Subgroups — #18009568

Order 4736.

104 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	#14558401	C₂	1	1	yes	maximal, characteristic
3	#14557788	C₂	1	1	yes	maximal, characteristic
4	#11924615	—	2	1	no	—
5	#11924610	—	2	1	no	—
6	C₂×#10596929	C₂²	1	1	yes	characteristic
7	#11924512	—	2	1	no	—
8	#11924468	C₄	1	1	yes	characteristic, complemented
9	#11924460	—	2	1	no	—
10	C₂×Q₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₃₇	—	2	1	no	—
12	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
13	C₂²⋊#3866	—	4	1	no	—
14	C₄⋊#3866	—	4	1	no	—
15	C₄×#3866	—	2	2	no	—
16	Q₁₆×C₃₇	—	4	1	no	—
17	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
18	#10596938	—	4	1	no	—
19	C₄⋊Dic₃₇	—	2	1	no	—
20	#10596936	—	4	1	no	—
21	C₂×#64436	D₄	1	1	yes	characteristic
22	#10596929	—	4	1	no	—
23	#10596927	—	4	1	no	—
24	C₂²×D₃₇	D₈	1	1	yes	characteristic
25	C₂×#3866	—	4	2	no	—
26	Q₈×C₃₇	—	4	1	no	—
27	Q₈×C₃₇	—	4	1	no	—
28	C₂×C₄×C₃₇	—	4	1	no	—
29	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×Dic₃₇	—	4	1	no	—
31	C₂×Dic₃₇	SD₁₆	1	1	yes	characteristic
32	C₄×D₃₇	—	2	1	no	—
33	C₄×D₃₇	—	2	1	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	#3866	—	8	2	no	—
40	C₄×C₃₇	—	8	1	no	—
41	C₄×C₃₇	#99	1	1	yes	characteristic
42	C₄×C₃₇	#104	1	1	yes	characteristic
43	Dic₃₇	—	2	1	no	—
44	Dic₃₇	—	8	1	no	—
45	#1340	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	—	2	1	no	—
47	C₂×C₃₇	#327	1	1	yes	characteristic
48	D₃₇	—	4	1	no	—
49	#470	—	37	1	no	—
50	#349	—	37	1	no	—
51	H(3,ℤ/4)	—	37	1	no	—
52	C₃₇	#1340	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₁₆	#3866	1	1	yes	characteristic, complemented
54	C₂×M₁₆	—	37	1	no	—
55	C₂²⋊Q₈	—	74	1	no	—
56	#117	—	74	1	no	—
57	M₃₂	—	74	1	no	—
58	#106	—	37	1	no	—
59	#103	—	74	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂²×C₄	—	37	1	no	—
62	Q₁₆	—	4	1	no	—
63	M₁₆	—	148	1	no	—
64	C₂×C₈	—	37	1	no	—
65	C₂×C₈	C₂×#3866	1	1	yes	characteristic
66	C₄⋊C₄	—	74	1	no	—
67	C₄⋊C₄	—	148	1	no	—
68	C₄⋊C₄	—	148	1	no	—
69	C₂²⋊C₄	—	148	1	no	—
70	C₂²⋊C₄	—	148	1	no	—
71	C₄²	—	74	2	no	—
72	C₁₆	—	148	1	no	—
73	C₂³	—	37	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	4	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	37	1	no	—
78	C₂×C₄	—	74	1	no	—
79	C₂×C₄	—	74	1	no	—
80	C₂×C₄	—	148	2	no	—
81	C₂×C₄	—	148	1	no	—
82	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	74	1	no	—
85	C₂²	—	74	1	no	—
86	C₂²	—	148	1	no	—
87	C₂²	#11924598	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	296	1	no	—
90	C₄	—	296	2	no	—
91	C₄	—	74	1	no	—
92	C₄	#11924594	1	1	yes	characteristic
93	C₄	#11924600	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	148	1	no	—
96	C₂	#14558384	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14558384
commutator	C₂×C₈×C₃₇	C₂×C₄
Frattini	C₂×C₈	C₂×#3866
Fitting	C₂×Q₁₆×C₃₇	C₄
socle	C₂×C₃₇	#327
prime radical	C₂²×D₃₇	D₈
cosocle	C₂×#10596929	C₂²
hypercenter	C₂×Q₁₆	#3866
hypocenter	C₃₇	#1340
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
8. #11924468	C₄	semidirect
10. C₂×Q₁₆×C₃₇	C₄	semidirect
52. C₃₇	#1340	semidirect
53. C₂×Q₁₆	#3866	semidirect

Maximal subgroups

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

subgroup	index
#14558430	2
#14558401	2
#14557788	2
#1340	37