Finite Group Databasebeta

← #14770203

Subgroups — #14770203

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×#10623045C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3#13071546C211yesmaximal, characteristic, complemented
4#13069579C211yesmaximal, characteristic, complemented
5#13069570C211yesmaximal, characteristic, complemented
6#13069054C211yesmaximal, characteristic, complemented
7#13069053C211yesmaximal, characteristic, complemented
8#13068938C211yesmaximal, characteristic, complemented
9#13068932C211yesmaximal, characteristic, complemented
10#13068709C211yesmaximal, characteristic, complemented
11#13068702C211yesmaximal, characteristic, complemented
12#13068625C211yesmaximal, characteristic, complemented
13#13068430C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983—21no—
20C2×#66983C2211yescharacteristic
21C2×C4×C22⋊D11—21no—
22C2×C4×C22⋊D11C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24#10623045—24no—
25#10623045C418yescomplemented
26C2×#66951—21no—
27C2×#66948C2211yescharacteristic
28C2×#66947—21no—
29C2×#66946C2211yescharacteristic
30C2×#66945C2211yescharacteristic
31C2×C4⋊C4×D11C2211yescharacteristic
32C2×#66943C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622741—24no—
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622590C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46#10622569—21no—
47#10622558—21no—
48C4×(C2×D11)⋊C4—21no—
49#10622546—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×C22⋊D11D411yescharacteristic
66C22×D44—21no—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C4×D11C2311yescharacteristic
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—41no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#117—22no—
77C11×#117—41no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4C2×C414yescomplemented
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89#66983—22no—
90#66983—28no—
91#66983C2×C414yescomplemented
92C4×C22⋊D11—28no—
93C4×C22⋊D11C2×C414yes—
94C4×C22⋊D11D414yes—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4D411yescharacteristic
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4D411yescharacteristic
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C2×#4313—22no—
114C2×#4313—22no—
115C2×#4313—41no—
116#66951—28no—
117#66948—22no—
118#66948C2×C414yes—
119#66947—28no—
120#66946—22no—
121#66946C2×C414yescomplemented
122#66945—22no—
123#66945C2×C414yes—
124C4⋊C4×D11—22no—
125C4⋊C4×D11—41no—
126#66943—22no—
127#66943C2×C414yescomplemented
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C22⋊(C11⋊C8)—22no—
134#66885—22no—
135#66885—41no—
136(C2×D11)⋊C8—22no—
137Dic11⋊C8—22no—
138C8×Dic11—22no—
139#66873—22no—
140#66873—41no—
141#22501—111nomaximal, Sylow
142C24×C11C2×D411yescharacteristic
143C23×D11—21no—
144C23×D11C2×D411yescharacteristic
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—24no—
153C22×C4×C11—21no—
154C22×C4×C11—81no—
155C22×C4×C11—81no—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—41no—
162C2×C22⋊D11—41no—
163C2×C22⋊D11—42no—
164C2×C22⋊D11—42no—
165C2×C22⋊D11C22⋊C414yes—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C2×D44—24no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—81no—
179C2×D44—81no—
180C2×D44C22×C412yes—
181C2×C4×D11—24no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—42no—
187C2×C4×D11—42no—
188C2×C4×D11—81no—
189C2×C4×D11—81no—
190C2×C4×D11—81no—
191C2×C4×D11C22×C412yes—
192C2×C4×D11C2×D412yes—
193C11×M16—44no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11#4112yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4C22×C412yes—
207C11×C4⋊C4C22×C412yes—
208C11×C4⋊C4#4112yes—
209C11×C22⋊C4—42no—
210C42×C11—42no—
211C22⋊Dic11—81no—
212C22⋊Dic11C22⋊C414yes—
213(C2×D11)⋊C4—24no—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—24no—
216(C2×D11)⋊C4—24no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4C22⋊C414yes—
219C4⋊Dic11—24no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11C22×C412yes—
226Dic11⋊C4—24no—
227Dic11⋊C4—42no—
228Dic11⋊C4C22⋊C414yes—
229C4×Dic11—24no—
230C4×Dic11—81no—
231C4×Dic11C22×C412yes—
232C4×Dic11C2×D412yes—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239#4313—44no—
240C2×#553—111no—
241C2×#436—111no—
242#2352—111no—
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#1736D1111yescharacteristic, complemented
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11C2×C22⋊C412yes—
262C23×C11C22×D411yescharacteristic
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—22no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11C2×C22⋊C412yes—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
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—84no—
296C2×C4×C11C2×C22⋊C412yes—
297C2×C4×C11C23×C411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C2×#4111yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C112−1+411yescharacteristic
303C22⋊D11—44no—
304C22⋊D11—48no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—22no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11C2×C22⋊C412yes—
321C2×Dic11C2×C22⋊C412yes—
322C2×Dic11C2×C22⋊C412yes—
323D44—22no—
324D44—22no—
325D44—41no—
326D44—41no—
327D44—84no—
328C4×D11—22no—
329C4×D11—22no—
330C4×D11—22no—
331C4×D11—22no—
332C4×D11—84no—
333C4×D11—84no—
334C8×C11—22no—
335C8×C11—41no—
336C11⋊C8—41no—
337C11⋊C8—41no—
338C22×M16—111no—
339C22×M16C2×D1111yescharacteristic
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—111no—
350C2×C4×D4—221no—
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—221no—
365#387—221no—
366#386—221no—
367#382—111no—
368#380—111no—
369#380—111no—
370C4×C4⋊C4—111no—
371C4×C22⋊C4—221no—
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#340C2×D1111yescharacteristic
381#340C2×D1111yescharacteristic
382#340C2×D1111yescharacteristic
383#340C2×D1111yescharacteristic
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11C22×C22⋊C411yescharacteristic
392C22×C11#54611yescharacteristic
393C22×C11#54711yescharacteristic
394C22×C11#57511yescharacteristic
395C22×C11#57511yescharacteristic
396C22×C11#57611yescharacteristic
397C22×C11#57711yescharacteristic
398C2×D11—22no—
399C2×D11—22no—
400C2×D11—22no—
401C2×D11—41no—
402C2×D11—41no—
403C2×D11—41no—
404C2×D11—41no—
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—42no—
414C4×C11—42no—
415C4×C11—42no—
416C4×C11—81no—
417C4×C11C4×#4111yescharacteristic
418C4×C11#52011yescharacteristic
419C4×C11#54611yescharacteristic
420C4×C11#54711yescharacteristic
421Dic11—22no—
422Dic11—22no—
423Dic11—22no—
424Dic11—42no—
425Dic11—81no—
426Dic11—81no—
427C22×D4—111no—
428C22×D4—111no—
429C22×D4—221no—
430C22×D4—221no—
431C23×C4—21no—
432C23×C4—111no—
433C23×C4—221no—
434C23×C4—221no—
435C23×C4C22×D1111yescharacteristic
436C2×M16—22no—
437C2×M16—22no—
438C2×M16—41no—
439C2×M16—222no—
440C2×M16—222no—
441C2×M16—441no—
442C22×C8—111no—
443C22×C8—111no—
444C22×C8C22×D1111yescharacteristic
445C22×C8C22×D1111yescharacteristic
446#126—228no—
447#125—114no—
448#125—222no—
449#123—228no—
450#121—114no—
451#121—114no—
452#121—222no—
453#121—228no—
454#121—222no—
455C4×D4—114no—
456C4×D4—114no—
457C4×D4—114no—
458C4×D4—222no—
459C4×D4—228no—
460#117—22no—
461#117—41no—
462#117—114no—
463#117—222no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—441no—
475C2×C4⋊C4C4×D1114yescomplemented
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C42—21no—
490C2×C42—111no—
491C2×C42—221no—
492C2×C42—221no—
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—221no—
502#95—221no—
503#95—221no—
504#95—221no—
505#95—221no—
506C2×C11—42no—
507C2×C11#233911yescharacteristic
508C2×C11#289611yescharacteristic
509C2×C11#289711yescharacteristic
510C2×C11#332211yescharacteristic
511C2×C11#332611yescharacteristic
512C2×C11#335111yescharacteristic
513C2×C11#335511yescharacteristic
514D11—42no—
515D11—82no—
516C24—111no—
517C24—221no—
518C24D4×D1111yescharacteristic
519C2×D4—114no—
520C2×D4—112no—
521C2×D4—224no—
522C2×D4—224no—
523C2×D4—221no—
524C2×D4—221no—
525C2×D4—221no—
526C2×D4—221no—
527C2×D4—221no—
528C2×D4—441no—
529C2×D4—441no—
530C2×D4—442no—
531C2×D4—442no—
532C2×D4—881no—
533C2×D4—881no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—111no—
546C22×C4—111no—
547C22×C4—111no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—224no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—442no—
559C22×C4—442no—
560C22×C4—881no—
561C22×C4—881no—
562C22×C4—881no—
563C22×C4C2×C4×D1112yes—
564C22×C4D4×D1111yescharacteristic
565C22×C4D4×D1112yes—
566C22×C4C23×D1111yescharacteristic
567M16—44no—
568M16—444no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8#433912yes—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—114no—
588C4⋊C4—112no—
589C4⋊C4—224no—
590C4⋊C4—224no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—442no—
597C4⋊C4C2×C4×D1112yes—
598C4⋊C4C2×C4×D1112yes—
599C4⋊C4#433912yes—
600C22⋊C4—42no—
601C22⋊C4—114no—
602C22⋊C4—114no—
603C22⋊C4—224no—
604C22⋊C4—224no—
605C22⋊C4—224no—
606C22⋊C4—224no—
607C22⋊C4—442no—
608C22⋊C4—881no—
609C42—42no—
610C42—112no—
611C42—112no—
612C42—224no—
613C42—881no—
614C11#2250111yescharacteristic, complemented, Sylow
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—112no—
622C23—221no—
623C23—221no—
624C23—221no—
625C23—221no—
626C23—221no—
627C23—221no—
628C23—222no—
629C23—441no—
630C23—441no—
631C23—441no—
632C23—441no—
633C23—441no—
634C23—441no—
635C23C22⋊C4×D1112yes—
636C23C2×D4×D1111yescharacteristic
637D4—222no—
638D4—222no—
639D4—444no—
640D4—448no—
641D4—441no—
642D4—441no—
643D4—884no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
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—84no—
663C2×C4—112no—
664C2×C4—112no—
665C2×C4—112no—
666C2×C4—221no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
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—884no—
687C2×C4C22⋊C4×D1112yes—
688C2×C4C22×C4×D1111yescharacteristic
689C2×C4C2×#433911yescharacteristic
690C2×C4C2×#433911yescharacteristic
691C2×C4C2×D4×D1111yescharacteristic
692C2×C4#6703711yescharacteristic
693C2×C4#6704011yescharacteristic
694C8—22no—
695C8—41no—
696C8—441no—
697C8—441no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—222no—
706C22—222no—
707C22—222no—
708C22—441no—
709C22—441no—
710C22—441no—
711C22—441no—
712C22—442no—
713C22—442no—
714C22—442no—
715C22—881no—
716C22—881no—
717C22—881no—
718C22—881no—
719C22C2×C22⋊C4×D1111yescharacteristic
720C22#1062302111yescharacteristic
721C22#1062303811yescharacteristic
722C22#1062330511yescharacteristic
723C22#1062330611yescharacteristic
724C22#1062330811yescharacteristic
725C22#1062330811yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—81no—
731C4—222no—
732C4—222no—
733C4—222no—
734C4—442no—
735C4—881no—
736C4—881no—
737C4C4×#433911yescharacteristic
738C4#1062302111yescharacteristic
739C4#1062303511yescharacteristic
740C4#1062303811yescharacteristic
741C2—42no—
742C2—442no—
743C2—882no—
744C2#1307144311yescharacteristic
745C2#1307713411yescharacteristic
746C2#1307714111yescharacteristic
747C2#1308081811yescharacteristic
748C2#1308087011yescharacteristic
749C2#1308117711yescharacteristic
750C2#1308121811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC2×#10623045C2
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#22501
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. #13071546C2semidirect
4. #13069579C2semidirect
5. #13069570C2semidirect
6. #13069054C2semidirect
7. #13069053C2semidirect
8. #13068938C2semidirect
9. #13068932C2semidirect
10. #13068709C2semidirect
11. #13068702C2semidirect
12. #13068625C2semidirect
13. #13068430C2semidirect
14. #13068334C2semidirect
15. C11×#1736C2semidirect
25. #10623045C4semidirect
80. C2×C11×C4⋊C4C2×C4semidirect
91. #66983C2×C4semidirect
121. #66946C2×C4semidirect
127. #66943C2×C4semidirect
254. #1736D11semidirect
475. C2×C4⋊C4C4×D11semidirect
614. C11#22501semidirect

Maximal subgroups

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

subgroupindex
C2×#106230452
C2×#106227412
#130715462
#130695792
#130695702
#130690542
#130690532
#130689382
#130689322
#130687092
#130687022
#130686252
#130684302
#130683342
C11×#17362
#2250111