Subgroups — #13068790

Order 1408.

212 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	C₂×#66886	C₂	1	4	yes	maximal
3	#10622537	C₂	1	1	yes	maximal, characteristic
4	C₂×#66867	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×M₁₆	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×#4318	C₂²	1	2	yes	—
8	C₂²×C₁₁⋊C₈	C₂²	1	2	yes	—
9	C₁₁×C₄⋊C₈	—	2	2	no	—
10	#66886	—	2	8	no	—
11	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
12	#66867	C₄	1	4	yes	—
13	C₂²×C₄×C₁₁	Q₈	1	2	yes	—
14	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
15	C₁₁×M₁₆	—	2	4	no	—
16	C₂×C₈×C₁₁	—	2	2	no	—
17	C₄²×C₁₁	C₂×C₄	1	2	yes	—
18	C₄²×C₁₁	D₄	1	2	yes	—
19	#4318	—	2	4	no	—
20	C₂×C₁₁⋊C₈	—	2	2	no	—
21	C₂×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
22	C₂×C₁₁⋊C₈	D₄	1	4	yes	—
23	C₂×C₁₁⋊C₈	Q₈	1	4	yes	—
24	#1849	—	11	1	no	maximal, Sylow
25	C₂³×C₁₁	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₄×C₁₁	—	4	2	no	—
27	C₂×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
28	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
30	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
32	C₈×C₁₁	—	4	2	no	—
33	C₁₁⋊C₈	—	4	2	no	—
34	C₁₁⋊C₈	C₄⋊C₄	1	8	yes	—
35	C₂×#108	—	11	4	no	—
36	#423	—	11	1	no	—
37	#423	D₁₁	1	1	yes	characteristic
38	C₂×#97	—	11	1	no	—
39	C₂²×C₁₁	—	2	2	no	—
40	C₂²×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₁₁	C₄⋊Q₈	1	2	yes	—
42	C₄×C₁₁	—	2	4	no	—
43	C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
44	C₄×C₁₁	#127	1	1	yes	characteristic
45	C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
46	C₂×M₁₆	—	11	2	no	—
47	C₂×M₁₆	C₂×D₁₁	1	2	yes	—
48	C₂²×C₈	—	11	2	no	—
49	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
50	#108	—	22	8	no	—
51	C₄⋊C₈	—	2	2	no	—
52	C₄⋊C₈	—	22	2	no	—
53	#97	—	11	4	no	—
54	C₂×C₁₁	—	2	2	no	—
55	C₂×C₁₁	#384	1	1	yes	characteristic
56	C₂×C₁₁	#430	1	2	yes	—
57	C₂²×C₄	Dic₂₂	1	2	yes	—
58	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
59	M₁₆	—	2	4	no	—
60	M₁₆	—	22	4	no	—
61	C₂×C₈	—	2	2	no	—
62	C₂×C₈	—	11	4	no	—
63	C₂×C₈	—	11	4	no	—
64	C₂×C₈	—	11	4	no	—
65	C₂×C₈	—	22	2	no	—
66	C₄²	C₄×D₁₁	1	2	yes	—
67	C₄²	C₂²⋊D₁₁	1	2	yes	—
68	C₁₁	#1849	1	1	yes	characteristic, complemented, Sylow
69	C₂³	C₂×Dic₂₂	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	Dic₁₁⋊C₄	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
73	C₂×C₄	D₄×D₁₁	1	2	yes	—
74	C₂×C₄	Q₈×D₁₁	1	2	yes	—
75	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
76	C₈	—	4	2	no	—
77	C₈	—	11	8	no	—
78	C₈	—	44	2	no	—
79	C₂²	—	2	2	no	—
80	C₂²	#66941	1	2	yes	—
81	C₂²	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
82	C₄	—	2	4	no	—
83	C₄	C₄⋊C₄×D₁₁	1	2	yes	—
84	C₄	#66993	1	1	yes	characteristic
85	C₄	#66997	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	#10622589	1	1	yes	characteristic
88	C₂	#10622737	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₁₁×#423	C₂
socle	C₂²×C₁₁	C₂×C₄⋊C₄
prime radical	C₂³×C₁₁	C₂×Q₈
cosocle	C₂²×C₄×C₁₁	C₂³
hypercenter	#423	D₁₁
hypocenter	C₁₁	#1849
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
68. C₁₁	#1849	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
C₂×#66886	2
#10622537	2
C₂×#66867	2
#1849	11