Subgroups — #16854108

Order 3968.

648 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758465	C₂	1	6	yes	maximal
2	#14520919	C₂	1	1	yes	maximal, characteristic
3	#14520918	C₂	1	6	yes	maximal
4	C₄²×Dic₃₁	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#384	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₆₂	C₂²	1	4	yes	—
7	C₂×C₄⋊C₄×C₃₁	C₂²	1	6	yes	—
8	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₃₁	C₂²	1	6	yes	—
10	C₂×Dic₃₁⋊C₄	C₂²	1	12	yes	—
11	C₂×C₄×Dic₃₁	C₂²	1	3	yes	—
12	C₂×C₄×Dic₃₁	C₂²	1	3	yes	—
13	#11758465	—	2	24	no	—
14	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
15	C₂²×C₄×C₃₁	C₂³	1	3	yes	—
16	C₂²×Dic₃₁	C₂³	1	4	yes	—
17	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
18	C₂²×Dic₃₁	C₂³	1	3	yes	—
19	C₂×Dic₆₂	—	2	24	no	—
20	C₄⋊C₄×C₃₁	—	2	12	no	—
21	C₄²×C₃₁	Q₈	1	4	yes	complemented
22	C₄⋊Dic₃₁	—	2	12	no	—
23	Dic₃₁⋊C₄	—	2	24	no	—
24	C₄×Dic₃₁	D₄	1	12	yes	—
25	C₄×Dic₃₁	Q₈	1	12	yes	complemented
26	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
27	C₂×C₄×C₃₁	—	2	12	no	—
28	C₂×C₄×C₃₁	C₂×D₄	1	6	yes	—
29	C₂×C₄×C₃₁	C₂×Q₈	1	6	yes	—
30	C₂×C₄×C₃₁	C₂×Q₈	1	6	yes	—
31	C₂×Dic₃₁	—	2	12	no	—
32	C₂×Dic₃₁	C₂×D₄	1	6	yes	—
33	C₂×Dic₃₁	C₂×D₄	1	6	yes	—
34	C₂×Dic₃₁	C₂×Q₈	1	12	yes	—
35	Dic₆₂	—	4	16	no	—
36	#2868	—	31	1	no	maximal, Sylow
37	C₂²×C₃₁	C₂²×D₄	1	3	yes	—
38	C₂²×C₃₁	C₂²×Q₈	1	1	yes	characteristic
39	C₂²×C₃₁	C₂²×Q₈	1	3	yes	—
40	C₄×C₃₁	—	4	4	no	—
41	C₄×C₃₁	C₄⋊Q₈	1	12	yes	complemented
42	Dic₃₁	—	4	4	no	—
43	Dic₃₁	#127	1	4	yes	—
44	Dic₃₁	C₄⋊Q₈	1	12	yes	complemented
45	C₂×C₄⋊Q₈	—	31	6	no	—
46	#384	—	31	6	no	—
47	#384	—	31	1	no	—
48	#384	D₃₁	1	1	yes	characteristic
49	C₄³	—	31	1	no	—
50	C₂×C₃₁	C₂×#127	1	1	yes	characteristic
51	C₂×C₃₁	C₂×C₄⋊Q₈	1	3	yes	—
52	C₂×C₃₁	C₂×C₄⋊Q₈	1	3	yes	—
53	C₂²×Q₈	—	31	4	no	—
54	C₄⋊Q₈	—	62	24	no	—
55	C₂×C₄⋊C₄	—	31	12	no	—
56	C₂×C₄⋊C₄	—	31	6	no	—
57	C₂×C₄⋊C₄	C₂×D₃₁	1	6	yes	—
58	C₂×C₄²	—	31	3	no	—
59	C₂×C₄²	—	31	3	no	—
60	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
61	C₃₁	#2868	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	62	24	no	—
63	C₂²×C₄	—	31	3	no	—
64	C₂²×C₄	—	31	1	no	—
65	C₂²×C₄	—	31	4	no	—
66	C₂²×C₄	C₂²×D₃₁	1	4	yes	—
67	C₂²×C₄	C₂²×D₃₁	1	3	yes	—
68	C₄⋊C₄	—	2	12	no	—
69	C₄⋊C₄	—	62	24	no	—
70	C₄⋊C₄	—	62	12	no	—
71	C₄²	—	31	12	no	—
72	C₄²	—	31	12	no	—
73	C₄²	Dic₆₂	1	4	yes	complemented
74	C₂³	C₂³×D₃₁	1	1	yes	characteristic
75	Q₈	—	124	16	no	—
76	C₂×C₄	—	2	12	no	—
77	C₂×C₄	—	31	6	no	—
78	C₂×C₄	—	31	6	no	—
79	C₂×C₄	—	31	12	no	—
80	C₂×C₄	—	62	12	no	—
81	C₂×C₄	C₂×Dic₆₂	1	6	yes	—
82	C₂×C₄	D₄×D₃₁	1	6	yes	—
83	C₂×C₄	Q₈×D₃₁	1	6	yes	—
84	C₂²	C₂²×Dic₆₂	1	1	yes	characteristic
85	C₂²	C₂×D₄×D₃₁	1	3	yes	—
86	C₂²	C₂×Q₈×D₃₁	1	3	yes	—
87	C₄	—	4	4	no	—
88	C₄	—	31	4	no	—
89	C₄	—	31	12	no	—
90	C₄	—	124	4	no	—
91	C₄	#11758465	1	12	yes	complemented
92	C₂	#127×D₃₁	1	1	yes	characteristic
93	C₂	C₄⋊Q₈×D₃₁	1	3	yes	—
94	C₂	C₂×#11758465	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₁
commutator, socle, prime radical, cosocle	C₂³×C₃₁	C₂⁴
Fitting	C₃₁×#384	C₂
hypercenter	#384	D₃₁
hypocenter	C₃₁	#2868
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ #384

Complements

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

N	H ≅ G/N	type
21. C₄²×C₃₁	Q₈	semidirect
25. C₄×Dic₃₁	Q₈	semidirect
41. C₄×C₃₁	C₄⋊Q₈	semidirect
44. Dic₃₁	C₄⋊Q₈	semidirect
61. C₃₁	#2868	semidirect
73. C₄²	Dic₆₂	semidirect
91. C₄	#11758465	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11758465	2
#14520919	2
#14520918	2
C₄²×Dic₃₁	2
C₃₁×#384	2
#2868	31