Subgroups — #17992573

Order 4736.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557651	C₂	1	1	yes	maximal, characteristic
2	#14557354	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#322	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924558	C₄	1	1	yes	characteristic
5	#11924542	—	2	1	no	—
6	#11924476	—	2	1	no	—
7	#11924472	C₄	1	1	yes	characteristic
8	#11924464	—	2	1	no	—
9	C₄×C₈×C₃₇	—	2	1	no	—
10	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	#10596962	—	2	1	no	—
12	C₂×C₈×C₃₇	—	2	2	no	—
13	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
15	C₄²×C₃₇	D₄	1	1	yes	characteristic
16	#10596934	—	2	1	no	—
17	Dic₁₄₈	C₈	1	1	yes	characteristic, complemented
18	D₂₉₆	C₈	1	1	yes	characteristic, complemented
19	#10596930	—	2	1	no	—
20	#10596929	—	4	1	no	—
21	C₈×D₃₇	—	4	1	no	—
22	#10596925	—	4	1	no	—
23	C₂×C₄×C₃₇	—	2	1	no	—
24	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₃₇	—	4	1	no	—
26	D₁₄₈	—	2	1	no	—
27	C₄×D₃₇	—	4	1	no	—
28	Dic₇₄	—	2	1	no	—
29	C₈×C₃₇	—	4	2	no	—
30	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
31	C₈×C₃₇	M₁₆	1	1	yes	characteristic
32	C₈×C₃₇	D₈	1	1	yes	characteristic
33	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
34	#64436	—	4	1	no	—
35	C₂²×C₃₇	#104	1	1	yes	characteristic
36	C₂×D₃₇	—	4	1	no	—
37	C₄×C₃₇	—	2	2	no	—
38	C₄×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₃₇	#102	1	1	yes	characteristic
40	Dic₃₇	—	4	1	no	—
41	#1336	—	37	1	no	maximal, Sylow
42	C₂×C₃₇	—	2	1	no	—
43	C₂×C₃₇	D₄⋊C₈	1	1	yes	characteristic
44	D₃₇	—	8	1	no	—
45	#443	—	37	1	no	—
46	#364	—	37	1	no	—
47	#322	D₃₇	1	1	yes	characteristic, complemented
48	C₃₇	#1336	1	1	yes	characteristic, complemented, Sylow
49	#135	—	37	1	no	—
50	#131	—	74	1	no	—
51	M₃₂	—	74	1	no	—
52	#108	—	37	1	no	—
53	#104	—	74	1	no	—
54	C₄×C₈	—	2	1	no	—
55	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
56	#41	—	74	1	no	—
57	Q₁₆	—	37	1	no	—
58	SD₁₆	—	74	1	no	—
59	D₈	—	37	1	no	—
60	M₁₆	—	74	1	no	—
61	M₁₆	—	148	1	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	148	1	no	—
64	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
65	C₂×C₈	D₁₄₈	1	1	yes	characteristic
66	C₄²	C₂²⋊D₃₇	1	1	yes	characteristic
67	C₁₆	—	148	1	no	—
68	Q₈	—	74	1	no	—
69	D₄	—	74	1	no	—
70	D₄	—	148	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	148	1	no	—
73	C₂×C₄	#10596938	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	148	1	no	—
76	C₈	C₈×D₃₇	1	1	yes	characteristic
77	C₈	#10596929	1	1	yes	characteristic
78	C₈	#10596930	1	1	yes	characteristic
79	C₈	D₂₉₆	1	1	yes	characteristic
80	C₂²	—	148	1	no	—
81	C₂²	#11924464	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	148	1	no	—
84	C₄	#11924448	1	1	yes	characteristic
85	C₄	#11924458	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	296	1	no	—
88	C₂	#14557262	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924458
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#322	C₂
socle	C₂×C₃₇	D₄⋊C₈
prime radical	#11924558	C₄
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#322	D₃₇
hypocenter	C₃₇	#1336
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #322

Complements

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

N	H ≅ G/N	type
2. #14557354	C₂	semidirect
3. C₃₇×#322	C₂	semidirect
17. Dic₁₄₈	C₈	semidirect
18. D₂₉₆	C₈	semidirect
47. #322	D₃₇	semidirect
48. C₃₇	#1336	semidirect

Maximal subgroups

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

subgroup	index
#14557651	2
#14557354	2
C₃₇×#322	2
#1336	37