Finite Group Databasebeta

← #34079813

Subgroups — #34079813

Order 19328.

366 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 125 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#23752746C211yesmaximal, characteristic
2#23752618C211yesmaximal, characteristic, complemented
3#23752604C211yesmaximal, characteristic, complemented
4#23752580C211yesmaximal, characteristic, complemented
5#23752574C211yesmaximal, characteristic, complemented
6#23752451C212yesmaximal, complemented
7#23752443C212yesmaximal
8#23752317C212yesmaximal, complemented
9#23752310C212yesmaximal, complemented
10C2×#18012650C211yesmaximal, characteristic, complemented
11#533×C151C211yesmaximal, characteristic, complemented
12C2×#14558994C2212yes—
13C2×#14558991C2212yes—
14C22×C151⋊C8C2212yes—
15#18012733—21no—
16#18012731C2211yescharacteristic
17#18012727C2211yescharacteristic
18#18012722—21no—
19#18012718C2211yescharacteristic
20#18012713C2211yescharacteristic
21C4×Dic302C2211yescharacteristic
22C4×D604C2211yescharacteristic
23C4×C22⋊D151—21no—
24#18012696—21no—
25#18012672C2212yes—
26#18012670C2212yes—
27#18012663C2212yes—
28#18012663C2212yes—
29#18012662C2212yes—
30#18012659C2212yes—
31#18012650C2212yes—
32#18012650C2211yescharacteristic
33#18012650C2211yescharacteristic
34C4⋊Q8×C151C2211yescharacteristic
35C4⋊Q8×C151C2211yescharacteristic
36#125×C151—21no—
37C22⋊Q8×C151—21no—
38C22⋊Q8×C151C2212yes—
39C4×Q8×C151—21no—
40C4×Q8×C151C2212yes—
41#117×C151—21no—
42C2×C42×C151C2211yescharacteristic
43C2×Dic302C2311yescharacteristic
44C2×D604C2311yescharacteristic
45C2×C22⋊D151—21no—
46C2×C4×D151—21no—
47#14558994—24no—
48#14558991—24no—
49C2×C151⋊C8—24no—
50C2×C151⋊C8C2312yes—
51C2×C151⋊C8C2312yes—
52C4⋊Dic151C2311yescharacteristic
53C4⋊Dic151C2311yescharacteristic
54Dic151⋊C4—21no—
55Dic151⋊C4—21no—
56Dic151⋊C4—21no—
57Dic151⋊C4—21no—
58C22⋊Dic151—21no—
59(C2×D151)⋊C4—21no—
60(C2×D151)⋊C4—21no—
61(C2×D151)⋊C4—21no—
62(C2×D151)⋊C4—21no—
63C4×Dic151—21no—
64C2×Q8×C151—21no—
65C2×Q8×C151C2312yes—
66C22×C4×C151D411yescharacteristic
67C22×C4×C151D411yescharacteristic
68C22×C4×C151C2311yescharacteristic
69C4⋊C4×C151—21no—
70C4⋊C4×C151—21no—
71C4⋊C4×C151—21no—
72C4⋊C4×C151—22no—
73C4⋊C4×C151—22no—
74C4⋊C4×C151C2312yes—
75C22⋊C4×C151—22no—
76C42×C151—22no—
77C42×C151D411yescharacteristic
78C42×C151D411yescharacteristic
79C42×C151C2311yescharacteristic
80C42×C151C2311yescharacteristic
81C22×D151—21no—
82Dic302—22no—
83D604—22no—
84C22⋊D151—42no—
85C2×Dic151—21no—
86C2×Dic151—21no—
87C2×Dic151—21no—
88C4×D151—42no—
89C151⋊C8—22no—
90C151⋊C8#4114yes—
91C23×C151C2×D411yescharacteristic
92Q8×C151—22no—
93Q8×C151—22no—
94Q8×C151—42no—
95C2×C4×C151—22no—
96C2×C4×C151—22no—
97C2×C4×C151—22no—
98C2×C4×C151—22no—
99C2×C4×C151—41no—
100C2×C4×C151C2×D411yescharacteristic
101C2×C4×C151C2×D411yescharacteristic
102C2×C4×C151C2×D411yescharacteristic
103C2×C4×C151C2×D411yescharacteristic
104C2×C4×C151C2×D411yescharacteristic
105C2×C4×C151C2411yescharacteristic
106C22×C151—21no—
107C22×C151—21no—
108C22×C151#13712yes—
109C22×C151C22×D411yescharacteristic
110C2×D151—41no—
111C2×D151—41no—
112C2×D151—41no—
113C4×C151—21no—
114C4×C151—21no—
115C4×C151—21no—
116C4×C151—21no—
117C4×C151—21no—
118C4×C151—42no—
119C4×C151—42no—
120C4×C151C2×#4112yes—
121Dic151—41no—
122Dic151—41no—
123Dic151—41no—
124C2×C151—22no—
125C2×C151#53211yescharacteristic
126C2×C151C2×#13711yescharacteristic
127C2×C151#57511yescharacteristic
128D151—81no—
129C151#318111yescharacteristic, complemented, Sylow
130#3181—1511nomaximal, Sylow
131#533D15111yescharacteristic, complemented
132#529—1511no—
133#501—1511no—
134#497—1511no—
135#491—1511no—
136#489—1511no—
137#467—1512no—
138#465—1512no—
139#441—1512no—
140#440—1512no—
141C2×#97—1511no—
142C2×Q16—1512no—
143C2×SD16—1512no—
144C22×C8—1512no—
145C4⋊Q8C2×D15111yescharacteristic
146C4⋊Q8C2×D15111yescharacteristic
147#126—3021no—
148#125—21no—
149#125—1511no—
150#124—1511no—
151#123—3021no—
152C22⋊Q8—21no—
153C22⋊Q8—1511no—
154C22⋊Q8C2×D15112yes—
155#121—1511no—
156C4×Q8—21no—
157C4×Q8—1511no—
158C4×Q8C2×D15112yes—
159C4×D4—3021no—
160C4×D4—1511no—
161#117—21no—
162#117—3021no—
163C2×C42C2×D15111yescharacteristic
164#107—1512no—
165#106—1512no—
166#103—1512no—
167#103—1512no—
168#103—1512no—
169#102—1512no—
170#97—1512no—
171#97—1511no—
172#97—1511no—
173C2×Q8—21no—
174C2×Q8—1511no—
175C2×Q8C22×D15112yes—
176C2×D4—3021no—
177C2×D4—1511no—
178C22×C4—3021no—
179C22×C4C22⋊D15111yescharacteristic
180C22×C4C22⋊D15111yescharacteristic
181C22×C4C22×D15111yescharacteristic
182Q16—3024no—
183SD16—3024no—
184C2×C8—3024no—
185C2×C8—1512no—
186C2×C8—1512no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—3021no—
193C4⋊C4—3021no—
194C4⋊C4—3021no—
195C4⋊C4—3021no—
196C4⋊C4—1511no—
197C4⋊C4—1511no—
198C4⋊C4C22×D15112yes—
199C22⋊C4—22no—
200C22⋊C4—3021no—
201C22⋊C4—3021no—
202C22⋊C4—3021no—
203C22⋊C4—3021no—
204C22⋊C4—3021no—
205C42—22no—
206C42—3021no—
207C42C22⋊D15111yescharacteristic
208C42C22⋊D15111yescharacteristic
209C42C22×D15111yescharacteristic
210C42C22×D15111yescharacteristic
211C23—3021no—
212C23C2×C22⋊D15111yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—3022no—
217D4—3022no—
218D4—6042no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—3021no—
225C2×C4—3021no—
226C2×C4—3021no—
227C2×C4—6042no—
228C2×C4C2×C22⋊D15111yescharacteristic
229C2×C4C2×C22⋊D15111yescharacteristic
230C2×C4C2×C22⋊D15111yescharacteristic
231C2×C4C2×C22⋊D15111yescharacteristic
232C2×C4C2×C22⋊D15111yescharacteristic
233C2×C4C23×D15111yescharacteristic
234C8—3022no—
235C8—1514no—
236C22—21no—
237C22—21no—
238C22—6041no—
239C22—6041no—
240C22—6041no—
241C22#1801277012yes—
242C22C22×C22⋊D15111yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—42no—
250C4—6041no—
251C4—6041no—
252C4—6041no—
253C4#41×D15112yes—
254C2—22no—
255C2—12081no—
256C2#2375275811yescharacteristic
257C2C2×#1801277011yescharacteristic
258C2#2375301011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#533×C151C2
socleC22×C151C22×D4
prime radical#18012713C22
hypercenter#533D151
hypocenterC151#3181
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23752618C2semidirect
3. #23752604C2semidirect
4. #23752580C2semidirect
5. #23752574C2semidirect
6. #23752451C2semidirect
8. #23752317C2semidirect
9. #23752310C2semidirect
10. C2×#18012650C2semidirect
11. #533×C151C2semidirect
129. C151#3181semidirect
131. #533D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237526182
#237526042
#237525802
#237525742
#237524512
#237524432
#237523172
#237523102
C2×#180126502
#533×C1512
#3181151