Group #20295488 — subgroups

Subgroups — C₂×C₄×D₄₃₆ #20295488

Order 6976.

426 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 183 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	C₂²×D₄₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₁₀₉	C₂	1	2	yes	maximal, complemented
3	C₄×D₄₃₆	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄⋊Dic₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13182006	C₂	1	2	yes	maximal, complemented
6	C₂×C₄²×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₁₀₉	C₂²	1	2	yes	—
8	C₂×D₄₃₆	C₄	1	8	yes	direct product factor
9	C₂×D₄₃₆	C₂²	1	4	yes	—
10	C₂²×Dic₁₀₉	C₂²	1	2	yes	—
11	C₂×C₄×D₁₀₉	—	2	8	no	—
12	C₂×C₄×D₁₀₉	C₂²	1	8	yes	complemented
13	C₄⋊Dic₁₀₉	C₂²	1	4	yes	complemented
14	#13182006	C₂²	1	8	yes	complemented
15	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₄²×C₁₀₉	C₂²	1	4	yes	complemented
19	C₂³×C₁₀₉	C₂³	1	1	yes	characteristic
20	C₂²×D₁₀₉	—	2	4	no	—
21	C₂²×D₁₀₉	—	2	4	no	—
22	C₂²×D₁₀₉	C₂×C₄	1	8	yes	complemented
23	C₂²×D₁₀₉	C₂³	1	4	yes	—
24	C₂×C₄×C₁₀₉	—	2	2	no	—
25	C₂×C₄×C₁₀₉	C₂×C₄	1	4	yes	complemented
26	C₂×C₄×C₁₀₉	D₄	1	4	yes	complemented
27	C₂×C₄×C₁₀₉	C₂³	1	2	yes	—
28	C₂×C₄×C₁₀₉	C₂³	1	2	yes	—
29	C₂×C₄×C₁₀₉	C₂³	1	2	yes	—
30	C₂×Dic₁₀₉	—	2	4	no	—
31	C₂×Dic₁₀₉	C₂³	1	4	yes	—
32	D₄₃₆	C₂×C₄	1	16	yes	direct product factor
33	C₄×D₁₀₉	—	2	16	no	—
34	C₂²×C₁₀₉	C₂²×C₄	1	2	yes	—
35	C₂²×C₁₀₉	C₂×D₄	1	2	yes	—
36	C₂²×C₁₀₉	#41	1	2	yes	—
37	C₂²×C₁₀₉	C₂⁴	1	1	yes	characteristic
38	C₂×D₁₀₉	—	2	16	no	—
39	C₂×D₁₀₉	—	2	4	no	—
40	C₂×D₁₀₉	—	2	4	no	—
41	C₂×D₁₀₉	C₂²×C₄	1	8	yes	complemented
42	C₄×C₁₀₉	—	2	2	no	—
43	C₄×C₁₀₉	C₂²×C₄	1	4	yes	complemented
44	C₄×C₁₀₉	C₂×D₄	1	4	yes	complemented
45	Dic₁₀₉	—	2	4	no	—
46	C₂×C₁₀₉	C₄×D₄	1	4	yes	complemented
47	C₂×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
48	C₂×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
49	C₂×C₁₀₉	C₂×#41	1	1	yes	characteristic
50	D₁₀₉	—	2	8	no	—
51	C₁₀₉	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₄×D₄	—	109	1	no	maximal, Sylow
53	C₂²×D₄	—	109	1	no	—
54	C₂³×C₄	—	109	2	no	—
55	C₄×D₄	—	109	8	no	—
56	C₂×C₄⋊C₄	—	109	1	no	—
57	C₂×C₂²⋊C₄	—	109	2	no	—
58	C₂×C₄²	D₁₀₉	1	1	yes	characteristic, complemented
59	C₂⁴	—	109	2	no	—
60	C₂×D₄	—	109	8	no	—
61	C₂×D₄	—	109	4	no	—
62	C₂²×C₄	—	109	2	no	—
63	C₂²×C₄	—	109	8	no	—
64	C₂²×C₄	—	218	8	no	—
65	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
66	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
67	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
68	C₄⋊C₄	—	109	4	no	—
69	C₂²⋊C₄	—	109	8	no	—
70	C₄²	C₂×D₁₀₉	1	4	yes	complemented
71	C₂³	—	109	8	no	—
72	C₂³	—	109	4	no	—
73	C₂³	—	218	4	no	—
74	C₂³	—	218	4	no	—
75	C₂³	C₂²×D₁₀₉	1	1	yes	characteristic
76	D₄	—	109	16	no	—
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	109	4	no	—
79	C₂×C₄	—	218	4	no	—
80	C₂×C₄	—	218	16	no	—
81	C₂×C₄	C₄×D₁₀₉	1	4	yes	complemented
82	C₂×C₄	D₄₃₆	1	4	yes	direct product factor
83	C₂×C₄	C₂²×D₁₀₉	1	2	yes	—
84	C₂×C₄	C₂²×D₁₀₉	1	2	yes	—
85	C₂×C₄	C₂²×D₁₀₉	1	2	yes	—
86	C₂²	—	109	8	no	—
87	C₂²	—	218	16	no	—
88	C₂²	—	218	4	no	—
89	C₂²	—	218	4	no	—
90	C₂²	C₂×C₄×D₁₀₉	1	2	yes	—
91	C₂²	C₂×D₄₃₆	1	2	yes	—
92	C₂²	#13182029	1	2	yes	—
93	C₂²	C₂³×D₁₀₉	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	218	4	no	—
96	C₄	C₂×C₄×D₁₀₉	1	4	yes	complemented
97	C₄	C₂×D₄₃₆	1	4	yes	direct product factor
98	C₂	—	218	8	no	—
99	C₂	C₄×D₄₃₆	1	4	yes	direct product factor
100	C₂	C₂²×C₄×D₁₀₉	1	1	yes	characteristic
101	C₂	C₂²×D₄₃₆	1	1	yes	characteristic
102	C₂	C₂×#13182029	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₄₃₆

C₂

yes

maximal, characteristic

C₂²×C₄×D₁₀₉

C₂

yes

maximal, complemented

C₄×D₄₃₆

C₂

yes

maximal, direct product factor

C₂×C₄⋊Dic₁₀₉

C₂

yes

maximal, characteristic, complemented

C₂×#13182006

C₂

yes

maximal, complemented

C₂×C₄²×C₁₀₉

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₀₉

C₂²

yes

—

C₂×D₄₃₆

C₄

yes

direct product factor

C₂×D₄₃₆

C₂²

yes

—

C₂²×Dic₁₀₉

C₂²

yes

—

C₂×C₄×D₁₀₉

—

C₂×C₄×D₁₀₉

C₂²

yes

complemented

C₄⋊Dic₁₀₉

C₂²

yes

complemented

#13182006

C₂²

yes

complemented

C₂²×C₄×C₁₀₉

C₂²

yes

characteristic

C₂²×C₄×C₁₀₉

C₂²

yes

characteristic

C₂²×C₄×C₁₀₉

C₂²

yes

characteristic

C₄²×C₁₀₉

C₂²

yes

complemented

C₂³×C₁₀₉

C₂³

yes

characteristic

C₂²×D₁₀₉

—

C₂²×D₁₀₉

—

C₂²×D₁₀₉

C₂×C₄

yes

complemented

C₂²×D₁₀₉

C₂³

yes

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

C₂×C₄

yes

complemented

C₂×C₄×C₁₀₉

D₄

yes

complemented

C₂×C₄×C₁₀₉

C₂³

yes

—

C₂×C₄×C₁₀₉

C₂³

yes

—

C₂×C₄×C₁₀₉

C₂³

yes

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

C₂³

yes

—

D₄₃₆

C₂×C₄

yes

direct product factor

C₄×D₁₀₉

—

C₂²×C₁₀₉

C₂²×C₄

yes

—

C₂²×C₁₀₉

C₂×D₄

yes

—

C₂²×C₁₀₉

#41

yes

—

C₂²×C₁₀₉

C₂⁴

yes

characteristic

C₂×D₁₀₉

—

C₂×D₁₀₉

—

C₂×D₁₀₉

—

C₂×D₁₀₉

C₂²×C₄

yes

complemented

C₄×C₁₀₉

—

C₄×C₁₀₉

C₂²×C₄

yes

complemented

C₄×C₁₀₉

C₂×D₄

yes

complemented

Dic₁₀₉

—

C₂×C₁₀₉

C₄×D₄

yes

complemented

C₂×C₁₀₉

C₂³×C₄

yes

characteristic

C₂×C₁₀₉

C₂²×D₄

yes

characteristic

C₂×C₁₀₉

C₂×#41

yes

characteristic

D₁₀₉

—

C₁₀₉

C₂×C₄×D₄

yes

characteristic, complemented, Sylow

C₂×C₄×D₄

—

109

maximal, Sylow

C₂²×D₄

—

109

—

C₂³×C₄

—

109

—

C₄×D₄

—

109

—

C₂×C₄⋊C₄

—

109

—

C₂×C₂²⋊C₄

—

109

—

C₂×C₄²

D₁₀₉

yes

characteristic, complemented

C₂⁴

—

109

—

C₂×D₄

—

109

—

C₂×D₄

—

109

—

C₂²×C₄

—

109

—

C₂²×C₄

—

109

—

C₂²×C₄

—

218

—

C₂²×C₄

C₂×D₁₀₉

yes

characteristic

C₂²×C₄

C₂×D₁₀₉

yes

characteristic

C₂²×C₄

C₂×D₁₀₉

yes

characteristic

C₄⋊C₄

—

109

—

C₂²⋊C₄

—

109

—

C₄²

C₂×D₁₀₉

yes

complemented

C₂³

—

109

—

C₂³

—

109

—

C₂³

—

218

—

C₂³

—

218

—

C₂³

C₂²×D₁₀₉

yes

characteristic

D₄

—

109

—

C₂×C₄

—

C₂×C₄

—

109

—

C₂×C₄

—

218

—

C₂×C₄

—

218

—

C₂×C₄

C₄×D₁₀₉

yes

complemented

C₂×C₄

D₄₃₆

yes

direct product factor

C₂×C₄

C₂²×D₁₀₉

yes

—

C₂×C₄

C₂²×D₁₀₉

yes

—

C₂×C₄

C₂²×D₁₀₉

yes

—

C₂²

—

109

—

C₂²

—

218

—

C₂²

—

218

—

C₂²

—

218

—

C₂²

C₂×C₄×D₁₀₉

yes

—

C₂²

C₂×D₄₃₆

yes

—

C₂²

#13182029

yes

—

C₂²

C₂³×D₁₀₉

yes

characteristic

C₄

—

C₄

—

218

—

C₄

C₂×C₄×D₁₀₉

yes

complemented

C₄

C₂×D₄₃₆

yes

direct product factor

C₂

—

218

—

C₂

C₄×D₄₃₆

yes

direct product factor

100

C₂

C₂²×C₄×D₁₀₉

yes

characteristic

101

C₂

C₂²×D₄₃₆

yes

characteristic

102

C₂

C₂×#13182029

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₀₉
commutator	C₂×C₁₀₉	C₂³×C₄
Frattini	C₂²	C₂³×D₁₀₉
Fitting	C₂×C₄²×C₁₀₉	C₂
socle	C₂³×C₁₀₉	C₂³
hypercenter	C₂×C₄²	D₁₀₉
hypocenter	C₁₀₉	C₂×C₄×D₄
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

subgroup

G/H

center

C₂²×C₄

C₂×D₁₀₉

commutator

C₂×C₁₀₉

C₂³×C₄

Frattini

C₂²

C₂³×D₁₀₉

Fitting

C₂×C₄²×C₁₀₉

C₂

socle

C₂³×C₁₀₉

C₂³

hypercenter

C₂×C₄²

D₁₀₉

hypocenter

C₁₀₉

C₂×C₄×D₄

LCS

G ▷ C₂×C₁₀₉ ▷ C₁₀₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

N	H ≅ G/N	type
2. C₂²×C₄×D₁₀₉	C₂	semidirect
3. C₄×D₄₃₆	C₂	direct (N × H)
4. C₂×C₄⋊Dic₁₀₉	C₂	semidirect
5. C₂×#13182006	C₂	semidirect
6. C₂×C₄²×C₁₀₉	C₂	semidirect
8. C₂×D₄₃₆	C₄	direct (N × H)
12. C₂×C₄×D₁₀₉	C₂²	semidirect
13. C₄⋊Dic₁₀₉	C₂²	semidirect
14. #13182006	C₂²	semidirect
18. C₄²×C₁₀₉	C₂²	semidirect
22. C₂²×D₁₀₉	C₂×C₄	semidirect
25. C₂×C₄×C₁₀₉	C₂×C₄	semidirect
26. C₂×C₄×C₁₀₉	D₄	semidirect
32. D₄₃₆	C₂×C₄	direct (N × H)
41. C₂×D₁₀₉	C₂²×C₄	semidirect
43. C₄×C₁₀₉	C₂²×C₄	semidirect
44. C₄×C₁₀₉	C₂×D₄	semidirect
46. C₂×C₁₀₉	C₄×D₄	semidirect
51. C₁₀₉	C₂×C₄×D₄	semidirect
58. C₂×C₄²	D₁₀₉	semidirect
70. C₄²	C₂×D₁₀₉	semidirect
81. C₂×C₄	C₄×D₁₀₉	semidirect
82. C₂×C₄	D₄₃₆	direct (N × H)
96. C₄	C₂×C₄×D₁₀₉	semidirect
97. C₄	C₂×D₄₃₆	direct (N × H)
99. C₂	C₄×D₄₃₆	direct (N × H)

H ≅ G/N

type

2. C₂²×C₄×D₁₀₉

C₂

semidirect

3. C₄×D₄₃₆

C₂

direct (N × H)

4. C₂×C₄⋊Dic₁₀₉

C₂

semidirect

5. C₂×#13182006

C₂

semidirect

6. C₂×C₄²×C₁₀₉

C₂

semidirect

8. C₂×D₄₃₆

C₄

direct (N × H)

12. C₂×C₄×D₁₀₉

C₂²

semidirect

13. C₄⋊Dic₁₀₉

C₂²

semidirect

14. #13182006

C₂²

semidirect

18. C₄²×C₁₀₉

C₂²

semidirect

22. C₂²×D₁₀₉

C₂×C₄

semidirect

25. C₂×C₄×C₁₀₉

C₂×C₄

semidirect

26. C₂×C₄×C₁₀₉

D₄

semidirect

32. D₄₃₆

C₂×C₄

direct (N × H)

41. C₂×D₁₀₉

C₂²×C₄

semidirect

43. C₄×C₁₀₉

C₂²×C₄

semidirect

44. C₄×C₁₀₉

C₂×D₄

semidirect

46. C₂×C₁₀₉

C₄×D₄

semidirect

51. C₁₀₉

C₂×C₄×D₄

semidirect

58. C₂×C₄²

D₁₀₉

semidirect

70. C₄²

C₂×D₁₀₉

semidirect

81. C₂×C₄

C₄×D₁₀₉

semidirect

82. C₂×C₄

D₄₃₆

direct (N × H)

96. C₄

C₂×C₄×D₁₀₉

semidirect

97. C₄

C₂×D₄₃₆

direct (N × H)

99. C₂

C₄×D₄₃₆

direct (N × H)

Subgroups — C₂×C₄×D₄₃₆ #20295488

Conjugacy classes of subgroups

Complements

Subgroups — C2×C4×D436 #20295488

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄×D₄₃₆ #20295488