Finite Group Databasebeta

← #34080291

Subgroups — #34080291

Order 19328.

332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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#23752769C211yesmaximal, characteristic, complemented
2#23752746C211yesmaximal, characteristic
3#23752614C212yesmaximal, complemented
4#23752567C212yesmaximal, complemented
5#23752554C212yesmaximal, complemented
6#23752537C212yesmaximal
7#23752508C211yesmaximal, characteristic, complemented
8#23752503C211yesmaximal, characteristic, complemented
9#23752498C211yesmaximal, characteristic, complemented
10#23752493C211yesmaximal, characteristic, complemented
11#431×C151C211yesmaximal, characteristic, complemented
12#18012739C2211yescharacteristic
13#18012739C2211yescharacteristic
14#18012733—21no—
15#18012731C2211yescharacteristic
16#18012731C2212yes—
17#18012727C2211yescharacteristic
18#18012722—21no—
19#18012718—21no—
20#18012718—21no—
21#18012718C2211yescharacteristic
22#18012713C2211yescharacteristic
23C4×Dic302—21no—
24C4×Dic302—21no—
25C4×Dic302C2211yescharacteristic
26C4×D604C2211yescharacteristic
27C4×C22⋊D151—21no—
28#18012698C2212yes—
29#18012696—21no—
30#18012673C2212yes—
31#18012673C2212yes—
32#18012671C2212yes—
33#18012671C2212yes—
34#18012664C2212yes—
35#18012664C2212yes—
36#18012661C2212yes—
37#18012661C2212yes—
38C2×C42×C151C2211yescharacteristic
39C4⋊C8×C151C2211yescharacteristic
40C4⋊C8×C151C2211yescharacteristic
41C22⋊C8×C151C2212yes—
42C4×C8×C151C2212yes—
43C2×Dic302—21no—
44C2×Dic302—21no—
45C2×Dic302C2311yescharacteristic
46C2×D604C2311yescharacteristic
47C2×C22⋊D151—21no—
48C2×C4×D151—21no—
49C4⋊Dic151—21no—
50C4⋊Dic151—21no—
51C4⋊Dic151C2311yescharacteristic
52C4⋊Dic151C2311yescharacteristic
53C4⋊Dic151C2312yes—
54C4⋊Dic151C2312yes—
55Dic151⋊C4—21no—
56Dic151⋊C4—21no—
57Dic151⋊C4—21no—
58Dic151⋊C4—22no—
59Dic151⋊C4—22no—
60Dic151⋊C4—21no—
61C22⋊Dic151—22no—
62C22⋊Dic151—21no—
63(C2×D151)⋊C4—21no—
64(C2×D151)⋊C4—21no—
65(C2×D151)⋊C4—21no—
66(C2×D151)⋊C4—21no—
67C4×Dic151—21no—
68C4×Dic151—22no—
69C22×C4×C151D411yescharacteristic
70C22×C4×C151D411yescharacteristic
71C22×C4×C151C2311yescharacteristic
72C2×C8×C151C2312yes—
73C2×C8×C151C2312yes—
74C42×C151D411yescharacteristic
75C42×C151D411yescharacteristic
76C42×C151C2311yescharacteristic
77C42×C151C2311yescharacteristic
78C22×D151—21no—
79Dic302—21no—
80Dic302—21no—
81Dic302—42no—
82Dic302—42no—
83D604—21no—
84D604—21no—
85C22⋊D151—42no—
86C2×Dic151—21no—
87C2×Dic151—21no—
88C2×Dic151—22no—
89C2×Dic151—22no—
90C2×Dic151—21no—
91C4×D151—42no—
92C23×C151C2×D411yescharacteristic
93C2×C4×C151—22no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—41no—
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2×D411yescharacteristic
99C2×C4×C151C2×D411yescharacteristic
100C2×C4×C151C2×D411yescharacteristic
101C2×C4×C151C2×D411yescharacteristic
102C2×C4×C151C2411yescharacteristic
103C8×C151—22no—
104C8×C151—22no—
105C22×C151—21no—
106C22×C151—21no—
107C22×C151—21no—
108C22×C151C22×D411yescharacteristic
109C2×D151—41no—
110C2×D151—41no—
111C2×D151—41no—
112C4×C151—21no—
113C4×C151—21no—
114C4×C151—21no—
115C4×C151—21no—
116C4×C151#13512yes—
117C4×C1512−1+411yescharacteristic
118C4×C1512−1+411yescharacteristic
119Dic151—41no—
120Dic151—41no—
121Dic151—42no—
122Dic151—41no—
123Dic151—42no—
124C2×C151—41no—
125C2×C151#53611yescharacteristic
126C2×C151C2×#13511yescharacteristic
127C2×C151#57511yescharacteristic
128D151—81no—
129C151#323311yescharacteristic, complemented, Sylow
130#3233—1511nomaximal, Sylow
131#533—1511no—
132#529—1511no—
133#499—1512no—
134#488—1512no—
135#485—1512no—
136#482—1512no—
137#477—1511no—
138#476—1511no—
139#475—1511no—
140#474—1511no—
141#431D15111yescharacteristic, complemented
142C4⋊Q8—1511no—
143C4⋊Q8—1511no—
144#126—3021no—
145#125—1511no—
146#125—1512no—
147#124—1511no—
148#123—3021no—
149C22⋊Q8—3021no—
150C22⋊Q8—3021no—
151C22⋊Q8—1511no—
152#121—1511no—
153C4×Q8—3021no—
154C4×Q8—3021no—
155C4×Q8—1511no—
156C4×D4—3021no—
157C4×D4—1511no—
158#117—3021no—
159#117—1512no—
160C2×C42C2×D15111yescharacteristic
161#107—1512no—
162#107—1512no—
163#106—1512no—
164#106—1512no—
165C4⋊C8C2×D15111yescharacteristic
166C4⋊C8C2×D15111yescharacteristic
167#103—1512no—
168#103—1512no—
169#102—1512no—
170#102—1512no—
171C22⋊C8C2×D15112yes—
172C4×C8C2×D15112yes—
173C2×Q8—3021no—
174C2×Q8—3021no—
175C2×Q8—1511no—
176C2×D4—3021no—
177C2×D4—1511no—
178C22×C4—3021no—
179C22×C4D60411yescharacteristic
180C22×C4D60411yescharacteristic
181C22×C4C22×D15111yescharacteristic
182C2×C8C22×D15112yes—
183C2×C8C22×D15112yes—
184C4⋊C4—3021no—
185C4⋊C4—3021no—
186C4⋊C4—3021no—
187C4⋊C4—3022no—
188C4⋊C4—3022no—
189C4⋊C4—3021no—
190C4⋊C4—3021no—
191C4⋊C4—3021no—
192C4⋊C4—1512no—
193C4⋊C4—1512no—
194C4⋊C4—1511no—
195C4⋊C4—1511no—
196C22⋊C4—3022no—
197C22⋊C4—3021no—
198C22⋊C4—3021no—
199C22⋊C4—3021no—
200C22⋊C4—3021no—
201C22⋊C4—3021no—
202C42—3021no—
203C42—3022no—
204C42D60411yescharacteristic
205C42D60411yescharacteristic
206C42C22×D15111yescharacteristic
207C42C22×D15111yescharacteristic
208C23—3021no—
209C23C2×D60411yescharacteristic
210Q8—3021no—
211Q8—3021no—
212Q8—6042no—
213Q8—6042no—
214D4—3021no—
215D4—3021no—
216D4—6042no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—3021no—
222C2×C4—3021no—
223C2×C4—3022no—
224C2×C4—3022no—
225C2×C4—3021no—
226C2×C4—6042no—
227C2×C4C2×D60411yescharacteristic
228C2×C4C2×D60411yescharacteristic
229C2×C4C2×D60411yescharacteristic
230C2×C4C2×D60411yescharacteristic
231C2×C4C2×D60411yescharacteristic
232C2×C4C23×D15111yescharacteristic
233C8—22no—
234C8—22no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—6041no—
239C22—6041no—
240C22—6041no—
241C22C22×D60411yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—6041no—
247C4—6042no—
248C4—6041no—
249C4—6042no—
250C4—6041no—
251C4#1801276112yes—
252C4#1801278611yescharacteristic
253C4#1801278611yescharacteristic
254C2—41no—
255C2—12081no—
256C2#2375278811yescharacteristic
257C2C2×#1801276111yescharacteristic
258C2#2375301211yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#431×C151C2
socleC22×C151C22×D4
prime radical#18012713C22
hypercenter#431D151
hypocenterC151#3233
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #23752769C2semidirect
3. #23752614C2semidirect
4. #23752567C2semidirect
5. #23752554C2semidirect
7. #23752508C2semidirect
8. #23752503C2semidirect
9. #23752498C2semidirect
10. #23752493C2semidirect
11. #431×C151C2semidirect
129. C151#3233semidirect
141. #431D151semidirect

Maximal subgroups

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

subgroupindex
#237527692
#237527462
#237526142
#237525672
#237525542
#237525372
#237525082
#237525032
#237524982
#237524932
#431×C1512
#3233151