Group #34044551 — subgroups

Subgroups — #34044551

Order 19072.

260 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 129 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×#18011840	C₂	1	2	yes	maximal
2	C₂×C₄×#11924746	C₂	1	1	yes	maximal, characteristic
3	#23749471	C₂	1	1	yes	maximal, characteristic
4	#23749379	C₂	1	2	yes	maximal
5	C₂×#97×C₁₄₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11924746	C₂²	1	2	yes	—
7	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
9	#18011840	C₄	1	8	yes	complemented
10	C₄×#11924746	—	2	2	no	—
11	#18011818	C₄	1	4	yes	—
12	C₂²×C₈×C₁₄₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
14	#97×C₁₄₉	—	2	2	no	—
15	C₂²×Dic₁₄₉	C₂×C₄	1	2	yes	—
16	C₂²×Dic₁₄₉	C₂×C₄	1	2	yes	—
17	C₂×#11924746	—	2	2	no	—
18	C₂×#11924746	—	2	2	no	—
19	C₂×#11924746	C₂×C₄	1	4	yes	—
20	C₄×Dic₁₄₉	—	2	2	no	—
21	C₄×Dic₁₄₉	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₁₄₉	—	2	2	no	—
25	C₂×C₈×C₁₄₉	—	2	2	no	—
26	C₂×C₈×C₁₄₉	C₂×C₄	1	4	yes	—
27	C₄²×C₁₄₉	D₄	1	2	yes	—
28	C₄²×C₁₄₉	Q₈	1	2	yes	—
29	C₂×Dic₁₄₉	—	2	4	no	—
30	C₂×Dic₁₄₉	—	2	2	no	—
31	C₂×Dic₁₄₉	—	2	4	no	—
32	C₂×Dic₁₄₉	C₄²	1	4	yes	—
33	#11924746	—	2	4	no	—
34	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₄₉	—	2	4	no	—
36	C₂×C₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
37	C₂×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₄₉	#41	1	2	yes	—
41	C₈×C₁₄₉	—	2	4	no	—
42	C₂²×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
43	C₂²×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₁₄₉	#117	1	1	yes	characteristic
45	C₂²×C₁₄₉	#131	1	4	yes	—
46	C₄×C₁₄₉	—	2	4	no	—
47	C₄×C₁₄₉	C₄×D₄	1	2	yes	—
48	C₄×C₁₄₉	C₄×Q₈	1	2	yes	—
49	Dic₁₄₉	—	2	4	no	—
50	Dic₁₄₉	—	4	2	no	—
51	C₂×C₁₄₉	C₄×C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₁₄₉	#405	1	2	yes	—
53	C₂×C₁₄₉	#424	1	2	yes	—
54	C₂×C₁₄₉	#433	1	2	yes	—
55	C₁₄₉	#1768	1	1	yes	characteristic, complemented, Sylow
56	#1768	—	149	1	no	maximal, Sylow
57	C₂×C₄⋊C₈	—	149	2	no	—
58	C₂×#97	D₁₄₉	1	1	yes	characteristic
59	C₂×C₄×C₈	—	149	1	no	—
60	#376	—	149	1	no	—
61	#336	—	149	2	no	—
62	C₂²×C₈	—	149	2	no	—
63	C₂²×C₈	C₂×D₁₄₉	1	2	yes	—
64	C₂×C₄²	—	149	1	no	—
65	C₂×C₄²	—	149	1	no	—
66	C₂×C₄²	C₂×D₁₄₉	1	1	yes	characteristic
67	C₄⋊C₈	—	149	8	no	—
68	#97	—	2	2	no	—
69	C₄×C₈	—	298	2	no	—
70	#95	—	149	4	no	—
71	C₂²×C₄	—	149	2	no	—
72	C₂²×C₄	—	149	2	no	—
73	C₂²×C₄	C₄×D₁₄₉	1	2	yes	—
74	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	298	2	no	—
78	C₂×C₈	—	298	2	no	—
79	C₂×C₈	—	149	4	no	—
80	C₂×C₈	C₄×D₁₄₉	1	4	yes	—
81	C₄²	—	298	2	no	—
82	C₄²	—	149	4	no	—
83	C₄²	C₂²⋊D₁₄₉	1	2	yes	—
84	C₄²	Dic₂₉₈	1	2	yes	—
85	C₂³	C₂×C₄×D₁₄₉	1	1	yes	characteristic
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	298	4	no	—
88	C₂×C₄	—	298	4	no	—
89	C₂×C₄	—	298	2	no	—
90	C₂×C₄	—	149	4	no	—
91	C₂×C₄	#14558715	1	4	yes	—
92	C₂×C₄	C₂×C₄×D₁₄₉	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	1	yes	characteristic
94	C₂×C₄	C₂×Dic₂₉₈	1	1	yes	characteristic
95	C₂×C₄	#14558736	1	2	yes	—
96	C₈	—	2	4	no	—
97	C₈	—	298	4	no	—
98	C₂²	C₄²×D₁₄₉	1	1	yes	characteristic
99	C₂²	C₂×#14558715	1	1	yes	characteristic
100	C₂²	#18011868	1	1	yes	characteristic
101	C₂²	#18011919	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	298	4	no	—
104	C₄	—	596	2	no	—
105	C₄	C₄×C₂²⋊D₁₄₉	1	2	yes	—
106	C₄	C₄×Dic₂₉₈	1	2	yes	—
107	C₂	C₄×#14558715	1	1	yes	characteristic
108	C₂	#23749582	1	2	yes	—
109	C₂	#23749653	1	2	yes	—
110	C₂	#23749687	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#18011840

C₂

yes

maximal

C₂×C₄×#11924746

C₂

yes

maximal, characteristic

#23749471

C₂

yes

maximal, characteristic

#23749379

C₂

yes

maximal

C₂×#97×C₁₄₉

C₂

yes

maximal, characteristic

C₂²×#11924746

C₂²

yes

—

C₂×C₄×Dic₁₄₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₄₉

C₂²

yes

characteristic

#18011840

C₄

yes

complemented

C₄×#11924746

—

#18011818

C₄

yes

—

C₂²×C₈×C₁₄₉

C₂²

yes

—

C₂×C₄²×C₁₄₉

C₂²

yes

characteristic

#97×C₁₄₉

—

C₂²×Dic₁₄₉

C₂×C₄

yes

—

C₂²×Dic₁₄₉

C₂×C₄

yes

—

C₂×#11924746

—

C₂×#11924746

—

C₂×#11924746

C₂×C₄

yes

—

C₄×Dic₁₄₉

—

C₄×Dic₁₄₉

C₂×C₄

yes

—

C₂²×C₄×C₁₄₉

C₂×C₄

yes

—

C₂²×C₄×C₁₄₉

C₂³

yes

characteristic

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

C₂×C₄

yes

—

C₄²×C₁₄₉

D₄

yes

—

C₄²×C₁₄₉

Q₈

yes

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

C₄²

yes

—

#11924746

—

C₂³×C₁₄₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₄₉

C₂²×C₄

yes

—

C₂×C₄×C₁₄₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₄₉

#41

yes

—

C₈×C₁₄₉

—

C₂²×C₁₄₉

C₂×C₄²

yes

characteristic

C₂²×C₁₄₉

C₂×C₄⋊C₄

yes

C₂²×C₁₄₉

yes

C₂²×C₁₄₉

yes

—

C₄×C₁₄₉

—

C₄×C₁₄₉

C₄×D₄

yes

—

C₄×C₁₄₉

C₄×Q₈

yes

—

Dic₁₄₉

—

Dic₁₄₉

—

C₂×C₁₄₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₄₉

#405

yes

—

C₂×C₁₄₉

#424

yes

—

C₂×C₁₄₉

#433

yes

—

C₁₄₉

#1768

yes

characteristic, complemented, Sylow

#1768

—

149

maximal, Sylow

C₂×C₄⋊C₈

—

149

—

C₂×#97

D₁₄₉

yes

characteristic

C₂×C₄×C₈

—

149

—

#376

—

149

—

#336

—

149

—

C₂²×C₈

—

149

—

C₂²×C₈

C₂×D₁₄₉

yes

—

C₂×C₄²

—

149

—

C₂×C₄²

—

149

—

C₂×C₄²

C₂×D₁₄₉

yes

characteristic

C₄⋊C₈

—

149

—

#97

—

C₄×C₈

—

298

—

#95

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

C₄×D₁₄₉

yes

—

C₂²×C₄

C₂²×D₁₄₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

149

—

C₂×C₈

C₄×D₁₄₉

yes

—

C₄²

—

298

—

C₄²

—

149

—

C₄²

C₂²⋊D₁₄₉

yes

—

C₄²

Dic₂₉₈

yes

—

C₂³

C₂×C₄×D₁₄₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

149

—

C₂×C₄

#14558715

yes

—

C₂×C₄

C₂×C₄×D₁₄₉

yes

—

C₂×C₄

C₂×C₂²⋊D₁₄₉

yes

characteristic

C₂×C₄

C₂×Dic₂₉₈

yes

characteristic

C₂×C₄

#14558736

yes

—

C₈

—

C₈

—

298

—

C₂²

C₄²×D₁₄₉

yes

characteristic

C₂²

C₂×#14558715

yes

characteristic

100

C₂²

#18011868

yes

characteristic

101

C₂²

#18011919

yes

—

102

C₄

—

103

C₄

—

298

—

104

C₄

—

596

—

105

C₄

C₄×C₂²⋊D₁₄₉

yes

—

106

C₄

C₄×Dic₂₉₈

yes

—

107

C₂

C₄×#14558715

yes

characteristic

108

C₂

#23749582

yes

—

109

C₂

#23749653

yes

—

110

C₂

#23749687

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₄₉
commutator	C₂²×C₁₄₉	C₂×C₄²
Fitting	C₂×#97×C₁₄₉	C₂
socle, prime radical	C₂³×C₁₄₉	C₂²×C₄
cosocle	C₂²×C₄×C₁₄₉	C₂³
hypercenter	C₂×#97	D₁₄₉
hypocenter	C₁₄₉	#1768
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₄₉

commutator

C₂²×C₁₄₉

C₂×C₄²

Fitting

C₂×#97×C₁₄₉

C₂

socle, prime radical

C₂³×C₁₄₉

C₂²×C₄

cosocle

C₂²×C₄×C₁₄₉

C₂³

hypercenter

C₂×#97

D₁₄₉

C₁₄₉

G ▷ C₂²×C₁₄₉ ▷ C₁₄₉

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
9. #18011840	C₄	semidirect
55. C₁₄₉	#1768	semidirect

H ≅ G/N

type

9. #18011840

C₄

semidirect

55. C₁₄₉

#1768

semidirect

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

subgroup	index
C₂×#18011840	2
C₂×C₄×#11924746	2
#23749471	2
#23749379	2
C₂×#97×C₁₄₉	2
#1768	149

subgroup

index

C₂×#97×C₁₄₉

149

Subgroups — #34044551

Conjugacy classes of subgroups

Complements

Maximal subgroups