Finite Group Databasebeta

← #14806894

Subgroups — #14806894

Order 2816.

1108 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622609C211yesmaximal, characteristic, complemented
2C2×#10622665C211yesmaximal, characteristic, complemented
3#13072067C211yesmaximal, characteristic
4#13069951C211yesmaximal, characteristic, complemented
5#13069816C211yesmaximal, characteristic, complemented
6#13069764C211yesmaximal, characteristic, complemented
7#13069624C211yesmaximal, characteristic, complemented
8#13068957C211yesmaximal, characteristic, complemented
9#13068924C211yesmaximal, characteristic, complemented
10#13068923C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic, complemented
13#13068809C211yesmaximal, characteristic, complemented
14#13068337C211yesmaximal, characteristic, complemented
15C2×C11×#552C211yesmaximal, characteristic
16C11×#552—24no—
17C11×#552—24no—
18C2×C11×#126—21no—
19C2×C11×#125—21no—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117—21no—
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C2×#66977C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37#10622833—21no—
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622665—24no—
43#10622609—24no—
44#10622597—21no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622561—21no—
52#10622555—21no—
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—21no—
69C22×Dic22C2311yescharacteristic
70C11×#126—28no—
71C11×#125—28no—
72C11×#125—22no—
73C11×#125—22no—
74C11×#123—28no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8D414yes—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C11×#117—28no—
84C11×#117—22no—
85C11×#117D414yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11—21no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×#4326—22no—
110C2×#4326—22no—
111C2×#4326—41no—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—41no—
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118#66977—22no—
119#66977—22no—
120#66977—22no—
121#66977—41no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×#4318—22no—
126C2×#4318—22no—
127C2×#4318—41no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132#66899—22no—
133#66899—22no—
134#66899—41no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C22⋊(C11⋊C8)—22no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—41no—
142#66874—22no—
143#66874—22no—
144#66874—22no—
145#66872—22no—
146#66872—22no—
147#66871—22no—
148#25562—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×C11C2×D412yes—
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—24no—
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—42no—
176C22×C4×C11—42no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2411yescharacteristic
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—42no—
189C22×Dic11—42no—
190C22×Dic11—81no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4C2×D412yes—
208C11×C4⋊C4C2×D412yes—
209C11×C4⋊C4C2×D412yes—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C42×C11—24no—
216C42×C11—24no—
217C42×C11—21no—
218C42×C11—21no—
219C22⋊Dic11—42no—
220C22⋊Dic11—42no—
221C22⋊Dic11—81no—
222#4326—44no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—42no—
229C4⋊Dic11#4112yes—
230Dic11⋊C4—42no—
231Dic11⋊C4—42no—
232Dic11⋊C4—81no—
233#4318—44no—
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—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8#4112yes—
246C2×#552D1111yescharacteristic
247C2×#485—111no—
248C2×#470—111no—
249#2417—111no—
250#2059—111no—
251#2036—111no—
252#2026—111no—
253#2001—111no—
254#1878—111no—
255#1872—111no—
256#1872—111no—
257#1870—111no—
258#1865—111no—
259#1853—111no—
260#1736—111no—
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—21no—
273C23×C11#12012yes—
274C23×C11#13712yes—
275C23×C11C22×D411yescharacteristic
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—41no—
279Q8×C11—41no—
280D4×C11—44no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—48no—
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—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11#12012yes—
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C112−1+411yescharacteristic
320C2×Dic11—22no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—84no—
333Dic22—41no—
334Dic22—41no—
335Dic22—41no—
336Dic22—41no—
337C11⋊C8—22no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C22×Q16—111no—
342C22×M16—111no—
343#552—24no—
344#552—24no—
345C2×#126—21no—
346C2×#125—21no—
347C2×#125C2×D1111yescharacteristic
348C2×#123—21no—
349C2×C22⋊Q8—111no—
350C2×C22⋊Q8—111no—
351C2×C22⋊Q8C2×D1111yescharacteristic
352C2×C22⋊Q8C2×D1111yescharacteristic
353C2×C4×Q8C2×D1111yescharacteristic
354C2×C4×D4C2×D1111yescharacteristic
355C2×#117—21no—
356C2×#117C2×D1111yescharacteristic
357C22×C4⋊C4—111no—
358C22×C4⋊C4C2×D1111yescharacteristic
359#485—224no—
360#470—224no—
361C2×#107—111no—
362C2×#106—111no—
363C2×#106—111no—
364C2×#103—111no—
365C2×#103—111no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#103—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8—111no—
373#398—221no—
374#396—221no—
375#391—111no—
376#389—111no—
377#386—221no—
378#380—111no—
379#380—221no—
380#340—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384#340—111no—
385#340—111no—
386#336—111no—
387#336—111no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11C2×#12011yescharacteristic
403C22×C11#54611yescharacteristic
404C22×C11#54711yescharacteristic
405C22×C11C2×#13711yescharacteristic
406C22×C11#57511yescharacteristic
407C22×C11#57711yescharacteristic
408C22×C11#57811yescharacteristic
409C4×C11—22no—
410C4×C11—41no—
411C4×C11—42no—
412C4×C11—41no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11—41no—
416C4×C11—42no—
417C4×C11#53211yescharacteristic
418C4×C11#53711yescharacteristic
419C4×C11#54611yescharacteristic
420C4×C11#54711yescharacteristic
421Dic11—42no—
422Dic11—81no—
423Dic11—81no—
424Dic11—81no—
425C22×Q8—111no—
426C22×Q8C22×D1111yescharacteristic
427C22×D4C22⋊D1111yescharacteristic
428C23×C4—21no—
429C23×C4—221no—
430C23×C4C22×D1111yescharacteristic
431C23×C4C22×D1111yescharacteristic
432C2×Q16—222no—
433C2×Q16—222no—
434C2×Q16—441no—
435C2×M16—222no—
436C2×M16—222no—
437C2×M16—441no—
438C22×C8—111no—
439C22×C8—111no—
440C22×C8—111no—
441C22×C8—111no—
442#126—28no—
443#125—28no—
444#125—22no—
445#125—22no—
446#123—28no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—222no—
451C22⋊Q8—222no—
452C22⋊Q8—222no—
453C22⋊Q8—441no—
454C22⋊Q8C22⋊D1114yes—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×D4—22no—
458C4×D4—22no—
459#117—28no—
460#117—22no—
461#117C22⋊D1114yes—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—222no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—441no—
479C2×C4⋊C4C22⋊D1111yescharacteristic
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C4⋊C4C22×D1111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4C22⋊D1111yescharacteristic
490C2×C22⋊C4C22⋊D1111yescharacteristic
491C2×C42—21no—
492C2×C42—21no—
493C2×C42C22×D1111yescharacteristic
494#107—222no—
495#106—222no—
496#106—222no—
497#103—222no—
498#103—222no—
499#103—222no—
500#103—222no—
501#103—222no—
502#103—441no—
503C22⋊C8—222no—
504C22⋊C8—222no—
505C22⋊C8—441no—
506#95—221no—
507#95—221no—
508#95—221no—
509#95—221no—
510C2×C11—42no—
511C2×C11—42no—
512C2×C11#243011yescharacteristic
513C2×C11#300711yescharacteristic
514C2×C11#301311yescharacteristic
515C2×C11#331211yescharacteristic
516C2×C11#332311yescharacteristic
517C2×C11#334411yescharacteristic
518C2×C11#335211yescharacteristic
519C24C2×C22⋊D1111yescharacteristic
520C24C2×C22⋊D1111yescharacteristic
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—221no—
527C2×Q8—221no—
528C2×Q8—221no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—221no—
532C2×Q8C2×C22⋊D1112yes—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—41no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—442no—
558C22×C4—442no—
559C22×C4—881no—
560C22×C4C2×C22⋊D1111yescharacteristic
561C22×C4C2×C22⋊D1111yescharacteristic
562C22×C4C2×C22⋊D1111yescharacteristic
563C22×C4C2×C22⋊D1111yescharacteristic
564C22×C4C2×C22⋊D1112yes—
565C22×C4C2×C22⋊D1112yes—
566C22×C4C23×D1111yescharacteristic
567Q16—444no—
568M16—444no—
569C2×C8—112no—
570C2×C8—221no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—112no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—442no—
598C4⋊C4—442no—
599C4⋊C4—442no—
600C4⋊C4—881no—
601C4⋊C4C2×C22⋊D1112yes—
602C4⋊C4C2×C22⋊D1112yes—
603C4⋊C4C2×C22⋊D1112yes—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—442no—
610C22⋊C4—442no—
611C22⋊C4—881no—
612C42—24no—
613C42—24no—
614C42—21no—
615C42—21no—
616C11#2556211yescharacteristic, complemented, Sylow
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23#6700412yes—
630C23#6700612yes—
631C23C22×C22⋊D1111yescharacteristic
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636Q8—441no—
637Q8—441no—
638Q8—441no—
639Q8—441no—
640D4—44no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—48no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—222no—
674C2×C4—441no—
675C2×C4—441no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—884no—
686C2×C4#6700612yes—
687C2×C4#41×D1111yescharacteristic
688C2×C4#41×D1111yescharacteristic
689C2×C4#6704211yescharacteristic
690C2×C4#6704311yescharacteristic
691C2×C4C22×C22⋊D1111yescharacteristic
692C2×C4C22×C22⋊D1111yescharacteristic
693C8—222no—
694C8—441no—
695C8—441no—
696C8—441no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22#1062335311yescharacteristic
712C22C2×#6700411yescharacteristic
713C22#1062335511yescharacteristic
714C22#1062336011yescharacteristic
715C22#1062336811yescharacteristic
716C22#1062336911yescharacteristic
717C22C2×#6700611yescharacteristic
718C4—22no—
719C4—41no—
720C4—42no—
721C4—41no—
722C4—42no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—442no—
727C4—881no—
728C4—881no—
729C4—881no—
730C4#1062335511yescharacteristic
731C4#1062336011yescharacteristic
732C4#1062336311yescharacteristic
733C4#1062336411yescharacteristic
734C2—42no—
735C2—42no—
736C2#1307222011yescharacteristic
737C2#1307787611yescharacteristic
738C2#1307793111yescharacteristic
739C2#1308066111yescharacteristic
740C2#1308082611yescharacteristic
741C2#1308107111yescharacteristic
742C2#1308118511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#552C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#552D11
hypocenterC11#25562
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#10622609C2semidirect
2. C2×#10622665C2semidirect
4. #13069951C2semidirect
5. #13069816C2semidirect
6. #13069764C2semidirect
7. #13069624C2semidirect
8. #13068957C2semidirect
9. #13068924C2semidirect
10. #13068923C2semidirect
12. #13068884C2semidirect
13. #13068809C2semidirect
14. #13068337C2semidirect
616. C11#25562semidirect

Maximal subgroups

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

subgroupindex
C2×#106226092
C2×#106226652
#130720672
#130699512
#130698162
#130697642
#130696242
#130689572
#130689242
#130689232
#130689142
#130688842
#130688092
#130683372
C2×C11×#5522
#2556211