Subgroups — #22578324

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	C₈×Dic₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#14555513	—	2	2	no	—
4	C₂×#11764040	C₂²	1	1	yes	characteristic
5	C₄×Dic₁₃₇	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₃₇	C₄	1	1	yes	characteristic
7	C₂×Dic₁₃₇	C₈	1	1	yes	characteristic
8	C₂×Dic₁₃₇	C₈	1	1	yes	characteristic
9	#11764040	D₄	1	1	yes	characteristic
10	#11764040	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₃₇	—	2	1	no	—
13	C₂²×C₁₃₇	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₃₇	M₁₆	1	1	yes	characteristic
16	Dic₁₃₇	—	2	1	no	—
17	Dic₁₃₇	C₁₆	1	2	yes	complemented
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	#10587739	1	1	yes	characteristic
27	C₄²	—	137	1	no	—
28	C₁₆	—	274	2	no	—
29	C₂×C₄	—	137	1	no	—
30	C₂×C₄	—	137	1	no	—
31	C₂×C₄	C₂×#10587739	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	137	1	no	—
34	C₈	—	137	1	no	—
35	C₂²	#14555518	1	1	yes	characteristic
36	C₄	—	274	1	no	—
37	C₄	—	137	2	no	—
38	C₄	C₄⋊#10587739	1	1	yes	characteristic
39	C₄	#14555519	1	1	yes	characteristic
40	C₂	#17984155	1	1	yes	characteristic
41	C₂	#17984161	1	1	yes	characteristic
42	C₂	#17984163	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
17. Dic₁₃₇	C₁₆	semidirect
21. C₁₃₇	C₄⋊C₁₆	semidirect