Subgroups — #47981224

Order 35456.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31800407	C₂	1	1	yes	maximal, characteristic
2	#31799755	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₂₇₇	C₂	1	1	yes	maximal, characteristic
4	#22579880	—	2	1	no	—
5	#22579814	—	2	1	no	—
6	#22579814	C₄	1	2	yes	—
7	C₄⋊#14555660	—	2	1	no	—
8	C₂×C₁₆×C₂₇₇	—	2	1	no	—
9	C₄×C₈×C₂₇₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₅₅₄	—	4	1	no	—
11	C₂×#14555660	—	4	1	no	—
12	C₄⋊Dic₂₇₇	—	2	2	no	—
13	C₄⋊Dic₂₇₇	—	4	1	no	—
14	C₂×C₈×C₂₇₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₇₇	D₄	1	1	yes	characteristic
16	C₄²×C₂₇₇	D₄	1	1	yes	characteristic
17	C₁₆×C₂₇₇	—	4	1	no	—
18	Dic₅₅₄	—	8	2	no	—
19	C₂×Dic₂₇₇	—	4	2	no	—
20	#14555660	—	8	1	no	—
21	C₂×C₄×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₇₇	D₈	1	1	yes	characteristic
23	C₂×C₄×C₂₇₇	SD₁₆	1	1	yes	characteristic
24	C₈×C₂₇₇	—	2	1	no	—
25	C₈×C₂₇₇	SD₁₆	1	1	yes	characteristic
26	C₈×C₂₇₇	Q₁₆	1	1	yes	characteristic
27	C₂²×C₂₇₇	#102	1	1	yes	characteristic
28	C₄×C₂₇₇	—	2	1	no	—
29	C₄×C₂₇₇	#101	1	1	yes	characteristic
30	C₄×C₂₇₇	#103	1	1	yes	characteristic
31	C₄×C₂₇₇	SD₃₂	1	1	yes	characteristic
32	C₄×C₂₇₇	Q₃₂	1	1	yes	characteristic
33	Dic₂₇₇	—	8	2	no	—
34	C₂×C₂₇₇	#332	1	1	yes	characteristic
35	C₂×C₂₇₇	#358	1	1	yes	characteristic
36	C₂×C₂₇₇	#361	1	1	yes	characteristic
37	C₂₇₇	#1365	1	1	yes	characteristic, complemented, Sylow
38	#1365	—	277	1	no	maximal, Sylow
39	#500	—	277	1	no	—
40	C₄⋊C₁₆	D₂₇₇	1	1	yes	characteristic
41	#335	—	277	1	no	—
42	C₄⋊Q₈	—	554	1	no	—
43	C₂×C₁₆	—	2	1	no	—
44	#107	—	277	2	no	—
45	#107	—	554	1	no	—
46	C₄⋊C₈	—	554	1	no	—
47	C₄×C₈	C₂×D₂₇₇	1	1	yes	characteristic
48	C₂×Q₈	—	1108	1	no	—
49	C₂×C₈	—	1108	1	no	—
50	C₂×C₈	C₄×D₂₇₇	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₂₇₇	1	1	yes	characteristic
52	C₄⋊C₄	—	554	2	no	—
53	C₄⋊C₄	—	1108	1	no	—
54	C₄²	D₁₁₀₈	1	1	yes	characteristic
55	C₁₆	—	4	1	no	—
56	Q₈	—	2216	2	no	—
57	C₂×C₄	—	1108	2	no	—
58	C₂×C₄	#17984540	1	1	yes	characteristic
59	C₂×C₄	D₂₂₁₆	1	1	yes	characteristic
60	C₂×C₄	#17984552	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	2216	1	no	—
63	C₈	#17984551	1	1	yes	characteristic
64	C₈	#17984553	1	1	yes	characteristic
65	C₂²	#22579802	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	2216	2	no	—
68	C₄	#22579798	1	1	yes	characteristic
69	C₄	#22579803	1	1	yes	characteristic
70	C₄	#22579825	1	1	yes	characteristic
71	C₄	Dic₂₂₁₆	1	1	yes	characteristic
72	C₂	#31799747	1	1	yes	characteristic
73	C₂	#31799807	1	1	yes	characteristic
74	C₂	#31799816	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22579802
commutator	C₂×C₈×C₂₇₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₇₇
Fitting	C₄⋊C₁₆×C₂₇₇	C₂
socle, prime radical	C₂²×C₂₇₇	#102
cosocle	C₄×C₈×C₂₇₇	C₂²
hypercenter	C₄⋊C₁₆	D₂₇₇
hypocenter	C₂₇₇	#1365
LCS	G ▷ C₂×C₈×C₂₇₇ ▷ C₂×C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
37. C₂₇₇	#1365	semidirect

Maximal subgroups

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

subgroup	index
#31800407	2
#31799755	2
C₄⋊C₁₆×C₂₇₇	2
#1365	277