Subgroups — #47983306

Order 35456.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31800025	C₂	1	2	yes	maximal
2	C₂×#22579790	C₂	1	1	yes	maximal, characteristic
3	#31799767	C₂	1	1	yes	maximal, characteristic
4	#31799766	C₂	1	2	yes	maximal
5	#341×C₂₇₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#17984547	C₂²	1	2	yes	—
7	C₂²×#14555660	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₂₇₇	C₂²	1	1	yes	characteristic
9	#22579809	—	2	4	no	—
10	#22579790	C₄	1	4	yes	—
11	C₂×M₁₆×C₂₇₇	C₂²	1	2	yes	—
12	C₂²×C₈×C₂₇₇	C₂²	1	1	yes	characteristic
13	C₂²×Dic₂₇₇	Q₈	1	2	yes	—
14	#17984547	—	2	2	no	—
15	#17984547	—	2	2	no	—
16	C₂×#14555660	—	2	2	no	—
17	C₂×#14555660	—	2	2	no	—
18	C₂×#14555660	C₂×C₄	1	2	yes	—
19	C₄×Dic₂₇₇	C₂×C₄	1	2	yes	—
20	C₄×Dic₂₇₇	D₄	1	2	yes	—
21	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
22	M₁₆×C₂₇₇	—	2	2	no	—
23	M₁₆×C₂₇₇	—	2	2	no	—
24	C₂×C₈×C₂₇₇	—	2	2	no	—
25	C₂×C₈×C₂₇₇	—	2	2	no	—
26	C₂×C₈×C₂₇₇	C₂×C₄	1	2	yes	—
27	C₂×Dic₂₇₇	—	4	2	no	—
28	C₂×Dic₂₇₇	C₄⋊C₄	1	4	yes	—
29	#14555660	—	2	2	no	—
30	#14555660	—	4	2	no	—
31	C₂³×C₂₇₇	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₇₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₂₇₇	#41	1	2	yes	—
35	C₂×C₄×C₂₇₇	#41	1	2	yes	—
36	C₈×C₂₇₇	—	2	2	no	—
37	C₈×C₂₇₇	—	4	2	no	—
38	C₂²×C₂₇₇	—	2	2	no	—
39	C₂²×C₂₇₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₂₇₇	#125	1	2	yes	—
41	C₄×C₂₇₇	#117	1	1	yes	characteristic
42	C₄×C₂₇₇	#117	1	1	yes	characteristic
43	C₄×C₂₇₇	#124	1	2	yes	—
44	Dic₂₇₇	—	2	4	no	—
45	C₂×C₂₇₇	—	2	2	no	—
46	C₂×C₂₇₇	#382	1	1	yes	characteristic
47	C₂×C₂₇₇	#430	1	2	yes	—
48	C₂₇₇	#1838	1	1	yes	characteristic, complemented, Sylow
49	#1838	—	277	1	no	maximal, Sylow
50	#423	—	277	2	no	—
51	C₂×#97	—	277	1	no	—
52	#341	—	277	2	no	—
53	#341	—	277	1	no	—
54	#341	D₂₇₇	1	1	yes	characteristic
55	C₂×M₁₆	—	277	2	no	—
56	C₂×M₁₆	C₂×D₂₇₇	1	2	yes	—
57	C₂²×C₈	—	277	1	no	—
58	C₂²×C₈	C₂×D₂₇₇	1	1	yes	characteristic
59	C₂×C₄²	—	277	1	no	—
60	C₄⋊C₈	—	554	4	no	—
61	#97	—	277	4	no	—
62	C₂²×C₄	—	277	2	no	—
63	C₂²×C₄	C₂²×D₂₇₇	1	1	yes	characteristic
64	M₁₆	—	2	2	no	—
65	M₁₆	—	2	2	no	—
66	M₁₆	—	554	2	no	—
67	M₁₆	—	554	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	277	2	no	—
71	C₂×C₈	—	554	2	no	—
72	C₂×C₈	—	554	2	no	—
73	C₂×C₈	C₄×D₂₇₇	1	2	yes	—
74	C₄²	—	277	2	no	—
75	C₄²	—	277	2	no	—
76	C₂³	Q₈×D₂₇₇	1	1	yes	characteristic
77	C₂×C₄	—	277	4	no	—
78	C₂×C₄	—	1108	2	no	—
79	C₂×C₄	C₂×C₄×D₂₇₇	1	1	yes	characteristic
80	C₂×C₄	D₄×D₂₇₇	1	1	yes	characteristic
81	C₂×C₄	#17984562	1	2	yes	—
82	C₂×C₄	#17984563	1	2	yes	—
83	C₈	—	2	2	no	—
84	C₈	—	4	2	no	—
85	C₈	—	554	2	no	—
86	C₈	—	1108	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	C₄⋊C₄×D₂₇₇	1	1	yes	characteristic
89	C₂²	#22579870	1	2	yes	—
90	C₄	—	554	4	no	—
91	C₄	#22579836	1	1	yes	characteristic
92	C₄	#22579837	1	1	yes	characteristic
93	C₄	#22579866	1	2	yes	—
94	C₂	—	2	2	no	—
95	C₂	#31799866	1	1	yes	characteristic
96	C₂	#31800049	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₇₇
commutator	C₂×C₄×C₂₇₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₇₇
Fitting	#341×C₂₇₇	C₂
socle	C₂²×C₂₇₇	C₂×C₄⋊C₄
prime radical	C₂³×C₂₇₇	C₂×Q₈
cosocle	C₂²×C₄×C₂₇₇	C₂³
hypercenter	#341	D₂₇₇
hypocenter	C₂₇₇	#1838
LCS	G ▷ C₂×C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

Complements

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

N	H ≅ G/N	type
48. C₂₇₇	#1838	semidirect

Maximal subgroups

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

subgroup	index
#31800025	2
C₂×#22579790	2
#31799767	2
#31799766	2
#341×C₂₇₇	2
#1838	277