Subgroups — #18009549

Order 4736.

100 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, complemented
2	#14558421	C₂	1	1	yes	maximal, characteristic, complemented
3	#14557610	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596927	—	2	1	no	—
5	C₂×#10596927	—	2	1	no	—
6	C₂×#10596929	—	2	1	no	—
7	C₄×D₁₄₈	C₄	1	1	yes	characteristic
8	#11924448	—	2	1	no	—
9	C₄×#64436	C₂²	1	1	yes	characteristic
10	C₄⋊C₈×C₃₇	C₄	1	1	yes	characteristic
11	C₂×D₁₄₈	C₈	1	1	yes	characteristic
12	C₂×C₄×D₃₇	—	2	1	no	—
13	C₂×C₈×C₃₇	—	2	1	no	—
14	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
15	#10596938	—	2	1	no	—
16	C₄⋊Dic₃₇	C₈	1	1	yes	characteristic
17	C₂×#64436	D₄	1	1	yes	characteristic
18	C₂×#64436	D₄	1	1	yes	characteristic
19	#10596929	—	4	1	no	—
20	#10596929	—	4	1	no	—
21	#10596927	—	2	2	no	—
22	#10596927	—	4	1	no	—
23	C₂²×D₃₇	—	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	C₂×Dic₃₇	—	2	1	no	—
28	D₁₄₈	—	4	1	no	—
29	C₄×D₃₇	—	4	1	no	—
30	C₄×D₃₇	—	4	1	no	—
31	C₈×C₃₇	—	4	1	no	—
32	#64436	—	2	1	no	—
33	#64436	D₈	1	1	yes	characteristic
34	#64436	SD₁₆	1	1	yes	characteristic
35	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
36	C₂×D₃₇	—	4	1	no	—
37	C₂×D₃₇	—	4	1	no	—
38	C₂×D₃₇	—	4	1	no	—
39	C₄×C₃₇	—	2	1	no	—
40	C₄×C₃₇	—	2	1	no	—
41	C₄×C₃₇	#102	1	1	yes	characteristic
42	C₄×C₃₇	#104	1	1	yes	characteristic
43	Dic₃₇	—	4	1	no	—
44	#1330	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	D₄⋊C₈	1	1	yes	characteristic
46	C₂×C₃₇	#349	1	1	yes	characteristic
47	C₂×C₃₇	#350	1	1	yes	characteristic
48	D₃₇	—	8	1	no	—
49	#436	—	37	1	no	—
50	C₄⋊C₁₆	—	37	1	no	—
51	#346	—	37	1	no	—
52	C₃₇	#1330	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	74	1	no	—
54	C₄×D₄	—	37	1	no	—
55	C₂×C₁₆	—	74	1	no	—
56	C₂×C₁₆	—	74	1	no	—
57	C₄⋊C₈	#3866	1	1	yes	characteristic
58	C₂²⋊C₈	—	74	1	no	—
59	C₄×C₈	—	37	1	no	—
60	C₂×D₄	—	37	1	no	—
61	C₂²×C₄	—	74	1	no	—
62	M₁₆	—	148	1	no	—
63	M₁₆	—	148	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	37	1	no	—
66	C₂×C₈	—	37	1	no	—
67	C₄⋊C₄	—	37	1	no	—
68	C₂²⋊C₄	—	74	1	no	—
69	C₄²	C₂×#3866	1	1	yes	characteristic
70	C₁₆	—	74	2	no	—
71	C₁₆	—	148	1	no	—
72	C₂³	—	74	1	no	—
73	D₄	—	148	1	no	—
74	C₂×C₄	—	74	1	no	—
75	C₂×C₄	—	148	1	no	—
76	C₂×C₄	—	148	1	no	—
77	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
78	C₂×C₄	#10596953	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
80	C₈	—	4	1	no	—
81	C₈	—	37	1	no	—
82	C₈	—	37	1	no	—
83	C₈	—	74	1	no	—
84	C₂²	—	148	1	no	—
85	C₂²	—	148	1	no	—
86	C₂²	—	148	1	no	—
87	C₂²	#11924593	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	148	1	no	—
91	C₄	#11924598	1	1	yes	characteristic
92	C₄	#11924601	1	1	yes	characteristic
93	C₂	—	296	1	no	—
94	C₂	#14558381	1	1	yes	characteristic
95	C₂	#14558430	1	1	yes	characteristic
96	C₂	#14558432	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#3866
commutator	C₂×C₄×C₃₇	C₂×C₈
Frattini	C₄²	C₂×#3866
Fitting	C₄⋊C₈×C₃₇	C₄
socle	C₂²×C₃₇	C₂²⋊C₈
prime radical	C₂×D₁₄₈	C₈
cosocle	C₄×#64436	C₂²
hypercenter	C₄⋊C₈	#3866
hypocenter	C₃₇	#1330
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₄⋊#10596927	C₂	semidirect
2. #14558421	C₂	semidirect
52. C₃₇	#1330	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
#14557610	2
#1330	37