Subgroups — #42122669

Order 27712.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28357287	C₂	1	2	yes	maximal, complemented
2	#28357216	C₂	1	1	yes	maximal, characteristic
3	C₂×#16812365	—	2	2	no	—
4	C₂×D₁₇₃₂	C₄	1	1	yes	characteristic
5	C₂×C₂²⋊D₄₃₃	—	2	2	no	—
6	C₄×Dic₄₃₃	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₄₃₃	C₄	1	1	yes	characteristic
8	#16812365	—	4	2	no	—
9	C₂²×D₄₃₃	—	2	1	no	—
10	D₁₇₃₂	—	4	1	no	—
11	C₂²⋊D₄₃₃	—	4	2	no	—
12	C₂²⋊D₄₃₃	—	4	2	no	—
13	C₂×Dic₄₃₃	D₄	1	2	yes	—
14	C₂³×C₄₃₃	—	2	1	no	—
15	D₄×C₄₃₃	—	4	1	no	—
16	C₂×C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄₃₃	—	4	1	no	—
18	C₂²×C₄₃₃	—	4	2	no	—
19	C₂²×C₄₃₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×D₄₃₃	—	4	1	no	—
21	C₂×D₄₃₃	—	4	2	no	—
22	C₄×C₄₃₃	—	2	1	no	—
23	Dic₄₃₃	D₈	1	2	yes	—
24	Dic₄₃₃	SD₁₆	1	2	yes	—
25	C₂×C₄₃₃	—	8	1	no	—
26	C₂×C₄₃₃	#100	1	1	yes	characteristic
27	C₂×C₄₃₃	#102	1	2	yes	—
28	D₄₃₃	—	8	1	no	—
29	C₄₃₃	#331	1	1	yes	characteristic, complemented, Sylow
30	#331	—	433	1	no	maximal, Sylow
31	#127	—	433	1	no	—
32	C₄⋊C₈	—	433	2	no	—
33	C₂×D₄	—	866	2	no	—
34	C₂×D₄	—	433	1	no	—
35	C₂×D₄	#13181884	1	1	yes	characteristic
36	C₂×C₈	—	866	2	no	—
37	C₄²	—	433	1	no	—
38	C₂³	—	2	1	no	—
39	C₂³	—	866	1	no	—
40	D₄	—	4	1	no	—
41	D₄	—	1732	1	no	—
42	D₄	—	1732	2	no	—
43	D₄	—	1732	2	no	—
44	C₂×C₄	—	433	2	no	—
45	C₂×C₄	C₂×#13181884	1	1	yes	characteristic
46	C₈	—	1732	2	no	—
47	C₂²	—	4	1	no	—
48	C₂²	—	4	2	no	—
49	C₂²	—	1732	1	no	—
50	C₂²	—	1732	2	no	—
51	C₂²	C₂²⋊#13181884	1	1	yes	characteristic
52	C₄	—	2	1	no	—
53	C₄	—	433	2	no	—
54	C₄	—	433	2	no	—
55	C₂	—	8	1	no	—
56	C₂	—	3464	1	no	—
57	C₂	#28357280	1	1	yes	characteristic
58	C₂	#28357282	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²⋊#13181884
commutator	C₂×C₄×C₄₃₃	C₂×C₄
Frattini	C₂×C₄	C₂×#13181884
Fitting	C₂×D₄×C₄₃₃	C₄
socle	C₂²×C₄₃₃	C₂²⋊C₄
prime radical	#28357216	C₂
cosocle	C₄×Dic₄₃₃	C₂²
hypercenter	C₂×D₄	#13181884
hypocenter	C₄₃₃	#331
LCS	G ▷ C₂×C₄×C₄₃₃ ▷ C₂²×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #28357287	C₂	semidirect
29. C₄₃₃	#331	semidirect

Maximal subgroups

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

subgroup	index
#28357287	2
#28357216	2
#331	433