Subgroups — C₂×#17983999 #22577352

Order 8768.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11764040	C₂	1	2	yes	maximal
2	#17983999	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄²×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11764040	C₄	1	8	yes	complemented
5	C₂×#11764040	C₂²	1	4	yes	—
6	C₂²×C₄×C₁₃₇	C₄	1	2	yes	—
7	C₂²×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
8	C₄²×C₁₃₇	C₄	1	2	yes	—
9	C₄²×C₁₃₇	C₂²	1	2	yes	—
10	#11764040	C₂×C₄	1	8	yes	complemented
11	C₂³×C₁₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₃₇	—	2	4	no	—
13	C₂×C₄×C₁₃₇	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₁₃₇	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
17	C₂²×C₁₃₇	C₄²	1	2	yes	—
18	C₂²×C₁₃₇	M₁₆	1	4	yes	—
19	C₂²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
20	C₄×C₁₃₇	—	2	4	no	—
21	C₄×C₁₃₇	C₄²	1	2	yes	—
22	C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
23	C₂×C₁₃₇	#97	1	4	yes	complemented
24	C₂×C₁₃₇	C₂×C₄²	1	1	yes	characteristic
25	C₂×C₁₃₇	C₂×M₁₆	1	2	yes	—
26	C₁₃₇	C₂×#97	1	1	yes	characteristic, complemented, Sylow
27	C₂×#97	—	137	1	no	maximal, Sylow
28	C₂²×C₈	—	137	2	no	—
29	C₂×C₄²	D₁₃₇	1	1	yes	characteristic
30	#97	—	137	4	no	—
31	C₂²×C₄	Dic₁₃₇	1	2	yes	—
32	C₂²×C₄	C₂×D₁₃₇	1	1	yes	characteristic
33	C₂×C₈	—	137	8	no	—
34	C₂×C₈	—	137	4	no	—
35	C₄²	Dic₁₃₇	1	2	yes	—
36	C₄²	C₂×D₁₃₇	1	2	yes	—
37	C₂³	C₂×Dic₁₃₇	1	1	yes	characteristic
38	C₂×C₄	—	2	4	no	—
39	C₂×C₄	C₄×D₁₃₇	1	4	yes	—
40	C₂×C₄	C₂×Dic₁₃₇	1	4	yes	—
41	C₂×C₄	C₂×Dic₁₃₇	1	1	yes	characteristic
42	C₂×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
43	C₈	—	137	8	no	—
44	C₂²	C₄×Dic₁₃₇	1	2	yes	—
45	C₂²	#14555494	1	4	yes	—
46	C₂²	C₂²×Dic₁₃₇	1	1	yes	characteristic
47	C₄	—	2	4	no	—
48	C₄	C₄×Dic₁₃₇	1	2	yes	—
49	C₄	C₂×C₄×D₁₃₇	1	2	yes	—
50	C₂	#17983999	1	4	yes	direct product factor
51	C₂	C₂×C₄×Dic₁₃₇	1	1	yes	characteristic
52	C₂	C₂×#14555494	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₃₇
commutator	C₂×C₁₃₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₁₃₇
Fitting	C₂×C₄²×C₁₃₇	C₂
socle	C₂³×C₁₃₇	C₂×C₄
hypercenter	C₂×C₄²	D₁₃₇
hypocenter	C₁₃₇	C₂×#97
LCS	G ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #17983999	C₂	direct (N × H)
4. C₂×#11764040	C₄	semidirect
10. #11764040	C₂×C₄	semidirect
23. C₂×C₁₃₇	#97	semidirect
26. C₁₃₇	C₂×#97	semidirect
50. C₂	#17983999	direct (N × H)

Subgroups — C2×#17983999 #22577352

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17983999 #22577352