Subgroups — #16790251

Order 3328.

370 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#6092	C₂	1	6	yes	maximal
2	#13114523	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6092	C₂²	1	4	yes	—
4	C₁₃×#376	C₄	1	1	yes	characteristic
5	C₂×#88043	C₄	1	3	yes	—
6	C₂×C₄×#1055	C₂²	1	3	yes	—
7	C₄⋊#6092	—	2	12	no	—
8	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
9	C₂²×#1055	C₂×C₄	1	3	yes	—
10	C₂²×#1055	C₂³	1	1	yes	characteristic
11	C₂×#6092	—	2	12	no	—
12	C₁₃×#95	C₈	1	4	yes	—
13	#88043	—	2	6	no	—
14	C₄×#1055	D₄	1	6	yes	—
15	C₄×#1055	Q₈	1	6	yes	—
16	#12899	—	13	1	no	maximal, Sylow
17	C₂²×C₄×C₁₃	C₂×C₈	1	6	yes	—
18	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
19	C₄²×C₁₃	C₄⋊C₄	1	6	yes	—
20	C₄²×C₁₃	M₁₆	1	6	yes	—
21	C₂×#1055	—	2	6	no	—
22	C₂×#1055	C₄⋊C₄	1	6	yes	—
23	C₂×#1055	C₂×D₄	1	3	yes	—
24	C₂×#1055	C₂×Q₈	1	3	yes	—
25	#6092	—	4	4	no	—
26	C₂×C₄⋊C₁₆	—	13	6	no	—
27	#1726	—	13	1	no	—
28	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₃	—	2	12	no	—
30	C₂×C₄×C₁₃	C₄⋊C₈	1	12	yes	—
31	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
32	C₂×C₄×C₁₃	C₂×M₁₆	1	3	yes	—
33	#1055	—	2	6	no	—
34	#1055	#127	1	1	yes	characteristic
35	#1055	C₄⋊Q₈	1	3	yes	—
36	C₂²×C₁₆	—	13	4	no	—
37	C₂×#97	—	13	3	no	—
38	C₂×C₄×C₈	—	13	3	no	—
39	#376	#261	1	1	yes	characteristic
40	C₄⋊C₁₆	—	26	12	no	—
41	C₂²×C₁₃	C₂×C₄⋊C₈	1	3	yes	—
42	C₂²×C₁₃	#504	1	4	yes	—
43	C₄×C₁₃	—	2	12	no	—
44	C₄×C₁₃	#384	1	1	yes	characteristic
45	C₄×C₁₃	#423	1	3	yes	—
46	C₂²×C₈	—	13	1	no	—
47	C₂²×C₈	—	13	3	no	—
48	C₂×C₄²	C₂×#261	1	3	yes	—
49	C₂×C₁₆	—	26	12	no	—
50	#97	—	26	6	no	—
51	C₄×C₈	—	13	6	no	—
52	C₄×C₈	—	13	6	no	—
53	#95	#1057	1	4	yes	—
54	C₂×C₁₃	#1842	1	1	yes	characteristic
55	C₂×C₁₃	#2151	1	6	yes	—
56	C₂²×C₄	C₂×#1057	1	6	yes	—
57	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
58	C₂×C₈	—	13	3	no	—
59	C₂×C₈	—	13	3	no	—
60	C₂×C₈	—	13	6	no	—
61	C₂×C₈	—	26	6	no	—
62	C₄²	#6118	1	6	yes	—
63	C₄²	C₄⋊#261	1	6	yes	—
64	C₁₆	—	52	4	no	—
65	C₁₃	#12899	1	1	yes	characteristic, complemented, Sylow
66	C₂³	C₂²×#1057	1	1	yes	characteristic
67	C₂×C₄	—	2	12	no	—
68	C₂×C₄	C₄⋊#1057	1	12	yes	—
69	C₂×C₄	C₂×#6118	1	3	yes	—
70	C₂×C₄	C₂×C₄⋊#261	1	3	yes	—
71	C₈	—	13	1	no	—
72	C₈	—	13	3	no	—
73	C₈	—	26	6	no	—
74	C₂²	C₂×C₄⋊#1057	1	3	yes	—
75	C₂²	#11719162	1	4	yes	—
76	C₄	—	2	12	no	—
77	C₄	#11719052	1	3	yes	—
78	C₄	#11719059	1	1	yes	characteristic
79	C₂	#13130768	1	1	yes	characteristic
80	C₂	#13131171	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#261
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₈
Fitting	C₁₃×#376	C₄
cosocle	C₂²×#1055	C₂³
hypercenter	#376	#261
hypocenter	C₁₃	#12899
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
65. C₁₃	#12899	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊#6092	2
#13114523	2
#12899	13