Subgroups — #47982754

Order 35456.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31800400	C₂	1	3	yes	maximal, complemented
2	#31800375	C₂	1	3	yes	maximal
3	C₈²×C₂₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17984552	—	2	6	no	—
5	#22579880	C₂²	1	3	yes	—
6	#22579877	C₂²	1	1	yes	characteristic
7	#22579812	—	2	6	no	—
8	C₄×C₈×C₂₇₇	C₂²	1	3	yes	—
9	C₂×Dic₅₅₄	—	2	3	no	—
10	C₂×D₁₁₀₈	—	2	3	no	—
11	#17984552	—	4	12	no	—
12	C₄⋊Dic₂₇₇	—	2	6	no	—
13	C₂×C₈×C₂₇₇	D₄	1	6	yes	—
14	C₄²×C₂₇₇	C₂³	1	1	yes	characteristic
15	C₂²×D₂₇₇	—	4	1	no	—
16	Dic₅₅₄	—	4	6	no	—
17	D₁₁₀₈	—	4	6	no	—
18	C₂×Dic₂₇₇	—	4	3	no	—
19	C₂×C₄×C₂₇₇	C₂×D₄	1	3	yes	—
20	C₈×C₂₇₇	SD₁₆	1	12	yes	complemented
21	C₂²×C₂₇₇	#127	1	1	yes	characteristic
22	C₂×D₂₇₇	—	8	3	no	—
23	C₄×C₂₇₇	C₂×SD₁₆	1	6	yes	—
24	Dic₂₇₇	—	8	3	no	—
25	C₂×C₂₇₇	#492	1	3	yes	—
26	D₂₇₇	—	16	1	no	—
27	C₂₇₇	#1705	1	1	yes	characteristic, complemented, Sylow
28	#1705	—	277	1	no	maximal, Sylow
29	#498	—	277	3	no	—
30	#492	—	277	3	no	—
31	C₈²	D₂₇₇	1	1	yes	characteristic, complemented
32	C₂×SD₁₆	—	554	6	no	—
33	C₄⋊Q₈	—	277	3	no	—
34	#127	—	277	1	no	—
35	#106	—	554	6	no	—
36	C₄×C₈	C₂×D₂₇₇	1	3	yes	—
37	C₂×Q₈	—	554	3	no	—
38	C₂×D₄	—	554	3	no	—
39	SD₁₆	—	1108	12	no	—
40	C₂×C₈	D₁₁₀₈	1	6	yes	—
41	C₄⋊C₄	—	554	6	no	—
42	C₄²	C₂²×D₂₇₇	1	1	yes	characteristic
43	C₂³	—	1108	1	no	—
44	Q₈	—	1108	6	no	—
45	D₄	—	1108	6	no	—
46	C₂×C₄	—	1108	3	no	—
47	C₂×C₄	C₂×D₁₁₀₈	1	3	yes	—
48	C₈	#17984552	1	12	yes	complemented
49	C₂²	—	2216	3	no	—
50	C₂²	#22579877	1	1	yes	characteristic
51	C₄	—	2216	3	no	—
52	C₄	C₂×#17984552	1	6	yes	—
53	C₂	—	4432	1	no	—
54	C₂	#31800375	1	3	yes	—

	subgroup	G/H
center	C₂²	#22579877
commutator, cosocle	C₄²×C₂₇₇	C₂³
Frattini	C₄²	C₂²×D₂₇₇
Fitting	C₈²×C₂₇₇	C₂
socle	C₂²×C₂₇₇	#127
prime radical	#22579877	C₂²
hypercenter	C₈²	D₂₇₇
hypocenter	C₂₇₇	#1705
LCS	G ▷ C₄²×C₂₇₇ ▷ C₂²×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #31800400	C₂	semidirect
3. C₈²×C₂₇₇	C₂	semidirect
20. C₈×C₂₇₇	SD₁₆	semidirect
27. C₂₇₇	#1705	semidirect
31. C₈²	D₂₇₇	semidirect
48. C₈	#17984552	semidirect

Maximal subgroups

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

subgroup	index
#31800400	2
#31800375	2
C₈²×C₂₇₇	2
#1705	277