Subgroups — #31800921

Order 17728.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22579955	C₂	1	1	yes	maximal, characteristic
2	#22579950	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₂₇₇	C₂	1	1	yes	maximal, characteristic
4	#17984573	—	2	1	no	—
5	#17984566	—	2	1	no	—
6	Q₈×D₂₇₇	—	2	1	no	—
7	Dic₁₁₀₈	C₄	1	1	yes	characteristic
8	#17984553	—	2	1	no	—
9	C₈×D₂₇₇	C₂²	1	1	yes	characteristic
10	Q₁₆×C₂₇₇	C₄	1	1	yes	characteristic
11	#14555667	—	4	1	no	—
12	Dic₅₅₄	—	2	1	no	—
13	Dic₅₅₄	—	4	1	no	—
14	C₄×D₂₇₇	—	4	1	no	—
15	C₄×D₂₇₇	D₄	1	1	yes	characteristic
16	#14555660	D₄	1	1	yes	characteristic
17	Q₈×C₂₇₇	—	2	1	no	—
18	C₈×C₂₇₇	C₂×C₄	1	1	yes	characteristic
19	C₂×D₂₇₇	SD₁₆	1	1	yes	characteristic
20	C₄×C₂₇₇	—	4	1	no	—
21	C₄×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₂₇₇	—	4	1	no	—
23	Dic₂₇₇	D₈	1	1	yes	characteristic
24	C₂×C₂₇₇	#102	1	1	yes	characteristic
25	D₂₇₇	—	2	1	no	—
26	C₂₇₇	#362	1	1	yes	characteristic, complemented, Sylow
27	#362	—	277	1	no	maximal, Sylow
28	C₂×Q₁₆	—	277	1	no	—
29	M₃₂	—	277	1	no	—
30	#108	—	277	1	no	—
31	C₂×Q₈	—	554	1	no	—
32	Q₁₆	—	277	1	no	—
33	Q₁₆	—	554	1	no	—
34	Q₁₆	#11764308	1	1	yes	characteristic
35	M₁₆	—	554	1	no	—
36	C₂×C₈	—	277	1	no	—
37	C₁₆	—	554	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	554	1	no	—
40	Q₈	—	1108	1	no	—
41	C₂×C₄	—	277	1	no	—
42	C₂×C₄	—	1108	1	no	—
43	C₈	—	277	1	no	—
44	C₈	—	1108	1	no	—
45	C₈	C₂×#11764308	1	1	yes	characteristic
46	C₂²	—	277	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	277	1	no	—
49	C₄	—	1108	1	no	—
50	C₄	C₂²⋊#11764308	1	1	yes	characteristic
51	C₂	—	554	1	no	—
52	C₂	#22579942	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22579942
commutator	C₈×C₂₇₇	C₂×C₄
Frattini	C₈	C₂×#11764308
Fitting	Q₁₆×C₂₇₇	C₄
socle	C₂×C₂₇₇	#102
prime radical	C₂×D₂₇₇	SD₁₆
cosocle	C₈×D₂₇₇	C₂²
hypercenter	Q₁₆	#11764308
hypocenter	C₂₇₇	#362
LCS	G ▷ C₈×C₂₇₇ ▷ C₄×C₂₇₇ ▷ C₂×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
26. C₂₇₇	#362	semidirect

Maximal subgroups

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

subgroup	index
#22579955	2
#22579950	2
Q₁₆×D₂₇₇	2
#362	277