Finite Group Databasebeta

← #34069508

Subgroups — #34069508

Order 19328.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#18012735C211yesmaximal, characteristic
2#23752216C212yesmaximal, complemented
3C2×#18012656C211yesmaximal, characteristic, complemented
4#23751971C212yesmaximal, complemented
5#518×C151C211yesmaximal, characteristic, complemented
6C22×D604C2211yescharacteristic
7C22×C22⋊D151—22no—
8C2×#14558988C2212yes—
9#18012735—22no—
10#18012735C414yescomplemented
11C2×C4×Dic151C2211yescharacteristic
12#18012659—24no—
13#18012656—22no—
14C22×D4×C151C2211yescharacteristic
15C4×D4×C151—24no—
16#117×C151C2212yes—
17C2×C22⋊C4×C151—22no—
18C23×D151—21no—
19C2×D604—22no—
20C2×D604—21no—
21C2×D604—22no—
22C2×D604C2×C412yescomplemented
23C2×C22⋊D151—28no—
24C2×C22⋊D151—48no—
25C22×Dic151—21no—
26#14558988—22no—
27#14558988—22no—
28C2×C151⋊C8—22no—
29C4×Dic151—21no—
30C4×Dic151C2×C412yescomplemented
31C24×C151D412yes—
32C2×D4×C151—22no—
33C2×D4×C151—22no—
34C2×D4×C151C2×C412yes—
35C2×D4×C151D412yes—
36C22×C4×C151—24no—
37C22×C4×C151C2311yescharacteristic
38C4⋊C4×C151D414yescomplemented
39C22⋊C4×C151—24no—
40C22⋊C4×C151—22no—
41C42×C151—22no—
42C22×D151—22no—
43C22×D151—44no—
44C22×D151—41no—
45C22×D151—41no—
46D604—24no—
47D604—42no—
48C22⋊D151—416no—
49C2×Dic151—24no—
50C2×Dic151—22no—
51C151⋊C8—42no—
52C23×C151—22no—
53C23×C151—22no—
54C23×C151—44no—
55C23×C151C22⋊C414yes—
56C23×C151C2×D411yescharacteristic
57D4×C151—24no—
58D4×C151—24no—
59C2×C4×C151—24no—
60C2×C4×C151—84no—
61C2×C4×C151C22×C411yescharacteristic
62C2×C4×C151C2×D412yes—
63C2×C4×C151C2×D411yescharacteristic
64C2×C4×C151#4112yes—
65C22×C151—22no—
66C22×C151—24no—
67C22×C151—44no—
68C22×C151—44no—
69C22×C151—82no—
70C22×C151C2×C22⋊C411yescharacteristic
71C22×C151#12011yescharacteristic
72C22×C151#12311yescharacteristic
73C2×D151—44no—
74C2×D151—42no—
75C2×D151—82no—
76C2×D151—82no—
77C4×C151—44no—
78C4×C151C4×D412yes—
79C4×C151#12112yes—
80Dic151—24no—
81C2×C151—21no—
82C2×C151—21no—
83C2×C151—44no—
84C2×C151#38611yescharacteristic
85C2×C151#45312yes—
86D151—82no—
87C151#188711yescharacteristic, complemented, Sylow
88#1887—1511nomaximal, Sylow
89C2×#127—1511no—
90#518D15111yescharacteristic, complemented
91#418—1512no—
92C2×#100—1511no—
93#339—1512no—
94C22×D4—3022no—
95C22×D4—1511no—
96C22×D4C2×D15111yescharacteristic
97C2×M16—1512no—
98#127—3022no—
99#127—1514no—
100C4×D4—24no—
101#117C2×D15112yes—
102C2×C22⋊C4—22no—
103C2×C42—1511no—
104#102—3024no—
105#100—3022no—
106C24—3021no—
107C24C22⋊D15112yes—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—3028no—
111C2×D4—3022no—
112C2×D4—3021no—
113C2×D4—3022no—
114C2×D4—6048no—
115C2×D4—1512no—
116C2×D4C4×D15112yes—
117C2×D4D60412yes—
118C22×C4—24no—
119C22×C4—3021no—
120C22×C4C22×D15111yescharacteristic
121M16—3022no—
122M16—3022no—
123C2×C8—3022no—
124C4⋊C4C22⋊D15114yescomplemented
125C22⋊C4—24no—
126C22⋊C4—22no—
127C42—22no—
128C42—3021no—
129C42—1512no—
130C23—22no—
131C23—22no—
132C23—44no—
133C23—3022no—
134C23—6044no—
135C23—6041no—
136C23—6041no—
137C23(C2×D151)⋊C414yes—
138C23C2×C22⋊D15111yescharacteristic
139D4—24no—
140D4—24no—
141D4—3024no—
142D4—60416no—
143D4—6042no—
144C2×C4—24no—
145C2×C4—84no—
146C2×C4—3024no—
147C2×C4—3022no—
148C2×C4C2×C4×D15111yescharacteristic
149C2×C4C2×C22⋊D15112yes—
150C2×C4C2×D60411yescharacteristic
151C2×C4#1455900412yes—
152C8—6042no—
153C22—22no—
154C22—24no—
155C22—44no—
156C22—44no—
157C22—82no—
158C22—6044no—
159C22—6042no—
160C22—12082no—
161C22—12082no—
162C22C2×(C2×D151)⋊C411yescharacteristic
163C22#1801270811yescharacteristic
164C22#1801272211yescharacteristic
165C4—44no—
166C4—3024no—
167C4C4×C22⋊D15112yes—
168C4#1801271312yes—
169C2—21no—
170C2—21no—
171C2—44no—
172C2—12082no—
173C2#2375209111yescharacteristic
174C2#2375238012yes—
subgroupG/H
centerC22#18012708
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#518×C151C2
socleC22×C151#120
prime radicalC2×#18012735C2
cosocleC22×C4×C151C23
hypercenter#518D151
hypocenterC151#1887
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #23752216C2semidirect
3. C2×#18012656C2semidirect
4. #23751971C2semidirect
5. #518×C151C2semidirect
10. #18012735C4semidirect
22. C2×D604C2×C4semidirect
30. C4×Dic151C2×C4semidirect
38. C4⋊C4×C151D4semidirect
87. C151#1887semidirect
90. #518D151semidirect
124. C4⋊C4C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127352
#237522162
C2×#180126562
#237519712
#518×C1512
#1887151