Subgroups — #18010931

Order 4736.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924610	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10596927	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#10596927	C₂	1	4	yes	maximal, complemented
4	#14557489	C₂	1	1	yes	maximal, characteristic
5	#11924610	—	2	2	no	—
6	C₂×#10596927	—	2	2	no	—
7	C₂×#10596927	C₂²	1	2	yes	—
8	C₂×#10596927	C₂²	1	2	yes	—
9	C₂×#10596934	C₄	1	1	yes	characteristic
10	C₂²×#64436	C₂²	1	1	yes	characteristic
11	#11924447	C₄	1	2	yes	—
12	C₄×#64436	C₂²	1	2	yes	—
13	#117×C₃₇	C₄	1	1	yes	characteristic
14	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₄⋊C₄×C₃₇	C₈	1	2	yes	—
16	C₂²⋊C₄×C₃₇	C₈	1	2	yes	—
17	C₄²×C₃₇	C₂×C₄	1	2	yes	—
18	#10596934	—	2	2	no	—
19	C₂×#64436	C₂×C₄	1	2	yes	—
20	C₂×#64436	C₂×C₄	1	1	yes	characteristic
21	C₂×#64436	D₄	1	2	yes	—
22	C₂×#64436	Q₈	1	2	yes	—
23	C₂×#64436	C₂³	1	1	yes	characteristic
24	#10596927	—	2	2	no	—
25	#10596927	—	2	2	no	—
26	C₂³×C₃₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₃₇	C₂×C₈	1	4	yes	—
29	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₃₇	M₁₆	1	2	yes	—
31	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
32	#64436	—	2	2	no	—
33	#64436	C₄⋊C₄	1	2	yes	—
34	#64436	C₂×D₄	1	1	yes	characteristic
35	#64436	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₃₇	—	2	2	no	—
37	C₂²×C₃₇	C₄⋊C₈	1	2	yes	—
38	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₃₇	—	2	4	no	—
40	C₄×C₃₇	C₄⋊C₈	1	2	yes	—
41	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
43	#2151	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	2	2	no	—
45	C₂×C₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic
46	C₂×C₃₇	#504	1	2	yes	—
47	C₂×M₃₂	—	37	1	no	—
48	C₂²×C₁₆	—	37	1	no	—
49	#405	—	37	1	no	—
50	C₄⋊C₁₆	—	37	4	no	—
51	C₃₇	#2151	1	1	yes	characteristic, complemented, Sylow
52	C₂×M₁₆	—	37	1	no	—
53	C₂²×C₈	—	37	1	no	—
54	#117	#3866	1	1	yes	characteristic
55	M₃₂	—	74	2	no	—
56	C₂×C₁₆	—	37	2	no	—
57	C₂×C₁₆	—	37	2	no	—
58	C₂×C₁₆	—	74	2	no	—
59	#97	—	37	2	no	—
60	C₄×C₈	—	37	2	no	—
61	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
62	M₁₆	—	74	2	no	—
63	C₂×C₈	—	37	2	no	—
64	C₂×C₈	—	37	2	no	—
65	C₂×C₈	—	37	1	no	—
66	C₂×C₈	—	37	1	no	—
67	C₂×C₈	—	37	2	no	—
68	C₄⋊C₄	#64438	1	2	yes	—
69	C₂²⋊C₄	#64438	1	2	yes	—
70	C₄²	C₂×#3866	1	2	yes	—
71	C₁₆	—	74	2	no	—
72	C₁₆	—	74	2	no	—
73	C₂³	C₂×#64438	1	1	yes	characteristic
74	C₂×C₄	#10596953	1	2	yes	—
75	C₂×C₄	C₄⋊#3866	1	2	yes	—
76	C₂×C₄	C₂×#64438	1	4	yes	—
77	C₂×C₄	C₂×#64438	1	1	yes	characteristic
78	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
79	C₈	—	37	1	no	—
80	C₈	—	37	2	no	—
81	C₈	—	37	1	no	—
82	C₈	—	74	2	no	—
83	C₂²	—	2	2	no	—
84	C₂²	C₄⋊#64438	1	2	yes	—
85	C₂²	C₂²×#64438	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄⋊#64438	1	2	yes	—
88	C₄	C₂×C₄⋊#3866	1	1	yes	characteristic
89	C₄	C₂×#10596953	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#64438	1	1	yes	characteristic
92	C₂	#14558591	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3866
commutator, socle	C₂²×C₃₇	C₂²×C₈
Fitting	#117×C₃₇	C₄
prime radical	C₂³×C₃₇	C₂×C₈
cosocle	C₂×#64436	C₂³
hypercenter	#117	#3866
hypocenter	C₃₇	#2151
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. C₄⋊#10596927	C₂	semidirect
51. C₃₇	#2151	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924610	2
C₂²×#10596927	2
C₄⋊#10596927	2
#14557489	2
#2151	37