Group #19133391 — subgroups

Subgroups — C₈×D₃₄₄ #19133391

Order 5504.

196 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 77 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	C₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic
2	C₈×D₁₇₂	C₂	1	2	yes	maximal, complemented
3	#14582652	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582628	C₂	1	2	yes	maximal, complemented
5	C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₄₄	C₄	1	1	yes	characteristic
7	C₂×C₈×D₄₃	—	2	2	no	—
8	C₄×D₁₇₂	C₂²	1	2	yes	—
9	#13063259	C₄	1	1	yes	characteristic
10	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
11	#13063247	C₄	1	2	yes	—
12	(C₂×D₄₃)⋊C₈	—	2	2	no	—
13	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×D₁₇₂	C₂×C₄	1	2	yes	—
17	C₂×C₄×D₄₃	—	2	2	no	—
18	C₂×C₈×C₄₃	—	2	1	no	—
19	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
23	C₄²×C₄₃	C₂³	1	1	yes	characteristic
24	(C₂×D₄₃)⋊C₄	—	2	2	no	—
25	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
26	C₂×C₄₃⋊C₈	—	2	2	no	—
27	D₃₄₄	C₈	1	4	yes	direct product factor
28	C₈×D₄₃	—	4	4	no	—
29	C₂²×D₄₃	—	2	2	no	—
30	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
33	C₂×Dic₄₃	—	2	2	no	—
34	D₁₇₂	—	2	2	no	—
35	D₁₇₂	C₂×C₈	1	4	yes	complemented
36	C₄×D₄₃	—	4	2	no	—
37	C₄×D₄₃	—	4	2	no	—
38	C₈×C₄₃	—	2	2	no	—
39	C₈×C₄₃	—	2	1	no	—
40	C₈×C₄₃	—	2	1	no	—
41	C₈×C₄₃	C₂×C₈	1	2	yes	complemented
42	C₈×C₄₃	D₈	1	2	yes	complemented
43	C₄₃⋊C₈	—	4	2	no	—
44	C₂²×C₄₃	C₄×D₄	1	1	yes	characteristic
45	C₂×D₄₃	—	2	4	no	—
46	C₂×D₄₃	—	4	2	no	—
47	C₂×D₄₃	—	4	2	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
50	C₄×C₄₃	#131	1	1	yes	characteristic
51	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
52	C₄×C₄₃	#135	1	1	yes	characteristic
53	Dic₄₃	—	4	2	no	—
54	C₈×D₈	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	C₈×D₄	1	1	yes	characteristic
56	C₂×C₄₃	C₄×D₈	1	1	yes	characteristic
57	C₂×C₄₃	#443	1	1	yes	characteristic
58	D₄₃	—	4	4	no	—
59	C₄×D₈	—	43	1	no	—
60	C₈×D₄	—	43	2	no	—
61	#335	—	43	1	no	—
62	D₄⋊C₈	—	43	2	no	—
63	C₈²	D₄₃	1	1	yes	characteristic, complemented
64	C₄₃	C₈×D₈	1	1	yes	characteristic, complemented, Sylow
65	C₂×D₈	—	43	1	no	—
66	C₂²×C₈	—	86	2	no	—
67	C₄×D₄	—	43	2	no	—
68	#107	—	43	1	no	—
69	C₄⋊C₈	—	43	2	no	—
70	#102	—	43	2	no	—
71	C₂²⋊C₈	—	86	2	no	—
72	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
73	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
74	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
75	C₂×D₄	—	43	2	no	—
76	C₂²×C₄	—	86	2	no	—
77	D₈	—	43	4	no	—
78	C₂×C₈	—	2	1	no	—
79	C₂×C₈	—	86	2	no	—
80	C₂×C₈	—	172	4	no	—
81	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
82	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
83	C₂×C₈	D₁₇₂	1	1	yes	characteristic
84	C₂×C₈	D₁₇₂	1	1	yes	characteristic
85	C₄⋊C₄	—	43	2	no	—
86	C₂²⋊C₄	—	86	2	no	—
87	C₄²	C₂²×D₄₃	1	1	yes	characteristic
88	C₂³	—	86	2	no	—
89	D₄	—	43	4	no	—
90	D₄	—	86	2	no	—
91	C₂×C₄	—	86	2	no	—
92	C₂×C₄	—	172	2	no	—
93	C₂×C₄	—	172	2	no	—
94	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
95	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
96	C₂×C₄	#10621898	1	1	yes	characteristic
97	C₈	—	2	2	no	—
98	C₈	—	2	1	no	—
99	C₈	—	2	1	no	—
100	C₈	—	172	2	no	—
101	C₈	C₈×D₄₃	1	2	yes	complemented
102	C₈	D₃₄₄	1	2	yes	direct product factor
103	C₂²	—	86	4	no	—
104	C₂²	—	172	2	no	—
105	C₂²	—	172	2	no	—
106	C₂²	C₄×D₁₇₂	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	172	2	no	—
109	C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
110	C₄	#13063331	1	1	yes	characteristic
111	C₄	C₂×D₃₄₄	1	1	yes	characteristic
112	C₄	#13063347	1	1	yes	characteristic
113	C₂	—	172	4	no	—
114	C₂	C₈×D₁₇₂	1	1	yes	characteristic
115	C₂	C₄×D₃₄₄	1	1	yes	characteristic
116	C₂	#14583017	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₃₄₄

C₂

yes

maximal, characteristic

C₈×D₁₇₂

C₂

yes

maximal, complemented

#14582652

C₂

yes

maximal, characteristic, complemented

#14582628

C₂

yes

maximal, complemented

C₈²×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×D₃₄₄

C₄

yes

characteristic

C₂×C₈×D₄₃

—

C₄×D₁₇₂

C₂²

yes

—

#13063259

C₄

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063247

C₄

yes

—

(C₂×D₄₃)⋊C₈

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

C₂×C₄

yes

—

C₂×C₄×D₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

—

D₃₄₄

C₈

yes

direct product factor

C₈×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

C₂×C₈

yes

complemented

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂×C₈

yes

complemented

C₈×C₄₃

D₈

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

C₄×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²×C₈

yes

characteristic

C₄×C₄₃

#131

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

#135

yes

characteristic

Dic₄₃

—

C₈×D₈

—

maximal, Sylow

C₂×C₄₃

C₈×D₄

yes

characteristic

C₂×C₄₃

C₄×D₈

yes

characteristic

C₂×C₄₃

#443

yes

characteristic

D₄₃

—

C₄×D₈

—

C₈×D₄

—

#335

—

D₄⋊C₈

—

C₈²

D₄₃

yes

characteristic, complemented

C₄₃

C₈×D₈

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂²×C₈

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

#102

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

#10621898

yes

characteristic

C₈

—

C₈

—

C₈

—

100

C₈

—

172

—

101

C₈

C₈×D₄₃

yes

complemented

102

C₈

D₃₄₄

yes

direct product factor

103

C₂²

—

104

C₂²

—

172

—

105

C₂²

—

172

—

106

C₂²

C₄×D₁₇₂

yes

characteristic

107

C₄

—

108

C₄

—

172

—

109

C₄

C₂×C₈×D₄₃

yes

characteristic

110

C₄

#13063331

yes

characteristic

111

C₄

C₂×D₃₄₄

yes

characteristic

112

C₄

#13063347

yes

characteristic

113

C₂

—

172

—

114

C₂

C₈×D₁₇₂

yes

characteristic

115

C₂

C₄×D₃₄₄

yes

characteristic

116

C₂

#14583017

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₁₇₂
commutator	C₄×C₄₃	C₂²×C₈
Frattini	C₄²	C₂²×D₄₃
Fitting	C₈²×C₄₃	C₂
socle	C₂²×C₄₃	C₄×D₄
hypercenter	C₈²	D₄₃
hypocenter	C₄₃	C₈×D₈
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

subgroup

G/H

center

C₂×C₈

D₁₇₂

commutator

C₄×C₄₃

C₂²×C₈

Frattini

C₄²

C₂²×D₄₃

Fitting

C₈²×C₄₃

C₂

socle

C₂²×C₄₃

C₄×D₄

hypercenter

C₈²

D₄₃

hypocenter

C₄₃

C₈×D₈

LCS

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

N	H ≅ G/N	type
2. C₈×D₁₇₂	C₂	semidirect
3. #14582652	C₂	semidirect
4. #14582628	C₂	semidirect
5. C₈²×C₄₃	C₂	semidirect
27. D₃₄₄	C₈	direct (N × H)
35. D₁₇₂	C₂×C₈	semidirect
41. C₈×C₄₃	C₂×C₈	semidirect
42. C₈×C₄₃	D₈	semidirect
63. C₈²	D₄₃	semidirect
64. C₄₃	C₈×D₈	semidirect
101. C₈	C₈×D₄₃	semidirect
102. C₈	D₃₄₄	direct (N × H)

H ≅ G/N

type

2. C₈×D₁₇₂

C₂

semidirect

3. #14582652

C₂

semidirect

4. #14582628

C₂

semidirect

5. C₈²×C₄₃

C₂

semidirect

27. D₃₄₄

C₈

direct (N × H)

35. D₁₇₂

C₂×C₈

semidirect

41. C₈×C₄₃

C₂×C₈

semidirect

42. C₈×C₄₃

D₈

semidirect

63. C₈²

D₄₃

semidirect

64. C₄₃

C₈×D₈

semidirect

101. C₈

C₈×D₄₃

semidirect

102. C₈

D₃₄₄

direct (N × H)

Subgroups — C₈×D₃₄₄ #19133391

Conjugacy classes of subgroups

Complements

Subgroups — C8×D344 #19133391

Conjugacy classes of subgroups

Complements

Subgroups — C₈×D₃₄₄ #19133391