Subgroups — #17994203

Order 4736.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557910	C₂	1	1	yes	maximal, characteristic
2	#14557881	C₂	1	4	yes	maximal, complemented
3	C₈×#64436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₂₉₆	—	2	2	no	—
6	#11924533	C₂²	1	2	yes	—
7	#11924456	—	2	8	no	—
8	C₄×#64436	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₃₇	—	2	2	no	—
10	C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
11	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₃₇	—	2	2	no	—
13	C₂×D₁₄₈	—	2	2	no	—
14	C₂×D₁₄₈	—	2	4	no	—
15	Q₁₆×C₃₇	—	4	4	no	—
16	C₂×C₈×C₃₇	D₄	1	2	yes	—
17	C₄⋊C₄×C₃₇	—	2	4	no	—
18	C₄²×C₃₇	C₂³	1	1	yes	characteristic
19	C₂×#64436	D₄	1	4	yes	—
20	D₂₉₆	—	4	4	no	—
21	C₂²×D₃₇	—	4	2	no	—
22	Q₈×C₃₇	—	4	4	no	—
23	C₂×C₄×C₃₇	—	4	2	no	—
24	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
26	D₁₄₈	—	4	4	no	—
27	D₁₄₈	—	4	8	no	—
28	C₈×C₃₇	D₈	1	4	yes	—
29	#64436	—	2	4	no	—
30	C₂²×C₃₇	#127	1	1	yes	characteristic
31	C₂×D₃₇	—	8	2	no	—
32	C₂×D₃₇	—	8	4	no	—
33	C₄×C₃₇	—	8	2	no	—
34	C₄×C₃₇	C₂×D₈	1	2	yes	—
35	C₄×C₃₇	#135	1	4	yes	—
36	#1709	—	37	1	no	maximal, Sylow
37	C₂×C₃₇	#493	1	1	yes	characteristic
38	C₂×C₃₇	#495	1	2	yes	—
39	D₃₇	—	16	2	no	—
40	#494	D₃₇	1	1	yes	characteristic, complemented
41	#493	—	37	1	no	—
42	#486	—	37	4	no	—
43	C₈²	—	37	1	no	—
44	C₃₇	#1709	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₁₆	—	2	2	no	—
46	C₂×D₈	—	74	2	no	—
47	C₄⋊Q₈	C₂×D₃₇	1	2	yes	—
48	#127	—	37	2	no	—
49	#102	—	74	8	no	—
50	C₄×C₈	—	37	2	no	—
51	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
52	C₂×Q₈	—	2	2	no	—
53	C₂×D₄	—	74	4	no	—
54	C₂×D₄	—	74	2	no	—
55	Q₁₆	—	4	4	no	—
56	D₈	—	148	4	no	—
57	C₂×C₈	—	37	4	no	—
58	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
59	C₄⋊C₄	—	2	4	no	—
60	C₄²	C₂²×D₃₇	1	1	yes	characteristic
61	C₂³	—	148	2	no	—
62	Q₈	—	4	4	no	—
63	D₄	—	148	4	no	—
64	D₄	—	148	8	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	D₄×D₃₇	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
68	C₈	—	74	4	no	—
69	C₈	#10596939	1	4	yes	—
70	C₂²	—	296	2	no	—
71	C₂²	—	296	4	no	—
72	C₂²	#11924532	1	1	yes	characteristic
73	C₄	—	8	2	no	—
74	C₄	C₂×#10596939	1	2	yes	—
75	C₄	#11924559	1	4	yes	—
76	C₂	—	592	2	no	—
77	C₂	#14557909	1	1	yes	characteristic
78	C₂	#14557918	1	2	yes	—

	subgroup	G/H
center	C₂²	#11924532
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₃₇×#494	C₂
socle	C₂²×C₃₇	#127
prime radical	#14557910	C₂
hypercenter	#494	D₃₇
hypocenter	C₃₇	#1709
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
2. #14557881	C₂	semidirect
3. C₈×#64436	C₂	semidirect
4. C₃₇×#494	C₂	semidirect
40. #494	D₃₇	semidirect
44. C₃₇	#1709	semidirect

Maximal subgroups

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

subgroup	index
#14557910	2
#14557881	2
C₈×#64436	2
C₃₇×#494	2
#1709	37