Subgroups — #17994267

Order 4736.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557938	C₂	1	2	yes	maximal, complemented
2	#14557913	C₂	1	1	yes	maximal, characteristic, complemented
3	#14557906	C₂	1	1	yes	maximal, characteristic
4	#14557880	C₂	1	2	yes	maximal
5	C₃₇×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₄₈	—	2	2	no	—
7	C₂×#10596930	—	2	2	no	—
8	#11924536	C₂²	1	2	yes	—
9	#11924536	C₂²	1	1	yes	characteristic
10	#11924533	C₂²	1	1	yes	characteristic
11	#11924470	—	2	4	no	—
12	#11924458	—	2	4	no	—
13	C₄×C₈×C₃₇	C₂²	1	2	yes	—
14	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×D₁₄₈	—	2	1	no	—
16	C₂×D₁₄₈	—	2	2	no	—
17	C₂×Dic₇₄	—	2	1	no	—
18	C₂×Dic₇₄	—	2	2	no	—
19	C₂×C₈×C₃₇	D₄	1	4	yes	—
20	C₂×C₈×C₃₇	D₄	1	2	yes	—
21	C₄²×C₃₇	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₃₇	—	2	2	no	—
23	C₄⋊Dic₃₇	—	2	2	no	—
24	C₄⋊Dic₃₇	—	2	2	no	—
25	Dic₁₄₈	—	4	4	no	—
26	#10596930	—	4	4	no	—
27	C₂²×D₃₇	—	4	1	no	—
28	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
30	C₂×Dic₃₇	—	4	2	no	—
31	C₂×Dic₃₇	—	4	1	no	—
32	D₁₄₈	—	4	2	no	—
33	D₁₄₈	—	4	4	no	—
34	Dic₇₄	—	4	2	no	—
35	Dic₇₄	—	4	4	no	—
36	C₈×C₃₇	—	2	4	no	—
37	C₈×C₃₇	D₈	1	4	yes	—
38	C₂²×C₃₇	#127	1	1	yes	characteristic
39	C₂×D₃₇	—	8	1	no	—
40	C₂×D₃₇	—	8	2	no	—
41	C₄×C₃₇	C₂×D₈	1	2	yes	—
42	C₄×C₃₇	#137	1	4	yes	—
43	Dic₃₇	—	8	1	no	—
44	Dic₃₇	—	8	2	no	—
45	#1722	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	#493	1	1	yes	characteristic
47	C₂×C₃₇	#497	1	2	yes	—
48	D₃₇	—	16	1	no	—
49	#500	—	37	2	no	—
50	#494	—	37	1	no	—
51	#492	—	37	1	no	—
52	#486	—	37	2	no	—
53	#322	D₃₇	1	1	yes	characteristic, complemented
54	C₃₇	#1722	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	—	74	2	no	—
56	C₂×SD₁₆	—	74	2	no	—
57	C₄⋊Q₈	—	37	2	no	—
58	C₄⋊Q₈	—	37	1	no	—
59	#127	—	37	1	no	—
60	#107	—	74	4	no	—
61	#102	—	74	4	no	—
62	C₄×C₈	C₂×D₃₇	1	2	yes	—
63	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
64	C₂×Q₈	—	74	1	no	—
65	C₂×Q₈	—	74	2	no	—
66	C₂×D₄	—	74	2	no	—
67	C₂×D₄	—	74	1	no	—
68	Q₁₆	—	148	4	no	—
69	SD₁₆	—	148	4	no	—
70	C₂×C₈	D₁₄₈	1	4	yes	—
71	C₂×C₈	D₁₄₈	1	2	yes	—
72	C₄⋊C₄	—	74	2	no	—
73	C₄⋊C₄	—	74	2	no	—
74	C₄⋊C₄	—	74	2	no	—
75	C₄²	C₂²×D₃₇	1	1	yes	characteristic
76	C₂³	—	148	1	no	—
77	Q₈	—	148	2	no	—
78	Q₈	—	148	4	no	—
79	D₄	—	148	2	no	—
80	D₄	—	148	4	no	—
81	C₂×C₄	—	148	2	no	—
82	C₂×C₄	—	148	1	no	—
83	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
84	C₂×C₄	C₂×D₁₄₈	1	2	yes	—
85	C₈	—	2	4	no	—
86	C₈	D₂₉₆	1	4	yes	—
87	C₂²	—	296	1	no	—
88	C₂²	—	296	2	no	—
89	C₂²	#11924533	1	1	yes	characteristic
90	C₄	—	296	1	no	—
91	C₄	—	296	2	no	—
92	C₄	C₂×D₂₉₆	1	2	yes	—
93	C₄	#11924569	1	4	yes	—
94	C₂	—	592	1	no	—
95	C₂	#14557910	1	1	yes	characteristic
96	C₂	#14557927	1	2	yes	—

	subgroup	G/H
center	C₂²	#11924533
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₃₇×#322	C₂
socle	C₂²×C₃₇	#127
prime radical	#11924533	C₂²
hypercenter	#322	D₃₇
hypocenter	C₃₇	#1722
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
1. #14557938	C₂	semidirect
2. #14557913	C₂	semidirect
5. C₃₇×#322	C₂	semidirect
53. #322	D₃₇	semidirect
54. C₃₇	#1722	semidirect

Maximal subgroups

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

subgroup	index
#14557938	2
#14557913	2
#14557906	2
#14557880	2
C₃₇×#322	2
#1722	37