Finite Group Databasebeta

← #14730924

Subgroups — #14730924

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079764C211yesmaximal, characteristic, complemented
2C2×#10622705C211yesmaximal, characteristic, complemented
3#13078431C211yesmaximal, characteristic
4#13067756C214yesmaximal, complemented
5#13067750C214yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067071C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic
9C11×#3503C211yesmaximal, characteristic
10Q82×C11C2212yes—
11C11×#557—21no—
12C11×#554—22no—
13C11×#554C2212yes—
14D4×Q8×C11—22no—
15D4×Q8×C11—21no—
16C11×#544—22no—
17C11×#544—21no—
18C11×#533—21no—
19C11×#533C2211yescharacteristic
20C2×C11×C4⋊Q8—21no—
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520—21no—
23C4×C11×#41C2211yescharacteristic
24C22×#4326—22no—
25C2×#66922C2211yescharacteristic
26#10622845—21no—
27#10622705—22no—
28#10622705C2214yes—
29#10622694—21no—
30#10622691—21no—
31#10622657—22no—
32#10622634C2212yes—
33#10622634C2214yes—
34#10622633—21no—
35#10622621C2212yes—
36#10622620—21no—
37#10622608—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622184C2214yes—
42Q8⋊(C11⋊C8)C2214yes—
43Q8⋊(C11⋊C8)C2212yes—
44D4⋊(C11⋊C8)C2212yes—
45C2×C11×#41D411yescharacteristic
46C22×Q8×C11—22no—
47C22×Q8×C11D412yes—
48C22×Dic22—21no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—24no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yes—
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8C2312yes—
60C11×#125—22no—
61C11×#125—24no—
62C11×#125—22no—
63C11×#125—21no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8D412yes—
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11—21no—
75C4×Q8×C11D411yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C4×Q8×C11C2312yes—
78C4×D4×C11—24no—
79C4×D4×C11—22no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C11×#117—22no—
85C11×#117—21no—
86C11×#117—21no—
87C11×#117D411yescharacteristic
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×#4326—28no—
95C2×#4326—48no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×#4318—21no—
99C22×C11⋊C8—21no—
100#66922—21no—
101#66922—21no—
102#66922—21no—
103#66922C2312yes—
104#66899—22no—
105#66899—24no—
106#66896—22no—
107C22⋊(C11⋊C8)—21no—
108#66872—22no—
109#66871—22no—
110#66871—24no—
111C4⋊(C11⋊C8)—21no—
112C4⋊(C11⋊C8)C2312yes—
113C4⋊(C11⋊C8)C2312yes—
114C4×C11⋊C8—21no—
115C4×C11⋊C8—21no—
116C4×C11⋊C8C2312yes—
117#18623—111nomaximal, Sylow
118C11×#41—22no—
119C11×#41Q1614yescomplemented
120C2×Q8×C11—24no—
121C2×Q8×C11—22no—
122C2×Q8×C11—21no—
123C2×Q8×C11—44no—
124C2×Q8×C11—84no—
125C2×Q8×C11C2×D412yes—
126C2×Q8×C11C2×D411yescharacteristic
127C2×Q8×C11C2×D414yes—
128C2×D4×C11—21no—
129C2×D4×C11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×Dic11—41no—
139C2×Dic22—22no—
140C2×Dic22—44no—
141C2×Dic22—41no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D411yescharacteristic
159C11×C4⋊C4C2×D411yescharacteristic
160C11×C22⋊C4—24no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—21no—
163C11×C22⋊C4—21no—
164C11×C22⋊C4—21no—
165C42×C11—24no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—22no—
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2411yescharacteristic
174#4326—416no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11—41no—
178C4⋊Dic11—41no—
179#4318—42no—
180C2×C11⋊C8—24no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184#3503D1111yescharacteristic
185#3230—111no—
186C2×#494—111no—
187#3079—111no—
188#1633—114no—
189#1632—114no—
190#1548—111no—
191#1493—111no—
192#1476—111no—
193C23×C11—21no—
194C23×C11#12011yescharacteristic
195Q8×C11—21no—
196Q8×C11—24no—
197Q8×C11—44no—
198Q8×C11—44no—
199Q8×C11—42no—
200Q8×C11—84no—
201Q8×C11C2×Q1612yescomplemented
202D4×C11—24no—
203D4×C11—21no—
204D4×C11C2×Q1612yescomplemented
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—82no—
217C2×C4×C11—84no—
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11C2×Q1612yes—
222C2×C4×C11#13712yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×Dic11—42no—
227C2×Dic11—82no—
228Dic22—44no—
229Dic22—82no—
230C11⋊C8—24no—
231C11⋊C8—42no—
232C11⋊C8—42no—
233C22×Q16—222no—
234Q82C2×D1112yes—
235#557—21no—
236#554—22no—
237#554C2×D1112yes—
238D4×Q8—22no—
239D4×Q8—21no—
240#544—22no—
241#544—21no—
242#533—21no—
243#533C2×D1111yescharacteristic
244C2×C4⋊Q8—21no—
245C2×C4⋊Q8—111no—
246C2×C4⋊Q8C2×D1111yescharacteristic
247#520—21no—
248C4×#41C2×D1111yescharacteristic
249#500—221no—
250#494—114no—
251#494—222no—
252#487—221no—
253#484—222no—
254#477—112no—
255#477—114no—
256#476—112no—
257#475—221no—
258#474—221no—
259#431—111no—
260#428—221no—
261#423—111no—
262#417—221no—
263C2×C4×C8—111no—
264#333—114no—
265Q8⋊C8—114no—
266Q8⋊C8—112no—
267D4⋊C8—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—22no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11#45112yes—
274C22×C11C2×#12011yescharacteristic
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—42no—
280C4×C11—41no—
281C4×C11—44no—
282C4×C11—42no—
283C4×C11#45112yes—
284C4×C11#45312yes—
285C4×C11C22×Q1611yescharacteristic
286C4×C11C2×#13711yescharacteristic
287C4×C11#57812yes—
288Dic11—82no—
289C2×#41C22⋊D1111yescharacteristic
290C22×Q8—22no—
291C22×Q8—221no—
292C22×Q8C22⋊D1112yes—
293C2×Q16—228no—
294C2×Q16—448no—
295C2×M16—221no—
296C22×C8—221no—
297C4⋊Q8—22no—
298C4⋊Q8—22no—
299C4⋊Q8—24no—
300C4⋊Q8—22no—
301C4⋊Q8—22no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—112no—
305C4⋊Q8—221no—
306C4⋊Q8—221no—
307C4⋊Q8—221no—
308C4⋊Q8C22⋊D1112yes—
309C4⋊Q8C22⋊D1111yescharacteristic
310C4⋊Q8C22⋊D1111yescharacteristic
311C4⋊Q8C22×D1112yes—
312#125—22no—
313#125—24no—
314#125—22no—
315#125—21no—
316C22⋊Q8—22no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—22no—
320C22⋊Q8—24no—
321C22⋊Q8—21no—
322C22⋊Q8C22⋊D1112yes—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8—21no—
327C4×Q8C22⋊D1111yescharacteristic
328C4×Q8C22×D1111yescharacteristic
329C4×Q8C22×D1112yes—
330C4×D4—24no—
331C4×D4—22no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4C22⋊D1111yescharacteristic
335C4×D4C22×D1111yescharacteristic
336#117—22no—
337#117—21no—
338#117—21no—
339#117C22⋊D1111yescharacteristic
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C42—21no—
347C2×C42C22×D1111yescharacteristic
348#107—222no—
349#107—224no—
350#106—222no—
351C4⋊C8—112no—
352C4⋊C8—112no—
353C4⋊C8—221no—
354#103—222no—
355#103—224no—
356#102—222no—
357C22⋊C8—221no—
358C4×C8—112no—
359C4×C8—221no—
360C4×C8—221no—
361C2×C11—22no—
362C2×C11—42no—
363C2×C11C2×#45111yescharacteristic
364C2×C11#301111yescharacteristic
365C2×C11C2×#45311yescharacteristic
366#41—22no—
367#41#432614yescomplemented
368C2×Q8—24no—
369C2×Q8—22no—
370C2×Q8—21no—
371C2×Q8—44no—
372C2×Q8—84no—
373C2×Q8—222no—
374C2×Q8—444no—
375C2×Q8—441no—
376C2×Q8C2×C22⋊D1112yes—
377C2×Q8C2×C22⋊D1111yescharacteristic
378C2×Q8C2×C22⋊D1114yes—
379C2×D4—21no—
380C2×D4C2×C22⋊D1111yescharacteristic
381C22×C4—21no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—441no—
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390Q16—4416no—
391M16—442no—
392C2×C8—224no—
393C2×C8—222no—
394C2×C8—222no—
395C2×C8—222no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—24no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C4⋊C4C2×C22⋊D1111yescharacteristic
416C4⋊C4C2×C22⋊D1112yes—
417C4⋊C4C2×C22⋊D1111yescharacteristic
418C22⋊C4—24no—
419C22⋊C4—22no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—21no—
423C42—24no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42—22no—
428C42C2×C22⋊D1111yescharacteristic
429C42C2×C22⋊D1111yescharacteristic
430C42C2×C22⋊D1111yescharacteristic
431C42C23×D1111yescharacteristic
432C11#1862311yescharacteristic, complemented, Sylow
433C23—21no—
434C23#6700611yescharacteristic
435Q8—21no—
436Q8—24no—
437Q8—44no—
438Q8—44no—
439Q8—42no—
440Q8—84no—
441Q8—444no—
442Q8—882no—
443Q8C2×#432612yescomplemented
444D4—24no—
445D4—21no—
446D4C2×#432612yescomplemented
447C2×C4—21no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—82no—
459C2×C4—84no—
460C2×C4—442no—
461C2×C4—882no—
462C2×C4#6699512yes—
463C2×C4C2×#432612yes—
464C2×C4#6700611yescharacteristic
465C2×C4#6700611yescharacteristic
466C2×C4#6700611yescharacteristic
467C2×C4C22×C22⋊D1111yescharacteristic
468C2×C4C22×C22⋊D1111yescharacteristic
469C2×C4C22×C22⋊D1111yescharacteristic
470C8—224no—
471C8—442no—
472C8—442no—
473C22—21no—
474C22—21no—
475C22—22no—
476C22—41no—
477C22—41no—
478C22#1062284112yes—
479C22C2×#6700611yescharacteristic
480C4—22no—
481C4—21no—
482C4—21no—
483C4—41no—
484C4—42no—
485C4—41no—
486C4—44no—
487C4—42no—
488C4—882no—
489C4#1062284112yes—
490C4#1062285412yes—
491C4C2×#6699511yescharacteristic
492C4C22×#432611yescharacteristic
493C4#1062336912yes—
494C2—22no—
495C2—42no—
496C2C2×#1062284111yescharacteristic
497C2#1307791111yescharacteristic
498C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radicalC2×C11×#41D4
hypercenter#3503D11
hypocenterC11#18623
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13079764C2semidirect
2. C2×#10622705C2semidirect
4. #13067756C2semidirect
5. #13067750C2semidirect
6. #13067297C2semidirect
7. #13067071C2semidirect
119. C11×#41Q16semidirect
201. Q8×C11C2×Q16semidirect
204. D4×C11C2×Q16semidirect
367. #41#4326semidirect
432. C11#18623semidirect
443. Q8C2×#4326semidirect
446. D4C2×#4326semidirect

Maximal subgroups

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

subgroupindex
#130797642
C2×#106227052
#130784312
#130677562
#130677502
#130672972
#130670712
#130669982
C11×#35032
#1862311