Subgroups — C₄⋊#14555513 #22578323

Order 8768.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14555513	C₂	1	2	yes	maximal
2	C₄×#11764040	C₂	1	1	yes	maximal, characteristic
3	#14555513	—	2	2	no	—
4	C₂×#11764040	C₄	1	1	yes	characteristic
5	C₂×#11764040	C₂²	1	1	yes	characteristic
6	C₄²×C₁₃₇	C₄	1	1	yes	characteristic
7	#11764040	—	2	1	no	—
8	#11764040	D₄	1	1	yes	characteristic
9	#11764040	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₃₇	C₈	1	1	yes	characteristic
11	C₂×C₄×C₁₃₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₁₃₇	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₃₇	—	2	1	no	—
15	C₄×C₁₃₇	C₁₆	1	2	yes	complemented
16	C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₃₇	M₁₆	1	1	yes	characteristic
18	C₂×C₁₃₇	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₃₇	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₁₃₇	M₃₂	1	1	yes	characteristic
21	C₁₃₇	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	137	1	no	maximal, Sylow
23	C₂×C₁₆	—	137	2	no	—
24	C₄×C₈	—	137	1	no	—
25	C₂×C₈	—	137	1	no	—
26	C₂×C₈	—	137	1	no	—
27	C₄²	#10587739	1	1	yes	characteristic
28	C₁₆	—	274	2	no	—
29	C₂×C₄	#11764047	1	1	yes	characteristic
30	C₂×C₄	#11764047	1	1	yes	characteristic
31	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
32	C₈	—	274	1	no	—
33	C₈	—	137	1	no	—
34	C₈	—	137	1	no	—
35	C₂²	C₂×#11764047	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	#14555513	1	2	yes	complemented
38	C₄	C₄⋊#10587739	1	1	yes	characteristic
39	C₄	#14555520	1	1	yes	characteristic
40	C₂	C₄⋊#11764047	1	1	yes	characteristic
41	C₂	C₂×#14555513	1	1	yes	characteristic
42	C₂	#17984162	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#10587739
commutator	C₂×C₁₃₇	C₂×C₁₆
Fitting	C₄²×C₁₃₇	C₄
socle	C₂²×C₁₃₇	C₂×C₈
hypercenter	C₄²	#10587739
hypocenter	C₁₃₇	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
15. C₄×C₁₃₇	C₁₆	semidirect
21. C₁₃₇	C₄⋊C₁₆	semidirect
37. C₄	#14555513	semidirect

Subgroups — C4⋊#14555513 #22578323

Conjugacy classes of subgroups

Complements

Subgroups — C₄⋊#14555513 #22578323