Finite Group Databasebeta

← #14775870

Subgroups — #14775870

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#13078398C211yesmaximal, characteristic
2#13077565C211yesmaximal, characteristic, complemented
3#13077185C211yesmaximal, characteristic
4#13069389C211yesmaximal, characteristic, complemented
5#13069368C211yesmaximal, characteristic, complemented
6#13069363C211yesmaximal, characteristic, complemented
7#13069213C211yesmaximal, characteristic, complemented
8#13069213C211yesmaximal, characteristic, complemented
9#13068892C211yesmaximal, characteristic
10#13068892C211yesmaximal, characteristic
11#13068473C211yesmaximal, characteristic, complemented
12#13068457C211yesmaximal, characteristic
13#13068450C211yesmaximal, characteristic
14#13068427C211yesmaximal, characteristic
15C11×#1995C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×#66960C2211yescharacteristic
18C2×#66960C2211yescharacteristic
19C4×#4339C2211yescharacteristic
20C11×#423C2211yescharacteristic
21C11×#376C2211yescharacteristic
22C2×#66886C2211yescharacteristic
23C2×#66886C2211yescharacteristic
24#10622732C2211yescharacteristic
25#10622732C2211yescharacteristic
26#10622707C411yescharacteristic, complemented
27#10622704C411yescharacteristic, complemented
28#10622700C411yescharacteristic, complemented
29#10622697C411yescharacteristic, complemented
30#10622679C411yescharacteristic, complemented
31#10622679C411yescharacteristic, complemented
32#10622676C411yescharacteristic, complemented
33#10622676C411yescharacteristic, complemented
34#10622637—21no—
35#10622637—21no—
36#10622637—21no—
37Q8×C11⋊C8—21no—
38#10622615C2211yescharacteristic
39#10622615C2211yescharacteristic
40#10622612C2211yescharacteristic
41#10622612C2211yescharacteristic
42#10622611C2211yescharacteristic
43#10622611C2211yescharacteristic
44#10622610C2211yescharacteristic
45#10622610C2211yescharacteristic
46C2×#66869C2211yescharacteristic
47C2×#66869C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C4×#4318C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622452—21no—
54#10622452—21no—
55#10622450—21no—
56D11×C4⋊C8—21no—
57C11×#339C2211yescharacteristic
58C11×#339C2211yescharacteristic
59C11×#339C2211yescharacteristic
60C11×#339C2211yescharacteristic
61#10622196C2211yescharacteristic
62#10622196C2211yescharacteristic
63#10622162C2211yescharacteristic
64#10622162C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C11×C4⋊Q8C2×C411yescharacteristic
71C11×C4⋊Q8C2×C411yescharacteristic
72C11×#125C2×C411yescharacteristic
73C11×#125C2×C411yescharacteristic
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C11×#117C2311yescharacteristic
79C11×#117C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C4×C22⋊D11—21no—
84C4×C22⋊D11—21no—
85#66979C2311yescharacteristic
86C2×#4318C2311yescharacteristic
87C2×#4318C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92#66960—22no—
93#66960—22no—
94#66960—41no—
95#66960—41no—
96C2×#4313—21no—
97C2×#4313—21no—
98C2×C8×D11—21no—
99C2×C8×D11—21no—
100C4×D44C2×C411yescharacteristic
101C4×D44C2×C411yescharacteristic
102#66925—21no—
103C42×D11—21no—
104C4×Dic22C2×C411yescharacteristic
105C4×Dic22C2×C411yescharacteristic
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×#95—21no—
109C11×#95—21no—
110#66886—41no—
111#66886—41no—
112Dic11⋊C8—21no—
113Dic11⋊C8—21no—
114Dic11⋊C8—21no—
115Dic11⋊C8—21no—
116#66874C2×C411yescharacteristic
117#66874C2×C411yescharacteristic
118#66874C2×C411yescharacteristic
119#66874C2×C411yescharacteristic
120#66873C2×C411yescharacteristic
121#66873C2×C411yescharacteristic
122#66873C2×C411yescharacteristic
123#66873C2×C411yescharacteristic
124#66872C2×C411yescharacteristic
125#66872C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66872C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129#66871C2×C411yescharacteristic
130#66871C2×C411yescharacteristic
131#66871C2×C411yescharacteristic
132#66869—22no—
133#66869Q814yescomplemented
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2×C411yescharacteristic
140C4⋊(C11⋊C8)C2×C411yescharacteristic
141C4⋊(C11⋊C8)C2×C411yescharacteristic
142C4⋊(C11⋊C8)D411yescharacteristic
143C4⋊(C11⋊C8)D411yescharacteristic
144C4⋊(C11⋊C8)D411yescharacteristic
145C4⋊(C11⋊C8)D411yescharacteristic
146#66867—21no—
147#66867—21no—
148#66867—21no—
149#66867—41no—
150C4×C11⋊C8—21no—
151C4×C11⋊C8—21no—
152C4×C11⋊C8—21no—
153C4×C11⋊C8—41no—
154#22984—111nomaximal, Sylow
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11#4111yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—21no—
163#4339—21no—
164#4339—21no—
165#4339C2×Q812yes—
166#4339#4112yes—
167C2×D44C22×C411yescharacteristic
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×Dic22C22×C411yescharacteristic
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—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C22×C411yescharacteristic
185C11×C4⋊C4C22×C411yescharacteristic
186C11×C4⋊C4C22×C411yescharacteristic
187C11×C4⋊C4C22×C411yescharacteristic
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11C22×C411yescharacteristic
196C42×C11C22×C411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2×Q812yes—
200C22⋊Dic11—21no—
201(C2×D11)⋊C4—21no—
202(C2×D11)⋊C4—21no—
203C4⋊Dic11C22×C411yescharacteristic
204C4⋊Dic11C22×C411yescharacteristic
205Dic11⋊C4—21no—
206Dic11⋊C4—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210#4318—21no—
211#4318—21no—
212#4318—21no—
213#4318C2×Q812yes—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
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⋊C8C22×C411yescharacteristic
225C2×C11⋊C8C22×C411yescharacteristic
226C2×C11⋊C8C22×C411yescharacteristic
227C2×C11⋊C8C22×C411yescharacteristic
228C2×C11⋊C8C2×D411yescharacteristic
229C2×C11⋊C8C2×D411yescharacteristic
230C2×C11⋊C8C2×D411yescharacteristic
231C2×C11⋊C8C2×D411yescharacteristic
232#4313—42no—
233#4313—42no—
234C8×D11—42no—
235C8×D11—42no—
236#3076—111no—
237#2962—111no—
238#2906—111no—
239#1995D1111yescharacteristic, complemented
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×C11C2×#4111yescharacteristic
252C22×D11—21no—
253Q8×C11—42no—
254Q8×C11—81no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11C4×D411yescharacteristic
268C2×C4×C11C4×D411yescharacteristic
269C2×C4×C11C4×D411yescharacteristic
270C2×C4×C11C4×D411yescharacteristic
271C2×C4×C11C23×C411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×Q811yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C22⋊D11—22no—
278C22⋊D11—22no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282D44—21no—
283D44C4×Q812yes—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—42no—
287C4×D11—81no—
288Dic22—21no—
289Dic22C4×Q812yes—
290C8×C11—41no—
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—22no—
301C11⋊C8—41no—
302C2×#131—111no—
303C2×#131—111no—
304#533C2×D1111yescharacteristic
305C4×#41—111no—
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—221no—
329#423C2×D1111yescharacteristic
330C2×C4⋊C8—111no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—221no—
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#376C2×D1111yescharacteristic
343#341—111no—
344#341—111no—
345#339—111no—
346#339—111no—
347#339C2×D1111yescharacteristic
348#339C2×D1111yescharacteristic
349#339C2×D1111yescharacteristic
350#339C2×D1111yescharacteristic
351#336—111no—
352#336—111no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11C2×C4×D411yescharacteristic
356C22×C11#55211yescharacteristic
357C22×C11#55411yescharacteristic
358C2×D11—22no—
359C2×D11—41no—
360C2×D11—41no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—81no—
371C4×C11C2×C4×Q811yescharacteristic
372C4×C11#52011yescharacteristic
373C4×C11#54611yescharacteristic
374C4×C11D4×Q811yescharacteristic
375Dic11—22no—
376Dic11—41no—
377Dic11—41no—
378C2×#41—111no—
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⋊Q8C4×D1111yescharacteristic
396C4⋊Q8C4×D1111yescharacteristic
397#125C4×D1111yescharacteristic
398#125C4×D1111yescharacteristic
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—111no—
404C4×Q8—111no—
405C4×D4—111no—
406C4×D4—111no—
407C4×D4—221no—
408C4×D4—221no—
409#117—111no—
410#117—221no—
411#117C22×D1111yescharacteristic
412#117C22×D1111yescharacteristic
413C2×C42—221no—
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—21no—
428C4⋊C8—21no—
429C4⋊C8—111no—
430C4⋊C8—111no—
431C4⋊C8—111no—
432C4⋊C8—111no—
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⋊C8—221no—
442C4⋊C8—221no—
443C4⋊C8—221no—
444C4⋊C8—221no—
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—21no—
464#95—21no—
465C2×C11—21no—
466C2×C11—21no—
467C2×C11#236011yescharacteristic
468C2×C11#295511yescharacteristic
469C2×C11#295711yescharacteristic
470D11—42no—
471#41—112no—
472#41—112no—
473#41—221no—
474#41—221no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—111no—
478C2×D4—111no—
479C2×D4—221no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4#434111yescharacteristic
486C22×C4#434111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—112no—
493M16—221no—
494M16—221no—
495M16—221no—
496M16—442no—
497M16—442no—
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—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—111no—
527C4⋊C4—111no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4C2×C4×D1111yescharacteristic
531C4⋊C4C2×C4×D1111yescharacteristic
532C4⋊C4C2×C4×D1111yescharacteristic
533C4⋊C4C2×C4×D1111yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—221no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42C2×C4×D1111yescharacteristic
548C42C2×C4×D1111yescharacteristic
549C42D4×D1111yescharacteristic
550C42D4×D1111yescharacteristic
551C42Q8×D1112yes—
552C11#2298411yescharacteristic, complemented, Sylow
553C23—221no—
554C23C2×#434111yescharacteristic
555Q8—42no—
556Q8—81no—
557Q8—112no—
558Q8—221no—
559D4—112no—
560D4—222no—
561D4—222no—
562D4—221no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—221no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—442no—
581C2×C4—881no—
582C2×C4(C22⋊D11)⋊C411yescharacteristic
583C2×C4(C22⋊D11)⋊C411yescharacteristic
584C2×C4(C22⋊D11)⋊C411yescharacteristic
585C2×C4(C22⋊D11)⋊C411yescharacteristic
586C2×C4C22×C4×D1111yescharacteristic
587C2×C4C2×D4×D1111yescharacteristic
588C2×C4C2×Q8×D1111yescharacteristic
589C2×C4#6704011yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#6704211yescharacteristic
592C8—41no—
593C8—41no—
594C8—222no—
595C8—221no—
596C8—221no—
597C8—221no—
598C8—221no—
599C8—221no—
600C8—221no—
601C8—221no—
602C8—221no—
603C8—441no—
604C22—21no—
605C22—21no—
606C22—222no—
607C22—441no—
608C22—441no—
609C22C2×(C22⋊D11)⋊C411yescharacteristic
610C22#1062316611yescharacteristic
611C22#1062317011yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—222no—
623C4—441no—
624C4—441no—
625C4C4×Q8×D1111yescharacteristic
626C4#1062310511yescharacteristic
627C4#1062320711yescharacteristic
628C4#1062325811yescharacteristic
629C2—21no—
630C2—21no—
631C2—442no—
632C2#1307162611yescharacteristic
633C2#1307751511yescharacteristic
634C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1995C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#1995D11
hypocenterC11#22984
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
2. #13077565C2semidirect
4. #13069389C2semidirect
5. #13069368C2semidirect
6. #13069363C2semidirect
7. #13069213C2semidirect
8. #13069213C2semidirect
11. #13068473C2semidirect
15. C11×#1995C2semidirect
26. #10622707C4semidirect
27. #10622704C4semidirect
28. #10622700C4semidirect
29. #10622697C4semidirect
30. #10622679C4semidirect
31. #10622679C4semidirect
32. #10622676C4semidirect
33. #10622676C4semidirect
133. #66869Q8semidirect
239. #1995D11semidirect
552. C11#22984semidirect

Maximal subgroups

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

subgroupindex
#130783982
#130775652
#130771852
#130693892
#130693682
#130693632
#130692132
#130688922
#130684732
#130684572
#130684502
#130684272
C11×#19952
#2298411