Subgroups — #16847494

Order 3968.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₃₁	C₂	1	1	yes	maximal, characteristic
2	#14521086	C₂	1	2	yes	maximal
3	#14520877	C₂	1	1	yes	maximal, characteristic, complemented
4	#14520874	C₂	1	2	yes	maximal, complemented
5	C₃₁×#367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
7	#11758469	—	2	2	no	—
8	C₂×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
9	C₃₁×#107	C₂²	1	2	yes	—
10	#11758406	C₂²	1	2	yes	—
11	C₂×C₃₁⋊C₁₆	C₂²	1	1	yes	characteristic
12	#11758396	—	2	2	no	—
13	C₁₆×D₃₁	C₄	1	4	yes	complemented
14	C₂×C₄×D₃₁	D₄	1	1	yes	characteristic
15	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₃₁	—	2	2	no	—
17	(C₂×D₃₁)⋊C₄	—	4	2	no	—
18	C₄⋊Dic₃₁	—	2	2	no	—
19	C₄×Dic₃₁	—	4	2	no	—
20	C₂×C₃₁⋊C₈	D₄	1	1	yes	characteristic
21	C₈×D₃₁	C₂×C₄	1	2	yes	—
22	C₈×D₃₁	Q₈	1	2	yes	—
23	C₁₆×C₃₁	C₂×C₄	1	2	yes	—
24	C₃₁⋊C₁₆	C₂×C₄	1	2	yes	—
25	C₂²×D₃₁	D₈	1	1	yes	characteristic
26	C₂×C₄×C₃₁	—	4	2	no	—
27	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₃₁	—	4	2	no	—
29	C₂×Dic₃₁	D₈	1	1	yes	characteristic
30	C₄×D₃₁	C₄⋊C₄	1	2	yes	—
31	C₄×D₃₁	Q₁₆	1	2	yes	—
32	C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₃₁	C₂×Q₈	1	1	yes	characteristic
34	C₃₁⋊C₈	C₄⋊C₄	1	2	yes	—
35	#2158	—	31	1	no	maximal, Sylow
36	C₂²×C₃₁	C₂×D₈	1	1	yes	characteristic
37	C₂×D₃₁	—	2	2	no	—
38	C₂×D₃₁	#107	1	2	yes	—
39	C₄×C₃₁	—	8	2	no	—
40	C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
42	Dic₃₁	—	8	2	no	—
43	Dic₃₁	#107	1	2	yes	—
44	C₂²×C₁₆	—	31	1	no	—
45	#427	—	31	2	no	—
46	#367	—	31	1	no	—
47	#367	D₃₁	1	1	yes	characteristic, complemented
48	#366	—	31	2	no	—
49	C₂×C₃₁	C₂×#107	1	1	yes	characteristic
50	C₂×C₃₁	#508	1	2	yes	—
51	D₃₁	—	2	2	no	—
52	C₂²×C₈	—	31	1	no	—
53	#117	—	62	2	no	—
54	C₂×C₁₆	—	31	1	no	—
55	C₂×C₁₆	—	31	4	no	—
56	C₂×C₁₆	C₂×D₃₁	1	1	yes	characteristic
57	#107	—	31	2	no	—
58	#107	C₂×D₃₁	1	2	yes	—
59	#106	—	62	2	no	—
60	C₃₁	#2158	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	—	31	1	no	—
62	C₂×C₈	—	31	1	no	—
63	C₂×C₈	—	31	2	no	—
64	C₂×C₈	—	31	2	no	—
65	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	62	2	no	—
68	C₂²⋊C₄	—	124	2	no	—
69	C₄²	—	124	2	no	—
70	C₁₆	—	31	2	no	—
71	C₁₆	C₄×D₃₁	1	2	yes	—
72	C₂³	—	31	1	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	31	1	no	—
75	C₂×C₄	—	31	2	no	—
76	C₂×C₄	—	31	2	no	—
77	C₂×C₄	—	124	2	no	—
78	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
79	C₈	—	31	2	no	—
80	C₈	C₂×C₄×D₃₁	1	1	yes	characteristic
81	C₈	Q₈×D₃₁	1	1	yes	characteristic
82	C₂²	—	31	2	no	—
83	C₂²	—	62	2	no	—
84	C₂²	D₈×D₃₁	1	1	yes	characteristic
85	C₄	—	8	2	no	—
86	C₄	—	31	2	no	—
87	C₄	—	248	2	no	—
88	C₄	C₄⋊C₄×D₃₁	1	1	yes	characteristic
89	C₄	Q₁₆×D₃₁	1	1	yes	characteristic
90	C₂	—	62	2	no	—
91	C₂	#107×D₃₁	1	1	yes	characteristic
92	C₂	#14521480	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₃₁
commutator	C₈×C₃₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₁
Fitting	C₃₁×#367	C₂
socle	C₂²×C₃₁	C₂×D₈
prime radical	C₂²×D₃₁	D₈
cosocle	C₂×C₈×C₃₁	C₂³
hypercenter	#367	D₃₁
hypocenter	C₃₁	#2158
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
3. #14520877	C₂	semidirect
4. #14520874	C₂	semidirect
5. C₃₁×#367	C₂	semidirect
13. C₁₆×D₃₁	C₄	semidirect
47. #367	D₃₁	semidirect
60. C₃₁	#2158	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₃₁	2
#14521086	2
#14520877	2
#14520874	2
C₃₁×#367	2
#2158	31