Subgroups — #14558585

Order 2368.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924603	C₂	1	1	yes	maximal, characteristic
2	#11924603	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#64438	C₂	1	1	yes	maximal, characteristic
4	#11924591	C₂	1	1	yes	maximal, characteristic
5	#11924591	C₂	1	1	yes	maximal, characteristic
6	C₄×#64438	C₂	1	1	yes	maximal, characteristic
7	#11924501	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₇₄	C₄	1	1	yes	characteristic
9	C₂×#64438	C₂²	1	1	yes	characteristic
10	C₂×#64438	C₂²	1	1	yes	characteristic
11	C₂×#64438	C₂²	1	1	yes	characteristic
12	C₂×#64438	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₃₇	C₄	1	1	yes	characteristic
14	#10596936	C₄	1	1	yes	characteristic
15	#10596936	C₄	1	1	yes	characteristic
16	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
17	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
18	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
26	Dic₇₄	—	2	2	no	—
27	#64438	—	2	1	no	—
28	#64438	—	2	1	no	—
29	#64438	—	2	1	no	—
30	#64438	Q₈	1	2	yes	complemented
31	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₃₇	—	2	1	no	—
33	C₄×C₃₇	—	2	1	no	—
34	C₄×C₃₇	—	2	1	no	—
35	Dic₃₇	—	2	1	no	—
36	Dic₃₇	—	2	1	no	—
37	Dic₃₇	M₁₆	1	2	yes	—
38	Dic₃₇	C₂×Q₈	1	1	yes	characteristic
39	Dic₃₇	#41	1	1	yes	characteristic
40	C₂×C₃₇	C₄×Q₈	1	1	yes	characteristic
41	C₂×C₃₇	C₂×M₁₆	1	1	yes	characteristic
42	C₂×C₃₇	#131	1	1	yes	characteristic
43	#446	—	37	1	no	maximal, Sylow
44	C₃₇	#446	1	1	yes	characteristic, complemented, Sylow
45	C₄×Q₈	—	37	1	no	—
46	C₄⋊C₈	—	37	1	no	—
47	C₄⋊C₈	—	37	1	no	—
48	C₄⋊C₈	—	37	1	no	—
49	#97	—	37	1	no	—
50	#97	—	37	1	no	—
51	C₄×C₈	—	37	1	no	—
52	C₂×Q₈	—	37	1	no	—
53	C₂×C₈	—	37	1	no	—
54	C₂×C₈	—	37	1	no	—
55	C₂×C₈	—	37	1	no	—
56	C₂×C₈	—	37	1	no	—
57	C₄⋊C₄	—	37	1	no	—
58	C₄⋊C₄	—	37	1	no	—
59	C₄⋊C₄	#3866	1	1	yes	characteristic
60	C₄²	—	37	1	no	—
61	C₄²	—	37	1	no	—
62	C₄²	—	37	1	no	—
63	Q₈	—	74	2	no	—
64	C₂×C₄	—	37	1	no	—
65	C₂×C₄	—	37	1	no	—
66	C₂×C₄	—	37	1	no	—
67	C₂×C₄	—	37	1	no	—
68	C₂×C₄	C₂×#3866	1	1	yes	characteristic
69	C₂×C₄	C₂×#3866	1	1	yes	characteristic
70	C₂×C₄	C₂×#3866	1	1	yes	characteristic
71	C₈	—	37	2	no	—
72	C₈	—	74	1	no	—
73	C₈	—	74	1	no	—
74	C₈	—	74	1	no	—
75	C₂²	C₂²×#3866	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	2	1	no	—
78	C₄	—	2	1	no	—
79	C₄	—	37	1	no	—
80	C₄	—	37	1	no	—
81	C₄	—	37	2	no	—
82	C₄	—	74	1	no	—
83	C₄	—	74	1	no	—
84	C₂	Q₈×#3866	1	1	yes	characteristic
85	C₂	D₃₇⋊M₁₆	1	1	yes	characteristic
86	C₂	#11924623	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#3866
commutator, socle, prime radical	C₂²×C₃₇	C₂²×C₄
Fitting	C₄⋊C₄×C₃₇	C₄
cosocle	C₂×Dic₃₇	C₂³
hypercenter	C₄⋊C₄	#3866
hypocenter	C₃₇	#446
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
30. #64438	Q₈	semidirect
44. C₃₇	#446	semidirect

Maximal subgroups

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

subgroup	index
#11924603	2
C₄⋊#64438	2
#11924591	2
C₄×#64438	2
#11924501	2
#446	37