Subgroups — C₄×Dic₇₈₈ #27161175

Order 12608.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₈₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃₉₄	C₂	1	2	yes	maximal
3	#20263260	C₂	1	1	yes	maximal, characteristic
4	#20263251	C₂	1	2	yes	maximal
5	C₄×C₈×C₁₉₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₉₄	C₂²	1	2	yes	—
7	Dic₇₈₈	C₄	1	4	yes	direct product factor
8	C₄⋊Dic₁₉₇	C₂²	1	2	yes	—
9	#15691337	—	2	2	no	—
10	C₄×Dic₁₉₇	—	2	2	no	—
11	C₂×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
13	C₄²×C₁₉₇	C₂²	1	1	yes	characteristic
14	Dic₃₉₄	—	2	2	no	—
15	Dic₃₉₄	C₂×C₄	1	4	yes	—
16	C₂×Dic₁₉₇	—	2	2	no	—
17	C₂×Dic₁₉₇	—	2	2	no	—
18	C₂×C₄×C₁₉₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₉₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
21	C₈×C₁₉₇	—	2	1	no	—
22	C₈×C₁₉₇	C₂×C₄	1	2	yes	—
23	C₂²×C₁₉₇	C₂×D₄	1	1	yes	characteristic
24	C₄×C₁₉₇	—	2	1	no	—
25	C₄×C₁₉₇	Q₁₆	1	2	yes	complemented
26	C₄×C₁₉₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₁₉₇	#41	1	1	yes	characteristic
28	Dic₁₉₇	—	2	4	no	—
29	Dic₁₉₇	—	4	2	no	—
30	C₂×C₁₉₇	C₄×D₄	1	1	yes	characteristic
31	C₂×C₁₉₇	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₁₉₇	#135	1	1	yes	characteristic
33	C₁₉₇	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×Q₁₆	—	197	1	no	maximal, Sylow
35	C₂×Q₁₆	—	197	1	no	—
36	C₄×Q₈	—	197	2	no	—
37	#107	—	197	1	no	—
38	#103	—	197	2	no	—
39	C₄×C₈	D₁₉₇	1	1	yes	characteristic
40	C₂×Q₈	—	197	2	no	—
41	Q₁₆	—	197	4	no	—
42	C₂×C₈	C₂×D₁₉₇	1	1	yes	characteristic
43	C₂×C₈	C₂×D₁₉₇	1	1	yes	characteristic
44	C₄⋊C₄	—	394	2	no	—
45	C₄⋊C₄	—	197	2	no	—
46	C₄²	—	394	2	no	—
47	C₄²	C₂×D₁₉₇	1	1	yes	characteristic
48	Q₈	—	394	2	no	—
49	Q₈	—	197	4	no	—
50	C₂×C₄	—	394	2	no	—
51	C₂×C₄	—	394	2	no	—
52	C₂×C₄	D₇₈₈	1	1	yes	characteristic
53	C₂×C₄	D₇₈₈	1	1	yes	characteristic
54	C₂×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	C₄×D₁₉₇	1	2	yes	—
57	C₂²	C₂×D₇₈₈	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	788	2	no	—
60	C₄	—	394	4	no	—
61	C₄	Dic₇₈₈	1	2	yes	direct product factor
62	C₄	C₂×C₄×D₁₉₇	1	1	yes	characteristic
63	C₄	#15691358	1	1	yes	characteristic
64	C₂	C₄×D₇₈₈	1	1	yes	characteristic
65	C₂	C₂×Dic₇₈₈	1	1	yes	characteristic
66	C₂	#20263348	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₇₈₈
commutator	C₄×C₁₉₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₉₇
Fitting	C₄×C₈×C₁₉₇	C₂
socle, prime radical	C₂²×C₁₉₇	C₂×D₄
cosocle	C₂×C₄×C₁₉₇	C₂³
hypercenter	C₄×C₈	D₁₉₇
hypocenter	C₁₉₇	C₄×Q₁₆
LCS	G ▷ C₄×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
7. Dic₇₈₈	C₄	direct (N × H)
25. C₄×C₁₉₇	Q₁₆	semidirect
33. C₁₉₇	C₄×Q₁₆	semidirect
61. C₄	Dic₇₈₈	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×Dic₇₈₈	2
C₄×Dic₃₉₄	2
#20263260	2
#20263251	2
C₄×C₈×C₁₉₇	2
C₄×Q₁₆	197

Subgroups — C4×Dic788 #27161175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₇₈₈ #27161175