Finite Group Databasebeta

← #34060218

Subgroups — #34060218

Order 19072.

332 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 62 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
1#23750645C212yesmaximal, complemented
2#23750483C214yesmaximal, complemented
3C2×#18011907C211yesmaximal, characteristic
4#18011978C2214yescomplemented
5C22⋊#11924753—22no—
6#18011966—22no—
7C22×D596C411yescharacteristic
8C22×C22⋊D149—22no—
9#18011907—22no—
10#18011907C412yes—
11#18011907C2212yes—
12C2×C4×Dic149C2211yescharacteristic
13C22×D4×C149C411yescharacteristic
14C2×#11924753—24no—
15C23×D149—21no—
16C2×D596—21no—
17C2×D596—42no—
18C2×D596C2×C412yes—
19C2×C22⋊D149—24no—
20C2×C22⋊D149—24no—
21C2×C22⋊D149—48no—
22C22×Dic149D412yes—
23C4×Dic149C2×C411yescharacteristic
24C4×Dic149D412yes—
25C4×Dic149C2311yescharacteristic
26C24×C149—21no—
27C2×D4×C149—21no—
28C2×D4×C149—42no—
29C2×D4×C149C2×C412yes—
30C22×C4×C149C2×C411yescharacteristic
31#11924753—44no—
32C22×D149—22no—
33C22×D149—44no—
34C22×D149—42no—
35D596—42no—
36D596—42no—
37C22⋊D149—48no—
38C22⋊D149—48no—
39C2×Dic149—24no—
40C2×Dic149C22⋊C412yes—
41C2×Dic149C2×D412yes—
42C23×C149—22no—
43C23×C149—44no—
44C23×C149—42no—
45C23×C149C22⋊C411yescharacteristic
46D4×C149—42no—
47D4×C149—42no—
48C2×C4×C149—22no—
49C2×C4×C149C22⋊C411yescharacteristic
50C2×C4×C149C22×C411yescharacteristic
51C22×C149—22no—
52C22×C149—42no—
53C22×C149—44no—
54C22×C149—84no—
55C22×C149#10012yes—
56C22×C149C2×C22⋊C411yescharacteristic
57C2×D149—42no—
58C2×D149—44no—
59C2×D149—84no—
60C4×C149—21no—
61C4×C149—21no—
62Dic149—22no—
63Dic149AGL(1,ℤ/8)14yes—
64C2×C149—22no—
65C2×C149—82no—
66C2×C149C2×#10011yescharacteristic
67C2×C149#41812yes—
68D149—82no—
69C149#155511yescharacteristic, complemented, Sylow
70#1555—1491nomaximal, Sylow
71C2×#127—1491no—
72#432—1492no—
73#331—1494no—
74C22×D4—2982no—
75C22×D4—1491no—
76C22×D4#1059701011yescharacteristic
77#127—2982no—
78#127—1492no—
79#127—1492no—
80C2×C42—1491no—
81C4⋊C8—1494no—
82C22⋊C8—2982no—
83#97—2982no—
84C24—21no—
85C24—2981no—
86C2×D4—21no—
87C2×D4—42no—
88C2×D4—2984no—
89C2×D4—2984no—
90C2×D4—2981no—
91C2×D4—5962no—
92C2×D4—5968no—
93C2×D4—1492no—
94C2×D4C2×#1059701012yes—
95C22×C4—1492no—
96C22×C4C2×#1059701011yescharacteristic
97C2×C8—2984no—
98C42—1492no—
99C42—1491no—
100C42—1491no—
101C23—22no—
102C23—44no—
103C23—42no—
104C23—2982no—
105C23—5964no—
106C23—5962no—
107C23C22⋊#1059701011yescharacteristic
108D4—42no—
109D4—42no—
110D4—5962no—
111D4—5962no—
112D4—5968no—
113D4—5968no—
114C2×C4—22no—
115C2×C4—2984no—
116C2×C4—1492no—
117C2×C4—1492no—
118C2×C4C22⋊#1059701011yescharacteristic
119C2×C4C22×#1059701011yescharacteristic
120C8—5964no—
121C22—22no—
122C22—42no—
123C22—44no—
124C22—84no—
125C22—5962no—
126C22—5964no—
127C22—11924no—
128C22#1801197112yes—
129C22C2×C22⋊#1059701011yescharacteristic
130C4—21no—
131C4—21no—
132C4—2982no—
133C4—1494no—
134C2—22no—
135C2—82no—
136C2—11922no—
137C2C2×#1801197111yescharacteristic
138C2#2375061712yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#18011907C2
cosocleC4×Dic149C23
hypercenterC22×D4#10597010
hypocenterC149#1555
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #23750645C2semidirect
2. #23750483C2semidirect
4. #18011978C22semidirect
69. C149#1555semidirect

Maximal subgroups

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

subgroupindex
#237506452
#237504832
C2×#180119072
#1555149