Subgroups — #47984927

Order 35456.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#17984538	C₂	1	1	yes	maximal, characteristic
2	#31799957	C₂	1	1	yes	maximal, characteristic
3	#31799820	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₂₇₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#17984547	C₄	1	1	yes	characteristic
6	#22579839	C₄	1	1	yes	characteristic
7	C₂×#17984538	—	2	2	no	—
8	C₂×#17984538	C₂²	1	2	yes	—
9	#22579790	C₄	1	2	yes	—
10	C₈×Dic₂₇₇	C₂²	1	2	yes	—
11	C₂²×C₈×C₂₇₇	C₂²	1	1	yes	characteristic
12	M₃₂×C₂₇₇	—	2	2	no	—
13	C₂×C₁₆×C₂₇₇	C₂²	1	2	yes	—
14	#17984547	—	2	2	no	—
15	C₂×#14555660	C₂×C₄	1	2	yes	—
16	C₄⋊Dic₂₇₇	C₈	1	2	yes	—
17	C₂²⋊Dic₂₇₇	C₈	1	2	yes	—
18	C₄×Dic₂₇₇	C₂×C₄	1	2	yes	—
19	#17984538	—	2	2	no	—
20	C₂²×C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₂₇₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₂₇₇	D₄	1	2	yes	—
23	C₂×C₈×C₂₇₇	Q₈	1	2	yes	—
24	C₂×C₈×C₂₇₇	C₂³	1	1	yes	characteristic
25	C₁₆×C₂₇₇	—	2	2	no	—
26	C₂×Dic₂₇₇	C₂×C₈	1	4	yes	—
27	#14555660	—	2	2	no	—
28	C₂³×C₂₇₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₂₇₇	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₂₇₇	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₂₇₇	M₁₆	1	2	yes	—
32	C₂×C₄×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₂₇₇	C₄⋊C₄	1	2	yes	—
34	C₈×C₂₇₇	C₂×D₄	1	1	yes	characteristic
35	C₈×C₂₇₇	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₂₇₇	—	2	2	no	—
37	C₂²×C₂₇₇	C₄⋊C₈	1	2	yes	—
38	C₂²×C₂₇₇	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₂₇₇	C₄⋊C₈	1	2	yes	—
40	C₄×C₂₇₇	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₂₇₇	C₂×M₁₆	1	1	yes	characteristic
42	Dic₂₇₇	—	2	4	no	—
43	C₂×C₂₇₇	—	2	2	no	—
44	C₂×C₂₇₇	C₂×C₄⋊C₈	1	1	yes	characteristic
45	C₂×C₂₇₇	#504	1	2	yes	—
46	C₂₇₇	#2151	1	1	yes	characteristic, complemented, Sylow
47	#2151	—	277	1	no	maximal, Sylow
48	C₂×M₃₂	D₂₇₇	1	1	yes	characteristic
49	C₂²×C₁₆	—	277	1	no	—
50	#405	—	277	1	no	—
51	C₄⋊C₁₆	—	277	4	no	—
52	C₂×M₁₆	—	277	1	no	—
53	C₂²×C₈	C₂×D₂₇₇	1	1	yes	characteristic
54	#117	—	277	1	no	—
55	M₃₂	—	2	2	no	—
56	C₂×C₁₆	—	277	2	no	—
57	C₂×C₁₆	—	554	2	no	—
58	C₂×C₁₆	C₂×D₂₇₇	1	2	yes	—
59	#97	—	277	2	no	—
60	C₄×C₈	—	277	2	no	—
61	C₂²×C₄	C₄×D₂₇₇	1	1	yes	characteristic
62	M₁₆	—	554	2	no	—
63	C₂×C₈	—	277	2	no	—
64	C₂×C₈	C₄×D₂₇₇	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₂₇₇	1	2	yes	—
66	C₂×C₈	Dic₅₅₄	1	2	yes	—
67	C₂×C₈	C₂²×D₂₇₇	1	1	yes	characteristic
68	C₄⋊C₄	—	277	2	no	—
69	C₂²⋊C₄	—	277	2	no	—
70	C₄²	—	277	2	no	—
71	C₁₆	—	2	2	no	—
72	C₁₆	—	554	2	no	—
73	C₂³	C₈×D₂₇₇	1	1	yes	characteristic
74	C₂×C₄	—	277	4	no	—
75	C₂×C₄	#17984542	1	2	yes	—
76	C₂×C₄	C₈×D₂₇₇	1	1	yes	characteristic
77	C₂×C₄	#17984546	1	2	yes	—
78	C₂×C₄	C₂×C₄×D₂₇₇	1	1	yes	characteristic
79	C₈	—	554	2	no	—
80	C₈	#17984542	1	2	yes	—
81	C₈	C₂×C₂²⋊D₂₇₇	1	1	yes	characteristic
82	C₈	C₂×Dic₅₅₄	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	#22579809	1	2	yes	—
85	C₂²	C₂×C₈×D₂₇₇	1	1	yes	characteristic
86	C₄	—	554	4	no	—
87	C₄	#22579809	1	2	yes	—
88	C₄	C₂×#17984542	1	1	yes	characteristic
89	C₄	C₂×#17984546	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×#22579809	1	1	yes	characteristic
92	C₂	#31800420	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₂₇₇
commutator, socle	C₂²×C₂₇₇	C₂²×C₈
Fitting	C₂×M₃₂×C₂₇₇	C₂
prime radical	C₂³×C₂₇₇	C₂×C₈
cosocle	C₂×C₈×C₂₇₇	C₂³
hypercenter	C₂×M₃₂	D₂₇₇
hypocenter	C₂₇₇	#2151
LCS	G ▷ C₂²×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #31799820	C₂	semidirect
46. C₂₇₇	#2151	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#17984538	2
#31799957	2
#31799820	2
C₂×M₃₂×C₂₇₇	2
#2151	277