Finite Group Databasebeta

← #34077234

Subgroups — #34077234

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#23752141C212yesmaximal, complemented
2#23752130C212yesmaximal, complemented
3#23752129C211yesmaximal, characteristic, complemented
4#23752129C212yesmaximal, complemented
5#23752122C212yesmaximal, complemented
6#23752122C212yesmaximal, complemented
7#23752113C211yesmaximal, characteristic, complemented
8#23752101C212yesmaximal, complemented
9#400×C151C211yesmaximal, characteristic, complemented
10C22×D604C2211yescharacteristic
11C22×D604C2211yescharacteristic
12C22×D604C2212yes—
13C22×D604C2212yes—
14C2×Dic151⋊C4C2212yes—
15C2×(C2×D151)⋊C4C2212yes—
16C2×(C2×D151)⋊C4C2212yes—
17C2×(C2×D151)⋊C4C2212yes—
18C2×(C2×D151)⋊C4C2212yes—
19C2×(C2×D151)⋊C4C2212yes—
20C2×(C2×D151)⋊C4C2212yes—
21C2×(C2×D151)⋊C4C2212yes—
22C2×(C2×D151)⋊C4C2212yes—
23C2×C4×Dic151C2211yescharacteristic
24C151⋊#95C2212yes—
25C151⋊#95C2211yescharacteristic
26C2×C4⋊C4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28#95×C151C2212yes—
29#95×C151C2212yes—
30#95×C151C2211yescharacteristic
31C23×D151C2312yes—
32C23×D151C2312yes—
33C2×D604—22no—
34C2×D604—41no—
35C2×D604—41no—
36C2×D604—42no—
37C2×D604—42no—
38C2×D604—42no—
39C2×D604—42no—
40C2×D604—42no—
41C2×D604—42no—
42C2×D604—41no—
43C2×D604—42no—
44C22×Dic151C2312yes—
45C22×Dic151C2312yes—
46Dic151⋊C4—42no—
47(C2×D151)⋊C4—24no—
48(C2×D151)⋊C4—42no—
49(C2×D151)⋊C4—42no—
50(C2×D151)⋊C4—42no—
51(C2×D151)⋊C4—42no—
52(C2×D151)⋊C4—42no—
53(C2×D151)⋊C4—42no—
54(C2×D151)⋊C4—42no—
55C4×Dic151—41no—
56C22×C4×C151C2311yescharacteristic
57C22×C4×C151C2312yes—
58C22×C4×C151C2312yes—
59C22×C4×C151C2311yescharacteristic
60C22×C4×C151C2311yescharacteristic
61C4⋊C4×C151—41no—
62C4⋊C4×C151—41no—
63C22×D151—22no—
64C22×D151—22no—
65C22×D151—22no—
66C22×D151—22no—
67C22×D151—22no—
68C22×D151—22no—
69C22×D151—22no—
70C22×D151—22no—
71C22×D151—22no—
72C22×D151—22no—
73C22×D151—22no—
74C22×D151—22no—
75C22×D151—22no—
76C22×D151—22no—
77D604—44no—
78D604—44no—
79D604—48no—
80D604—48no—
81C2×Dic151—22no—
82C2×Dic151—22no—
83C2×Dic151—22no—
84C2×Dic151—22no—
85C2×Dic151—22no—
86C2×Dic151—22no—
87C23×C151C2411yescharacteristic
88C2×C4×C151—21no—
89C2×C4×C151—21no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151—22no—
93C2×C4×C151—22no—
94C2×C4×C151—22no—
95C2×C4×C151—22no—
96C2×C4×C151—22no—
97C2×C4×C151—21no—
98C2×C4×C151—22no—
99C2×C4×C151—21no—
100C2×C4×C151#4112yes—
101C22×C151C2×#4111yescharacteristic
102C22×C151H(5,𝔽2)11yescharacteristic
103C22×C151H(5,𝔽2)11yescharacteristic
104C22×C151H(5,𝔽2)12yes—
105C22×C151H(5,𝔽2)12yes—
106C2×D151—42no—
107C2×D151—42no—
108C2×D151—42no—
109C2×D151—42no—
110C2×D151—42no—
111C2×D151—42no—
112C2×D151—42no—
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—41no—
123C4×C151—42no—
124C4×C151—42no—
125Dic151—42no—
126Dic151—42no—
127C2×C151#53811yescharacteristic
128C2×C151#54012yes—
129C2×C151#56011yescharacteristic
130C2×C151#56012yes—
131C2×C151H(3,𝔽4)11yescharacteristic
132D151—82no—
133D151—82no—
134C151#282811yescharacteristic, complemented, Sylow
135#2828—1511nomaximal, Sylow
136#400D15111yescharacteristic, complemented
137#397—1512no—
138#394—1512no—
139#394—1511no—
140#394—1512no—
141#392—1512no—
142#392—1512no—
143#390—1511no—
144#388—1512no—
145C22×D4—1511no—
146C22×D4—1512no—
147C22×D4—1511no—
148C22×D4—1512no—
149C2×C4⋊C4—1512no—
150C2×C4⋊C4C2×D15111yescharacteristic
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⋊C4—1512no—
159C2×C22⋊C4—1512no—
160C2×C42—1511no—
161#95—1512no—
162#95—1511no—
163#95C2×D15112yes—
164#95C2×D15112yes—
165#95C2×D15111yescharacteristic
166C24—1512no—
167C24—1512no—
168C2×D4—3022no—
169C2×D4—6041no—
170C2×D4—6041no—
171C2×D4—6041no—
172C2×D4—6042no—
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×C4C22×D15112yes—
182C22×C4C22×D15111yescharacteristic
183C22×C4C22×D15112yes—
184C22×C4C22×D15111yescharacteristic
185C22×C4C22×D15111yescharacteristic
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—6042no—
189C22⋊C4—3024no—
190C22⋊C4—6042no—
191C22⋊C4—6042no—
192C22⋊C4—6042no—
193C22⋊C4—6042no—
194C22⋊C4—6042no—
195C22⋊C4—6042no—
196C22⋊C4—6042no—
197C42—6041no—
198C23—3022no—
199C23—3022no—
200C23—3022no—
201C23—3022no—
202C23—3022no—
203C23—3022no—
204C23—3022no—
205C23—3022no—
206C23—3022no—
207C23—3022no—
208C23—3022no—
209C23—3022no—
210C23—3022no—
211C23—3022no—
212C23C23×D15111yescharacteristic
213D4—6044no—
214D4—6044no—
215D4—6048no—
216D4—6048no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—3022no—
230C2×C4—3022no—
231C2×C4—3022no—
232C2×C4—3022no—
233C2×C4—3022no—
234C2×C4—3022no—
235C2×C4#1455900512yes—
236C22—6042no—
237C22—6042no—
238C22—6042no—
239C22—6042no—
240C22—6042no—
241C22—6042no—
242C22—6042no—
243C22—6042no—
244C22—6042no—
245C22—6042no—
246C22—6042no—
247C22—6042no—
248C22—6042no—
249C22—6042no—
250C22C2×#1455900511yescharacteristic
251C22#1801278411yescharacteristic
252C22#1801278511yescharacteristic
253C22#1801278512yes—
254C22#1801278512yes—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—42no—
259C4—42no—
260C4—6042no—
261C4—6042no—
262C2—12082no—
263C2—12082no—
264C2#2375280211yescharacteristic
265C2#2375281812yes—
266C2#2375295211yescharacteristic
267C2#2375295312yes—
268C2#2375295411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#400×C151C2
hypercenter#400D151
hypocenterC151#2828
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #23752141C2semidirect
2. #23752130C2semidirect
3. #23752129C2semidirect
4. #23752129C2semidirect
5. #23752122C2semidirect
6. #23752122C2semidirect
7. #23752113C2semidirect
8. #23752101C2semidirect
9. #400×C151C2semidirect
134. C151#2828semidirect
136. #400D151semidirect

Maximal subgroups

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

subgroupindex
#237521412
#237521302
#237521292
#237521222
#237521132
#237521012
#400×C1512
#2828151