Finite Group Databasebeta

← #34068091

Subgroups — #34068091

Order 19328.

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

normal subgroups only

This group has 260 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#23752799C211yesmaximal, characteristic
2#23752370C211yesmaximal, characteristic, complemented
3#23752350C211yesmaximal, characteristic, complemented
4#23752125C211yesmaximal, characteristic, complemented
5#23751948C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic, complemented
7#327×C151C211yesmaximal, characteristic, complemented
8C22×Dic302C2211yescharacteristic
9C2×Dic604—21no—
10C2×#14558992—21no—
11#18012734—21no—
12#18012725—21no—
13#18012723—21no—
14#18012718C2211yescharacteristic
15#18012711—21no—
16#18012707—21no—
17D4×Dic151—21no—
18C2×(C2×D151)⋊C4—21no—
19C2×(C2×D151)⋊C4C2211yescharacteristic
20#18012664—21no—
21#18012662—21no—
22C22⋊(C151⋊C8)C2211yescharacteristic
23C151⋊#95—21no—
24#121×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C23×D151D411yescharacteristic
28C2×Dic302—21no—
29C2×Dic302—21no—
30C2×Dic302—42no—
31C2×Dic302D411yescharacteristic
32C2×C22⋊D151—21no—
33C2×C22⋊D151—21no—
34C22×Dic151—21no—
35C22×Dic151—21no—
36C22×Dic151D411yescharacteristic
37Dic604—42no—
38#14558992—42no—
39C2×C151⋊C8—21no—
40C4⋊Dic151—21no—
41C4⋊Dic151D411yescharacteristic
42Dic151⋊C4—21no—
43C22⋊Dic151—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—
50C4×Dic151—21no—
51C2×D4×C151—21no—
52C2×D4×C151D411yescharacteristic
53C22×C4×C151—21no—
54C22×C4×C151C2311yescharacteristic
55C2×C8×C151—21no—
56C4⋊C4×C151D411yescharacteristic
57C22⋊C4×C151—21no—
58C22×D151—21no—
59C22×D151—21no—
60C22×D151—21no—
61C22×D151—41no—
62C22×D151—41no—
63Dic302—22no—
64Dic302—22no—
65Dic302—41no—
66Dic302—41no—
67Dic302—41no—
68C22⋊D151—81no—
69C22⋊D151—81no—
70C2×Dic151—22no—
71C2×Dic151—21no—
72C2×Dic151—21no—
73C2×Dic151—21no—
74C2×Dic151—41no—
75C2×Dic151—41no—
76C2×Dic151—41no—
77C2×Dic151—81no—
78C151⋊C8—41no—
79C23×C151—21no—
80C23×C151C2×D411yescharacteristic
81D4×C151—41no—
82D4×C151—41no—
83D4×C151—41no—
84C2×C4×C151—21no—
85C2×C4×C151—41no—
86C2×C4×C151—41no—
87C2×C4×C151—41no—
88C2×C4×C151—41no—
89C2×C4×C151C2×D411yescharacteristic
90C2×C4×C151C2×D411yescharacteristic
91C8×C151—41no—
92C22×C151—21no—
93C22×C151—21no—
94C22×C151—41no—
95C22×C151—41no—
96C22×C151—41no—
97C22×C151#12011yescharacteristic
98C22×C151#13511yescharacteristic
99C22×C151#13711yescharacteristic
100C2×D151—42no—
101C2×D151—41no—
102C2×D151—41no—
103C2×D151—41no—
104C2×D151—81no—
105C4×C151—21no—
106C4×C151—21no—
107C4×C151—41no—
108C4×C151—81no—
109Dic151—41no—
110Dic151—41no—
111Dic151—42no—
112Dic151—41no—
113C2×C151—21no—
114C2×C151—21no—
115C2×C151—81no—
116C2×C151#45211yescharacteristic
117C2×C151#45511yescharacteristic
118C2×C151B(4,𝔽2)11yescharacteristic
119D151—81no—
120C151#160611yescharacteristic, complemented, Sylow
121#1606—1511nomaximal, Sylow
122#538—1511no—
123#451—1511no—
124#448—1511no—
125#393—1511no—
126#328—1511no—
127#327D15111yescharacteristic, complemented
128#323—1511no—
129C22×Q8—1511no—
130C2×Q16—3021no—
131C2×SD16—3021no—
132#126—3021no—
133#124—3021no—
134#123—3021no—
135C22⋊Q8—1511no—
136#121—3021no—
137#121C2×D15111yescharacteristic
138#120—3021no—
139C4×D4—3021no—
140C2×C22⋊C4—3021no—
141C2×C22⋊C4—1511no—
142#103—3021no—
143#103—3021no—
144C22⋊C8—1511no—
145C22⋊C8C2×D15111yescharacteristic
146#95—3021no—
147#95C2×D15111yescharacteristic
148C24—1511no—
149C2×Q8—3021no—
150C2×Q8—3021no—
151C2×Q8—6042no—
152C2×Q8—1511no—
153C2×D4—21no—
154C2×D4—3021no—
155C2×D4—3021no—
156C2×D4D60411yescharacteristic
157C22×C4—21no—
158C22×C4—3021no—
159C22×C4—3021no—
160C22×C4—1511no—
161C22×C4C22×D15111yescharacteristic
162Q16—6042no—
163SD16—6042no—
164C2×C8—21no—
165C2×C8—3021no—
166C4⋊C4—3021no—
167C4⋊C4—3021no—
168C4⋊C4—1511no—
169C4⋊C4D60411yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—3021no—
172C22⋊C4—3021no—
173C22⋊C4—3021no—
174C22⋊C4—3021no—
175C22⋊C4—3021no—
176C22⋊C4—3021no—
177C22⋊C4—6042no—
178C42—3021no—
179C23—21no—
180C23—3021no—
181C23—3021no—
182C23—3021no—
183C23—6041no—
184C23—6041no—
185C23D4×D15111yescharacteristic
186Q8—3022no—
187Q8—3022no—
188Q8—6041no—
189Q8—6041no—
190Q8—6041no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—12081no—
195D4—12081no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—3022no—
202C2×C4—3021no—
203C2×C4—3021no—
204C2×C4—3021no—
205C2×C4—6041no—
206C2×C4—6041no—
207C2×C4—6041no—
208C2×C4—12081no—
209C2×C4D4×D15111yescharacteristic
210C2×C4C2×D60411yescharacteristic
211C8—41no—
212C8—6041no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—6042no—
219C22—6041no—
220C22—6041no—
221C22—6041no—
222C22—12081no—
223C22#1801270911yescharacteristic
224C22#1801275811yescharacteristic
225C22#1801276811yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—81no—
230C4—6041no—
231C4—6041no—
232C4—6042no—
233C4—6041no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—12081no—
238C2#2375237511yescharacteristic
239C2#2375239111yescharacteristic
240C2#2375240011yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#327×C151C2
socleC22×C151#120
prime radical#23752799C2
hypercenter#327D151
hypocenterC151#1606
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. #23752370C2semidirect
3. #23752350C2semidirect
4. #23752125C2semidirect
5. #23751948C2semidirect
6. #23751935C2semidirect
7. #327×C151C2semidirect
120. C151#1606semidirect
127. #327D151semidirect

Maximal subgroups

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

subgroupindex
#237527992
#237523702
#237523502
#237521252
#237519482
#237519352
#327×C1512
#1606151