Finite Group Databasebeta

← #14765103

Subgroups — #14765103

Order 2816.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071311C211yesmaximal, characteristic, complemented
2#13071208C211yesmaximal, characteristic, complemented
3#13069499C211yesmaximal, characteristic, complemented
4#13069483C211yesmaximal, characteristic, complemented
5#13069315C211yesmaximal, characteristic, complemented
6#13069294C211yesmaximal, characteristic, complemented
7#13069259C211yesmaximal, characteristic, complemented
8#13069238C211yesmaximal, characteristic, complemented
9#13068966C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic, complemented
11#13068934C211yesmaximal, characteristic, complemented
12#13068806C211yesmaximal, characteristic, complemented
13#13068556C211yesmaximal, characteristic, complemented
14#13068384C211yesmaximal, characteristic, complemented
15C2×C11×#449C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C11×#449C418yescomplemented
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31#10622834—21no—
32#10622834C2211yescharacteristic
33#10622834C2211yescharacteristic
34#10622834C2211yescharacteristic
35#10622833—21no—
36#10622833—21no—
37#10622833—21no—
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622825—21no—
43#10622825—21no—
44#10622825C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×#66882C2211yescharacteristic
47C2×#66882C2211yescharacteristic
48C2×#66879C2211yescharacteristic
49C2×C8×Dic11C2211yescharacteristic
50#10622598C2211yescharacteristic
51C4⋊C4×Dic11C2211yescharacteristic
52#10622564—21no—
53#10622563—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×Dic11—21no—
75C2×C11×SD16—41no—
76C2×C11×SD16—41no—
77C2×C11×SD16C2×C414yescomplemented
78C2×C11×D8—41no—
79C2×C11×D8—41no—
80C2×C11×D8C2×C414yescomplemented
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×#121—22no—
84C11×#121C2×C414yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C22⋊Dic11—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⋊Dic11D411yescharacteristic
96C2×C22⋊Dic11D411yescharacteristic
97D4×Dic11—41no—
98D4×Dic11—41no—
99#66979—41no—
100#66979—41no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11—41no—
105C2×C4⋊Dic11D411yescharacteristic
106C2×C4⋊Dic11D411yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4×Dic11—21no—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C11×#103C2×C414yescomplemented
117C11×#102C2×C414yescomplemented
118C11×C22⋊C8C2×C414yescomplemented
119#66899—41no—
120#66899—41no—
121#66896—41no—
122#66896—41no—
123#66896—41no—
124#66896—41no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C22⋊(C11⋊C8)—22no—
133#66882—41no—
134#66882—41no—
135#66879—41no—
136C8×Dic11—41no—
137#22055—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C11×#41—44no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C22×C412yes—
151C2×D4×C11—24no—
152C2×D4×C11—24no—
153C2×D4×C11—21no—
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—42no—
164C2×D4×C11—42no—
165C2×D4×C11—81no—
166C2×D4×C11—81no—
167C2×D4×C11C22×C412yes—
168C2×D4×C11C22×C412yes—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—24no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11C22×C412yes—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11#4112yes—
181C22×C4×C11C2411yescharacteristic
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—42no—
187C22×Dic11—42no—
188C22×Dic11—81no—
189C22×Dic11—81no—
190C22×Dic11—81no—
191C22×Dic11—81no—
192C22×Dic11C2×D411yescharacteristic
193C22×Dic11C2×D411yescharacteristic
194C22×Dic11C2×D411yescharacteristic
195C22×Dic11C2×D411yescharacteristic
196C11×SD16—44no—
197C11×D8—44no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11C22×C412yes—
203C2×C8×C11C22×C412yes—
204C11×C4⋊C4—21no—
205C11×C4⋊C4C22×C412yes—
206C11×C22⋊C4—24no—
207C22⋊Dic11—41no—
208C22⋊Dic11—41no—
209C22⋊Dic11—42no—
210C22⋊Dic11—81no—
211C22⋊Dic11—81no—
212C22⋊Dic11—81no—
213C22⋊Dic11—81no—
214C22⋊Dic11—81no—
215C22⋊Dic11—81no—
216C22⋊Dic11—81no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—41no—
226C4⋊Dic11—41no—
227C4⋊Dic11—42no—
228C4⋊Dic11—81no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233C4×Dic11—81no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×#449D1111yescharacteristic
241#2324—111no—
242#2311—111no—
243#1973—111no—
244#1970—111no—
245#1936—111no—
246#1933—111no—
247#1928—111no—
248#1925—111no—
249#1879—111no—
250#1877—111no—
251#1874—111no—
252#1852—111no—
253#1788—111no—
254#1750—111no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
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×C11C4×D412yes—
276C23×C11C22×D411yescharacteristic
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—41no—
280Q8×C11—41no—
281D4×C11—22no—
282D4×C11—22no—
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—48no—
286D4×C11—41no—
287D4×C11—41no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11—84no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—48no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11C4×D412yes—
305C2×C4×C11C23×C411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11H(5,𝔽2)11yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
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—41no—
324C2×Dic11—41no—
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—84no—
336C2×Dic11—84no—
337C8×C11—22no—
338C8×C11—22no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C22×#41C2×D1111yescharacteristic
342C22×SD16C2×D1111yescharacteristic
343C22×D8C2×D1111yescharacteristic
344C2×#121C2×D1111yescharacteristic
345C2×C4×D4—111no—
346C2×#117—111no—
347C22×C4⋊C4—111no—
348#449Dic1118yescomplemented
349C2×#107—111no—
350C2×#107—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#103C2×D1111yescharacteristic
354C2×#102—111no—
355C2×#102—111no—
356C2×#102—111no—
357C2×#102—111no—
358C2×#102C2×D1111yescharacteristic
359C2×C22⋊C8—111no—
360C2×C22⋊C8C2×D1111yescharacteristic
361C2×#97—111no—
362C2×C4×C8—111no—
363#391—111no—
364#391—111no—
365#390—111no—
366#390—111no—
367#390—111no—
368#390—221no—
369#389—111no—
370#388—221no—
371#386—221no—
372#386—221no—
373#386—221no—
374#385—221no—
375#380—111no—
376#380—221no—
377#380—221no—
378C4×C4⋊C4—111no—
379#340—111no—
380#340—111no—
381#340—111no—
382#340—111no—
383#336—111no—
384#336—111no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11C2×C4×D411yescharacteristic
407C22×C11#53411yescharacteristic
408C22×C11#53511yescharacteristic
409C22×C11#57611yescharacteristic
410C22×C11#57611yescharacteristic
411C22×C11#57711yescharacteristic
412C22×C11#57811yescharacteristic
413C4×C11—22no—
414C4×C11—42no—
415C4×C11—42no—
416C4×C11#51811yescharacteristic
417C4×C11#51811yescharacteristic
418C4×C11#53811yescharacteristic
419C4×C11#53811yescharacteristic
420Dic11—41no—
421Dic11—41no—
422Dic11—41no—
423Dic11—41no—
424Dic11—81no—
425Dic11—81no—
426Dic11—81no—
427Dic11—81no—
428C2×#41—22no—
429C2×#41—41no—
430C2×#41—41no—
431C2×#41—41no—
432C2×#41—41no—
433C2×#41C2×Dic1114yescomplemented
434C22×Q8C22×D1111yescharacteristic
435C22×D4—21no—
436C22×D4—21no—
437C22×D4C22×D1111yescharacteristic
438C22×D4C22×D1111yescharacteristic
439C23×C4—21no—
440C23×C4—221no—
441C23×C4—221no—
442C23×C4C22×D1111yescharacteristic
443C2×SD16—41no—
444C2×SD16—41no—
445C2×SD16C2×Dic1114yescomplemented
446C2×D8—41no—
447C2×D8—41no—
448C2×D8C2×Dic1114yescomplemented
449C22×C8—111no—
450C22×C8—111no—
451C22×C8C22×D1111yescharacteristic
452C22×C8C22×D1111yescharacteristic
453#121—22no—
454#121C2×Dic1114yes—
455C4×D4—441no—
456C4×D4—441no—
457#117—441no—
458#117—441no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4—221no—
467C2×C4⋊C4—441no—
468C2×C4⋊C4—441no—
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—111no—
472C2×C22⋊C4—111no—
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—221no—
484#107—441no—
485#107—441no—
486#103—441no—
487#103—441no—
488#103C2×Dic1114yescomplemented
489#102—441no—
490#102—441no—
491#102—441no—
492#102—441no—
493#102C2×Dic1114yescomplemented
494C22⋊C8—222no—
495C22⋊C8C2×Dic1114yescomplemented
496#97—441no—
497C4×C8—441no—
498#95—221no—
499#95—221no—
500#95—221no—
501#95—221no—
502#95—221no—
503#95—221no—
504#95—221no—
505C2×C11—42no—
506C2×C11—82no—
507C2×C11—82no—
508C2×C11#232111yescharacteristic
509C2×C11#294611yescharacteristic
510C2×C11#295111yescharacteristic
511C2×C11#319811yescharacteristic
512C2×C11#320311yescharacteristic
513C2×C11#322011yescharacteristic
514C2×C11#322511yescharacteristic
515C24—21no—
516C24—21no—
517C24D4×D1111yescharacteristic
518#41—44no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8C22×Dic1112yes—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4C22×Dic1112yes—
545C2×D4C22×Dic1112yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—442no—
564C22×C4—442no—
565C22×C4—881no—
566C22×C4—881no—
567C22×C4—881no—
568C22×C4—881no—
569C22×C4D4×D1111yescharacteristic
570C22×C4#434112yes—
571C22×C4C22×Dic1112yes—
572C22×C4C23×D1111yescharacteristic
573SD16—44no—
574D8—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8C22×Dic1112yes—
586C2×C8C22×Dic1112yes—
587C4⋊C4—21no—
588C4⋊C4—221no—
589C4⋊C4—221no—
590C4⋊C4—221no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—441no—
597C4⋊C4—441no—
598C4⋊C4—442no—
599C4⋊C4—881no—
600C4⋊C4C22×Dic1112yes—
601C22⋊C4—24no—
602C22⋊C4—441no—
603C22⋊C4—441no—
604C22⋊C4—442no—
605C22⋊C4—881no—
606C22⋊C4—881no—
607C22⋊C4—881no—
608C22⋊C4—881no—
609C22⋊C4—881no—
610C22⋊C4—881no—
611C22⋊C4—881no—
612C42—221no—
613C42—221no—
614C42—221no—
615C42—221no—
616C42—881no—
617C11#2205511yescharacteristic, complemented, Sylow
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23D4×Dic1112yes—
639C23C2×D4×D1111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—48no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—84no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—48no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
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—884no—
693C2×C4D4×Dic1112yes—
694C2×C4C2×#434111yescharacteristic
695C2×C4#6703711yescharacteristic
696C2×C4#6703711yescharacteristic
697C2×C4#6703711yescharacteristic
698C2×C4#6703711yescharacteristic
699C2×C4C23×Dic1111yescharacteristic
700C8—22no—
701C8—22no—
702C8—441no—
703C8—441no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22#1062312011yescharacteristic
726C22#1062312311yescharacteristic
727C22#1062330011yescharacteristic
728C22#1062330211yescharacteristic
729C22#1062330511yescharacteristic
730C22#1062330611yescharacteristic
731C22C2×D4×Dic1111yescharacteristic
732C4—22no—
733C4—42no—
734C4—42no—
735C4—441no—
736C4—441no—
737C4—441no—
738C4—441no—
739C4—881no—
740C4—881no—
741C4—881no—
742C4—881no—
743C4#1062312411yescharacteristic
744C4#1062312411yescharacteristic
745C4#1062332911yescharacteristic
746C4#1062332911yescharacteristic
747C2—42no—
748C2—82no—
749C2—82no—
750C2#1307127711yescharacteristic
751C2#1307744911yescharacteristic
752C2#1307749211yescharacteristic
753C2#1307946511yescharacteristic
754C2#1307951511yescharacteristic
755C2#1307966411yescharacteristic
756C2#1307972111yescharacteristic
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#22055
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. #13071311C2semidirect
2. #13071208C2semidirect
3. #13069499C2semidirect
4. #13069483C2semidirect
5. #13069315C2semidirect
6. #13069294C2semidirect
7. #13069259C2semidirect
8. #13069238C2semidirect
9. #13068966C2semidirect
10. #13068952C2semidirect
11. #13068934C2semidirect
12. #13068806C2semidirect
13. #13068556C2semidirect
14. #13068384C2semidirect
23. C11×#449C4semidirect
65. C2×C11×#41C2×C4semidirect
77. C2×C11×SD16C2×C4semidirect
80. C2×C11×D8C2×C4semidirect
116. C11×#103C2×C4semidirect
117. C11×#102C2×C4semidirect
118. C11×C22⋊C8C2×C4semidirect
348. #449Dic11semidirect
433. C2×#41C2×Dic11semidirect
445. C2×SD16C2×Dic11semidirect
448. C2×D8C2×Dic11semidirect
488. #103C2×Dic11semidirect
493. #102C2×Dic11semidirect
495. C22⋊C8C2×Dic11semidirect
617. C11#22055semidirect

Maximal subgroups

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

subgroupindex
#130713112
#130712082
#130694992
#130694832
#130693152
#130692942
#130692592
#130692382
#130689662
#130689522
#130689342
#130688062
#130685562
#130683842
C2×C11×#4492
#2205511