Subgroups — C₄×Dic₁₉₄ #15690776

Order 3104.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₉₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₉₇	C₂	1	1	yes	maximal, characteristic
3	#13095490	C₂	1	2	yes	maximal
4	C₄×Dic₉₇	C₂	1	2	yes	maximal
5	C₄²×C₉₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₉₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₉₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₉₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₉₇	C₂²	1	2	yes	—
10	C₂×Dic₉₇	C₂²	1	2	yes	—
11	Dic₁₉₄	C₄	1	4	yes	direct product factor
12	C₂²×C₉₇	C₂³	1	1	yes	characteristic
13	C₄×C₉₇	—	2	1	no	—
14	C₄×C₉₇	C₂×C₄	1	2	yes	—
15	C₄×C₉₇	Q₈	1	2	yes	complemented
16	Dic₉₇	—	2	2	no	—
17	Dic₉₇	C₂×C₄	1	4	yes	—
18	C₂×C₉₇	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₉₇	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₉₇	#41	1	1	yes	characteristic
21	C₉₇	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
22	C₄×Q₈	—	97	1	no	maximal, Sylow
23	C₂×Q₈	—	97	1	no	—
24	C₄⋊C₄	—	97	2	no	—
25	C₄⋊C₄	—	97	1	no	—
26	C₄²	—	97	2	no	—
27	C₄²	D₉₇	1	1	yes	characteristic
28	Q₈	—	97	4	no	—
29	C₂×C₄	—	97	2	no	—
30	C₂×C₄	—	97	2	no	—
31	C₂×C₄	C₂×D₉₇	1	1	yes	characteristic
32	C₂×C₄	C₂×D₉₇	1	1	yes	characteristic
33	C₂×C₄	C₂×D₉₇	1	1	yes	characteristic
34	C₂²	C₂²×D₉₇	1	1	yes	characteristic
35	C₄	—	2	1	no	—
36	C₄	—	97	4	no	—
37	C₄	—	194	2	no	—
38	C₄	Dic₁₉₄	1	2	yes	direct product factor
39	C₄	C₄×D₉₇	1	2	yes	—
40	C₂	C₂×C₄×D₉₇	1	1	yes	characteristic
41	C₂	C₂×Dic₁₉₄	1	1	yes	characteristic
42	C₂	#13095511	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₉₇
commutator	C₂×C₉₇	C₂²×C₄
Frattini	C₂²	C₂²×D₉₇
Fitting	C₄²×C₉₇	C₂
socle, prime radical, cosocle	C₂²×C₉₇	C₂³
hypercenter	C₄²	D₉₇
hypocenter	C₉₇	C₄×Q₈
LCS	G ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
11. Dic₁₉₄	C₄	direct (N × H)
15. C₄×C₉₇	Q₈	semidirect
21. C₉₇	C₄×Q₈	semidirect
38. C₄	Dic₁₉₄	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×Dic₁₉₄	2
C₄⋊Dic₉₇	2
#13095490	2
C₄×Dic₉₇	2
C₄²×C₉₇	2
C₄×Q₈	97

Subgroups — C4×Dic194 #15690776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₁₉₄ #15690776