Subgroups — C₁₆×#11764308 #31800886

Order 17728.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₇₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×#11764308	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₂₇₇	C₂	1	1	yes	maximal, characteristic
4	D₂₇₇⋊C₈	C₄	1	1	yes	characteristic
5	C₄×#11764308	C₄	1	1	yes	characteristic
6	#17984566	C₄	1	2	yes	complemented
7	C₈×D₂₇₇	C₂²	1	1	yes	characteristic
8	#17984538	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₂₇₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#11764308	C₈	1	2	yes	—
11	#14555667	C₈	1	2	yes	—
12	C₄×D₂₇₇	C₂×C₄	1	1	yes	characteristic
13	#14555660	C₂×C₄	1	1	yes	characteristic
14	C₈×C₂₇₇	C₂×C₄	1	1	yes	characteristic
15	C₂×D₂₇₇	C₂×C₈	1	1	yes	characteristic
16	#11764308	C₁₆	1	4	yes	direct product factor
17	C₄×C₂₇₇	C₄²	1	1	yes	characteristic
18	Dic₂₇₇	C₂×C₈	1	1	yes	characteristic
19	C₂×C₂₇₇	C₄×C₈	1	1	yes	characteristic
20	D₂₇₇	C₂×C₁₆	1	2	yes	—
21	C₂₇₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	277	1	no	maximal, Sylow
23	C₂×C₁₆	—	277	1	no	—
24	C₂×C₁₆	—	277	1	no	—
25	C₄×C₈	—	277	1	no	—
26	C₂×C₈	—	277	1	no	—
27	C₂×C₈	—	277	1	no	—
28	C₄²	—	277	1	no	—
29	C₁₆	—	277	2	no	—
30	C₁₆	—	277	1	no	—
31	C₁₆	#11764308	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	277	2	no	—
33	C₂×C₄	—	277	1	no	—
34	C₈	—	277	2	no	—
35	C₈	—	277	1	no	—
36	C₈	C₂×#11764308	1	1	yes	characteristic
37	C₂²	—	277	1	no	—
38	C₄	—	277	4	no	—
39	C₄	—	277	1	no	—
40	C₄	C₄×#11764308	1	1	yes	characteristic
41	C₂	—	277	2	no	—
42	C₂	C₈×#11764308	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#11764308
commutator, hypocenter	C₂₇₇	C₄×C₁₆
Frattini	C₈	C₂×#11764308
Fitting	C₁₆×C₂₇₇	C₄
socle	C₂×C₂₇₇	C₄×C₈
prime radical	C₂×D₂₇₇	C₂×C₈
cosocle	C₈×D₂₇₇	C₂²
LCS	G ▷ C₂₇₇
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
6. #17984566	C₄	semidirect
8. #17984538	C₄	semidirect
9. C₁₆×C₂₇₇	C₄	semidirect
16. #11764308	C₁₆	direct (N × H)
21. C₂₇₇	C₄×C₁₆	semidirect
31. C₁₆	#11764308	direct (N × H)

Maximal subgroups

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

subgroup	index
D₂₇₇⋊C₁₆	2
C₈×#11764308	2
C₁₆×D₂₇₇	2
C₄×C₁₆	277

Subgroups — C16×#11764308 #31800886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×#11764308 #31800886