Subgroups — #16843749

Order 3968.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521429	C₂	1	1	yes	maximal, characteristic
2	#14520870	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#364	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₂₄	—	2	1	no	—
5	C₂×Dic₁₂₄	—	2	1	no	—
6	#11758446	C₄	1	2	yes	—
7	C₃₁×M₃₂	—	2	1	no	—
8	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
9	#11758400	—	2	1	no	—
10	C₂×Dic₆₂	—	2	2	no	—
11	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
12	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
13	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₃₁	—	4	2	no	—
15	Dic₁₂₄	—	4	1	no	—
16	Dic₁₂₄	—	4	1	no	—
17	Dic₁₂₄	—	4	1	no	—
18	Dic₁₂₄	—	4	1	no	—
19	C₁₆×C₃₁	—	4	1	no	—
20	C₃₁⋊C₁₆	—	4	1	no	—
21	C₂×C₄×C₃₁	—	2	1	no	—
22	C₂×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₃₁	—	4	2	no	—
24	Dic₆₂	—	4	2	no	—
25	Dic₆₂	—	4	2	no	—
26	C₈×C₃₁	D₈	1	1	yes	characteristic
27	C₈×C₃₁	D₈	1	1	yes	characteristic
28	C₈×C₃₁	SD₁₆	1	1	yes	characteristic
29	C₈×C₃₁	SD₁₆	1	1	yes	characteristic
30	#1358	—	31	1	no	maximal, Sylow
31	C₂²×C₃₁	#100	1	1	yes	characteristic
32	C₄×C₃₁	—	2	2	no	—
33	C₄×C₃₁	#102	1	1	yes	characteristic
34	C₄×C₃₁	#102	1	1	yes	characteristic
35	Dic₃₁	—	8	2	no	—
36	#494	—	31	1	no	—
37	#364	—	31	1	no	—
38	#364	D₃₁	1	1	yes	characteristic
39	C₂×C₃₁	—	2	1	no	—
40	C₂×C₃₁	#331	1	1	yes	characteristic
41	C₂×Q₁₆	—	62	1	no	—
42	C₂×Q₁₆	—	62	1	no	—
43	C₄⋊Q₈	—	31	2	no	—
44	M₃₂	—	2	1	no	—
45	M₃₂	—	62	1	no	—
46	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
47	C₃₁	#1358	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	62	2	no	—
49	Q₁₆	—	124	1	no	—
50	Q₁₆	—	124	1	no	—
51	Q₁₆	—	124	1	no	—
52	Q₁₆	—	124	1	no	—
53	C₂×C₈	D₁₂₄	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₃₁	1	1	yes	characteristic
55	C₄⋊C₄	—	124	2	no	—
56	C₄²	C₄×D₃₁	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₁₆	—	124	1	no	—
59	Q₈	—	124	2	no	—
60	Q₈	—	124	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	124	2	no	—
63	C₂×C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
64	C₈	#92470	1	1	yes	characteristic
65	C₈	D₂₄₈	1	1	yes	characteristic
66	C₈	#92479	1	1	yes	characteristic
67	C₈	#92481	1	1	yes	characteristic
68	C₂²	#11758411	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	248	2	no	—
71	C₄	#11758397	1	1	yes	characteristic
72	C₄	#11758409	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	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	C₂²×C₃₁	#100
cosocle	C₄×C₈×C₃₁	C₂²
hypercenter	#364	D₃₁
hypocenter	C₃₁	#1358
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
47. C₃₁	#1358	semidirect

Maximal subgroups

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

subgroup	index
#14521429	2
#14520870	2
C₃₁×#364	2
#1358	31