Subgroups — #13070488

Order 1408.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₄₄	C₂	1	2	yes	maximal
3	C₁₁×#346	C₂	1	1	yes	maximal, characteristic
4	#10622143	C₂	1	1	yes	maximal, characteristic
5	#10622141	C₂	1	2	yes	maximal
6	C₂×Dic₄₄	C₂²	1	2	yes	—
7	C₄×Dic₂₂	—	2	2	no	—
8	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	#66882	C₂²	1	2	yes	—
12	#66880	—	2	2	no	—
13	Dic₈₈	C₄	1	4	yes	complemented
14	C₂×Dic₂₂	—	2	2	no	—
15	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
17	C₄²×C₁₁	D₄	1	1	yes	characteristic
18	C₄⋊Dic₁₁	—	2	2	no	—
19	Dic₁₁⋊C₄	—	4	2	no	—
20	C₄×Dic₁₁	—	4	2	no	—
21	Dic₄₄	—	2	2	no	—
22	Dic₄₄	C₂×C₄	1	4	yes	—
23	C₁₁×C₁₆	—	2	1	no	—
24	C₁₁×C₁₆	C₂×C₄	1	2	yes	—
25	#2176	—	11	1	no	maximal, Sylow
26	C₂×C₄×C₁₁	D₈	1	2	yes	—
27	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₁₁	—	4	2	no	—
29	C₂×Dic₁₁	—	4	2	no	—
30	Dic₂₂	—	2	4	no	—
31	Dic₂₂	—	4	2	no	—
32	C₈×C₁₁	—	2	1	no	—
33	C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₁	#41	1	1	yes	characteristic
35	C₂×Q₃₂	—	11	1	no	—
36	C₄×Q₁₆	—	11	2	no	—
37	#367	—	11	1	no	—
38	#358	—	11	2	no	—
39	#346	D₁₁	1	1	yes	characteristic
40	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
41	C₄×C₁₁	—	2	2	no	—
42	C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
43	C₄×C₁₁	#135	1	1	yes	characteristic
44	Dic₁₁	—	4	4	no	—
45	Dic₁₁	—	8	2	no	—
46	C₂×Q₁₆	—	11	2	no	—
47	C₄×Q₈	—	22	2	no	—
48	Q₃₂	—	11	4	no	—
49	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
50	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
51	#107	—	11	2	no	—
52	#103	—	22	2	no	—
53	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
54	C₂×C₁₁	C₄×D₈	1	1	yes	characteristic
55	C₂×C₁₁	#510	1	2	yes	—
56	C₂×Q₈	—	22	2	no	—
57	Q₁₆	—	11	4	no	—
58	Q₁₆	—	22	2	no	—
59	C₂×C₈	D₄₄	1	1	yes	characteristic
60	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
61	C₄⋊C₄	—	22	2	no	—
62	C₄⋊C₄	—	44	2	no	—
63	C₄²	—	44	2	no	—
64	C₄²	D₄₄	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	C₄×D₁₁	1	2	yes	—
67	C₁₁	#2176	1	1	yes	characteristic, complemented, Sylow
68	Q₈	—	22	4	no	—
69	Q₈	—	44	2	no	—
70	C₂×C₄	—	44	2	no	—
71	C₂×C₄	—	44	2	no	—
72	C₂×C₄	D₈₈	1	2	yes	—
73	C₂×C₄	C₂×D₄₄	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
76	C₈	#4339	1	1	yes	characteristic
77	C₂²	C₂×D₈₈	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	44	4	no	—
80	C₄	—	88	2	no	—
81	C₄	C₄×D₄₄	1	1	yes	characteristic
82	C₄	#66957	1	1	yes	characteristic
83	C₂	C₄×D₈₈	1	1	yes	characteristic
84	C₂	#10622522	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈₈
commutator	C₈×C₁₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₁
Fitting	C₁₁×#346	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₈
cosocle	C₂×C₈×C₁₁	C₂³
hypercenter	#346	D₁₁
hypocenter	C₁₁	#2176
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
13. Dic₈₈	C₄	semidirect
67. C₁₁	#2176	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₈₈	2
C₄×Dic₄₄	2
C₁₁×#346	2
#10622143	2
#10622141	2
#2176	11