Subgroups — #97×D₁₁₃ #20298545

Order 7232.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₁₃	C₂	1	2	yes	maximal
2	C₄²×D₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#16813533	C₂	1	1	yes	maximal, characteristic, complemented
4	#16813532	C₂	1	2	yes	maximal, complemented
5	#97×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₁₃	C₄	1	2	yes	—
7	C₂×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
8	C₂×#11744751	C₂²	1	2	yes	—
9	C₈×D₁₁₃	C₄	1	8	yes	complemented
10	C₄×Dic₁₁₃	C₄	1	2	yes	—
11	C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₁₃	C₂²	1	2	yes	—
13	C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂²×D₁₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₁₃	C₂×C₄	1	2	yes	—
18	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₁₃	—	2	4	no	—
20	C₄×D₁₁₃	C₂×C₄	1	4	yes	—
21	C₈×C₁₁₃	C₂×C₄	1	4	yes	complemented
22	#11744751	C₂×C₄	1	4	yes	complemented
23	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₁₁₃	C₄²	1	2	yes	—
25	C₂×D₁₁₃	M₁₆	1	4	yes	—
26	C₄×C₁₁₃	—	2	2	no	—
27	C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
28	Dic₁₁₃	—	2	2	no	—
29	Dic₁₁₃	C₄²	1	2	yes	—
30	C₂×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₁₁₃	C₂×M₁₆	1	2	yes	—
32	D₁₁₃	#97	1	4	yes	direct product factor
33	C₁₁₃	C₂×#97	1	1	yes	characteristic, complemented, Sylow
34	C₂×#97	—	113	1	no	maximal, Sylow
35	C₂²×C₈	—	113	2	no	—
36	C₂×C₄²	—	113	1	no	—
37	#97	—	113	2	no	—
38	#97	—	113	1	no	—
39	#97	D₁₁₃	1	1	yes	characteristic, direct product factor
40	C₂²×C₄	—	113	1	no	—
41	C₂²×C₄	—	113	2	no	—
42	C₂×C₈	—	113	2	no	—
43	C₂×C₈	—	113	8	no	—
44	C₂×C₈	C₂×D₁₁₃	1	2	yes	—
45	C₄²	—	113	2	no	—
46	C₄²	—	113	1	no	—
47	C₄²	C₂×D₁₁₃	1	1	yes	characteristic
48	C₂³	—	113	1	no	—
49	C₂×C₄	—	113	1	no	—
50	C₂×C₄	—	113	4	no	—
51	C₂×C₄	—	113	2	no	—
52	C₂×C₄	—	226	4	no	—
53	C₂×C₄	C₄×D₁₁₃	1	2	yes	—
54	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
55	C₈	—	113	4	no	—
56	C₈	C₄×D₁₁₃	1	4	yes	complemented
57	C₂²	—	113	2	no	—
58	C₂²	—	113	4	no	—
59	C₂²	C₂×C₄×D₁₁₃	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	—	113	2	no	—
62	C₄	—	226	2	no	—
63	C₄	C₂×C₄×D₁₁₃	1	2	yes	—
64	C₂	—	113	4	no	—
65	C₂	C₄²×D₁₁₃	1	1	yes	characteristic
66	C₂	M₁₆×D₁₁₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₁₃
commutator	C₂×C₁₁₃	C₂×C₄²
Fitting	#97×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂²×C₄
hypercenter	#97	D₁₁₃
hypocenter	C₁₁₃	C₂×#97
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
3. #16813533	C₂	semidirect
4. #16813532	C₂	semidirect
5. #97×C₁₁₃	C₂	semidirect
9. C₈×D₁₁₃	C₄	semidirect
21. C₈×C₁₁₃	C₂×C₄	semidirect
22. #11744751	C₂×C₄	semidirect
32. D₁₁₃	#97	direct (N × H)
33. C₁₁₃	C₂×#97	semidirect
39. #97	D₁₁₃	direct (N × H)
56. C₈	C₄×D₁₁₃	semidirect

Subgroups — #97×D113 #20298545

Conjugacy classes of subgroups

Complements

Subgroups — #97×D₁₁₃ #20298545