Group #38787067 — subgroups

Subgroups — (C₂×#13107944)⋊Q₈ #38787067

Order 25664.

186 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#13107944	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#13107944	C₂	1	1	yes	maximal, characteristic
3	(C₂×#13107944)⋊C₄	C₂	1	4	yes	maximal
4	C₂×Q₈×D₄₀₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#13107944	C₂²	1	2	yes	—
6	C₂²×#13107944	C₂²	1	2	yes	—
7	C₄⋊#13107944	—	2	2	no	—
8	C₄×#13107944	—	2	2	no	—
9	C₂×Dic₈₀₂	C₄	1	2	yes	complemented
10	C₂×Dic₈₀₂	C₄	1	1	yes	characteristic, complemented
11	Q₈×D₄₀₁	—	2	2	no	—
12	Q₈×D₄₀₁	—	2	2	no	—
13	C₂×C₄×D₄₀₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄₀₁	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₀₁	C₄	1	1	yes	characteristic, complemented
16	C₂×#13107944	—	2	2	no	—
17	C₂×#13107944	—	2	2	no	—
18	C₂×#13107944	—	2	2	no	—
19	C₂×#13107944	—	2	4	no	—
20	C₂×#13107944	Q₈	1	4	yes	complemented
21	C₂²×D₄₀₁	C₂³	1	1	yes	characteristic
22	Dic₈₀₂	—	2	2	no	—
23	Dic₈₀₂	—	2	4	no	—
24	C₂×Dic₄₀₁	C₂×C₄	1	2	yes	—
25	C₂×Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
26	C₄×D₄₀₁	—	2	2	no	—
27	C₄×D₄₀₁	—	2	2	no	—
28	C₄×D₄₀₁	D₄	1	2	yes	—
29	C₄×D₄₀₁	D₄	1	2	yes	—
30	Q₈×C₄₀₁	—	2	2	no	—
31	C₂×C₄×C₄₀₁	C₂×C₄	1	2	yes	—
32	C₂×C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄₀₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×D₄₀₁	C₂×D₄	1	1	yes	characteristic
35	C₂×D₄₀₁	C₂×D₄	1	1	yes	characteristic
36	C₂×D₄₀₁	C₂×Q₈	1	2	yes	—
37	C₂×D₄₀₁	#41	1	2	yes	—
38	#13107944	—	2	4	no	—
39	#13107944	—	4	2	no	—
40	C₄×C₄₀₁	—	2	2	no	—
41	C₄×C₄₀₁	C₂²⋊C₄	1	2	yes	—
42	Dic₄₀₁	—	2	2	no	—
43	Dic₄₀₁	C₂²⋊C₄	1	2	yes	—
44	C₂×C₄₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄₀₁	C₄×Q₈	1	2	yes	—
46	D₄₀₁	C₂²⋊Q₈	1	2	yes	—
47	D₄₀₁	#124	1	1	yes	characteristic
48	D₄₀₁	C₄⋊Q₈	1	1	yes	characteristic
49	C₄₀₁	#391	1	1	yes	characteristic, complemented, Sylow
50	#391	—	401	1	no	maximal, Sylow
51	C₂²×Q₈	—	401	1	no	—
52	C₂×C₄⋊C₄	—	401	1	no	—
53	C₂×C₄²	—	401	1	no	—
54	#95	—	401	4	no	—
55	C₂×Q₈	—	802	2	no	—
56	C₂×Q₈	—	802	2	no	—
57	C₂×Q₈	—	401	1	no	—
58	C₂×Q₈	—	401	2	no	—
59	C₂×Q₈	#13107944	1	1	yes	characteristic, complemented
60	C₂²×C₄	—	401	2	no	—
61	C₂²×C₄	—	401	2	no	—
62	C₂²×C₄	—	401	2	no	—
63	C₂²×C₄	—	401	1	no	—
64	C₄⋊C₄	—	802	2	no	—
65	C₄²	—	802	2	no	—
66	C₂³	—	401	1	no	—
67	Q₈	—	2	2	no	—
68	Q₈	—	802	4	no	—
69	Q₈	—	802	2	no	—
70	C₂×C₄	—	802	2	no	—
71	C₂×C₄	—	802	2	no	—
72	C₂×C₄	—	802	2	no	—
73	C₂×C₄	—	802	2	no	—
74	C₂×C₄	—	802	2	no	—
75	C₂×C₄	—	802	4	no	—
76	C₂×C₄	—	401	4	no	—
77	C₂×C₄	—	401	2	no	—
78	C₂×C₄	—	401	1	no	—
79	C₂×C₄	—	401	2	no	—
80	C₂×C₄	—	401	2	no	—
81	C₂×C₄	C₂×#13107944	1	2	yes	—
82	C₂×C₄	C₂×#13107944	1	1	yes	characteristic
83	C₂²	—	401	1	no	—
84	C₂²	—	401	1	no	—
85	C₂²	—	401	2	no	—
86	C₂²	—	401	2	no	—
87	C₂²	C₂²×#13107944	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	802	4	no	—
90	C₄	—	802	2	no	—
91	C₄	—	1604	2	no	—
92	C₄	—	401	2	no	—
93	C₄	C₂²⋊#13107944	1	2	yes	—
94	C₂	—	401	2	no	—
95	C₂	—	401	1	no	—
96	C₂	—	401	1	no	—
97	C₂	C₂×C₂²⋊#13107944	1	1	yes	characteristic
98	C₂	Q₈×#13107944	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#13107944

C₂

yes

maximal, characteristic

C₂×C₄×#13107944

C₂

yes

maximal, characteristic

(C₂×#13107944)⋊C₄

C₂

yes

maximal

C₂×Q₈×D₄₀₁

C₂

yes

maximal, characteristic

C₂²×#13107944

C₂²

yes

—

C₂²×#13107944

C₂²

yes

—

C₄⋊#13107944

—

C₄×#13107944

—

C₂×Dic₈₀₂

C₄

yes

complemented

C₂×Dic₈₀₂

C₄

yes

characteristic, complemented

Q₈×D₄₀₁

—

Q₈×D₄₀₁

—

C₂×C₄×D₄₀₁

C₂²

yes

—

C₂×C₄×D₄₀₁

C₂²

yes

characteristic

C₂×Q₈×C₄₀₁

C₄

yes

characteristic, complemented

—

—

—

—

Q₈

yes

complemented

C₂²×D₄₀₁

C₂³

yes

characteristic

Dic₈₀₂

—

Dic₈₀₂

—

C₂×Dic₄₀₁

C₂×C₄

yes

—

C₂×Dic₄₀₁

C₂×C₄

yes

characteristic

C₄×D₄₀₁

—

C₄×D₄₀₁

—

C₄×D₄₀₁

D₄

yes

—

C₄×D₄₀₁

D₄

yes

—

Q₈×C₄₀₁

—

C₂×C₄×C₄₀₁

C₂×C₄

yes

—

C₂×C₄×C₄₀₁

C₂×C₄

yes

characteristic

C₂²×C₄₀₁

C₂²×C₄

yes

characteristic

C₂×D₄₀₁

C₂×D₄

yes

characteristic

C₂×D₄₀₁

C₂×D₄

yes

characteristic

C₂×D₄₀₁

C₂×Q₈

yes

—

C₂×D₄₀₁

#41

yes

—

#13107944

—

#13107944

—

C₄×C₄₀₁

—

C₄×C₄₀₁

C₂²⋊C₄

yes

—

Dic₄₀₁

—

Dic₄₀₁

C₂²⋊C₄

yes

—

C₂×C₄₀₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄₀₁

C₄×Q₈

yes

—

D₄₀₁

C₂²⋊Q₈

yes

—

D₄₀₁

#124

yes

characteristic

D₄₀₁

C₄⋊Q₈

yes

characteristic

C₄₀₁

#391

yes

characteristic, complemented, Sylow

#391

—

401

maximal, Sylow

C₂²×Q₈

—

401

—

C₂×C₄⋊C₄

—

401

—

C₂×C₄²

—

401

—

#95

—

401

—

C₂×Q₈

—

802

—

C₂×Q₈

—

802

—

C₂×Q₈

—

401

—

C₂×Q₈

—

401

—

C₂×Q₈

#13107944

yes

characteristic, complemented

C₂²×C₄

—

401

—

C₂²×C₄

—

401

—

C₂²×C₄

—

401

—

C₂²×C₄

—

401

—

C₄⋊C₄

—

802

—

C₄²

—

802

—

C₂³

—

401

—

Q₈

—

Q₈

—

802

—

Q₈

—

802

—

C₂×C₄

—

802

—

C₂×C₄

—

802

—

C₂×C₄

—

802

—

C₂×C₄

—

802

—

C₂×C₄

—

802

—

C₂×C₄

—

802

—

C₂×C₄

—

401

—

C₂×C₄

—

401

—

C₂×C₄

—

401

—

C₂×C₄

—

401

—

C₂×C₄

—

401

—

C₂×C₄

C₂×#13107944

yes

—

C₂×C₄

C₂×#13107944

yes

characteristic

C₂²

—

401

—

C₂²

—

401

—

C₂²

—

401

—

C₂²

—

401

—

C₂²

C₂²×#13107944

yes

characteristic

C₄

—

C₄

—

802

—

C₄

—

802

—

C₄

—

1604

—

C₄

—

401

—

C₄

C₂²⋊#13107944

yes

—

C₂

—

401

—

C₂

—

401

—

C₂

—

401

—

C₂

C₂×C₂²⋊#13107944

yes

characteristic

C₂

Q₈×#13107944

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#13107944
commutator, socle	C₂²×C₄₀₁	C₂²×C₄
Fitting	C₂×Q₈×C₄₀₁	C₄
prime radical, cosocle	C₂²×D₄₀₁	C₂³
hypercenter	C₂×Q₈	#13107944
hypocenter	C₄₀₁	#391
LCS	G ▷ C₂²×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

subgroup

G/H

center, Frattini

C₂²

C₂²×#13107944

commutator, socle

C₂²×C₄₀₁

C₂²×C₄

Fitting

C₂×Q₈×C₄₀₁

C₄

prime radical, cosocle

C₂²×D₄₀₁

C₂³

C₂×Q₈

C₄₀₁

G ▷ C₂²×C₄₀₁ ▷ C₄₀₁

C₁ ◁ C₂² ◁ C₂×Q₈

N	H ≅ G/N	type
9. C₂×Dic₈₀₂	C₄	semidirect
10. C₂×Dic₈₀₂	C₄	semidirect
15. C₂×Q₈×C₄₀₁	C₄	semidirect
20. C₂×#13107944	Q₈	semidirect
49. C₄₀₁	#391	semidirect
59. C₂×Q₈	#13107944	semidirect

H ≅ G/N

type

9. C₂×Dic₈₀₂

C₄

semidirect

10. C₂×Dic₈₀₂

C₄

semidirect

15. C₂×Q₈×C₄₀₁

C₄

semidirect

20. C₂×#13107944

Q₈

semidirect

49. C₄₀₁

#391

semidirect

59. C₂×Q₈

#13107944

semidirect

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

subgroup	index
C₂×C₄⋊#13107944	2
C₂×C₄×#13107944	2
(C₂×#13107944)⋊C₄	2
C₂×Q₈×D₄₀₁	2
#391	401

subgroup

index

C₂×Q₈×D₄₀₁

401

Subgroups — (C₂×#13107944)⋊Q₈ #38787067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C2×#13107944)⋊Q8 #38787067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#13107944)⋊Q₈ #38787067