharacteristic
736C2#1308118511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2415C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2415D11
hypocenterC11#25557
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
2. C2×#10622657C2semidirect
3. C2×#10622665C2semidirect
4. #13069954C2semidirect
5. #13069819C2semidirect
6. #13069767C2semidirect
7. #13069624C2semidirect
8. #13068960C2semidirect
9. #13068929C2semidirect
10. #13068928C2semidirect
12. #13068869C2semidirect
13. #13068813C2semidirect
14. #13068337C2semidirect
611. C11#25557semidirect

Maximal subgroups

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

subgroupindex
C2×#106230722
C2×#106226572
C2×#106226652
#130699542
#130698192
#130697672
#130696242
#130689602
#130689292
#130689282
#130689142
#130688692
#130688132
#130683372
C11×#24152
#2555711