Subgroups — #16777004

Order 3328.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129866	C₂	1	2	yes	maximal
2	#13114452	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#494	C₄	1	1	yes	characteristic
4	#11718739	—	2	2	no	—
5	#11718360	C₄	1	1	yes	characteristic
6	C₄⋊#6092	—	2	2	no	—
7	C₈×#1055	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×Q₁₆	—	4	1	no	—
9	C₁₃×C₄⋊Q₈	—	2	1	no	—
10	C₂×Dic₅₂	—	4	1	no	—
11	#88123	—	2	1	no	—
12	C₂×#6092	—	4	2	no	—
13	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	#88047	—	4	2	no	—
15	#88047	—	4	2	no	—
16	C₄×#1055	D₄	1	2	yes	—
17	#7098	—	13	1	no	maximal, Sylow
18	C₂×Q₈×C₁₃	—	4	1	no	—
19	C₂×Dic₂₆	—	4	1	no	—
20	C₁₃×Q₁₆	—	8	2	no	—
21	C₂×C₈×C₁₃	—	2	1	no	—
22	C₁₃×C₄⋊C₄	—	4	2	no	—
23	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₄⋊Dic₁₃	—	4	2	no	—
25	C₂×#1055	D₈	1	2	yes	—
26	C₂×#1055	SD₁₆	1	2	yes	—
27	Dic₅₂	—	8	2	no	—
28	#6092	—	8	2	no	—
29	#1713	—	13	1	no	—
30	#1370	—	13	2	no	—
31	Q₈×C₁₃	—	8	2	no	—
32	C₂×C₄×C₁₃	—	8	1	no	—
33	C₂×C₄×C₁₃	#100	1	1	yes	characteristic
34	C₂×C₄×C₁₃	#102	1	2	yes	—
35	C₂×Dic₁₃	—	8	1	no	—
36	Dic₂₆	—	8	2	no	—
37	C₈×C₁₃	—	2	2	no	—
38	#1055	—	2	2	no	—
39	#1055	SD₃₂	1	2	yes	—
40	#1055	Q₃₂	1	2	yes	—
41	#500	—	26	2	no	—
42	#494	—	13	1	no	—
43	#494	#261	1	1	yes	characteristic
44	C₄⋊C₁₆	—	26	2	no	—
45	C₈²	—	13	1	no	—
46	C₂²×C₁₃	#331	1	1	yes	characteristic
47	C₄×C₁₃	—	2	1	no	—
48	C₄×C₁₃	—	16	1	no	—
49	C₄×C₁₃	#358	1	2	yes	—
50	C₄×C₁₃	#362	1	2	yes	—
51	Dic₁₃	—	16	1	no	—
52	C₂×Q₁₆	—	4	1	no	—
53	C₂×Q₁₆	—	52	1	no	—
54	C₄⋊Q₈	—	2	1	no	—
55	C₄⋊Q₈	—	26	1	no	—
56	C₂×C₁₆	—	52	2	no	—
57	#107	—	52	2	no	—
58	#107	—	52	2	no	—
59	C₄×C₈	—	13	2	no	—
60	C₄×C₈	C₂×#261	1	1	yes	characteristic
61	C₂×C₁₃	#1357	1	1	yes	characteristic
62	C₂×C₁₃	#1362	1	2	yes	—
63	C₂×Q₈	—	4	1	no	—
64	C₂×Q₈	—	52	1	no	—
65	Q₁₆	—	8	2	no	—
66	Q₁₆	—	104	2	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	13	2	no	—
69	C₂×C₈	—	13	2	no	—
70	C₄⋊C₄	—	4	2	no	—
71	C₄⋊C₄	—	52	2	no	—
72	C₄²	C₂²⋊#261	1	1	yes	characteristic
73	C₁₆	—	104	2	no	—
74	C₁₃	#7098	1	1	yes	characteristic, complemented, Sylow
75	Q₈	—	8	2	no	—
76	Q₈	—	104	2	no	—
77	C₂×C₄	—	8	1	no	—
78	C₂×C₄	—	104	1	no	—
79	C₂×C₄	#88115	1	2	yes	—
80	C₂×C₄	#88121	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	13	2	no	—
83	C₈	—	13	2	no	—
84	C₈	—	26	2	no	—
85	C₂²	#11718297	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	16	1	no	—
88	C₄	—	208	1	no	—
89	C₄	#11718280	1	2	yes	—
90	C₄	#11718282	1	2	yes	—
91	C₂	#13129844	1	1	yes	characteristic
92	C₂	#13129851	1	2	yes	—

	subgroup	G/H
center	C₂²	#11718297
commutator	C₄×C₈×C₁₃	C₂×C₄
Frattini	C₄×C₈	C₂×#261
Fitting	C₁₃×#494	C₄
socle, prime radical	C₂²×C₁₃	#331
cosocle	C₈×#1055	C₂²
hypercenter	#494	#261
hypocenter	C₁₃	#7098
LCS	G ▷ C₄×C₈×C₁₃ ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
74. C₁₃	#7098	semidirect

Maximal subgroups

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

subgroup	index
#13129866	2
#13114452	2
#7098	13