Finite Group Databasebeta

← #34068161

Subgroups — #34068161

Order 19328.

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

normal subgroups only

This group has 240 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#23752545C211yesmaximal, characteristic, complemented
3#23752531C211yesmaximal, characteristic, complemented
4#23752149C211yesmaximal, 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⋊Dic151—21no—
16C2×C4⋊Dic151C2211yescharacteristic
17C2×(C2×D151)⋊C4—21no—
18C2×(C2×D151)⋊C4C2211yescharacteristic
19#18012672—21no—
20#18012671—21no—
21#18012663—21no—
22#18012661—21no—
23C22⋊(C151⋊C8)C2211yescharacteristic
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⋊Dic151—42no—
39C4⋊Dic151D411yescharacteristic
40Dic151⋊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—21no—
47(C2×D151)⋊C4—42no—
48C4×Dic151—21no—
49C2×Q8×C151D411yescharacteristic
50C22×C4×C151—21no—
51C22×C4×C151C2311yescharacteristic
52C2×C8×C151—21no—
53C4⋊C4×C151—21no—
54C4⋊C4×C151D411yescharacteristic
55C22⋊C4×C151—21no—
56C22×D151—21no—
57C22×D151—21no—
58C22×D151—21no—
59C22×D151—21no—
60C22×D151—41no—
61C22×D151—41no—
62D604—41no—
63D604—81no—
64D604—81no—
65C22⋊D151—41no—
66C22⋊D151—41no—
67C2×Dic151—21no—
68C2×Dic151—21no—
69C2×Dic151—41no—
70C2×Dic151—41no—
71C2×Dic151—41no—
72C2×Dic151—41no—
73C4×D151—81no—
74C151⋊C8—41no—
75C23×C151C2×D411yescharacteristic
76Q8×C151—41no—
77C2×C4×C151—22no—
78C2×C4×C151—21no—
79C2×C4×C151—21no—
80C2×C4×C151—41no—
81C2×C4×C151—41no—
82C2×C4×C151—41no—
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D411yescharacteristic
85C8×C151—41no—
86C22×C151—21no—
87C22×C151—21no—
88C22×C151#12011yescharacteristic
89C22×C151#13511yescharacteristic
90C22×C151#13711yescharacteristic
91C2×D151—42no—
92C2×D151—41no—
93C2×D151—41no—
94C2×D151—41no—
95C2×D151—41no—
96C2×D151—41no—
97C2×D151—41no—
98C2×D151—81no—
99C4×C151—21no—
100C4×C151—21no—
101C4×C151—42no—
102C4×C151—41no—
103C4×C151—41no—
104Dic151—41no—
105Dic151—41no—
106Dic151—81no—
107C2×C151—21no—
108C2×C151—21no—
109C2×C151#45211yescharacteristic
110C2×C151#45311yescharacteristic
111C2×C151#45811yescharacteristic
112D151—81no—
113D151—81no—
114C151#161811yescharacteristic, complemented, Sylow
115#1618—1511nomaximal, Sylow
116#538—1511no—
117#484—1511no—
118#481—1511no—
119#399—1511no—
120#328D15111yescharacteristic, complemented
121#327—1511no—
122#323—1511no—
123#126—3021no—
124#124—3021no—
125#123—3021no—
126C22⋊Q8C2×D15111yescharacteristic
127#121—3021no—
128#121—1511no—
129#120—3021no—
130C4×D4—3021no—
131C2×C4⋊C4—3021no—
132C2×C4⋊C4—1511no—
133C2×C22⋊C4—3021no—
134C2×C22⋊C4—1511no—
135#107—3021no—
136#106—3021no—
137#103—3021no—
138#102—3021no—
139C22⋊C8—1511no—
140C22⋊C8C2×D15111yescharacteristic
141#95C2×D15111yescharacteristic
142C24—1511no—
143C2×Q8D60411yescharacteristic
144C2×D4—3021no—
145C2×D4—3021no—
146C2×D4—3021no—
147C2×D4—1511no—
148C22×C4—21no—
149C22×C4—3021no—
150C22×C4—3021no—
151C22×C4—1511no—
152C22×C4C22×D15111yescharacteristic
153C2×C8—21no—
154C2×C8—3021no—
155C4⋊C4—21no—
156C4⋊C4—3021no—
157C4⋊C4—3021no—
158C4⋊C4—3021no—
159C4⋊C4—6042no—
160C4⋊C4—1511no—
161C4⋊C4D60411yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—3021no—
164C22⋊C4—3021no—
165C22⋊C4—3021no—
166C22⋊C4—3021no—
167C22⋊C4—3021no—
168C22⋊C4—3021no—
169C22⋊C4—6042no—
170C42—3021no—
171C23—3021no—
172C23—3021no—
173C23—3021no—
174C23—3021no—
175C23—6041no—
176C23—6041no—
177C23D4×D15111yescharacteristic
178Q8—41no—
179D4—6041no—
180D4—6041no—
181D4—6041no—
182D4—12081no—
183D4—12081no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—3021no—
191C2×C4—3021no—
192C2×C4—6041no—
193C2×C4—6041no—
194C2×C4—6041no—
195C2×C4—6041no—
196C2×C4—12081no—
197C2×C4D4×D15111yescharacteristic
198C2×C4C2×D60411yescharacteristic
199C8—41no—
200C8—6041no—
201C22—21no—
202C22—21no—
203C22—6042no—
204C22—6041no—
205C22—6041no—
206C22—6041no—
207C22—6041no—
208C22—6041no—
209C22—6041no—
210C22—12081no—
211C22#1801270911yescharacteristic
212C22#1801276011yescharacteristic
213C22#1801277111yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—41no—
219C4—6041no—
220C4—6041no—
221C4—12081no—
222C2—21no—
223C2—21no—
224C2—12081no—
225C2—12081no—
226C2#2375237711yescharacteristic
227C2#2375238111yescharacteristic
228C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#328×C151C2
socleC22×C151#120
prime radical#23752802C2
hypercenter#328D151
hypocenterC151#1618
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. #23752545C2semidirect
3. #23752531C2semidirect
4. #23752149C2semidirect
5. #23751945C2semidirect
6. #23751935C2semidirect
7. #328×C151C2semidirect
114. C151#1618semidirect
120. #328D151semidirect

Maximal subgroups

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

subgroupindex
#237528022
#237525452
#237525312
#237521492
#237519452
#237519352
#328×C1512
#1618151