Finite Group Databasebeta

← #34068040

Subgroups — #34068040

Order 19328.

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

normal subgroups only

This group has 272 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#23752807C211yesmaximal, characteristic, complemented
2#23752365C211yesmaximal, characteristic, complemented
3#23752345C211yesmaximal, characteristic
4#23752130C211yesmaximal, characteristic, complemented
5#23751948C211yesmaximal, characteristic, complemented
6#23751937C211yesmaximal, characteristic, complemented
7#327×C151C211yesmaximal, characteristic, complemented
8C22×D604C2211yescharacteristic
9C2×#14558993—21no—
10C2×#14558989—21no—
11#18012732—21no—
12#18012729—21no—
13#18012720—21no—
14#18012720—21no—
15#18012718C2211yescharacteristic
16#18012716—21no—
17D4×Dic151—21no—
18C2×Dic151⋊C4C2211yescharacteristic
19C2×(C2×D151)⋊C4—21no—
20C2×(C2×D151)⋊C4—21no—
21#18012661—21no—
22#18012659—21no—
23C22⋊(C151⋊C8)C2211yescharacteristic
24#121×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C23×D151—21no—
28C2×Dic302D411yescharacteristic
29C2×D604—21no—
30C2×D604—21no—
31C2×D604—42no—
32C22×Dic151—21no—
33C22×Dic151D411yescharacteristic
34C22×Dic151D411yescharacteristic
35#14558993—42no—
36#14558989—42no—
37C2×C151⋊C8—21no—
38C4⋊Dic151—21no—
39C4⋊Dic151D411yescharacteristic
40Dic151⋊C4—21no—
41Dic151⋊C4—21no—
42Dic151⋊C4—21no—
43Dic151⋊C4—21no—
44Dic151⋊C4—21no—
45C22⋊Dic151—21no—
46C22⋊Dic151—21no—
47C22⋊Dic151—21no—
48C22⋊Dic151—21no—
49(C2×D151)⋊C4—42no—
50(C2×D151)⋊C4—42no—
51C4×Dic151—21no—
52C2×D4×C151—21no—
53C2×D4×C151D411yescharacteristic
54C22×C4×C151—21no—
55C22×C4×C151C2311yescharacteristic
56C2×C8×C151—21no—
57C4⋊C4×C151D411yescharacteristic
58C22⋊C4×C151—21no—
59C22×D151—22no—
60C22×D151—41no—
61C22×D151—41no—
62C22×D151—41no—
63C22×D151—41no—
64C22×D151—41no—
65C22×D151—41no—
66Dic302—41no—
67D604—22no—
68D604—22no—
69D604—41no—
70D604—41no—
71C2×Dic151—21no—
72C2×Dic151—21no—
73C2×Dic151—21no—
74C2×Dic151—21no—
75C2×Dic151—21no—
76C2×Dic151—21no—
77C2×Dic151—41no—
78C2×Dic151—81no—
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×C151#13511yescharacteristic
100C22×C151AGL(1,ℤ/8)11yescharacteristic
101C2×D151—42no—
102C2×D151—42no—
103C2×D151—42no—
104C2×D151—81no—
105C2×D151—81no—
106C2×D151—81no—
107C2×D151—81no—
108C4×C151—21no—
109C4×C151—21no—
110C4×C151—41no—
111C4×C151—81no—
112Dic151—41no—
113Dic151—41no—
114Dic151—41no—
115Dic151—41no—
116C2×C151—21no—
117C2×C151—21no—
118C2×C151—81no—
119C2×C151#44911yescharacteristic
120C2×C151#45411yescharacteristic
121C2×C151B(4,𝔽2)11yescharacteristic
122D151—82no—
123C151#159711yescharacteristic, complemented, Sylow
124#1597—1511nomaximal, Sylow
125#539—1511no—
126#450—1511no—
127#447—1511no—
128#394—1511no—
129#328—1511no—
130#327D15111yescharacteristic, complemented
131#324—1511no—
132C22×D4—1511no—
133C2×SD16—3021no—
134C2×D8—3021no—
135#126—3021no—
136#125—3021no—
137#123—3021no—
138#123—3021no—
139C22⋊Q8—3021no—
140C22⋊Q8—1511no—
141#121C2×D15111yescharacteristic
142C4×D4—3021no—
143C2×C4⋊C4—1511no—
144C2×C22⋊C4—3021no—
145C2×C22⋊C4—3021no—
146#102—3021no—
147#102—3021no—
148C22⋊C8—1511no—
149C22⋊C8C2×D15111yescharacteristic
150#95C2×D15111yescharacteristic
151C24—3021no—
152C2×Q8—1511no—
153C2×D4—21no—
154C2×D4—3021no—
155C2×D4—3021no—
156C2×D4—6042no—
157C2×D4D60411yescharacteristic
158C22×C4—21no—
159C22×C4—3021no—
160C22×C4—1511no—
161C22×C4—1511no—
162C22×C4C22×D15111yescharacteristic
163SD16—6042no—
164D8—6042no—
165C2×C8—21no—
166C2×C8—3021no—
167C4⋊C4—3021no—
168C4⋊C4—3021no—
169C4⋊C4—3021no—
170C4⋊C4—3021no—
171C4⋊C4—3021no—
172C4⋊C4—3021no—
173C4⋊C4—1511no—
174C4⋊C4D60411yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—3021no—
177C22⋊C4—3021no—
178C22⋊C4—3021no—
179C22⋊C4—3021no—
180C22⋊C4—6042no—
181C22⋊C4—6042no—
182C42—3021no—
183C23—21no—
184C23—3022no—
185C23—6041no—
186C23—6041no—
187C23—6041no—
188C23—6041no—
189C23—6041no—
190C23—6041no—
191C23D4×D15111yescharacteristic
192Q8—6041no—
193D4—41no—
194D4—41no—
195D4—41no—
196D4—3022no—
197D4—3022no—
198D4—6041no—
199D4—6041no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—3021no—
206C2×C4—3021no—
207C2×C4—3021no—
208C2×C4—3021no—
209C2×C4—3021no—
210C2×C4—3021no—
211C2×C4—6041no—
212C2×C4—12081no—
213C2×C4D4×D15111yescharacteristic
214C2×C4C2×D60411yescharacteristic
215C8—41no—
216C8—6041no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—6042no—
223C22—6042no—
224C22—6042no—
225C22—12081no—
226C22—12081no—
227C22—12081no—
228C22—12081no—
229C22#1801270911yescharacteristic
230C22#1801276011yescharacteristic
231C22#1801276311yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—81no—
236C4—6041no—
237C4—6041no—
238C4—6041no—
239C4—6041no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—12082no—
244C2#2375235811yescharacteristic
245C2#2375238611yescharacteristic
246C2#2375240011yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#327×C151C2
socleC22×C151#120
prime radical#23752345C2
hypercenter#327D151
hypocenterC151#1597
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
1. #23752807C2semidirect
2. #23752365C2semidirect
4. #23752130C2semidirect
5. #23751948C2semidirect
6. #23751937C2semidirect
7. #327×C151C2semidirect
123. C151#1597semidirect
130. #327D151semidirect

Maximal subgroups

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

subgroupindex
#237528072
#237523652
#237523452
#237521302
#237519482
#237519372
#327×C1512
#1597151