Subgroups — #14557735

Order 2368.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596941	C₂	1	2	yes	maximal
2	C₄×D₁₄₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#64436	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924460	C₂	1	2	yes	maximal, complemented
5	C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₃₇	C₂²	1	2	yes	—
7	C₂×D₁₄₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₃₇	—	2	1	no	—
9	C₄⋊C₄×C₃₇	—	2	1	no	—
10	C₄⋊C₄×C₃₇	—	2	1	no	—
11	C₄²×C₃₇	C₂²	1	1	yes	characteristic
12	#10596941	—	2	4	no	—
13	#10596938	—	2	1	no	—
14	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
15	C₂×#64436	C₂²	1	2	yes	—
16	C₂²×D₃₇	—	2	1	no	—
17	Q₈×C₃₇	—	2	2	no	—
18	Q₈×C₃₇	—	2	2	no	—
19	C₂×C₄×C₃₇	—	2	2	no	—
20	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
22	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
23	C₂×Dic₃₇	—	2	1	no	—
24	D₁₄₈	—	2	1	no	—
25	D₁₄₈	D₄	1	2	yes	—
26	C₄×D₃₇	—	4	2	no	—
27	#64436	—	2	2	no	—
28	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
29	C₂×D₃₇	—	2	2	no	—
30	C₂×D₃₇	—	4	1	no	—
31	C₂×D₃₇	—	4	1	no	—
32	C₄×C₃₇	—	2	1	no	—
33	C₄×C₃₇	—	4	2	no	—
34	C₄×C₃₇	SD₁₆	1	2	yes	complemented
35	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₃₇	#41	1	1	yes	characteristic
37	Dic₃₇	—	4	1	no	—
38	C₂×C₃₇	#121	1	1	yes	characteristic
39	C₂×C₃₇	C₂×SD₁₆	1	1	yes	characteristic
40	C₂×C₃₇	#137	1	1	yes	characteristic
41	D₃₇	—	4	2	no	—
42	#461	—	37	1	no	maximal, Sylow
43	C₃₇	#461	1	1	yes	characteristic, complemented, Sylow
44	C₂×SD₁₆	—	37	2	no	—
45	C₄⋊Q₈	D₃₇	1	1	yes	characteristic, complemented
46	C₄×D₄	—	37	1	no	—
47	C₄⋊C₈	—	37	1	no	—
48	#103	—	37	2	no	—
49	C₂×Q₈	C₂×D₃₇	1	2	yes	—
50	C₂×D₄	—	37	1	no	—
51	C₂²×C₄	—	74	1	no	—
52	SD₁₆	—	74	4	no	—
53	C₂×C₈	—	37	2	no	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	—	37	1	no	—
57	C₂²⋊C₄	—	74	1	no	—
58	C₄²	C₂×D₃₇	1	1	yes	characteristic
59	C₂³	—	74	1	no	—
60	Q₈	—	2	2	no	—
61	Q₈	—	2	2	no	—
62	D₄	—	37	2	no	—
63	D₄	—	74	1	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	74	1	no	—
66	C₂×C₄	—	148	2	no	—
67	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
69	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
70	C₈	—	74	2	no	—
71	C₂²	—	74	2	no	—
72	C₂²	—	148	1	no	—
73	C₂²	—	148	1	no	—
74	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	2	no	—
77	C₄	—	148	1	no	—
78	C₄	#10596941	1	2	yes	complemented
79	C₄	D₄×D₃₇	1	1	yes	characteristic
80	C₄	#10596964	1	1	yes	characteristic
81	C₂	—	148	2	no	—
82	C₂	#11924507	1	1	yes	characteristic
83	C₂	C₂×#10596941	1	1	yes	characteristic
84	C₂	#11924567	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₄⋊Q₈×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	C₂×D₁₄₈	C₂²
hypercenter	C₄⋊Q₈	D₃₇
hypocenter	C₃₇	#461
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
3. C₄⋊#64436	C₂	semidirect
4. #11924460	C₂	semidirect
5. C₄⋊Q₈×C₃₇	C₂	semidirect
34. C₄×C₃₇	SD₁₆	semidirect
43. C₃₇	#461	semidirect
45. C₄⋊Q₈	D₃₇	semidirect
78. C₄	#10596941	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596941	2
C₄×D₁₄₈	2
C₄⋊#64436	2
#11924460	2
C₄⋊Q₈×C₃₇	2
#461	37