Finite Group Databasebeta

← #14814719

Subgroups — #14814719

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072067C211yesmaximal, characteristic
2#13070178C211yesmaximal, characteristic, complemented
3#13070053C211yesmaximal, characteristic, complemented
4#13070025C211yesmaximal, characteristic, complemented
5#13069812C211yesmaximal, characteristic, complemented
6#13069250C211yesmaximal, characteristic, complemented
7#13069201C211yesmaximal, characteristic, complemented
8#13069047C211yesmaximal, characteristic, complemented
9#13068928C211yesmaximal, characteristic, complemented
10#13068928C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic
12#13068808C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14#13068337C211yesmaximal, characteristic, complemented
15C11×#2354C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C11×#390—21no—
24C11×#388—21no—
25C11×#388—21no—
26C11×#384C2211yescharacteristic
27C11×#380C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C4×C11×C4⋊C4—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31#10622833—21no—
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622597—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622561—21no—
44#10622555—21no—
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622167C2211yescharacteristic
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22C2311yescharacteristic
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C11×#117—22no—
67C11×#117—22no—
68C11×#117—41no—
69C11×#117—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—41no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96#66977—22no—
97#66977—22no—
98#66977—22no—
99#66977—41no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×#4318—22no—
104C2×#4318—41no—
105C2×#4318—41no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118C22⋊(C11⋊C8)—41no—
119C22⋊(C11⋊C8)—41no—
120#66874—22no—
121#66874—41no—
122#66874—41no—
123#66874—41no—
124#66872—22no—
125#66872—41no—
126#26223—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C24×C11C2×D411yescharacteristic
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—41no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4112yes—
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—81no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—81no—
176C11×C4⋊C4#4112yes—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—81no—
182C11×C22⋊C4—81no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186C42×C11—42no—
187C42×C11—42no—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190C22⋊Dic11—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201#4318—44no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214#2417—111no—
215#2354D1111yescharacteristic
216#2100—111no—
217#2077—111no—
218#2072—111no—
219#2035—111no—
220#1927—111no—
221#1920—111no—
222#1894—111no—
223#1873—111no—
224#1873—111no—
225#1870—111no—
226#1853—111no—
227#1825—111no—
228#1736—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11#12312yes—
243C23×C11C22×D411yescharacteristic
244D4×C11—44no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
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×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—41no—
274C2×C4×C11—41no—
275C2×C4×C11#12312yes—
276C2×C4×C11#13712yes—
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×Dic11—22no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—84no—
296Dic22—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×M16—111no—
305C2×C22⋊Q8—111no—
306C2×C22⋊Q8—111no—
307C2×C4×D4C2×D1111yescharacteristic
308C2×#117C2×D1111yescharacteristic
309C2×#117C2×D1111yescharacteristic
310C22×C4⋊C4—111no—
311C2×#106—111no—
312C2×#106—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×C22⋊C8—111no—
318C2×C22⋊C8—111no—
319C2×C22⋊C8—111no—
320#398—221no—
321#396—221no—
322#391—111no—
323#390—21no—
324#389—111no—
325#388—21no—
326#388—21no—
327#386—221no—
328#384C2×D1111yescharacteristic
329#380—111no—
330#380—221no—
331#380C2×D1111yescharacteristic
332#380C2×D1111yescharacteristic
333C4×C4⋊C4—21no—
334C4×C4⋊C4C2×D1111yescharacteristic
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#336—111no—
346#336—111no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11C2×#12311yescharacteristic
362C22×C11#54611yescharacteristic
363C22×C11#54611yescharacteristic
364C22×C11C2×#13711yescharacteristic
365C22×C11#57511yescharacteristic
366C22×C11#57711yescharacteristic
367C22×C11#57711yescharacteristic
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—81no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11#52911yescharacteristic
377C4×C11#53811yescharacteristic
378C4×C11#55311yescharacteristic
379C4×C11#55311yescharacteristic
380Dic11—42no—
381Dic11—81no—
382Dic11—81no—
383Dic11—81no—
384C22×Q8—111no—
385C22×D4C22⋊D1111yescharacteristic
386C23×C4—221no—
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C2×M16—222no—
390C2×M16—441no—
391C2×M16—441no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—111no—
396C22⋊Q8—222no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399C22⋊Q8—441no—
400C4×D4—22no—
401C4×D4—22no—
402#117—22no—
403#117—22no—
404#117—41no—
405#117—41no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—441no—
417C2×C4⋊C4C22⋊D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4C22⋊D1111yescharacteristic
430C2×C22⋊C4C22⋊D1111yescharacteristic
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42C22×D1111yescharacteristic
435#106—222no—
436#106—441no—
437#103—222no—
438#103—441no—
439#103—441no—
440#103—441no—
441C22⋊C8—222no—
442C22⋊C8—441no—
443C22⋊C8—441no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11—42no—
452C2×C11—81no—
453C2×C11#244411yescharacteristic
454C2×C11#309511yescharacteristic
455C2×C11#309911yescharacteristic
456C2×C11#331111yescharacteristic
457C2×C11#331711yescharacteristic
458C2×C11#332911yescharacteristic
459C2×C11#333111yescharacteristic
460C24C2×C22⋊D1111yescharacteristic
461C24C2×C22⋊D1111yescharacteristic
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—41no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—881no—
492C22×C4#433912yes—
493C22×C4#433912yes—
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499M16—444no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—81no—
522C4⋊C4—112no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—881no—
532C4⋊C4#434112yes—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C22⋊C4—81no—
538C22⋊C4—81no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—881no—
542C42—21no—
543C42—21no—
544C42—42no—
545C42—42no—
546C42—42no—
547C11#2622311yescharacteristic, complemented, Sylow
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23#6698212yes—
562C23C22×C22⋊D1111yescharacteristic
563Q8—441no—
564Q8—441no—
565Q8—441no—
566Q8—441no—
567D4—44no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—222no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—884no—
611C2×C4#6698212yes—
612C2×C4#6700412yes—
613C2×C4C2×#433911yescharacteristic
614C2×C4C2×#433911yescharacteristic
615C2×C4C2×#434111yescharacteristic
616C2×C4#6703711yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C2×C4#6704211yescharacteristic
619C8—441no—
620C8—441no—
621C8—441no—
622C8—441no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22C2×#6698211yescharacteristic
638C22#1062333711yescharacteristic
639C22#1062335311yescharacteristic
640C22C2×#6700411yescharacteristic
641C22#1062336011yescharacteristic
642C22#1062336711yescharacteristic
643C22#1062336811yescharacteristic
644C4—22no—
645C4—22no—
646C4—41no—
647C4—42no—
648C4—41no—
649C4—81no—
650C4—81no—
651C4—81no—
652C4—442no—
653C4—881no—
654C4—881no—
655C4—881no—
656C4#1062306911yescharacteristic
657C4#1062307111yescharacteristic
658C4#1062309111yescharacteristic
659C4#1062309611yescharacteristic
660C2—42no—
661C2—81no—
662C2#1307236011yescharacteristic
663C2#1307856411yescharacteristic
664C2#1307860511yescharacteristic
665C2#1308064611yescharacteristic
666C2#1308074211yescharacteristic
667C2#1308090411yescharacteristic
668C2#1308093211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2354D11
hypocenterC11#26223
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #13070178C2semidirect
3. #13070053C2semidirect
4. #13070025C2semidirect
5. #13069812C2semidirect
6. #13069250C2semidirect
7. #13069201C2semidirect
8. #13069047C2semidirect
9. #13068928C2semidirect
10. #13068928C2semidirect
12. #13068808C2semidirect
13. #13068711C2semidirect
14. #13068337C2semidirect
547. C11#26223semidirect

Maximal subgroups

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

subgroupindex
#130720672
#130701782
#130700532
#130700252
#130698122
#130692502
#130692012
#130690472
#130689282
#130689142
#130688082
#130687112
#130683372
C11×#23542
#2622311