Subgroups — #376×D₃₇ #17996921

Order 4736.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₃₇	C₂	1	3	yes	maximal
2	#14557379	C₂	1	3	yes	maximal, complemented
3	#14557378	C₂	1	4	yes	maximal, complemented
4	#95×D₃₇	C₂	1	4	yes	maximal
5	C₃₇×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₃₇	C₂²	1	6	yes	—
7	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₃₇	C₂²	1	6	yes	—
9	C₂×C₄×Dic₃₇	C₂²	1	3	yes	—
10	C₄²×D₃₇	C₄	1	24	yes	complemented
11	#11924443	C₂²	1	12	yes	—
12	C₂×C₄²×C₃₇	C₂²	1	3	yes	—
13	#95×C₃₇	C₂²	1	4	yes	—
14	C₂³×D₃₇	C₂³	1	1	yes	characteristic
15	C₂²×C₄×C₃₇	C₂³	1	6	yes	—
16	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₃₇	C₂³	1	6	yes	—
18	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
19	C₂×C₄×D₃₇	—	2	24	no	—
20	C₂×C₄×D₃₇	C₂×C₄	1	24	yes	—
21	C₂×C₄×D₃₇	C₂×C₄	1	12	yes	—
22	C₄²×C₃₇	C₂×C₄	1	12	yes	complemented
23	C₄×Dic₃₇	C₂×C₄	1	12	yes	complemented
24	C₄×Dic₃₇	C₂×C₄	1	24	yes	complemented
25	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
26	C₂²×D₃₇	C₂²×C₄	1	6	yes	—
27	C₂²×D₃₇	#41	1	8	yes	—
28	C₂×C₄×C₃₇	—	2	12	no	—
29	C₂×C₄×C₃₇	C₂²×C₄	1	12	yes	—
30	C₂×C₄×C₃₇	C₂²×C₄	1	6	yes	—
31	C₂×Dic₃₇	—	2	12	no	—
32	C₂×Dic₃₇	C₂²×C₄	1	12	yes	—
33	C₂×Dic₃₇	C₂²×C₄	1	6	yes	—
34	C₄×D₃₇	—	2	48	no	—
35	C₄×D₃₇	C₄²	1	16	yes	—
36	C₂²×C₃₇	C₂³×C₄	1	3	yes	—
37	C₂²×C₃₇	C₂×#41	1	4	yes	—
38	C₂×D₃₇	C₂×C₄²	1	4	yes	—
39	C₂×D₃₇	#117	1	24	yes	—
40	C₄×C₃₇	—	2	12	no	—
41	C₄×C₃₇	C₂×C₄²	1	4	yes	—
42	Dic₃₇	—	2	12	no	—
43	Dic₃₇	C₂×C₄²	1	4	yes	—
44	C₂×#376	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	C₂²×C₄²	1	1	yes	characteristic
46	C₂×C₃₇	C₂×#117	1	6	yes	—
47	D₃₇	#376	1	8	yes	direct product factor
48	C₂²×C₄²	—	37	3	no	—
49	#376	—	37	3	no	—
50	#376	—	37	4	no	—
51	#376	D₃₇	1	1	yes	characteristic, direct product factor
52	C₂×#95	—	37	4	no	—
53	C₃₇	C₂×#376	1	1	yes	characteristic, complemented, Sylow
54	C₂³×C₄	—	37	1	no	—
55	C₂³×C₄	—	37	6	no	—
56	C₂×C₄²	—	37	6	no	—
57	C₂×C₄²	—	37	3	no	—
58	C₂×C₄²	—	37	24	no	—
59	C₂×C₄²	C₂×D₃₇	1	3	yes	—
60	#95	—	37	12	no	—
61	#95	C₂×D₃₇	1	4	yes	—
62	C₂⁴	—	37	1	no	—
63	C₂²×C₄	—	37	1	no	—
64	C₂²×C₄	—	37	12	no	—
65	C₂²×C₄	—	37	6	no	—
66	C₂²×C₄	—	37	24	no	—
67	C₂²×C₄	—	74	24	no	—
68	C₂²×C₄	C₂²×D₃₇	1	6	yes	—
69	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
70	C₄²	—	37	24	no	—
71	C₄²	—	37	12	no	—
72	C₄²	C₄×D₃₇	1	12	yes	complemented
73	C₂³	—	37	6	no	—
74	C₂³	—	37	8	no	—
75	C₂³	C₂³×D₃₇	1	1	yes	characteristic
76	C₂×C₄	—	2	12	no	—
77	C₂×C₄	—	37	6	no	—
78	C₂×C₄	—	37	16	no	—
79	C₂×C₄	—	37	12	no	—
80	C₂×C₄	—	74	48	no	—
81	C₂×C₄	—	74	12	no	—
82	C₂×C₄	C₂×C₄×D₃₇	1	12	yes	—
83	C₂×C₄	C₂×C₄×D₃₇	1	6	yes	—
84	C₂²	—	37	4	no	—
85	C₂²	—	37	24	no	—
86	C₂²	C₂²×C₄×D₃₇	1	3	yes	—
87	C₂²	#41×D₃₇	1	4	yes	—
88	C₄	—	2	12	no	—
89	C₄	—	37	4	no	—
90	C₄	—	74	12	no	—
91	C₄	C₄²×D₃₇	1	4	yes	—
92	C₂	—	37	8	no	—
93	C₂	C₂×C₄²×D₃₇	1	1	yes	characteristic
94	C₂	#117×D₃₇	1	6	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₃₇
commutator	C₂×C₃₇	C₂²×C₄²
Frattini	C₂³	C₂³×D₃₇
Fitting	C₃₇×#376	C₂
socle, cosocle	C₂³×C₃₇	C₂⁴
prime radical	C₂³×D₃₇	C₂³
hypercenter	#376	D₃₇
hypocenter	C₃₇	C₂×#376
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
2. #14557379	C₂	semidirect
3. #14557378	C₂	semidirect
5. C₃₇×#376	C₂	semidirect
10. C₄²×D₃₇	C₄	semidirect
22. C₄²×C₃₇	C₂×C₄	semidirect
23. C₄×Dic₃₇	C₂×C₄	semidirect
24. C₄×Dic₃₇	C₂×C₄	semidirect
47. D₃₇	#376	direct (N × H)
51. #376	D₃₇	direct (N × H)
53. C₃₇	C₂×#376	semidirect
72. C₄²	C₄×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₃₇	2
#14557379	2
#14557378	2
#95×D₃₇	2
C₃₇×#376	2
C₂×#376	37

Subgroups — #376×D37 #17996921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #376×D₃₇ #17996921