Subgroups — #47981261

Order 35456.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22579816	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₂₇₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#17984547	—	2	2	no	—
4	#22579816	—	2	2	no	—
5	#22579816	C₄	1	4	yes	—
6	C₂²×C₈×C₂₇₇	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₂₇₇	—	2	2	no	—
8	C₂×C₁₆×C₂₇₇	C₄	1	2	yes	—
9	#17984547	—	2	4	no	—
10	#17984547	—	4	2	no	—
11	C₂×#14555660	—	4	2	no	—
12	C₂²×C₄×C₂₇₇	D₄	1	1	yes	characteristic
13	C₂×C₈×C₂₇₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₇₇	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₂₇₇	D₄	1	2	yes	—
16	C₂×C₈×C₂₇₇	Q₈	1	1	yes	characteristic
17	C₁₆×C₂₇₇	—	2	2	no	—
18	#14555660	—	4	4	no	—
19	C₂³×C₂₇₇	Q₁₆	1	1	yes	characteristic
20	C₂×C₄×C₂₇₇	C₂²⋊C₄	1	2	yes	—
21	C₂×C₄×C₂₇₇	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₇₇	D₈	1	1	yes	characteristic
23	C₂×C₄×C₂₇₇	SD₁₆	1	2	yes	—
24	C₈×C₂₇₇	C₄²	1	1	yes	characteristic
25	C₈×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₇₇	C₄⋊C₄	1	2	yes	—
27	C₂²×C₂₇₇	—	2	2	no	—
28	C₂²×C₂₇₇	#103	1	2	yes	—
29	C₂²×C₂₇₇	#107	1	1	yes	characteristic
30	C₄×C₂₇₇	#95	1	1	yes	characteristic
31	C₄×C₂₇₇	#102	1	2	yes	—
32	C₄×C₂₇₇	#106	1	1	yes	characteristic
33	C₂×C₂₇₇	—	2	2	no	—
34	C₂×C₂₇₇	#340	1	1	yes	characteristic
35	C₂×C₂₇₇	#368	1	2	yes	—
36	C₂₇₇	#1381	1	1	yes	characteristic, complemented, Sylow
37	#1381	—	277	1	no	maximal, Sylow
38	C₂²×C₁₆	D₂₇₇	1	1	yes	characteristic
39	C₂×#108	—	277	2	no	—
40	C₂×M₁₆	—	554	2	no	—
41	C₂²×C₈	C₂×D₂₇₇	1	1	yes	characteristic
42	C₂×C₁₆	—	2	2	no	—
43	C₂×C₁₆	Dic₂₇₇	1	2	yes	—
44	#108	—	277	4	no	—
45	#108	—	554	2	no	—
46	C₂²×C₄	D₁₁₀₈	1	1	yes	characteristic
47	M₁₆	—	554	4	no	—
48	M₁₆	—	1108	2	no	—
49	C₂×C₈	—	1108	2	no	—
50	C₂×C₈	C₄×D₂₇₇	1	2	yes	—
51	C₂×C₈	C₂×Dic₂₇₇	1	1	yes	characteristic
52	C₂×C₈	C₂²⋊D₂₇₇	1	2	yes	—
53	C₂×C₈	Dic₅₅₄	1	1	yes	characteristic
54	C₁₆	—	2	2	no	—
55	C₂³	Dic₁₁₀₈	1	1	yes	characteristic
56	C₂×C₄	#17984540	1	2	yes	—
57	C₂×C₄	C₄⋊Dic₂₇₇	1	1	yes	characteristic
58	C₂×C₄	D₂₂₁₆	1	1	yes	characteristic
59	C₂×C₄	#17984552	1	2	yes	—
60	C₈	—	1108	4	no	—
61	C₈	C₄×Dic₂₇₇	1	1	yes	characteristic
62	C₈	C₂²⋊Dic₂₇₇	1	1	yes	characteristic
63	C₈	#17984542	1	2	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	#22579805	1	2	yes	—
66	C₂²	#22579814	1	1	yes	characteristic
67	C₄	#22579787	1	1	yes	characteristic
68	C₄	#22579802	1	2	yes	—
69	C₄	#22579812	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	#31799765	1	1	yes	characteristic
72	C₂	#31799832	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₂₂₁₆
commutator	C₈×C₂₇₇	C₄²
Frattini	C₂²×C₈	C₂×D₂₇₇
Fitting	C₂²×C₁₆×C₂₇₇	C₂
socle	C₂²×C₂₇₇	#107
prime radical	C₂³×C₂₇₇	Q₁₆
cosocle	C₂²×C₈×C₂₇₇	C₂²
hypercenter	C₂²×C₁₆	D₂₇₇
hypocenter	C₂₇₇	#1381
LCS	G ▷ C₈×C₂₇₇ ▷ C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
36. C₂₇₇	#1381	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22579816	2
C₂²×C₁₆×C₂₇₇	2
#1381	277