Finite Group Databasebeta

← #14770210

Subgroups — #14770210

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×#10623145C211yesmaximal, characteristic
2C2×#10622342C211yesmaximal, characteristic, complemented
3#13071541C211yesmaximal, characteristic, complemented
4#13069579C211yesmaximal, characteristic, complemented
5#13069570C211yesmaximal, characteristic, complemented
6#13069055C211yesmaximal, characteristic, complemented
7#13069051C211yesmaximal, characteristic, complemented
8#13068935C211yesmaximal, characteristic, complemented
9#13068712C211yesmaximal, characteristic, complemented
10#13068701C211yesmaximal, characteristic, complemented
11#13068624C211yesmaximal, characteristic, complemented
12#102×Dic11C211yesmaximal, characteristic, complemented
13#13068335C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#1874C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66991—21no—
19C2×#66991C2211yescharacteristic
20C2×#66988—21no—
21C2×D4×Dic11C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26#10623145—24no—
27#10623145C418yescomplemented
28C2×#66945C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×#66943C2211yescharacteristic
31C2×(C22⋊D11)⋊C4—21no—
32C2×#66932—21no—
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622826—21no—
39#10622825C2211yescharacteristic
40C4×C22⋊Dic11—21no—
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622603—21no—
45#10622600C2211yescharacteristic
46#10622591—21no—
47#10622590C2211yescharacteristic
48C4⋊C4×Dic11C2211yescharacteristic
49#10622342—24no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11D411yescharacteristic
68C23×Dic11—21no—
69C22×C4×D11—21no—
70C22×C4×D11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#121—22no—
74C11×#121C2×C414yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11D411yescharacteristic
87#66991—28no—
88#66991—22no—
89#66991C2×C414yescomplemented
90#66988—28no—
91D4×Dic11—22no—
92D4×Dic11C2×C414yescomplemented
93C4×C22⋊D11C2×C414yes—
94C4×C22⋊D11D414yes—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4D411yescharacteristic
98#66979—22no—
99#66979C2×C414yes—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
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×Dic11—21no—
111C2×C4×Dic11C2311yescharacteristic
112C2×#4318—22no—
113C2×#4318—22no—
114C2×#4318—41no—
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C2×#4313—22no—
118C2×#4313—22no—
119C2×#4313—41no—
120#66945—22no—
121#66945—41no—
122C4⋊C4×D11—22no—
123C4⋊C4×D11C2×C414yescomplemented
124#66943—22no—
125#66943C2×C414yescomplemented
126(C22⋊D11)⋊C4—28no—
127#66932—28no—
128C11×#102—22no—
129C11×#102—41no—
130C11×C22⋊C8—22no—
131#66896—22no—
132#66896—41no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138(C2×D11)⋊C8—22no—
139Dic11⋊C8—22no—
140C8×Dic11—22no—
141#22501—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C23×D11C2×D411yescharacteristic
145C2×D4×C11—24no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—81no—
152C2×D4×C11—81no—
153C2×D4×C11C22×C412yes—
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—21no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—81no—
164C22×C4×C11C22×C412yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—24no—
169C2×C22⋊D11—41no—
170C2×C22⋊D11—41no—
171C2×C22⋊D11—42no—
172C2×C22⋊D11—42no—
173C2×C22⋊D11C22⋊C414yes—
174C22×Dic11—24no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—81no—
180C22×Dic11—81no—
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184C2×C4×D11—24no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—81no—
190C2×C4×D11—81no—
191C2×C4×D11C22×C412yes—
192C2×C4×D11C2×D412yes—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4C22×C412yes—
205C11×C4⋊C4#4112yes—
206C11×C22⋊C4—24no—
207C22⋊Dic11—24no—
208C22⋊Dic11—24no—
209C22⋊Dic11—24no—
210C22⋊Dic11—42no—
211C22⋊Dic11C22⋊C414yes—
212(C2×D11)⋊C4—42no—
213(C2×D11)⋊C4—81no—
214(C2×D11)⋊C4C22⋊C414yes—
215C4⋊Dic11—24no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11C22×C412yes—
223C4⋊Dic11C22×C412yes—
224Dic11⋊C4—24no—
225Dic11⋊C4—24no—
226Dic11⋊C4C22⋊C414yes—
227C4×Dic11—24no—
228C4×Dic11—42no—
229C4×Dic11—81no—
230C4×Dic11C22×C412yes—
231C4×Dic11C2×D412yes—
232#4318—44no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8#4112yes—
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#1874D1111yescharacteristic, complemented
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—22no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11C2×C22⋊C412yes—
269C23×C11C22×D411yescharacteristic
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11C2×C22⋊C412yes—
277D4×C11—22no—
278D4×C11—22no—
279D4×C11—41no—
280D4×C11—41no—
281D4×C11—84no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
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—84no—
298C2×C4×C11C2×C22⋊C412yes—
299C2×C4×C11C23×C411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C112−1+411yescharacteristic
305C22⋊D11—44no—
306C22⋊D11—48no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—84no—
326C2×Dic11C2×C22⋊C412yes—
327C2×Dic11C2×C22⋊C412yes—
328C2×Dic11C2×C22⋊C412yes—
329C4×D11—22no—
330C4×D11—22no—
331C4×D11—22no—
332C4×D11—22no—
333C4×D11—84no—
334C8×C11—41no—
335C8×C11—41no—
336C11⋊C8—22no—
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—221no—
347C2×#121C2×D1111yescharacteristic
348C2×C4×D4—111no—
349C2×C4×D4—111no—
350C2×C4×D4—221no—
351C2×#117—111no—
352C2×#117—111no—
353C22×C4⋊C4—111no—
354C22×C4⋊C4C2×D1111yescharacteristic
355#436—224no—
356C2×C4⋊C8—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×#102C2×D1111yescharacteristic
360C2×#102C2×D1111yescharacteristic
361C2×C22⋊C8—111no—
362C2×C22⋊C8C2×D1111yescharacteristic
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#340—111no—
381#340—111no—
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×C11—42no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11C22×C22⋊C411yescharacteristic
399C22×C11#54611yescharacteristic
400C22×C11#54711yescharacteristic
401C22×C11#57511yescharacteristic
402C22×C11#57511yescharacteristic
403C22×C11#57611yescharacteristic
404C22×C11#57711yescharacteristic
405C2×D11—22no—
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—41no—
409C2×D11—41no—
410C2×D11—41no—
411C2×D11—41no—
412C4×C11—22no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11—81no—
416C4×C11C4×#4111yescharacteristic
417C4×C11#52011yescharacteristic
418C4×C11#54611yescharacteristic
419C4×C11#54711yescharacteristic
420Dic11—22no—
421Dic11—22no—
422Dic11—22no—
423Dic11—42no—
424Dic11—42no—
425Dic11—81no—
426Dic11—81no—
427C22×D4—21no—
428C22×D4—111no—
429C22×D4—221no—
430C22×D4C22×D1111yescharacteristic
431C23×C4—21no—
432C23×C4—111no—
433C23×C4—221no—
434C23×C4—221no—
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×C8C22×D1111yescharacteristic
445C22×C8C22×D1111yescharacteristic
446#126—228no—
447#125—114no—
448#125—222no—
449#123—228no—
450#121—22no—
451#121—114no—
452#121—222no—
453#121—228no—
454#121C4×D1114yes—
455C4×D4—114no—
456C4×D4—114no—
457C4×D4—114no—
458C4×D4—222no—
459C4×D4—228no—
460#117—114no—
461#117—222no—
462#117—222no—
463#117—441no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—114no—
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⋊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—111no—
490C2×C42—221no—
491C2×C42—221no—
492C2×C42—221no—
493C4⋊C8—222no—
494#102—22no—
495#102—41no—
496#102—222no—
497#102—441no—
498C22⋊C8—22no—
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—82no—
508C2×C11#233911yescharacteristic
509C2×C11#289611yescharacteristic
510C2×C11#289711yescharacteristic
511C2×C11#332211yescharacteristic
512C2×C11#332611yescharacteristic
513C2×C11#335111yescharacteristic
514C2×C11#335511yescharacteristic
515D11—42no—
516C24—21no—
517C24—111no—
518C24D4×D1111yescharacteristic
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—81no—
526C2×D4—81no—
527C2×D4—114no—
528C2×D4—224no—
529C2×D4—441no—
530C2×D4—441no—
531C2×D4—442no—
532C2×D4—442no—
533C2×D4C2×C4×D1112yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—111no—
545C22×C4—111no—
546C22×C4—111no—
547C22×C4—112no—
548C22×C4—112no—
549C22×C4—224no—
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—221no—
559C22×C4—881no—
560C22×C4—881no—
561C22×C4—881no—
562C22×C4—881no—
563C22×C4C2×C4×D1112yes—
564C22×C4D4×D1111yescharacteristic
565C22×C4D4×D1112yes—
566C22×C4C23×D1111yescharacteristic
567M16—444no—
568M16—444no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—112no—
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—42no—
586C4⋊C4—114no—
587C4⋊C4—112no—
588C4⋊C4—112no—
589C4⋊C4—224no—
590C4⋊C4—224no—
591C4⋊C4—224no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4C2×C4×D1112yes—
599C4⋊C4#434112yes—
600C22⋊C4—24no—
601C22⋊C4—114no—
602C22⋊C4—114no—
603C22⋊C4—224no—
604C22⋊C4—224no—
605C22⋊C4—224no—
606C22⋊C4—442no—
607C22⋊C4—442no—
608C22⋊C4—881no—
609C42—112no—
610C42—112no—
611C42—224no—
612C42—442no—
613C42—881no—
614C11#2250111yescharacteristic, complemented, Sylow
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—112no—
629C23—221no—
630C23—221no—
631C23—221no—
632C23—221no—
633C23—221no—
634C23—221no—
635C23C22⋊C4×D1112yes—
636C23C2×D4×D1111yescharacteristic
637D4—22no—
638D4—22no—
639D4—41no—
640D4—41no—
641D4—84no—
642D4—444no—
643D4—448no—
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—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—84no—
660C2×C4—112no—
661C2×C4—112no—
662C2×C4—112no—
663C2×C4—221no—
664C2×C4—221no—
665C2×C4—221no—
666C2×C4—221no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
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—884no—
687C2×C4C22⋊C4×D1112yes—
688C2×C4C22×C4×D1111yescharacteristic
689C2×C4C2×D4×D1111yescharacteristic
690C2×C4C2×#434111yescharacteristic
691C2×C4#6703711yescharacteristic
692C2×C4#41×D1111yescharacteristic
693C2×C4#6704311yescharacteristic
694C8—41no—
695C8—41no—
696C8—222no—
697C8—441no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—222no—
713C22—222no—
714C22—222no—
715C22—441no—
716C22—441no—
717C22—441no—
718C22—441no—
719C22C2×C22⋊C4×D1111yescharacteristic
720C22#1062312211yescharacteristic
721C22#1062318611yescharacteristic
722C22#1062328811yescharacteristic
723C22#1062329311yescharacteristic
724C22#1062330411yescharacteristic
725C22#1062330811yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—81no—
730C4—222no—
731C4—222no—
732C4—222no—
733C4—442no—
734C4—442no—
735C4—881no—
736C4—881no—
737C4C4×#434111yescharacteristic
738C4#1062307711yescharacteristic
739C4#1062314111yescharacteristic
740C4#1062314211yescharacteristic
741C2—42no—
742C2—82no—
743C2—442no—
744C2#1307144211yescharacteristic
745C2#1307713211yescharacteristic
746C2#1307713711yescharacteristic
747C2#1308082111yescharacteristic
748C2#1308087311yescharacteristic
749C2#1308118011yescharacteristic
750C2#1308122211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×#10623145C2
cosocleC22×C4×C11C24
hypercenter#1874D11
hypocenterC11#22501
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#10622342C2semidirect
3. #13071541C2semidirect
4. #13069579C2semidirect
5. #13069570C2semidirect
6. #13069055C2semidirect
7. #13069051C2semidirect
8. #13068935C2semidirect
9. #13068712C2semidirect
10. #13068701C2semidirect
11. #13068624C2semidirect
12. #102×Dic11C2semidirect
13. #13068335C2semidirect
14. #13068334C2semidirect
15. C11×#1874C2semidirect
27. #10623145C4semidirect
89. #66991C2×C4semidirect
92. D4×Dic11C2×C4semidirect
123. C4⋊C4×D11C2×C4semidirect
125. #66943C2×C4semidirect
248. #1874D11semidirect
614. C11#22501semidirect

Maximal subgroups

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

subgroupindex
C2×#106231452
C2×#106223422
#130715412
#130695792
#130695702
#130690552
#130690512
#130689352
#130687122
#130687012
#130686242
#102×Dic112
#130683352
#130683342
C11×#18742
#2250111