Finite Group Databasebeta

← #14761618

Subgroups — #14761618

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078404C211yesmaximal, characteristic
2#13077553C211yesmaximal, characteristic, complemented
3#13077044C211yesmaximal, characteristic
4#13069559C211yesmaximal, characteristic, complemented
5#13069389C211yesmaximal, characteristic, complemented
6#13069213C211yesmaximal, characteristic, complemented
7#13069213C211yesmaximal, characteristic, complemented
8#13068889C211yesmaximal, characteristic
9#13068889C211yesmaximal, characteristic
10#13068499C211yesmaximal, characteristic, complemented
11#13068494C211yesmaximal, characteristic, complemented
12#13068491C211yesmaximal, characteristic, complemented
13#13068461C211yesmaximal, characteristic
14#13068454C211yesmaximal, characteristic
15C11×#1806C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17C2×#67001C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19#10623001C2211yescharacteristic
20C11×#423C2211yescharacteristic
21C2×C11×#104C2211yescharacteristic
22C2×C11×#104C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
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#10622611C2211yescharacteristic
41#10622611C2211yescharacteristic
42#10622610—21no—
43#10622610—21no—
44#10622610C2211yescharacteristic
45#10622610C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C4×#4318—21no—
48C4×#4318C2211yescharacteristic
49C2×#66867—21no—
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622441—21no—
54#10622441—21no—
55#10622441—21no—
56#10622441—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×C11×C4⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83#67001—22no—
84#67001—22no—
85#67001—22no—
86#67001Q814yescomplemented
87#66979C2311yescharacteristic
88#66979C2311yescharacteristic
89#66977—21no—
90#66977—21no—
91C2×#4318—21no—
92C2×#4318—21no—
93C2×#4318C2311yescharacteristic
94C2×#4318C2311yescharacteristic
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66923C2×C411yescharacteristic
102#66923C2×C411yescharacteristic
103#66922C2×C411yescharacteristic
104#66922C2×C411yescharacteristic
105C4×Dic22—21no—
106C4×Dic22—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×#104—22no—
110C11×#104—22no—
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—22no—
121#66886—22no—
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)C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2×C411yescharacteristic
140C4⋊(C11⋊C8)C2×C411yescharacteristic
141C4⋊(C11⋊C8)C2×C411yescharacteristic
142#66867—21no—
143#66867—21no—
144#66867—21no—
145#66867—22no—
146#66867D411yescharacteristic
147#66867D411yescharacteristic
148#66867D411yescharacteristic
149#66867D411yescharacteristic
150C4×C11⋊C8—21no—
151C4×C11⋊C8—21no—
152C4×C11⋊C8—21no—
153C4×C11⋊C8—22no—
154#21629—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×M16—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11C22×C411yescharacteristic
194C42×C11C22×C411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C22⋊Dic11—21no—
198C22⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11C22×C411yescharacteristic
202C4⋊Dic11C22×C411yescharacteristic
203C4⋊Dic11C22×C411yescharacteristic
204C4⋊Dic11C22×C411yescharacteristic
205Dic11⋊C4—21no—
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208Dic11⋊C4—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211#4318—24no—
212#4318—24no—
213#4318—21no—
214#4318—21no—
215#4318C2×Q812yes—
216#4318#4112yes—
217C2×C11⋊C8—24no—
218C2×C11⋊C8—24no—
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—21no—
227C2×C11⋊C8C22×C411yescharacteristic
228C2×C11⋊C8C22×C411yescharacteristic
229C2×C11⋊C8C22×C411yescharacteristic
230C2×C11⋊C8C22×C411yescharacteristic
231C2×C11⋊C8C2×D411yescharacteristic
232C2×C11⋊C8C2×D411yescharacteristic
233C2×C11⋊C8C2×D411yescharacteristic
234C2×C11⋊C8C2×D411yescharacteristic
235C2×C11⋊C8C2×Q812yes—
236C2×C11⋊C8#4112yes—
237#3076—111no—
238#2961—111no—
239#2875—111no—
240#1986—111no—
241#1950—111no—
242#1922—111no—
243#1922—111no—
244#1866—111no—
245#1866—111no—
246#1806D1111yescharacteristic
247#1773—111no—
248#1772—111no—
249#1771—111no—
250#1765—111no—
251#1764—111no—
252C23×C11—21no—
253C23×C11C2×#4111yescharacteristic
254Q8×C11—21no—
255Q8×C11C4×Q812yes—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—21no—
259D4×C11C4×Q812yes—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
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×C11—81no—
275C2×C4×C11C4×D411yescharacteristic
276C2×C4×C11C4×D411yescharacteristic
277C2×C4×C11C4×D411yescharacteristic
278C2×C4×C11C4×D411yescharacteristic
279C2×C4×C11C23×C411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×Q811yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289Dic22—81no—
290Dic22—81no—
291C8×C11—41no—
292C8×C11—41no—
293C11⋊C8—21no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—21no—
297C11⋊C8—22no—
298C11⋊C8—21no—
299C11⋊C8—22no—
300C11⋊C8—21no—
301C11⋊C8C22⋊Q812yes—
302C11⋊C8C22⋊Q812yes—
303C2×#131—111no—
304C2×#131—111no—
305#533—111no—
306C4×#41C2×D1111yescharacteristic
307#479—111no—
308#479—111no—
309#478—111no—
310#478—111no—
311#477—111no—
312#476—111no—
313#475—111no—
314#474—111no—
315#446—221no—
316#446—221no—
317#446—221no—
318#446—221no—
319C2×#108—111no—
320C2×#108—111no—
321#427—111no—
322#427—111no—
323#424—111no—
324#424—111no—
325#423C2×D1111yescharacteristic
326C2×C4⋊C8—111no—
327C2×#104C2×D1111yescharacteristic
328C2×#104C2×D1111yescharacteristic
329#416—111no—
330#416—111no—
331#405—111no—
332#405—111no—
333#405—111no—
334#405—111no—
335#405—221no—
336#405—221no—
337C4×M16—111no—
338C4×M16—221no—
339C2×#97—111no—
340C2×#97—111no—
341C2×#97—221no—
342C2×C4×C8—111no—
343C4×C4⋊C4C2×D1111yescharacteristic
344#341—111no—
345#341—111no—
346#339—111no—
347#339—111no—
348#339—111no—
349#339—111no—
350#339C2×D1111yescharacteristic
351#339C2×D1111yescharacteristic
352#336—111no—
353#336—111no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11C2×C4×D411yescharacteristic
360C22×C11#52911yescharacteristic
361C22×C11#53311yescharacteristic
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—22no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—81no—
371C4×C11C2×C4×Q811yescharacteristic
372C4×C11C4×#4111yescharacteristic
373C4×C11C2×C22⋊Q811yescharacteristic
374C4×C11#52511yescharacteristic
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—41no—
379C2×#41C22×D1111yescharacteristic
380#131—114no—
381#131—222no—
382#131—222no—
383#131—222no—
384C2×M16—111no—
385C2×M16—111no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16C22×D1111yescharacteristic
389C2×M16C22×D1111yescharacteristic
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—221no—
395C22×C8—221no—
396C4⋊Q8—111no—
397C4⋊Q8—111no—
398#125—111no—
399#125—111no—
400C22⋊Q8—221no—
401C22⋊Q8—221no—
402C4×Q8—221no—
403C4×Q8—221no—
404C4×Q8C4×D1111yescharacteristic
405C4×Q8C4×D1111yescharacteristic
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C4×D1111yescharacteristic
409C4×D4C4×D1111yescharacteristic
410#117—21no—
411#117—111no—
412#117—111no—
413#117C22×D1111yescharacteristic
414C2×C4⋊C4—21no—
415C2×C42—21no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419#108—222no—
420#108—222no—
421#107—111no—
422#107—111no—
423#107—111no—
424#107—111no—
425#106—111no—
426#106—111no—
427#106—111no—
428#106—111no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—111no—
435C4⋊C8—221no—
436C4⋊C8—221no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439#104—22no—
440#104—22no—
441#103—111no—
442#103—111no—
443#103—111no—
444#103—111no—
445#102—111no—
446#102—111no—
447#102—111no—
448#102—111no—
449#97—111no—
450#97—111no—
451#97—111no—
452#97—111no—
453#97—222no—
454#97—221no—
455#97—221no—
456#97—221no—
457#97—221no—
458#97—221no—
459C4×C8—222no—
460C4×C8—221no—
461C4×C8—221no—
462C4×C8—221no—
463C4×C8—221no—
464C4×C8—221no—
465#95—21no—
466C2×C11—21no—
467C2×C11—21no—
468C2×C11—42no—
469C2×C11C4×C22⋊Q811yescharacteristic
470C2×C11#295611yescharacteristic
471C2×C11#295711yescharacteristic
472#41—21no—
473#41—21no—
474#41#434112yes—
475#41Q8×D1112yes—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8C2×C4×D1111yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D1111yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4#434111yescharacteristic
487C22×C4#434111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—112no—
494M16—112no—
495M16—224no—
496M16—224no—
497M16—221no—
498M16—221no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—111no—
502C2×C8—111no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—111no—
509C2×C8—111no—
510C2×C8—111no—
511C2×C8—224no—
512C2×C8—224no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—42no—
524C4⋊C4—111no—
525C4⋊C4—111no—
526C4⋊C4—111no—
527C4⋊C4—111no—
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—21no—
538C22⋊C4—21no—
539C22⋊C4—221no—
540C22⋊C4—221no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—221no—
549C42—221no—
550C42C2×C4×D1111yescharacteristic
551C42C2×C4×D1111yescharacteristic
552C42D4×D1111yescharacteristic
553C42D4×D1111yescharacteristic
554C11#2162911yescharacteristic, complemented, Sylow
555C23—21no—
556C23C2×#434111yescharacteristic
557Q8—21no—
558Q8—881no—
559Q8—881no—
560Q8#6694012yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4#6694012yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4(C22⋊D11)⋊C411yescharacteristic
585C2×C4(C22⋊D11)⋊C411yescharacteristic
586C2×C4(C22⋊D11)⋊C411yescharacteristic
587C2×C4(C22⋊D11)⋊C411yescharacteristic
588C2×C4C22×C4×D1111yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4C2×#434111yescharacteristic
591C2×C4C2×Q8×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C8—41no—
595C8—41no—
596C8—112no—
597C8—112no—
598C8—221no—
599C8—221no—
600C8—221no—
601C8—221no—
602C8—221no—
603C8—221no—
604C8—222no—
605C8—222no—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22C2×(C22⋊D11)⋊C411yescharacteristic
612C22#1062313111yescharacteristic
613C22#1062315311yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—81no—
623C4—441no—
624C4—441no—
625C4—441no—
626C4—441no—
627C4C2×#6694011yescharacteristic
628C4#1062305311yescharacteristic
629C4#1062313711yescharacteristic
630C4D11×C22⋊Q811yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2#1307114411yescharacteristic
635C2#1307752211yescharacteristic
636C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1806C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenter#1806D11
hypocenterC11#21629
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #13077553C2semidirect
4. #13069559C2semidirect
5. #13069389C2semidirect
6. #13069213C2semidirect
7. #13069213C2semidirect
10. #13068499C2semidirect
11. #13068494C2semidirect
12. #13068491C2semidirect
32. #10622635C4semidirect
33. #10622635C4semidirect
34. #10622634C4semidirect
35. #10622633C4semidirect
36. #10622622C4semidirect
37. #10622622C4semidirect
38. #10622621C4semidirect
39. #10622620C4semidirect
86. #67001Q8semidirect
554. C11#21629semidirect

Maximal subgroups

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

subgroupindex
#130784042
#130775532
#130770442
#130695592
#130693892
#130692132
#130688892
#130684992
#130684942
#130684912
#130684612
#130684542
C11×#18062
#2162911