Finite Group Databasebeta

← #34060394

Subgroups — #34060394

Order 19072.

432 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C2×D149⋊M16C212yesmaximal
2#23750505C214yesmaximal, complemented
3C2×C4⋊C4×D149C211yesmaximal, characteristic
4C2×#14558746—22no—
5D149⋊M16—24no—
6D149⋊M16C418yescomplemented
7C2×#14558745C2214yes—
8C2×D149⋊C8—22no—
9C22×C4×D149C412yes—
10C22×C4×D149C2211yescharacteristic
11C2×C4⋊Dic149C411yescharacteristic
12C2×#14558715C2212yes—
13C4⋊C4×D149—22no—
14C4⋊C4×D149—22no—
15C2×C4⋊C4×C149C411yescharacteristic
16#14558746—28no—
17#14558745—24no—
18#14558745C2×C418yescomplemented
19D149⋊C8—28no—
20C2×#11924753—24no—
21C23×D149C2×C411yescharacteristic
22C22×Dic149C2×C412yes—
23C22×Dic149C2311yescharacteristic
24C2×C4×D149—22no—
25C2×C4×D149—22no—
26C2×C4×D149—44no—
27C2×C4×D149C2×C414yes—
28C2×C4×D149D412yes—
29C2×C4×D149D412yes—
30C2×C4×D149D412yes—
31C2×C4×D149Q812yes—
32C4⋊Dic149—22no—
33#14558715—24no—
34C22×C4×C149C2×C412yes—
35C22×C4×C149C2×C411yescharacteristic
36C4⋊C4×C149—22no—
37#11924753—28no—
38C22×D149—22no—
39C22×D149—22no—
40C22×D149C4212yes—
41C22×D149C22⋊C411yescharacteristic
42C22×D149C22⋊C411yescharacteristic
43C22×D149C4⋊C412yes—
44C2×Dic149—22no—
45C2×Dic149—42no—
46C2×Dic149C22×C412yes—
47C2×Dic149C2×D411yescharacteristic
48C2×Dic149C2×D412yes—
49C2×Dic149C2×Q811yescharacteristic
50C4×D149—44no—
51C4×D149—44no—
52C4×D149C22⋊C414yes—
53C4×D149C22⋊C414yes—
54C4×D149C4⋊C414yes—
55C4×D149C4⋊C414yes—
56C23×C149C22×C411yescharacteristic
57C2×C4×C149—22no—
58C2×C4×C149—42no—
59C2×C4×C149C4212yes—
60C2×C4×C149C22⋊C412yes—
61C2×C4×C149C4⋊C412yes—
62C22×C149—21no—
63C22×C149—21no—
64C22×C149C2×C4211yescharacteristic
65C22×C149C2×C22⋊C411yescharacteristic
66C22×C149C2×C4⋊C411yescharacteristic
67C2×D149—21no—
68C2×D149—21no—
69C2×D149—24no—
70C2×D149—24no—
71C2×D149#9512yes—
72C2×D149#9512yes—
73C2×D149#10012yes—
74C2×D149#10112yes—
75C4×C149—42no—
76C4×C149#9514yes—
77Dic149—42no—
78Dic149C2×C22⋊C412yes—
79Dic149C2×C4⋊C412yes—
80C2×C149—21no—
81C2×C149—21no—
82C2×C149C2×#9511yescharacteristic
83C2×C149C2×#10011yescharacteristic
84C2×C149C2×#10111yescharacteristic
85D149—22no—
86D149#34314yescomplemented
87C149C2×#34311yescharacteristic, complemented, Sylow
88C2×#343—1491nomaximal, Sylow
89C22×M16—1492no—
90C22×C4⋊C4—1491no—
91#343—1494no—
92C23×C4—1492no—
93C23×C4—1491no—
94C2×M16—2984no—
95C2×M16—2982no—
96C2×M16—1494no—
97C2×M16—1498no—
98C22×C8—2982no—
99C2×C4⋊C4—2982no—
100C2×C4⋊C4—2982no—
101C2×C4⋊C4—1492no—
102C2×C4⋊C4—1491no—
103C2×C4⋊C4#1059701011yescharacteristic
104C24—1491no—
105C22×C4—2982no—
106C22×C4—2982no—
107C22×C4—5964no—
108C22×C4—1492no—
109C22×C4—1491no—
110C22×C4—1494no—
111C22×C4—1492no—
112C22×C4—1492no—
113C22×C4—1492no—
114C22×C4—1492no—
115C22×C4C2×#1059701012yes—
116C22×C4C2×#1059701011yescharacteristic
117M16—2984no—
118M16—2988no—
119M16—1498no—
120C2×C8—2984no—
121C2×C8—2988no—
122C4⋊C4—22no—
123C4⋊C4—2984no—
124C4⋊C4—2982no—
125C23—2982no—
126C23—2982no—
127C23—1492no—
128C23—1491no—
129C23—1492no—
130C23—1491no—
131C23C22×#1059701011yescharacteristic
132C2×C4—22no—
133C2×C4—42no—
134C2×C4—2982no—
135C2×C4—5964no—
136C2×C4—5964no—
137C2×C4—5962no—
138C2×C4—1492no—
139C2×C4—1492no—
140C2×C4—1491no—
141C2×C4—1491no—
142C2×C4—1494no—
143C2×C4—1494no—
144C2×C4—1494no—
145C2×C4—1494no—
146C2×C4C4×#1059701012yes—
147C2×C4C22⋊#1059701012yes—
148C2×C4C4⋊#1059701012yes—
149C8—2988no—
150C22—21no—
151C22—21no—
152C22—2984no—
153C22—2984no—
154C22—2981no—
155C22—2981no—
156C22—1492no—
157C22—1492no—
158C22—1492no—
159C22—1492no—
160C22C2×C4×#1059701011yescharacteristic
161C22C2×C22⋊#1059701011yescharacteristic
162C22C2×C4⋊#1059701011yescharacteristic
163C4—42no—
164C4—5962no—
165C4—1492no—
166C4—1492no—
167C4(C2×#10597010)⋊C414yes—
168C2—21no—
169C2—21no—
170C2—2982no—
171C2—1494no—
172C2C2×(C2×#10597010)⋊C411yescharacteristic
173C2D149⋊#10011yescharacteristic
174C2D149⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC22×C149C2×C42
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149C2×C4
cosocleC22×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149C2×#343
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #23750505C2semidirect
6. D149⋊M16C4semidirect
18. #14558745C2×C4semidirect
86. D149#343semidirect
87. C149C2×#343semidirect

Maximal subgroups

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

subgroupindex
C2×D149⋊M162
#237505052
C2×C4⋊C4×D1492
C2×#343149