Subgroups — #16856235

Order 3968.

348 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521606	C₂	1	2	yes	maximal
2	#14521458	C₂	1	8	yes	maximal, complemented
3	#14521087	C₂	1	4	yes	maximal
4	C₂×C₃₁×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₃₁	C₂²	1	2	yes	—
6	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
7	#11758503	C₂²	1	4	yes	—
8	#11758501	—	2	4	no	—
9	#11758447	C₂²	1	4	yes	—
10	#11758446	C₂²	1	4	yes	—
11	C₄×Dic₆₂	—	2	4	no	—
12	C₃₁×#97	C₂²	1	4	yes	—
13	#11758406	C₂²	1	8	yes	—
14	#11758405	C₂²	1	8	yes	—
15	C₂²×C₄×C₃₁	D₄	1	2	yes	—
16	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
17	C₂×Dic₆₂	—	2	4	no	—
18	C₂×C₈×C₃₁	Q₈	1	8	yes	complemented
19	C₂×C₈×C₃₁	C₂³	1	4	yes	—
20	C₄²×C₃₁	D₄	1	2	yes	—
21	C₄²×C₃₁	C₂³	1	2	yes	—
22	C₂²⋊Dic₃₁	—	2	4	no	—
23	C₄⋊Dic₃₁	—	2	4	no	—
24	C₄⋊Dic₃₁	C₂³	1	8	yes	—
25	Dic₃₁⋊C₄	—	2	8	no	—
26	C₄×Dic₃₁	—	2	4	no	—
27	C₂³×C₃₁	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₃₁	—	4	2	no	—
29	C₂×C₄×C₃₁	C₂×D₄	1	4	yes	—
30	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₃₁	C₂×Q₈	1	4	yes	—
32	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
33	C₂×Dic₃₁	—	2	8	no	—
34	Dic₆₂	—	4	8	no	—
35	C₈×C₃₁	C₂×Q₈	1	8	yes	—
36	#3162	—	31	1	no	maximal, Sylow
37	C₂²×C₃₁	—	2	2	no	—
38	C₂²×C₃₁	C₄⋊Q₈	1	2	yes	—
39	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
40	C₄×C₃₁	—	2	4	no	—
41	C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
42	C₄×C₃₁	C₂²×Q₈	1	2	yes	—
43	Dic₃₁	—	4	8	no	—
44	#533	—	31	2	no	—
45	#501	—	31	8	no	—
46	#427	—	31	4	no	—
47	C₂×#97	D₃₁	1	1	yes	characteristic
48	C₂×C₃₁	—	2	2	no	—
49	C₂×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
50	C₂×C₃₁	#575	1	2	yes	—
51	C₂²×C₈	C₂×D₃₁	1	2	yes	—
52	C₄⋊Q₈	—	31	4	no	—
53	#125	—	31	4	no	—
54	C₂²⋊Q₈	—	62	4	no	—
55	C₄×Q₈	—	62	4	no	—
56	#117	—	31	4	no	—
57	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
58	#107	—	31	8	no	—
59	#106	—	31	8	no	—
60	#97	C₂×D₃₁	1	4	yes	—
61	C₃₁	#3162	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	62	4	no	—
63	C₂²×C₄	D₁₂₄	1	2	yes	—
64	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
65	C₂×C₈	Dic₆₂	1	8	yes	complemented
66	C₂×C₈	C₂²×D₃₁	1	4	yes	—
67	C₄⋊C₄	—	31	8	no	—
68	C₄⋊C₄	—	62	8	no	—
69	C₄⋊C₄	—	62	4	no	—
70	C₂²⋊C₄	—	62	4	no	—
71	C₄²	—	62	4	no	—
72	C₄²	D₁₂₄	1	2	yes	—
73	C₄²	C₂²×D₃₁	1	2	yes	—
74	C₂³	C₂×D₁₂₄	1	1	yes	characteristic
75	Q₈	—	124	8	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	—	62	8	no	—
78	C₂×C₄	C₂×Dic₆₂	1	4	yes	—
79	C₂×C₄	C₂×D₁₂₄	1	4	yes	—
80	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
81	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
82	C₈	C₂×Dic₆₂	1	8	yes	—
83	C₂²	—	2	2	no	—
84	C₂²	#11758446	1	2	yes	—
85	C₂²	C₂²×D₁₂₄	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	—	124	8	no	—
88	C₄	#11758446	1	2	yes	—
89	C₄	C₂²×Dic₆₂	1	2	yes	—
90	C₂	—	2	2	no	—
91	C₂	C₂×#11758446	1	1	yes	characteristic
92	C₂	#14521849	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₂₄
commutator, cosocle	C₂×C₄×C₃₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₃₁
Fitting	C₂×C₃₁×#97	C₂
socle	C₂²×C₃₁	C₂²×D₄
prime radical	C₂³×C₃₁	C₂×D₄
hypercenter	C₂×#97	D₃₁
hypocenter	C₃₁	#3162
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
2. #14521458	C₂	semidirect
18. C₂×C₈×C₃₁	Q₈	semidirect
61. C₃₁	#3162	semidirect
65. C₂×C₈	Dic₆₂	semidirect

Maximal subgroups

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

subgroup	index
#14521606	2
#14521458	2
#14521087	2
C₂×C₃₁×#97	2
#3162	31