Subgroups — #44399340

Order 29056.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28409412	C₂	1	1	yes	maximal, characteristic, complemented
2	#28409409	C₂	1	1	yes	maximal, characteristic
3	#28409379	C₂	1	4	yes	maximal, complemented
4	C₈²×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₉₀₈	—	2	2	no	—
6	C₂×D₁₈₁₆	—	2	2	no	—
7	#20300288	C₂²	1	2	yes	—
8	#20300285	C₂²	1	2	yes	—
9	#20300210	—	2	8	no	—
10	C₄×C₈×C₂₂₇	C₂²	1	2	yes	—
11	C₄×C₈×C₂₂₇	C₂²	1	1	yes	characteristic
12	C₂×Dic₄₅₄	—	2	2	no	—
13	C₂×D₉₀₈	—	2	2	no	—
14	C₂×D₉₀₈	—	2	4	no	—
15	Dic₉₀₈	—	4	4	no	—
16	D₁₈₁₆	—	4	4	no	—
17	C₄⋊Dic₂₂₇	—	2	4	no	—
18	C₂×C₈×C₂₂₇	D₄	1	4	yes	—
19	C₂×C₈×C₂₂₇	D₄	1	2	yes	—
20	C₄²×C₂₂₇	C₂³	1	1	yes	characteristic
21	C₂²×D₂₂₇	—	4	2	no	—
22	Dic₄₅₄	—	4	4	no	—
23	D₉₀₈	—	4	4	no	—
24	D₉₀₈	—	4	8	no	—
25	C₂×Dic₂₂₇	—	4	2	no	—
26	C₂×C₄×C₂₂₇	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₂₂₇	C₂×D₄	1	2	yes	—
28	C₈×C₂₂₇	—	2	4	no	—
29	C₈×C₂₂₇	D₈	1	4	yes	—
30	C₂²×C₂₂₇	#127	1	1	yes	characteristic
31	C₂×D₂₂₇	—	8	2	no	—
32	C₂×D₂₂₇	—	8	4	no	—
33	C₄×C₂₂₇	C₂×D₈	1	2	yes	—
34	C₄×C₂₂₇	#135	1	4	yes	—
35	Dic₂₂₇	—	8	2	no	—
36	C₂×C₂₂₇	#493	1	1	yes	characteristic
37	C₂×C₂₂₇	#495	1	2	yes	—
38	D₂₂₇	—	16	2	no	—
39	C₂₂₇	#1709	1	1	yes	characteristic, complemented, Sylow
40	#1709	—	227	1	no	maximal, Sylow
41	#494	—	227	1	no	—
42	#493	—	227	1	no	—
43	#486	—	227	4	no	—
44	C₈²	D₂₂₇	1	1	yes	characteristic, complemented
45	C₂×Q₁₆	—	454	2	no	—
46	C₂×D₈	—	454	2	no	—
47	C₄⋊Q₈	—	227	2	no	—
48	#127	—	227	2	no	—
49	#102	—	454	8	no	—
50	C₄×C₈	C₂×D₂₂₇	1	2	yes	—
51	C₄×C₈	C₂×D₂₂₇	1	1	yes	characteristic
52	C₂×Q₈	—	454	2	no	—
53	C₂×D₄	—	454	4	no	—
54	C₂×D₄	—	454	2	no	—
55	Q₁₆	—	908	4	no	—
56	D₈	—	908	4	no	—
57	C₂×C₈	D₉₀₈	1	4	yes	—
58	C₂×C₈	D₉₀₈	1	2	yes	—
59	C₄⋊C₄	—	454	4	no	—
60	C₄²	C₂²×D₂₂₇	1	1	yes	characteristic
61	C₂³	—	908	2	no	—
62	Q₈	—	908	4	no	—
63	D₄	—	908	4	no	—
64	D₄	—	908	8	no	—
65	C₂×C₄	—	908	2	no	—
66	C₂×C₄	C₂×D₉₀₈	1	1	yes	characteristic
67	C₂×C₄	C₂×D₉₀₈	1	2	yes	—
68	C₈	—	2	4	no	—
69	C₈	D₁₈₁₆	1	4	yes	—
70	C₂²	—	1816	2	no	—
71	C₂²	—	1816	4	no	—
72	C₂²	#20300285	1	1	yes	characteristic
73	C₄	—	1816	2	no	—
74	C₄	C₂×D₁₈₁₆	1	2	yes	—
75	C₄	#20300310	1	4	yes	—
76	C₂	—	3632	2	no	—
77	C₂	#28409409	1	1	yes	characteristic
78	C₂	#28409416	1	2	yes	—

	subgroup	G/H
center	C₂²	#20300285
commutator, cosocle	C₄²×C₂₂₇	C₂³
Frattini	C₄²	C₂²×D₂₂₇
Fitting	C₈²×C₂₂₇	C₂
socle	C₂²×C₂₂₇	#127
prime radical	#28409409	C₂
hypercenter	C₈²	D₂₂₇
hypocenter	C₂₂₇	#1709
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
1. #28409412	C₂	semidirect
3. #28409379	C₂	semidirect
4. C₈²×C₂₂₇	C₂	semidirect
39. C₂₂₇	#1709	semidirect
44. C₈²	D₂₂₇	semidirect

Maximal subgroups

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

subgroup	index
#28409412	2
#28409409	2
#28409379	2
C₈²×C₂₂₇	2
#1709	227