Group #34060609 — subgroups

Subgroups — #34060609

Order 19072.

216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 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×#18011978	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#11924753	C₂	1	1	yes	maximal, characteristic
3	#23750491	C₂	1	4	yes	maximal
4	#23749470	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11924753	C₂²	1	2	yes	—
6	C₂²×#11924753	C₂²	1	2	yes	—
7	#18011978	—	2	2	no	—
8	C₄⋊#11924753	—	2	2	no	—
9	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	—
10	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
11	#18011818	C₄	1	1	yes	characteristic
12	#18011818	C₄	1	2	yes	—
13	#95×C₁₄₉	C₄	1	1	yes	characteristic
14	C₂×#11924753	—	2	2	no	—
15	C₂×#11924753	—	2	2	no	—
16	C₂×#11924753	—	2	4	no	—
17	C₂×#11924753	—	2	4	no	—
18	C₂²×Dic₁₄₉	C₂×C₄	1	2	yes	—
19	C₂²×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
21	C₄×Dic₁₄₉	—	2	2	no	—
22	C₄×Dic₁₄₉	—	2	2	no	—
23	C₄×Dic₁₄₉	D₄	1	2	yes	—
24	C₄×Dic₁₄₉	Q₈	1	2	yes	—
25	C₂²×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
27	#11924753	—	4	2	no	—
28	#11924753	—	4	2	no	—
29	C₂×Dic₁₄₉	—	2	1	no	—
30	C₂×Dic₁₄₉	—	2	1	no	—
31	C₂×Dic₁₄₉	—	2	2	no	—
32	C₂×Dic₁₄₉	—	2	2	no	—
33	C₂×Dic₁₄₉	—	2	2	no	—
34	C₂×Dic₁₄₉	C₄⋊C₄	1	2	yes	—
35	C₂×Dic₁₄₉	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₁₄₉	C₂×Q₈	1	1	yes	characteristic
37	C₂×Dic₁₄₉	#41	1	2	yes	—
38	C₂×Dic₁₄₉	#41	1	2	yes	—
39	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₄₉	—	2	2	no	—
41	C₂×C₄×C₁₄₉	—	2	2	no	—
42	C₂×C₄×C₁₄₉	—	2	2	no	—
43	C₂×C₄×C₁₄₉	—	2	2	no	—
44	C₂×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
45	C₂²×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₁₄₉	#117	1	2	yes	—
47	C₂²×C₁₄₉	#131	1	2	yes	—
48	C₂²×C₁₄₉	#131	1	1	yes	characteristic
49	C₂²×C₁₄₉	#131	1	1	yes	characteristic
50	C₄×C₁₄₉	—	2	2	no	—
51	C₄×C₁₄₉	—	4	2	no	—
52	Dic₁₄₉	—	2	2	no	—
53	Dic₁₄₉	—	4	2	no	—
54	Dic₁₄₉	#124	1	1	yes	characteristic
55	Dic₁₄₉	#124	1	1	yes	characteristic
56	Dic₁₄₉	#125	1	2	yes	—
57	C₂×C₁₄₉	#382	1	1	yes	characteristic
58	C₂×C₁₄₉	#424	1	1	yes	characteristic
59	C₂×C₁₄₉	#424	1	1	yes	characteristic
60	C₂×C₁₄₉	#433	1	2	yes	—
61	C₂×C₁₄₉	#433	1	2	yes	—
62	C₁₄₉	#1832	1	1	yes	characteristic, complemented, Sylow
63	#1832	—	149	1	no	maximal, Sylow
64	C₂×C₄⋊C₈	—	149	1	no	—
65	C₂×C₄⋊C₈	—	149	1	no	—
66	#376	—	149	1	no	—
67	#336	—	149	4	no	—
68	C₂²×C₈	—	149	2	no	—
69	C₂²×C₈	—	149	2	no	—
70	C₂×C₄²	—	149	2	no	—
71	C₂×C₄²	—	149	1	no	—
72	C₄⋊C₈	—	298	2	no	—
73	C₄⋊C₈	—	298	2	no	—
74	#95	—	149	1	no	—
75	#95	—	149	2	no	—
76	#95	#10597010	1	1	yes	characteristic
77	C₂²×C₄	—	149	2	no	—
78	C₂²×C₄	—	149	1	no	—
79	C₂²×C₄	—	149	1	no	—
80	C₂²×C₄	C₂×#10597010	1	2	yes	—
81	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
82	C₂×C₈	—	298	2	no	—
83	C₂×C₈	—	298	2	no	—
84	C₂×C₈	—	298	4	no	—
85	C₂×C₈	—	298	4	no	—
86	C₄²	—	298	2	no	—
87	C₄²	—	298	2	no	—
88	C₄²	—	149	2	no	—
89	C₄²	—	149	2	no	—
90	C₂³	C₂²×#10597010	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	298	1	no	—
96	C₂×C₄	—	298	1	no	—
97	C₂×C₄	—	298	2	no	—
98	C₂×C₄	—	298	2	no	—
99	C₂×C₄	—	298	2	no	—
100	C₂×C₄	—	149	2	no	—
101	C₂×C₄	—	149	1	no	—
102	C₂×C₄	—	149	1	no	—
103	C₂×C₄	—	149	2	no	—
104	C₂×C₄	—	149	2	no	—
105	C₂×C₄	C₄⋊#10597010	1	2	yes	—
106	C₈	—	596	2	no	—
107	C₈	—	596	2	no	—
108	C₂²	C₂×C₄⋊#10597010	1	1	yes	characteristic
109	C₂²	#18011990	1	2	yes	—
110	C₂²	#18011998	1	2	yes	—
111	C₂²	#18011998	1	1	yes	characteristic
112	C₂²	#18011999	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	4	2	no	—
115	C₄	—	298	2	no	—
116	C₄	—	596	2	no	—
117	C₄	—	149	1	no	—
118	C₄	—	149	1	no	—
119	C₄	—	149	2	no	—
120	C₂	#23750569	1	1	yes	characteristic
121	C₂	#23750631	1	1	yes	characteristic
122	C₂	#23750632	1	1	yes	characteristic
123	C₂	#23750649	1	2	yes	—
124	C₂	#23750650	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#18011978

C₂

yes

maximal, characteristic

C₂×C₄⋊#11924753

C₂

yes

maximal, characteristic

#23750491

C₂

yes

maximal

#23749470

C₂

yes

maximal, characteristic

C₂²×#11924753

C₂²

yes

—

C₂²×#11924753

C₂²

yes

—

#18011978

—

C₄⋊#11924753

—

C₂×C₄×Dic₁₄₉

C₂²

yes

—

C₂×C₄×Dic₁₄₉

C₂²

yes

characteristic

#18011818

C₄

yes

characteristic

#18011818

C₄

yes

—

#95×C₁₄₉

C₄

yes

—

—

—

—

C₂²×Dic₁₄₉

C₂×C₄

yes

—

C₂²×Dic₁₄₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₄₉

C₂³

yes

characteristic

C₄×Dic₁₄₉

—

C₄×Dic₁₄₉

—

C₄×Dic₁₄₉

D₄

yes

—

C₄×Dic₁₄₉

Q₈

yes

—

C₂²×C₄×C₁₄₉

C₂×C₄

yes

—

C₂²×C₄×C₁₄₉

C₂×C₄

yes

characteristic

#11924753

—

#11924753

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

C₄⋊C₄

yes

—

C₂×Dic₁₄₉

C₂×D₄

yes

characteristic

C₂×Dic₁₄₉

C₂×Q₈

yes

characteristic

C₂×Dic₁₄₉

#41

yes

—

C₂×Dic₁₄₉

#41

yes

—

C₂³×C₁₄₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

C₄⋊C₄

yes

—

C₂²×C₁₄₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₄₉

#117

yes

—

C₂²×C₁₄₉

#131

yes

—

C₂²×C₁₄₉

yes

C₂²×C₁₄₉

yes

C₄×C₁₄₉

—

C₄×C₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

yes

Dic₁₄₉

yes

Dic₁₄₉

yes

—

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

—

C₂×C₁₄₉

#433

yes

—

C₁₄₉

#1832

yes

characteristic, complemented, Sylow

#1832

—

149

maximal, Sylow

C₂×C₄⋊C₈

—

149

—

C₂×C₄⋊C₈

—

149

—

#376

—

149

—

#336

—

149

—

C₂²×C₈

—

149

—

C₂²×C₈

—

149

—

C₂×C₄²

—

149

—

C₂×C₄²

—

149

—

C₄⋊C₈

—

298

—

C₄⋊C₈

—

298

—

#95

—

149

—

#95

—

149

—

#95

#10597010

yes

characteristic

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

C₂×#10597010

yes

—

C₂²×C₄

C₂×#10597010

yes

characteristic

C₂×C₈

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

298

—

C₄²

—

298

—

C₄²

—

298

—

C₄²

—

149

—

C₄²

—

149

—

C₂³

C₂²×#10597010

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

100

C₂×C₄

—

149

—

101

C₂×C₄

—

149

—

102

C₂×C₄

—

149

—

103

C₂×C₄

—

149

—

104

C₂×C₄

—

149

—

105

C₂×C₄

C₄⋊#10597010

yes

—

106

C₈

—

596

—

107

C₈

—

596

—

108

C₂²

C₂×C₄⋊#10597010

yes

characteristic

109

C₂²

#18011990

yes

—

110

C₂²

#18011998

yes

—

111

C₂²

#18011998

yes

characteristic

112

C₂²

#18011999

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

298

—

116

C₄

—

596

—

117

C₄

—

149

—

118

C₄

—

149

—

119

C₄

—

149

—

120

C₂

#23750569

yes

characteristic

121

C₂

#23750631

yes

characteristic

122

C₂

#23750632

yes

characteristic

123

C₂

#23750649

yes

—

124

C₂

#23750650

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#10597010
commutator, socle, prime radical	C₂³×C₁₄₉	C₂²×C₄
Fitting	#95×C₁₄₉	C₄
cosocle	C₂²×Dic₁₄₉	C₂³
hypercenter	#95	#10597010
hypocenter	C₁₄₉	#1832
LCS	G ▷ C₂³×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#10597010

commutator, socle, prime radical

C₂³×C₁₄₉

C₂²×C₄

Fitting

#95×C₁₄₉

C₄

cosocle

C₂²×Dic₁₄₉

C₂³

C₁₄₉

G ▷ C₂³×C₁₄₉ ▷ C₁₄₉

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
62. C₁₄₉	#1832	semidirect

H ≅ G/N

type

62. C₁₄₉

#1832

semidirect

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

subgroup	index
C₂×#18011978	2
C₂×C₄⋊#11924753	2
#23750491	2
#23749470	2
#1832	149

subgroup

index

149

Subgroups — #34060609

Conjugacy classes of subgroups

Complements

Maximal subgroups