Subgroups — #43247725

Order 28352.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₈₈₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#20296771	C₂	1	1	yes	maximal, characteristic
3	#28381809	C₂	1	4	yes	maximal, complemented
4	#117×C₄₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₈₈₆	—	2	1	no	—
6	C₂×Dic₈₈₆	—	2	2	no	—
7	C₂×Dic₈₈₆	C₄	1	4	yes	complemented
8	C₂×Dic₈₈₆	C₂²	1	2	yes	—
9	C₂²×Dic₄₄₃	—	2	1	no	—
10	#20296771	—	2	2	no	—
11	C₂×C₄₄₃⋊C₈	C₂²	1	2	yes	—
12	C₂²×C₄×C₄₄₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₄₄₃	C₂²	1	2	yes	—
14	C₂²⋊C₄×C₄₄₃	—	2	1	no	—
15	C₄²×C₄₄₃	—	2	1	no	—
16	Dic₈₈₆	—	2	4	no	—
17	Dic₈₈₆	—	2	2	no	—
18	Dic₈₈₆	C₂×C₄	1	4	yes	—
19	C₂×Dic₄₄₃	—	2	4	no	—
20	C₂×Dic₄₄₃	—	2	2	no	—
21	C₄₄₃⋊C₈	—	2	2	no	—
22	C₂³×C₄₄₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₄₄₃	—	2	2	no	—
24	C₂×C₄×C₄₄₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₄₄₃	D₄	1	1	yes	characteristic
26	C₂×C₄×C₄₄₃	D₄	1	2	yes	—
27	C₂×C₄×C₄₄₃	C₂³	1	1	yes	characteristic
28	C₂²×C₄₄₃	—	2	2	no	—
29	C₂²×C₄₄₃	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₄₄₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₄₃	—	4	2	no	—
32	C₄×C₄₄₃	C₂²⋊C₄	1	2	yes	—
33	C₄×C₄₄₃	C₂²×C₄	1	1	yes	characteristic
34	C₄×C₄₄₃	C₂×D₄	1	1	yes	characteristic
35	Dic₄₄₃	—	2	4	no	—
36	C₂×C₄₄₃	—	2	2	no	—
37	C₂×C₄₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₄₄₃	#137	1	2	yes	—
39	C₄₄₃	#419	1	1	yes	characteristic, complemented, Sylow
40	#419	—	443	1	no	maximal, Sylow
41	C₂²×Q₈	—	443	1	no	—
42	C₂×M₁₆	—	443	1	no	—
43	#117	D₄₄₃	1	1	yes	characteristic
44	#103	—	443	4	no	—
45	C₂×Q₈	—	886	1	no	—
46	C₂×Q₈	—	886	2	no	—
47	C₂×Q₈	—	443	4	no	—
48	C₂×Q₈	—	443	2	no	—
49	C₂²×C₄	—	886	1	no	—
50	C₂²×C₄	C₂×D₄₄₃	1	1	yes	characteristic
51	M₁₆	—	886	2	no	—
52	C₂×C₈	—	443	2	no	—
53	C₄⋊C₄	C₂×D₄₄₃	1	2	yes	—
54	C₂²⋊C₄	—	2	1	no	—
55	C₄²	—	2	1	no	—
56	C₂³	C₂²⋊D₄₄₃	1	1	yes	characteristic
57	Q₈	—	886	4	no	—
58	Q₈	—	886	2	no	—
59	Q₈	—	443	4	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	886	4	no	—
62	C₂×C₄	—	886	2	no	—
63	C₂×C₄	C₄×D₄₄₃	1	2	yes	—
64	C₂×C₄	C₂²⋊D₄₄₃	1	1	yes	characteristic
65	C₂×C₄	D₁₇₇₂	1	2	yes	—
66	C₂×C₄	C₂²×D₄₄₃	1	1	yes	characteristic
67	C₈	—	886	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	(C₂×D₄₄₃)⋊C₄	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₄₄₃	1	1	yes	characteristic
71	C₄	—	4	2	no	—
72	C₄	—	886	4	no	—
73	C₄	(C₂×D₄₄₃)⋊C₄	1	2	yes	—
74	C₄	C₂×C₄×D₄₄₃	1	1	yes	characteristic
75	C₄	C₂×D₁₇₇₂	1	1	yes	characteristic
76	C₂	—	2	2	no	—
77	C₂	C₂×(C₂×D₄₄₃)⋊C₄	1	1	yes	characteristic
78	C₂	#28381916	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₄₃
commutator	C₄×C₄₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₄₃
Fitting	#117×C₄₄₃	C₂
socle	C₂²×C₄₄₃	C₂×D₄
prime radical	C₂³×C₄₄₃	D₄
cosocle	C₂×C₄×C₄₄₃	C₂³
hypercenter	#117	D₄₄₃
hypocenter	C₄₄₃	#419
LCS	G ▷ C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #28381809	C₂	semidirect
7. C₂×Dic₈₈₆	C₄	semidirect
39. C₄₄₃	#419	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₈₈₆	2
C₂×#20296771	2
#28381809	2
#117×C₄₄₃	2
#419	443