Subgroups — #14668488

Order 2816.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070869	C₂	1	4	yes	maximal
2	#13068234	C₂	1	2	yes	maximal
3	C₈×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₈	—	2	8	no	—
5	#10622312	C₂²	1	4	yes	—
6	#10622295	—	2	4	no	—
7	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
8	C₈²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₄₄	—	2	8	no	—
10	#66922	—	2	4	no	—
11	C₂×C₁₁×C₁₆	D₄	1	4	yes	—
12	C₄×C₈×C₁₁	D₄	1	2	yes	—
13	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
14	#66882	—	4	8	no	—
15	Dic₈₈	—	4	16	no	—
16	#12516	—	11	1	no	maximal, Sylow
17	C₂×Dic₂₂	—	4	4	no	—
18	C₂×C₈×C₁₁	D₈	1	4	yes	—
19	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
20	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
21	C₄⋊Dic₁₁	—	4	8	no	—
22	Dic₄₄	—	4	16	no	—
23	C₁₁×C₁₆	D₈	1	8	yes	—
24	#2247	—	11	4	no	—
25	#1713	—	11	2	no	—
26	C₈×C₁₆	D₁₁	1	1	yes	characteristic
27	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
28	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
29	C₂×Dic₁₁	—	8	4	no	—
30	Dic₂₂	—	8	8	no	—
31	C₈×C₁₁	Q₃₂	1	8	yes	complemented
32	C₈×C₁₁	C₂×D₈	1	4	yes	—
33	C₂×Q₃₂	—	22	8	no	—
34	#500	—	22	4	no	—
35	#494	—	11	4	no	—
36	C₄×C₁₆	C₂×D₁₁	1	2	yes	—
37	C₈²	C₂×D₁₁	1	1	yes	characteristic
38	C₂²×C₁₁	#493	1	1	yes	characteristic
39	C₄×C₁₁	#493	1	2	yes	—
40	C₄×C₁₁	C₂×Q₃₂	1	4	yes	—
41	Dic₁₁	—	16	4	no	—
42	C₂×Q₁₆	—	22	8	no	—
43	C₄⋊Q₈	—	22	4	no	—
44	Q₃₂	—	44	16	no	—
45	C₂×C₁₆	D₄₄	1	4	yes	—
46	#107	—	44	8	no	—
47	C₄×C₈	D₄₄	1	2	yes	—
48	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
49	C₂×C₁₁	#1712	1	1	yes	characteristic
50	C₂×C₁₁	#2247	1	2	yes	—
51	C₂×Q₈	—	44	4	no	—
52	Q₁₆	—	44	16	no	—
53	C₂×C₈	D₈₈	1	4	yes	—
54	C₂×C₈	C₂×D₄₄	1	2	yes	—
55	C₄⋊C₄	—	44	8	no	—
56	C₄²	C₂×D₄₄	1	1	yes	characteristic
57	C₁₆	D₈₈	1	8	yes	—
58	C₁₁	#12516	1	1	yes	characteristic, complemented, Sylow
59	Q₈	—	88	8	no	—
60	C₂×C₄	—	88	4	no	—
61	C₂×C₄	#66927	1	1	yes	characteristic
62	C₂×C₄	C₂×D₈₈	1	2	yes	—
63	C₈	Dic₈₈	1	8	yes	complemented
64	C₈	C₂×D₈₈	1	4	yes	—
65	C₂²	#10622308	1	1	yes	characteristic
66	C₄	—	176	4	no	—
67	C₄	#10622308	1	2	yes	—
68	C₄	C₂×Dic₈₈	1	4	yes	—
69	C₂	#13068231	1	1	yes	characteristic
70	C₂	#13070869	1	2	yes	—

	subgroup	G/H
center	C₂²	#10622308
commutator, cosocle	C₄×C₈×C₁₁	C₂³
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₈×C₁₁×C₁₆	C₂
socle, prime radical	C₂²×C₁₁	#493
hypercenter	C₈×C₁₆	D₁₁
hypocenter	C₁₁	#12516
LCS	G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
31. C₈×C₁₁	Q₃₂	semidirect
58. C₁₁	#12516	semidirect
63. C₈	Dic₈₈	semidirect

Maximal subgroups

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

subgroup	index
#13070869	2
#13068234	2
C₈×C₁₁×C₁₆	2
#12516	11