Finite Group Databasebeta

← #34080316

Subgroups — #34080316

Order 19328.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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#23752769C211yesmaximal, characteristic
2#23752622C212yesmaximal, complemented
3#23752582C212yesmaximal, complemented
4#23752547C212yesmaximal
5#23752542C212yesmaximal
6#23752516C214yesmaximal, complemented
7#23752269C211yesmaximal, characteristic
8C2×#125×C151C211yesmaximal, characteristic
9#18012739C2211yescharacteristic
10#18012739C2211yescharacteristic
11#18012731—21no—
12#18012718—21no—
13#18012718C2212yes—
14C4×Dic302—21no—
15C4×Dic302C2212yes—
16#18012698—21no—
17#18012672C2214yes—
18#18012670C2214yes—
19C4⋊(C151⋊C8)C2212yes—
20#18012662C2214yes—
21#18012662C2214yes—
22C22⋊(C151⋊C8)C2212yes—
23#18012650C2212yes—
24#125×C151—21no—
25#125×C151—21no—
26#125×C151C2212yes—
27#125×C151C2212yes—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151C2211yescharacteristic
31C2×C4⋊C4×C151C2211yescharacteristic
32C2×C42×C151C2211yescharacteristic
33C2×Dic302—21no—
34C2×Dic302C2312yes—
35C2×C151⋊C8C2314yes—
36C4⋊Dic151—21no—
37C4⋊Dic151—21no—
38C4⋊Dic151—21no—
39C4⋊Dic151C2312yes—
40Dic151⋊C4—22no—
41Dic151⋊C4—22no—
42C22⋊Dic151—22no—
43C4×Dic151—22no—
44C22×C4×C151—21no—
45C22×C4×C151—21no—
46C22×C4×C151D411yescharacteristic
47C22×C4×C151D411yescharacteristic
48C22×C4×C151C2311yescharacteristic
49C4⋊C4×C151—22no—
50C4⋊C4×C151—22no—
51C4⋊C4×C151—22no—
52C4⋊C4×C151—22no—
53C4⋊C4×C151—21no—
54C4⋊C4×C151—21no—
55C4⋊C4×C151C2312yes—
56C4⋊C4×C151C2312yes—
57C42×C151D411yescharacteristic
58C42×C151D411yescharacteristic
59C42×C151C2311yescharacteristic
60C42×C151C2311yescharacteristic
61Dic302—24no—
62Dic302—42no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C151⋊C8—24no—
66C23×C151C2×D411yescharacteristic
67C2×C4×C151—22no—
68C2×C4×C151—22no—
69C2×C4×C151—22no—
70C2×C4×C151—22no—
71C2×C4×C151—41no—
72C2×C4×C151—42no—
73C2×C4×C151—42no—
74C2×C4×C151C2×D411yescharacteristic
75C2×C4×C151C2×D411yescharacteristic
76C2×C4×C151C2×D411yescharacteristic
77C2×C4×C151C2×D411yescharacteristic
78C2×C4×C151C2×D411yescharacteristic
79C2×C4×C151C2411yescharacteristic
80C22×C151—21no—
81C22×C151—21no—
82C22×C151#13712yes—
83C22×C151C22×D411yescharacteristic
84C4×C151—21no—
85C4×C151—21no—
86C4×C151—21no—
87C4×C151—21no—
88C4×C151—21no—
89C4×C151—42no—
90C4×C151—42no—
91C4×C1512−1+412yes—
92Dic151—42no—
93Dic151—42no—
94C2×C151—22no—
95C2×C151#53611yescharacteristic
96C2×C151C2×#13711yescharacteristic
97C2×C151#57511yescharacteristic
98C151#323611yescharacteristic, complemented, Sylow
99#3236—1511nomaximal, Sylow
100#533—1511no—
101C2×#125D15111yescharacteristic
102#501—1512no—
103#491—1512no—
104#484—1512no—
105#483—1512no—
106#479—1514no—
107#432—1511no—
108C4⋊Q8—1511no—
109C4⋊Q8—1511no—
110#125—21no—
111#125—21no—
112#125—3021no—
113#125C2×D15112yes—
114#125C2×D15112yes—
115C22⋊Q8—3021no—
116C22⋊Q8—1512no—
117C4×Q8—3021no—
118C4×Q8—1512no—
119#117—3021no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D15111yescharacteristic
123C2×C4⋊C4C2×D15111yescharacteristic
124C2×C42C2×D15111yescharacteristic
125#107—1514no—
126#106—1514no—
127C4⋊C8—1512no—
128#103—1514no—
129#103—1514no—
130C22⋊C8—1512no—
131#97—1512no—
132C2×Q8—3021no—
133C2×Q8—1512no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4C22⋊D15111yescharacteristic
137C22×C4C22⋊D15111yescharacteristic
138C22×C4C22×D15111yescharacteristic
139C2×C8—1514no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—3022no—
147C4⋊C4—3022no—
148C4⋊C4—3021no—
149C4⋊C4—3021no—
150C4⋊C4—3021no—
151C4⋊C4—1512no—
152C4⋊C4C22×D15112yes—
153C4⋊C4C22×D15112yes—
154C22⋊C4—3022no—
155C42—3022no—
156C42C22⋊D15111yescharacteristic
157C42C22⋊D15111yescharacteristic
158C42C22×D15111yescharacteristic
159C42C22×D15111yescharacteristic
160C23C2×C22⋊D15111yescharacteristic
161Q8—3024no—
162Q8—6042no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—3022no—
171C2×C4—3022no—
172C2×C4C2×C22⋊D15111yescharacteristic
173C2×C4C2×C22⋊D15111yescharacteristic
174C2×C4C2×C22⋊D15111yescharacteristic
175C2×C4C2×C22⋊D15111yescharacteristic
176C2×C4C2×C22⋊D15111yescharacteristic
177C2×C4C23×D15111yescharacteristic
178C8—3024no—
179C22—21no—
180C22—21no—
181C22#1801276912yes—
182C22C22×C22⋊D15111yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—42no—
189C4—42no—
190C4—6042no—
191C4—6042no—
192C4#1801278712yes—
193C2—22no—
194C2#2375278611yescharacteristic
195C2C2×#1801276911yescharacteristic
196C2#2375301011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#125×C151C2
socleC22×C151C22×D4
prime radicalC23×C151C2×D4
hypercenterC2×#125D151
hypocenterC151#3236
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #23752622C2semidirect
3. #23752582C2semidirect
6. #23752516C2semidirect
98. C151#3236semidirect

Maximal subgroups

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

subgroupindex
#237527692
#237526222
#237525822
#237525472
#237525422
#237525162
#237522692
C2×#125×C1512
#3236151