Finite Group Databasebeta

← #34080289

Subgroups — #34080289

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#23752746C211yesmaximal, characteristic
2#23752611C212yesmaximal, complemented
3#23752569C212yesmaximal, complemented
4#23752553C212yesmaximal, complemented
5#23752536C212yesmaximal
6#23752504C211yesmaximal, characteristic, complemented
7#23752499C211yesmaximal, characteristic, complemented
8#23752494C211yesmaximal, characteristic, complemented
9#23752489C211yesmaximal, characteristic, complemented
10#23752265C211yesmaximal, characteristic, complemented
11#533×C151C211yesmaximal, characteristic, complemented
12#18012733—21no—
13#18012731C2211yescharacteristic
14#18012727C2211yescharacteristic
15#18012722—21no—
16#18012718C2211yescharacteristic
17#18012713C2211yescharacteristic
18C4×Dic302C2211yescharacteristic
19C4×D604C2211yescharacteristic
20C4×C22⋊D151—21no—
21#18012696—21no—
22#18012672C2212yes—
23#18012672C2212yes—
24#18012670C2212yes—
25#18012670C2212yes—
26C4⋊(C151⋊C8)C2211yescharacteristic
27C4⋊(C151⋊C8)C2211yescharacteristic
28#18012662C2212yes—
29#18012662C2212yes—
30#18012659C2212yes—
31#18012659C2212yes—
32C22⋊(C151⋊C8)C2212yes—
33C4×C151⋊C8C2212yes—
34C4⋊Q8×C151C2211yescharacteristic
35C4⋊Q8×C151C2211yescharacteristic
36#125×C151C2212yes—
37C22⋊Q8×C151—21no—
38C22⋊Q8×C151—21no—
39C4×Q8×C151—21no—
40C4×Q8×C151—21no—
41#117×C151C2212yes—
42C2×C42×C151C2211yescharacteristic
43C2×Dic302C2311yescharacteristic
44C2×D604C2311yescharacteristic
45C2×C22⋊D151—21no—
46C2×C4×D151—21no—
47C2×C151⋊C8C2312yes—
48C2×C151⋊C8C2312yes—
49C4⋊Dic151C2311yescharacteristic
50C4⋊Dic151C2311yescharacteristic
51Dic151⋊C4—21no—
52Dic151⋊C4—21no—
53Dic151⋊C4—21no—
54Dic151⋊C4—21no—
55C22⋊Dic151—21no—
56(C2×D151)⋊C4—21no—
57(C2×D151)⋊C4—21no—
58(C2×D151)⋊C4—21no—
59(C2×D151)⋊C4—21no—
60C4×Dic151—21no—
61C2×Q8×C151—21no—
62C2×Q8×C151—21no—
63C22×C4×C151D411yescharacteristic
64C22×C4×C151D411yescharacteristic
65C22×C4×C151C2311yescharacteristic
66C4⋊C4×C151—22no—
67C4⋊C4×C151—22no—
68C4⋊C4×C151—21no—
69C4⋊C4×C151—21no—
70C4⋊C4×C151C2312yes—
71C4⋊C4×C151C2312yes—
72C22⋊C4×C151—22no—
73C42×C151—22no—
74C42×C151D411yescharacteristic
75C42×C151D411yescharacteristic
76C42×C151C2311yescharacteristic
77C42×C151C2311yescharacteristic
78C22×D151—21no—
79Dic302—21no—
80Dic302—21no—
81D604—21no—
82D604—21no—
83C22⋊D151—42no—
84C2×Dic151—21no—
85C2×Dic151—21no—
86C2×Dic151—21no—
87C4×D151—42no—
88C151⋊C8—22no—
89C151⋊C8—22no—
90C23×C151C2×D411yescharacteristic
91Q8×C151—42no—
92Q8×C151—42no—
93C2×C4×C151—22no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—22no—
97C2×C4×C151—22no—
98C2×C4×C151—41no—
99C2×C4×C151C2×D411yescharacteristic
100C2×C4×C151C2×D411yescharacteristic
101C2×C4×C151C2×D411yescharacteristic
102C2×C4×C151C2×D411yescharacteristic
103C2×C4×C151C2×D411yescharacteristic
104C2×C4×C151C2411yescharacteristic
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—42no—
117C4×C151—42no—
118C4×C151#13512yes—
119C4×C1512−1+411yescharacteristic
120C4×C1512−1+411yescharacteristic
121Dic151—41no—
122Dic151—41no—
123Dic151—41no—
124C2×C151—41no—
125C2×C151#53611yescharacteristic
126C2×C151C2×#13511yescharacteristic
127C2×C151#57511yescharacteristic
128D151—81no—
129C151#323311yescharacteristic, complemented, Sylow
130#3233—1511nomaximal, Sylow
131#533D15111yescharacteristic, complemented
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#431—1511no—
142C4⋊Q8C2×D15111yescharacteristic
143C4⋊Q8C2×D15111yescharacteristic
144#126—3021no—
145#125—1511no—
146#125C2×D15112yes—
147#124—1511no—
148#123—3021no—
149C22⋊Q8—21no—
150C22⋊Q8—21no—
151C22⋊Q8—1511no—
152#121—1511no—
153C4×Q8—21no—
154C4×Q8—21no—
155C4×Q8—1511no—
156C4×D4—3021no—
157C4×D4—1511no—
158#117—3021no—
159#117C2×D15112yes—
160C2×C42C2×D15111yescharacteristic
161#107—1512no—
162#107—1512no—
163#106—1512no—
164#106—1512no—
165C4⋊C8—1511no—
166C4⋊C8—1511no—
167#103—1512no—
168#103—1512no—
169#102—1512no—
170#102—1512no—
171C22⋊C8—1512no—
172C4×C8—1512no—
173C2×Q8—21no—
174C2×Q8—21no—
175C2×Q8—1511no—
176C2×D4—3021no—
177C2×D4—1511no—
178C22×C4—3021no—
179C22×C4C22⋊D15111yescharacteristic
180C22×C4C22⋊D15111yescharacteristic
181C22×C4C22×D15111yescharacteristic
182C2×C8—1512no—
183C2×C8—1512no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—3021no—
189C4⋊C4—3021no—
190C4⋊C4—3021no—
191C4⋊C4—3021no—
192C4⋊C4—1511no—
193C4⋊C4—1511no—
194C4⋊C4C22×D15112yes—
195C4⋊C4C22×D15112yes—
196C22⋊C4—22no—
197C22⋊C4—3021no—
198C22⋊C4—3021no—
199C22⋊C4—3021no—
200C22⋊C4—3021no—
201C22⋊C4—3021no—
202C42—22no—
203C42—3021no—
204C42C22⋊D15111yescharacteristic
205C42C22⋊D15111yescharacteristic
206C42C22×D15111yescharacteristic
207C42C22×D15111yescharacteristic
208C23—3021no—
209C23C2×C22⋊D15111yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—3021no—
213Q8—3021no—
214D4—3021no—
215D4—3021no—
216D4—6042no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—3021no—
224C2×C4—3021no—
225C2×C4—3021no—
226C2×C4—6042no—
227C2×C4C2×C22⋊D15111yescharacteristic
228C2×C4C2×C22⋊D15111yescharacteristic
229C2×C4C2×C22⋊D15111yescharacteristic
230C2×C4C2×C22⋊D15111yescharacteristic
231C2×C4C2×C22⋊D15111yescharacteristic
232C2×C4C23×D15111yescharacteristic
233C8—3022no—
234C8—3022no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—6041no—
239C22—6041no—
240C22—6041no—
241C22C22×C22⋊D15111yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—6041no—
249C4—6041no—
250C4—6041no—
251C4#1801275912yes—
252C4#1801278711yescharacteristic
253C4#1801278711yescharacteristic
254C2—41no—
255C2—12081no—
256C2#2375278611yescharacteristic
257C2C2×#1801275911yescharacteristic
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#3233
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. #23752611C2semidirect
3. #23752569C2semidirect
4. #23752553C2semidirect
6. #23752504C2semidirect
7. #23752499C2semidirect
8. #23752494C2semidirect
9. #23752489C2semidirect
10. #23752265C2semidirect
11. #533×C151C2semidirect
129. C151#3233semidirect
131. #533D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237526112
#237525692
#237525532
#237525362
#237525042
#237524992
#237524942
#237524892
#237522652
#533×C1512
#3233151