Subgroups — #17997877

Order 4736.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₄₈	C₂	1	6	yes	maximal, complemented
2	#14557470	C₂	1	4	yes	maximal, complemented
3	#14557443	C₂	1	4	yes	maximal, complemented
4	C₃₇×#376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₄₈	C₂²	1	6	yes	—
6	C₂²×C₄×D₃₇	C₂²	1	4	yes	—
7	C₄×D₁₄₈	—	2	24	no	—
8	C₂×C₄⋊Dic₃₇	C₂²	1	6	yes	—
9	C₂×#10596938	C₂²	1	12	yes	—
10	C₂×C₄²×C₃₇	C₂²	1	3	yes	—
11	#95×C₃₇	C₂²	1	4	yes	—
12	C₂³×D₃₇	C₂³	1	4	yes	—
13	C₂²×C₄×C₃₇	C₂³	1	6	yes	—
14	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
15	C₂²×Dic₃₇	C₂³	1	4	yes	—
16	C₂×D₁₄₈	—	2	24	no	—
17	C₂×D₁₄₈	—	2	12	no	—
18	C₂×C₄×D₃₇	—	2	24	no	—
19	C₄²×C₃₇	D₄	1	12	yes	complemented
20	#10596938	—	2	24	no	—
21	C₄⋊Dic₃₇	—	2	12	no	—
22	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
23	C₂²×D₃₇	—	2	12	no	—
24	C₂²×D₃₇	—	2	12	no	—
25	C₂²×D₃₇	#41	1	8	yes	—
26	C₂×C₄×C₃₇	—	2	12	no	—
27	C₂×C₄×C₃₇	C₂×D₄	1	12	yes	—
28	C₂×C₄×C₃₇	C₂×D₄	1	6	yes	—
29	C₂×Dic₃₇	—	2	12	no	—
30	D₁₄₈	—	2	48	no	—
31	C₄×D₃₇	—	4	16	no	—
32	C₂²×C₃₇	C₂²×D₄	1	3	yes	—
33	C₂²×C₃₇	C₂×#41	1	4	yes	—
34	C₂×D₃₇	—	2	24	no	—
35	C₂×D₃₇	—	4	12	no	—
36	C₂×D₃₇	—	4	4	no	—
37	C₄×C₃₇	—	2	12	no	—
38	C₄×C₃₇	#127	1	4	yes	—
39	Dic₃₇	—	4	4	no	—
40	#2397	—	37	1	no	maximal, Sylow
41	C₂×C₃₇	#525	1	6	yes	—
42	C₂×C₃₇	C₂×#127	1	1	yes	characteristic
43	D₃₇	—	4	8	no	—
44	C₂×C₄×D₄	—	37	6	no	—
45	#399	—	37	4	no	—
46	#392	—	37	4	no	—
47	#376	D₃₇	1	1	yes	characteristic, complemented
48	C₃₇	#2397	1	1	yes	characteristic, complemented, Sylow
49	C₂²×D₄	—	37	6	no	—
50	C₂³×C₄	—	37	4	no	—
51	C₄×D₄	—	74	24	no	—
52	C₂×C₄⋊C₄	—	37	6	no	—
53	C₂×C₂²⋊C₄	—	37	12	no	—
54	C₂×C₄²	C₂×D₃₇	1	3	yes	—
55	#95	C₂×D₃₇	1	4	yes	—
56	C₂⁴	—	37	4	no	—
57	C₂×D₄	—	74	24	no	—
58	C₂×D₄	—	74	12	no	—
59	C₂²×C₄	—	37	4	no	—
60	C₂²×C₄	—	74	24	no	—
61	C₂²×C₄	C₂²×D₃₇	1	6	yes	—
62	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
63	C₄⋊C₄	—	74	12	no	—
64	C₂²⋊C₄	—	74	24	no	—
65	C₄²	D₁₄₈	1	12	yes	complemented
66	C₂³	—	37	8	no	—
67	C₂³	—	74	12	no	—
68	C₂³	—	74	12	no	—
69	C₂³	C₂³×D₃₇	1	1	yes	characteristic
70	D₄	—	74	48	no	—
71	C₂×C₄	—	2	12	no	—
72	C₂×C₄	—	74	12	no	—
73	C₂×C₄	—	148	16	no	—
74	C₂×C₄	C₂×D₁₄₈	1	12	yes	—
75	C₂×C₄	C₂×D₁₄₈	1	6	yes	—
76	C₂²	—	74	24	no	—
77	C₂²	—	148	12	no	—
78	C₂²	—	148	4	no	—
79	C₂²	C₂²×D₁₄₈	1	3	yes	—
80	C₂²	#41×D₃₇	1	4	yes	—
81	C₄	—	2	12	no	—
82	C₄	—	148	4	no	—
83	C₄	#11924533	1	4	yes	—
84	C₂	—	148	8	no	—
85	C₂	#14558045	1	6	yes	—
86	C₂	C₂×#11924533	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₃₇
commutator, socle, cosocle	C₂³×C₃₇	C₂⁴
Frattini	C₂³	C₂³×D₃₇
Fitting	C₃₇×#376	C₂
hypercenter	#376	D₃₇
hypocenter	C₃₇	#2397
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×D₁₄₈	C₂	semidirect
2. #14557470	C₂	semidirect
3. #14557443	C₂	semidirect
4. C₃₇×#376	C₂	semidirect
19. C₄²×C₃₇	D₄	semidirect
47. #376	D₃₇	semidirect
48. C₃₇	#2397	semidirect
65. C₄²	D₁₄₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₁₄₈	2
#14557470	2
#14557443	2
C₃₇×#376	2
#2397	37