Subgroups — C₂×C₄×#11764308 #22579956

Order 8864.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11764308	C₂	1	2	yes	maximal
2	C₄×#11764308	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×D₂₇₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11764308	C₄	1	8	yes	direct product factor
5	C₂×#11764308	C₂²	1	4	yes	—
6	C₂²×D₂₇₇	C₂²	1	1	yes	characteristic
7	C₂×Dic₂₇₇	C₄	1	1	yes	characteristic, complemented
8	C₄×D₂₇₇	C₄	1	2	yes	complemented
9	C₄×D₂₇₇	C₂²	1	2	yes	—
10	C₂×C₄×C₂₇₇	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₂₇₇	C₂×C₄	1	1	yes	characteristic
12	C₂×D₂₇₇	C₂×C₄	1	1	yes	characteristic
13	C₂×D₂₇₇	C₂×C₄	1	4	yes	—
14	C₂×D₂₇₇	C₂³	1	1	yes	characteristic
15	#11764308	C₂×C₄	1	8	yes	direct product factor
16	C₄×C₂₇₇	C₂×C₄	1	2	yes	complemented
17	Dic₂₇₇	C₂×C₄	1	2	yes	complemented
18	C₂×C₂₇₇	C₄²	1	2	yes	complemented
19	C₂×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
20	D₂₇₇	C₄²	1	2	yes	complemented
21	D₂₇₇	C₂²×C₄	1	2	yes	—
22	C₂₇₇	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₄²	—	277	1	no	maximal, Sylow
24	C₂²×C₄	—	277	2	no	—
25	C₂²×C₄	—	277	1	no	—
26	C₄²	—	277	4	no	—
27	C₂³	—	277	1	no	—
28	C₂×C₄	—	277	8	no	—
29	C₂×C₄	—	277	4	no	—
30	C₂×C₄	—	277	1	no	—
31	C₂×C₄	—	277	2	no	—
32	C₂×C₄	—	277	2	no	—
33	C₂×C₄	#11764308	1	1	yes	characteristic, direct product factor
34	C₂²	—	277	4	no	—
35	C₂²	—	277	1	no	—
36	C₂²	—	277	1	no	—
37	C₂²	C₂×#11764308	1	1	yes	characteristic
38	C₄	—	277	8	no	—
39	C₄	—	277	2	no	—
40	C₄	C₂×#11764308	1	2	yes	direct product factor
41	C₂	—	277	2	no	—
42	C₂	—	277	2	no	—
43	C₂	C₄×#11764308	1	2	yes	direct product factor
44	C₂	C₂²×#11764308	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	#11764308
commutator, hypocenter	C₂₇₇	C₂×C₄²
Frattini	C₂	C₂²×#11764308
Fitting	C₂×C₄×C₂₇₇	C₄
socle	C₂²×C₂₇₇	C₂×C₄
LCS	G ▷ C₂₇₇
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×#11764308	C₂	direct (N × H)
4. C₂×#11764308	C₄	direct (N × H)
7. C₂×Dic₂₇₇	C₄	semidirect
8. C₄×D₂₇₇	C₄	semidirect
10. C₂×C₄×C₂₇₇	C₄	semidirect
15. #11764308	C₂×C₄	direct (N × H)
16. C₄×C₂₇₇	C₂×C₄	semidirect
17. Dic₂₇₇	C₂×C₄	semidirect
18. C₂×C₂₇₇	C₄²	semidirect
20. D₂₇₇	C₄²	semidirect
22. C₂₇₇	C₂×C₄²	semidirect
33. C₂×C₄	#11764308	direct (N × H)
40. C₄	C₂×#11764308	direct (N × H)
43. C₂	C₄×#11764308	direct (N × H)

Subgroups — C2×C4×#11764308 #22579956

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄×#11764308 #22579956