Subgroups — #47981359

Order 35456.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₂₁₆	C₂	1	1	yes	maximal, characteristic
2	#31799836	C₂	1	1	yes	maximal, characteristic
3	#368×C₂₇₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₀₈	—	2	1	no	—
5	Dic₂₂₁₆	—	2	1	no	—
6	Dic₂₂₁₆	C₄	1	2	yes	—
7	#22579786	—	2	1	no	—
8	C₂×C₁₆×C₂₇₇	C₂²	1	1	yes	characteristic
9	#108×C₂₇₇	—	2	1	no	—
10	C₂×Dic₅₅₄	—	4	1	no	—
11	Dic₁₁₀₈	—	2	2	no	—
12	Dic₁₁₀₈	—	4	1	no	—
13	M₁₆×C₂₇₇	—	4	1	no	—
14	C₂×C₈×C₂₇₇	D₄	1	1	yes	characteristic
15	C₁₆×C₂₇₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₇₇	D₄	1	1	yes	characteristic
17	Dic₅₅₄	—	4	2	no	—
18	Dic₅₅₄	—	8	1	no	—
19	C₂×Dic₂₇₇	—	8	1	no	—
20	C₂×C₄×C₂₇₇	D₈	1	1	yes	characteristic
21	C₈×C₂₇₇	—	8	1	no	—
22	C₈×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₇₇	SD₁₆	1	1	yes	characteristic
24	C₂²×C₂₇₇	SD₃₂	1	1	yes	characteristic
25	C₄×C₂₇₇	#102	1	1	yes	characteristic
26	C₄×C₂₇₇	D₁₆	1	1	yes	characteristic
27	Dic₂₇₇	—	8	2	no	—
28	C₂×C₂₇₇	—	2	1	no	—
29	C₂×C₂₇₇	#357	1	1	yes	characteristic
30	C₂₇₇	#1420	1	1	yes	characteristic, complemented, Sylow
31	#1420	—	277	1	no	maximal, Sylow
32	C₂×Q₃₂	—	277	1	no	—
33	M₆₄	—	277	1	no	—
34	#368	D₂₇₇	1	1	yes	characteristic
35	C₂×Q₁₆	—	554	1	no	—
36	Q₃₂	—	277	2	no	—
37	Q₃₂	—	554	1	no	—
38	C₂×C₁₆	C₂×D₂₇₇	1	1	yes	characteristic
39	#108	—	2	1	no	—
40	C₃₂	—	554	1	no	—
41	C₂×Q₈	—	1108	1	no	—
42	Q₁₆	—	554	2	no	—
43	Q₁₆	—	1108	1	no	—
44	M₁₆	—	4	1	no	—
45	C₂×C₈	C₂²⋊D₂₇₇	1	1	yes	characteristic
46	C₁₆	C₄×D₂₇₇	1	1	yes	characteristic
47	C₁₆	D₁₁₀₈	1	1	yes	characteristic
48	Q₈	—	1108	2	no	—
49	Q₈	—	2216	1	no	—
50	C₂×C₄	—	2216	1	no	—
51	C₂×C₄	#17984548	1	1	yes	characteristic
52	C₈	—	8	1	no	—
53	C₈	#17984540	1	1	yes	characteristic
54	C₈	#17984550	1	1	yes	characteristic
55	C₂²	#22579823	1	1	yes	characteristic
56	C₄	—	2216	2	no	—
57	C₄	#22579800	1	1	yes	characteristic
58	C₄	#22579821	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#31799802	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31799802
commutator	C₁₆×C₂₇₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₇₇
Fitting	#368×C₂₇₇	C₂
socle	C₂×C₂₇₇	#357
prime radical	C₂²×C₂₇₇	SD₃₂
cosocle	C₂×C₁₆×C₂₇₇	C₂²
hypercenter	#368	D₂₇₇
hypocenter	C₂₇₇	#1420
LCS	G ▷ C₁₆×C₂₇₇ ▷ C₈×C₂₇₇ ▷ C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
30. C₂₇₇	#1420	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₂₂₁₆	2
#31799836	2
#368×C₂₇₇	2
#1420	277