Finite Group Databasebeta

← #34080477

Subgroups — #34080477

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#23752746C211yesmaximal, characteristic
2#23752519C212yesmaximal, complemented
3#23752504C211yesmaximal, characteristic, complemented
4#23752499C211yesmaximal, characteristic, complemented
5#23752468C212yesmaximal, complemented
6#23752460C212yesmaximal
7#23752434C212yesmaximal, complemented
8#23752419C211yesmaximal, characteristic, complemented
9#23752414C211yesmaximal, characteristic, complemented
10#23752236C211yesmaximal, characteristic, complemented
11#533×C151C211yesmaximal, characteristic, complemented
12C2×#14558994C2212yes—
13C2×#14558991C2212yes—
14C2×#14558988C2212yes—
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—
27C4⋊(C151⋊C8)C2211yescharacteristic
28C4⋊(C151⋊C8)C2211yescharacteristic
29C4⋊(C151⋊C8)C2212yes—
30#18012663C2212yes—
31#18012663C2212yes—
32#18012662C2212yes—
33#18012659C2212yes—
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—42no—
48#14558991—42no—
49#14558988—42no—
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—21no—
83Dic302—21no—
84D604—21no—
85D604—21no—
86C22⋊D151—42no—
87C2×Dic151—21no—
88C2×Dic151—21no—
89C2×Dic151—21no—
90C4×D151—42no—
91C151⋊C8—22no—
92C151⋊C8—22no—
93C23×C151C2×D411yescharacteristic
94Q8×C151—22no—
95Q8×C151—22no—
96Q8×C151—42no—
97C2×C4×C151—22no—
98C2×C4×C151—21no—
99C2×C4×C151—21no—
100C2×C4×C151—22no—
101C2×C4×C151—22no—
102C2×C4×C151—41no—
103C2×C4×C151C2×D411yescharacteristic
104C2×C4×C151C2×D411yescharacteristic
105C2×C4×C151C2×D411yescharacteristic
106C2×C4×C151C2×D411yescharacteristic
107C2×C4×C151C2×D411yescharacteristic
108C2×C4×C151C2411yescharacteristic
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—42no—
121C4×C151—42no—
122C4×C151#13712yes—
123C4×C151H(5,𝔽2)11yescharacteristic
124C4×C1512−1+411yescharacteristic
125Dic151—41no—
126Dic151—41no—
127Dic151—41no—
128C2×C151—41no—
129C2×C151#53711yescharacteristic
130C2×C151C2×#13711yescharacteristic
131C2×C151#57511yescharacteristic
132D151—81no—
133C151#325211yescharacteristic, complemented, Sylow
134#3252—1511nomaximal, Sylow
135#533D15111yescharacteristic, complemented
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#423—1511no—
146C2×Q16—1512no—
147C2×SD16—1512no—
148C2×M16—1512no—
149C4⋊Q8C2×D15111yescharacteristic
150C4⋊Q8C2×D15111yescharacteristic
151#126—3021no—
152#125—21no—
153#125—1511no—
154#124—1511no—
155#123—3021no—
156C22⋊Q8—21no—
157C22⋊Q8—1511no—
158C22⋊Q8C2×D15112yes—
159#121—1511no—
160C4×Q8—21no—
161C4×Q8—1511no—
162C4×Q8C2×D15112yes—
163C4×D4—3021no—
164C4×D4—1511no—
165#117—21no—
166#117—3021no—
167C2×C42C2×D15111yescharacteristic
168#107—1512no—
169#106—1512no—
170C4⋊C8—1511no—
171C4⋊C8—1511no—
172C4⋊C8—1512no—
173#103—1512no—
174#103—1512no—
175#103—1512no—
176#102—1512no—
177C2×Q8—21no—
178C2×Q8—1511no—
179C2×Q8C22×D15112yes—
180C2×D4—3021no—
181C2×D4—1511no—
182C22×C4—3021no—
183C22×C4C22⋊D15111yescharacteristic
184C22×C4C22⋊D15111yescharacteristic
185C22×C4C22×D15111yescharacteristic
186Q16—6042no—
187SD16—6042no—
188M16—6042no—
189C2×C8—1512no—
190C2×C8—1512no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—3021no—
197C4⋊C4—3021no—
198C4⋊C4—3021no—
199C4⋊C4—3021no—
200C4⋊C4—1511no—
201C4⋊C4—1511no—
202C4⋊C4C22×D15112yes—
203C22⋊C4—22no—
204C22⋊C4—3021no—
205C22⋊C4—3021no—
206C22⋊C4—3021no—
207C22⋊C4—3021no—
208C22⋊C4—3021no—
209C42—22no—
210C42—3021no—
211C42C22⋊D15111yescharacteristic
212C42C22⋊D15111yescharacteristic
213C42C22×D15111yescharacteristic
214C42C22×D15111yescharacteristic
215C23—3021no—
216C23C2×C22⋊D15111yescharacteristic
217Q8—22no—
218Q8—22no—
219Q8—42no—
220Q8—3021no—
221Q8—3021no—
222D4—3021no—
223D4—3021no—
224D4—6042no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—3021no—
232C2×C4—3021no—
233C2×C4—3021no—
234C2×C4—6042no—
235C2×C4C2×C22⋊D15111yescharacteristic
236C2×C4C2×C22⋊D15111yescharacteristic
237C2×C4C2×C22⋊D15111yescharacteristic
238C2×C4C2×C22⋊D15111yescharacteristic
239C2×C4C2×C22⋊D15111yescharacteristic
240C2×C4C23×D15111yescharacteristic
241C8—3022no—
242C8—3022no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—6041no—
247C22—6041no—
248C22—6041no—
249C22C22×C22⋊D15111yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—42no—
255C4—42no—
256C4—6041no—
257C4—6041no—
258C4—6041no—
259C4#1801277012yes—
260C4#1801278511yescharacteristic
261C4#1801278611yescharacteristic
262C2—41no—
263C2—12081no—
264C2#2375279011yescharacteristic
265C2C2×#1801277011yescharacteristic
266C2#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#3252
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. #23752519C2semidirect
3. #23752504C2semidirect
4. #23752499C2semidirect
5. #23752468C2semidirect
7. #23752434C2semidirect
8. #23752419C2semidirect
9. #23752414C2semidirect
10. #23752236C2semidirect
11. #533×C151C2semidirect
133. C151#3252semidirect
135. #533D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237525192
#237525042
#237524992
#237524682
#237524602
#237524342
#237524192
#237524142
#237522362
#533×C1512
#3252151