Subgroups — #13070397

Order 1408.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic
2	#10622493	C₂	1	2	yes	maximal
3	C₁₁×#366	C₂	1	1	yes	maximal, characteristic, complemented
4	#10622142	C₂	1	1	yes	maximal, characteristic, complemented
5	#10622128	C₂	1	2	yes	maximal, complemented
6	C₂×C₈×D₁₁	C₂²	1	1	yes	characteristic
7	#66945	—	2	2	no	—
8	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	C₁₁×#107	C₂²	1	2	yes	—
10	#66882	C₂²	1	2	yes	—
11	C₂×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
12	#66872	—	2	2	no	—
13	C₁₆×D₁₁	C₄	1	4	yes	complemented
14	C₂×C₄×D₁₁	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
16	C₁₁×C₄⋊C₄	—	2	2	no	—
17	(C₂×D₁₁)⋊C₄	—	4	2	no	—
18	C₄⋊Dic₁₁	—	2	2	no	—
19	C₄×Dic₁₁	—	4	2	no	—
20	C₂×C₁₁⋊C₈	D₄	1	1	yes	characteristic
21	C₈×D₁₁	C₂×C₄	1	2	yes	—
22	C₈×D₁₁	Q₈	1	2	yes	—
23	C₁₁×C₁₆	C₂×C₄	1	2	yes	—
24	C₁₁⋊C₁₆	C₂×C₄	1	2	yes	—
25	#2158	—	11	1	no	maximal, Sylow
26	C₂²×D₁₁	D₈	1	1	yes	characteristic
27	C₂×C₄×C₁₁	—	4	2	no	—
28	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₁₁	—	4	2	no	—
30	C₂×Dic₁₁	D₈	1	1	yes	characteristic
31	C₄×D₁₁	C₄⋊C₄	1	2	yes	—
32	C₄×D₁₁	Q₁₆	1	2	yes	—
33	C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
35	C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
36	C₂²×C₁₆	—	11	1	no	—
37	#427	—	11	2	no	—
38	#367	—	11	2	no	—
39	#366	—	11	1	no	—
40	#366	D₁₁	1	1	yes	characteristic, complemented
41	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
42	C₂×D₁₁	—	2	1	no	—
43	C₂×D₁₁	—	2	1	no	—
44	C₂×D₁₁	#107	1	2	yes	—
45	C₄×C₁₁	—	8	2	no	—
46	C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
48	Dic₁₁	—	8	2	no	—
49	Dic₁₁	#107	1	2	yes	—
50	C₂²×C₈	—	11	1	no	—
51	#117	—	22	2	no	—
52	C₂×C₁₆	—	11	1	no	—
53	C₂×C₁₆	—	11	4	no	—
54	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
55	#107	—	11	2	no	—
56	#107	C₂×D₁₁	1	2	yes	—
57	#106	—	22	2	no	—
58	C₂×C₁₁	C₂×#107	1	1	yes	characteristic
59	C₂×C₁₁	#508	1	1	yes	characteristic
60	C₂×C₁₁	#508	1	1	yes	characteristic
61	D₁₁	—	2	2	no	—
62	C₂²×C₄	—	11	1	no	—
63	C₂×C₈	—	11	1	no	—
64	C₂×C₈	—	11	2	no	—
65	C₂×C₈	—	11	2	no	—
66	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	22	2	no	—
69	C₂²⋊C₄	—	44	2	no	—
70	C₄²	—	44	2	no	—
71	C₁₆	—	11	2	no	—
72	C₁₆	C₄×D₁₁	1	2	yes	—
73	C₁₁	#2158	1	1	yes	characteristic, complemented, Sylow
74	C₂³	—	11	1	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	11	1	no	—
77	C₂×C₄	—	11	2	no	—
78	C₂×C₄	—	11	2	no	—
79	C₂×C₄	—	44	2	no	—
80	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
81	C₈	—	11	2	no	—
82	C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
83	C₈	Q₈×D₁₁	1	1	yes	characteristic
84	C₂²	—	11	2	no	—
85	C₂²	—	22	1	no	—
86	C₂²	—	22	1	no	—
87	C₂²	D₈×D₁₁	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	—	11	2	no	—
90	C₄	—	88	2	no	—
91	C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
92	C₄	Q₁₆×D₁₁	1	1	yes	characteristic
93	C₂	—	22	2	no	—
94	C₂	D₁₁×#107	1	1	yes	characteristic
95	C₂	#10622525	1	1	yes	characteristic
96	C₂	#10622532	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₁
commutator	C₈×C₁₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₁
Fitting	C₁₁×#366	C₂
socle	C₂²×C₁₁	C₂×D₈
prime radical	C₂²×D₁₁	D₈
cosocle	C₂×C₈×C₁₁	C₂³
hypercenter	#366	D₁₁
hypocenter	C₁₁	#2158
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
3. C₁₁×#366	C₂	semidirect
4. #10622142	C₂	semidirect
5. #10622128	C₂	semidirect
13. C₁₆×D₁₁	C₄	semidirect
40. #366	D₁₁	semidirect
73. C₁₁	#2158	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₁₁	2
#10622493	2
C₁₁×#366	2
#10622142	2
#10622128	2
#2158	11