Subgroups — #16845342

Order 3968.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521447	C₂	1	1	yes	maximal, characteristic
2	#14521445	C₂	1	2	yes	maximal
3	#14521401	C₂	1	2	yes	maximal
4	#14520770	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#494	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₃₁	—	2	2	no	—
7	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	#11758446	C₂²	1	2	yes	—
10	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	#11758405	—	2	2	no	—
12	#11758398	—	2	4	no	—
13	#11758396	—	2	4	no	—
14	C₄×C₃₁⋊C₈	C₂²	1	2	yes	—
15	C₂×Q₈×C₃₁	—	2	1	no	—
16	C₂×Q₈×C₃₁	—	2	1	no	—
17	C₂×Dic₆₂	—	2	2	no	—
18	Q₁₆×C₃₁	—	4	4	no	—
19	C₂×C₈×C₃₁	D₄	1	2	yes	—
20	C₄⋊C₄×C₃₁	—	2	2	no	—
21	C₄⋊C₄×C₃₁	—	2	2	no	—
22	C₄²×C₃₁	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₃₁	—	2	2	no	—
24	C₄⋊Dic₃₁	—	2	2	no	—
25	C₂×C₃₁⋊C₈	D₄	1	4	yes	—
26	Q₈×C₃₁	—	4	2	no	—
27	Q₈×C₃₁	—	4	2	no	—
28	C₂×C₄×C₃₁	—	4	1	no	—
29	C₂×C₄×C₃₁	—	4	1	no	—
30	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
31	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₃₁	—	4	2	no	—
33	Dic₆₂	—	4	4	no	—
34	C₈×C₃₁	SD₁₆	1	4	yes	—
35	C₃₁⋊C₈	—	2	4	no	—
36	#1716	—	31	1	no	maximal, Sylow
37	C₂²×C₃₁	#127	1	1	yes	characteristic
38	C₄×C₃₁	—	8	1	no	—
39	C₄×C₃₁	—	8	1	no	—
40	C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
41	C₄×C₃₁	#137	1	4	yes	—
42	Dic₃₁	—	8	2	no	—
43	#498	—	31	2	no	—
44	#498	—	31	1	no	—
45	#494	D₃₁	1	1	yes	characteristic
46	#487	—	31	2	no	—
47	#322	—	31	1	no	—
48	C₂×C₃₁	#492	1	1	yes	characteristic
49	C₂×C₃₁	#497	1	2	yes	—
50	C₂×Q₁₆	—	2	2	no	—
51	C₄⋊Q₈	—	31	2	no	—
52	C₄⋊Q₈	C₂×D₃₁	1	1	yes	characteristic
53	C₄⋊Q₈	C₂×D₃₁	1	1	yes	characteristic
54	#106	—	62	4	no	—
55	#106	—	62	2	no	—
56	#103	—	62	4	no	—
57	C₄×C₈	—	31	2	no	—
58	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
59	C₃₁	#1716	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	2	1	no	—
62	C₂×Q₈	—	62	2	no	—
63	Q₁₆	—	4	4	no	—
64	C₂×C₈	—	31	4	no	—
65	C₂×C₈	C₂²⋊D₃₁	1	2	yes	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	62	2	no	—
69	C₄⋊C₄	—	62	2	no	—
70	C₄²	C₂²×D₃₁	1	1	yes	characteristic
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	Q₈	—	124	4	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	124	2	no	—
77	C₂×C₄	D₄×D₃₁	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
79	C₈	—	62	4	no	—
80	C₈	#92480	1	4	yes	—
81	C₂²	#11758517	1	1	yes	characteristic
82	C₄	—	8	1	no	—
83	C₄	—	8	1	no	—
84	C₄	—	248	2	no	—
85	C₄	#11758495	1	4	yes	—
86	C₄	C₂×#92480	1	2	yes	—
87	C₂	#14521421	1	1	yes	characteristic
88	C₂	#14521442	1	2	yes	—

	subgroup	G/H
center	C₂²	#11758517
commutator, cosocle	C₄²×C₃₁	C₂³
Frattini	C₄²	C₂²×D₃₁
Fitting	C₃₁×#494	C₂
socle, prime radical	C₂²×C₃₁	#127
hypercenter	#494	D₃₁
hypocenter	C₃₁	#1716
LCS	G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
59. C₃₁	#1716	semidirect

Maximal subgroups

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

subgroup	index
#14521447	2
#14521445	2
#14521401	2
#14520770	2
C₃₁×#494	2
#1716	31