Finite Group Databasebeta

← #34069548

Subgroups — #34069548

Order 19328.

412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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×#18012713C211yesmaximal, characteristic
2C2×#18012661C212yesmaximal, complemented
3#23752072C211yesmaximal, characteristic, complemented
4#23751975C212yesmaximal, complemented
5C22×M16×C151C211yesmaximal, characteristic, complemented
6C22×D604C2211yescharacteristic
7C22×C22⋊D151—21no—
8#18012713—22no—
9#18012713C414yescomplemented
10C2×C4⋊Dic151C2212yes—
11C2×C4⋊Dic151C2211yescharacteristic
12C2×C22⋊Dic151—21no—
13C2×(C2×D151)⋊C4—21no—
14#18012661—24no—
15C151⋊#95—21no—
16C23×C4×C151C2211yescharacteristic
17C2×M16×C151—22no—
18C2×M16×C151—24no—
19C22×C8×C151C2212yes—
20C23×D151—21no—
21C2×D604—22no—
22C2×D604—21no—
23C2×D604—22no—
24C2×D604C2×C412yes—
25C2×C22⋊D151—24no—
26C2×C22⋊D151—44no—
27C22×Dic151—21no—
28C22×Dic151—22no—
29C4⋊Dic151—21no—
30C4⋊Dic151—22no—
31C4⋊Dic151—22no—
32C4⋊Dic151C2×C412yes—
33C22⋊Dic151—42no—
34(C2×D151)⋊C4—24no—
35C24×C151D411yescharacteristic
36C22×C4×C151—22no—
37C22×C4×C151—22no—
38C22×C4×C151C2×C412yes—
39C22×C4×C151D412yes—
40C22×C4×C151D411yescharacteristic
41C22×C4×C151C2311yescharacteristic
42M16×C151—28no—
43C2×C8×C151—22no—
44C2×C8×C151—22no—
45C2×C8×C151D414yescomplemented
46C22×D151—22no—
47C22×D151—42no—
48C22×D151—42no—
49C22×D151—41no—
50C22×D151—41no—
51D604—24no—
52D604—41no—
53D604—41no—
54C22⋊D151—48no—
55C2×Dic151—22no—
56C2×Dic151—42no—
57C2×Dic151—42no—
58C2×Dic151—42no—
59C2×Dic151—42no—
60C23×C151—22no—
61C23×C151—21no—
62C23×C151—22no—
63C23×C151—21no—
64C23×C151C22⋊C412yes—
65C23×C151C2×D411yescharacteristic
66C2×C4×C151—22no—
67C2×C4×C151—24no—
68C2×C4×C151—22no—
69C2×C4×C151—22no—
70C2×C4×C151C22⋊C412yes—
71C2×C4×C151C22×C411yescharacteristic
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D411yescharacteristic
74C2×C4×C151#4112yes—
75C8×C151—24no—
76C22×C151—22no—
77C22×C151—22no—
78C22×C151—22no—
79C22×C151—42no—
80C22×C151—42no—
81C22×C151C2×C22⋊C411yescharacteristic
82C22×C151#12112yes—
83C22×C151AGL(1,ℤ/8)11yescharacteristic
84C22×C151AGL(1,ℤ/8)12yes—
85C22×C151#13711yescharacteristic
86C2×D151—42no—
87C2×D151—42no—
88C2×D151—42no—
89C2×D151—82no—
90C2×D151—82no—
91C4×C151—22no—
92C4×C151C4×D412yes—
93C4×C151#12011yescharacteristic
94C4×C151#12311yescharacteristic
95Dic151—42no—
96Dic151—82no—
97C2×C151—42no—
98C2×C151#38611yescharacteristic
99C2×C151#41711yescharacteristic
100C2×C151#41811yescharacteristic
101C2×C151#46812yes—
102C2×C151#46912yes—
103D151—82no—
104C151#189511yescharacteristic, complemented, Sylow
105#1895—1511nomaximal, Sylow
106C22×M16D15111yescharacteristic, complemented
107C2×#121—1511no—
108C2×#102—1512no—
109#380—1511no—
110#340—1512no—
111C22×D4—3021no—
112C22×D4—1511no—
113C23×C4C2×D15111yescharacteristic
114C2×M16—22no—
115C2×M16—24no—
116C22×C8C2×D15112yes—
117#121—3022no—
118#121—1514no—
119C2×C4⋊C4—1512no—
120C2×C4⋊C4—1511no—
121C2×C22⋊C4—3021no—
122C2×C22⋊C4—3021no—
123#102—3024no—
124#95—3021no—
125C24—3021no—
126C24D60411yescharacteristic
127C2×D4—3024no—
128C2×D4—3022no—
129C2×D4—3021no—
130C2×D4—3022no—
131C2×D4—6044no—
132C2×D4—1512no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—3021no—
136C22×C4—3022no—
137C22×C4C4×D15112yes—
138C22×C4C22⋊D15112yes—
139C22×C4D60411yescharacteristic
140C22×C4C22×D15111yescharacteristic
141M16—28no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8C22⋊D15114yescomplemented
145C4⋊C4—3021no—
146C4⋊C4—3022no—
147C4⋊C4—3022no—
148C4⋊C4—1512no—
149C22⋊C4—3024no—
150C22⋊C4—6042no—
151C23—22no—
152C23—21no—
153C23—22no—
154C23—21no—
155C23—3022no—
156C23—6042no—
157C23—6042no—
158C23—6041no—
159C23—6041no—
160C23(C2×D151)⋊C412yes—
161C23C2×D60411yescharacteristic
162D4—3024no—
163D4—6048no—
164D4—6041no—
165D4—6041no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—3022no—
171C2×C4—6042no—
172C2×C4—6042no—
173C2×C4—6042no—
174C2×C4—6042no—
175C2×C4(C2×D151)⋊C412yes—
176C2×C4C2×C4×D15111yescharacteristic
177C2×C4C2×C22⋊D15112yes—
178C2×C4C2×C22⋊D15111yescharacteristic
179C2×C4#1455900412yes—
180C8—24no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—6042no—
187C22—6042no—
188C22—6042no—
189C22—12082no—
190C22—12082no—
191C22C2×(C2×D151)⋊C411yescharacteristic
192C22#1801271312yes—
193C22#1801276712yes—
194C22#1801276711yescharacteristic
195C22#1801277211yescharacteristic
196C4—22no—
197C4—6042no—
198C4—12082no—
199C4C4×C22⋊D15112yes—
200C4#1801270811yescharacteristic
201C4#1801272211yescharacteristic
202C2—42no—
203C2—12082no—
204C2#2375209111yescharacteristic
205C2#2375221411yescharacteristic
206C2#2375221811yescharacteristic
207C2#2375245812yes—
208C2#2375246512yes—
subgroupG/H
centerC23C2×D604
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
FittingC22×M16×C151C2
socleC23×C151C2×D4
prime radicalC2×#18012713C2
cosocleC22×C4×C151C23
hypercenterC22×M16D151
hypocenterC151#1895
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#18012661C2semidirect
3. #23752072C2semidirect
4. #23751975C2semidirect
5. C22×M16×C151C2semidirect
9. #18012713C4semidirect
45. C2×C8×C151D4semidirect
104. C151#1895semidirect
106. C22×M16D151semidirect
144. C2×C8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127132
C2×#180126612
#237520722
#237519752
C22×M16×C1512
#1895151