Finite Group Databasebeta

← #14770201

Subgroups — #14770201

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic
2C2×#10622625C211yesmaximal, characteristic, complemented
3#13069580C211yesmaximal, characteristic, complemented
4#13069573C211yesmaximal, characteristic, complemented
5#13069052C211yesmaximal, characteristic, complemented
6#13069052C211yesmaximal, characteristic, complemented
7#13068938C211yesmaximal, characteristic, complemented
8#13068933C211yesmaximal, characteristic, complemented
9#13068708C211yesmaximal, characteristic, complemented
10#13068700C211yesmaximal, characteristic, complemented
11#13068623C211yesmaximal, characteristic, complemented
12C4×#66873C211yesmaximal, characteristic, complemented
13#13068337C211yesmaximal, characteristic, complemented
14#13068335C211yesmaximal, characteristic, complemented
15C11×#2352C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66992—21no—
20C2×#66983C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26#10623096—24no—
27#10623096C418yescomplemented
28C2×#66951—21no—
29C2×#66936—21no—
30C2×(C22⋊D11)⋊C4—21no—
31C2×C4×D44C2211yescharacteristic
32C2×#66923C2211yescharacteristic
33C11×#388—21no—
34C11×#387—21no—
35C11×#386—21no—
36C11×#382C2211yescharacteristic
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622625—24no—
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11D411yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11—21no—
68C23×Dic11—21no—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C4×D4×C11C2×C414yes—
72C4×D4×C11D414yes—
73C11×#117—22no—
74C11×#117—41no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D411yescharacteristic
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—21no—
92#66992—28no—
93#66983—22no—
94#66983—22no—
95#66983C2×C414yes—
96#66983C2×C414yescomplemented
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100#66979—22no—
101#66979C2×C414yes—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11C2×C414yescomplemented
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×C4×Dic11—21no—
111C2×#4318—22no—
112C2×#4318—22no—
113C2×#4318—22no—
114C2×#4318—22no—
115C2×#4318—41no—
116C2×#4318—41no—
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121#66951—28no—
122#66936—28no—
123(C22⋊D11)⋊C4—28no—
124C4×D44—22no—
125C4×D44C2×C414yescomplemented
126#66923—22no—
127#66923C2×C414yescomplemented
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C22⋊(C11⋊C8)—22no—
134C22⋊(C11⋊C8)—22no—
135#66873—22no—
136#66873—22no—
137#66873—41no—
138#66873—41no—
139C4⋊(C11⋊C8)—22no—
140C4×C11⋊C8—22no—
141#22501—111nomaximal, Sylow
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11C22⋊C414yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—81no—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C22×C412yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—24no—
173C2×C22⋊D11—24no—
174C2×C22⋊D11—42no—
175C2×C22⋊D11—42no—
176C2×C22⋊D11—81no—
177C2×C22⋊D11—81no—
178C22×Dic11—24no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—81no—
183C22×Dic11—81no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44C22×C412yes—
190C2×C4×D11—24no—
191C2×C4×D11—81no—
192C2×C4×D11—81no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
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⋊C4C22⋊C414yes—
202C11×C4⋊C4#4112yes—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—81no—
206C11×C22⋊C4C22⋊C414yes—
207C11×C22⋊C4C22⋊C414yes—
208C42×C11—42no—
209C42×C11—81no—
210C42×C11C22×C412yes—
211C42×C11C2×D412yes—
212C22⋊Dic11—24no—
213(C2×D11)⋊C4—24no—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—24no—
216C4⋊Dic11—24no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11C22×C412yes—
221C4⋊Dic11C22×C412yes—
222C4⋊Dic11C22×C412yes—
223Dic11⋊C4—24no—
224Dic11⋊C4—24no—
225C4×Dic11—24no—
226#4318—44no—
227#4318—44no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
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#4112yes—
240C2×#553—111no—
241C2×#436—111no—
242#2352D1111yescharacteristic, complemented
243#1991—111no—
244#1989—111no—
245#1895—111no—
246#1895—111no—
247#1875—111no—
248#1874—111no—
249#1825—111no—
250#1823—111no—
251#1804—111no—
252C4×#102—111no—
253#1736—111no—
254#1736—111no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
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×C11C2×C22⋊C412yes—
268C23×C11C2×C22⋊C412yes—
269C23×C11C22×D411yescharacteristic
270C22×D11—22no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—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—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
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—84no—
307C2×C4×C11C2×C22⋊C412yes—
308C2×C4×C11C2×C22⋊C412yes—
309C2×C4×C11C2×C22⋊C412yes—
310C2×C4×C11C2×C22⋊C412yes—
311C2×C4×C11C23×C411yescharacteristic
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C112−1+411yescharacteristic
317C22⋊D11—48no—
318C22⋊D11—84no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—84no—
329D44—22no—
330D44—22no—
331D44—41no—
332D44—41no—
333C4×D11—84no—
334C11⋊C8—22no—
335C11⋊C8—41no—
336C11⋊C8—41no—
337C11⋊C8—41no—
338C22×M16—111no—
339C22×M16—111no—
340#553—118no—
341#553—224no—
342C2×#126—221no—
343C2×#125—111no—
344C2×#123—221no—
345C2×#121—111no—
346C2×#121—111no—
347C2×#121—221no—
348C2×C4×D4—111no—
349C2×C4×D4—221no—
350C2×C4×D4C2×D1111yescharacteristic
351C2×#117—111no—
352C2×#117C2×D1111yescharacteristic
353C22×C4⋊C4—111no—
354C22×C4⋊C4C2×D1111yescharacteristic
355#436—224no—
356C2×C4⋊C8—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
363C2×C4×C8—111no—
364#388—21no—
365#387—21no—
366#386—21no—
367#382C2×D1111yescharacteristic
368#380C2×D1111yescharacteristic
369#380C2×D1111yescharacteristic
370C4×C4⋊C4C2×D1111yescharacteristic
371C4×C22⋊C4—21no—
372#340—111no—
373#340—111no—
374#340—111no—
375#340—111no—
376#340—111no—
377#340—111no—
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—22no—
388C22×C11—22no—
389C22×C11—22no—
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×C11C22×C22⋊C411yescharacteristic
399C22×C11#54611yescharacteristic
400C22×C11#54711yescharacteristic
401C22×C11#57511yescharacteristic
402C22×C11#57511yescharacteristic
403C22×C11#57611yescharacteristic
404C22×C11#57711yescharacteristic
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—81no—
409C2×D11—81no—
410C2×D11—81no—
411C2×D11—81no—
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—22no—
416C4×C11—42no—
417C4×C11—81no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11C4×#4111yescharacteristic
421C4×C11#52011yescharacteristic
422C4×C11#54611yescharacteristic
423C4×C11#54711yescharacteristic
424Dic11—42no—
425Dic11—42no—
426Dic11—42no—
427C22×D4—111no—
428C22×D4—221no—
429C22×D4—221no—
430C22×D4C22⋊D1111yescharacteristic
431C23×C4—21no—
432C23×C4—221no—
433C23×C4—221no—
434C23×C4C22×D1111yescharacteristic
435C23×C4C22×D1111yescharacteristic
436C2×M16—222no—
437C2×M16—222no—
438C2×M16—222no—
439C2×M16—222no—
440C2×M16—441no—
441C2×M16—441no—
442C22×C8—111no—
443C22×C8—111no—
444C22×C8—111no—
445C22×C8—111no—
446#126—228no—
447#125—114no—
448#125—222no—
449#123—228no—
450#121—114no—
451#121—114no—
452#121—228no—
453#121—222no—
454#121—222no—
455C4×D4—114no—
456C4×D4—228no—
457C4×D4—222no—
458C4×D4C4×D1114yes—
459C4×D4D4414yes—
460#117—22no—
461#117—41no—
462#117—114no—
463#117—222no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—114no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—222no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4C22⋊D1111yescharacteristic
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4C22⋊D1111yescharacteristic
488C2×C22⋊C4C22⋊D1111yescharacteristic
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—221no—
492C2×C42C22×D1111yescharacteristic
493C4⋊C8—222no—
494#102—222no—
495#102—222no—
496#102—441no—
497#102—441no—
498C22⋊C8—222no—
499C22⋊C8—222no—
500C4×C8—222no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506C2×C11—42no—
507C2×C11—42no—
508C2×C11#233911yescharacteristic
509C2×C11#289611yescharacteristic
510C2×C11#289711yescharacteristic
511C2×C11#332211yescharacteristic
512C2×C11#332611yescharacteristic
513C2×C11#335111yescharacteristic
514C2×C11#335511yescharacteristic
515D11—82no—
516C24—221no—
517C24C2×C22⋊D1111yescharacteristic
518C24C2×C22⋊D1111yescharacteristic
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—112no—
522C2×D4—224no—
523C2×D4—224no—
524C2×D4—221no—
525C2×D4—221no—
526C2×D4—221no—
527C2×D4—221no—
528C2×D4—221no—
529C2×D4—442no—
530C2×D4—442no—
531C2×D4—881no—
532C2×D4—881no—
533C2×D4(C2×D11)⋊C414yes—
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—42no—
547C22×C4—42no—
548C22×C4—81no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—224no—
553C22×C4—224no—
554C22×C4—881no—
555C22×C4—881no—
556C22×C4—881no—
557C22×C4—881no—
558C22×C4C2×C4×D1112yes—
559C22×C4C2×C4×D1112yes—
560C22×C4C2×D4412yes—
561C22×C4C2×D4412yes—
562C22×C4C2×C22⋊D1111yescharacteristic
563C22×C4C2×C22⋊D1111yescharacteristic
564C22×C4C2×C22⋊D1111yescharacteristic
565C22×C4C2×C22⋊D1111yescharacteristic
566C22×C4C23×D1111yescharacteristic
567M16—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—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—112no—
590C4⋊C4—112no—
591C4⋊C4—112no—
592C4⋊C4—224no—
593C4⋊C4—224no—
594C4⋊C4—224no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4(C2×D11)⋊C414yes—
599C4⋊C4#434112yes—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C22⋊C4—224no—
604C22⋊C4—224no—
605C22⋊C4—224no—
606C22⋊C4—224no—
607C22⋊C4(C2×D11)⋊C414yes—
608C22⋊C4(C2×D11)⋊C414yes—
609C42—42no—
610C42—81no—
611C42—224no—
612C42C2×C4×D1112yes—
613C42C2×D4412yes—
614C11#2250111yescharacteristic, complemented, Sylow
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—222no—
628C23—441no—
629C23—441no—
630C23—441no—
631C23—441no—
632C23—441no—
633C23—441no—
634C23C2×(C2×D11)⋊C412yes—
635C23C2×(C2×D11)⋊C412yes—
636C23C22×C22⋊D1111yescharacteristic
637D4—44no—
638D4—222no—
639D4—222no—
640D4—448no—
641D4—441no—
642D4—441no—
643D4—884no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
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—84no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—884no—
683C2×C4—884no—
684C2×C4C2×(C2×D11)⋊C412yes—
685C2×C4C2×(C2×D11)⋊C412yes—
686C2×C4C2×(C2×D11)⋊C412yes—
687C2×C4C2×(C2×D11)⋊C412yes—
688C2×C4C22×C4×D1111yescharacteristic
689C2×C4C22×D4411yescharacteristic
690C2×C4C2×#434111yescharacteristic
691C2×C4#6703711yescharacteristic
692C2×C4#41×D1111yescharacteristic
693C2×C4#6704311yescharacteristic
694C8—222no—
695C8—441no—
696C8—441no—
697C8—441no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—442no—
713C22—442no—
714C22—442no—
715C22—881no—
716C22—881no—
717C22—881no—
718C22—881no—
719C22C22×(C2×D11)⋊C411yescharacteristic
720C22#1062333711yescharacteristic
721C22#1062335311yescharacteristic
722C22#1062335311yescharacteristic
723C22#1062335511yescharacteristic
724C22#1062336611yescharacteristic
725C22#1062336811yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4—442no—
735C4—442no—
736C4—442no—
737C4C4×#434111yescharacteristic
738C4#1062307711yescharacteristic
739C4#1062308511yescharacteristic
740C4#1062308611yescharacteristic
741C2—42no—
742C2—42no—
743C2—882no—
744C2#1307144111yescharacteristic
745C2#1307713311yescharacteristic
746C2#1307713911yescharacteristic
747C2#1308081711yescharacteristic
748C2#1308086911yescharacteristic
749C2#1308117611yescharacteristic
750C2#1308121611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2352C2
socleC23×C11C22×D4
prime radicalC2×#10623096C2
cosocleC22×C4×C11C24
hypercenter#2352D11
hypocenterC11#22501
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#10622625C2semidirect
3. #13069580C2semidirect
4. #13069573C2semidirect
5. #13069052C2semidirect
6. #13069052C2semidirect
7. #13068938C2semidirect
8. #13068933C2semidirect
9. #13068708C2semidirect
10. #13068700C2semidirect
11. #13068623C2semidirect
12. C4×#66873C2semidirect
13. #13068337C2semidirect
14. #13068335C2semidirect
15. C11×#2352C2semidirect
27. #10623096C4semidirect
96. #66983C2×C4semidirect
104. C2×C4⋊Dic11C2×C4semidirect
125. C4×D44C2×C4semidirect
127. #66923C2×C4semidirect
242. #2352D11semidirect
614. C11#22501semidirect

Maximal subgroups

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

subgroupindex
C2×#106230962
C2×#106226252
#130695802
#130695732
#130690522
#130689382
#130689332
#130687082
#130687002
#130686232
C4×#668732
#130683372
#130683352
C11×#23522
#2250111