Subgroups — #18009573

Order 4736.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558430	C₂	1	1	yes	maximal, characteristic
2	#14558402	C₂	1	1	yes	maximal, characteristic
3	#14557792	C₂	1	1	yes	maximal, characteristic
4	D₃₇⋊M₁₆	—	2	1	no	—
5	#11924610	—	2	1	no	—
6	C₂×Dic₁₄₈	C₄	1	1	yes	characteristic
7	C₂×#10596929	C₂²	1	1	yes	characteristic
8	#11924516	—	2	1	no	—
9	#11924459	—	2	1	no	—
10	#106×C₃₇	C₄	1	1	yes	characteristic
11	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
12	C₂×Dic₇₄	—	2	1	no	—
13	#10596957	—	4	1	no	—
14	#10596953	—	4	1	no	—
15	D₃₇⋊C₈	—	2	2	no	—
16	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₄⋊C₄×C₃₇	—	2	1	no	—
18	#10596938	—	4	1	no	—
19	C₄⋊Dic₃₇	—	4	1	no	—
20	C₂×#64436	D₄	1	1	yes	characteristic
21	Dic₁₄₈	—	4	1	no	—
22	#10596929	—	4	1	no	—
23	#10596927	—	4	1	no	—
24	C₂²×D₃₇	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₃₇	—	4	1	no	—
26	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₃₇	—	4	1	no	—
28	C₂×Dic₃₇	D₈	1	1	yes	characteristic
29	C₄×D₃₇	—	2	1	no	—
30	C₄×D₃₇	—	2	1	no	—
31	Dic₇₄	—	4	1	no	—
32	Dic₇₄	—	4	1	no	—
33	#64438	—	4	2	no	—
34	C₈×C₃₇	—	2	1	no	—
35	#64436	—	2	1	no	—
36	C₂²×C₃₇	#102	1	1	yes	characteristic
37	C₂×D₃₇	—	2	1	no	—
38	C₂×D₃₇	—	4	1	no	—
39	C₄×C₃₇	—	8	1	no	—
40	C₄×C₃₇	#99	1	1	yes	characteristic
41	C₄×C₃₇	#104	1	1	yes	characteristic
42	Dic₃₇	—	2	1	no	—
43	Dic₃₇	—	8	1	no	—
44	#1342	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	—	2	1	no	—
46	C₂×C₃₇	#327	1	1	yes	characteristic
47	D₃₇	—	4	1	no	—
48	#470	—	37	1	no	—
49	#349	—	37	1	no	—
50	#338	—	37	1	no	—
51	C₃₇	#1342	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₁₆	—	37	1	no	—
53	C₂×M₁₆	—	37	1	no	—
54	C₂×M₁₆	—	74	1	no	—
55	C₂²⋊Q₈	—	74	1	no	—
56	M₃₂	—	74	1	no	—
57	#106	#3866	1	1	yes	characteristic
58	#103	—	74	1	no	—
59	C₂×Q₈	—	74	1	no	—
60	C₂²×C₄	—	37	1	no	—
61	Q₁₆	—	148	1	no	—
62	M₁₆	—	148	1	no	—
63	M₁₆	—	148	1	no	—
64	M₁₆	—	148	1	no	—
65	C₂×C₈	—	37	1	no	—
66	C₂×C₈	—	74	2	no	—
67	C₂×C₈	C₂×#3866	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₄⋊C₄	—	148	1	no	—
70	C₂²⋊C₄	—	148	1	no	—
71	C₁₆	—	148	1	no	—
72	C₂³	—	37	1	no	—
73	Q₈	—	148	1	no	—
74	Q₈	—	148	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	37	1	no	—
77	C₂×C₄	—	74	1	no	—
78	C₂×C₄	—	74	1	no	—
79	C₂×C₄	—	148	1	no	—
80	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	74	1	no	—
83	C₈	—	148	2	no	—
84	C₂²	—	74	1	no	—
85	C₂²	—	148	1	no	—
86	C₂²	#11924598	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	296	1	no	—
89	C₄	—	74	1	no	—
90	C₄	#11924595	1	1	yes	characteristic
91	C₄	#11924601	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	148	1	no	—
94	C₂	#14558385	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14558385
commutator	C₂×C₈×C₃₇	C₂×C₄
Frattini	C₂×C₈	C₂×#3866
Fitting	#106×C₃₇	C₄
socle	C₂×C₃₇	#327
prime radical	C₂²×D₃₇	SD₁₆
cosocle	C₂×#10596929	C₂²
hypercenter	#106	#3866
hypocenter	C₃₇	#1342
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
51. C₃₇	#1342	semidirect

Maximal subgroups

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

subgroup	index
#14558430	2
#14558402	2
#14557792	2
#1342	37