Subgroups — #16778190

Order 3328.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129968	C₂	1	2	yes	maximal
2	#13114442	C₂	1	1	yes	maximal, characteristic
3	#11718360	C₄	1	1	yes	characteristic, complemented
4	#11718356	C₂²	1	1	yes	characteristic
5	#11718355	—	2	2	no	—
6	#11718225	—	2	2	no	—
7	C₈²×C₁₃	C₄	1	1	yes	characteristic, complemented
8	C₂×Dic₅₂	—	4	1	no	—
9	C₂×D₁₀₄	—	4	1	no	—
10	#88128	D₄	1	2	yes	—
11	#88123	—	2	1	no	—
12	#88107	—	4	2	no	—
13	C₄×C₈×C₁₃	—	2	1	no	—
14	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	#88061	—	4	4	no	—
16	#7530	—	13	1	no	maximal, Sylow
17	C₂×D₅₂	—	2	2	no	—
18	C₂×D₅₂	—	4	2	no	—
19	C₂×Dic₂₆	—	4	1	no	—
20	C₂²⋊#261	—	8	2	no	—
21	C₂×C₈×C₁₃	—	2	1	no	—
22	C₂×C₈×C₁₃	—	2	2	no	—
23	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₄⋊Dic₁₃	—	4	2	no	—
25	Dic₅₂	—	8	2	no	—
26	D₁₀₄	—	8	2	no	—
27	#1709	—	13	1	no	—
28	#1408	—	13	2	no	—
29	C₂²×D₁₃	—	4	2	no	—
30	C₂×#261	—	16	2	no	—
31	C₂×C₄×C₁₃	—	2	1	no	—
32	C₂×C₄×C₁₃	#99	1	1	yes	characteristic
33	C₂×Dic₁₃	—	8	1	no	—
34	D₅₂	—	8	2	no	—
35	D₅₂	—	8	4	no	—
36	Dic₂₆	—	8	2	no	—
37	C₈×C₁₃	—	2	2	no	—
38	C₈×C₁₃	—	4	2	no	—
39	#494	—	13	1	no	—
40	#493	—	13	1	no	—
41	#486	—	26	2	no	—
42	#353	—	26	2	no	—
43	C₈²	#261	1	1	yes	characteristic, complemented
44	C₂²×C₁₃	#353	1	1	yes	characteristic
45	C₂×D₁₃	—	8	2	no	—
46	C₂×D₁₃	—	16	2	no	—
47	#261	—	32	2	no	—
48	C₄×C₁₃	—	2	2	no	—
49	C₄×C₁₃	—	2	1	no	—
50	Dic₁₃	—	16	1	no	—
51	C₂×Q₁₆	—	52	1	no	—
52	C₂×D₈	—	52	1	no	—
53	C₄⋊Q₈	—	26	1	no	—
54	#127	—	13	2	no	—
55	#102	—	52	4	no	—
56	#99	—	52	2	no	—
57	C₄×C₈	—	2	1	no	—
58	C₄×C₈	C₂×#261	1	1	yes	characteristic
59	C₂×C₁₃	—	2	1	no	—
60	C₂×C₁₃	#1408	1	1	yes	characteristic
61	D₁₃	—	16	2	no	—
62	C₂×Q₈	—	52	1	no	—
63	C₂×D₄	—	26	2	no	—
64	C₂×D₄	—	52	2	no	—
65	Q₁₆	—	104	2	no	—
66	D₈	—	104	2	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	2	2	no	—
69	C₄⋊C₄	—	52	2	no	—
70	C₂²⋊C₄	—	104	2	no	—
71	C₄²	C₂²⋊#261	1	1	yes	characteristic
72	C₁₃	#7530	1	1	yes	characteristic, complemented, Sylow
73	C₂³	—	52	2	no	—
74	Q₈	—	104	2	no	—
75	D₄	—	104	2	no	—
76	D₄	—	104	4	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	104	1	no	—
79	C₂×C₄	—	208	2	no	—
80	C₂×C₄	#88107	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	2	no	—
83	C₂²	—	104	2	no	—
84	C₂²	—	208	2	no	—
85	C₂²	#11718225	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	—	416	2	no	—
89	C₄	—	208	1	no	—
90	C₂	—	2	1	no	—
91	C₂	—	208	2	no	—
92	C₂	#13129968	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13129968
commutator	C₄×C₈×C₁₃	C₂×C₄
Frattini	C₄×C₈	C₂×#261
Fitting	C₈²×C₁₃	C₄
socle	C₂×C₁₃	#1408
prime radical, cosocle	#11718356	C₂²
hypercenter	C₈²	#261
hypocenter	C₁₃	#7530
LCS	G ▷ C₄×C₈×C₁₃ ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
3. #11718360	C₄	semidirect
7. C₈²×C₁₃	C₄	semidirect
43. C₈²	#261	semidirect
72. C₁₃	#7530	semidirect

Maximal subgroups

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

subgroup	index
#13129968	2
#13114442	2
#7530	13