Finite Group Databasebeta

← #34080484

Subgroups — #34080484

Order 19328.

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

normal subgroups only

This group has 348 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#23752520C212yesmaximal, complemented
4#23752508C211yesmaximal, characteristic, complemented
5#23752503C211yesmaximal, characteristic, complemented
6#23752470C212yesmaximal, complemented
7#23752458C212yesmaximal
8#23752435C212yesmaximal, complemented
9#23752423C211yesmaximal, characteristic, complemented
10#23752418C211yesmaximal, characteristic, complemented
11#423×C151C211yesmaximal, characteristic, complemented
12C2×Dic604C2212yes—
13C2×#14558993C2212yes—
14#18012739C2211yescharacteristic
15#18012739C2211yescharacteristic
16#18012733—21no—
17#18012731—21no—
18#18012731C2211yescharacteristic
19#18012727C2211yescharacteristic
20#18012722—21no—
21#18012718—21no—
22#18012718C2212yes—
23#18012718C2211yescharacteristic
24#18012713C2211yescharacteristic
25C4×Dic302—21no—
26C4×Dic302C2211yescharacteristic
27C4×Dic302C2212yes—
28C4×D604C2211yescharacteristic
29C4×C22⋊D151—21no—
30#18012698—21no—
31#18012696—21no—
32#18012673C2212yes—
33#18012671C2212yes—
34#18012664C2212yes—
35#18012664C2212yes—
36#18012664C2212yes—
37#18012661C2212yes—
38C2×M16×C151C2212yes—
39C2×C42×C151C2211yescharacteristic
40C4⋊C8×C151C2211yescharacteristic
41C4⋊C8×C151C2211yescharacteristic
42C4⋊C8×C151C2212yes—
43C2×Dic302—21no—
44C2×Dic302C2311yescharacteristic
45C2×Dic302C2312yes—
46C2×D604C2311yescharacteristic
47C2×C22⋊D151—21no—
48C2×C4×D151—21no—
49Dic604—42no—
50#14558993—42no—
51C4⋊Dic151—21no—
52C4⋊Dic151—21no—
53C4⋊Dic151—21no—
54C4⋊Dic151C2311yescharacteristic
55C4⋊Dic151C2312yes—
56C4⋊Dic151C2311yescharacteristic
57Dic151⋊C4—21no—
58Dic151⋊C4—21no—
59Dic151⋊C4—21no—
60Dic151⋊C4—22no—
61Dic151⋊C4—22no—
62Dic151⋊C4—21no—
63C22⋊Dic151—22no—
64C22⋊Dic151—21no—
65(C2×D151)⋊C4—21no—
66(C2×D151)⋊C4—21no—
67(C2×D151)⋊C4—21no—
68(C2×D151)⋊C4—21no—
69C4×Dic151—21no—
70C4×Dic151—22no—
71C22×C4×C151D411yescharacteristic
72C22×C4×C151D411yescharacteristic
73C22×C4×C151C2311yescharacteristic
74M16×C151—42no—
75C2×C8×C151C2312yes—
76C2×C8×C151C2312yes—
77C42×C151D411yescharacteristic
78C42×C151D411yescharacteristic
79C42×C151C2311yescharacteristic
80C42×C151C2311yescharacteristic
81C22×D151—21no—
82Dic302—22no—
83Dic302—21no—
84Dic302—21no—
85Dic302—22no—
86Dic302—42no—
87D604—21no—
88D604—21no—
89C22⋊D151—42no—
90C2×Dic151—21no—
91C2×Dic151—21no—
92C2×Dic151—22no—
93C2×Dic151—22no—
94C2×Dic151—21no—
95C4×D151—42no—
96C23×C151C2×D411yescharacteristic
97C2×C4×C151—22no—
98C2×C4×C151—21no—
99C2×C4×C151—21no—
100C2×C4×C151—41no—
101C2×C4×C151C2×D411yescharacteristic
102C2×C4×C151C2×D411yescharacteristic
103C2×C4×C151C2×D411yescharacteristic
104C2×C4×C151C2×D411yescharacteristic
105C2×C4×C151C2×D411yescharacteristic
106C2×C4×C151C2411yescharacteristic
107C8×C151—22no—
108C8×C151—22no—
109C22×C151—21no—
110C22×C151—21no—
111C22×C151—21no—
112C22×C151C22×D411yescharacteristic
113C2×D151—41no—
114C2×D151—41no—
115C2×D151—41no—
116C4×C151—21no—
117C4×C151—21no—
118C4×C151—21no—
119C4×C151—21no—
120C4×C151#13712yes—
121C4×C151H(5,𝔽2)11yescharacteristic
122C4×C1512−1+411yescharacteristic
123Dic151—41no—
124Dic151—42no—
125Dic151—41no—
126Dic151—41no—
127Dic151—42no—
128C2×C151—41no—
129C2×C151#53711yescharacteristic
130C2×C151C2×#13711yescharacteristic
131C2×C151#57511yescharacteristic
132D151—81no—
133C151#325211yescharacteristic, complemented, Sylow
134#3252—1511nomaximal, Sylow
135#533—1511no—
136#529—1511no—
137#479—1512no—
138#477—1511no—
139#476—1511no—
140#470—1512no—
141#468—1512no—
142#464—1512no—
143#462—1511no—
144#461—1511no—
145#423D15111yescharacteristic, complemented
146C2×Q16—1512no—
147C2×SD16—1512no—
148C2×M16C2×D15112yes—
149C4⋊Q8—1511no—
150C4⋊Q8—1511no—
151#126—3021no—
152#125—3021no—
153#125—1511no—
154#124—1511no—
155#123—3021no—
156C22⋊Q8—3021no—
157C22⋊Q8—1511no—
158C22⋊Q8—1512no—
159#121—1511no—
160C4×Q8—3021no—
161C4×Q8—1511no—
162C4×Q8—1512no—
163C4×D4—3021no—
164C4×D4—1511no—
165#117—3021no—
166#117—3021no—
167C2×C42C2×D15111yescharacteristic
168#107—1512no—
169#106—1512no—
170C4⋊C8C2×D15111yescharacteristic
171C4⋊C8C2×D15111yescharacteristic
172C4⋊C8C2×D15112yes—
173#103—1512no—
174#103—1512no—
175#103—1512no—
176#102—1512no—
177C2×Q8—3021no—
178C2×Q8—1511no—
179C2×Q8—1512no—
180C2×D4—3021no—
181C2×D4—1511no—
182C22×C4—3021no—
183C22×C4D60411yescharacteristic
184C22×C4D60411yescharacteristic
185C22×C4C22×D15111yescharacteristic
186Q16—6042no—
187SD16—6042no—
188M16—42no—
189C2×C8C22×D15112yes—
190C2×C8C22×D15112yes—
191C4⋊C4—3021no—
192C4⋊C4—3021no—
193C4⋊C4—3021no—
194C4⋊C4—3022no—
195C4⋊C4—3022no—
196C4⋊C4—3021no—
197C4⋊C4—3021no—
198C4⋊C4—3021no—
199C4⋊C4—3021no—
200C4⋊C4—1512no—
201C4⋊C4—1511no—
202C4⋊C4—1511no—
203C22⋊C4—3022no—
204C22⋊C4—3021no—
205C22⋊C4—3021no—
206C22⋊C4—3021no—
207C22⋊C4—3021no—
208C22⋊C4—3021no—
209C42—3021no—
210C42—3022no—
211C42D60411yescharacteristic
212C42D60411yescharacteristic
213C42C22×D15111yescharacteristic
214C42C22×D15111yescharacteristic
215C23—3021no—
216C23C2×D60411yescharacteristic
217Q8—3022no—
218Q8—3021no—
219Q8—3021no—
220Q8—3022no—
221Q8—6042no—
222D4—3021no—
223D4—3021no—
224D4—6042no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—3021no—
230C2×C4—3022no—
231C2×C4—3021no—
232C2×C4—3022no—
233C2×C4—3021no—
234C2×C4—6042no—
235C2×C4C2×D60411yescharacteristic
236C2×C4C2×D60411yescharacteristic
237C2×C4C2×D60411yescharacteristic
238C2×C4C2×D60411yescharacteristic
239C2×C4C2×D60411yescharacteristic
240C2×C4C23×D15111yescharacteristic
241C8—22no—
242C8—22no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—6041no—
247C22—6041no—
248C22—6041no—
249C22C22×D60411yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—6041no—
255C4—6041no—
256C4—6042no—
257C4—6041no—
258C4—6042no—
259C4#1801277212yes—
260C4#1801278411yescharacteristic
261C4#1801278711yescharacteristic
262C2—41no—
263C2—12081no—
264C2#2375279311yescharacteristic
265C2C2×#1801277211yescharacteristic
266C2#2375301211yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#423×C151C2
socleC22×C151C22×D4
prime radical#18012713C22
hypercenter#423D151
hypocenterC151#3252
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #23752769C2semidirect
3. #23752520C2semidirect
4. #23752508C2semidirect
5. #23752503C2semidirect
6. #23752470C2semidirect
8. #23752435C2semidirect
9. #23752423C2semidirect
10. #23752418C2semidirect
11. #423×C151C2semidirect
133. C151#3252semidirect
145. #423D151semidirect

Maximal subgroups

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

subgroupindex
#237527692
#237527462
#237525202
#237525082
#237525032
#237524702
#237524582
#237524352
#237524232
#237524182
#423×C1512
#3252151