Subgroups — #18011000

Order 4736.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558575	C₂	1	2	yes	maximal, complemented
2	#14558462	C₂	1	1	yes	maximal, characteristic, complemented
3	#14558447	C₂	1	2	yes	maximal, complemented
4	#14558420	C₂	1	1	yes	maximal, characteristic, complemented
5	#14557962	C₂	1	1	yes	maximal, characteristic
6	#11924623	—	2	2	no	—
7	D₃₇⋊C₁₆	C₂²	1	1	yes	characteristic
8	#11924607	C₂²	1	2	yes	—
9	#11924600	—	2	2	no	—
10	C₈×#3866	C₂²	1	1	yes	characteristic
11	#11924555	C₂²	1	2	yes	—
12	Dic₂₉₆	C₄	1	1	yes	characteristic, complemented
13	#11924480	C₄	1	2	yes	complemented
14	C₁₆×D₃₇	C₂²	1	1	yes	characteristic
15	D₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
16	#10596964	—	2	2	no	—
17	#10596957	—	4	2	no	—
18	C₂×#64438	—	4	2	no	—
19	C₄×#3866	D₄	1	1	yes	characteristic
20	#10596953	—	2	2	no	—
21	D₃₇⋊C₈	D₄	1	1	yes	characteristic
22	D₈×C₃₇	C₂×C₄	1	2	yes	—
23	#10596940	—	2	2	no	—
24	Dic₁₄₈	C₂×C₄	1	2	yes	—
25	C₈×D₃₇	C₂³	1	1	yes	characteristic
26	#10596927	—	2	1	no	—
27	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
28	#10596925	C₂×C₄	1	1	yes	characteristic
29	C₂×#3866	—	2	1	no	—
30	D₄×C₃₇	—	2	2	no	—
31	C₂²⋊D₃₇	—	4	2	no	—
32	C₂×Dic₃₇	—	4	2	no	—
33	C₄×D₃₇	C₂×D₄	1	1	yes	characteristic
34	Dic₇₄	—	2	2	no	—
35	#64438	—	4	2	no	—
36	#64438	D₈	1	2	yes	—
37	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
38	#64436	#41	1	1	yes	characteristic
39	C₂²×C₃₇	—	4	2	no	—
40	C₂×D₃₇	#135	1	1	yes	characteristic
41	#3866	—	4	1	no	—
42	C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
43	Dic₃₇	—	4	2	no	—
44	Dic₃₇	C₂×D₈	1	1	yes	characteristic
45	#2179	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	—	8	2	no	—
47	C₂×C₃₇	C₄×D₈	1	1	yes	characteristic
48	D₃₇	—	2	1	no	—
49	#508	—	37	1	no	—
50	#443	—	37	2	no	—
51	#368	—	37	1	no	—
52	#359	—	37	2	no	—
53	#346	—	37	1	no	—
54	C₃₇	#2179	1	1	yes	characteristic, complemented, Sylow
55	#135	—	37	2	no	—
56	#131	—	74	2	no	—
57	Q₃₂	—	37	1	no	—
58	SD₃₂	—	37	2	no	—
59	D₁₆	#3866	1	1	yes	characteristic, complemented
60	C₂×C₁₆	—	37	1	no	—
61	C₂×C₁₆	—	37	1	no	—
62	#108	—	37	2	no	—
63	#104	—	74	2	no	—
64	C₄×C₈	—	37	1	no	—
65	#41	—	74	2	no	—
66	Q₁₆	—	37	2	no	—
67	SD₁₆	—	74	2	no	—
68	D₈	C₂×#3866	1	2	yes	—
69	M₁₆	—	74	2	no	—
70	M₁₆	—	148	2	no	—
71	C₂×C₈	—	37	1	no	—
72	C₂×C₈	—	37	1	no	—
73	C₂×C₈	—	148	2	no	—
74	C₄²	—	37	1	no	—
75	C₁₆	—	37	1	no	—
76	C₁₆	—	74	1	no	—
77	C₁₆	C₂×#3866	1	1	yes	characteristic
78	Q₈	—	74	2	no	—
79	D₄	—	2	2	no	—
80	D₄	—	148	2	no	—
81	C₂×C₄	—	37	1	no	—
82	C₂×C₄	—	74	1	no	—
83	C₂×C₄	—	148	2	no	—
84	C₈	—	37	2	no	—
85	C₈	—	37	1	no	—
86	C₈	—	148	2	no	—
87	C₈	C₂²×#3866	1	1	yes	characteristic
88	C₂²	—	4	2	no	—
89	C₂²	—	37	1	no	—
90	C₄	—	37	1	no	—
91	C₄	—	148	1	no	—
92	C₄	—	148	2	no	—
93	C₄	D₄×#3866	1	1	yes	characteristic
94	C₂	—	8	2	no	—
95	C₂	—	74	1	no	—
96	C₂	D₈×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×#3866
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₈	C₂²×#3866
Fitting	D₁₆×C₃₇	C₄
socle	C₂×C₃₇	C₄×D₈
prime radical	#14557962	C₂
cosocle	C₈×D₃₇	C₂³
hypercenter	D₁₆	#3866
hypocenter	C₃₇	#2179
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #14558575	C₂	semidirect
2. #14558462	C₂	semidirect
3. #14558447	C₂	semidirect
4. #14558420	C₂	semidirect
12. Dic₂₉₆	C₄	semidirect
13. #11924480	C₄	semidirect
15. D₁₆×C₃₇	C₄	semidirect
54. C₃₇	#2179	semidirect
59. D₁₆	#3866	semidirect

Maximal subgroups

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

subgroup	index
#14558575	2
#14558462	2
#14558447	2
#14558420	2
#14557962	2
#2179	37