Finite Group Databasebeta

← #34067652

Subgroups — #34067652

Order 19328.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#23752725C211yesmaximal, characteristic
2#23752174C211yesmaximal, characteristic, complemented
3#23752071C211yesmaximal, characteristic, complemented
4#23751949C211yesmaximal, characteristic, complemented
5#23751947C211yesmaximal, characteristic, complemented
6#23751945C211yesmaximal, characteristic, complemented
7#328×C151C211yesmaximal, characteristic, complemented
8C2×#14559005C411yescharacteristic, complemented
9C22×C4×D151C2211yescharacteristic
10C2×#14558987—21no—
11#18012724—21no—
12#18012715C411yescharacteristic, complemented
13#18012714C411yescharacteristic, complemented
14#18012713C2211yescharacteristic
15#18012709—21no—
16#18012701—21no—
17(C22⋊D151)⋊C4—21no—
18#18012697C411yescharacteristic, complemented
19C2×Dic151⋊C4—21no—
20C2×(C2×D151)⋊C4—21no—
21C22⋊(C151⋊C8)C2211yescharacteristic
22(C2×D151)⋊C8—21no—
23C151⋊#95C2211yescharacteristic
24C22⋊Q8×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C23×D151D411yescharacteristic
28#14559005—42no—
29C2×D604—21no—
30C2×D604—21no—
31C2×D604C2×C411yescharacteristic
32C2×C22⋊D151—21no—
33C22×Dic151—21no—
34C22×Dic151D411yescharacteristic
35C2×C4×D151—21no—
36C2×C4×D151—42no—
37C2×C4×D151C2×C411yescharacteristic
38C2×C4×D151C2×C411yescharacteristic
39C2×C4×D151D411yescharacteristic
40C2×C4×D151D411yescharacteristic
41#14558987—42no—
42C2×C151⋊C8—21no—
43C4⋊Dic151C2×C411yescharacteristic
44Dic151⋊C4—21no—
45Dic151⋊C4—42no—
46(C2×D151)⋊C4—21no—
47(C2×D151)⋊C4—21no—
48(C2×D151)⋊C4—21no—
49(C2×D151)⋊C4—21no—
50(C2×D151)⋊C4—42no—
51C4×Dic151—21no—
52C2×Q8×C151C2×C411yescharacteristic
53C22×C4×C151—21no—
54C22×C4×C151C2311yescharacteristic
55C2×C8×C151—21no—
56C4⋊C4×C151—21no—
57C4⋊C4×C151C2×C411yescharacteristic
58C22⋊C4×C151—21no—
59C22×D151—21no—
60C22×D151—21no—
61C22×D151—21no—
62C22×D151—41no—
63C22×D151—41no—
64C22×D151C22⋊C411yescharacteristic
65C22×D151C22⋊C411yescharacteristic
66D604—41no—
67D604—42no—
68D604—42no—
69C22⋊D151—41no—
70C22⋊D151—41no—
71C2×Dic151—22no—
72C2×Dic151—21no—
73C2×Dic151—41no—
74C2×Dic151—41no—
75C2×Dic151—41no—
76C2×Dic151C22⋊C411yescharacteristic
77C2×Dic151C22⋊C411yescharacteristic
78C4×D151—22no—
79C4×D151—22no—
80C4×D151—41no—
81C4×D151—41no—
82C4×D151—42no—
83C151⋊C8—41no—
84C23×C151C2×D411yescharacteristic
85Q8×C151—41no—
86C2×C4×C151—21no—
87C2×C4×C151—21no—
88C2×C4×C151—41no—
89C2×C4×C151—41no—
90C2×C4×C151—41no—
91C2×C4×C151—41no—
92C2×C4×C151C22×C411yescharacteristic
93C2×C4×C151C2×D411yescharacteristic
94C8×C151—41no—
95C22×C151—21no—
96C22×C151—21no—
97C22×C151C2×C22⋊C411yescharacteristic
98C22×C151AGL(1,ℤ/8)11yescharacteristic
99C22×C151#13711yescharacteristic
100C2×D151—21no—
101C2×D151—21no—
102C2×D151—21no—
103C2×D151—21no—
104C2×D151—21no—
105C2×D151—21no—
106C2×D151—42no—
107C2×D151—42no—
108C2×D151—41no—
109C2×D151—41no—
110C2×D151—41no—
111C4×C151—21no—
112C4×C151—21no—
113C4×C151—41no—
114C4×C151—41no—
115C4×C151—81no—
116Dic151—21no—
117Dic151—41no—
118Dic151—81no—
119Dic151#9912yes—
120C2×C151—21no—
121C2×C151—21no—
122C2×C151C2×#9911yescharacteristic
123C2×C151#41711yescharacteristic
124C2×C151#42111yescharacteristic
125D151—41no—
126D151—41no—
127D151—81no—
128C151#151311yescharacteristic, complemented, Sylow
129#1513—1511nomaximal, Sylow
130#525—1511no—
131#407—1511no—
132#380—1511no—
133#328—1511no—
134#328D15111yescharacteristic, complemented
135#327—1511no—
136#327—1511no—
137C2×#41—1511no—
138C23×C4—1511no—
139C2×M16—3021no—
140#123—3021no—
141C22⋊Q8—1511no—
142C22⋊Q8C2×D15111yescharacteristic
143#121—1511no—
144#121—1511no—
145#120—3021no—
146C4×D4—3021no—
147C4×D4—3021no—
148#117—1511no—
149C2×C4⋊C4—3021no—
150C2×C22⋊C4—3021no—
151C22⋊C8—3021no—
152C22⋊C8—1511no—
153C22⋊C8C2×D15111yescharacteristic
154#95—1511no—
155#95C2×D15111yescharacteristic
156C24—1511no—
157#41—6042no—
158C2×Q8C4×D15111yescharacteristic
159C2×D4—3021no—
160C2×D4—3021no—
161C2×D4—3021no—
162C2×D4—1511no—
163C22×C4—21no—
164C22×C4—3021no—
165C22×C4—3021no—
166C22×C4—6042no—
167C22×C4—1511no—
168C22×C4—1511no—
169C22×C4—1511no—
170C22×C4—1511no—
171C22×C4—1511no—
172C22×C4C22×D15111yescharacteristic
173M16—6042no—
174C2×C8—21no—
175C2×C8—3021no—
176C4⋊C4—21no—
177C4⋊C4—3021no—
178C4⋊C4—6042no—
179C4⋊C4—1511no—
180C4⋊C4C4×D15111yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—3021no—
183C22⋊C4—3021no—
184C22⋊C4—3021no—
185C22⋊C4—3021no—
186C22⋊C4—6042no—
187C42—3021no—
188C23—3021no—
189C23—3021no—
190C23—3021no—
191C23—6041no—
192C23—6041no—
193C23—1511no—
194C23—1511no—
195C23D4×D15111yescharacteristic
196Q8—41no—
197D4—6041no—
198D4—6042no—
199D4—6042no—
200D4—6041no—
201D4—6041no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—3022no—
209C2×C4—3022no—
210C2×C4—3022no—
211C2×C4—3021no—
212C2×C4—6041no—
213C2×C4—6041no—
214C2×C4—6042no—
215C2×C4—6041no—
216C2×C4—6041no—
217C2×C4—6041no—
218C2×C4—1511no—
219C2×C4—1511no—
220C2×C4C2×C4×D15111yescharacteristic
221C2×C4D4×D15111yescharacteristic
222C8—41no—
223C8—6041no—
224C22—21no—
225C22—21no—
226C22—3021no—
227C22—3021no—
228C22—3021no—
229C22—3021no—
230C22—3021no—
231C22—3021no—
232C22—6042no—
233C22—6042no—
234C22—6041no—
235C22—6041no—
236C22—6041no—
237C22C22⋊C4×D15111yescharacteristic
238C22#1801276611yescharacteristic
239C22#1801277111yescharacteristic
240C4—21no—
241C4—21no—
242C4—41no—
243C4—41no—
244C4—81no—
245C4—3021no—
246C4—6041no—
247C4—1512no—
248C4—12081no—
249C2—21no—
250C2—21no—
251C2—6041no—
252C2—6041no—
253C2—12081no—
254C2#99×D15111yescharacteristic
255C2#2375221211yescharacteristic
256C2#2375222711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D151
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#328×C151C2
socleC22×C151C2×C22⋊C4
prime radical#23752725C2
cosocleC22×C4×C151C23
hypercenter#328D151
hypocenterC151#1513
LCSG ▷ C2×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. #23752174C2semidirect
3. #23752071C2semidirect
4. #23751949C2semidirect
5. #23751947C2semidirect
6. #23751945C2semidirect
7. #328×C151C2semidirect
8. C2×#14559005C4semidirect
12. #18012715C4semidirect
13. #18012714C4semidirect
18. #18012697C4semidirect
128. C151#1513semidirect
134. #328D151semidirect

Maximal subgroups

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

subgroupindex
#237527252
#237521742
#237520712
#237519492
#237519472
#237519452
#328×C1512
#1513151