Subgroups — #383×D₃₇ #17996984

Order 4736.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
2	#14557401	C₂	1	1	yes	maximal, characteristic, complemented
3	#14557400	C₂	1	6	yes	maximal, complemented
4	#95×D₃₇	C₂	1	6	yes	maximal
5	C₃₇×#383	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₃₇	C₂²	1	4	yes	—
7	C₂²×C₄×D₃₇	C₂²	1	3	yes	—
8	C₂×C₄×Dic₃₇	C₂²	1	3	yes	—
9	C₄²×D₃₇	C₄	1	8	yes	complemented
10	#11924443	C₂²	1	12	yes	—
11	#11924443	C₂²	1	6	yes	—
12	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
13	#95×C₃₇	C₂²	1	6	yes	—
14	C₂³×D₃₇	C₂³	1	1	yes	characteristic
15	C₂²×C₄×C₃₇	C₂³	1	4	yes	—
16	C₂²×C₄×C₃₇	C₂³	1	3	yes	—
17	C₂²×Dic₃₇	C₂³	1	4	yes	—
18	C₂²×Dic₃₇	C₂³	1	3	yes	—
19	C₂×C₄×D₃₇	—	2	12	no	—
20	C₂×C₄×D₃₇	—	2	24	no	—
21	C₂×C₄×D₃₇	C₂×C₄	1	12	yes	—
22	C₄²×C₃₇	C₂×C₄	1	4	yes	complemented
23	C₄×Dic₃₇	C₂×C₄	1	12	yes	complemented
24	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
25	C₂²×D₃₇	C₂²×C₄	1	2	yes	—
26	C₂²×D₃₇	#41	1	12	yes	—
27	C₂×C₄×C₃₇	—	2	6	no	—
28	C₂×C₄×C₃₇	—	2	12	no	—
29	C₂×C₄×C₃₇	C₂²×C₄	1	6	yes	—
30	C₂×Dic₃₇	—	2	6	no	—
31	C₂×Dic₃₇	—	2	12	no	—
32	C₂×Dic₃₇	C₂²×C₄	1	6	yes	—
33	C₄×D₃₇	—	2	24	no	—
34	C₄×D₃₇	—	4	16	no	—
35	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
36	C₂²×C₃₇	C₂×#41	1	6	yes	—
37	C₂×D₃₇	#117	1	12	yes	—
38	C₂×D₃₇	#126	1	16	yes	—
39	C₄×C₃₇	—	2	6	no	—
40	C₄×C₃₇	—	4	4	no	—
41	Dic₃₇	—	2	6	no	—
42	Dic₃₇	—	4	4	no	—
43	C₂×#383	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	C₂×#117	1	3	yes	—
45	C₂×C₃₇	C₂×#126	1	4	yes	—
46	D₃₇	#383	1	8	yes	direct product factor
47	C₂²×C₄²	—	37	1	no	—
48	#383	—	37	1	no	—
49	#383	—	37	6	no	—
50	#383	D₃₇	1	1	yes	characteristic, direct product factor
51	C₂×#95	—	37	6	no	—
52	C₃₇	C₂×#383	1	1	yes	characteristic, complemented, Sylow
53	C₂³×C₄	—	37	3	no	—
54	C₂³×C₄	—	37	4	no	—
55	C₂×C₄²	—	37	3	no	—
56	C₂×C₄²	—	37	8	no	—
57	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
58	#95	—	37	12	no	—
59	#95	—	37	6	no	—
60	#95	C₂×D₃₇	1	6	yes	—
61	C₂⁴	—	37	1	no	—
62	C₂²×C₄	—	37	3	no	—
63	C₂²×C₄	—	37	12	no	—
64	C₂²×C₄	—	37	4	no	—
65	C₂²×C₄	—	74	12	no	—
66	C₂²×C₄	—	74	24	no	—
67	C₂²×C₄	C₂²×D₃₇	1	4	yes	—
68	C₂²×C₄	C₂²×D₃₇	1	3	yes	—
69	C₄²	—	37	12	no	—
70	C₄²	C₄×D₃₇	1	4	yes	complemented
71	C₂³	—	37	2	no	—
72	C₂³	—	37	12	no	—
73	C₂³	C₂³×D₃₇	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	2	12	no	—
76	C₂×C₄	—	37	6	no	—
77	C₂×C₄	—	74	24	no	—
78	C₂×C₄	—	74	6	no	—
79	C₂×C₄	—	74	12	no	—
80	C₂×C₄	—	148	16	no	—
81	C₂×C₄	C₂×C₄×D₃₇	1	6	yes	—
82	C₂²	—	37	12	no	—
83	C₂²	—	37	16	no	—
84	C₂²	C₂²×C₄×D₃₇	1	1	yes	characteristic
85	C₂²	#41×D₃₇	1	6	yes	—
86	C₄	—	2	6	no	—
87	C₄	—	4	4	no	—
88	C₄	—	74	6	no	—
89	C₄	—	148	4	no	—
90	C₂	—	37	8	no	—
91	C₂	#117×D₃₇	1	3	yes	—
92	C₂	#126×D₃₇	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₇
commutator	C₂²×C₃₇	C₂³×C₄
Fitting	C₃₇×#383	C₂
socle, cosocle	C₂³×C₃₇	C₂⁴
prime radical	C₂³×D₃₇	C₂³
hypercenter	#383	D₃₇
hypocenter	C₃₇	C₂×#383
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ #383

Complements

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

N	H ≅ G/N	type
2. #14557401	C₂	semidirect
3. #14557400	C₂	semidirect
5. C₃₇×#383	C₂	semidirect
9. C₄²×D₃₇	C₄	semidirect
22. C₄²×C₃₇	C₂×C₄	semidirect
23. C₄×Dic₃₇	C₂×C₄	semidirect
46. D₃₇	#383	direct (N × H)
50. #383	D₃₇	direct (N × H)
52. C₃₇	C₂×#383	semidirect
70. 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
#14557401	2
#14557400	2
#95×D₃₇	2
C₃₇×#383	2
C₂×#383	37

Subgroups — #383×D37 #17996984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #383×D₃₇ #17996984