Subgroups — #13070872

Order 1408.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#66864	C₂	1	4	yes	maximal, complemented
2	#10622312	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622308	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₄₄	—	2	1	no	—
6	C₂×Dic₄₄	C₂²	1	2	yes	—
7	C₂×D₈₈	—	2	1	no	—
8	C₂×D₈₈	C₂²	1	2	yes	—
9	#66927	—	2	1	no	—
10	#66922	—	2	1	no	—
11	C₂×C₁₁×C₁₆	C₂²	1	2	yes	—
12	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	#66864	—	2	8	no	—
14	C₂×D₄₄	—	2	2	no	—
15	C₂×D₄₄	—	4	2	no	—
16	C₂×Dic₂₂	—	2	2	no	—
17	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₁	—	4	2	no	—
21	Dic₄₄	—	2	4	no	—
22	Dic₄₄	—	4	2	no	—
23	D₈₈	—	2	4	no	—
24	D₈₈	—	4	2	no	—
25	C₁₁×C₁₆	D₄	1	4	yes	complemented
26	#2248	—	11	1	no	maximal, Sylow
27	C₂²×D₁₁	—	4	2	no	—
28	C₂×C₄×C₁₁	D₈	1	2	yes	—
29	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₁₁	—	4	2	no	—
31	D₄₄	—	4	2	no	—
32	D₄₄	—	4	2	no	—
33	D₄₄	—	8	4	no	—
34	Dic₂₂	—	4	2	no	—
35	Dic₂₂	—	4	2	no	—
36	C₈×C₁₁	D₈	1	2	yes	—
37	C₈×C₁₁	C₂×D₄	1	2	yes	—
38	C₂×SD₃₂	—	11	4	no	—
39	#494	—	11	1	no	—
40	#493	—	11	1	no	—
41	C₄×C₁₆	D₁₁	1	1	yes	characteristic, complemented
42	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
43	C₂×D₁₁	—	8	2	no	—
44	C₂×D₁₁	—	8	4	no	—
45	C₄×C₁₁	SD₃₂	1	4	yes	complemented
46	C₄×C₁₁	#127	1	1	yes	characteristic
47	C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
48	Dic₁₁	—	8	2	no	—
49	C₂×Q₁₆	—	11	2	no	—
50	C₂×Q₁₆	—	22	1	no	—
51	C₂×D₈	—	11	2	no	—
52	C₂×D₈	—	22	1	no	—
53	C₄⋊Q₈	—	22	1	no	—
54	#127	—	22	1	no	—
55	SD₃₂	—	22	8	no	—
56	C₂×C₁₆	C₂×D₁₁	1	2	yes	—
57	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
58	C₂×C₁₁	#493	1	1	yes	characteristic
59	C₂×C₁₁	C₂×SD₃₂	1	2	yes	—
60	D₁₁	—	16	2	no	—
61	C₂×Q₈	—	22	2	no	—
62	C₂×D₄	—	22	2	no	—
63	C₂×D₄	—	44	2	no	—
64	Q₁₆	—	22	4	no	—
65	Q₁₆	—	44	2	no	—
66	D₈	—	22	4	no	—
67	D₈	—	44	2	no	—
68	C₂×C₈	D₄₄	1	1	yes	characteristic
69	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
70	C₄⋊C₄	—	44	2	no	—
71	C₄²	D₄₄	1	1	yes	characteristic
72	C₁₆	D₄₄	1	4	yes	complemented
73	C₁₁	#2248	1	1	yes	characteristic, complemented, Sylow
74	C₂³	—	44	2	no	—
75	Q₈	—	44	2	no	—
76	Q₈	—	44	2	no	—
77	D₄	—	44	2	no	—
78	D₄	—	44	2	no	—
79	D₄	—	88	4	no	—
80	C₂×C₄	—	44	2	no	—
81	C₂×C₄	D₈₈	1	2	yes	—
82	C₂×C₄	C₂×D₄₄	1	1	yes	characteristic
83	C₈	D₈₈	1	2	yes	—
84	C₈	C₂×D₄₄	1	2	yes	—
85	C₂²	—	88	4	no	—
86	C₂²	—	88	2	no	—
87	C₂²	C₂×D₈₈	1	1	yes	characteristic
88	C₄	—	88	2	no	—
89	C₄	#66864	1	4	yes	complemented
90	C₄	#66927	1	1	yes	characteristic
91	C₄	C₂×D₈₈	1	1	yes	characteristic
92	C₂	—	176	2	no	—
93	C₂	#10622308	1	1	yes	characteristic
94	C₂	C₂×#66864	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈₈
commutator, cosocle	C₂×C₈×C₁₁	C₂³
Frattini	C₂×C₈	C₂²×D₁₁
Fitting	C₄×C₁₁×C₁₆	C₂
socle	C₂²×C₁₁	C₂×D₈
prime radical	#10622308	C₂
hypercenter	C₄×C₁₆	D₁₁
hypocenter	C₁₁	#2248
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#66864	C₂	semidirect
2. #10622312	C₂	semidirect
4. C₄×C₁₁×C₁₆	C₂	semidirect
25. C₁₁×C₁₆	D₄	semidirect
41. C₄×C₁₆	D₁₁	semidirect
45. C₄×C₁₁	SD₃₂	semidirect
72. C₁₆	D₄₄	semidirect
73. C₁₁	#2248	semidirect
89. C₄	#66864	semidirect

Maximal subgroups

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

subgroup	index
C₂×#66864	2
#10622312	2
#10622308	2
C₄×C₁₁×C₁₆	2
#2248	11