Finite Group Databasebeta

← #14788755

Subgroups — #14788755

Order 2816.

1144 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×#10622670C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic, complemented
4#13069859C211yesmaximal, characteristic, complemented
5#13069852C211yesmaximal, characteristic, complemented
6#13069699C211yesmaximal, characteristic, complemented
7#13069693C211yesmaximal, characteristic
8#13069557C211yesmaximal, characteristic, complemented
9#13069433C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic
12#13068870C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068621C211yesmaximal, characteristic, complemented
15C2×C11×#556C211yesmaximal, characteristic, complemented
16C11×#556—24no—
17C11×#556—24no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#126—21no—
20C2×C11×#126—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×C22⋊Q8—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117—21no—
29C2×#66999—21no—
30C22×#4325C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622670—24no—
44#10622639—24no—
45#10622607—21no—
46#10622607—21no—
47#10622600—21no—
48C2×#66873C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622548C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8—22no—
72C11×#126—28no—
73C11×#126—28no—
74C11×#124—22no—
75C11×#124—22no—
76C11×#124—22no—
77C11×#124D414yes—
78C11×C22⋊Q8—28no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×Q8×C11—22no—
84C4×Q8×C11D414yes—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C11×#117—28no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—21no—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106#66999—44no—
107C2×#4325—22no—
108C2×#4325—22no—
109C2×#4325—22no—
110C2×#4325—22no—
111C2×#4325—22no—
112C2×#4325—41no—
113C2×#4323—22no—
114C2×#4323—22no—
115C2×#4323—41no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C4×D44—22no—
133C4×D44—22no—
134#66899—22no—
135#66899—22no—
136#66899—22no—
137#66899—41no—
138#66899—41no—
139#66899—41no—
140#66896—22no—
141#66896—22no—
142#66896—41no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145#66873—22no—
146#66871—22no—
147C4⋊(C11⋊C8)—22no—
148#66867—22no—
149#24205—111nomaximal, Sylow
150C24×C11—21no—
151C23×D11—21no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—41no—
165C2×Q8×C11C2×D412yes—
166C2×Q8×C11C2×D412yes—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11C2×D412yes—
173C22×C4×C11—24no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44—21no—
194C2×D44#4112yes—
195C2×C4×D11—42no—
196C2×C4×D11—42no—
197C2×C4×D11—42no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4C2×D412yes—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C42×C11—24no—
213C42×C11—24no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11C2×D412yes—
219C42×C11C2×D412yes—
220#4325—28no—
221#4325—44no—
222#4323—44no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—81no—
227(C2×D11)⋊C4—81no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—42no—
235C4⋊Dic11—81no—
236Dic11⋊C4—42no—
237Dic11⋊C4—42no—
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—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8#4112yes—
250C2×#556D1111yescharacteristic, complemented
251C2×#463—111no—
252C2×#440—111no—
253#2538—111no—
254#2043—111no—
255#2042—111no—
256#2013—111no—
257#2012—111no—
258#1985—111no—
259#1959—111no—
260#1880—111no—
261#1879—111no—
262#1863—111no—
263#1862—111no—
264#1803—111no—
265C23×C11—22no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11C22×D411yescharacteristic
273C22×D11—22no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280Q8×C11—22no—
281Q8×C11—22no—
282Q8×C11—22no—
283Q8×C11—22no—
284Q8×C11—44no—
285Q8×C11—41no—
286Q8×C11—41no—
287Q8×C11—41no—
288Q8×C11—41no—
289D4×C11—22no—
290D4×C11—22no—
291D4×C11—41no—
292D4×C11—41no—
293C2×C4×C11—21no—
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—22no—
301C2×C4×C11—21no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—48no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11#12012yes—
319C2×C4×C11#12012yes—
320C2×C4×C11AGL(1,ℤ/8)12yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C112−1+411yescharacteristic
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336D44—22no—
337D44—22no—
338D44—41no—
339D44—41no—
340C4×D11—84no—
341C11⋊C8—22no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C11⋊C8—41no—
345C22×SD16—111no—
346C22×SD16—111no—
347C22×D8—111no—
348#556—24no—
349#556—24no—
350C2×C4⋊Q8C2×D1111yescharacteristic
351C2×#126—21no—
352C2×#126—21no—
353C2×#124C2×D1111yescharacteristic
354C2×#124C2×D1111yescharacteristic
355C2×C22⋊Q8—21no—
356C2×C22⋊Q8—221no—
357C2×C4×Q8C2×D1111yescharacteristic
358C2×C4×Q8C2×D1111yescharacteristic
359C2×C4×Q8C2×D1111yescharacteristic
360C2×C4×D4—111no—
361C2×C4×D4C2×D1111yescharacteristic
362C2×#117—21no—
363#463—224no—
364#440—224no—
365C2×#107—111no—
366C2×C4⋊C8—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#103—111no—
370C2×#103—111no—
371C2×#103—111no—
372C2×#103—111no—
373C2×#102—111no—
374C2×#102—111no—
375C2×#102—111no—
376C2×#102—111no—
377C2×#97—111no—
378#396—221no—
379#396—221no—
380#390—111no—
381#390—111no—
382#389—111no—
383#389—111no—
384#384—111no—
385#380—221no—
386#340—111no—
387#340—111no—
388#336—111no—
389#336—111no—
390#336—111no—
391#336—111no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11C2×#12011yescharacteristic
400C22×C11#54811yescharacteristic
401C22×C11#55011yescharacteristic
402C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
403C22×C11#57511yescharacteristic
404C22×C11#57711yescharacteristic
405C22×C11#57811yescharacteristic
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—81no—
410C2×D11—81no—
411C2×D11—81no—
412C2×D11—81no—
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—22no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11—41no—
419C4×C11—42no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11#52511yescharacteristic
423C4×C11#53711yescharacteristic
424C4×C11#54611yescharacteristic
425C4×C11#54711yescharacteristic
426Dic11—81no—
427Dic11—81no—
428Dic11—81no—
429C22×Q8C22⋊D1111yescharacteristic
430C22×Q8C22×D1111yescharacteristic
431C22×Q8C22×D1111yescharacteristic
432C22×D4—111no—
433C22×D4C22×D1111yescharacteristic
434C23×C4—21no—
435C23×C4—221no—
436C2×SD16—222no—
437C2×SD16—222no—
438C2×SD16—222no—
439C2×SD16—222no—
440C2×SD16—222no—
441C2×SD16—441no—
442C2×D8—222no—
443C2×D8—222no—
444C2×D8—441no—
445C22×C8—111no—
446C22×C8—111no—
447C22×C8—111no—
448C22×C8—111no—
449C4⋊Q8—22no—
450C4⋊Q8—22no—
451#126—28no—
452#126—28no—
453#124—22no—
454#124—22no—
455#124—22no—
456#124C22⋊D1114yes—
457C22⋊Q8—28no—
458C22⋊Q8—444no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×Q8—22no—
464C4×Q8C22⋊D1114yes—
465C4×D4—22no—
466C4×D4—22no—
467C4×D4—222no—
468C4×D4—222no—
469#117—28no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4C22⋊D1111yescharacteristic
482C2×C4⋊C4C22⋊D1111yescharacteristic
483C2×C4⋊C4C22⋊D1111yescharacteristic
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C42—21no—
496C2×C42—21no—
497C2×C42C22×D1111yescharacteristic
498C2×C42C22×D1111yescharacteristic
499C2×C42C22×D1111yescharacteristic
500#107—222no—
501C4⋊C8—222no—
502#103—222no—
503#103—222no—
504#103—222no—
505#103—441no—
506#103—441no—
507#103—441no—
508#102—222no—
509#102—222no—
510#102—222no—
511#102—441no—
512#97—222no—
513#95—221no—
514#95—221no—
515C2×C11—82no—
516C2×C11#240711yescharacteristic
517C2×C11#300611yescharacteristic
518C2×C11#301311yescharacteristic
519C2×C11#336711yescharacteristic
520C2×C11#337611yescharacteristic
521C2×C11#339711yescharacteristic
522C2×C11#340211yescharacteristic
523D11—82no—
524C24—21no—
525C24—221no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—41no—
539C2×Q8C2×C22⋊D1112yes—
540C2×Q8C2×C22⋊D1112yes—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—112no—
547C2×D4—221no—
548C2×D4—221no—
549C2×D4—221no—
550C2×D4—221no—
551C2×D4—221no—
552C2×D4C2×C22⋊D1112yes—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—442no—
563C22×C4—442no—
564C22×C4—442no—
565C22×C4C2×C22⋊D1111yescharacteristic
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C23×D1111yescharacteristic
572SD16—228no—
573SD16—444no—
574D8—444no—
575C2×C8—112no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—442no—
602C4⋊C4—442no—
603C4⋊C4—442no—
604C4⋊C4—881no—
605C4⋊C4C2×C22⋊D1112yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—442no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C22⋊C4—881no—
615C22⋊C4—881no—
616C42—24no—
617C42—24no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42C2×C22⋊D1112yes—
623C42C2×C22⋊D1112yes—
624C11#2420511yescharacteristic, complemented, Sylow
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—222no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23C22×C22⋊D1111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—44no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649D4—22no—
650D4—22no—
651D4—41no—
652D4—41no—
653D4—222no—
654D4—222no—
655D4—441no—
656D4—441no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—48no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—884no—
692C2×C4#6700212yes—
693C2×C4#6700612yes—
694C2×C4#6700612yes—
695C2×C4#41×D1111yescharacteristic
696C2×C4#41×D1111yescharacteristic
697C2×C4#6704211yescharacteristic
698C2×C4#6704311yescharacteristic
699C2×C4C22×C22⋊D1111yescharacteristic
700C2×C4C22×C22⋊D1111yescharacteristic
701C8—222no—
702C8—441no—
703C8—441no—
704C8—441no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—442no—
713C22—442no—
714C22—442no—
715C22—881no—
716C22—881no—
717C22—881no—
718C22—881no—
719C22C2×#6700211yescharacteristic
720C22#1062335311yescharacteristic
721C22#1062336211yescharacteristic
722C22#1062336511yescharacteristic
723C22#1062336811yescharacteristic
724C22#1062336911yescharacteristic
725C22C2×#6700611yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—41no—
735C4—881no—
736C4—881no—
737C4—881no—
738C4#1062335511yescharacteristic
739C4#1062335911yescharacteristic
740C4#1062336011yescharacteristic
741C4#1062336411yescharacteristic
742C2—82no—
743C2—882no—
744C2#1307195511yescharacteristic
745C2#1307786811yescharacteristic
746C2#1307793111yescharacteristic
747C2#1308133011yescharacteristic
748C2#1308143711yescharacteristic
749C2#1308163611yescharacteristic
750C2#1308169111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#556D11
hypocenterC11#24205
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
3. #13073534C2semidirect
4. #13069859C2semidirect
5. #13069852C2semidirect
6. #13069699C2semidirect
8. #13069557C2semidirect
9. #13069433C2semidirect
10. #13068971C2semidirect
12. #13068870C2semidirect
13. #13068863C2semidirect
14. #13068621C2semidirect
15. C2×C11×#556C2semidirect
250. C2×#556D11semidirect
624. C11#24205semidirect

Maximal subgroups

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

subgroupindex
C2×#106226702
C2×#106226392
#130735342
#130698592
#130698522
#130696992
#130696932
#130695572
#130694332
#130689712
#130689642
#130688702
#130688632
#130686212
C2×C11×#5562
#2420511