Finite Group Databasebeta

← #14775860

Subgroups — #14775860

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078404C211yesmaximal, characteristic
2#13077563C211yesmaximal, characteristic, complemented
3#13077184C211yesmaximal, characteristic
4#13069597C211yesmaximal, characteristic, complemented
5#13069391C211yesmaximal, characteristic, complemented
6#13069368C211yesmaximal, characteristic, complemented
7#13069363C211yesmaximal, characteristic, complemented
8#13069218C211yesmaximal, characteristic, complemented
9#13069218C211yesmaximal, characteristic, complemented
10#13068889C211yesmaximal, characteristic
11#13068889C211yesmaximal, characteristic
12#13068473C211yesmaximal, characteristic, complemented
13#13068461C211yesmaximal, characteristic
14#13068454C211yesmaximal, characteristic
15C11×#1759C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17C2×#67001C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19#10623001C2211yescharacteristic
20C2×C11×#104C2211yescharacteristic
21C2×C11×#104C2211yescharacteristic
22C4×C11×M16C2211yescharacteristic
23C11×#376C2211yescharacteristic
24#10622846C2211yescharacteristic
25#10622846C2211yescharacteristic
26C2×#66886C2211yescharacteristic
27C2×#66886C2211yescharacteristic
28#10622735C2211yescharacteristic
29#10622735C2211yescharacteristic
30#10622732C2211yescharacteristic
31#10622732C2211yescharacteristic
32#10622635C411yescharacteristic, complemented
33#10622635C411yescharacteristic, complemented
34#10622634C411yescharacteristic, complemented
35#10622633C411yescharacteristic, complemented
36#10622622C411yescharacteristic, complemented
37#10622622C411yescharacteristic, complemented
38#10622621C411yescharacteristic, complemented
39#10622620C411yescharacteristic, complemented
40#10622612—21no—
41#10622612—21no—
42#10622612C2211yescharacteristic
43#10622612C2211yescharacteristic
44#10622611C2211yescharacteristic
45#10622611C2211yescharacteristic
46#10622537—21no—
47#10622537C2211yescharacteristic
48C2×C4⋊(C11⋊C8)—21no—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622314—21no—
54#10622314—21no—
55#10622292—21no—
56C8×Dic22—21no—
57C11×#339C2211yescharacteristic
58C11×#339C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63#10622161C2211yescharacteristic
64#10622161C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C4×Q8×C11C2×C411yescharacteristic
71C4×Q8×C11C2×C411yescharacteristic
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11C2×C411yescharacteristic
75C4×D4×C11C2×C411yescharacteristic
76C11×#117—21no—
77C11×#117C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82#67001—22no—
83#67001—22no—
84#67001—41no—
85#67001—41no—
86#66979C2311yescharacteristic
87#66979C2311yescharacteristic
88#66977—21no—
89#66977—21no—
90C2×#4318—21no—
91C2×#4318—21no—
92C2×#4318C2311yescharacteristic
93C2×#4318C2311yescharacteristic
94C22×C11⋊C8—21no—
95C22×C11⋊C8—21no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66923C2×C411yescharacteristic
101#66923C2×C411yescharacteristic
102#66922C2×C411yescharacteristic
103#66922C2×C411yescharacteristic
104C4×Dic22—21no—
105C4×Dic22—21no—
106C11×#104—22no—
107C11×#104Q814yescomplemented
108C11×#97—21no—
109C4×C8×C11—21no—
110C11×#95—21no—
111C11×#95—21no—
112#66899C2×C411yescharacteristic
113#66899C2×C411yescharacteristic
114#66899C2×C411yescharacteristic
115#66899C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119#66896C2×C411yescharacteristic
120#66886—41no—
121#66886—41no—
122#66879—21no—
123#66879—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128C8×Dic11—21no—
129C8×Dic11—21no—
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66872C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135#66871C2×C411yescharacteristic
136#66871C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)—21no—
143C4⋊(C11⋊C8)—21no—
144C4⋊(C11⋊C8)C2×C411yescharacteristic
145C4⋊(C11⋊C8)C2×C411yescharacteristic
146C4⋊(C11⋊C8)C2×C411yescharacteristic
147C4⋊(C11⋊C8)C2×C411yescharacteristic
148C4⋊(C11⋊C8)D411yescharacteristic
149C4⋊(C11⋊C8)D411yescharacteristic
150C4⋊(C11⋊C8)D411yescharacteristic
151C4⋊(C11⋊C8)D411yescharacteristic
152#66867—41no—
153C4×C11⋊C8—41no—
154#22984—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×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11#4111yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16C2×Q812yes—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11C22×C411yescharacteristic
192C42×C11C22×C411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×Q812yes—
196C22⋊Dic11—21no—
197C22⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C22×C411yescharacteristic
201C4⋊Dic11C22×C411yescharacteristic
202C4⋊Dic11C22×C411yescharacteristic
203C4⋊Dic11C22×C411yescharacteristic
204Dic11⋊C4—21no—
205Dic11⋊C4—21no—
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210#4318—21no—
211#4318—21no—
212#4318—21no—
213#4318—21no—
214#4318—42no—
215#4318—42no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—42no—
227C2×C11⋊C8—42no—
228C2×C11⋊C8C22×C411yescharacteristic
229C2×C11⋊C8C22×C411yescharacteristic
230C2×C11⋊C8C22×C411yescharacteristic
231C2×C11⋊C8C22×C411yescharacteristic
232C2×C11⋊C8C2×D411yescharacteristic
233C2×C11⋊C8C2×D411yescharacteristic
234C2×C11⋊C8C2×D411yescharacteristic
235C2×C11⋊C8C2×D411yescharacteristic
236#3076—111no—
237#2962—111no—
238#2906—111no—
239#1995—111no—
240#1950—111no—
241#1946—111no—
242#1945—111no—
243#1922—111no—
244#1922—111no—
245#1866—111no—
246#1866—111no—
247#1768—111no—
248#1765—111no—
249#1764—111no—
250#1759D1111yescharacteristic
251C23×C11—21no—
252C23×C11C2×#4111yescharacteristic
253Q8×C11—21no—
254Q8×C11C4×Q812yes—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—21no—
258D4×C11C4×Q812yes—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—81no—
274C2×C4×C11C4×D411yescharacteristic
275C2×C4×C11C4×D411yescharacteristic
276C2×C4×C11C4×D411yescharacteristic
277C2×C4×C11C4×D411yescharacteristic
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×Q811yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C112−1+411yescharacteristic
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288Dic22—42no—
289Dic22—81no—
290C8×C11—22no—
291C8×C11—41no—
292C11⋊C8—21no—
293C11⋊C8—21no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—21no—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—21no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C2×#131—111no—
303C2×#131—111no—
304#533—111no—
305C4×#41C2×D1111yescharacteristic
306#479—111no—
307#479—111no—
308#478—111no—
309#478—111no—
310#477—111no—
311#476—111no—
312#475—111no—
313#474—111no—
314#446—221no—
315#446—221no—
316#446—221no—
317C8×Q8—221no—
318C2×#108—111no—
319C2×#108—111no—
320#427—111no—
321#427—111no—
322#424—111no—
323#424—111no—
324#424—111no—
325#424—111no—
326#424—221no—
327#424—221no—
328#423—111no—
329#423—221no—
330C2×C4⋊C8—111no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—221no—
333C2×#104C2×D1111yescharacteristic
334C2×#104C2×D1111yescharacteristic
335#416—111no—
336#416—111no—
337#405—111no—
338#405—111no—
339C4×M16C2×D1111yescharacteristic
340C2×#97—111no—
341C2×C4×C8—111no—
342#376C2×D1111yescharacteristic
343#341—111no—
344#341—111no—
345#339—111no—
346#339—111no—
347#339—111no—
348#339—111no—
349#339C2×D1111yescharacteristic
350#339C2×D1111yescharacteristic
351#336—111no—
352#336—111no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11C2×C4×D411yescharacteristic
359C22×C11#55211yescharacteristic
360C22×C11#55411yescharacteristic
361C4×C11—22no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—81no—
370C4×C11C2×C4×Q811yescharacteristic
371C4×C11#52011yescharacteristic
372C4×C11#54611yescharacteristic
373C4×C11D4×Q811yescharacteristic
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378C2×#41C22×D1111yescharacteristic
379#131—222no—
380#131—222no—
381#131—441no—
382#131—441no—
383C2×M16—111no—
384C2×M16—111no—
385C2×M16—221no—
386C2×M16—221no—
387C2×M16C22×D1111yescharacteristic
388C2×M16C22×D1111yescharacteristic
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—221no—
394C22×C8—221no—
395C4⋊Q8—111no—
396C4⋊Q8—111no—
397#125—111no—
398#125—111no—
399C22⋊Q8—221no—
400C22⋊Q8—221no—
401C4×Q8—221no—
402C4×Q8—221no—
403C4×Q8C4×D1111yescharacteristic
404C4×Q8C4×D1111yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C4×D1111yescharacteristic
408C4×D4C4×D1111yescharacteristic
409#117—21no—
410#117—111no—
411#117—111no—
412#117C22×D1111yescharacteristic
413C2×C42—21no—
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416C2×C42C22×D1111yescharacteristic
417#108—441no—
418#108—441no—
419#107—111no—
420#107—111no—
421#107—111no—
422#107—111no—
423#106—111no—
424#106—111no—
425#106—111no—
426#106—111no—
427C4⋊C8—111no—
428C4⋊C8—111no—
429C4⋊C8—111no—
430C4⋊C8—111no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—111no—
435C4⋊C8—221no—
436C4⋊C8—221no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439C4⋊C8—221no—
440C4⋊C8—221no—
441C4⋊C8—221no—
442C4⋊C8—221no—
443C4⋊C8—221no—
444C4⋊C8—221no—
445#104—22no—
446#104Dic2214yescomplemented
447#103—111no—
448#103—111no—
449#103—111no—
450#103—111no—
451#102—111no—
452#102—111no—
453#102—111no—
454#102—111no—
455#97—21no—
456#97—221no—
457#97—221no—
458#97—441no—
459C4×C8—21no—
460C4×C8—221no—
461C4×C8—221no—
462C4×C8—441no—
463#95—21no—
464#95—21no—
465C2×C11—21no—
466C2×C11—21no—
467C2×C11—42no—
468C2×C11#236011yescharacteristic
469C2×C11#295511yescharacteristic
470C2×C11#295711yescharacteristic
471#41—21no—
472#41—21no—
473#41C2×Dic2212yes—
474#41#433912yes—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8C2×C4×D1111yescharacteristic
478C2×D4—21no—
479C2×D4C2×C4×D1111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4#434111yescharacteristic
486C22×C4#434111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488M16—21no—
489M16—21no—
490M16—21no—
491M16—221no—
492M16—221no—
493M16—221no—
494M16—221no—
495M16—442no—
496M16—442no—
497M16C2×Dic2212yes—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—111no—
503C2×C8—111no—
504C2×C8—111no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—442no—
519C2×C8—442no—
520C4⋊C4—21no—
521C4⋊C4—21no—
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⋊C4C2×C4×D1111yescharacteristic
533C4⋊C4C2×C4×D1111yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—221no—
546C42—221no—
547C42C2×Dic2212yes—
548C42C2×C4×D1111yescharacteristic
549C42C2×C4×D1111yescharacteristic
550C42D4×D1111yescharacteristic
551C42D4×D1111yescharacteristic
552C11#2298411yescharacteristic, complemented, Sylow
553C23—21no—
554C23C2×#434111yescharacteristic
555Q8—21no—
556Q8—442no—
557Q8—881no—
558Q8C4×Dic2212yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4C4×Dic2212yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—81no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4(C22⋊D11)⋊C411yescharacteristic
583C2×C4(C22⋊D11)⋊C411yescharacteristic
584C2×C4(C22⋊D11)⋊C411yescharacteristic
585C2×C4(C22⋊D11)⋊C411yescharacteristic
586C2×C4C22×Dic2211yescharacteristic
587C2×C4C22×C4×D1111yescharacteristic
588C2×C4C2×#433911yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4#6704211yescharacteristic
591C2×C4#6704311yescharacteristic
592C8—22no—
593C8—41no—
594C8—221no—
595C8—221no—
596C8—221no—
597C8—221no—
598C8—221no—
599C8—221no—
600C8—221no—
601C8—221no—
602C8—441no—
603C8—441no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C2×(C22⋊D11)⋊C411yescharacteristic
610C22#1062307211yescharacteristic
611C22#1062307411yescharacteristic
612C4—22no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—81no—
621C4—441no—
622C4—441no—
623C4—441no—
624C4—441no—
625C4C2×C4×Dic2211yescharacteristic
626C4#1062305411yescharacteristic
627C4D4×Dic2211yescharacteristic
628C4#1062308111yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#1307161911yescharacteristic
633C2#1307751511yescharacteristic
634C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1759C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenter#1759D11
hypocenterC11#22984
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #13077563C2semidirect
4. #13069597C2semidirect
5. #13069391C2semidirect
6. #13069368C2semidirect
7. #13069363C2semidirect
8. #13069218C2semidirect
9. #13069218C2semidirect
12. #13068473C2semidirect
32. #10622635C4semidirect
33. #10622635C4semidirect
34. #10622634C4semidirect
35. #10622633C4semidirect
36. #10622622C4semidirect
37. #10622622C4semidirect
38. #10622621C4semidirect
39. #10622620C4semidirect
107. C11×#104Q8semidirect
446. #104Dic22semidirect
552. C11#22984semidirect

Maximal subgroups

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

subgroupindex
#130784042
#130775632
#130771842
#130695972
#130693912
#130693682
#130693632
#130692182
#130688892
#130684732
#130684612
#130684542
C11×#17592
#2298411