Finite Group Databasebeta

← #14775864

Subgroups — #14775864

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#13077559C211yesmaximal, characteristic, complemented
3#13069596C211yesmaximal, characteristic, complemented
4#13069389C211yesmaximal, characteristic, complemented
5#13069366C211yesmaximal, characteristic, complemented
6#13069361C211yesmaximal, characteristic, complemented
7#13069212C211yesmaximal, characteristic, complemented
8#13069212C211yesmaximal, characteristic, complemented
9#13068891C211yesmaximal, characteristic
10#13068891C211yesmaximal, characteristic
11#13068475C211yesmaximal, characteristic, complemented
12#13068458C211yesmaximal, characteristic
13#13068451C211yesmaximal, characteristic
14#13068426C211yesmaximal, characteristic
15C11×#2906C211yesmaximal, characteristic
16C2×C11×#131C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19#10623001C2211yescharacteristic
20C11×#424—21no—
21C11×#424—21no—
22C11×#424C2211yescharacteristic
23C11×#424C2211yescharacteristic
24C11×#423—21no—
25C11×#423C2211yescharacteristic
26C2×C11×C4⋊C8—21no—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×#66901C2211yescharacteristic
29C2×#66901C2211yescharacteristic
30#10622846C2211yescharacteristic
31#10622846C2211yescharacteristic
32C2×#66886C2211yescharacteristic
33C2×#66886C2211yescharacteristic
34#10622715C2211yescharacteristic
35#10622715C2211yescharacteristic
36#10622714C2211yescharacteristic
37#10622714C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40#10622635C411yescharacteristic, complemented
41#10622635C411yescharacteristic, complemented
42#10622634C411yescharacteristic, complemented
43#10622633C411yescharacteristic, complemented
44#10622622C411yescharacteristic, complemented
45#10622622C411yescharacteristic, complemented
46#10622621C411yescharacteristic, complemented
47#10622620C411yescharacteristic, complemented
48#10622611C2211yescharacteristic
49#10622611C2211yescharacteristic
50#10622545C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C4×#4318C2211yescharacteristic
53#10622444—21no—
54#10622443—21no—
55#10622441—21no—
56#10622441—21no—
57#10622196C2211yescharacteristic
58#10622196C2211yescharacteristic
59#10622193C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622193C2211yescharacteristic
62#10622193C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622188C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622170C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C11×#131—22no—
69C11×#131—22no—
70C11×#131—41no—
71C11×#131—41no—
72C2×C11×M16—21no—
73C2×C11×M16—21no—
74C2×C11×M16C2311yescharacteristic
75C2×C11×M16C2311yescharacteristic
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C4×Q8×C11C2×C411yescharacteristic
81C4×Q8×C11C2×C411yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11C2×C411yescharacteristic
85C4×D4×C11C2×C411yescharacteristic
86C11×#117—21no—
87C11×#117C2311yescharacteristic
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90#66979C2311yescharacteristic
91#66979C2311yescharacteristic
92#66977—21no—
93#66977—21no—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
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×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8D411yescharacteristic
113C11×C4⋊C8D411yescharacteristic
114C11×C4⋊C8D411yescharacteristic
115C11×C4⋊C8D411yescharacteristic
116#66901—22no—
117#66901Q814yescomplemented
118#66899C2×C411yescharacteristic
119#66899C2×C411yescharacteristic
120#66899C2×C411yescharacteristic
121#66899C2×C411yescharacteristic
122#66896C2×C411yescharacteristic
123#66896C2×C411yescharacteristic
124#66896C2×C411yescharacteristic
125#66896C2×C411yescharacteristic
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66886—41no—
129#66886—41no—
130#66879—21no—
131#66879—21no—
132#66879—41no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137C8×Dic11—21no—
138C8×Dic11—21no—
139C8×Dic11—41no—
140#66872C2×C411yescharacteristic
141#66872C2×C411yescharacteristic
142#66872C2×C411yescharacteristic
143#66872C2×C411yescharacteristic
144#66871C2×C411yescharacteristic
145#66871C2×C411yescharacteristic
146#66871C2×C411yescharacteristic
147#66871C2×C411yescharacteristic
148C4⋊(C11⋊C8)C2×C411yescharacteristic
149C4⋊(C11⋊C8)C2×C411yescharacteristic
150C4⋊(C11⋊C8)C2×C411yescharacteristic
151C4⋊(C11⋊C8)C2×C411yescharacteristic
152#66867—21no—
153C4×C11⋊C8—21no—
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#4111yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×Dic11—21no—
169C22×Dic11—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16—21no—
176C11×M16—42no—
177C11×M16—42no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—42no—
185C2×C8×C11—42no—
186C2×C8×C11C2×D411yescharacteristic
187C2×C8×C11C2×D411yescharacteristic
188C2×C8×C11C2×D411yescharacteristic
189C2×C8×C11C2×D411yescharacteristic
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C4⋊C4C22×C411yescharacteristic
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11C22×C411yescharacteristic
201C42×C11C22×C411yescharacteristic
202C42×C11C2×D411yescharacteristic
203C42×C11C2×D411yescharacteristic
204C22⋊Dic11—21no—
205C22⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C22×C411yescharacteristic
209C4⋊Dic11C22×C411yescharacteristic
210C4⋊Dic11C22×C411yescharacteristic
211C4⋊Dic11C22×C411yescharacteristic
212Dic11⋊C4—21no—
213Dic11⋊C4—21no—
214Dic11⋊C4—21no—
215Dic11⋊C4—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11C2×Q812yes—
222#4318—21no—
223#4318—21no—
224#4318—21no—
225#4318C2×Q812yes—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8C22×C411yescharacteristic
233C2×C11⋊C8C22×C411yescharacteristic
234C2×C11⋊C8C22×C411yescharacteristic
235C2×C11⋊C8C22×C411yescharacteristic
236#3076—111no—
237#2962—111no—
238#2906D1111yescharacteristic
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#1759—111no—
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—41no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—81no—
268C2×C4×C11C4×D411yescharacteristic
269C2×C4×C11C4×D411yescharacteristic
270C2×C4×C11C4×D411yescharacteristic
271C2×C4×C11C4×D411yescharacteristic
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×Q811yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C112−1+411yescharacteristic
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—22no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288Dic22—42no—
289Dic22—81no—
290C8×C11—21no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—41no—
295C8×C11—41no—
296C11⋊C8—21no—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—21no—
300C11⋊C8—22no—
301C11⋊C8—41no—
302C2×#131C2×D1111yescharacteristic
303C2×#131C2×D1111yescharacteristic
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—21no—
323#424—21no—
324#424—111no—
325#424—111no—
326#424C2×D1111yescharacteristic
327#424C2×D1111yescharacteristic
328#423—21no—
329#423C2×D1111yescharacteristic
330C2×C4⋊C8—21no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8C2×D1111yescharacteristic
333C2×#104—111no—
334C2×#104—111no—
335#416—111no—
336#416—111no—
337#405—111no—
338#405—111no—
339C4×M16—111no—
340C2×#97—111no—
341C2×C4×C8—111no—
342#376—111no—
343#341—111no—
344#341—111no—
345#339—111no—
346#339—111no—
347#339—111no—
348#339—111no—
349#339—111no—
350#339—111no—
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—41no—
367C4×C11—41no—
368C4×C11C2×C4×Q811yescharacteristic
369C4×C11#52011yescharacteristic
370C4×C11#54611yescharacteristic
371C4×C11D4×Q811yescharacteristic
372Dic11—42no—
373Dic11—41no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—81no—
378C2×#41C22×D1111yescharacteristic
379#131—22no—
380#131—22no—
381#131—41no—
382#131—41no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—111no—
386C2×M16—111no—
387C2×M16C22×D1111yescharacteristic
388C2×M16C22×D1111yescharacteristic
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
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×C42—111no—
415C2×C42—111no—
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—21no—
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8—21no—
433C4⋊C8—111no—
434C4⋊C8—111no—
435C4⋊C8—111no—
436C4⋊C8—111no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439C4⋊C8—221no—
440C4⋊C8—221no—
441C4⋊C8C22⋊D1111yescharacteristic
442C4⋊C8C22⋊D1111yescharacteristic
443C4⋊C8C22⋊D1111yescharacteristic
444C4⋊C8C22⋊D1111yescharacteristic
445#104—114no—
446#104—222no—
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—221no—
456#97—221no—
457#97—221no—
458#97—441no—
459C4×C8—221no—
460C4×C8—221no—
461C4×C8—221no—
462C4×C8—441no—
463#95—221no—
464#95—221no—
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#41#434112yes—
474#41Q8×D1112yes—
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—221no—
484C22×C4—221no—
485C22×C4#433911yescharacteristic
486C22×C4#433911yescharacteristic
487C22×C4C23×D1111yescharacteristic
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—42no—
493M16—42no—
494M16—112no—
495M16—221no—
496M16—221no—
497M16—221no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—42no—
505C2×C8—42no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—111no—
509C2×C8—111no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8C2×C22⋊D1111yescharacteristic
517C2×C8C2×C22⋊D1111yescharacteristic
518C2×C8C2×C22⋊D1111yescharacteristic
519C2×C8C2×C22⋊D1111yescharacteristic
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—112no—
543C42—221no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42C2×C4×D1111yescharacteristic
549C42C2×C4×D1111yescharacteristic
550C42C2×C22⋊D1111yescharacteristic
551C42C2×C22⋊D1111yescharacteristic
552C11#2298411yescharacteristic, complemented, Sylow
553C23—21no—
554C23C2×#433911yescharacteristic
555Q8—21no—
556Q8—442no—
557Q8—881no—
558Q8#6694012yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4#6694012yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—81no—
572C2×C4—222no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4C4×C22⋊D1111yescharacteristic
583C2×C4C4×C22⋊D1111yescharacteristic
584C2×C4C4×C22⋊D1111yescharacteristic
585C2×C4C4×C22⋊D1111yescharacteristic
586C2×C4C22×C4×D1111yescharacteristic
587C2×C4C2×#434111yescharacteristic
588C2×C4#6703711yescharacteristic
589C2×C4C2×Q8×D1111yescharacteristic
590C2×C4#6704011yescharacteristic
591C2×C4C22×C22⋊D1111yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—221no—
599C8—221no—
600C8—221no—
601C8—221no—
602C8—222no—
603C8—441no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22#1062304211yescharacteristic
610C22#1062304411yescharacteristic
611C22C2×C4×C22⋊D1111yescharacteristic
612C4—22no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—442no—
620C4—441no—
621C4—441no—
622C4—441no—
623C4—441no—
624C4—881no—
625C4C2×#6694011yescharacteristic
626C4#1062303511yescharacteristic
627C4#1062333711yescharacteristic
628C4Q8×C22⋊D1111yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#1307162111yescharacteristic
633C2#1307751711yescharacteristic
634C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2906C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenter#2906D11
hypocenterC11#22984
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #13077559C2semidirect
3. #13069596C2semidirect
4. #13069389C2semidirect
5. #13069366C2semidirect
6. #13069361C2semidirect
7. #13069212C2semidirect
8. #13069212C2semidirect
11. #13068475C2semidirect
40. #10622635C4semidirect
41. #10622635C4semidirect
42. #10622634C4semidirect
43. #10622633C4semidirect
44. #10622622C4semidirect
45. #10622622C4semidirect
46. #10622621C4semidirect
47. #10622620C4semidirect
117. #66901Q8semidirect
552. C11#22984semidirect

Maximal subgroups

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

subgroupindex
#130784042
#130775592
#130695962
#130693892
#130693662
#130693612
#130692122
#130688912
#130684752
#130684582
#130684512
#130684262
C11×#29062
#2298411