Subgroups — #18009564

Order 4736.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#10596927	C₂	1	1	yes	maximal, characteristic
2	#14558421	C₂	1	1	yes	maximal, characteristic
3	#14557664	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596927	—	2	1	no	—
5	C₂×#10596927	—	2	1	no	—
6	C₄⋊#64436	—	2	1	no	—
7	C₄⋊#64436	C₄	1	1	yes	characteristic
8	#11924447	—	2	1	no	—
9	C₄×#64436	C₂²	1	1	yes	characteristic
10	C₄×Q₈×C₃₇	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₃₇	C₈	1	1	yes	characteristic
12	C₄⋊C₄×C₃₇	—	2	1	no	—
13	C₄⋊C₄×C₃₇	C₈	1	1	yes	characteristic
14	C₄²×C₃₇	—	2	1	no	—
15	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×#64436	—	2	1	no	—
17	C₂×#64436	D₄	1	1	yes	characteristic
18	C₂×#64436	D₄	1	1	yes	characteristic
19	#10596927	—	2	2	no	—
20	#10596927	—	4	1	no	—
21	Q₈×C₃₇	—	4	1	no	—
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	—	2	1	no	—
24	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
27	#64436	—	2	1	no	—
28	#64436	—	4	1	no	—
29	#64436	SD₁₆	1	1	yes	characteristic
30	#64436	Q₁₆	1	1	yes	characteristic
31	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₃₇	—	2	1	no	—
33	C₄×C₃₇	—	2	1	no	—
34	C₄×C₃₇	—	4	1	no	—
35	C₄×C₃₇	—	4	1	no	—
36	C₄×C₃₇	#103	1	1	yes	characteristic
37	C₄×C₃₇	#104	1	1	yes	characteristic
38	#1338	—	37	1	no	maximal, Sylow
39	C₂×C₃₇	Q₈⋊C₈	1	1	yes	characteristic
40	C₂×C₃₇	#349	1	1	yes	characteristic
41	C₂×C₃₇	#350	1	1	yes	characteristic
42	#446	—	37	1	no	—
43	C₄⋊C₁₆	—	37	1	no	—
44	#346	—	37	1	no	—
45	C₃₇	#1338	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₈	#3866	1	1	yes	characteristic
47	C₂×C₁₆	—	74	1	no	—
48	C₂×C₁₆	—	74	1	no	—
49	C₄⋊C₈	—	37	1	no	—
50	C₄⋊C₈	—	74	1	no	—
51	#97	—	74	1	no	—
52	C₄×C₈	—	37	1	no	—
53	C₂×Q₈	#64438	1	1	yes	characteristic
54	C₂×C₈	—	37	1	no	—
55	C₂×C₈	—	37	1	no	—
56	C₂×C₈	—	74	1	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	#64438	1	1	yes	characteristic
59	C₄²	—	2	1	no	—
60	C₄²	C₂×#3866	1	1	yes	characteristic
61	C₁₆	—	74	2	no	—
62	C₁₆	—	148	1	no	—
63	Q₈	—	4	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₂×#64438	1	1	yes	characteristic
67	C₂×C₄	#10596957	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
69	C₈	—	37	1	no	—
70	C₈	—	37	1	no	—
71	C₈	—	74	1	no	—
72	C₈	—	148	1	no	—
73	C₂²	C₂²⋊#64438	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	#11924599	1	1	yes	characteristic
79	C₄	#11924601	1	1	yes	characteristic
80	C₂	Q₈⋊#64438	1	1	yes	characteristic
81	C₂	#14558429	1	1	yes	characteristic
82	C₂	#14558431	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#3866
commutator	C₂×C₄×C₃₇	C₂×C₈
Frattini	C₄²	C₂×#3866
Fitting	C₄×Q₈×C₃₇	C₄
socle, prime radical	C₂²×C₃₇	C₂²⋊C₈
cosocle	C₄×#64436	C₂²
hypercenter	C₄×Q₈	#3866
hypocenter	C₃₇	#1338
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
45. C₃₇	#1338	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#10596927	2
#14558421	2
#14557664	2
#1338	37