Finite Group Databasebeta

← #14764969

Subgroups — #14764969

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic11C211yesmaximal, characteristic, complemented
2#13071107C211yesmaximal, characteristic, complemented
3#13069483C211yesmaximal, characteristic, complemented
4#13069472C211yesmaximal, characteristic, complemented
5#13069301C211yesmaximal, characteristic, complemented
6#13069294C211yesmaximal, characteristic, complemented
7#13069259C211yesmaximal, characteristic, complemented
8#13069245C211yesmaximal, characteristic, complemented
9#13068966C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic, complemented
11#13068939C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic, complemented
13#13068556C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#449C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×D4×Dic11—21no—
21C2×D4×Dic11C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C11×#449C418yescomplemented
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622834C2211yescharacteristic
33#10622834C2211yescharacteristic
34#10622834C2211yescharacteristic
35#10622833—21no—
36#10622833—21no—
37#10622833—21no—
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622825C2211yescharacteristic
43C4×C22⋊Dic11—21no—
44C4×C22⋊Dic11—21no—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×#66882C2211yescharacteristic
47C2×#66881C2211yescharacteristic
48C2×C8×Dic11C2211yescharacteristic
49C2×C8×Dic11C2211yescharacteristic
50#10622598C2211yescharacteristic
51C4⋊C4×Dic11C2211yescharacteristic
52#10622564—21no—
53C22⋊C4×Dic11—21no—
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C2×C11×#41—22no—
61C2×C11×#41—41no—
62C2×C11×#41—41no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41C2×C414yescomplemented
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C23×Dic11—21no—
74C23×Dic11D411yescharacteristic
75C23×Dic11D411yescharacteristic
76C2×C11×SD16—41no—
77C2×C11×SD16—41no—
78C2×C11×SD16C2×C414yescomplemented
79C2×C11×D8—41no—
80C2×C11×D8—41no—
81C2×C11×D8C2×C414yescomplemented
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×#121—22no—
85C11×#121C2×C414yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97D4×Dic11—41no—
98D4×Dic11—41no—
99D4×Dic11—44no—
100#66979—41no—
101#66979—41no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—41no—
110C2×C4×Dic11—41no—
111C2×C4×Dic11D411yescharacteristic
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C11×#103C2×C414yescomplemented
118C11×#102C2×C414yescomplemented
119C11×C22⋊C8C2×C414yescomplemented
120#66899—41no—
121#66899—41no—
122#66896—41no—
123#66896—41no—
124#66896—41no—
125#66896—41no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C22⋊(C11⋊C8)—22no—
134#66882—41no—
135#66881—41no—
136C8×Dic11—41no—
137C8×Dic11—41no—
138#22045—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C22×C412yes—
152C2×D4×C11—24no—
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11C22×C412yes—
169C2×D4×C11C22×C412yes—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—24no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11C22×C412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11#4112yes—
182C22×C4×C11C2411yescharacteristic
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—41no—
191C22×Dic11—41no—
192C22×Dic11—41no—
193C22×Dic11—42no—
194C22×Dic11—42no—
195C22×Dic11—42no—
196C22×Dic11C2×D411yescharacteristic
197C22×Dic11C2×D411yescharacteristic
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200C11×SD16—44no—
201C11×D8—44no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11C22×C412yes—
207C2×C8×C11C22×C412yes—
208C11×C4⋊C4—21no—
209C11×C4⋊C4C22×C412yes—
210C11×C22⋊C4—24no—
211C22⋊Dic11—42no—
212C22⋊Dic11—42no—
213C22⋊Dic11—42no—
214C22⋊Dic11—42no—
215C22⋊Dic11—42no—
216C22⋊Dic11—42no—
217C22⋊Dic11—42no—
218C22⋊Dic11—42no—
219C22⋊Dic11—42no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—42no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233C4×Dic11—41no—
234C4×Dic11—41no—
235C4×Dic11—42no—
236C4×Dic11—42no—
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×#449D1111yescharacteristic
244C4×#121—111no—
245#2297—111no—
246#1970—111no—
247#1968—111no—
248#1934—111no—
249#1933—111no—
250#1928—111no—
251#1926—111no—
252#1879—111no—
253#1877—111no—
254#1875—111no—
255#1854—111no—
256#1788—111no—
257C4×C22⋊C8—111no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11C4×D412yes—
279C23×C11C22×D411yescharacteristic
280Q8×C11—22no—
281Q8×C11—22no—
282Q8×C11—41no—
283Q8×C11—41no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—22no—
288D4×C11—48no—
289D4×C11—48no—
290D4×C11—41no—
291D4×C11—41no—
292D4×C11—41no—
293D4×C11—41no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—48no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11C4×D412yes—
308C2×C4×C11C23×C411yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—44no—
324C2×Dic11—44no—
325C2×Dic11—41no—
326C2×Dic11—41no—
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—
336C2×Dic11—41no—
337C2×Dic11—84no—
338C2×Dic11#13512yes—
339C2×Dic11#13512yes—
340C2×Dic11AGL(1,ℤ/8)12yes—
341C8×C11—22no—
342C8×C11—22no—
343C11⋊C8—41no—
344C11⋊C8—41no—
345C22×#41C2×D1111yescharacteristic
346C22×SD16C2×D1111yescharacteristic
347C22×D8C2×D1111yescharacteristic
348C2×#121C2×D1111yescharacteristic
349C2×C4×D4—111no—
350C2×C4×D4—221no—
351C2×#117—111no—
352C22×C42—111no—
353#449Dic1118yescomplemented
354C2×#107—111no—
355C2×#106—111no—
356C2×#103—111no—
357C2×#103—111no—
358C2×#103C2×D1111yescharacteristic
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×#102C2×D1111yescharacteristic
364C2×C22⋊C8—111no—
365C2×C22⋊C8C2×D1111yescharacteristic
366C2×C4×C8—111no—
367C2×C4×C8—111no—
368#391—111no—
369#391—111no—
370#390—111no—
371#390—111no—
372#390—111no—
373#389—111no—
374#388—221no—
375#386—221no—
376#386—221no—
377#386—221no—
378#380—111no—
379C4×C4⋊C4—111no—
380C4×C22⋊C4—221no—
381C4×C22⋊C4—221no—
382C4×C22⋊C4—221no—
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#336—111no—
388#336—111no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11C2×C4×D411yescharacteristic
411C22×C11#53411yescharacteristic
412C22×C11#53511yescharacteristic
413C22×C11C2×#13511yescharacteristic
414C22×C11C2×#13511yescharacteristic
415C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
416C22×C11#57511yescharacteristic
417C4×C11—22no—
418C4×C11—42no—
419C4×C11—42no—
420C4×C11#51811yescharacteristic
421C4×C11#51811yescharacteristic
422C4×C11#53811yescharacteristic
423C4×C11#53811yescharacteristic
424Dic11—22no—
425Dic11—22no—
426Dic11—22no—
427Dic11—41no—
428Dic11—81no—
429Dic11—81no—
430Dic11—81no—
431Dic11—81no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41—41no—
437C2×#41C2×Dic1114yescomplemented
438C22×Q8C22×D1111yescharacteristic
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C22×D1111yescharacteristic
442C22×D4C22×D1111yescharacteristic
443C23×C4—21no—
444C23×C4—111no—
445C23×C4—111no—
446C23×C4—221no—
447C23×C4C22×D1111yescharacteristic
448C2×SD16—41no—
449C2×SD16—41no—
450C2×SD16C2×Dic1114yescomplemented
451C2×D8—41no—
452C2×D8—41no—
453C2×D8C2×Dic1114yescomplemented
454C22×C8—111no—
455C22×C8—111no—
456C22×C8C22×D1111yescharacteristic
457C22×C8C22×D1111yescharacteristic
458#121—22no—
459#121C2×Dic1114yes—
460C4×D4—441no—
461C4×D4—441no—
462C4×D4—444no—
463#117—441no—
464#117—441no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4C22×D1111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—221no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C42—111no—
482C2×C42—111no—
483C2×C42—111no—
484C2×C42—111no—
485C2×C42—221no—
486C2×C42—221no—
487C2×C42—441no—
488C2×C42—441no—
489#107—441no—
490#106—441no—
491#103—441no—
492#103—441no—
493#103C2×Dic1114yescomplemented
494#102—441no—
495#102—441no—
496#102—441no—
497#102—441no—
498#102C2×Dic1114yescomplemented
499C22⋊C8—222no—
500C22⋊C8C2×Dic1114yescomplemented
501C4×C8—441no—
502C4×C8—441no—
503#95—221no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508#95—221no—
509#95—221no—
510C2×C11—42no—
511C2×C11—82no—
512C2×C11—82no—
513C2×C11#232111yescharacteristic
514C2×C11C4×#13511yescharacteristic
515C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
516C2×C11#318811yescharacteristic
517C2×C11#319111yescharacteristic
518C2×C11#320711yescharacteristic
519C2×C11#321211yescharacteristic
520C24—21no—
521C24—21no—
522C24D4×D1111yescharacteristic
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8C22×Dic1112yes—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4C22×Dic1112yes—
550C2×D4C22×Dic1112yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—111no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—111no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—442no—
572C22×C4—441no—
573C22×C4—441no—
574C22×C4—441no—
575C22×C4—442no—
576C22×C4—442no—
577C22×C4D4×D1111yescharacteristic
578C22×C4#434112yes—
579C22×C4C22×Dic1112yes—
580C22×C4C23×D1111yescharacteristic
581SD16—44no—
582D8—44no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8C22×Dic1112yes—
594C2×C8C22×Dic1112yes—
595C4⋊C4—21no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—442no—
605C4⋊C4C22×Dic1112yes—
606C22⋊C4—24no—
607C22⋊C4—442no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—442no—
611C22⋊C4—442no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C42—221no—
617C42—221no—
618C42—221no—
619C42—221no—
620C42—441no—
621C42—441no—
622C42—442no—
623C42—442no—
624C11#2204511yescharacteristic, complemented, Sylow
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23D4×Dic1112yes—
646C23C2×D4×D1111yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—48no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—112no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—444no—
687C2×C4—444no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—884no—
701C2×C4D4×Dic1112yes—
702C2×C4C2×#434111yescharacteristic
703C2×C4#6703711yescharacteristic
704C2×C4#6703711yescharacteristic
705C2×C4#6703711yescharacteristic
706C2×C4#6703711yescharacteristic
707C2×C4C23×Dic1111yescharacteristic
708C8—22no—
709C8—22no—
710C8—441no—
711C8—441no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22#1062312011yescharacteristic
734C22#1062312311yescharacteristic
735C22D11×#13511yescharacteristic
736C22D11×#13511yescharacteristic
737C22D11×AGL(1,ℤ/8)11yescharacteristic
738C22#1062330411yescharacteristic
739C22C2×D4×Dic1111yescharacteristic
740C4—22no—
741C4—42no—
742C4—42no—
743C4—222no—
744C4—222no—
745C4—222no—
746C4—441no—
747C4—881no—
748C4—881no—
749C4—881no—
750C4—881no—
751C4#1062312411yescharacteristic
752C4#1062312411yescharacteristic
753C4#1062332911yescharacteristic
754C4#1062332911yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#1307127711yescharacteristic
759C2#135×Dic1111yescharacteristic
760C2AGL(1,ℤ/8)×Dic1111yescharacteristic
761C2#1307937911yescharacteristic
762C2#1307940611yescharacteristic
763C2#1307954711yescharacteristic
764C2#1307958911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#449C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#449D11
hypocenterC11#22045
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #121×Dic11C2semidirect
2. #13071107C2semidirect
3. #13069483C2semidirect
4. #13069472C2semidirect
5. #13069301C2semidirect
6. #13069294C2semidirect
7. #13069259C2semidirect
8. #13069245C2semidirect
9. #13068966C2semidirect
10. #13068952C2semidirect
11. #13068939C2semidirect
12. #13068817C2semidirect
13. #13068556C2semidirect
14. C22⋊C8×Dic11C2semidirect
24. C11×#449C4semidirect
65. C2×C11×#41C2×C4semidirect
78. C2×C11×SD16C2×C4semidirect
81. C2×C11×D8C2×C4semidirect
117. C11×#103C2×C4semidirect
118. C11×#102C2×C4semidirect
119. C11×C22⋊C8C2×C4semidirect
353. #449Dic11semidirect
437. C2×#41C2×Dic11semidirect
450. C2×SD16C2×Dic11semidirect
453. C2×D8C2×Dic11semidirect
493. #103C2×Dic11semidirect
498. #102C2×Dic11semidirect
500. C22⋊C8C2×Dic11semidirect
624. C11#22045semidirect

Maximal subgroups

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

subgroupindex
#121×Dic112
#130711072
#130694832
#130694722
#130693012
#130692942
#130692592
#130692452
#130689662
#130689522
#130689392
#130688172
#130685562
C22⋊C8×Dic112
C2×C11×#4492
#2204511