Finite Group Databasebeta

← #34068128

Subgroups — #34068128

Order 19328.

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

normal subgroups only

This group has 288 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#23752530C211yesmaximal, characteristic, complemented
3#23752147C211yesmaximal, characteristic, complemented
4#23751947C211yesmaximal, characteristic, complemented
5#23751946C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic, complemented
7#481×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×Dic151⋊C4—21no—
16C2×(C2×D151)⋊C4—21no—
17C2×(C2×D151)⋊C4C2211yescharacteristic
18#18012670—21no—
19#18012659—21no—
20C22⋊(C151⋊C8)C2211yescharacteristic, complemented
21C151⋊#95C2211yescharacteristic, complemented
22#121×C151C2211yescharacteristic
23C2×C4⋊C4×C151C2211yescharacteristic, complemented
24#106×C151—21no—
25#102×C151—21no—
26C22⋊C8×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⋊Dic151D411yescharacteristic
41Dic151⋊C4—21no—
42Dic151⋊C4—42no—
43C22⋊Dic151—21no—
44(C2×D151)⋊C4—21no—
45(C2×D151)⋊C4—21no—
46(C2×D151)⋊C4—21no—
47(C2×D151)⋊C4—21no—
48(C2×D151)⋊C4—42no—
49C2×D4×C151—21no—
50C2×D4×C151D411yescharacteristic
51C22×C4×C151—21no—
52C22×C4×C151C2311yescharacteristic
53C2×C8×C151—21no—
54C4⋊C4×C151—21no—
55C4⋊C4×C151—21no—
56C4⋊C4×C151D411yescharacteristic
57C22⋊C4×C151—21no—
58C22×D151—21no—
59C22×D151—21no—
60C22×D151—21no—
61C22×D151—42no—
62C22×D151—41no—
63C22×D151—41no—
64C22×D151—81no—
65C22×D151—81no—
66C22×D151SD1612yes—
67D604—41no—
68D604—42no—
69C22⋊D151—42no—
70C22⋊D151—41no—
71C22⋊D151—41no—
72C22⋊D151—81no—
73C2×Dic151—22no—
74C2×Dic151—21no—
75C2×Dic151—21no—
76C2×Dic151—41no—
77C2×Dic151—41no—
78C2×Dic151—41no—
79C4×D151—42no—
80C151⋊C8—41no—
81C23×C151—21no—
82C23×C151C2×D411yescharacteristic
83D4×C151—41no—
84D4×C151—41no—
85D4×C151—41no—
86C2×C4×C151—21no—
87C2×C4×C151—41no—
88C2×C4×C151—41no—
89C2×C4×C151—41no—
90C2×C4×C151—41no—
91C2×C4×C151C2×D411yescharacteristic
92C2×C4×C151C2×D411yescharacteristic
93C8×C151—41no—
94C22×C151—21no—
95C22×C151—21no—
96C22×C151—41no—
97C22×C151—41no—
98C22×C151—41no—
99C22×C151#12011yescharacteristic
100C22×C151C2×SD1611yescharacteristic
101C22×C151AGL(1,ℤ/8)11yescharacteristic
102C2×D151—22no—
103C2×D151—41no—
104C2×D151—41no—
105C2×D151—42no—
106C2×D151—41no—
107C2×D151—41no—
108C2×D151—41no—
109C2×D151—81no—
110C2×D151—84no—
111C4×C151—21no—
112C4×C151—21no—
113C4×C151—41no—
114C4×C151—81no—
115Dic151—42no—
116Dic151—41no—
117Dic151—41no—
118C2×C151—21no—
119C2×C151—21no—
120C2×C151—81no—
121C2×C151#45011yescharacteristic
122C2×C151#45311yescharacteristic
123C2×C151#45811yescharacteristic
124D151—42no—
125D151—81no—
126C151#161311yescharacteristic, complemented, Sylow
127#1613—1511nomaximal, Sylow
128#534—1511no—
129#481—1511no—
130#481D15111yescharacteristic, complemented
131#399—1511no—
132#327—1511no—
133#327—1511no—
134#323—1511no—
135C22×D4—3021no—
136#123—3021no—
137#123—3021no—
138#121—3021no—
139#121—1511no—
140#121C2×D15111yescharacteristic
141#120—3021no—
142#120—3021no—
143C2×C4⋊C4—3021no—
144C2×C4⋊C4C2×D15111yescharacteristic, complemented
145C2×C22⋊C4—3021no—
146C2×C22⋊C4—1511no—
147#106—21no—
148#106—3021no—
149#102—21no—
150#102—3021no—
151C22⋊C8—1511no—
152C22⋊C8C2×D15111yescharacteristic, complemented
153#95—1511no—
154C24—3021no—
155C24—1511no—
156C2×D4—21no—
157C2×D4—3021no—
158C2×D4—3021no—
159C2×D4—3021no—
160C2×D4—3021no—
161C2×D4—6042no—
162C2×D4—6042no—
163C2×D4—1511no—
164C2×D4C22⋊D15111yescharacteristic
165C22×C4—21no—
166C22×C4—3021no—
167C22×C4—3021no—
168C22×C4—1511no—
169C22×C4C22×D15111yescharacteristic
170C2×C8—21no—
171C2×C8—3021no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—3021no—
175C4⋊C4—6042no—
176C4⋊C4—1511no—
177C4⋊C4C22⋊D15111yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—3021no—
180C22⋊C4—3021no—
181C22⋊C4—3021no—
182C22⋊C4—3021no—
183C22⋊C4—3021no—
184C22⋊C4—6042no—
185C23—21no—
186C23—3021no—
187C23—3021no—
188C23—3021no—
189C23—6041no—
190C23—6041no—
191C23—6042no—
192C23—1512no—
193C23—12081no—
194C23—12081no—
195C23D4×D15111yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—6041no—
200D4—6042no—
201D4—6042no—
202D4—6041no—
203D4—6041no—
204D4—12081no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—3022no—
211C2×C4—3021no—
212C2×C4—3021no—
213C2×C4—6042no—
214C2×C4—6041no—
215C2×C4—6041no—
216C2×C4—6041no—
217C2×C4D4×D15111yescharacteristic
218C2×C4C2×C22⋊D15111yescharacteristic
219C8—41no—
220C8—6041no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—3022no—
227C22—6042no—
228C22—6041no—
229C22—6041no—
230C22—6041no—
231C22—6041no—
232C22—6041no—
233C22—12081no—
234C22—12084no—
235C22#1801270711yescharacteristic
236C22SD16×D15111yescharacteristic
237C22#1801276611yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—6042no—
243C4—6041no—
244C4—6041no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—6042no—
249C2—12081no—
250C2#2375236111yescharacteristic
251C2#2375237811yescharacteristic
252C2#2375240111yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#481×C151C2
socleC22×C151#120
prime radical#23752770C2
hypercenter#481D151
hypocenterC151#1613
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #23752530C2semidirect
3. #23752147C2semidirect
4. #23751947C2semidirect
5. #23751946C2semidirect
6. #23751935C2semidirect
7. #481×C151C2semidirect
20. C22⋊(C151⋊C8)C22semidirect
21. C151⋊#95C22semidirect
23. C2×C4⋊C4×C151C22semidirect
26. C22⋊C8×C151C22semidirect
126. C151#1613semidirect
130. #481D151semidirect
144. C2×C4⋊C4C2×D151semidirect
152. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527702
#237525302
#237521472
#237519472
#237519462
#237519352
#481×C1512
#1613151