Finite Group Databasebeta

← #13080310

Subgroups — #13080310

Order 1408.

546 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C22⋊D11C211yesmaximal, characteristic
2C22×#4324C211yesmaximal, characteristic, complemented
3C2×SD16×D11C211yesmaximal, characteristic, complemented
4#10623163C211yesmaximal, characteristic, complemented
5C11×#450C211yesmaximal, characteristic, complemented
6#10622788C211yesmaximal, characteristic, complemented
7#10622783C211yesmaximal, characteristic, complemented
8#10622775C211yesmaximal, characteristic, complemented
9#10622661C211yesmaximal, characteristic, complemented
10#10622391C211yesmaximal, characteristic, complemented
11#10622389C211yesmaximal, characteristic, complemented
12#10622375C211yesmaximal, characteristic, complemented
13#10622371C211yesmaximal, characteristic, complemented
14#10622351C211yesmaximal, characteristic, complemented
15(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×C22⋊D11—21no—
18C2×Q8×D11C2211yescharacteristic, complemented
19C2×D4×D11C2211yescharacteristic
20C22×Dic22C2211yescharacteristic, complemented
21C2×C11×SD16C2211yescharacteristic
22C2×C11×SD16C2211yescharacteristic, complemented
23C11×C22⋊Q8C2211yescharacteristic, complemented
24#67006—21no—
25#66997C2211yescharacteristic, complemented
26C2×#4325C2211yescharacteristic, complemented
27#66993C2211yescharacteristic
28#66992—21no—
29#66991C2211yescharacteristic
30#66990—21no—
31D4×Dic11C2211yescharacteristic
32C2×#4324—24no—
33C2×#4324C2211yescharacteristic
34C2×#4324C2211yescharacteristic
35C2×#4324C2211yescharacteristic, complemented
36C2×#4324C2211yescharacteristic, complemented
37#66983C2211yescharacteristic
38C4×C22⋊D11C2211yescharacteristic
39C22×C11⋊C8C2211yescharacteristic, complemented
40SD16×D11—24no—
41C2×#4314C2211yescharacteristic, complemented
42C2×#4314C2211yescharacteristic, complemented
43C2×C8×D11C2211yescharacteristic, complemented
44#66950C2211yescharacteristic, complemented
45#66949—21no—
46#66941—21no—
47#66940C2211yescharacteristic, complemented
48(C22⋊D11)⋊C4—21no—
49#66931—21no—
50C11×#102C2211yescharacteristic
51C11×#102C2211yescharacteristic, complemented
52C11×C22⋊C8C2211yescharacteristic, complemented
53#66899C2211yescharacteristic, complemented
54(C2×D11)⋊C8C2211yescharacteristic, complemented
55#66880C2211yescharacteristic, complemented
56#66880C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58C8×Dic11C2211yescharacteristic, complemented
59#66873C2211yescharacteristic, complemented
60#66872C2211yescharacteristic, complemented
61C24×C11—21no—
62C23×D11—21no—
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11—22no—
65C2×D4×C11—21no—
66C2×D4×C11—41no—
67C2×D4×C11C2311yescharacteristic
68C2×D4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11—21no—
74C2×C22⋊D11—21no—
75C2×C22⋊D11—44no—
76C2×C22⋊D11D411yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79Q8×D11—22no—
80Q8×D11—41no—
81D4×D11—22no—
82D4×D11—41no—
83C2×D44C2311yescharacteristic
84C2×C4×D11—21no—
85C2×C4×D11C2311yescharacteristic
86C2×Dic22—22no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—41no—
90C2×Dic22C2311yescharacteristic
91C2×Dic22C2311yescharacteristic
92C11×SD16—22no—
93C11×SD16—41no—
94C2×C8×C11C2311yescharacteristic
95C2×C8×C11C2311yescharacteristic
96C11×C4⋊C4—21no—
97C11×C4⋊C4C2311yescharacteristic
98C11×C22⋊C4—21no—
99C22⋊Dic11—21no—
100C22⋊Dic11—21no—
101C22⋊Dic11D411yescharacteristic
102#4325—22no—
103#4324—22no—
104#4324—22no—
105#4324—22no—
106#4324D414yescomplemented
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4D411yescharacteristic
110C4⋊Dic11—21no—
111C4⋊Dic11C2311yescharacteristic
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114Dic11⋊C4—21no—
115Dic11⋊C4D411yescharacteristic
116C4×Dic11—21no—
117C4×Dic11C2311yescharacteristic
118C2×C11⋊C8—22no—
119C2×C11⋊C8C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121#4314—22no—
122#4314—41no—
123C8×D11—22no—
124D4×SD16—111nomaximal, Sylow
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—81no—
130C23×C11C2×D411yescharacteristic
131C22×D11—21no—
132C22×D11—42no—
133C22×D11—42no—
134C22×D11—81no—
135C22×D11C2×D411yescharacteristic
136Q8×C11—21no—
137Q8×C11—21no—
138D4×C11—21no—
139D4×C11—21no—
140D4×C11—21no—
141D4×C11—42no—
142D4×C11C2×D412yes—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11C2×D411yescharacteristic
148C2×C4×C11C2411yescharacteristic
149C22⋊D11—42no—
150C22⋊D11—42no—
151C22⋊D11—42no—
152C22⋊D11—42no—
153C22⋊D11—81no—
154C22⋊D11SD1614yescomplemented
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11C2×D411yescharacteristic
161C2×Dic11C2×D411yescharacteristic
162C2×Dic11C2×D411yescharacteristic
163D44—21no—
164D44—21no—
165C4×D11—21no—
166C4×D11—21no—
167C4×D11—42no—
168Dic22—21no—
169Dic22—21no—
170Dic22—21no—
171Dic22—42no—
172Dic22—42no—
173Dic22C2×D412yescomplemented
174C8×C11—21no—
175C8×C11—21no—
176C11⋊C8—21no—
177C11⋊C8C2×D412yescomplemented
178C22×SD16—111no—
179C22×SD16—111no—
180D4×Q8—111no—
181D42—111no—
182#492—111no—
183#465—111no—
184#465—111no—
185#461—111no—
186#460—111no—
187#450—111no—
188#450D1111yescharacteristic, complemented
189#448—111no—
190#448—111no—
191C4×SD16—111no—
192C8×D4—111no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—22no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—84no—
202C22×C11C2×SD1612yescomplemented
203C22×C11C22×D411yescharacteristic
204C2×D11—21no—
205C2×D11—21no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—84no—
210C2×D11C2×SD1612yescomplemented
211C4×C11—21no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11C22×D411yescharacteristic
215C4×C11H(5,𝔽2)11yescharacteristic
216Dic11—22no—
217Dic11—21no—
218Dic11—21no—
219Dic11—41no—
220Dic11—41no—
221Dic11C2×SD1612yescomplemented
222C22×Q8—111no—
223C22×Q8—111no—
224C22×D4—111no—
225C22×D4—221no—
226C22×D4C2×D1111yescharacteristic
227C2×SD16—111no—
228C2×SD16—111no—
229C2×SD16—111no—
230C2×SD16—111no—
231C2×SD16—111no—
232C2×SD16—111no—
233C2×SD16—111no—
234C2×SD16—224no—
235C2×SD16—224no—
236C2×SD16C2×D1111yescharacteristic
237C2×SD16C2×D1111yescharacteristic, complemented
238C22×C8—111no—
239C22×C8—111no—
240C4⋊Q8—111no—
241C4⋊Q8—221no—
242#127—111no—
243C22⋊Q8—111no—
244C22⋊Q8—221no—
245C22⋊Q8—221no—
246C22⋊Q8C2×D1111yescharacteristic, complemented
247#121—111no—
248#121—111no—
249#121—221no—
250#120—221no—
251#120—221no—
252C4×Q8—111no—
253C4×D4—111no—
254C4×D4—111no—
255C4×D4—221no—
256#106—111no—
257C4⋊C8—111no—
258#103—111no—
259#103—111no—
260#103—111no—
261#102—111no—
262#102C2×D1111yescharacteristic
263#102C2×D1111yescharacteristic, complemented
264C22⋊C8—111no—
265C22⋊C8C2×D1111yescharacteristic, complemented
266C4×C8—111no—
267C2×C11—22no—
268C2×C11—42no—
269C2×C11—81no—
270C2×C11D4211yescharacteristic
271C2×C11C22×SD1611yescharacteristic
272C2×C11#57711yescharacteristic
273D11—22no—
274D11—81no—
275C24—21no—
276C24—221no—
277C2×Q8—111no—
278C2×Q8—111no—
279C2×Q8—221no—
280C2×Q8—222no—
281C2×Q8—221no—
282C2×Q8—222no—
283C2×Q8—441no—
284C2×Q8—441no—
285C2×Q8C22×D1111yescharacteristic
286C2×D4—22no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—111no—
290C2×D4—111no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—222no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—441no—
298C2×D4—444no—
299C2×D4C22×D1111yescharacteristic
300C2×D4C22×D1111yescharacteristic
301C22×C4—111no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4C22×D1111yescharacteristic
306SD16—22no—
307SD16—41no—
308SD16—114no—
309SD16—222no—
310SD16—222no—
311SD16—222no—
312SD16—222no—
313SD16—222no—
314SD16—441no—
315C2×C8—111no—
316C2×C8—111no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8C22×D1111yescharacteristic
320C2×C8C22×D1111yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—111no—
323C4⋊C4—111no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4C22×D1111yescharacteristic
329C22⋊C4—21no—
330C22⋊C4—111no—
331C22⋊C4—111no—
332C22⋊C4—221no—
333C22⋊C4—221no—
334C22⋊C4—221no—
335C22⋊C4—221no—
336C42—111no—
337C42—221no—
338C11D4×SD1611yescharacteristic, complemented, Sylow
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—111no—
345C23—221no—
346C23—442no—
347C23—442no—
348C23—881no—
349C23D4×D1111yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—112no—
353Q8—221no—
354Q8—221no—
355Q8—221no—
356Q8—442no—
357Q8—442no—
358D4—21no—
359D4—21no—
360D4—21no—
361D4—42no—
362D4—114no—
363D4—221no—
364D4—221no—
365D4—442no—
366D4—442no—
367D4—442no—
368D4—442no—
369D4—881no—
370D4D4×D1112yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—111no—
376C2×C4—111no—
377C2×C4—111no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4D4×D1111yescharacteristic
387C2×C4C23×D1111yescharacteristic
388C8—21no—
389C8—21no—
390C8—112no—
391C8—221no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—84no—
401C22—112no—
402C22—221no—
403C22—221no—
404C22—441no—
405C22—441no—
406C22—441no—
407C22—884no—
408C22SD16×D1112yescomplemented
409C22C2×D4×D1111yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—112no—
414C4—221no—
415C4—221no—
416C4—222no—
417C4—441no—
418C4—441no—
419C4C2×D4×D1111yescharacteristic
420C4#6703711yescharacteristic
421C2—22no—
422C2—42no—
423C2—81no—
424C2—222no—
425C2—881no—
426C2#1062312111yescharacteristic
427C2C2×SD16×D1111yescharacteristic
428C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#450C2
socleC22×C11C22×D4
prime radicalD4×C22⋊D11C2
hypercenter#450D11
hypocenterC11D4×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. C22×#4324C2semidirect
3. C2×SD16×D11C2semidirect
4. #10623163C2semidirect
5. C11×#450C2semidirect
6. #10622788C2semidirect
7. #10622783C2semidirect
8. #10622775C2semidirect
9. #10622661C2semidirect
10. #10622391C2semidirect
11. #10622389C2semidirect
12. #10622375C2semidirect
13. #10622371C2semidirect
14. #10622351C2semidirect
15. (C22⋊D11)⋊C8C2semidirect
18. C2×Q8×D11C22semidirect
20. C22×Dic22C22semidirect
22. C2×C11×SD16C22semidirect
23. C11×C22⋊Q8C22semidirect
25. #66997C22semidirect
26. C2×#4325C22semidirect
35. C2×#4324C22semidirect
36. C2×#4324C22semidirect
39. C22×C11⋊C8C22semidirect
41. C2×#4314C22semidirect
42. C2×#4314C22semidirect
43. C2×C8×D11C22semidirect
44. #66950C22semidirect
47. #66940C22semidirect
51. C11×#102C22semidirect
52. C11×C22⋊C8C22semidirect
53. #66899C22semidirect
54. (C2×D11)⋊C8C22semidirect
55. #66880C22semidirect
56. #66880C22semidirect
57. Dic11⋊C8C22semidirect
58. C8×Dic11C22semidirect
59. #66873C22semidirect
60. #66872C22semidirect
106. #4324D4semidirect
154. C22⋊D11SD16semidirect
173. Dic22C2×D4semidirect
177. C11⋊C8C2×D4semidirect
188. #450D11semidirect
202. C22×C11C2×SD16semidirect
210. C2×D11C2×SD16semidirect
221. Dic11C2×SD16semidirect
237. C2×SD16C2×D11semidirect
246. C22⋊Q8C2×D11semidirect
263. #102C2×D11semidirect
265. C22⋊C8C2×D11semidirect
338. C11D4×SD16semidirect
408. C22SD16×D11semidirect

Maximal subgroups

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

subgroupindex
D4×C22⋊D112
C22×#43242
C2×SD16×D112
#106231632
C11×#4502
#106227882
#106227832
#106227752
#106226612
#106223912
#106223892
#106223752
#106223712
#106223512
(C22⋊D11)⋊C82
D4×SD1611