Subgroups — #44399352

Order 29056.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28409437	C₂	1	4	yes	maximal
2	#28409412	C₂	1	2	yes	maximal
3	C₈²×C₂₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₉₀₈	—	2	4	no	—
5	#20300288	C₂²	1	4	yes	—
6	#20300222	—	2	8	no	—
7	C₄×C₈×C₂₂₇	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₂₂₇	C₂²	1	2	yes	—
9	C₂×Dic₄₅₄	—	2	4	no	—
10	Dic₉₀₈	—	4	8	no	—
11	C₄⋊Dic₂₂₇	—	2	8	no	—
12	C₂×C₈×C₂₂₇	D₄	1	2	yes	—
13	C₂×C₈×C₂₂₇	D₄	1	4	yes	—
14	C₄²×C₂₂₇	C₂³	1	1	yes	characteristic
15	Dic₄₅₄	—	4	8	no	—
16	C₂×Dic₂₂₇	—	4	4	no	—
17	C₂×C₄×C₂₂₇	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₂₇	C₂×D₄	1	2	yes	—
19	C₈×C₂₂₇	D₈	1	4	yes	—
20	C₈×C₂₂₇	Q₁₆	1	8	yes	complemented
21	C₂²×C₂₂₇	#127	1	1	yes	characteristic
22	C₄×C₂₂₇	C₂×D₈	1	2	yes	—
23	C₄×C₂₂₇	C₂×Q₁₆	1	4	yes	—
24	Dic₂₂₇	—	8	4	no	—
25	C₂×C₂₂₇	#493	1	1	yes	characteristic
26	C₂×C₂₂₇	#494	1	2	yes	—
27	C₂₂₇	#1713	1	1	yes	characteristic, complemented, Sylow
28	#1713	—	227	1	no	maximal, Sylow
29	#500	—	227	4	no	—
30	#494	—	227	2	no	—
31	C₈²	D₂₂₇	1	1	yes	characteristic
32	C₂×Q₁₆	—	454	4	no	—
33	C₄⋊Q₈	—	227	4	no	—
34	#107	—	454	8	no	—
35	C₄×C₈	C₂×D₂₂₇	1	1	yes	characteristic
36	C₄×C₈	C₂×D₂₂₇	1	2	yes	—
37	C₂×Q₈	—	454	4	no	—
38	Q₁₆	—	908	8	no	—
39	C₂×C₈	D₉₀₈	1	2	yes	—
40	C₂×C₈	D₉₀₈	1	4	yes	—
41	C₄⋊C₄	—	454	8	no	—
42	C₄²	C₂²×D₂₂₇	1	1	yes	characteristic
43	Q₈	—	908	8	no	—
44	C₂×C₄	—	908	4	no	—
45	C₂×C₄	C₂×D₉₀₈	1	1	yes	characteristic
46	C₂×C₄	C₂×D₉₀₈	1	2	yes	—
47	C₈	D₁₈₁₆	1	4	yes	—
48	C₈	Dic₉₀₈	1	8	yes	complemented
49	C₂²	#20300285	1	1	yes	characteristic
50	C₄	—	1816	4	no	—
51	C₄	C₂×D₁₈₁₆	1	2	yes	—
52	C₄	C₂×Dic₉₀₈	1	4	yes	—
53	C₂	#28409409	1	1	yes	characteristic
54	C₂	#28409412	1	2	yes	—

	subgroup	G/H
center	C₂²	#20300285
commutator, cosocle	C₄²×C₂₂₇	C₂³
Frattini	C₄²	C₂²×D₂₂₇
Fitting	C₈²×C₂₂₇	C₂
socle, prime radical	C₂²×C₂₂₇	#127
hypercenter	C₈²	D₂₂₇
hypocenter	C₂₂₇	#1713
LCS	G ▷ C₄²×C₂₂₇ ▷ C₂²×C₂₂₇ ▷ C₂₂₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₂₂₇	Q₁₆	semidirect
27. C₂₂₇	#1713	semidirect
48. C₈	Dic₉₀₈	semidirect

Maximal subgroups

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

subgroup	index
#28409437	2
#28409412	2
C₈²×C₂₂₇	2
#1713	227