Subgroups — #13066567

Order 1408.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#423	C₂	1	1	yes	maximal, characteristic
2	#10622191	C₂	1	2	yes	maximal
3	C₂×C₁₁×M₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₁₁	C₄	1	1	yes	characteristic
6	C₁₁×C₄⋊C₈	—	2	2	no	—
7	#66876	—	2	2	no	—
8	C₂²×C₄×C₁₁	—	2	1	no	—
9	C₂²×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
10	C₁₁×M₁₆	—	4	1	no	—
11	C₁₁×M₁₆	—	4	1	no	—
12	C₂×C₈×C₁₁	—	2	1	no	—
13	C₂×C₈×C₁₁	D₄	1	2	yes	—
14	C₄²×C₁₁	—	2	1	no	—
15	C₄²×C₁₁	C₈	1	1	yes	characteristic
16	C₄²×C₁₁	C₈	1	1	yes	characteristic
17	C₁₁⋊C₁₆	—	4	2	no	—
18	#1327	—	11	1	no	maximal, Sylow
19	C₂³×C₁₁	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₁	—	2	1	no	—
21	C₂×C₄×C₁₁	—	2	1	no	—
22	C₂×C₄×C₁₁	—	2	1	no	—
23	C₂×C₄×C₁₁	—	2	1	no	—
24	C₂×C₄×C₁₁	—	4	2	no	—
25	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
27	C₈×C₁₁	—	2	2	no	—
28	C₈×C₁₁	—	4	1	no	—
29	#423	D₁₁	1	1	yes	characteristic
30	#349	—	11	2	no	—
31	C₂²×C₁₁	—	2	1	no	—
32	C₂²×C₁₁	—	4	1	no	—
33	C₂²×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₁₁	—	2	2	no	—
35	C₄×C₁₁	—	2	1	no	—
36	C₄×C₁₁	—	4	1	no	—
37	C₄×C₁₁	#99	1	1	yes	characteristic
38	C₄×C₁₁	#101	1	1	yes	characteristic
39	C₂×M₁₆	Dic₁₁	1	1	yes	characteristic
40	C₂×M₁₆	C₂×D₁₁	1	1	yes	characteristic
41	C₂×C₄²	Dic₁₁	1	1	yes	characteristic
42	M₃₂	—	22	2	no	—
43	C₄⋊C₈	—	2	2	no	—
44	C₂×C₁₁	—	2	1	no	—
45	C₂×C₁₁	—	4	1	no	—
46	C₂×C₁₁	#324	1	1	yes	characteristic
47	C₂²×C₄	—	2	1	no	—
48	C₂²×C₄	C₂×Dic₁₁	1	1	yes	characteristic
49	M₁₆	—	4	1	no	—
50	M₁₆	—	4	1	no	—
51	C₂×C₈	—	2	1	no	—
52	C₂×C₈	C₂²⋊D₁₁	1	2	yes	—
53	C₄²	—	2	1	no	—
54	C₄²	C₁₁⋊C₈	1	1	yes	characteristic
55	C₄²	C₁₁⋊C₈	1	1	yes	characteristic
56	C₁₆	—	44	2	no	—
57	C₁₁	#1327	1	1	yes	characteristic, complemented, Sylow
58	C₂³	#4318	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	4	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	2	1	no	—
73	C₄	—	4	1	no	—
74	C₄	#66898	1	1	yes	characteristic
75	C₄	#66900	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	#10622166	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#66898
commutator	C₂×C₄×C₁₁	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₁₁
Fitting	C₁₁×#423	C₂
socle	C₂×C₁₁	#324
prime radical	C₂³×C₁₁	M₁₆
cosocle	C₂×C₁₁×M₁₆	C₂²
hypercenter	#423	D₁₁
hypocenter	C₁₁	#1327
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #423

Complements

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

N	H ≅ G/N	type
57. C₁₁	#1327	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#423	2
#10622191	2
#1327	11