Finite Group Databasebeta

← #14775841

Subgroups — #14775841

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078400C211yesmaximal, characteristic
2#13077560C211yesmaximal, characteristic, complemented
3#13077182C211yesmaximal, characteristic
4#13069591C211yesmaximal, characteristic, complemented
5#13069390C211yesmaximal, characteristic, complemented
6#13069364C211yesmaximal, characteristic, complemented
7#13069363C211yesmaximal, characteristic, complemented
8#13069215C211yesmaximal, characteristic, complemented
9#13069214C211yesmaximal, characteristic, complemented
10#13068893C211yesmaximal, characteristic
11#13068891C211yesmaximal, characteristic
12C4×Dic11⋊C8C211yesmaximal, characteristic, complemented
13#13068454C211yesmaximal, characteristic
14#104×Dic11C211yesmaximal, characteristic
15C11×#1764C211yesmaximal, characteristic
16C2×C11×#131C2211yescharacteristic
17#41×Dic11C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19#10623048C2211yescharacteristic
20C2×C11×#104C2211yescharacteristic
21C11×#416C2211yescharacteristic
22C11×#405C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66901C2211yescharacteristic
25#10622846C2211yescharacteristic
26C2×#66886C2211yescharacteristic
27#10622735C2211yescharacteristic
28#10622732—21no—
29#10622732C2211yescharacteristic
30#10622731—21no—
31#10622731C2211yescharacteristic
32M16×Dic11C2211yescharacteristic
33C2×#66883C2211yescharacteristic
34#10622719C2211yescharacteristic
35#10622715—21no—
36#10622715C2211yescharacteristic
37#10622715C2211yescharacteristic
38C2×Dic11⋊C8—21no—
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41#10622612C2211yescharacteristic
42#10622611C2211yescharacteristic
43C42×Dic11C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622412C411yescharacteristic, complemented
46#10622409C411yescharacteristic, complemented
47#10622407C411yescharacteristic, complemented
48#10622404C411yescharacteristic, complemented
49#10622379C411yescharacteristic, complemented
50#10622376C411yescharacteristic, complemented
51#10622374C411yescharacteristic, complemented
52#10622372C411yescharacteristic, complemented
53#10622314—21no—
54#10622314—21no—
55#10622292—21no—
56C8×Dic22—21no—
57C11×#341C2211yescharacteristic
58C11×#339C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622193C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C11×#131—22no—
69C11×#131—41no—
70C2×C11×M16—21no—
71C2×C11×M16C2311yescharacteristic
72C2×C11×M16C2311yescharacteristic
73C22×C8×C11—21no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#117C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78#67001—22no—
79#67001—41no—
80Q8×Dic11C2×C411yescharacteristic
81Q8×Dic11C2×C411yescharacteristic
82D4×Dic11—21no—
83D4×Dic11—21no—
84D4×Dic11C2×C411yescharacteristic
85D4×Dic11C2×C411yescharacteristic
86#66979—21no—
87#66979C2311yescharacteristic
88#66979C2311yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×#4318—21no—
95C2×#4318C2311yescharacteristic
96C2×#4318C2311yescharacteristic
97C22×C11⋊C8—21no—
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66943C2×C411yescharacteristic
101#66943C2×C411yescharacteristic
102#66941C2×C411yescharacteristic
103#66941C2×C411yescharacteristic
104#66931—21no—
105#66931—21no—
106C4×Dic22—21no—
107C4×Dic22—21no—
108C11×#104Q814yescomplemented
109C11×#103C2×C411yescharacteristic
110C11×#103C2×C411yescharacteristic
111C11×#102C2×C411yescharacteristic
112C11×#102C2×C411yescharacteristic
113C11×#97—21no—
114C4×C8×C11—21no—
115C4×C8×C11—41no—
116#66901—22no—
117#66899C2×C411yescharacteristic
118#66899C2×C411yescharacteristic
119#66896C2×C411yescharacteristic
120#66896C2×C411yescharacteristic
121#66886—41no—
122#66883—41no—
123#66882C2×C411yescharacteristic
124#66882C2×C411yescharacteristic
125#66881C2×C411yescharacteristic
126#66881C2×C411yescharacteristic
127#66879—21no—
128#66879—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137Dic11⋊C8C2×C411yescharacteristic
138Dic11⋊C8C2×C411yescharacteristic
139Dic11⋊C8C2×C411yescharacteristic
140Dic11⋊C8C2×C411yescharacteristic
141Dic11⋊C8D411yescharacteristic
142Dic11⋊C8D411yescharacteristic
143Dic11⋊C8D411yescharacteristic
144Dic11⋊C8D411yescharacteristic
145C8×Dic11—21no—
146C8×Dic11—21no—
147#66872C2×C411yescharacteristic
148#66872C2×C411yescharacteristic
149#66871C2×C411yescharacteristic
150#66871C2×C411yescharacteristic
151C4⋊(C11⋊C8)—21no—
152C4⋊(C11⋊C8)—21no—
153C4×C11⋊C8—41no—
154#22982—111nomaximal, Sylow
155C11×#41—21no—
156C11×#41—21no—
157C11×#41C2×Q812yes—
158C11×#41#4112yes—
159C2×Q8×C11C22×C411yescharacteristic
160C2×D4×C11—21no—
161C2×D4×C11C22×C411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11#4111yescharacteristic
169C22×Dic11#4111yescharacteristic
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16—42no—
176C11×M16C2×Q812yes—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—42no—
184C2×C8×C11C22×C411yescharacteristic
185C2×C8×C11C22×C411yescharacteristic
186C2×C8×C11C2×D411yescharacteristic
187C2×C8×C11C2×D411yescharacteristic
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C4⋊C4C22×C411yescharacteristic
190C11×C22⋊C4—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11C2×Q812yes—
194C22⋊Dic11—21no—
195C22⋊Dic11—21no—
196C22⋊Dic11—21no—
197C22⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C22×C411yescharacteristic
203C4⋊Dic11C22×C411yescharacteristic
204C4⋊Dic11C22×C411yescharacteristic
205C4⋊Dic11C22×C411yescharacteristic
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208Dic11⋊C4—21no—
209Dic11⋊C4—21no—
210C4×Dic11—24no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—42no—
218C4×Dic11C22×C411yescharacteristic
219C4×Dic11C22×C411yescharacteristic
220C4×Dic11C2×D411yescharacteristic
221C4×Dic11C2×D411yescharacteristic
222#4318—21no—
223#4318—21no—
224#4318—21no—
225#4318—21no—
226#4318—42no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—42no—
234C2×C11⋊C8C22×C411yescharacteristic
235C2×C11⋊C8C22×C411yescharacteristic
236C2×C11⋊C8C2×D411yescharacteristic
237C2×C11⋊C8C2×D411yescharacteristic
238#3076—111no—
239#2962—111no—
240#2906—111no—
241#1994—111no—
242#1950—111no—
243#1945—111no—
244#1945—111no—
245#1922—111no—
246#1922—111no—
247#1866—111no—
248#1866—111no—
249C4×C4⋊C8—111no—
250#1764—111no—
251#1764D1111yescharacteristic
252C4×#104—111no—
253C23×C11—21no—
254C23×C11C2×#4111yescharacteristic
255Q8×C11—21no—
256Q8×C11C4×Q812yes—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—21no—
260D4×C11C4×Q812yes—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11C23×C411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×Q811yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—42no—
285C2×Dic11—81no—
286C2×Dic11C4×D411yescharacteristic
287C2×Dic11C4×D411yescharacteristic
288C2×Dic11C4×D411yescharacteristic
289C2×Dic11C4×D411yescharacteristic
290Dic22—42no—
291Dic22—81no—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—21no—
295C8×C11—21no—
296C8×C11—22no—
297C8×C11—41no—
298C11⋊C8—21no—
299C11⋊C8—21no—
300C11⋊C8—21no—
301C11⋊C8—21no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C2×#131—111no—
305C2×#131C2×D1111yescharacteristic
306#533—111no—
307C4×#41—111no—
308#479—111no—
309#479—111no—
310#478—111no—
311#478—111no—
312#477—111no—
313#476—111no—
314#475—111no—
315#474—111no—
316#446—221no—
317#446—221no—
318#446—221no—
319C8×Q8—221no—
320C2×#108—111no—
321C2×#108—111no—
322#427—111no—
323#427—111no—
324#424—111no—
325#424—111no—
326#424—111no—
327#424—111no—
328#424—221no—
329#424—221no—
330#423—111no—
331#423—221no—
332C2×C4⋊C8—111no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—221no—
335C2×#104—111no—
336C2×#104C2×D1111yescharacteristic
337#416—111no—
338#416C2×D1111yescharacteristic
339#405—111no—
340#405C2×D1111yescharacteristic
341C4×M16—111no—
342C2×C4×C8—111no—
343C2×C4×C8C2×D1111yescharacteristic
344C43—111no—
345#341—111no—
346#341C2×D1111yescharacteristic
347#339—111no—
348#339—111no—
349#339—111no—
350#339—111no—
351#339—111no—
352#339C2×D1111yescharacteristic
353#336—111no—
354#336—111no—
355C22×C11—21no—
356C22×C11—21no—
357C22×C11—22no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11C2×C4×D411yescharacteristic
361C22×C11#55211yescharacteristic
362C22×C11#55411yescharacteristic
363C4×C11—24no—
364C4×C11—22no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11C2×C4×Q811yescharacteristic
368C4×C11#52011yescharacteristic
369C4×C11#54611yescharacteristic
370C4×C11D4×Q811yescharacteristic
371Dic11—21no—
372Dic11—21no—
373Dic11—21no—
374Dic11—42no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—41no—
379Dic11#44312yes—
380C2×#41C22×D1111yescharacteristic
381#131—22no—
382#131—41no—
383#131—222no—
384#131—441no—
385C2×M16—21no—
386C2×M16—111no—
387C2×M16—111no—
388C2×M16—221no—
389C2×M16C22×D1111yescharacteristic
390C2×M16C22×D1111yescharacteristic
391C22×C8—21no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—221no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C4⋊Q8—111no—
398C4⋊Q8—111no—
399#125—111no—
400#125—111no—
401C22⋊Q8—221no—
402C22⋊Q8—221no—
403C4×Q8—111no—
404C4×Q8—111no—
405C4×Q8—221no—
406C4×Q8—221no—
407C4×D4—111no—
408C4×D4—111no—
409C4×D4—221no—
410C4×D4—221no—
411#117—111no—
412#117—111no—
413#117—221no—
414#117C22×D1111yescharacteristic
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—221no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421#108—441no—
422#108—441no—
423#107—111no—
424#107—111no—
425#107—111no—
426#107—111no—
427#106—111no—
428#106—111no—
429#106—111no—
430#106—111no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—111no—
435C4⋊C8—111no—
436C4⋊C8—111no—
437C4⋊C8—111no—
438C4⋊C8—111no—
439C4⋊C8—221no—
440C4⋊C8—221no—
441C4⋊C8—221no—
442C4⋊C8—221no—
443C4⋊C8—221no—
444C4⋊C8—221no—
445C4⋊C8—221no—
446C4⋊C8—221no—
447C4⋊C8—221no—
448C4⋊C8—221no—
449#104—222no—
450#104Dic2214yescomplemented
451#103—111no—
452#103—111no—
453#103C4×D1111yescharacteristic
454#103C4×D1111yescharacteristic
455#102—111no—
456#102—111no—
457#102C4×D1111yescharacteristic
458#102C4×D1111yescharacteristic
459#97—21no—
460#97—221no—
461#97—221no—
462C4×C8—21no—
463C4×C8—41no—
464C4×C8—221no—
465C4×C8—221no—
466C4×C8—441no—
467C2×C11—21no—
468C2×C11—21no—
469C2×C11—42no—
470C2×C11#236011yescharacteristic
471C2×C11C2×#44311yescharacteristic
472C2×C11#295611yescharacteristic
473#41—21no—
474#41—21no—
475#41C2×Dic2212yes—
476#41#433912yes—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8C2×C4×D1111yescharacteristic
480C2×D4—21no—
481C2×D4C2×C4×D1111yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4C23×D1111yescharacteristic
490M16—21no—
491M16—21no—
492M16—21no—
493M16—42no—
494M16—221no—
495M16—221no—
496M16—221no—
497M16—221no—
498M16—442no—
499M16C2×Dic2212yes—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—42no—
507C2×C8—111no—
508C2×C8—111no—
509C2×C8—111no—
510C2×C8—111no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—442no—
518C2×C8C2×C4×D1111yescharacteristic
519C2×C8C2×C4×D1111yescharacteristic
520C2×C8D4×D1111yescharacteristic
521C2×C8D4×D1111yescharacteristic
522C4⋊C4—111no—
523C4⋊C4—111no—
524C4⋊C4—111no—
525C4⋊C4—111no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4C2×C4×D1111yescharacteristic
535C4⋊C4C2×C4×D1111yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C22⋊C4—221no—
540C22⋊C4—221no—
541C42—21no—
542C42—21no—
543C42—111no—
544C42—111no—
545C42—111no—
546C42—111no—
547C42—221no—
548C42—221no—
549C42—224no—
550C42—221no—
551C42—221no—
552C42—221no—
553C42—221no—
554C42—442no—
555C42C2×Dic2212yes—
556C11#2298211yescharacteristic, complemented, Sylow
557C23—21no—
558C23#41×D1111yescharacteristic
559Q8—21no—
560Q8—442no—
561Q8—881no—
562Q8C4×Dic2212yes—
563D4—22no—
564D4—22no—
565D4—21no—
566D4C4×Dic2212yes—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—111no—
576C2×C4—111no—
577C2×C4—111no—
578C2×C4—111no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—442no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—881no—
590C2×C4C22×Dic2211yescharacteristic
591C2×C4C22×C4×D1111yescharacteristic
592C2×C4C2×#433911yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4#6703711yescharacteristic
595C2×C4#6704311yescharacteristic
596C8—21no—
597C8—21no—
598C8—22no—
599C8—21no—
600C8—21no—
601C8—41no—
602C8—221no—
603C8—221no—
604C8—221no—
605C8—221no—
606C8—441no—
607C8—441no—
608C22—21no—
609C22—21no—
610C22—22no—
611C22—41no—
612C22—41no—
613C22#1062306211yescharacteristic
614C22#1062307011yescharacteristic
615C22C4×D4×D1111yescharacteristic
616C4—24no—
617C4—22no—
618C4—41no—
619C4—41no—
620C4—112no—
621C4—221no—
622C4—221no—
623C4—221no—
624C4—442no—
625C4—441no—
626C4—441no—
627C4—441no—
628C4—441no—
629C4C2×C4×Dic2211yescharacteristic
630C4#1062302111yescharacteristic
631C4D4×Dic2211yescharacteristic
632C4#1062307711yescharacteristic
633C2—21no—
634C2—21no—
635C2—42no—
636C2#1307162211yescharacteristic
637C2D11×#44311yescharacteristic
638C2#1307752111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1764C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenter#1764D11
hypocenterC11#22982
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1764

Complements

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

NH ≅ G/Ntype
2. #13077560C2semidirect
4. #13069591C2semidirect
5. #13069390C2semidirect
6. #13069364C2semidirect
7. #13069363C2semidirect
8. #13069215C2semidirect
9. #13069214C2semidirect
12. C4×Dic11⋊C8C2semidirect
45. #10622412C4semidirect
46. #10622409C4semidirect
47. #10622407C4semidirect
48. #10622404C4semidirect
49. #10622379C4semidirect
50. #10622376C4semidirect
51. #10622374C4semidirect
52. #10622372C4semidirect
108. C11×#104Q8semidirect
450. #104Dic22semidirect
556. C11#22982semidirect

Maximal subgroups

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

subgroupindex
#130784002
#130775602
#130771822
#130695912
#130693902
#130693642
#130693632
#130692152
#130692142
#130688932
#130688912
C4×Dic11⋊C82
#130684542
#104×Dic112
C11×#17642
#2298211