Group #20295576 — subgroups

Subgroups — #20295576

Order 6976.

310 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 119 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×#13182029	C₂	1	2	yes	maximal, complemented
2	#16812699	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812696	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812687	C₂	1	2	yes	maximal, complemented
5	#16812673	C₂	1	4	yes	maximal, complemented
6	C₄×D₄₃₆	C₂	1	4	yes	maximal, complemented
7	C₂×C₄²×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#13182029	—	2	8	no	—
9	C₂×Dic₂₁₈	C₂²	1	2	yes	—
10	C₂×D₄₃₆	C₂²	1	4	yes	—
11	C₂×D₄₃₆	C₂²	1	2	yes	—
12	C₂×C₂²⋊D₁₀₉	C₂²	1	4	yes	—
13	C₂×C₄×D₁₀₉	C₂²	1	4	yes	—
14	C₄⋊Dic₁₀₉	C₂²	1	4	yes	—
15	#13182006	C₂²	1	8	yes	—
16	C₂²×C₄×C₁₀₉	C₂²	1	2	yes	—
17	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₄²×C₁₀₉	C₂²	1	2	yes	—
19	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
20	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
21	C₂³×C₁₀₉	C₂³	1	1	yes	characteristic
22	C₂²×D₁₀₉	C₂³	1	4	yes	—
23	C₂×C₄×C₁₀₉	—	2	4	no	—
24	C₂×C₄×C₁₀₉	D₄	1	4	yes	complemented
25	C₂×C₄×C₁₀₉	C₂³	1	2	yes	—
26	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₁₀₉	C₂³	1	2	yes	—
28	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
29	C₂²⋊D₁₀₉	—	2	8	no	—
30	C₂×Dic₁₀₉	C₂³	1	4	yes	—
31	D₄₃₆	—	2	4	no	—
32	D₄₃₆	—	2	8	no	—
33	C₄×D₁₀₉	—	2	8	no	—
34	Dic₂₁₈	—	2	4	no	—
35	C₂²×C₁₀₉	—	2	2	no	—
36	C₂²×C₁₀₉	C₂×D₄	1	2	yes	—
37	C₂²×C₁₀₉	C₂⁴	1	1	yes	characteristic
38	C₂×D₁₀₉	—	2	4	no	—
39	C₂×D₁₀₉	—	2	8	no	—
40	C₄×C₁₀₉	—	2	2	no	—
41	C₄×C₁₀₉	C₂×D₄	1	2	yes	—
42	C₄×C₁₀₉	C₂×D₄	1	2	yes	—
43	C₄×C₁₀₉	#41	1	4	yes	complemented
44	Dic₁₀₉	—	2	4	no	—
45	C₂×C₁₀₉	—	2	2	no	—
46	C₂×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
47	C₂×C₁₀₉	C₂×#41	1	2	yes	—
48	D₁₀₉	—	4	4	no	—
49	C₁₀₉	#532	1	1	yes	characteristic, complemented, Sylow
50	#532	—	109	1	no	maximal, Sylow
51	C₂×#41	—	109	2	no	—
52	C₄⋊Q₈	—	109	1	no	—
53	#127	—	109	1	no	—
54	#124	—	109	2	no	—
55	#121	—	109	4	no	—
56	C₄×D₄	—	109	4	no	—
57	C₂×C₄²	D₁₀₉	1	1	yes	characteristic, complemented
58	#41	—	218	8	no	—
59	C₂×Q₈	—	109	2	no	—
60	C₂×D₄	—	109	4	no	—
61	C₂×D₄	—	109	4	no	—
62	C₂×D₄	—	109	2	no	—
63	C₂²×C₄	—	109	4	no	—
64	C₂²×C₄	C₂×D₁₀₉	1	2	yes	—
65	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
66	C₄⋊C₄	—	109	4	no	—
67	C₂²⋊C₄	—	109	8	no	—
68	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
69	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
70	C₄²	C₂×D₁₀₉	1	2	yes	—
71	C₂³	—	109	4	no	—
72	C₂³	C₂²×D₁₀₉	1	1	yes	characteristic
73	Q₈	—	218	4	no	—
74	D₄	—	218	8	no	—
75	D₄	—	218	4	no	—
76	D₄	—	218	8	no	—
77	C₂×C₄	—	2	4	no	—
78	C₂×C₄	—	109	4	no	—
79	C₂×C₄	—	218	8	no	—
80	C₂×C₄	D₄₃₆	1	4	yes	complemented
81	C₂×C₄	C₂²×D₁₀₉	1	2	yes	—
82	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
83	C₂×C₄	C₂²×D₁₀₉	1	2	yes	—
84	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
85	C₂²	—	2	2	no	—
86	C₂²	—	218	4	no	—
87	C₂²	—	218	8	no	—
88	C₂²	C₂×D₄₃₆	1	2	yes	—
89	C₂²	C₂³×D₁₀₉	1	1	yes	characteristic
90	C₄	—	2	2	no	—
91	C₄	—	218	4	no	—
92	C₄	C₂×D₄₃₆	1	2	yes	—
93	C₄	C₂×D₄₃₆	1	2	yes	—
94	C₄	#13182029	1	4	yes	complemented
95	C₂	—	2	2	no	—
96	C₂	—	436	4	no	—
97	C₂	C₂²×D₄₃₆	1	1	yes	characteristic
98	C₂	C₂×#13182029	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13182029

C₂

yes

maximal, complemented

#16812699

C₂

yes

maximal, characteristic, complemented

#16812696

C₂

yes

maximal, characteristic, complemented

#16812687

C₂

yes

maximal, complemented

#16812673

C₂

yes

maximal, complemented

C₄×D₄₃₆

C₂

yes

maximal, complemented

C₂×C₄²×C₁₀₉

C₂

yes

maximal, characteristic, complemented

#13182029

—

C₂×Dic₂₁₈

C₂²

yes

—

C₂×D₄₃₆

C₂²

yes

—

C₂×D₄₃₆

C₂²

yes

—

C₂×C₂²⋊D₁₀₉

C₂²

yes

—

C₂×C₄×D₁₀₉

C₂²

yes

—

C₄⋊Dic₁₀₉

C₂²

yes

—

#13182006

C₂²

yes

—

C₂²×C₄×C₁₀₉

C₂²

yes

—

C₂²×C₄×C₁₀₉

C₂²

yes

characteristic

C₄²×C₁₀₉

C₂²

yes

—

C₄²×C₁₀₉

C₂²

yes

characteristic

C₄²×C₁₀₉

C₂²

yes

characteristic

C₂³×C₁₀₉

C₂³

yes

characteristic

C₂²×D₁₀₉

C₂³

yes

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

D₄

yes

complemented

C₂×C₄×C₁₀₉

C₂³

yes

—

C₂×C₄×C₁₀₉

C₂³

yes

characteristic

C₂×C₄×C₁₀₉

C₂³

yes

—

C₂×C₄×C₁₀₉

C₂³

yes

characteristic

C₂²⋊D₁₀₉

—

C₂×Dic₁₀₉

C₂³

yes

—

D₄₃₆

—

D₄₃₆

—

C₄×D₁₀₉

—

Dic₂₁₈

—

C₂²×C₁₀₉

—

C₂²×C₁₀₉

C₂×D₄

yes

—

C₂²×C₁₀₉

C₂⁴

yes

characteristic

C₂×D₁₀₉

—

C₂×D₁₀₉

—

C₄×C₁₀₉

—

C₄×C₁₀₉

C₂×D₄

yes

—

C₄×C₁₀₉

C₂×D₄

yes

—

C₄×C₁₀₉

#41

yes

complemented

Dic₁₀₉

—

C₂×C₁₀₉

—

C₂×C₁₀₉

C₂²×D₄

yes

characteristic

C₂×C₁₀₉

C₂×#41

yes

—

D₁₀₉

—

C₁₀₉

#532

yes

characteristic, complemented, Sylow

#532

—

109

maximal, Sylow

C₂×#41

—

109

—

C₄⋊Q₈

—

109

—

#127

—

109

—

#124

—

109

—

#121

—

109

—

C₄×D₄

—

109

—

C₂×C₄²

D₁₀₉

yes

characteristic, complemented

#41

—

218

—

C₂×Q₈

—

109

—

C₂×D₄

—

109

—

C₂×D₄

—

109

—

C₂×D₄

—

109

—

C₂²×C₄

—

109

—

C₂²×C₄

C₂×D₁₀₉

yes

—

C₂²×C₄

C₂×D₁₀₉

yes

characteristic

C₄⋊C₄

—

109

—

C₂²⋊C₄

—

109

—

C₄²

C₂×D₁₀₉

yes

characteristic

C₄²

C₂×D₁₀₉

yes

characteristic

C₄²

C₂×D₁₀₉

yes

—

C₂³

—

109

—

C₂³

C₂²×D₁₀₉

yes

characteristic

Q₈

—

218

—

D₄

—

218

—

D₄

—

218

—

D₄

—

218

—

C₂×C₄

—

C₂×C₄

—

109

—

C₂×C₄

—

218

—

C₂×C₄

D₄₃₆

yes

complemented

C₂×C₄

C₂²×D₁₀₉

yes

—

C₂×C₄

C₂²×D₁₀₉

yes

characteristic

C₂×C₄

C₂²×D₁₀₉

yes

—

C₂×C₄

C₂²×D₁₀₉

yes

characteristic

C₂²

—

C₂²

—

218

—

C₂²

—

218

—

C₂²

C₂×D₄₃₆

yes

—

C₂²

C₂³×D₁₀₉

yes

characteristic

C₄

—

C₄

—

218

—

C₄

C₂×D₄₃₆

yes

—

C₄

C₂×D₄₃₆

yes

—

C₄

#13182029

yes

complemented

C₂

—

C₂

—

436

—

C₂

C₂²×D₄₃₆

yes

characteristic

C₂

C₂×#13182029

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₀₉
commutator, socle	C₂²×C₁₀₉	C₂⁴
Frattini	C₂²	C₂³×D₁₀₉
Fitting	C₂×C₄²×C₁₀₉	C₂
hypercenter	C₂×C₄²	D₁₀₉
hypocenter	C₁₀₉	#532
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

subgroup

G/H

center

C₂×C₄

C₂²×D₁₀₉

commutator, socle

C₂²×C₁₀₉

C₂⁴

Frattini

C₂²

C₂³×D₁₀₉

Fitting

C₂×C₄²×C₁₀₉

C₂

hypercenter

C₂×C₄²

D₁₀₉

C₁₀₉

G ▷ C₂²×C₁₀₉ ▷ C₁₀₉

C₁ ◁ C₂×C₄ ◁ C₂×C₄²

N	H ≅ G/N	type
1. C₂×#13182029	C₂	semidirect
2. #16812699	C₂	semidirect
3. #16812696	C₂	semidirect
4. #16812687	C₂	semidirect
5. #16812673	C₂	semidirect
6. C₄×D₄₃₆	C₂	semidirect
7. C₂×C₄²×C₁₀₉	C₂	semidirect
24. C₂×C₄×C₁₀₉	D₄	semidirect
43. C₄×C₁₀₉	#41	semidirect
49. C₁₀₉	#532	semidirect
57. C₂×C₄²	D₁₀₉	semidirect
80. C₂×C₄	D₄₃₆	semidirect
94. C₄	#13182029	semidirect

H ≅ G/N

type

1. C₂×#13182029

C₂

semidirect

2. #16812699

C₂

semidirect

3. #16812696

C₂

semidirect

4. #16812687

C₂

semidirect

5. #16812673

C₂

semidirect

6. C₄×D₄₃₆

C₂

semidirect

7. C₂×C₄²×C₁₀₉

C₂

semidirect

24. C₂×C₄×C₁₀₉

D₄

semidirect

43. C₄×C₁₀₉

#41

semidirect

49. C₁₀₉

#532

semidirect

57. C₂×C₄²

D₁₀₉

semidirect

80. C₂×C₄

D₄₃₆

semidirect

94. C₄

#13182029

semidirect

Subgroups — #20295576

Conjugacy classes of subgroups

Complements