Subgroups — #44416688

Order 29248.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20300718	C₂	1	3	yes	maximal
2	#28410459	C₂	1	3	yes	maximal, complemented
3	C₂²×Q₈×C₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄₅₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₄₅₇	C₂²	1	3	yes	—
6	#20300718	—	2	6	no	—
7	C₂×Q₈×C₄₅₇	—	2	6	no	—
8	C₂²×C₄×C₄₅₇	C₂²	1	3	yes	—
9	C₂²×D₄₅₇	—	2	3	no	—
10	C₂²×D₄₅₇	—	2	3	no	—
11	C₂²×D₄₅₇	Q₈	1	2	yes	complemented
12	C₂×Dic₄₅₇	—	2	3	no	—
13	C₂×Dic₄₅₇	—	2	6	no	—
14	C₂³×C₄₅₇	C₂³	1	1	yes	characteristic
15	Q₈×C₄₅₇	—	2	8	no	—
16	C₂×C₄×C₄₅₇	—	2	6	no	—
17	C₂×C₄×C₄₅₇	D₄	1	6	yes	—
18	C₂²×C₄₅₇	C₂×D₄	1	3	yes	—
19	C₂²×C₄₅₇	C₂×Q₈	1	1	yes	characteristic
20	C₂²×C₄₅₇	#41	1	3	yes	—
21	C₂×D₄₅₇	—	2	6	no	—
22	C₂×D₄₅₇	—	4	1	no	—
23	C₂×D₄₅₇	—	4	3	no	—
24	C₄×C₄₅₇	—	2	6	no	—
25	Dic₄₅₇	—	4	3	no	—
26	C₂×C₄₅₇	#120	1	1	yes	characteristic
27	C₂×C₄₅₇	C₂²⋊Q₈	1	3	yes	—
28	C₂×C₄₅₇	#124	1	3	yes	—
29	D₄₅₇	—	4	2	no	—
30	C₄₅₇	#393	1	1	yes	characteristic, complemented, Sylow
31	#393	—	457	1	no	maximal, Sylow
32	C₂²×Q₈	D₄₅₇	1	1	yes	characteristic, complemented
33	C₂×C₂²⋊C₄	—	457	3	no	—
34	#95	—	457	3	no	—
35	C₂⁴	—	457	1	no	—
36	C₂×Q₈	—	2	6	no	—
37	C₂²×C₄	—	457	3	no	—
38	C₂²×C₄	C₂×D₄₅₇	1	3	yes	—
39	C₂²⋊C₄	—	914	6	no	—
40	C₂³	—	914	3	no	—
41	C₂³	—	914	3	no	—
42	C₂³	—	457	2	no	—
43	C₂³	C₂²×D₄₅₇	1	1	yes	characteristic
44	Q₈	—	2	8	no	—
45	C₂×C₄	—	2	6	no	—
46	C₂×C₄	—	914	3	no	—
47	C₂×C₄	—	914	6	no	—
48	C₂×C₄	C₂²⋊D₄₅₇	1	6	yes	—
49	C₂²	—	1828	1	no	—
50	C₂²	—	1828	3	no	—
51	C₂²	—	914	6	no	—
52	C₂²	C₂×C₂²⋊D₄₅₇	1	3	yes	—
53	C₂²	Q₈×D₄₅₇	1	1	yes	characteristic
54	C₂²	#20300742	1	3	yes	—
55	C₄	—	2	6	no	—
56	C₄	—	1828	3	no	—
57	C₂	—	1828	2	no	—
58	C₂	#28410521	1	1	yes	characteristic
59	C₂	#28410528	1	3	yes	—
60	C₂	#28410541	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₅₇
commutator, socle, cosocle	C₂³×C₄₅₇	C₂³
Fitting	C₂²×Q₈×C₄₅₇	C₂
prime radical	C₂³×D₄₅₇	C₂²
hypercenter	C₂²×Q₈	D₄₅₇
hypocenter	C₄₅₇	#393
LCS	G ▷ C₂³×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. #28410459	C₂	semidirect
3. C₂²×Q₈×C₄₅₇	C₂	semidirect
11. C₂²×D₄₅₇	Q₈	semidirect
30. C₄₅₇	#393	semidirect
32. C₂²×Q₈	D₄₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20300718	2
#28410459	2
C₂²×Q₈×C₄₅₇	2
#393	457