Subgroups — #14674771

Order 2816.

230 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₆	C₂	1	4	yes	maximal
2	#13070869	C₂	1	2	yes	maximal
3	C₄×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₈	—	2	2	no	—
5	C₂×Dic₈₈	C₂²	1	4	yes	—
6	#10622312	—	2	2	no	—
7	C₂×C₁₁×C₃₂	C₂²	1	2	yes	—
8	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	Dic₁₇₆	—	2	8	no	—
10	C₂×Dic₄₄	—	2	4	no	—
11	C₂×Dic₄₄	—	4	2	no	—
12	#66922	—	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	Dic₈₈	—	2	8	no	—
17	Dic₈₈	—	4	4	no	—
18	C₁₁×C₃₂	D₄	1	4	yes	—
19	#13726	—	11	1	no	maximal, Sylow
20	C₂×Dic₂₂	—	4	4	no	—
21	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
22	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
23	C₄²×C₁₁	D₈	1	1	yes	characteristic
24	C₄⋊Dic₁₁	—	8	4	no	—
25	Dic₄₄	—	4	4	no	—
26	Dic₄₄	—	4	4	no	—
27	Dic₄₄	—	8	4	no	—
28	C₁₁×C₁₆	D₈	1	2	yes	—
29	C₁₁×C₁₆	C₂×D₄	1	2	yes	—
30	C₂×Q₆₄	—	11	4	no	—
31	#2247	—	11	2	no	—
32	C₄×C₃₂	D₁₁	1	1	yes	characteristic
33	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
34	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
35	C₂×Dic₁₁	—	8	4	no	—
36	Dic₂₂	—	8	4	no	—
37	Dic₂₂	—	8	4	no	—
38	C₈×C₁₁	D₁₆	1	2	yes	—
39	C₈×C₁₁	#127	1	1	yes	characteristic
40	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
41	C₂×Q₃₂	—	11	4	no	—
42	C₂×Q₃₂	—	22	2	no	—
43	#494	—	22	2	no	—
44	Q₆₄	—	22	8	no	—
45	C₂×C₃₂	C₂×D₁₁	1	2	yes	—
46	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
47	C₂²×C₁₁	C₂×D₁₆	1	1	yes	characteristic
48	C₄×C₁₁	Q₆₄	1	4	yes	complemented
49	C₄×C₁₁	#493	1	1	yes	characteristic
50	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
51	Dic₁₁	—	16	4	no	—
52	C₂×Q₁₆	—	22	4	no	—
53	C₂×Q₁₆	—	44	2	no	—
54	C₄⋊Q₈	—	44	2	no	—
55	Q₃₂	—	22	8	no	—
56	Q₃₂	—	44	4	no	—
57	C₂×C₁₆	D₄₄	1	1	yes	characteristic
58	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
59	C₄×C₈	D₄₄	1	1	yes	characteristic
60	C₃₂	D₄₄	1	4	yes	—
61	C₂×C₁₁	#2246	1	1	yes	characteristic
62	C₂×C₁₁	C₂×Q₆₄	1	2	yes	—
63	C₂×Q₈	—	44	4	no	—
64	Q₁₆	—	44	4	no	—
65	Q₁₆	—	44	4	no	—
66	Q₁₆	—	88	4	no	—
67	C₂×C₈	D₈₈	1	1	yes	characteristic
68	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
69	C₄⋊C₄	—	88	4	no	—
70	C₄²	D₈₈	1	1	yes	characteristic
71	C₁₆	D₈₈	1	2	yes	—
72	C₁₆	C₂×D₄₄	1	2	yes	—
73	C₁₁	#13726	1	1	yes	characteristic, complemented, Sylow
74	Q₈	—	88	4	no	—
75	Q₈	—	88	4	no	—
76	C₂×C₄	—	88	4	no	—
77	C₂×C₄	D₁₇₆	1	2	yes	—
78	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
79	C₈	D₁₇₆	1	2	yes	—
80	C₈	#66927	1	1	yes	characteristic
81	C₈	C₂×D₈₈	1	1	yes	characteristic
82	C₂²	C₂×D₁₇₆	1	1	yes	characteristic
83	C₄	—	176	4	no	—
84	C₄	Dic₁₇₆	1	4	yes	complemented
85	C₄	#10622308	1	1	yes	characteristic
86	C₄	C₂×D₁₇₆	1	1	yes	characteristic
87	C₂	#13070866	1	1	yes	characteristic
88	C₂	C₂×Dic₁₇₆	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, prime radical	C₂²×C₁₁	C₂×D₁₆
hypercenter	C₄×C₃₂	D₁₁
hypocenter	C₁₁	#13726
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
48. C₄×C₁₁	Q₆₄	semidirect
73. C₁₁	#13726	semidirect
84. C₄	Dic₁₇₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₇₆	2
#13070869	2
C₄×C₁₁×C₃₂	2
#13726	11