Subgroups — #16845312

Order 3968.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521447	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521422	C₂	1	1	yes	maximal, characteristic
3	#14521400	C₂	1	2	yes	maximal, complemented
4	#14521396	C₂	1	2	yes	maximal
5	C₈²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#92470	—	2	2	no	—
7	#11758451	C₂²	1	1	yes	characteristic
8	#11758446	C₂²	1	2	yes	—
9	#11758446	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₃₁	C₂²	1	2	yes	—
11	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	#11758409	—	2	4	no	—
13	#11758405	—	2	2	no	—
14	#11758404	—	2	4	no	—
15	C₂×D₁₂₄	—	2	2	no	—
16	C₂×D₁₂₄	—	2	1	no	—
17	C₂×Dic₆₂	—	2	2	no	—
18	C₂×Dic₆₂	—	2	1	no	—
19	C₂×C₈×C₃₁	D₄	1	4	yes	—
20	C₂×C₈×C₃₁	D₄	1	2	yes	—
21	C₄²×C₃₁	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₃₁	—	2	2	no	—
23	C₄⋊Dic₃₁	—	2	2	no	—
24	C₄⋊Dic₃₁	—	2	2	no	—
25	#92470	—	4	4	no	—
26	C₂²×D₃₁	—	4	1	no	—
27	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
29	C₂×Dic₃₁	—	4	1	no	—
30	C₂×Dic₃₁	—	4	2	no	—
31	D₁₂₄	—	4	2	no	—
32	D₁₂₄	—	4	4	no	—
33	Dic₆₂	—	4	2	no	—
34	Dic₆₂	—	4	4	no	—
35	C₈×C₃₁	—	2	4	no	—
36	C₈×C₃₁	SD₁₆	1	4	yes	—
37	#1708	—	31	1	no	maximal, Sylow
38	C₂²×C₃₁	#127	1	1	yes	characteristic
39	C₂×D₃₁	—	8	1	no	—
40	C₂×D₃₁	—	8	2	no	—
41	C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
42	C₄×C₃₁	#135	1	4	yes	—
43	Dic₃₁	—	8	1	no	—
44	Dic₃₁	—	8	2	no	—
45	#498	—	31	1	no	—
46	#492	—	31	1	no	—
47	#487	—	31	2	no	—
48	#486	—	31	2	no	—
49	C₈²	D₃₁	1	1	yes	characteristic, complemented
50	C₂×C₃₁	#492	1	1	yes	characteristic
51	C₂×C₃₁	#495	1	2	yes	—
52	D₃₁	—	16	1	no	—
53	C₂×SD₁₆	—	62	2	no	—
54	C₄⋊Q₈	—	31	2	no	—
55	C₄⋊Q₈	—	31	1	no	—
56	#127	—	31	1	no	—
57	#106	—	62	2	no	—
58	#103	—	62	4	no	—
59	#102	—	62	4	no	—
60	C₄×C₈	C₂×D₃₁	1	2	yes	—
61	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
62	C₃₁	#1708	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₈	—	62	2	no	—
64	C₂×Q₈	—	62	1	no	—
65	C₂×D₄	—	62	2	no	—
66	C₂×D₄	—	62	1	no	—
67	SD₁₆	—	124	4	no	—
68	C₂×C₈	D₁₂₄	1	4	yes	—
69	C₂×C₈	D₁₂₄	1	2	yes	—
70	C₄⋊C₄	—	62	2	no	—
71	C₄⋊C₄	—	62	2	no	—
72	C₄⋊C₄	—	62	2	no	—
73	C₄²	C₂²×D₃₁	1	1	yes	characteristic
74	C₂³	—	124	1	no	—
75	Q₈	—	124	2	no	—
76	Q₈	—	124	4	no	—
77	D₄	—	124	2	no	—
78	D₄	—	124	4	no	—
79	C₂×C₄	—	124	1	no	—
80	C₂×C₄	—	124	2	no	—
81	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
82	C₂×C₄	C₂×D₁₂₄	1	2	yes	—
83	C₈	—	2	4	no	—
84	C₈	#92470	1	4	yes	—
85	C₂²	—	248	1	no	—
86	C₂²	—	248	2	no	—
87	C₂²	#11758451	1	1	yes	characteristic
88	C₄	—	248	1	no	—
89	C₄	—	248	2	no	—
90	C₄	C₂×#92470	1	2	yes	—
91	C₄	#11758481	1	4	yes	—
92	C₂	—	496	1	no	—
93	C₂	#14521422	1	1	yes	characteristic
94	C₂	#14521433	1	2	yes	—

	subgroup	G/H
center	C₂²	#11758451
commutator, cosocle	C₄²×C₃₁	C₂³
Frattini	C₄²	C₂²×D₃₁
Fitting	C₈²×C₃₁	C₂
socle	C₂²×C₃₁	#127
prime radical	#11758451	C₂²
hypercenter	C₈²	D₃₁
hypocenter	C₃₁	#1708
LCS	G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #14521447	C₂	semidirect
3. #14521400	C₂	semidirect
5. C₈²×C₃₁	C₂	semidirect
49. C₈²	D₃₁	semidirect
62. C₃₁	#1708	semidirect

Maximal subgroups

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

subgroup	index
#14521447	2
#14521422	2
#14521400	2
#14521396	2
C₈²×C₃₁	2
#1708	31