Subgroups — D₁₁×#125 #10623218

Order 704.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊C₄×D₁₁	C₂	1	4	yes	maximal
3	C₄⋊C₄×D₁₁	C₂	1	2	yes	maximal
4	#66943	C₂	1	2	yes	maximal, complemented
5	#66942	C₂	1	4	yes	maximal, complemented
6	C₄²×D₁₁	C₂	1	1	yes	maximal, characteristic
7	#66923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₁	C₂²	1	2	yes	—
9	C₂×C₄×D₁₁	C₂²	1	4	yes	—
10	C₂×C₄×D₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
12	C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
13	C₄²×C₁₁	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₁₁	C₂²	1	2	yes	—
15	C₄⋊Dic₁₁	C₂²	1	4	yes	—
16	Dic₁₁⋊C₄	C₂²	1	4	yes	—
17	Dic₁₁⋊C₄	C₂²	1	4	yes	—
18	Dic₁₁⋊C₄	C₂²	1	4	yes	—
19	C₄×Dic₁₁	C₂²	1	2	yes	—
20	C₄×Dic₁₁	C₂²	1	1	yes	characteristic
21	C₂²×D₁₁	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₁₁	C₂³	1	2	yes	—
23	C₂×C₄×C₁₁	C₂³	1	4	yes	—
24	C₂×C₄×C₁₁	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₁	C₂³	1	2	yes	—
26	C₂×Dic₁₁	C₂³	1	4	yes	—
27	C₂×Dic₁₁	C₂³	1	1	yes	characteristic
28	C₄×D₁₁	—	2	4	no	—
29	C₄×D₁₁	—	2	8	no	—
30	C₄×D₁₁	Q₈	1	4	yes	—
31	C₂×#125	—	11	1	no	maximal, Sylow
32	C₂²×C₁₁	C₂⁴	1	1	yes	characteristic
33	C₂×D₁₁	C₂×Q₈	1	2	yes	—
34	C₂×D₁₁	#41	1	4	yes	—
35	C₄×C₁₁	—	2	2	no	—
36	C₄×C₁₁	—	2	4	no	—
37	C₄×C₁₁	C₂×Q₈	1	2	yes	—
38	Dic₁₁	—	2	2	no	—
39	Dic₁₁	—	2	4	no	—
40	Dic₁₁	C₂×Q₈	1	2	yes	—
41	#125	—	11	4	no	—
42	#125	—	11	2	no	—
43	#125	—	11	1	no	—
44	#125	D₁₁	1	1	yes	characteristic, direct product factor
45	C₂×C₄⋊C₄	—	11	2	no	—
46	C₂×C₄⋊C₄	—	11	4	no	—
47	C₂×C₄²	—	11	1	no	—
48	C₂×C₁₁	C₂²×Q₈	1	1	yes	characteristic
49	C₂×C₁₁	C₂×#41	1	2	yes	—
50	D₁₁	#125	1	4	yes	direct product factor
51	C₂²×C₄	—	11	1	no	—
52	C₂²×C₄	—	11	2	no	—
53	C₂²×C₄	—	11	4	no	—
54	C₄⋊C₄	—	11	4	no	—
55	C₄⋊C₄	—	11	4	no	—
56	C₄⋊C₄	—	11	4	no	—
57	C₄⋊C₄	—	11	4	no	—
58	C₄⋊C₄	—	11	2	no	—
59	C₄⋊C₄	C₂×D₁₁	1	4	yes	—
60	C₄⋊C₄	C₂×D₁₁	1	2	yes	—
61	C₄²	—	11	2	no	—
62	C₄²	—	11	1	no	—
63	C₄²	C₂×D₁₁	1	1	yes	characteristic
64	C₁₁	C₂×#125	1	1	yes	characteristic, complemented, Sylow
65	C₂³	—	11	1	no	—
66	C₂×C₄	—	11	1	no	—
67	C₂×C₄	—	11	4	no	—
68	C₂×C₄	—	11	2	no	—
69	C₂×C₄	—	11	4	no	—
70	C₂×C₄	—	22	4	no	—
71	C₂×C₄	—	22	8	no	—
72	C₂×C₄	C₂²×D₁₁	1	2	yes	—
73	C₂×C₄	C₂²×D₁₁	1	4	yes	—
74	C₂×C₄	C₂²×D₁₁	1	1	yes	characteristic
75	C₂²	—	11	2	no	—
76	C₂²	—	11	4	no	—
77	C₂²	C₂³×D₁₁	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	4	no	—
80	C₄	—	11	2	no	—
81	C₄	—	22	2	no	—
82	C₄	—	22	4	no	—
83	C₄	Q₈×D₁₁	1	2	yes	—
84	C₂	—	11	4	no	—
85	C₂	C₂×Q₈×D₁₁	1	1	yes	characteristic
86	C₂	#41×D₁₁	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁴
Fitting	C₁₁×#125	C₂
prime radical	C₂²×D₁₁	C₂³
hypercenter	#125	D₁₁
hypocenter	C₁₁	C₂×#125
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. C₁₁×#125	C₂	semidirect
4. #66943	C₂	semidirect
5. #66942	C₂	semidirect
7. #66923	C₂	semidirect
44. #125	D₁₁	direct (N × H)
50. D₁₁	#125	direct (N × H)
64. C₁₁	C₂×#125	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#125	2
C₄⋊C₄×D₁₁	2
#66943	2
#66942	2
C₄²×D₁₁	2
#66923	2
C₂×#125	11

Subgroups — D11×#125 #10623218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#125 #10623218