Finite Group Databasebeta

← #34068097

Subgroups — #34068097

Order 19328.

280 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 51 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#23752770C211yesmaximal, characteristic
2#23752526C211yesmaximal, characteristic, complemented
3#23752523C211yesmaximal, characteristic, complemented
4#23752139C211yesmaximal, characteristic, complemented
5#23751945C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic, complemented
7#327×C151C211yesmaximal, characteristic, complemented
8C2×D4×D151—21no—
9#18012724—21no—
10#18012721—21no—
11#18012713C2211yescharacteristic
12#18012711—21no—
13#18012709—21no—
14#18012707—21no—
15C2×C4⋊Dic151C2211yescharacteristic, complemented
16C2×(C2×D151)⋊C4—21no—
17C2×(C2×D151)⋊C4C2211yescharacteristic
18#18012673—21no—
19#18012672—21no—
20#18012661—21no—
21#18012660—21no—
22C22⋊(C151⋊C8)C2211yescharacteristic, complemented
23C151⋊#95—21no—
24#121×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic, complemented
26#95×C151C2211yescharacteristic, complemented
27C23×D151—21no—
28C23×D151D411yescharacteristic
29C2×D604—21no—
30C2×D604D411yescharacteristic
31C2×C22⋊D151—21no—
32C2×C22⋊D151—21no—
33C2×C22⋊D151—21no—
34D4×D151—42no—
35D4×D151—42no—
36C22×Dic151—21no—
37C22×Dic151D411yescharacteristic
38C2×C4×D151—21no—
39C2×C151⋊C8—21no—
40C4⋊Dic151—21no—
41C4⋊Dic151—21no—
42C4⋊Dic151D411yescharacteristic
43Dic151⋊C4—21no—
44C22⋊Dic151—21no—
45(C2×D151)⋊C4—21no—
46(C2×D151)⋊C4—21no—
47(C2×D151)⋊C4—21no—
48(C2×D151)⋊C4—21no—
49(C2×D151)⋊C4—42no—
50C2×D4×C151—21no—
51C2×D4×C151D411yescharacteristic
52C22×C4×C151—21no—
53C22×C4×C151C2311yescharacteristic
54C2×C8×C151—21no—
55C4⋊C4×C151D411yescharacteristic
56C22⋊C4×C151—21no—
57C22×D151—21no—
58C22×D151—21no—
59C22×D151—21no—
60C22×D151—42no—
61C22×D151—41no—
62C22×D151—41no—
63C22×D151—81no—
64C22×D151—81no—
65C22×D151D812yes—
66D604—41no—
67D604—42no—
68C22⋊D151—42no—
69C22⋊D151—41no—
70C22⋊D151—41no—
71C22⋊D151—81no—
72C2×Dic151—21no—
73C2×Dic151—21no—
74C2×Dic151—41no—
75C2×Dic151—41no—
76C2×Dic151—41no—
77C2×Dic151—41no—
78C4×D151—42no—
79C151⋊C8—41no—
80C23×C151—21no—
81C23×C151C2×D411yescharacteristic
82D4×C151—41no—
83D4×C151—41no—
84D4×C151—41no—
85C2×C4×C151—21no—
86C2×C4×C151—41no—
87C2×C4×C151—41no—
88C2×C4×C151—41no—
89C2×C4×C151—41no—
90C2×C4×C151C2×D411yescharacteristic
91C2×C4×C151C2×D411yescharacteristic
92C8×C151—41no—
93C22×C151—21no—
94C22×C151—21no—
95C22×C151—41no—
96C22×C151—41no—
97C22×C151—41no—
98C22×C151#12011yescharacteristic
99C22×C151C2×D811yescharacteristic
100C22×C151AGL(1,ℤ/8)11yescharacteristic
101C2×D151—22no—
102C2×D151—41no—
103C2×D151—41no—
104C2×D151—42no—
105C2×D151—41no—
106C2×D151—41no—
107C2×D151—41no—
108C2×D151—81no—
109C2×D151—84no—
110C4×C151—21no—
111C4×C151—21no—
112C4×C151—41no—
113C4×C151—81no—
114Dic151—41no—
115Dic151—41no—
116Dic151—81no—
117C2×C151—21no—
118C2×C151—21no—
119C2×C151—81no—
120C2×C151#44711yescharacteristic
121C2×C151#45511yescharacteristic
122C2×C151#45811yescharacteristic
123D151—42no—
124D151—81no—
125C151#160711yescharacteristic, complemented, Sylow
126#1607—1511nomaximal, Sylow
127#534—1511no—
128#480—1511no—
129#480—1511no—
130#397—1511no—
131#327—1511no—
132#327D15111yescharacteristic, complemented
133#323—1511no—
134C22×D4—3021no—
135#123—3021no—
136#123—3021no—
137#121—3021no—
138#121—1511no—
139#121C2×D15111yescharacteristic
140#120—3021no—
141#120—3021no—
142C2×C4⋊C4—1511no—
143C2×C22⋊C4—3021no—
144C2×C22⋊C4—1511no—
145#107—3021no—
146#107—3021no—
147#102—3021no—
148#102—3021no—
149C22⋊C8—1511no—
150C22⋊C8C2×D15111yescharacteristic, complemented
151#95—3021no—
152#95C2×D15111yescharacteristic, complemented
153C24—3021no—
154C24—1511no—
155C2×D4—21no—
156C2×D4—3021no—
157C2×D4—3021no—
158C2×D4—3021no—
159C2×D4—3021no—
160C2×D4—6042no—
161C2×D4—6042no—
162C2×D4—1511no—
163C2×D4D60411yescharacteristic
164C22×C4—21no—
165C22×C4—3021no—
166C22×C4—3021no—
167C22×C4—1511no—
168C22×C4C22×D15111yescharacteristic
169C2×C8—21no—
170C2×C8—3021no—
171C4⋊C4—3021no—
172C4⋊C4—3021no—
173C4⋊C4—3021no—
174C4⋊C4—1511no—
175C4⋊C4D60411yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—3021no—
178C22⋊C4—3021no—
179C22⋊C4—3021no—
180C22⋊C4—3021no—
181C22⋊C4—3021no—
182C22⋊C4—6042no—
183C23—21no—
184C23—3021no—
185C23—3021no—
186C23—3021no—
187C23—6041no—
188C23—6041no—
189C23—6042no—
190C23—1512no—
191C23—12081no—
192C23—12081no—
193C23D4×D15111yescharacteristic
194D4—41no—
195D4—41no—
196D4—41no—
197D4—6041no—
198D4—6042no—
199D4—6042no—
200D4—6041no—
201D4—6041no—
202D4—12081no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—3021no—
209C2×C4—3021no—
210C2×C4—6042no—
211C2×C4—6041no—
212C2×C4—6041no—
213C2×C4—6041no—
214C2×C4—6041no—
215C2×C4D4×D15111yescharacteristic
216C2×C4C2×D60411yescharacteristic
217C8—41no—
218C8—6041no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—3022no—
225C22—6042no—
226C22—6041no—
227C22—6041no—
228C22—6041no—
229C22—6041no—
230C22—6041no—
231C22—12081no—
232C22—12084no—
233C22#1801270911yescharacteristic
234C22D8×D15111yescharacteristic
235C22#1801276611yescharacteristic
236C4—21no—
237C4—21no—
238C4—41no—
239C4—81no—
240C4—6041no—
241C4—6041no—
242C4—12081no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—6042no—
247C2—12081no—
248C2#2375234711yescharacteristic
249C2#2375239111yescharacteristic
250C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#327×C151C2
socleC22×C151#120
prime radical#23752770C2
hypercenter#327D151
hypocenterC151#1607
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #23752526C2semidirect
3. #23752523C2semidirect
4. #23752139C2semidirect
5. #23751945C2semidirect
6. #23751935C2semidirect
7. #327×C151C2semidirect
15. C2×C4⋊Dic151C22semidirect
22. C22⋊(C151⋊C8)C22semidirect
25. C22⋊C8×C151C22semidirect
26. #95×C151C22semidirect
125. C151#1607semidirect
132. #327D151semidirect
150. C22⋊C8C2×D151semidirect
152. #95C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527702
#237525262
#237525232
#237521392
#237519452
#237519352
#327×C1512
#1607151