Subgroups — #14674768

Order 2816.

270 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₅₂	C₂	1	4	yes	maximal, complemented
2	#13070866	C₂	1	2	yes	maximal, complemented
3	C₄×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₇₆	—	2	2	no	—
5	C₂×D₁₇₆	C₂²	1	4	yes	—
6	#10622308	—	2	2	no	—
7	C₂×C₁₁×C₃₂	C₂²	1	2	yes	—
8	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	D₃₅₂	—	2	8	no	—
10	C₂×D₈₈	—	2	4	no	—
11	C₂×D₈₈	—	4	2	no	—
12	#66927	—	4	2	no	—
13	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
14	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
15	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
16	D₁₇₆	—	2	8	no	—
17	D₁₇₆	—	4	4	no	—
18	C₁₁×C₃₂	D₄	1	4	yes	complemented
19	#13725	—	11	1	no	maximal, Sylow
20	C₂×D₄₄	—	4	4	no	—
21	C₂×D₄₄	—	8	4	no	—
22	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
23	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
24	C₄²×C₁₁	D₈	1	1	yes	characteristic
25	D₈₈	—	4	4	no	—
26	D₈₈	—	4	4	no	—
27	D₈₈	—	8	4	no	—
28	C₁₁×C₁₆	D₈	1	2	yes	—
29	C₁₁×C₁₆	C₂×D₄	1	2	yes	—
30	C₂×D₃₂	—	11	4	no	—
31	#2246	—	11	2	no	—
32	C₄×C₃₂	D₁₁	1	1	yes	characteristic, complemented
33	C₂²×D₁₁	—	8	4	no	—
34	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
35	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
36	D₄₄	—	8	4	no	—
37	D₄₄	—	8	4	no	—
38	D₄₄	—	16	8	no	—
39	C₈×C₁₁	D₁₆	1	2	yes	—
40	C₈×C₁₁	#127	1	1	yes	characteristic
41	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
42	C₂×D₁₆	—	11	4	no	—
43	C₂×D₁₆	—	22	2	no	—
44	#493	—	22	2	no	—
45	D₃₂	—	22	8	no	—
46	C₂×C₃₂	C₂×D₁₁	1	2	yes	—
47	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
48	C₂²×C₁₁	C₂×D₁₆	1	1	yes	characteristic
49	C₂×D₁₁	—	16	4	no	—
50	C₂×D₁₁	—	16	8	no	—
51	C₄×C₁₁	D₃₂	1	4	yes	complemented
52	C₄×C₁₁	#493	1	1	yes	characteristic
53	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
54	C₂×D₈	—	22	4	no	—
55	C₂×D₈	—	44	2	no	—
56	#127	—	44	2	no	—
57	D₁₆	—	22	8	no	—
58	D₁₆	—	44	4	no	—
59	C₂×C₁₆	D₄₄	1	1	yes	characteristic
60	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
61	C₄×C₈	D₄₄	1	1	yes	characteristic
62	C₃₂	D₄₄	1	4	yes	complemented
63	C₂×C₁₁	#2246	1	1	yes	characteristic
64	C₂×C₁₁	C₂×D₃₂	1	2	yes	—
65	D₁₁	—	32	4	no	—
66	C₂×D₄	—	44	4	no	—
67	C₂×D₄	—	88	4	no	—
68	D₈	—	44	4	no	—
69	D₈	—	44	4	no	—
70	D₈	—	88	4	no	—
71	C₂×C₈	D₈₈	1	1	yes	characteristic
72	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
73	C₄²	D₈₈	1	1	yes	characteristic
74	C₁₆	D₈₈	1	2	yes	—
75	C₁₆	C₂×D₄₄	1	2	yes	—
76	C₁₁	#13725	1	1	yes	characteristic, complemented, Sylow
77	C₂³	—	88	4	no	—
78	D₄	—	88	4	no	—
79	D₄	—	88	4	no	—
80	D₄	—	176	8	no	—
81	C₂×C₄	D₁₇₆	1	2	yes	—
82	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
83	C₈	D₁₇₆	1	2	yes	—
84	C₈	#66927	1	1	yes	characteristic
85	C₈	C₂×D₈₈	1	1	yes	characteristic
86	C₂²	—	176	4	no	—
87	C₂²	—	176	8	no	—
88	C₂²	C₂×D₁₇₆	1	1	yes	characteristic
89	C₄	D₃₅₂	1	4	yes	complemented
90	C₄	#10622308	1	1	yes	characteristic
91	C₄	C₂×D₁₇₆	1	1	yes	characteristic
92	C₂	—	352	4	no	—
93	C₂	#13070866	1	1	yes	characteristic
94	C₂	C₂×D₃₅₂	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₇₆
commutator, cosocle	C₂×C₁₁×C₁₆	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₁
Fitting	C₄×C₁₁×C₃₂	C₂
socle	C₂²×C₁₁	C₂×D₁₆
hypercenter	C₄×C₃₂	D₁₁
hypocenter	C₁₁	#13725
LCS	G ▷ C₂×C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₃₅₂	C₂	semidirect
2. #13070866	C₂	semidirect
3. C₄×C₁₁×C₃₂	C₂	semidirect
18. C₁₁×C₃₂	D₄	semidirect
32. C₄×C₃₂	D₁₁	semidirect
51. C₄×C₁₁	D₃₂	semidirect
62. C₃₂	D₄₄	semidirect
76. C₁₁	#13725	semidirect
89. C₄	D₃₅₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₅₂	2
#13070866	2
C₄×C₁₁×C₃₂	2
#13725	11