Subgroups — #44400839

Order 29056.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28409832	C₂	1	3	yes	maximal, complemented
2	#28409000	C₂	1	3	yes	maximal, complemented
3	#338×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16813884	C₂²	1	3	yes	—
5	#20300321	—	2	6	no	—
6	#20300316	—	2	6	no	—
7	#20300310	—	2	6	no	—
8	C₂²×C₂₂₇⋊C₈	C₂²	1	1	yes	characteristic
9	(C₂×D₂₂₇)⋊C₈	—	2	6	no	—
10	C₂×M₁₆×C₂₂₇	C₂²	1	3	yes	—
11	#16813884	—	2	6	no	—
12	#16813884	—	2	6	no	—
13	C₂×Dic₄₅₄	D₄	1	3	yes	—
14	C₂×D₉₀₈	D₄	1	3	yes	—
15	C₂×C₂²⋊D₂₂₇	—	2	3	no	—
16	C₂×C₄×D₂₂₇	—	2	3	no	—
17	Dic₉₀₈	—	2	6	no	—
18	#16813873	—	2	12	no	—
19	D₁₈₁₆	—	2	6	no	—
20	C₂×C₂₂₇⋊C₈	—	2	3	no	—
21	C₂²×C₄×C₂₂₇	C₂³	1	1	yes	characteristic
22	M₁₆×C₂₂₇	—	2	6	no	—
23	C₂×C₈×C₂₂₇	D₄	1	6	yes	—
24	C₂²×D₂₂₇	—	2	3	no	—
25	Dic₄₅₄	—	2	6	no	—
26	D₉₀₈	—	2	6	no	—
27	C₂²⋊D₂₂₇	—	4	6	no	—
28	C₂×Dic₂₂₇	—	2	3	no	—
29	C₄×D₂₂₇	—	4	3	no	—
30	C₄×D₂₂₇	—	4	3	no	—
31	C₂₂₇⋊C₈	—	4	1	no	—
32	C₂³×C₂₂₇	#41	1	1	yes	characteristic
33	C₂×C₄×C₂₂₇	C₂×D₄	1	3	yes	—
34	C₂×C₄×C₂₂₇	C₂×D₄	1	3	yes	—
35	C₈×C₂₂₇	—	2	6	no	—
36	C₂²×C₂₂₇	—	4	1	no	—
37	C₂²×C₂₂₇	#121	1	3	yes	—
38	C₂×D₂₂₇	—	4	6	no	—
39	C₂×D₂₂₇	—	4	3	no	—
40	C₄×C₂₂₇	#120	1	3	yes	—
41	C₄×C₂₂₇	#127	1	1	yes	characteristic
42	Dic₂₂₇	—	4	3	no	—
43	C₂×C₂₂₇	—	2	3	no	—
44	C₂×C₂₂₇	#392	1	1	yes	characteristic
45	D₂₂₇	—	8	3	no	—
46	C₂₂₇	#2017	1	1	yes	characteristic, complemented, Sylow
47	#2017	—	227	1	no	maximal, Sylow
48	#575	—	227	3	no	—
49	#408	—	227	3	no	—
50	#338	D₂₂₇	1	1	yes	characteristic, complemented
51	C₂×#41	—	227	3	no	—
52	#137	—	454	6	no	—
53	AGL(1,ℤ/8)	—	454	6	no	—
54	#135	—	454	6	no	—
55	C₂×M₁₆	C₂×D₂₂₇	1	3	yes	—
56	C₂²×C₈	—	227	1	no	—
57	C₂²⋊C₈	—	454	6	no	—
58	#41	—	454	6	no	—
59	#41	—	454	6	no	—
60	C₂×Q₈	—	227	3	no	—
61	C₂×D₄	—	454	3	no	—
62	C₂×D₄	—	227	3	no	—
63	C₂²×C₄	—	454	3	no	—
64	C₂²×C₄	C₂²×D₂₂₇	1	1	yes	characteristic
65	Q₁₆	—	454	6	no	—
66	SD₁₆	—	454	12	no	—
67	D₈	—	454	6	no	—
68	M₁₆	—	2	6	no	—
69	C₂×C₈	—	454	3	no	—
70	C₂×C₈	D₉₀₈	1	6	yes	—
71	C₂³	—	454	3	no	—
72	C₂³	#16813885	1	1	yes	characteristic
73	Q₈	—	454	6	no	—
74	D₄	—	908	6	no	—
75	D₄	—	454	6	no	—
76	C₂×C₄	—	908	3	no	—
77	C₂×C₄	—	908	3	no	—
78	C₂×C₄	—	454	3	no	—
79	C₂×C₄	D₄×D₂₂₇	1	3	yes	—
80	C₂×C₄	C₂×D₉₀₈	1	3	yes	—
81	C₈	—	2	6	no	—
82	C₈	—	908	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	908	6	no	—
85	C₂²	—	908	3	no	—
86	C₂²	#20300263	1	3	yes	—
87	C₄	—	908	3	no	—
88	C₄	#20300258	1	3	yes	—
89	C₄	#20300285	1	1	yes	characteristic
90	C₂	—	2	3	no	—
91	C₂	—	1816	3	no	—
92	C₂	#28408942	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#20300285
commutator, cosocle	C₂²×C₄×C₂₂₇	C₂³
Frattini	C₂²×C₄	C₂²×D₂₂₇
Fitting	#338×C₂₂₇	C₂
socle	C₂×C₂₂₇	#392
hypercenter	#338	D₂₂₇
hypocenter	C₂₂₇	#2017
LCS	G ▷ C₂²×C₄×C₂₂₇ ▷ C₂×C₂₂₇ ▷ C₂₂₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #28409832	C₂	semidirect
2. #28409000	C₂	semidirect
3. #338×C₂₂₇	C₂	semidirect
46. C₂₂₇	#2017	semidirect
50. #338	D₂₂₇	semidirect

Maximal subgroups

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

subgroup	index
#28409832	2
#28409000	2
#338×C₂₂₇	2
#2017	227