Finite Group Databasebeta

← #34068127

Subgroups — #34068127

Order 19328.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#23752802C211yesmaximal, characteristic
2#23752540C211yesmaximal, characteristic, complemented
3#23752526C211yesmaximal, characteristic, complemented
4#23752139C211yesmaximal, characteristic, complemented
5#23751945C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic, complemented
7#328×C151C211yesmaximal, characteristic, complemented
8#18012734—21no—
9#18012728—21no—
10#18012724—21no—
11#18012714—21no—
12#18012713C2211yescharacteristic
13#18012709—21no—
14(C22⋊D151)⋊C4—21no—
15C2×C4⋊Dic151C2211yescharacteristic
16C2×(C2×D151)⋊C4—21no—
17C2×(C2×D151)⋊C4C2211yescharacteristic
18#18012673—21no—
19#18012670—21no—
20#18012663—21no—
21#18012661—21no—
22C22⋊(C151⋊C8)C2211yescharacteristic
23C151⋊#95—21no—
24C22⋊Q8×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C23×D151D411yescharacteristic
28C2×D604—21no—
29C2×D604—21no—
30C2×D604D411yescharacteristic
31C2×C22⋊D151—21no—
32C22×Dic151—21no—
33C22×Dic151D411yescharacteristic
34C2×C4×D151—21no—
35C2×C151⋊C8—21no—
36C4⋊Dic151—21no—
37C4⋊Dic151—21no—
38C4⋊Dic151D411yescharacteristic
39Dic151⋊C4—21no—
40(C2×D151)⋊C4—21no—
41(C2×D151)⋊C4—21no—
42(C2×D151)⋊C4—21no—
43(C2×D151)⋊C4—21no—
44(C2×D151)⋊C4—21no—
45(C2×D151)⋊C4—21no—
46(C2×D151)⋊C4—42no—
47C4×Dic151—21no—
48C2×Q8×C151D411yescharacteristic
49C22×C4×C151—21no—
50C22×C4×C151C2311yescharacteristic
51C2×C8×C151—21no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151D411yescharacteristic
54C22⋊C4×C151—21no—
55C22×D151—21no—
56C22×D151—21no—
57C22×D151—21no—
58C22×D151—21no—
59C22×D151—41no—
60C22×D151—41no—
61D604—41no—
62D604—81no—
63D604—81no—
64C22⋊D151—41no—
65C22⋊D151—41no—
66C2×Dic151—21no—
67C2×Dic151—21no—
68C2×Dic151—41no—
69C2×Dic151—41no—
70C2×Dic151—41no—
71C2×Dic151—41no—
72C4×D151—81no—
73C151⋊C8—41no—
74C23×C151C2×D411yescharacteristic
75Q8×C151—41no—
76C2×C4×C151—21no—
77C2×C4×C151—21no—
78C2×C4×C151—41no—
79C2×C4×C151—41no—
80C2×C4×C151—41no—
81C2×C4×C151—41no—
82C2×C4×C151C2×D411yescharacteristic
83C2×C4×C151C2×D411yescharacteristic
84C8×C151—41no—
85C22×C151—21no—
86C22×C151—21no—
87C22×C151#12011yescharacteristic
88C22×C151#13511yescharacteristic
89C22×C151AGL(1,ℤ/8)11yescharacteristic
90C2×D151—42no—
91C2×D151—41no—
92C2×D151—41no—
93C2×D151—41no—
94C2×D151—41no—
95C2×D151—41no—
96C2×D151—41no—
97C2×D151—81no—
98C4×C151—21no—
99C4×C151—21no—
100C4×C151—41no—
101C4×C151—41no—
102C4×C151—81no—
103Dic151—41no—
104Dic151—41no—
105Dic151—81no—
106C2×C151—21no—
107C2×C151—21no—
108C2×C151#44911yescharacteristic
109C2×C151#45511yescharacteristic
110C2×C151#45811yescharacteristic
111D151—81no—
112D151—81no—
113C151#161211yescharacteristic, complemented, Sylow
114#1612—1511nomaximal, Sylow
115#538—1511no—
116#483—1511no—
117#480—1511no—
118#397—1511no—
119#328D15111yescharacteristic, complemented
120#327—1511no—
121#323—1511no—
122#126—3021no—
123#124—3021no—
124#123—3021no—
125C22⋊Q8C2×D15111yescharacteristic
126#121—3021no—
127#121—1511no—
128#120—3021no—
129C4×D4—3021no—
130C2×C4⋊C4—1511no—
131C2×C22⋊C4—3021no—
132C2×C22⋊C4—1511no—
133#107—3021no—
134#106—3021no—
135#103—3021no—
136#102—3021no—
137C22⋊C8—1511no—
138C22⋊C8C2×D15111yescharacteristic
139#95—3021no—
140#95C2×D15111yescharacteristic
141C24—1511no—
142C2×Q8D60411yescharacteristic
143C2×D4—3021no—
144C2×D4—3021no—
145C2×D4—3021no—
146C2×D4—1511no—
147C22×C4—21no—
148C22×C4—3021no—
149C22×C4—3021no—
150C22×C4—1511no—
151C22×C4C22×D15111yescharacteristic
152C2×C8—21no—
153C2×C8—3021no—
154C4⋊C4—21no—
155C4⋊C4—3021no—
156C4⋊C4—3021no—
157C4⋊C4—3021no—
158C4⋊C4—1511no—
159C4⋊C4D60411yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—3021no—
162C22⋊C4—3021no—
163C22⋊C4—3021no—
164C22⋊C4—3021no—
165C22⋊C4—3021no—
166C22⋊C4—3021no—
167C22⋊C4—6042no—
168C42—3021no—
169C23—3021no—
170C23—3021no—
171C23—3021no—
172C23—3021no—
173C23—6041no—
174C23—6041no—
175C23D4×D15111yescharacteristic
176Q8—41no—
177D4—6041no—
178D4—6041no—
179D4—6041no—
180D4—12081no—
181D4—12081no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—3021no—
189C2×C4—3021no—
190C2×C4—6041no—
191C2×C4—6041no—
192C2×C4—6041no—
193C2×C4—6041no—
194C2×C4—12081no—
195C2×C4D4×D15111yescharacteristic
196C2×C4C2×D60411yescharacteristic
197C8—41no—
198C8—6041no—
199C22—21no—
200C22—21no—
201C22—6042no—
202C22—6041no—
203C22—6041no—
204C22—6041no—
205C22—6041no—
206C22—6041no—
207C22—6041no—
208C22—12081no—
209C22#1801270911yescharacteristic
210C22#1801276211yescharacteristic
211C22#1801276611yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—6041no—
218C4—6041no—
219C4—12081no—
220C2—21no—
221C2—21no—
222C2—12081no—
223C2—12081no—
224C2#2375236011yescharacteristic
225C2#2375239111yescharacteristic
226C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#328×C151C2
socleC22×C151#120
prime radical#23752802C2
hypercenter#328D151
hypocenterC151#1612
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #23752540C2semidirect
3. #23752526C2semidirect
4. #23752139C2semidirect
5. #23751945C2semidirect
6. #23751935C2semidirect
7. #328×C151C2semidirect
113. C151#1612semidirect
119. #328D151semidirect

Maximal subgroups

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

subgroupindex
#237528022
#237525402
#237525262
#237521392
#237519452
#237519352
#328×C1512
#1612151