Finite Group Databasebeta

← #14823163

Subgroups — #14823163

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622616C211yesmaximal, characteristic
2C2×#10622635C211yesmaximal, characteristic, complemented
3#13072968C211yesmaximal, characteristic
4#13069987C211yesmaximal, characteristic, complemented
5#13069954C211yesmaximal, characteristic, complemented
6#13069809C211yesmaximal, characteristic, complemented
7#13069617C211yesmaximal, characteristic
8#13069500C211yesmaximal, characteristic, complemented
9#13069247C211yesmaximal, characteristic, complemented
10#13069243C211yesmaximal, characteristic, complemented
11#13069231C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic, complemented
13#13068815C211yesmaximal, characteristic, complemented
14#13068514C211yesmaximal, characteristic, complemented
15C11×#2362C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#391C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#388—21no—
25C11×#388—21no—
26C11×#387—21no—
27C4×C11×C4⋊C4—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622635—24no—
37#10622616—24no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622572—21no—
47#10622570—21no—
48#10622552C2211yescharacteristic
49#10622552C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53#10622288—21no—
54#10622282—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—41no—
69C11×#117—22no—
70C11×#117—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
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⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×#4325—22no—
88C2×#4325—22no—
89C2×#4325—41no—
90#66983—22no—
91#66983—41no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66923—22no—
108#66923—41no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115#66899—22no—
116#66899—22no—
117#66899—22no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C22⋊(C11⋊C8)—22no—
121C22⋊(C11⋊C8)—22no—
122#66873—22no—
123#66873—22no—
124#66873—22no—
125#66872—22no—
126#66872—22no—
127#66872—22no—
128#66871—41no—
129#66871D414yes—
130C4⋊(C11⋊C8)—22no—
131#66867—22no—
132#26811—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—42no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—81no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4C2×D412yes—
177C11×C4⋊C4#4112yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—41no—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—42no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—42no—
187C42×C11—42no—
188C42×C11—42no—
189C22⋊Dic11—81no—
190#4325—44no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—81no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11C2×D412yes—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204C4×Dic11—81no—
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—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8#4112yes—
217C2×#482—111no—
218C2×#479—111no—
219#2490—111no—
220#2362D1111yescharacteristic, complemented
221#2065—111no—
222#2059—111no—
223#2035—111no—
224#2000—111no—
225#1973—111no—
226#1927—111no—
227#1926—111no—
228#1924—111no—
229#1880—111no—
230#1854—111no—
231#1776—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11C22×D411yescharacteristic
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—41no—
250Q8×C11—41no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
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—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C112−1+411yescharacteristic
288C22⋊D11—84no—
289C2×Dic11—22no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298D44—41no—
299D44—41no—
300D44—41no—
301D44—41no—
302C11⋊C8—22no—
303C11⋊C8—22no—
304C11⋊C8—41no—
305C11⋊C8—41no—
306C22×SD16—111no—
307C2×#125—111no—
308C2×C22⋊Q8C2×D1111yescharacteristic
309C2×#121—111no—
310C2×C4×Q8C2×D1111yescharacteristic
311C2×#117C2×D1111yescharacteristic
312#482—224no—
313#479—224no—
314C2×#107—111no—
315C2×#107—111no—
316C2×#106—111no—
317C2×#106—111no—
318C2×#106—111no—
319C2×C4⋊C8—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8—111no—
328C2×#97—111no—
329#397—221no—
330#394—221no—
331#391C2×D1111yescharacteristic
332#390—111no—
333#390—111no—
334#390—221no—
335#389C2×D1111yescharacteristic
336#388—21no—
337#388—21no—
338#388—221no—
339#387—21no—
340#380—111no—
341C4×C4⋊C4—21no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4C2×D1111yescharacteristic
344C4×C22⋊C4C2×D1111yescharacteristic
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#336—111no—
350#336—111no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11#52511yescharacteristic
359C22×C11D4211yescharacteristic
360C22×C11#54711yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57711yescharacteristic
364C22×C11#57711yescharacteristic
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—42no—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—41no—
380C4×C11—81no—
381C4×C11#53211yescharacteristic
382C4×C11#54211yescharacteristic
383C4×C11#54811yescharacteristic
384C4×C11#55111yescharacteristic
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8C22×D1111yescharacteristic
389C22×D4—111no—
390C22×D4—221no—
391C23×C4C22×D1111yescharacteristic
392C2×SD16—222no—
393C2×SD16—222no—
394C2×SD16—441no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8—111no—
399#125—222no—
400#125—441no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403#121—222no—
404#121—441no—
405C4×Q8—22no—
406C4×Q8—41no—
407#117—22no—
408#117—41no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4C22⋊D1111yescharacteristic
429C2×C22⋊C4C22⋊D1111yescharacteristic
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436#107—114no—
437#107—441no—
438#106—222no—
439#106—222no—
440#106—222no—
441C4⋊C8—222no—
442#103—222no—
443#103—222no—
444#103—222no—
445#102—222no—
446#102—222no—
447#102—222no—
448C22⋊C8—222no—
449C22⋊C8—222no—
450#97—222no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—221no—
456#95—221no—
457#95C22⋊D1111yescharacteristic
458#95C22⋊D1111yescharacteristic
459C2×C11—81no—
460C2×C11#246111yescharacteristic
461C2×C11#311111yescharacteristic
462C2×C11#312611yescharacteristic
463C2×C11#326711yescharacteristic
464C2×C11#327111yescharacteristic
465C2×C11#335011yescharacteristic
466C2×C11#335111yescharacteristic
467D11—161no—
468C24—221no—
469C24C2×C22⋊D1111yescharacteristic
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8#433912yes—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—442no—
483C2×D4—442no—
484C2×D4—881no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C2×C22⋊D1111yescharacteristic
501C22×C4C2×C22⋊D1111yescharacteristic
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504SD16—444no—
505C2×C8—112no—
506C2×C8—112no—
507C2×C8—221no—
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—
517C4⋊C4—24no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—112no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4#433912yes—
533C4⋊C4D4×D1112yes—
534C22⋊C4—24no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—42no—
538C22⋊C4—442no—
539C22⋊C4—442no—
540C22⋊C4—881no—
541C22⋊C4—881no—
542C22⋊C4—881no—
543C22⋊C4—881no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—42no—
549C42—42no—
550C42—42no—
551C42—881no—
552C11#2681111yescharacteristic, complemented, Sylow
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23C22×C22⋊D1111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—441no—
573D4—441no—
574D4—441no—
575D4—441no—
576D4—884no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—222no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4C2×#433911yescharacteristic
618C2×C4C2×#433911yescharacteristic
619C2×C4C2×D4×D1111yescharacteristic
620C2×C4#6703711yescharacteristic
621C2×C4#41×D1111yescharacteristic
622C2×C4#6704311yescharacteristic
623C8—222no—
624C8—222no—
625C8—441no—
626C8—441no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22—881no—
638C22—881no—
639C22—881no—
640C22—881no—
641C22#1062332211yescharacteristic
642C22D4×C22⋊D1111yescharacteristic
643C22#1062335311yescharacteristic
644C22#1062335311yescharacteristic
645C22#1062335511yescharacteristic
646C22#1062336811yescharacteristic
647C22#1062336811yescharacteristic
648C4—41no—
649C4—41no—
650C4—42no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—442no—
658C4—881no—
659C4—881no—
660C4#1062307911yescharacteristic
661C4#1062308311yescharacteristic
662C4#1062308711yescharacteristic
663C4#1062309211yescharacteristic
664C2—81no—
665C2—1761no—
666C2#1307257711yescharacteristic
667C2#1307872511yescharacteristic
668C2#1307890711yescharacteristic
669C2#1308014211yescharacteristic
670C2#1308020211yescharacteristic
671C2#1308116111yescharacteristic
672C2#1308117611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2362C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2362D11
hypocenterC11#26811
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. C2×#10622635C2semidirect
4. #13069987C2semidirect
5. #13069954C2semidirect
6. #13069809C2semidirect
8. #13069500C2semidirect
9. #13069247C2semidirect
10. #13069243C2semidirect
11. #13069231C2semidirect
12. #13068971C2semidirect
13. #13068815C2semidirect
14. #13068514C2semidirect
15. C11×#2362C2semidirect
220. #2362D11semidirect
552. C11#26811semidirect

Maximal subgroups

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

subgroupindex
C2×#106226162
C2×#106226352
#130729682
#130699872
#130699542
#130698092
#130696172
#130695002
#130692472
#130692432
#130692312
#130689712
#130688152
#130685142
C11×#23622
#2681111