Finite Group Databasebeta

← #34069549

Subgroups — #34069549

Order 19328.

412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14558988C211yesmaximal, characteristic, complemented
2C2×#18012660C212yesmaximal, complemented
3#23752072C211yesmaximal, characteristic, complemented
4#23751974C212yesmaximal, complemented
5C2×#121×C151C211yesmaximal, characteristic
6C2×#14558988—22no—
7C2×#14558988—24no—
8C22×C151⋊C8C2212yes—
9C2×C4⋊Dic151C2212yes—
10C2×C22⋊Dic151—21no—
11#18012660—24no—
12C151⋊#95—21no—
13C22×D4×C151—21no—
14C22×D4×C151C2211yescharacteristic
15C23×C4×C151C2211yescharacteristic
16#121×C151—22no—
17#121×C151C414yescomplemented
18C2×C4⋊C4×C151C2211yescharacteristic
19C2×C22⋊C4×C151—21no—
20C22×Dic151—22no—
21#14558988—28no—
22C2×C151⋊C8—22no—
23C2×C151⋊C8—22no—
24C2×C151⋊C8D414yescomplemented
25C4⋊Dic151—22no—
26C4⋊Dic151—22no—
27C22⋊Dic151—42no—
28C24×C151—21no—
29C24×C151D411yescharacteristic
30C2×D4×C151—24no—
31C2×D4×C151—22no—
32C2×D4×C151—21no—
33C2×D4×C151—22no—
34C2×D4×C151—44no—
35C2×D4×C151C2×C412yes—
36C22×C4×C151—22no—
37C22×C4×C151—22no—
38C22×C4×C151—21no—
39C22×C4×C151C2×C412yes—
40C22×C4×C151D411yescharacteristic
41C22×C4×C151D412yes—
42C22×C4×C151C2311yescharacteristic
43C4⋊C4×C151—21no—
44C4⋊C4×C151C2×C412yes—
45C22⋊C4×C151—24no—
46C2×Dic151—42no—
47C2×Dic151—42no—
48C2×Dic151—42no—
49C151⋊C8—24no—
50C23×C151—22no—
51C23×C151—21no—
52C23×C151—22no—
53C23×C151—21no—
54C23×C151—22no—
55C23×C151—42no—
56C23×C151—41no—
57C23×C151—42no—
58C23×C151—41no—
59C23×C151C22⋊C412yes—
60C23×C151C2×D411yescharacteristic
61D4×C151—24no—
62D4×C151—48no—
63D4×C151—41no—
64D4×C151—41no—
65C2×C4×C151—22no—
66C2×C4×C151—24no—
67C2×C4×C151—22no—
68C2×C4×C151—22no—
69C2×C4×C151—22no—
70C2×C4×C151—42no—
71C2×C4×C151C22⋊C412yes—
72C2×C4×C151C22×C411yescharacteristic
73C2×C4×C151C2×D412yes—
74C2×C4×C151C2×D411yescharacteristic
75C2×C4×C151#4112yes—
76C22×C151—22no—
77C22×C151—22no—
78C22×C151—22no—
79C22×C151—42no—
80C22×C151—42no—
81C22×C151—42no—
82C22×C151—42no—
83C22×C151—42no—
84C22×C151—82no—
85C22×C151—82no—
86C22×C151C2×C22⋊C411yescharacteristic
87C22×C151#12112yes—
88C22×C151AGL(1,ℤ/8)11yescharacteristic
89C22×C151AGL(1,ℤ/8)12yes—
90C22×C151#13711yescharacteristic
91C4×C151—22no—
92C4×C151—42no—
93C4×C151C4×D412yes—
94C4×C151#12011yescharacteristic
95C4×C151#12311yescharacteristic
96Dic151—82no—
97C2×C151—42no—
98C2×C151—82no—
99C2×C151#38611yescharacteristic
100C2×C151#41711yescharacteristic
101C2×C151#41811yescharacteristic
102C2×C151#46812yes—
103C2×C151#46912yes—
104C151#189511yescharacteristic, complemented, Sylow
105#1895—1511nomaximal, Sylow
106C22×M16—1511no—
107C2×#121D15111yescharacteristic
108C2×#102—1512no—
109#380—1511no—
110#340—1512no—
111C22×D4—21no—
112C22×D4C2×D15111yescharacteristic
113C23×C4C2×D15111yescharacteristic
114C2×M16—3022no—
115C2×M16—3024no—
116C22×C8—1512no—
117#121—22no—
118#121Dic15114yescomplemented
119C2×C4⋊C4—1512no—
120C2×C4⋊C4C2×D15111yescharacteristic
121C2×C22⋊C4—21no—
122C2×C22⋊C4—3021no—
123#102—3024no—
124#95—3021no—
125C24—21no—
126C24C22⋊D15111yescharacteristic
127C2×D4—24no—
128C2×D4—22no—
129C2×D4—21no—
130C2×D4—22no—
131C2×D4—44no—
132C2×D4C2×Dic15112yes—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—21no—
136C22×C4—3022no—
137C22×C4C2×Dic15112yes—
138C22×C4C22⋊D15111yescharacteristic
139C22×C4C22⋊D15112yes—
140C22×C4C22×D15111yescharacteristic
141M16—3028no—
142C2×C8—3022no—
143C2×C8—3022no—
144C2×C8—1514no—
145C4⋊C4—21no—
146C4⋊C4—3022no—
147C4⋊C4—3022no—
148C4⋊C4C2×Dic15112yes—
149C22⋊C4—24no—
150C22⋊C4—6042no—
151C23—22no—
152C23—21no—
153C23—22no—
154C23—21no—
155C23—22no—
156C23—42no—
157C23—41no—
158C23—42no—
159C23—41no—
160C23C22⋊Dic15112yes—
161C23C2×C22⋊D15111yescharacteristic
162D4—24no—
163D4—48no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—6042no—
173C2×C4—6042no—
174C2×C4—6042no—
175C2×C4C22⋊Dic15112yes—
176C2×C4C22×Dic15111yescharacteristic
177C2×C4D4×D15112yes—
178C2×C4C2×C22⋊D15111yescharacteristic
179C2×C4#1455900312yes—
180C8—3024no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—42no—
189C22—82no—
190C22—82no—
191C22C2×C22⋊Dic15111yescharacteristic
192C22#1801271112yes—
193C22#1801276411yescharacteristic
194C22#1801276512yes—
195C22#1801276911yescharacteristic
196C4—22no—
197C4—42no—
198C4—12082no—
199C4D4×Dic15112yes—
200C4#1801270711yescharacteristic
201C4#1801272011yescharacteristic
202C2—42no—
203C2—82no—
204C2#2375209211yescharacteristic
205C2#2375221311yescharacteristic
206C2#2375221711yescharacteristic
207C2#2375245612yes—
208C2#2375246312yes—
subgroupG/H
centerC23C2×C22⋊D151
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting, prime radicalC2×#121×C151C2
socleC23×C151C2×D4
cosocleC22×C4×C151C23
hypercenterC2×#121D151
hypocenterC151#1895
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#14558988C2semidirect
2. C2×#18012660C2semidirect
3. #23752072C2semidirect
4. #23751974C2semidirect
17. #121×C151C4semidirect
24. C2×C151⋊C8D4semidirect
104. C151#1895semidirect
118. #121Dic151semidirect

Maximal subgroups

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

subgroupindex
C22×#145589882
C2×#180126602
#237520722
#237519742
C2×#121×C1512
#1895151