Subgroups — #16843751

Order 3968.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521422	C₂	1	1	yes	maximal, characteristic
2	#14520870	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#92470	—	2	1	no	—
5	C₂×#92470	—	2	1	no	—
6	#11758451	C₄	1	1	yes	characteristic
7	#11758446	C₄	1	1	yes	characteristic
8	C₃₁×M₃₂	—	2	1	no	—
9	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	#11758400	—	2	1	no	—
11	C₂×D₁₂₄	—	2	1	no	—
12	C₂×D₁₂₄	—	4	1	no	—
13	C₂×Dic₆₂	—	2	1	no	—
14	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
15	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
16	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
17	C₄⋊Dic₃₁	—	4	1	no	—
18	#92470	—	4	1	no	—
19	#92470	—	4	1	no	—
20	#92470	—	4	1	no	—
21	#92470	—	4	1	no	—
22	C₁₆×C₃₁	—	4	1	no	—
23	C₃₁⋊C₁₆	—	4	1	no	—
24	C₂²×D₃₁	—	4	1	no	—
25	C₂×C₄×C₃₁	—	2	1	no	—
26	C₂×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₃₁	—	4	1	no	—
28	D₁₂₄	—	4	1	no	—
29	D₁₂₄	—	4	1	no	—
30	D₁₂₄	—	8	2	no	—
31	Dic₆₂	—	4	1	no	—
32	Dic₆₂	—	4	1	no	—
33	C₈×C₃₁	D₈	1	1	yes	characteristic
34	C₈×C₃₁	D₈	1	1	yes	characteristic
35	C₈×C₃₁	SD₁₆	1	1	yes	characteristic
36	C₈×C₃₁	SD₁₆	1	1	yes	characteristic
37	#1359	—	31	1	no	maximal, Sylow
38	C₂²×C₃₁	#100	1	1	yes	characteristic
39	C₂×D₃₁	—	8	2	no	—
40	C₂×D₃₁	—	8	1	no	—
41	C₄×C₃₁	—	2	2	no	—
42	C₄×C₃₁	#102	1	1	yes	characteristic
43	C₄×C₃₁	#102	1	1	yes	characteristic
44	Dic₃₁	—	8	1	no	—
45	#492	—	31	1	no	—
46	#364	—	31	1	no	—
47	#364	D₃₁	1	1	yes	characteristic, complemented
48	C₂×C₃₁	—	2	1	no	—
49	C₂×C₃₁	#331	1	1	yes	characteristic
50	D₃₁	—	16	1	no	—
51	C₂×SD₁₆	—	62	1	no	—
52	C₂×SD₁₆	—	62	1	no	—
53	C₄⋊Q₈	—	31	1	no	—
54	#127	—	31	1	no	—
55	M₃₂	—	2	1	no	—
56	M₃₂	—	62	1	no	—
57	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
58	C₃₁	#1359	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	62	1	no	—
60	C₂×D₄	—	62	1	no	—
61	C₂×D₄	—	124	1	no	—
62	SD₁₆	—	124	1	no	—
63	SD₁₆	—	124	1	no	—
64	SD₁₆	—	124	1	no	—
65	SD₁₆	—	124	1	no	—
66	C₂×C₈	D₁₂₄	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₃₁	1	1	yes	characteristic
68	C₄⋊C₄	—	124	1	no	—
69	C₄²	C₄×D₃₁	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	124	1	no	—
72	C₂³	—	124	1	no	—
73	Q₈	—	124	1	no	—
74	Q₈	—	124	1	no	—
75	D₄	—	124	1	no	—
76	D₄	—	124	1	no	—
77	D₄	—	248	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	124	1	no	—
80	C₂×C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
81	C₈	#92470	1	1	yes	characteristic
82	C₈	D₂₄₈	1	1	yes	characteristic
83	C₈	#92479	1	1	yes	characteristic
84	C₈	#92481	1	1	yes	characteristic
85	C₂²	—	248	2	no	—
86	C₂²	—	248	1	no	—
87	C₂²	#11758411	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	248	1	no	—
90	C₄	#11758397	1	1	yes	characteristic
91	C₄	#11758409	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	496	1	no	—
94	C₂	#14520792	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14520792
commutator	C₄²×C₃₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₃₁
Fitting	C₃₁×#364	C₂
socle	C₂×C₃₁	#331
prime radical	#11758451	C₄
cosocle	C₄×C₈×C₃₁	C₂²
hypercenter	#364	D₃₁
hypocenter	C₃₁	#1359
LCS	G ▷ C₄²×C₃₁ ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #14520870	C₂	semidirect
3. C₃₁×#364	C₂	semidirect
47. #364	D₃₁	semidirect
58. C₃₁	#1359	semidirect

Maximal subgroups

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

subgroup	index
#14521422	2
#14520870	2
C₃₁×#364	2
#1359	31