Subgroups — #16847598

Order 3968.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521481	C₂	1	1	yes	maximal, characteristic
2	#14521167	C₂	1	2	yes	maximal, complemented
3	#14520879	C₂	1	1	yes	maximal, characteristic, complemented
4	#14520857	C₂	1	2	yes	maximal, complemented
5	C₃₁×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	#11758481	C₂²	1	2	yes	—
7	#11758478	—	2	2	no	—
8	C₂×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	#11758407	C₂²	1	2	yes	—
12	#11758393	—	2	2	no	—
13	Dic₂₄₈	C₄	1	1	yes	characteristic, complemented
14	#11758388	C₄	1	2	yes	complemented
15	D₄₉₆	C₄	1	1	yes	characteristic, complemented
16	#92495	—	2	2	no	—
17	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
19	C₄²×C₃₁	D₄	1	1	yes	characteristic
20	#92474	—	2	2	no	—
21	Dic₁₂₄	C₂×C₄	1	2	yes	—
22	D₂₄₈	C₂×C₄	1	2	yes	—
23	#92470	—	2	2	no	—
24	#92469	—	4	2	no	—
25	C₈×D₃₁	—	4	2	no	—
26	C₁₆×C₃₁	—	2	1	no	—
27	C₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₃₁	—	2	1	no	—
30	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₃₁	—	4	2	no	—
32	D₁₂₄	—	2	2	no	—
33	C₄×D₃₁	—	4	2	no	—
34	Dic₆₂	—	2	2	no	—
35	C₈×C₃₁	D₈	1	2	yes	—
36	C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₃₁	#41	1	1	yes	characteristic
38	C₃₁⋊C₈	—	4	2	no	—
39	#2179	—	31	1	no	maximal, Sylow
40	C₂²×C₃₁	#135	1	1	yes	characteristic
41	C₂×D₃₁	—	4	2	no	—
42	C₄×C₃₁	—	4	1	no	—
43	C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
44	C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
45	Dic₃₁	—	4	2	no	—
46	#508	—	31	1	no	—
47	#443	—	31	2	no	—
48	#368	—	31	1	no	—
49	#359	—	31	2	no	—
50	#346	D₃₁	1	1	yes	characteristic, complemented
51	C₂×C₃₁	—	2	1	no	—
52	C₂×C₃₁	C₄×D₈	1	1	yes	characteristic
53	D₃₁	—	8	2	no	—
54	#135	—	31	2	no	—
55	#131	—	62	2	no	—
56	Q₃₂	—	31	1	no	—
57	SD₃₂	—	31	2	no	—
58	D₁₆	—	31	1	no	—
59	C₂×C₁₆	C₂×D₃₁	1	1	yes	characteristic
60	C₂×C₁₆	C₂×D₃₁	1	1	yes	characteristic
61	#108	—	31	2	no	—
62	#104	—	62	2	no	—
63	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
64	C₃₁	#2179	1	1	yes	characteristic, complemented, Sylow
65	#41	—	62	2	no	—
66	Q₁₆	—	31	2	no	—
67	SD₁₆	—	62	2	no	—
68	D₈	—	31	2	no	—
69	M₁₆	—	62	2	no	—
70	M₁₆	—	124	2	no	—
71	C₂×C₈	—	124	2	no	—
72	C₂×C₈	D₁₂₄	1	1	yes	characteristic
73	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
74	C₄²	D₁₂₄	1	1	yes	characteristic
75	C₁₆	—	2	1	no	—
76	C₁₆	C₄×D₃₁	1	1	yes	characteristic
77	C₁₆	C₄×D₃₁	1	1	yes	characteristic
78	Q₈	—	62	2	no	—
79	D₄	—	62	2	no	—
80	D₄	—	124	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	124	2	no	—
83	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
84	C₈	—	124	2	no	—
85	C₈	D₂₄₈	1	2	yes	—
86	C₈	C₂×C₄×D₃₁	1	1	yes	characteristic
87	C₈	#92495	1	1	yes	characteristic
88	C₂²	—	124	2	no	—
89	C₂²	#11758481	1	1	yes	characteristic
90	C₄	—	4	1	no	—
91	C₄	—	124	2	no	—
92	C₄	C₄×D₁₂₄	1	1	yes	characteristic
93	C₄	C₂×D₂₄₈	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	248	2	no	—
96	C₂	C₄×D₂₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₂₄₈
commutator	C₈×C₃₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₁
Fitting	C₃₁×#346	C₂
socle	C₂×C₃₁	C₄×D₈
prime radical	#14521481	C₂
cosocle	C₂×C₈×C₃₁	C₂³
hypercenter	#346	D₃₁
hypocenter	C₃₁	#2179
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #14521167	C₂	semidirect
3. #14520879	C₂	semidirect
4. #14520857	C₂	semidirect
5. C₃₁×#346	C₂	semidirect
13. Dic₂₄₈	C₄	semidirect
14. #11758388	C₄	semidirect
15. D₄₉₆	C₄	semidirect
50. #346	D₃₁	semidirect
64. C₃₁	#2179	semidirect

Maximal subgroups

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

subgroup	index
#14521481	2
#14521167	2
#14520879	2
#14520857	2
C₃₁×#346	2
#2179	31