Finite Group Databasebeta

← C2×#23750260 #34058130

Subgroups — C2×#23750260 #34058130

Order 19072.

2536 conjugacy classes of subgroups; only the 581 normal subgroups are shown.

normal subgroups only

This group has 2536 conjugacy classes of subgroups — too many to draw. Only its 581 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D149C214yesmaximal, complemented
2#23750260C2116yesmaximal, direct product factor
3C2×#18011882C214yesmaximal, complemented
4C2×#18011879C214yesmaximal, complemented
5C2×C4×D596C212yesmaximal, complemented
6C2×#127×C149C211yesmaximal, characteristic, complemented
7C24×D149C2214yescomplemented
8C22×D596C2212yes—
9C22×C22⋊D149C2218yescomplemented
10C2×D4×D149—232no—
11C2×D4×D149C22132yescomplemented
12C22×C4×D149C2214yescomplemented
13#18011882C22132yescomplemented
14#18011879C22132yescomplemented
15C4×D596C22116yescomplemented
16C2×C4⋊Dic149C2212yescomplemented
17C2×C22⋊Dic149C2214yescomplemented
18C2×#14558713C2214yescomplemented
19C22×D4×C149C2214yescomplemented
20C22×D4×C149C2212yescomplemented
21#127×C149C2218yescomplemented
22C2×C42×C149C2211yescharacteristic, complemented
23C23×D149—232no—
24C23×D149—48no—
25C23×D149C2314yes—
26C23×D149C23116yescomplemented
27C2×D596D4116yescomplemented
28C2×D596C2318yes—
29C2×C22⋊D149—232no—
30C2×C22⋊D149C23132yescomplemented
31D4×D149—2128no—
32C22×Dic149C2314yes—
33C2×C4×D149—216no—
34C2×C4×D149C23116yescomplemented
35C4⋊Dic149C2318yescomplemented
36C22⋊Dic149C23116yescomplemented
37#14558713C23116yescomplemented
38C24×C149C2314yes—
39C2×D4×C149—216no—
40C2×D4×C149—44no—
41C2×D4×C149C23116yescomplemented
42C2×D4×C149C2318yescomplemented
43C22×C4×C149C2311yescharacteristic
44C22×C4×C149C2312yes—
45C42×C149C2314yescomplemented
46C22×D149—28no—
47C22×D149—28no—
48C22×D149—264no—
49C22×D149—416no—
50C22×D149—464no—
51C22×D149C2×D4116yescomplemented
52C22×D149C2418yes—
53D596C2×D4132yescomplemented
54C22⋊D149—264no—
55C2×Dic149—28no—
56C2×Dic149C2418yes—
57C4×D149—232no—
58C23×C149—216no—
59C23×C149—28no—
60C23×C149C2418yes—
61C23×C149C2411yescharacteristic
62D4×C149—232no—
63D4×C149—48no—
64C2×C4×C149—22no—
65C2×C4×C149C2×D418yescomplemented
66C2×C4×C149C2412yes—
67C2×C4×C149C2414yes—
68C22×C149—216no—
69C22×C149—28no—
70C22×C149—416no—
71C22×C149C22×D414yes—
72C22×C149H(5,𝔽2)12yes—
73C22×C149C2511yescharacteristic
74C2×D149—232no—
75C2×D149—28no—
76C2×D149—28no—
77C2×D149—464no—
78C2×D149C22×D4116yescomplemented
79C4×C149—22no—
80C4×C149C22×D418yescomplemented
81Dic149—28no—
82C2×C149—48no—
83C2×C149D4214yescomplemented
84C2×C149C23×D412yes—
85C2×C149C2×H(5,𝔽2)11yescharacteristic
86D149—216no—
87C149C2×D4211yescharacteristic, complemented, Sylow
88C2×D42—1491nomaximal, Sylow
89C23×D4—1494no—
90D42—14916no—
91C2×#127D14911yescharacteristic, complemented
92C2×#121—1494no—
93C2×#120—1494no—
94C2×C4×D4—1492no—
95C25—1494no—
96C22×D4—29832no—
97C22×D4—1498no—
98C22×D4—14932no—
99C22×D4—1492no—
100C22×D4C2×D14914yescomplemented
101C22×D4C2×D14912yescomplemented
102C23×C4—1494no—
103#127C2×D14918yescomplemented
104#121—14932no—
105#120—14932no—
106C4×D4—14916no—
107C2×C4⋊C4—1492no—
108C2×C22⋊C4—1494no—
109C2×C22⋊C4—1494no—
110C2×C42C2×D14911yescharacteristic, complemented
111C24—29832no—
112C24—5968no—
113C24—14916no—
114C24—1494no—
115C24C22×D14914yes—
116C2×D4—216no—
117C2×D4—44no—
118C2×D4—298128no—
119C2×D4—29832no—
120C2×D4—14932no—
121C2×D4—14916no—
122C2×D4—1498no—
123C2×D4C22×D149116yescomplemented
124C2×D4C22×D14918yescomplemented
125C22×C4—29816no—
126C22×C4—1494no—
127C22×C4—14916no—
128C22×C4C22×D14911yescharacteristic
129C22×C4C22×D14912yes—
130C4⋊C4—1498no—
131C22⋊C4—14916no—
132C22⋊C4—14916no—
133C42C22×D14914yescomplemented
134C23—216no—
135C23—28no—
136C23—29864no—
137C23—2988no—
138C23—2988no—
139C23—59616no—
140C23—59664no—
141C23—14916no—
142C23—1498no—
143C23C23×D14918yes—
144C23C23×D14911yescharacteristic
145D4—232no—
146D4—48no—
147D4—29864no—
148D4—14932no—
149C2×C4—22no—
150C2×C4—2988no—
151C2×C4—29832no—
152C2×C4—1498no—
153C2×C4D4×D14918yescomplemented
154C2×C4C23×D14912yes—
155C2×C4C23×D14914yes—
156C22—216no—
157C22—28no—
158C22—416no—
159C22—2988no—
160C22—2988no—
161C22—29832no—
162C22—59664no—
163C22—14916no—
164C22C2×D4×D14914yes—
165C22#1801195612yes—
166C22C24×D14911yescharacteristic
167C4—22no—
168C4—2988no—
169C4C2×D4×D14918yescomplemented
170C2—48no—
171C2—29816no—
172C2#2375026014yesdirect product factor
173C2C22×D4×D14912yes—
174C2C2×#1801195611yescharacteristic
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#127×C149C2
socleC23×C149C24
hypercenterC2×#127D149
hypocenterC149C2×D42
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#127

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×D4×D149C2semidirect
2. #23750260C2direct (N × H)
3. C2×#18011882C2semidirect
4. C2×#18011879C2semidirect
5. C2×C4×D596C2semidirect
6. C2×#127×C149C2semidirect
7. C24×D149C22semidirect
9. C22×C22⋊D149C22semidirect
11. C2×D4×D149C22semidirect
12. C22×C4×D149C22semidirect
13. #18011882C22semidirect
14. #18011879C22semidirect
15. C4×D596C22semidirect
16. C2×C4⋊Dic149C22semidirect
17. C2×C22⋊Dic149C22semidirect
18. C2×#14558713C22semidirect
19. C22×D4×C149C22semidirect
20. C22×D4×C149C22semidirect
21. #127×C149C22semidirect
22. C2×C42×C149C22semidirect
26. C23×D149C23semidirect
27. C2×D596D4semidirect
30. C2×C22⋊D149C23semidirect
34. C2×C4×D149C23semidirect
35. C4⋊Dic149C23semidirect
36. C22⋊Dic149C23semidirect
37. #14558713C23semidirect
41. C2×D4×C149C23semidirect
42. C2×D4×C149C23semidirect
45. C42×C149C23semidirect
51. C22×D149C2×D4semidirect
53. D596C2×D4semidirect
65. C2×C4×C149C2×D4semidirect
78. C2×D149C22×D4semidirect
80. C4×C149C22×D4semidirect
83. C2×C149D42semidirect
87. C149C2×D42semidirect
91. C2×#127D149semidirect
100. C22×D4C2×D149semidirect
101. C22×D4C2×D149semidirect
103. #127C2×D149semidirect
110. C2×C42C2×D149semidirect
123. C2×D4C22×D149semidirect
124. C2×D4C22×D149semidirect
133. C42C22×D149semidirect
153. C2×C4D4×D149semidirect
169. C4C2×D4×D149semidirect
172. C2#23750260direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1492
#237502602
C2×#180118822
C2×#180118792
C2×C4×D5962
C2×#127×C1492
C2×D42149