Finite Group Databasebeta

← #34077229

Subgroups — #34077229

Order 19328.

508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752151C211yesmaximal, characteristic, complemented
2#23752140C212yesmaximal, complemented
3#23752129C211yesmaximal, characteristic, complemented
4#23752128C212yesmaximal, complemented
5#23752127C212yesmaximal, complemented
6#23752121C212yesmaximal, complemented
7#23752120C212yesmaximal, complemented
8#23752103C212yesmaximal, complemented
9#390×C151C211yesmaximal, characteristic, complemented
10C22×D604C2211yescharacteristic
11C22×C22⋊D151C2212yes—
12C22×C22⋊D151C2212yes—
13C2×C4⋊Dic151C2211yescharacteristic
14C2×Dic151⋊C4C2212yes—
15C2×C22⋊Dic151C2212yes—
16C2×C22⋊Dic151C2212yes—
17C2×(C2×D151)⋊C4C2212yes—
18C2×(C2×D151)⋊C4C2212yes—
19C2×(C2×D151)⋊C4C2212yes—
20C2×(C2×D151)⋊C4C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2211yescharacteristic
25C151⋊#95C2211yescharacteristic
26C22×D4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28C2×C22⋊C4×C151C2212yes—
29C2×C22⋊C4×C151C2212yes—
30C2×C42×C151C2211yescharacteristic
31C23×D151C2312yes—
32C2×D604—42no—
33C2×D604—41no—
34C2×C22⋊D151—42no—
35C2×C22⋊D151—42no—
36C2×C22⋊D151—42no—
37C2×C22⋊D151—42no—
38C2×C22⋊D151—42no—
39C2×C22⋊D151—42no—
40C22×Dic151C2312yes—
41C22×Dic151C2312yes—
42C22×Dic151C2312yes—
43C4⋊Dic151—41no—
44Dic151⋊C4—42no—
45C22⋊Dic151—42no—
46C22⋊Dic151—42no—
47(C2×D151)⋊C4—24no—
48(C2×D151)⋊C4—42no—
49(C2×D151)⋊C4—42no—
50(C2×D151)⋊C4—42no—
51C24×C151C2312yes—
52C2×D4×C151—22no—
53C2×D4×C151—41no—
54C2×D4×C151—41no—
55C22×C4×C151C2312yes—
56C22×C4×C151C2311yescharacteristic
57C22×C4×C151C2311yescharacteristic
58C22×C4×C151C2311yescharacteristic
59C4⋊C4×C151—41no—
60C22⋊C4×C151—42no—
61C22⋊C4×C151—42no—
62C42×C151—41no—
63C22×D151—22no—
64C22×D151—22no—
65C22×D151—22no—
66C22×D151—22no—
67C22×D151—22no—
68C22×D151—22no—
69C22×D151—22no—
70D604—44no—
71C22⋊D151—48no—
72C22⋊D151—48no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C2×Dic151—22no—
77C2×Dic151—22no—
78C2×Dic151—22no—
79C2×Dic151—22no—
80C2×Dic151—22no—
81C2×Dic151—22no—
82C23×C151—22no—
83C23×C151—22no—
84C23×C151—22no—
85C23×C151—22no—
86C23×C151—22no—
87C23×C151—22no—
88C23×C151—22no—
89C23×C151C2411yescharacteristic
90D4×C151—44no—
91C2×C4×C151—21no—
92C2×C4×C151—21no—
93C2×C4×C151—22no—
94C2×C4×C151—22no—
95C2×C4×C151—22no—
96C2×C4×C151—21no—
97C2×C4×C151—22no—
98C2×C4×C151—21no—
99C2×C4×C151—22no—
100C2×C4×C151#4112yes—
101C22×C151—42no—
102C22×C151—42no—
103C22×C151—42no—
104C22×C151—42no—
105C22×C151—42no—
106C22×C151—42no—
107C22×C151—42no—
108C22×C151C2×#4111yescharacteristic
109C22×C151H(5,𝔽2)11yescharacteristic
110C22×C151H(5,𝔽2)11yescharacteristic
111C22×C151H(5,𝔽2)12yes—
112C22×C151H(5,𝔽2)12yes—
113C2×D151—42no—
114C2×D151—42no—
115C2×D151—42no—
116C2×D151—42no—
117C2×D151—42no—
118C2×D151—42no—
119C2×D151—42no—
120C4×C151—22no—
121C4×C151—41no—
122C4×C151—42no—
123C4×C151—41no—
124Dic151—42no—
125Dic151—42no—
126Dic151—42no—
127C2×C151—82no—
128C2×C151#53811yescharacteristic
129C2×C151#54012yes—
130C2×C151#56011yescharacteristic
131C2×C151#56012yes—
132C2×C151H(3,𝔽4)11yescharacteristic
133D151—82no—
134C151#282811yescharacteristic, complemented, Sylow
135#2828—1511nomaximal, Sylow
136#400—1511no—
137#397—1512no—
138#394—1511no—
139#394—1512no—
140#394—1512no—
141#392—1512no—
142#392—1512no—
143#390D15111yescharacteristic, complemented
144#388—1512no—
145C22×D4—1512no—
146C22×D4—1512no—
147C22×D4—1511no—
148C22×D4C2×D15111yescharacteristic
149C2×C4⋊C4—1512no—
150C2×C4⋊C4—1511no—
151C2×C4⋊C4C2×D15111yescharacteristic
152C2×C22⋊C4—1512no—
153C2×C22⋊C4—1512no—
154C2×C22⋊C4—1512no—
155C2×C22⋊C4—1512no—
156C2×C22⋊C4—1512no—
157C2×C22⋊C4—1512no—
158C2×C22⋊C4C2×D15112yes—
159C2×C22⋊C4C2×D15112yes—
160C2×C42C2×D15111yescharacteristic
161#95—1512no—
162#95—1512no—
163#95—1512no—
164#95—1511no—
165#95—1511no—
166C24—1512no—
167C24C22×D15112yes—
168C2×D4—22no—
169C2×D4—41no—
170C2×D4—41no—
171C2×D4—6042no—
172C2×D4—6041no—
173C2×D4—6042no—
174C2×D4—6042no—
175C2×D4—6042no—
176C2×D4—6042no—
177C2×D4—6042no—
178C2×D4—6042no—
179C22×C4—1512no—
180C22×C4—1512no—
181C22×C4—1512no—
182C22×C4C22×D15111yescharacteristic
183C22×C4C22×D15112yes—
184C22×C4C22×D15111yescharacteristic
185C22×C4C22×D15111yescharacteristic
186C4⋊C4—41no—
187C4⋊C4—6042no—
188C4⋊C4—6041no—
189C22⋊C4—42no—
190C22⋊C4—42no—
191C22⋊C4—3024no—
192C22⋊C4—6042no—
193C22⋊C4—6042no—
194C22⋊C4—6042no—
195C22⋊C4—6042no—
196C22⋊C4—6042no—
197C42—41no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—3022no—
206C23—3022no—
207C23—3022no—
208C23—3022no—
209C23—3022no—
210C23—3022no—
211C23—3022no—
212C23C23×D15111yescharacteristic
213D4—44no—
214D4—6044no—
215D4—6048no—
216D4—6048no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—3022no—
227C2×C4—3022no—
228C2×C4—3022no—
229C2×C4—3022no—
230C2×C4—3022no—
231C2×C4—3022no—
232C2×C4—3022no—
233C2×C4—3022no—
234C2×C4—3022no—
235C2×C4#1455900412yes—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—6042no—
244C22—6042no—
245C22—6042no—
246C22—6042no—
247C22—6042no—
248C22—6042no—
249C22—6042no—
250C22C2×#1455900411yescharacteristic
251C22#1801278411yescharacteristic
252C22#1801278411yescharacteristic
253C22#1801278412yes—
254C22#1801278512yes—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—42no—
259C4—6042no—
260C4—6042no—
261C4—6042no—
262C2—82no—
263C2—12082no—
264C2#2375280011yescharacteristic
265C2#2375281312yes—
266C2#2375294911yescharacteristic
267C2#2375295012yes—
268C2#2375295411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#390×C151C2
hypercenter#390D151
hypocenterC151#2828
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #23752151C2semidirect
2. #23752140C2semidirect
3. #23752129C2semidirect
4. #23752128C2semidirect
5. #23752127C2semidirect
6. #23752121C2semidirect
7. #23752120C2semidirect
8. #23752103C2semidirect
9. #390×C151C2semidirect
134. C151#2828semidirect
143. #390D151semidirect

Maximal subgroups

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

subgroupindex
#237521512
#237521402
#237521292
#237521282
#237521272
#237521212
#237521202
#237521032
#390×C1512
#2828151