Subgroups — #16844437

Order 3968.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521106	C₂	1	2	yes	maximal
2	#14520798	C₂	1	4	yes	maximal, complemented
3	C₂×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₂²×Q₈×C₃₁	C₄	1	2	yes	—
5	C₃₁×C₄⋊Q₈	—	2	2	no	—
6	C₃₁×C₄⋊Q₈	C₄	1	2	yes	—
7	C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
9	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²⋊(C₃₁⋊C₈)	—	2	2	no	—
11	C₄⋊(C₃₁⋊C₈)	C₂²	1	4	yes	—
12	#11758391	—	2	2	no	—
13	C₂×Q₈×C₃₁	—	2	2	no	—
14	C₂×Q₈×C₃₁	—	4	4	no	—
15	C₂×Q₈×C₃₁	C₂×C₄	1	4	yes	—
16	C₂²×C₄×C₃₁	—	2	2	no	—
17	C₂²×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₃₁	D₄	1	2	yes	—
19	C₄⋊C₄×C₃₁	—	2	4	no	—
20	C₄⋊C₄×C₃₁	—	2	4	no	—
21	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₃₁	D₄	1	2	yes	—
23	C₄²×C₃₁	C₂³	1	1	yes	characteristic
24	C₂×C₃₁⋊C₈	—	2	4	no	—
25	C₂³×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
26	Q₈×C₃₁	—	4	4	no	—
27	Q₈×C₃₁	—	4	4	no	—
28	C₂×C₄×C₃₁	—	2	2	no	—
29	C₂×C₄×C₃₁	—	2	4	no	—
30	C₂×C₄×C₃₁	—	2	4	no	—
31	C₂×C₄×C₃₁	—	4	4	no	—
32	C₂×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
33	C₂×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
36	C₃₁⋊C₈	—	4	4	no	—
37	#1558	—	31	1	no	maximal, Sylow
38	C₂²×C₃₁	—	2	2	no	—
39	C₂²×C₃₁	#100	1	2	yes	—
40	C₂²×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₄×C₃₁	—	2	1	no	—
42	C₄×C₃₁	—	2	1	no	—
43	C₄×C₃₁	—	2	2	no	—
44	C₄×C₃₁	—	4	4	no	—
45	C₄×C₃₁	#137	1	4	yes	—
46	C₂×C₄⋊Q₈	D₃₁	1	1	yes	characteristic
47	#432	—	31	2	no	—
48	#333	—	31	4	no	—
49	C₂×C₃₁	—	2	2	no	—
50	C₂×C₃₁	C₂×#100	1	1	yes	characteristic
51	C₂×C₃₁	#419	1	2	yes	—
52	C₂²×Q₈	Dic₃₁	1	2	yes	—
53	C₄⋊Q₈	—	2	2	no	—
54	C₄⋊Q₈	Dic₃₁	1	2	yes	—
55	C₄⋊Q₈	C₂×D₃₁	1	2	yes	—
56	C₂×C₄⋊C₄	—	2	2	no	—
57	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
58	C₄⋊C₈	—	31	4	no	—
59	C₂²⋊C₈	—	62	2	no	—
60	#97	—	62	2	no	—
61	C₃₁	#1558	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	2	2	no	—
63	C₂×Q₈	—	4	4	no	—
64	C₂×Q₈	C₂×Dic₃₁	1	4	yes	—
65	C₂²×C₄	—	2	2	no	—
66	C₂²×C₄	C₂×Dic₃₁	1	1	yes	characteristic
67	C₂²×C₄	C₂²⋊D₃₁	1	2	yes	—
68	C₂×C₈	—	62	4	no	—
69	C₄⋊C₄	—	2	4	no	—
70	C₄⋊C₄	—	2	4	no	—
71	C₄²	C₂×Dic₃₁	1	1	yes	characteristic
72	C₄²	C₂²⋊D₃₁	1	2	yes	—
73	C₄²	C₂²×D₃₁	1	1	yes	characteristic
74	C₂³	C₂²⋊Dic₃₁	1	1	yes	characteristic
75	Q₈	—	4	4	no	—
76	Q₈	—	4	4	no	—
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	2	4	no	—
79	C₂×C₄	—	2	4	no	—
80	C₂×C₄	—	4	4	no	—
81	C₂×C₄	C₂²⋊Dic₃₁	1	2	yes	—
82	C₂×C₄	C₂²⋊Dic₃₁	1	1	yes	characteristic
83	C₂×C₄	C₂²×Dic₃₁	1	1	yes	characteristic
84	C₂×C₄	C₂×C₂²⋊D₃₁	1	2	yes	—
85	C₈	—	124	4	no	—
86	C₂²	—	2	2	no	—
87	C₂²	#11758421	1	2	yes	—
88	C₂²	C₂×C₂²⋊Dic₃₁	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	2	1	no	—
91	C₄	—	2	2	no	—
92	C₄	—	4	4	no	—
93	C₄	#11758519	1	4	yes	—
94	C₂	—	2	2	no	—
95	C₂	C₂×#11758421	1	1	yes	characteristic
96	C₂	#14521058	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₃₁
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₄²	C₂²×D₃₁
Fitting	C₂×C₃₁×C₄⋊Q₈	C₂
socle	C₂²×C₃₁	C₂×C₂²⋊C₄
prime radical	C₂³×C₃₁	C₂²⋊C₄
cosocle	C₄²×C₃₁	C₂³
hypercenter	C₂×C₄⋊Q₈	D₃₁
hypocenter	C₃₁	#1558
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #14520798	C₂	semidirect
61. C₃₁	#1558	semidirect

Maximal subgroups

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

subgroup	index
#14521106	2
#14520798	2
C₂×C₃₁×C₄⋊Q₈	2
#1558	31