Subgroups — #47984748

Order 35456.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31800051	C₂	1	1	yes	maximal, characteristic
2	#31800030	C₂	1	1	yes	maximal, characteristic
3	#31799774	C₂	1	2	yes	maximal
4	#31799766	C₂	1	2	yes	maximal
5	#338×C₂₇₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#17984547	C₂²	1	2	yes	—
7	C₂²×#14555660	C₂²	1	1	yes	characteristic
8	#22579839	C₂²	1	1	yes	characteristic
9	#22579816	—	2	2	no	—
10	#22579809	—	2	2	no	—
11	C₂×M₁₆×C₂₇₇	C₂²	1	2	yes	—
12	C₂×M₁₆×C₂₇₇	C₂²	1	1	yes	characteristic
13	#17984547	—	2	2	no	—
14	#17984547	—	2	2	no	—
15	C₂×#14555660	—	2	1	no	—
16	C₂×#14555660	—	2	2	no	—
17	C₂×#14555660	—	2	2	no	—
18	C₄⋊Dic₂₇₇	—	2	1	no	—
19	C₂²⋊Dic₂₇₇	Q₈	1	2	yes	—
20	C₄×Dic₂₇₇	—	2	1	no	—
21	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
22	M₁₆×C₂₇₇	—	2	2	no	—
23	M₁₆×C₂₇₇	—	2	2	no	—
24	M₁₆×C₂₇₇	—	2	2	no	—
25	C₂×C₈×C₂₇₇	—	2	2	no	—
26	C₂×C₈×C₂₇₇	D₄	1	2	yes	—
27	C₂×Dic₂₇₇	—	2	2	no	—
28	#14555660	—	4	1	no	—
29	#14555660	—	4	2	no	—
30	C₂³×C₂₇₇	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₄×C₂₇₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₂₇₇	#41	1	2	yes	—
33	C₂×C₄×C₂₇₇	#41	1	1	yes	characteristic
34	C₂×C₄×C₂₇₇	#41	1	2	yes	—
35	C₈×C₂₇₇	—	2	2	no	—
36	C₈×C₂₇₇	—	4	2	no	—
37	C₂²×C₂₇₇	—	4	1	no	—
38	C₂²×C₂₇₇	C₂²⋊Q₈	1	1	yes	characteristic
39	C₂²×C₂₇₇	#125	1	2	yes	—
40	C₄×C₂₇₇	#123	1	1	yes	characteristic
41	C₄×C₂₇₇	#124	1	1	yes	characteristic
42	C₄×C₂₇₇	#126	1	2	yes	—
43	Dic₂₇₇	—	4	2	no	—
44	C₂×C₂₇₇	—	2	1	no	—
45	C₂×C₂₇₇	—	2	2	no	—
46	C₂×C₂₇₇	#400	1	1	yes	characteristic
47	C₂₇₇	#2103	1	1	yes	characteristic, complemented, Sylow
48	#2103	—	277	1	no	maximal, Sylow
49	#430	—	277	1	no	—
50	#424	—	277	1	no	—
51	#344	—	277	2	no	—
52	#341	—	277	2	no	—
53	#338	D₂₇₇	1	1	yes	characteristic
54	C₂×M₁₆	—	277	2	no	—
55	C₂×M₁₆	C₂×D₂₇₇	1	2	yes	—
56	C₂×M₁₆	C₂×D₂₇₇	1	1	yes	characteristic
57	C₂²×C₈	—	277	1	no	—
58	#117	—	277	1	no	—
59	#108	—	554	2	no	—
60	C₄⋊C₈	—	554	2	no	—
61	C₂²×C₄	C₂²×D₂₇₇	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	2	2	no	—
64	M₁₆	—	2	2	no	—
65	M₁₆	—	554	2	no	—
66	M₁₆	—	554	2	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	554	1	no	—
69	C₂×C₈	—	554	2	no	—
70	C₂×C₈	—	554	2	no	—
71	C₂×C₈	D₁₁₀₈	1	2	yes	—
72	C₄⋊C₄	—	554	1	no	—
73	C₂²⋊C₄	—	277	2	no	—
74	C₄²	—	554	1	no	—
75	C₂³	Q₈×D₂₇₇	1	1	yes	characteristic
76	C₂×C₄	—	554	2	no	—
77	C₂×C₄	C₂×D₁₁₀₈	1	1	yes	characteristic
78	C₂×C₄	#17984562	1	2	yes	—
79	C₂×C₄	#17984562	1	1	yes	characteristic
80	C₂×C₄	#17984563	1	2	yes	—
81	C₈	—	2	2	no	—
82	C₈	—	4	2	no	—
83	C₈	—	1108	1	no	—
84	C₈	—	1108	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#22579860	1	1	yes	characteristic
87	C₂²	#22579870	1	2	yes	—
88	C₄	—	1108	2	no	—
89	C₄	#22579864	1	1	yes	characteristic
90	C₄	#22579868	1	1	yes	characteristic
91	C₄	#22579873	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#31799942	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#22579868
commutator, cosocle	C₂²×C₄×C₂₇₇	C₂³
Frattini	C₂²×C₄	C₂²×D₂₇₇
Fitting	#338×C₂₇₇	C₂
socle	C₂×C₂₇₇	#400
prime radical	C₂³×C₂₇₇	C₂×Q₈
hypercenter	#338	D₂₇₇
hypocenter	C₂₇₇	#2103
LCS	G ▷ C₂²×C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
47. C₂₇₇	#2103	semidirect

Maximal subgroups

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

subgroup	index
#31800051	2
#31800030	2
#31799774	2
#31799766	2
#338×C₂₇₇	2
#2103	277