Finite Group Databasebeta

← #34069096

Subgroups — #34069096

Order 19328.

380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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×D4×Dic151C211yesmaximal, characteristic
2C2×#18012654C211yesmaximal, characteristic
3#23752070C212yesmaximal, complemented
4#23751978C212yesmaximal, complemented
5C2×#99×C151C211yesmaximal, characteristic
6C23×Dic151C411yescharacteristic, complemented
7C23×Dic151C2211yescharacteristic
8D4×Dic151—22no—
9D4×Dic151—22no—
10C2×C4⋊Dic151C411yescharacteristic, complemented
11C2×Dic151⋊C4—22no—
12C2×C22⋊Dic151C411yescharacteristic, complemented
13C2×C22⋊Dic151C2212yes—
14C2×C22⋊Dic151C2211yescharacteristic
15C2×C4×Dic151C411yescharacteristic, complemented
16#18012654—22no—
17C151⋊#95—22no—
18C22×D4×C151C2211yescharacteristic
19C2×C22⋊C4×C151C2212yes—
20#99×C151—22no—
21C22×Dic151—21no—
22C22×Dic151—21no—
23C22×Dic151—22no—
24C22×Dic151—42no—
25C22×Dic151—42no—
26C22×Dic151C2×C411yescharacteristic
27C22×Dic151C2×C411yescharacteristic
28C22×Dic151C2×C411yescharacteristic
29C22×Dic151C2×C411yescharacteristic
30C22×Dic151D412yes—
31C22×Dic151D412yes—
32C4⋊Dic151—22no—
33Dic151⋊C4—44no—
34C22⋊Dic151—22no—
35C22⋊Dic151—22no—
36C22⋊Dic151—22no—
37C22⋊Dic151—22no—
38C4×Dic151—21no—
39C4×Dic151—21no—
40C24×C151C2×C411yescharacteristic
41C24×C151C2311yescharacteristic
42C2×D4×C151—22no—
43C2×D4×C151—22no—
44C2×D4×C151D412yes—
45C2×D4×C151Q812yes—
46C22×C4×C151—22no—
47C22×C4×C151C2×C411yescharacteristic
48C22⋊C4×C151—22no—
49C22⋊C4×C151—22no—
50C2×Dic151—24no—
51C2×Dic151—22no—
52C2×Dic151—21no—
53C2×Dic151—21no—
54C2×Dic151—41no—
55C2×Dic151—42no—
56C2×Dic151—42no—
57C2×Dic151—42no—
58C2×Dic151—41no—
59C2×Dic151—41no—
60C2×Dic151—42no—
61C2×Dic151—42no—
62C2×Dic151—42no—
63C2×Dic151C22⋊C411yescharacteristic
64C2×Dic151C22⋊C412yes—
65C2×Dic151C22⋊C411yescharacteristic
66C23×C151—21no—
67C23×C151—21no—
68C23×C151—41no—
69C23×C151—41no—
70C23×C151—41no—
71C23×C151—41no—
72C23×C151C4⋊C412yescomplemented
73C23×C151C22×C411yescharacteristic
74C23×C151C2×D412yes—
75C23×C151C2×D411yescharacteristic
76C23×C151C2×Q811yescharacteristic
77C23×C151#4112yes—
78D4×C151—24no—
79D4×C151—24no—
80C2×C4×C151—21no—
81C2×C4×C151—21no—
82C2×C4×C151—42no—
83C2×C4×C151—42no—
84C2×C4×C151—42no—
85C2×C4×C151C4⋊C412yescomplemented
86C22×C151—22no—
87C22×C151—21no—
88C22×C151—22no—
89C22×C151—21no—
90C22×C151—22no—
91C22×C151—41no—
92C22×C151—41no—
93C22×C151—42no—
94C22×C151—42no—
95C22×C151—42no—
96C22×C151—41no—
97C22×C151—41no—
98C22×C151C2×C22⋊C411yescharacteristic
99C22×C151C2×C4⋊C411yescharacteristic
100C22×C151#11711yescharacteristic
101C22×C151#12112yes—
102C22×C151C22⋊Q812yes—
103C4×C151—22no—
104C4×C151—82no—
105Dic151—21no—
106Dic151—22no—
107Dic151—41no—
108Dic151—41no—
109Dic151—82no—
110Dic151#9912yescomplemented
111C2×C151—22no—
112C2×C151—21no—
113C2×C151—21no—
114C2×C151—22no—
115C2×C151—42no—
116C2×C151#38011yescharacteristic
117C2×C151C2×#9911yescharacteristic
118C2×C151#41011yescharacteristic
119C151#179911yescharacteristic, complemented, Sylow
120#1799—1511nomaximal, Sylow
121C2×C4×D4—1511no—
122C2×#99—1511no—
123C2×#99D15111yescharacteristic
124#380—1512no—
125#342—1512no—
126C22×D4C2×D15111yescharacteristic
127C23×C4—1511no—
128C23×C4—1511no—
129C4×D4—3022no—
130C4×D4—3022no—
131C2×C4⋊C4—3022no—
132C2×C4⋊C4—1511no—
133C2×C22⋊C4—1512no—
134C2×C22⋊C4—1511no—
135C2×C22⋊C4—1511no—
136C2×C22⋊C4C2×D15112yes—
137C2×C42—1511no—
138#99—22no—
139#99—3022no—
140#95—3022no—
141C24C4×D15111yescharacteristic
142C24C22×D15111yescharacteristic
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C22⋊D15112yes—
146C2×D4Dic30212yes—
147C22×C4—22no—
148C22×C4—3021no—
149C22×C4—3021no—
150C22×C4—3022no—
151C22×C4—6042no—
152C22×C4—6042no—
153C22×C4—1511no—
154C22×C4—1512no—
155C22×C4—1511no—
156C22×C4—1511no—
157C22×C4—1511no—
158C22×C4—1512no—
159C22×C4C4×D15111yescharacteristic
160C4⋊C4—3022no—
161C4⋊C4—6044no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—3022no—
165C22⋊C4—3022no—
166C22⋊C4—3022no—
167C22⋊C4—3022no—
168C42—3021no—
169C42—3021no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23Dic151⋊C412yescomplemented
177C23C2×C4×D15111yescharacteristic
178C23D4×D15112yes—
179C23C2×C22⋊D15111yescharacteristic
180C23C2×Dic30211yescharacteristic
181C23#1455900312yes—
182D4—24no—
183D4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—3024no—
190C2×C4—3022no—
191C2×C4—3021no—
192C2×C4—3021no—
193C2×C4—6042no—
194C2×C4—6041no—
195C2×C4—6042no—
196C2×C4—6042no—
197C2×C4—6041no—
198C2×C4—6041no—
199C2×C4—6042no—
200C2×C4—6042no—
201C2×C4—6042no—
202C2×C4—1511no—
203C2×C4—1512no—
204C2×C4—1511no—
205C2×C4Dic151⋊C412yescomplemented
206C22—22no—
207C22—21no—
208C22—22no—
209C22—21no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22C22⋊C4×D15111yescharacteristic
219C22C2×Dic151⋊C411yescharacteristic
220C22#1801269511yescharacteristic
221C22#1801271112yes—
222C22#1801271612yes—
223C4—22no—
224C4—82no—
225C4—3021no—
226C4—3022no—
227C4—6041no—
228C4—6041no—
229C4—1512no—
230C4—12082no—
231C2—22no—
232C2—21no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2#2375207011yescharacteristic
237C2#99×D15111yescharacteristic
238C2#2375218411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D151
commutatorC23×C151C22×C4
FrattiniC24C22×D151
FittingC2×#99×C151C2
socleC22×C151C2×C22⋊C4
prime radicalC22×D4×C151C22
cosocleC24×C151C23
hypercenterC2×#99D151
hypocenterC151#1799
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #23752070C2semidirect
4. #23751978C2semidirect
6. C23×Dic151C4semidirect
10. C2×C4⋊Dic151C4semidirect
12. C2×C22⋊Dic151C4semidirect
15. C2×C4×Dic151C4semidirect
72. C23×C151C4⋊C4semidirect
85. C2×C4×C151C4⋊C4semidirect
110. Dic151#99semidirect
119. C151#1799semidirect
176. C23Dic151⋊C4semidirect
205. C2×C4Dic151⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1512
C2×#180126542
#237520702
#237519782
C2×#99×C1512
#1799151