Finite Group Databasebeta

← #14775432

Subgroups — #14775432

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078533C211yesmaximal, characteristic
2#13077344C211yesmaximal, characteristic
3#13077273C211yesmaximal, characteristic, complemented
4#13069370C211yesmaximal, characteristic, complemented
5#13069319C211yesmaximal, characteristic, complemented
6#13069265C211yesmaximal, characteristic, complemented
7#13069218C211yesmaximal, characteristic, complemented
8#13069063C211yesmaximal, characteristic
9#13068892C211yesmaximal, characteristic, complemented
10#13068822C211yesmaximal, characteristic, complemented
11#13068496C211yesmaximal, characteristic, complemented
12#13068459C211yesmaximal, characteristic, complemented
13#13068381C211yesmaximal, characteristic, complemented
14#13068324C211yesmaximal, characteristic, complemented
15C11×#1922C211yesmaximal, characteristic, complemented
16C2×#66960C2211yescharacteristic
17C2×M16×D11C2211yescharacteristic
18#10623055C2211yescharacteristic
19D11×#117C2211yescharacteristic
20C2×#66925C2211yescharacteristic
21C11×#427C2211yescharacteristic
22C11×#424C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C2×#66889C2211yescharacteristic
25#10622739C2211yescharacteristic
26C2×#66886C2211yescharacteristic
27#10622735C2211yescharacteristic
28#10622726C2211yescharacteristic
29#10622723C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66883C2211yescharacteristic
33#10622714C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622615C2211yescharacteristic
37#10622612C2211yescharacteristic
38#10622612C2211yescharacteristic
39#10622611C2211yescharacteristic
40C2×#66869C2211yescharacteristic
41#10622501C411yescharacteristic, complemented
42#10622498C411yescharacteristic, complemented
43#10622497C411yescharacteristic, complemented
44#10622495C411yescharacteristic, complemented
45#10622480C411yescharacteristic, complemented
46#10622479C411yescharacteristic, complemented
47#10622476C411yescharacteristic, complemented
48#10622475C411yescharacteristic, complemented
49#10622453—21no—
50#10622453—21no—
51#10622448—21no—
52#10622446—21no—
53#10622319—21no—
54#10622319—21no—
55#10622301—21no—
56C8×D44—21no—
57C11×#341C2211yescharacteristic
58C11×#339C2211yescharacteristic
59C11×#339C2211yescharacteristic
60C11×#336C2211yescharacteristic
61#10622196C2211yescharacteristic
62#10622193C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622162C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C11×#117C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77#66979C2311yescharacteristic
78C2×Dic11⋊C4—21no—
79C2×C4×Dic11C2311yescharacteristic
80C2×#4318C2311yescharacteristic
81C2×#4318C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66960—22no—
85#66960—41no—
86M16×D11—22no—
87M16×D11—41no—
88C2×#4313—21no—
89C2×#4313—21no—
90C2×C8×D11—21no—
91C2×C8×D11—21no—
92#66950C2×C411yescharacteristic
93#66950C2×C411yescharacteristic
94#66948C2×C411yescharacteristic
95#66948C2×C411yescharacteristic
96#66945C2×C411yescharacteristic
97#66945C2×C411yescharacteristic
98C4⋊C4×D11C2×C411yescharacteristic
99C4⋊C4×D11C2×C411yescharacteristic
100#66939—21no—
101#66935—21no—
102C22⋊C4×D11—21no—
103#66930—21no—
104C4×D44—21no—
105C4×D44—21no—
106#66925—21no—
107#66925—22no—
108#66925—41no—
109C42×D11—21no—
110C11×#107C2×C411yescharacteristic
111C11×#107C2×C411yescharacteristic
112C11×#106C2×C411yescharacteristic
113C11×#106C2×C411yescharacteristic
114C11×C4⋊C8—21no—
115C11×C4⋊C8—21no—
116C11×#97—21no—
117C4×C8×C11—21no—
118#66889—22no—
119#66886—22no—
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8C2×C411yescharacteristic
127(C2×D11)⋊C8C2×C411yescharacteristic
128(C2×D11)⋊C8C2×C411yescharacteristic
129(C2×D11)⋊C8C2×C411yescharacteristic
130(C2×D11)⋊C8D411yescharacteristic
131(C2×D11)⋊C8D411yescharacteristic
132(C2×D11)⋊C8D411yescharacteristic
133(C2×D11)⋊C8D411yescharacteristic
134#66883—41no—
135#66880C2×C411yescharacteristic
136#66880C2×C411yescharacteristic
137#66879—21no—
138#66879—21no—
139#66879—41no—
140C8×Dic11—21no—
141C8×Dic11—22no—
142C8×Dic11—21no—
143#66874C2×C411yescharacteristic
144#66874C2×C411yescharacteristic
145#66873C2×C411yescharacteristic
146#66873C2×C411yescharacteristic
147#66872C2×C411yescharacteristic
148#66872C2×C411yescharacteristic
149#66871C2×C411yescharacteristic
150#66871C2×C411yescharacteristic
151#66869—41no—
152C4⋊(C11⋊C8)—21no—
153C4⋊(C11⋊C8)—21no—
154C4⋊(C11⋊C8)—21no—
155C4⋊(C11⋊C8)—21no—
156#22951—111nomaximal, Sylow
157C23×D11#4111yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—21no—
161C22×Dic11—21no—
162C22×Dic11#4111yescharacteristic
163#4339—21no—
164#4339—21no—
165#4339—21no—
166#4339—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44C22×C411yescharacteristic
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11C22×C411yescharacteristic
178C2×C4×D11C22×C411yescharacteristic
179C2×C4×D11C2×D411yescharacteristic
180C2×C4×D11C2×D411yescharacteristic
181C2×Dic22C22×C411yescharacteristic
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16#4112yes—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11C22×C411yescharacteristic
193C2×C8×C11C22×C411yescharacteristic
194C2×C8×C11C2×D411yescharacteristic
195C2×C8×C11C2×D411yescharacteristic
196C11×C4⋊C4C22×C411yescharacteristic
197C11×C4⋊C4C22×C411yescharacteristic
198C11×C4⋊C4C22×C411yescharacteristic
199C11×C4⋊C4C22×C411yescharacteristic
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C22⋊Dic11—21no—
207(C2×D11)⋊C4—21no—
208(C2×D11)⋊C4—21no—
209(C2×D11)⋊C4—21no—
210(C2×D11)⋊C4—21no—
211(C2×D11)⋊C4—21no—
212(C2×D11)⋊C4—21no—
213(C2×D11)⋊C4—42no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11C22×C411yescharacteristic
217C4⋊Dic11C22×C411yescharacteristic
218Dic11⋊C4—21no—
219Dic11⋊C4—21no—
220Dic11⋊C4—42no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11#4112yes—
226#4318—21no—
227#4318—21no—
228#4318—21no—
229#4318—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8C22×C411yescharacteristic
237C2×C11⋊C8C22×C411yescharacteristic
238C2×C11⋊C8C2×D411yescharacteristic
239C2×C11⋊C8C2×D411yescharacteristic
240#4313—42no—
241#4313—42no—
242C8×D11—42no—
243C8×D11—42no—
244#3091—111no—
245#2933—111no—
246#2924—111no—
247#1946—111no—
248#1937—111no—
249#1929—111no—
250#1922—111no—
251#1922D1111yescharacteristic, complemented
252#1897—111no—
253#1866—111no—
254#1855—111no—
255#1772—111no—
256#1765—111no—
257#1750—111no—
258#1733—111no—
259C23×C11C2×#4111yescharacteristic
260C22×D11—21no—
261C22×D11—21no—
262C22×D11—21no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11C4×D411yescharacteristic
266C22×D11C4×D411yescharacteristic
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C22⋊D11—41no—
281C22⋊D11—41no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11C4×D411yescharacteristic
291C2×Dic11C4×D411yescharacteristic
292D44—21no—
293D44—21no—
294D44—42no—
295D44—81no—
296C4×D11—21no—
297C4×D11—21no—
298C4×D11—21no—
299C4×D11—21no—
300C4×D11—21no—
301C4×D11—21no—
302C4×D11—21no—
303C4×D11—21no—
304C4×D11—42no—
305C4×D11—41no—
306C4×D11—41no—
307C4×D11—81no—
308Dic22—21no—
309Dic22—21no—
310C8×C11—21no—
311C8×C11—21no—
312C8×C11—22no—
313C8×C11—21no—
314C8×C11—21no—
315C8×C11—41no—
316C11⋊C8—21no—
317C11⋊C8—21no—
318C11⋊C8—21no—
319C11⋊C8—21no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C2×#131—111no—
323C22×M16—111no—
324#525—111no—
325C2×#117—111no—
326C2×#117—111no—
327#485—111no—
328#485—111no—
329#484—111no—
330#483—111no—
331#482—111no—
332#482—111no—
333#481—111no—
334#480—111no—
335#436—221no—
336#435—221no—
337#435—221no—
338C8×D4—221no—
339#433—221no—
340#433—221no—
341#432—221no—
342#431—221no—
343C2×#108—111no—
344C2×#108—111no—
345#427—111no—
346#427C2×D1111yescharacteristic
347#424—111no—
348#424—111no—
349#424C2×D1111yescharacteristic
350C2×#104—111no—
351C2×#104—111no—
352#416—111no—
353#416—111no—
354#408—111no—
355#407—111no—
356C2×C22⋊C8—111no—
357C2×C22⋊C8—111no—
358#405—111no—
359#405—111no—
360#405C2×D1111yescharacteristic
361C2×#97—111no—
362C2×C4×C8—111no—
363#341—111no—
364#341C2×D1111yescharacteristic
365#339—111no—
366#339—111no—
367#339—111no—
368#339—111no—
369#339C2×D1111yescharacteristic
370#339C2×D1111yescharacteristic
371#336—111no—
372#336C2×D1111yescharacteristic
373C22×C11—21no—
374C22×C11—21no—
375C22×C11C2×C4×D411yescharacteristic
376C22×C11#55111yescharacteristic
377C22×C11#55211yescharacteristic
378C2×D11—21no—
379C2×D11—21no—
380C2×D11—21no—
381C2×D11—21no—
382C2×D11—21no—
383C2×D11—21no—
384C2×D11—41no—
385C2×D11—41no—
386C2×D11—41no—
387C2×D11—81no—
388C2×D11—81no—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—41no—
393C4×C11—81no—
394C4×C11C4×#4111yescharacteristic
395C4×C11#52011yescharacteristic
396C4×C11#54611yescharacteristic
397C4×C11#54711yescharacteristic
398Dic11—21no—
399Dic11—21no—
400Dic11—42no—
401Dic11—41no—
402Dic11—41no—
403Dic11—41no—
404C2×#41—111no—
405C23×C4—111no—
406#131—222no—
407#131—441no—
408C2×M16—111no—
409C2×M16—111no—
410C2×M16—221no—
411C2×M16—221no—
412C2×M16—222no—
413C2×M16—441no—
414C2×M16C22×D1111yescharacteristic
415C2×M16C22×D1111yescharacteristic
416C22×C8—111no—
417C22×C8—111no—
418C22×C8—221no—
419C22×C8—221no—
420C22×C8C22×D1111yescharacteristic
421C22×C8C22×D1111yescharacteristic
422#123—221no—
423C22⋊Q8—111no—
424C22⋊Q8—111no—
425#121—111no—
426#121—111no—
427#120—221no—
428C4×D4—221no—
429C4×D4—221no—
430#117—111no—
431#117—111no—
432#117—111no—
433#117—222no—
434#117—221no—
435#117—221no—
436#117—441no—
437#117C22×D1111yescharacteristic
438#117C22×D1111yescharacteristic
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C42—111no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447#108—222no—
448#108—441no—
449#107—111no—
450#107—111no—
451#107C4×D1111yescharacteristic
452#107C4×D1111yescharacteristic
453#106—111no—
454#106—111no—
455#106C4×D1111yescharacteristic
456#106C4×D1111yescharacteristic
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—221no—
460C4⋊C8—221no—
461C4⋊C8—221no—
462C4⋊C8—221no—
463#104—222no—
464#104—441no—
465#103—111no—
466#103—111no—
467#103—111no—
468#103—111no—
469#102—111no—
470#102—111no—
471#102—111no—
472#102—111no—
473C22⋊C8—111no—
474C22⋊C8—111no—
475C22⋊C8—111no—
476C22⋊C8—111no—
477C22⋊C8—111no—
478C22⋊C8—111no—
479C22⋊C8—111no—
480C22⋊C8—111no—
481C22⋊C8—221no—
482C22⋊C8—221no—
483C22⋊C8—221no—
484C22⋊C8—221no—
485#97—21no—
486#97—221no—
487#97—221no—
488#97—441no—
489C4×C8—21no—
490C4×C8—222no—
491C4×C8—221no—
492C4×C8—221no—
493C2×C11—21no—
494C2×C11—21no—
495C2×C11#235911yescharacteristic
496C2×C11#295511yescharacteristic
497C2×C11#295711yescharacteristic
498D11—41no—
499D11—41no—
500D11—81no—
501C24—111no—
502#41—221no—
503#41—221no—
504#41—221no—
505#41—221no—
506C2×Q8—111no—
507C2×D4—111no—
508C2×D4—221no—
509C2×D4—221no—
510C2×D4—221no—
511C22×C4—21no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4C23×D1111yescharacteristic
526M16—21no—
527M16—21no—
528M16—21no—
529M16—221no—
530M16—221no—
531M16—221no—
532M16—221no—
533M16—442no—
534M16—442no—
535M16#434312yes—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—111no—
543C2×C8—111no—
544C2×C8—111no—
545C2×C8—111no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—442no—
553C2×C8—442no—
554C2×C8C2×C4×D1111yescharacteristic
555C2×C8C2×C4×D1111yescharacteristic
556C2×C8D4×D1111yescharacteristic
557C2×C8D4×D1111yescharacteristic
558C4⋊C4—111no—
559C4⋊C4—111no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—442no—
565C4⋊C4C2×C4×D1111yescharacteristic
566C4⋊C4C2×C4×D1111yescharacteristic
567C4⋊C4C2×C4×D1111yescharacteristic
568C4⋊C4C2×C4×D1111yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—221no—
572C22⋊C4—221no—
573C22⋊C4—221no—
574C22⋊C4—221no—
575C22⋊C4—221no—
576C22⋊C4—221no—
577C22⋊C4—221no—
578C22⋊C4—442no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—112no—
584C42—221no—
585C42—221no—
586C42—221no—
587C42—221no—
588C11#2295111yescharacteristic, complemented, Sylow
589C23—111no—
590C23—111no—
591C23—221no—
592C23—221no—
593C23—221no—
594C23—441no—
595C23—441no—
596C23#41×D1111yescharacteristic
597Q8—221no—
598Q8—221no—
599D4—221no—
600D4—221no—
601D4—442no—
602D4—441no—
603D4—441no—
604D4—881no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—111no—
613C2×C4—111no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—222no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—442no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—881no—
634C2×C4C22×C4×D1111yescharacteristic
635C2×C4C2×D4×D1111yescharacteristic
636C2×C4C2×#434311yescharacteristic
637C2×C4#41×D1111yescharacteristic
638C2×C4#6704211yescharacteristic
639C2×C4#6704311yescharacteristic
640C8—21no—
641C8—21no—
642C8—22no—
643C8—21no—
644C8—21no—
645C8—41no—
646C8—221no—
647C8—221no—
648C8—221no—
649C8—221no—
650C8—441no—
651C8—441no—
652C22—21no—
653C22—21no—
654C22—221no—
655C22—221no—
656C22—221no—
657C22—221no—
658C22—221no—
659C22—221no—
660C22—441no—
661C22—441no—
662C22—441no—
663C22—881no—
664C22—881no—
665C22C4×D4×D1111yescharacteristic
666C22#1062322511yescharacteristic
667C22#1062323611yescharacteristic
668C4—41no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—81no—
673C4—221no—
674C4—221no—
675C4—442no—
676C4—441no—
677C4—441no—
678C4—441no—
679C4#1062305411yescharacteristic
680C4C4×#434311yescharacteristic
681C4#1062316111yescharacteristic
682C4#1062318611yescharacteristic
683C2—21no—
684C2—21no—
685C2—441no—
686C2—441no—
687C2—881no—
688C2#1307161511yescharacteristic
689C2#1307751411yescharacteristic
690C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1922C2
socleC22×C11C2×C4×D4
prime radical#10623055C22
cosocleC22×C4×C11C24
hypercenter#1922D11
hypocenterC11#22951
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
3. #13077273C2semidirect
4. #13069370C2semidirect
5. #13069319C2semidirect
6. #13069265C2semidirect
7. #13069218C2semidirect
9. #13068892C2semidirect
10. #13068822C2semidirect
11. #13068496C2semidirect
12. #13068459C2semidirect
13. #13068381C2semidirect
14. #13068324C2semidirect
15. C11×#1922C2semidirect
41. #10622501C4semidirect
42. #10622498C4semidirect
43. #10622497C4semidirect
44. #10622495C4semidirect
45. #10622480C4semidirect
46. #10622479C4semidirect
47. #10622476C4semidirect
48. #10622475C4semidirect
251. #1922D11semidirect
588. C11#22951semidirect

Maximal subgroups

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

subgroupindex
#130785332
#130773442
#130772732
#130693702
#130693192
#130692652
#130692182
#130690632
#130688922
#130688222
#130684962
#130684592
#130683812
#130683242
C11×#19222
#2295111