Subgroups — #13077010

Order 1408.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#66993	C₂	1	12	yes	maximal, complemented
3	C₂×#66927	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄×C₁₁	C₂²	1	6	yes	—
6	C₂²×C₂²⋊D₁₁	C₂²	1	16	yes	—
7	C₂²×D₄₄	C₂²	1	6	yes	—
8	C₁₁×#127	—	2	4	no	—
9	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
10	#66993	—	2	48	no	—
11	C₂×C₄×Dic₁₁	C₂²	1	6	yes	—
12	#66927	—	2	4	no	—
13	C₂⁴×C₁₁	C₂³	1	4	yes	—
14	C₂³×D₁₁	C₂³	1	4	yes	—
15	C₂×D₄×C₁₁	—	2	24	no	—
16	C₂×D₄×C₁₁	—	2	12	no	—
17	C₂²×C₄×C₁₁	C₂³	1	3	yes	—
18	C₂×C₂²⋊D₁₁	—	2	96	no	—
19	C₂²×Dic₁₁	C₂³	1	4	yes	—
20	C₂×D₄₄	—	2	12	no	—
21	C₂×D₄₄	—	2	24	no	—
22	C₄²×C₁₁	D₄	1	4	yes	complemented
23	C₄×Dic₁₁	D₄	1	24	yes	complemented
24	#2867	—	11	1	no	maximal, Sylow
25	C₂³×C₁₁	—	2	24	no	—
26	C₂³×C₁₁	—	2	4	no	—
27	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
28	C₂²×D₁₁	—	2	4	no	—
29	C₂²×D₁₁	—	2	24	no	—
30	D₄×C₁₁	—	4	24	no	—
31	C₂×C₄×C₁₁	C₂×D₄	1	12	yes	—
32	C₂×C₄×C₁₁	C₂×D₄	1	6	yes	—
33	C₂²⋊D₁₁	—	4	64	no	—
34	C₂×Dic₁₁	C₂×D₄	1	24	yes	—
35	D₄₄	—	4	24	no	—
36	C₂×#127	—	11	12	no	—
37	C₂×#127	—	11	1	no	—
38	C₂×#127	D₁₁	1	1	yes	characteristic, complemented
39	C₄³	—	11	1	no	—
40	C₂²×C₁₁	—	4	12	no	—
41	C₂²×C₁₁	—	4	16	no	—
42	C₂²×C₁₁	C₂²×D₄	1	6	yes	—
43	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
44	C₂×D₁₁	—	4	12	no	—
45	C₂×D₁₁	—	4	16	no	—
46	C₄×C₁₁	#127	1	12	yes	complemented
47	Dic₁₁	#127	1	16	yes	complemented
48	C₂²×D₄	—	11	16	no	—
49	C₂²×D₄	—	11	6	no	—
50	C₂²×D₄	C₂×D₁₁	1	6	yes	—
51	#127	—	2	4	no	—
52	#127	—	22	48	no	—
53	#127	—	22	4	no	—
54	C₂×C₄²	—	11	6	no	—
55	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
56	C₂×C₁₁	—	8	4	no	—
57	C₂×C₁₁	C₂×#127	1	4	yes	—
58	C₂×C₁₁	C₂×#127	1	3	yes	—
59	D₁₁	—	8	4	no	—
60	C₂⁴	—	11	4	no	—
61	C₂⁴	C₂²×D₁₁	1	4	yes	—
62	C₂×D₄	—	2	24	no	—
63	C₂×D₄	—	2	12	no	—
64	C₂×D₄	—	22	96	no	—
65	C₂×D₄	—	22	24	no	—
66	C₂×D₄	—	22	12	no	—
67	C₂²×C₄	—	11	4	no	—
68	C₂²×C₄	C₂²×D₁₁	1	3	yes	—
69	C₄²	—	11	24	no	—
70	C₄²	C₂²⋊D₁₁	1	4	yes	complemented
71	C₁₁	#2867	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	2	24	no	—
73	C₂³	—	2	4	no	—
74	C₂³	—	22	24	no	—
75	C₂³	—	22	4	no	—
76	C₂³	C₂³×D₁₁	1	1	yes	characteristic
77	D₄	—	4	24	no	—
78	D₄	—	44	64	no	—
79	D₄	—	44	24	no	—
80	C₂×C₄	—	11	24	no	—
81	C₂×C₄	D₄×D₁₁	1	12	yes	—
82	C₂×C₄	C₂×C₂²⋊D₁₁	1	6	yes	—
83	C₂²	—	4	16	no	—
84	C₂²	—	4	12	no	—
85	C₂²	—	44	16	no	—
86	C₂²	—	44	12	no	—
87	C₂²	C₂×D₄×D₁₁	1	6	yes	—
88	C₂²	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
89	C₄	—	11	16	no	—
90	C₄	#66993	1	12	yes	complemented
91	C₂	—	8	4	no	—
92	C₂	—	88	4	no	—
93	C₂	D₁₁×#127	1	4	yes	—
94	C₂	C₂×#66993	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₂×C₁₁×#127	C₂
hypercenter	C₂×#127	D₁₁
hypocenter	C₁₁	#2867
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×#127

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#127	C₂	semidirect
2. C₂×#66993	C₂	semidirect
3. C₂×#66927	C₂	semidirect
4. C₄²×Dic₁₁	C₂	semidirect
22. C₄²×C₁₁	D₄	semidirect
23. C₄×Dic₁₁	D₄	semidirect
38. C₂×#127	D₁₁	semidirect
46. C₄×C₁₁	#127	semidirect
47. Dic₁₁	#127	semidirect
70. C₄²	C₂²⋊D₁₁	semidirect
71. C₁₁	#2867	semidirect
90. C₄	#66993	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#127	2
C₂×#66993	2
C₂×#66927	2
C₄²×Dic₁₁	2
#2867	11