Subgroups — C₄×#13095519 #20261691

Order 6208.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095519	C₂	1	2	yes	maximal
2	C₄×#11715897	C₂	1	4	yes	maximal, complemented
3	C₄²×D₉₇	C₂	1	1	yes	maximal, characteristic
4	#13095519	C₄	1	8	yes	direct product factor
5	C₂×#11715897	C₂²	1	4	yes	—
6	C₂×C₄×D₉₇	C₄	1	2	yes	—
7	C₂×C₄×D₉₇	C₂²	1	1	yes	characteristic
8	C₄×Dic₉₇	C₄	1	1	yes	characteristic
9	C₄×Dic₉₇	C₂²	1	2	yes	—
10	C₄²×C₉₇	C₄	1	1	yes	characteristic
11	C₂²×D₉₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₉₇	C₂×C₄	1	2	yes	—
14	C₂×Dic₉₇	C₂×C₄	1	2	yes	—
15	C₂×Dic₉₇	C₂³	1	1	yes	characteristic
16	C₄×D₉₇	C₈	1	8	yes	complemented
17	C₄×D₉₇	C₂×C₄	1	4	yes	—
18	#11715897	C₂×C₄	1	8	yes	complemented
19	C₂²×C₉₇	C₂²×C₄	1	1	yes	characteristic
20	C₂×D₉₇	C₄²	1	2	yes	—
21	C₂×D₉₇	C₂×C₈	1	4	yes	—
22	C₄×C₉₇	C₄²	1	2	yes	—
23	C₄×C₉₇	C₂×C₈	1	4	yes	complemented
24	Dic₉₇	C₂×C₈	1	4	yes	complemented
25	Dic₉₇	C₂²×C₄	1	2	yes	—
26	C₂×C₉₇	C₂×C₄²	1	1	yes	characteristic
27	C₂×C₉₇	C₂²×C₈	1	2	yes	—
28	D₉₇	C₄×C₈	1	4	yes	complemented
29	C₉₇	C₂×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₄×C₈	—	97	1	no	maximal, Sylow
31	C₂²×C₈	—	97	2	no	—
32	C₂×C₄²	—	97	1	no	—
33	C₄×C₈	—	97	4	no	—
34	C₂²×C₄	—	97	2	no	—
35	C₂²×C₄	—	97	1	no	—
36	C₂×C₈	—	97	4	no	—
37	C₂×C₈	—	97	8	no	—
38	C₄²	—	97	1	no	—
39	C₄²	—	97	2	no	—
40	C₄²	#87604	1	1	yes	characteristic
41	C₂³	—	97	1	no	—
42	C₂×C₄	—	97	1	no	—
43	C₂×C₄	—	97	2	no	—
44	C₂×C₄	—	97	4	no	—
45	C₂×C₄	—	97	8	no	—
46	C₂×C₄	C₂×#87604	1	1	yes	characteristic
47	C₂×C₄	C₂×#87604	1	2	yes	—
48	C₈	—	97	8	no	—
49	C₂²	—	97	2	no	—
50	C₂²	—	97	4	no	—
51	C₂²	C₂²×#87604	1	1	yes	characteristic
52	C₄	—	97	2	no	—
53	C₄	—	97	4	no	—
54	C₄	C₄×#87604	1	2	yes	—
55	C₄	#13095519	1	4	yes	direct product factor
56	C₂	—	97	4	no	—
57	C₂	C₂×C₄×#87604	1	1	yes	characteristic
58	C₂	C₂×#13095519	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄²	#87604
commutator, hypocenter	C₉₇	C₂×C₄×C₈
Frattini	C₂²	C₂²×#87604
Fitting	C₄²×C₉₇	C₄
socle	C₂²×C₉₇	C₂²×C₄
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₄×#11715897	C₂	semidirect
4. #13095519	C₄	direct (N × H)
16. C₄×D₉₇	C₈	semidirect
18. #11715897	C₂×C₄	semidirect
23. C₄×C₉₇	C₂×C₈	semidirect
24. Dic₉₇	C₂×C₈	semidirect
28. D₉₇	C₄×C₈	semidirect
29. C₉₇	C₂×C₄×C₈	semidirect
55. C₄	#13095519	direct (N × H)

Subgroups — C4×#13095519 #20261691

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13095519 #20261691