Finite Group Databasebeta

← #14787795

Subgroups — #14787795

Order 2816.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic
2C2×#10622635C211yesmaximal, characteristic, complemented
3C2×C4×#4326C211yesmaximal, characteristic, complemented
4#13069819C211yesmaximal, characteristic, complemented
5#13069812C211yesmaximal, characteristic, complemented
6#13069624C211yesmaximal, characteristic, complemented
7#13069624C211yesmaximal, characteristic, complemented
8#13069580C211yesmaximal, characteristic, complemented
9#13069411C211yesmaximal, characteristic
10#13068929C211yesmaximal, characteristic, complemented
11#13068924C211yesmaximal, characteristic, complemented
12#13068813C211yesmaximal, characteristic, complemented
13#13068803C211yesmaximal, characteristic, complemented
14#13068628C211yesmaximal, characteristic, complemented
15C11×#2536C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66988—21no—
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26#10623072—24no—
27#10623072—24no—
28C2×#66942—21no—
29C2×#66932—21no—
30C2×#66930—21no—
31C2×#66923C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#398—21no—
34C11×#394—21no—
35C11×#388—21no—
36C11×#388—21no—
37C11×#382C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C11×#380C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47C4×#4326—24no—
48#10622635—24no—
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
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—41no—
72C11×C22⋊Q8—41no—
73C4×Q8×C11—22no—
74C4×Q8×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
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—22no—
98#66988—28no—
99#66979—22no—
100#66979—22no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107#66977—22no—
108#66977—22no—
109#66977—22no—
110#66977—22no—
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—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122#66942—28no—
123#66932—28no—
124#66930—28no—
125#66923—22no—
126#66923D414yes—
127C4×Dic22—22no—
128C4×Dic22D414yes—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133#66899—22no—
134#66899—22no—
135#66899—22no—
136C22⋊(C11⋊C8)—22no—
137C22⋊(C11⋊C8)—22no—
138C22⋊(C11⋊C8)—41no—
139C22⋊(C11⋊C8)—41no—
140#66874—22no—
141#66874—41no—
142#66874—41no—
143#66872—22no—
144#66871—22no—
145#66871—22no—
146C4⋊(C11⋊C8)—22no—
147C4×C11⋊C8—22no—
148#24127—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#4112yes—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
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×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
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—21no—
201C11×C4⋊C4—42no—
202C11×C4⋊C4—42no—
203C11×C4⋊C4—42no—
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—42no—
211C42×C11C2×D412yes—
212C42×C11C2×D412yes—
213C22⋊Dic11—24no—
214C22⋊Dic11—24no—
215C22⋊Dic11—24no—
216#4326—28no—
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—
231C2×C11⋊C8—21no—
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#4112yes—
243C2×#552—111no—
244C2×#479—111no—
245C2×C4×Q16—111no—
246#2536D1111yescharacteristic
247#2036—111no—
248#2035—111no—
249#2001—111no—
250#2001—111no—
251#1991—111no—
252#1954—111no—
253#1873—111no—
254#1872—111no—
255#1854—111no—
256#1852—111no—
257#1805—111no—
258C23×C11—21no—
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#13512yes—
272C23×C11C22×D411yescharacteristic
273Q8×C11—22no—
274Q8×C11—22no—
275Q8×C11—41no—
276Q8×C11—41no—
277D4×C11—44no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
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#12012yes—
309C2×C4×C11#12012yes—
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C112−1+411yescharacteristic
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—48no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329Dic22—22no—
330Dic22—22no—
331Dic22—41no—
332Dic22—41no—
333C11⋊C8—22no—
334C11⋊C8—41no—
335C11⋊C8—41no—
336C11⋊C8—41no—
337C22×Q16—111no—
338#552—224no—
339#552—224no—
340C2×#126—221no—
341C2×#125—111no—
342C2×#125—221no—
343C2×#123—221no—
344C2×C22⋊Q8—111no—
345C2×C22⋊Q8—111no—
346C2×C22⋊Q8C2×D1111yescharacteristic
347C2×C22⋊Q8C2×D1111yescharacteristic
348C2×C4×Q8—111no—
349C2×C4×Q8C2×D1111yescharacteristic
350C2×C4×D4C2×D1111yescharacteristic
351C2×#117—111no—
352C2×#117—221no—
353C22×C4⋊C4—111no—
354#479—224no—
355C4×Q16—224no—
356C2×#107—111no—
357C2×#107—111no—
358C2×#106—111no—
359C2×C4⋊C8—111no—
360C2×#103—111no—
361C2×#103—111no—
362C2×#103—111no—
363C2×#103—111no—
364C2×#103—111no—
365C2×#103—111no—
366C2×C22⋊C8—111no—
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C4×C8—111no—
371#398—21no—
372#394—21no—
373#388—21no—
374#388—21no—
375#382C2×D1111yescharacteristic
376#380C2×D1111yescharacteristic
377#380C2×D1111yescharacteristic
378#340—111no—
379#340—111no—
380#340—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—41no—
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×C11C2×#12011yescharacteristic
399C22×C11#54611yescharacteristic
400C22×C11#54711yescharacteristic
401C22×C11C2×#13511yescharacteristic
402C22×C11#57511yescharacteristic
403C22×C11#57811yescharacteristic
404C22×C11#57811yescharacteristic
405C4×C11—22no—
406C4×C11—22no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11—42no—
410C4×C11—81no—
411C4×C11—81no—
412C4×C11—81no—
413C4×C11#52511yescharacteristic
414C4×C11#53711yescharacteristic
415C4×C11#54811yescharacteristic
416C4×C11#55011yescharacteristic
417Dic11—42no—
418Dic11—42no—
419Dic11—42no—
420Dic11—42no—
421C22×Q8—111no—
422C22×Q8C22×D1111yescharacteristic
423C22×D4C22⋊D1111yescharacteristic
424C23×C4—221no—
425C23×C4C22×D1111yescharacteristic
426C23×C4C22×D1111yescharacteristic
427C2×Q16—222no—
428C2×Q16—222no—
429C2×Q16—222no—
430C22×C8—111no—
431C22×C8—111no—
432C22×C8—111no—
433C22×C8—111no—
434#126—228no—
435#125—114no—
436#125—228no—
437#125—222no—
438#123—228no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8—41no—
442C22⋊Q8—41no—
443C22⋊Q8—222no—
444C22⋊Q8—222no—
445C22⋊Q8—222no—
446C22⋊Q8—222no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8—114no—
450C4×Q8—222no—
451C4×D4—22no—
452C4×D4—22no—
453#117—228no—
454#117—222no—
455#117—222no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—222no—
463C2×C4⋊C4—222no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4—221no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4C22⋊D1111yescharacteristic
471C2×C4⋊C4C22×D1111yescharacteristic
472C2×C4⋊C4C22×D1111yescharacteristic
473C2×C4⋊C4C22×D1111yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C22⋊C4C22⋊D1111yescharacteristic
482C2×C22⋊C4C22⋊D1111yescharacteristic
483C2×C42—21no—
484C2×C42—221no—
485C2×C42—221no—
486C2×C42C22×D1111yescharacteristic
487#107—222no—
488#107—222no—
489#106—222no—
490C4⋊C8—222no—
491#103—222no—
492#103—222no—
493#103—222no—
494#103—222no—
495#103—441no—
496#103—441no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—441no—
500C22⋊C8—441no—
501C4×C8—222no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506C2×C11—42no—
507C2×C11—81no—
508C2×C11#240711yescharacteristic
509C2×C11#300211yescharacteristic
510C2×C11#301111yescharacteristic
511C2×C11#330011yescharacteristic
512C2×C11#332711yescharacteristic
513C2×C11#333611yescharacteristic
514C2×C11#335211yescharacteristic
515C24C2×C22⋊D1111yescharacteristic
516C24C2×C22⋊D1111yescharacteristic
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—112no—
523C2×Q8—221no—
524C2×Q8—221no—
525C2×Q8—221no—
526C2×Q8—221no—
527C2×Q8—221no—
528C2×Q8#434112yes—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—41no—
532C22×C4—21no—
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—21no—
548C22×C4—224no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—442no—
554C22×C4—442no—
555C22×C4C2×C22⋊D1111yescharacteristic
556C22×C4C2×C22⋊D1111yescharacteristic
557C22×C4C2×C22⋊D1111yescharacteristic
558C22×C4C2×C22⋊D1111yescharacteristic
559C22×C4C23×D1111yescharacteristic
560Q16—228no—
561C2×C8—112no—
562C2×C8—221no—
563C2×C8—221no—
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—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—112no—
584C4⋊C4—112no—
585C4⋊C4—112no—
586C4⋊C4—224no—
587C4⋊C4—224no—
588C4⋊C4—224no—
589C4⋊C4—224no—
590C4⋊C4—224no—
591C4⋊C4—224no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—224no—
602C22⋊C4—224no—
603C22⋊C4—224no—
604C42—42no—
605C42—224no—
606C42—224no—
607C42D4×D1112yes—
608C42D4×D1112yes—
609C11#2412711yescharacteristic, complemented, Sylow
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23#6700312yes—
624C23C22×C22⋊D1111yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—222no—
630Q8—222no—
631Q8—441no—
632Q8—441no—
633D4—44no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
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—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—448no—
669C2×C4—441no—
670C2×C4—441no—
671C2×C4—441no—
672C2×C4—441no—
673C2×C4—441no—
674C2×C4—441no—
675C2×C4—441no—
676C2×C4—441no—
677C2×C4#6699012yes—
678C2×C4#6699012yes—
679C2×C4C2×D4×D1111yescharacteristic
680C2×C4C2×D4×D1111yescharacteristic
681C2×C4C2×#434111yescharacteristic
682C2×C4#6703711yescharacteristic
683C2×C4#41×D1111yescharacteristic
684C2×C4#6704311yescharacteristic
685C8—222no—
686C8—441no—
687C8—441no—
688C8—441no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22C2×#6699011yescharacteristic
704C22#1062333711yescharacteristic
705C22C2×#6700311yescharacteristic
706C22#1062335311yescharacteristic
707C22#1062335511yescharacteristic
708C22#1062336911yescharacteristic
709C22#1062336911yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—42no—
715C4—81no—
716C4—81no—
717C4—81no—
718C4—442no—
719C4—442no—
720C4—442no—
721C4—442no—
722C4#1062312911yescharacteristic
723C4#1062313011yescharacteristic
724C4#1062313711yescharacteristic
725C4#1062313911yescharacteristic
726C2—42no—
727C2—81no—
728C2#1307195711yescharacteristic
729C2#1307783211yescharacteristic
730C2#1307790911yescharacteristic
731C2#1308050311yescharacteristic
732C2#1308088411yescharacteristic
733C2#1308097811yescharacteristic
734C2#1308118511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2536C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2536D11
hypocenterC11#24127
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. C2×#10622635C2semidirect
3. C2×C4×#4326C2semidirect
4. #13069819C2semidirect
5. #13069812C2semidirect
6. #13069624C2semidirect
7. #13069624C2semidirect
8. #13069580C2semidirect
10. #13068929C2semidirect
11. #13068924C2semidirect
12. #13068813C2semidirect
13. #13068803C2semidirect
14. #13068628C2semidirect
609. C11#24127semidirect

Maximal subgroups

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

subgroupindex
C2×#106230722
C2×#106226352
C2×C4×#43262
#130698192
#130698122
#130696242
#130695802
#130694112
#130689292
#130689242
#130688132
#130688032
#130686282
C11×#25362
#2412711