Finite Group Databasebeta

← #34068059

Subgroups — #34068059

Order 19328.

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

normal subgroups only

This group has 320 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, complemented
2#23752362C211yesmaximal, characteristic, complemented
3#23752348C211yesmaximal, characteristic, complemented
4#23752122C211yesmaximal, characteristic, complemented
5#23751945C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic, complemented
7#328×C151C211yesmaximal, characteristic, complemented
8C22×D604—21no—
9C22×D604C2211yescharacteristic
10C2×#14558991—21no—
11C2×D1208—21no—
12#18012734—21no—
13#18012728—21no—
14#18012724—21no—
15#18012714—21no—
16#18012713C2211yescharacteristic
17#18012709—21no—
18(C22⋊D151)⋊C4—21no—
19C2×(C2×D151)⋊C4—21no—
20C2×(C2×D151)⋊C4C2211yescharacteristic
21#18012661—21no—
22#18012659—21no—
23C22⋊(C151⋊C8)C2211yescharacteristic
24C22⋊Q8×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C23×D151—21no—
28C23×D151D411yescharacteristic
29C2×D604—21no—
30C2×D604—21no—
31C2×D604—21no—
32C2×D604—21no—
33C2×D604—42no—
34C2×D604—42no—
35C2×D604—42no—
36C2×D604—42no—
37C2×D604D411yescharacteristic, complemented
38C2×C22⋊D151—21no—
39C22×Dic151D411yescharacteristic
40C2×C4×D151—21no—
41#14558991—42no—
42D1208—42no—
43C2×C151⋊C8—21no—
44C4⋊Dic151D411yescharacteristic, complemented
45Dic151⋊C4—21no—
46(C2×D151)⋊C4—21no—
47(C2×D151)⋊C4—21no—
48(C2×D151)⋊C4—21no—
49(C2×D151)⋊C4—21no—
50(C2×D151)⋊C4—21no—
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—42no—
53C4×Dic151—21no—
54C2×Q8×C151D411yescharacteristic, complemented
55C22×C4×C151—21no—
56C22×C4×C151C2311yescharacteristic
57C2×C8×C151—21no—
58C4⋊C4×C151—21no—
59C4⋊C4×C151D411yescharacteristic, complemented
60C22⋊C4×C151—21no—
61C22×D151—22no—
62C22×D151—21no—
63C22×D151—21no—
64C22×D151—21no—
65C22×D151—21no—
66C22×D151—41no—
67C22×D151—41no—
68C22×D151—41no—
69C22×D151—41no—
70C22×D151—41no—
71C22×D151—41no—
72C22×D151—41no—
73C22×D151—41no—
74D604—22no—
75D604—22no—
76D604—41no—
77D604—41no—
78D604—41no—
79D604—48no—
80D604—81no—
81D604—81no—
82C22⋊D151—41no—
83C22⋊D151—41no—
84C2×Dic151—21no—
85C2×Dic151—21no—
86C2×Dic151—41no—
87C4×D151—81no—
88C151⋊C8—41no—
89C23×C151C2×D411yescharacteristic
90Q8×C151—41no—
91C2×C4×C151—22no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—41no—
95C2×C4×C151—41no—
96C2×C4×C151—41no—
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2×D411yescharacteristic
99C8×C151—41no—
100C22×C151—21no—
101C22×C151—21no—
102C22×C151#12011yescharacteristic
103C22×C151#13511yescharacteristic
104C22×C151AGL(1,ℤ/8)11yescharacteristic
105C2×D151—42no—
106C2×D151—42no—
107C2×D151—42no—
108C2×D151—41no—
109C2×D151—41no—
110C2×D151—41no—
111C2×D151—41no—
112C2×D151—42no—
113C2×D151—41no—
114C2×D151—41no—
115C2×D151—81no—
116C2×D151—81no—
117C2×D151—81no—
118C2×D151—81no—
119C2×D151—81no—
120C4×C151—21no—
121C4×C151—21no—
122C4×C151—42no—
123C4×C151—41no—
124C4×C151—41no—
125Dic151—41no—
126Dic151—41no—
127C2×C151—21no—
128C2×C151—21no—
129C2×C151#44911yescharacteristic
130C2×C151#45311yescharacteristic
131C2×C151B(4,𝔽2)11yescharacteristic
132D151—81no—
133D151—81no—
134D151—82no—
135C151#160011yescharacteristic, complemented, Sylow
136#1600—1511nomaximal, Sylow
137#538—1511no—
138#450—1511no—
139#447—1511no—
140#392—1511no—
141#328D15111yescharacteristic, complemented
142#327—1511no—
143#323—1511no—
144C22×D4—3021no—
145C22×D4—1511no—
146C2×SD16—3021no—
147C2×D8—3021no—
148#126—3021no—
149#124—3021no—
150#123—3021no—
151C22⋊Q8C2×D15111yescharacteristic
152#121—3021no—
153#121—1511no—
154#120—3021no—
155C4×D4—3021no—
156C2×C22⋊C4—3021no—
157C2×C22⋊C4—1511no—
158#102—3021no—
159#102—3021no—
160C22⋊C8—1511no—
161C22⋊C8C2×D15111yescharacteristic
162#95C2×D15111yescharacteristic
163C24—3021no—
164C24—1511no—
165C2×Q8D60411yescharacteristic, complemented
166C2×D4—3021no—
167C2×D4—3021no—
168C2×D4—3021no—
169C2×D4—3021no—
170C2×D4—3021no—
171C2×D4—6042no—
172C2×D4—6042no—
173C2×D4—6042no—
174C2×D4—6042no—
175C2×D4—1511no—
176C22×C4—21no—
177C22×C4—3021no—
178C22×C4—1511no—
179C22×C4C22×D15111yescharacteristic
180SD16—6042no—
181D8—6042no—
182C2×C8—21no—
183C2×C8—3021no—
184C4⋊C4—21no—
185C4⋊C4—3021no—
186C4⋊C4—1511no—
187C4⋊C4D60411yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—3021no—
190C22⋊C4—3021no—
191C22⋊C4—3021no—
192C22⋊C4—3021no—
193C22⋊C4—3021no—
194C22⋊C4—3021no—
195C22⋊C4—6042no—
196C42—3021no—
197C23—3022no—
198C23—3021no—
199C23—3021no—
200C23—3021no—
201C23—3021no—
202C23—6041no—
203C23—6041no—
204C23—6041no—
205C23—6041no—
206C23—6041no—
207C23—6041no—
208C23—6041no—
209C23—6041no—
210C23D4×D15111yescharacteristic
211Q8—41no—
212D4—3022no—
213D4—3022no—
214D4—6041no—
215D4—6041no—
216D4—6041no—
217D4—6048no—
218D4—6041no—
219D4—6041no—
220D4—12081no—
221D4—12081no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—3021no—
229C2×C4—3021no—
230C2×C4—6041no—
231C2×C4—12081no—
232C2×C4D4×D15111yescharacteristic
233C2×C4C2×D60411yescharacteristic
234C8—41no—
235C8—6041no—
236C22—21no—
237C22—21no—
238C22—6042no—
239C22—6042no—
240C22—6042no—
241C22—6041no—
242C22—6041no—
243C22—6041no—
244C22—6041no—
245C22—6042no—
246C22—6041no—
247C22—6041no—
248C22—12081no—
249C22—12081no—
250C22—12081no—
251C22—12081no—
252C22—12081no—
253C22#1801270911yescharacteristic
254C22#1801276211yescharacteristic
255C22#1801276611yescharacteristic
256C4—21no—
257C4—21no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—6041no—
262C4—6041no—
263C2—21no—
264C2—21no—
265C2—12081no—
266C2—12082no—
267C2—12081no—
268C2#2375236011yescharacteristic
269C2#2375238111yescharacteristic
270C2#2375240011yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#328×C151C2
socleC22×C151#120
hypercenter#328D151
hypocenterC151#1600
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
1. #23752802C2semidirect
2. #23752362C2semidirect
3. #23752348C2semidirect
4. #23752122C2semidirect
5. #23751945C2semidirect
6. #23751935C2semidirect
7. #328×C151C2semidirect
37. C2×D604D4semidirect
44. C4⋊Dic151D4semidirect
54. C2×Q8×C151D4semidirect
59. C4⋊C4×C151D4semidirect
135. C151#1600semidirect
141. #328D151semidirect
165. C2×Q8D604semidirect
187. C4⋊C4D604semidirect

Maximal subgroups

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

subgroupindex
#237528022
#237523622
#237523482
#237521222
#237519452
#237519352
#328×C1512
#1600151