Finite Group Databasebeta

← #34070755

Subgroups — #34070755

Order 19328.

280 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752773C211yesmaximal, characteristic
2#100×D151C211yesmaximal, characteristic, complemented
3#99×D151C211yesmaximal, characteristic, complemented
4#23752002C211yesmaximal, characteristic, complemented
5#23752000C211yesmaximal, characteristic, complemented
6#23751998C211yesmaximal, characteristic, complemented
7#352×C151C211yesmaximal, characteristic, complemented
8C22×D604C411yescharacteristic, complemented
9C2×D4×D151C2211yescharacteristic
10M16×D151—21no—
11#18012724—21no—
12#18012722C411yescharacteristic, complemented
13#18012714—21no—
14#18012712—21no—
15#18012709—21no—
16#18012709C411yescharacteristic, complemented
17#18012707C2211yescharacteristic
18C22⋊C4×D151—21no—
19C22⋊C4×D151C411yescharacteristic, complemented
20#18012656C2211yescharacteristic
21#18012655—21no—
22#18012654C2211yescharacteristic
23#18012653—21no—
24#123×C151C2211yescharacteristic
25#100×C151C2211yescharacteristic
26#99×C151C2211yescharacteristic
27C23×D151C2×C411yescharacteristic
28C23×D151C2×C411yescharacteristic, complemented
29C23×D151D411yescharacteristic
30C2×D604—21no—
31C2×D604—21no—
32C2×D604—21no—
33C2×D604—41no—
34C2×D604—41no—
35C2×D604D411yescharacteristic
36C2×C22⋊D151—21no—
37C2×C22⋊D151C2×C411yescharacteristic
38C2×C22⋊D151D411yescharacteristic
39D4×D151—41no—
40D4×D151—41no—
41C2×C4×D151—21no—
42C2×C4×D151—41no—
43C2×C4×D151D411yescharacteristic
44#14558988—21no—
45#14558987—41no—
46C8×D151—41no—
47Dic151⋊C4—21no—
48C22⋊Dic151—21no—
49C22⋊Dic151C2×C411yescharacteristic, complemented
50(C2×D151)⋊C4—21no—
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—21no—
53(C2×D151)⋊C4—21no—
54(C2×D151)⋊C4—41no—
55C2×D4×C151C2311yescharacteristic
56C22×C4×C151C2×C411yescharacteristic, complemented
57M16×C151—21no—
58C4⋊C4×C151—21no—
59C22⋊C4×C151—21no—
60C22⋊C4×C151—21no—
61C22⋊C4×C151C2×C411yescharacteristic, complemented
62C22×D151—21no—
63C22×D151—21no—
64C22×D151—21no—
65C22×D151—21no—
66C22×D151—21no—
67C22×D151—41no—
68C22×D151—81no—
69C22×D151—81no—
70C22×D151—81no—
71C22×D151C22⋊C411yescharacteristic
72C22×D151C22⋊C411yescharacteristic
73C22×D151C22⋊C411yescharacteristic
74D604—41no—
75D604—42no—
76D604—41no—
77D604—41no—
78D604—81no—
79C22⋊D151—41no—
80C22⋊D151—41no—
81C22⋊D151—81no—
82C2×Dic151—21no—
83C2×Dic151—41no—
84C2×Dic151C22⋊C411yescharacteristic
85C4×D151—21no—
86C4×D151—21no—
87C4×D151—81no—
88C4×D151—82no—
89C151⋊C8—41no—
90C23×C151C22×C411yescharacteristic
91C23×C151C2×D411yescharacteristic
92D4×C151—41no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—41no—
96C2×C4×C151—41no—
97C2×C4×C151C2×D411yescharacteristic
98C8×C151—41no—
99C22×C151—21no—
100C22×C151—21no—
101C22×C151—41no—
102C22×C151—41no—
103C22×C151C2×C22⋊C411yescharacteristic
104C2×D151—21no—
105C2×D151—21no—
106C2×D151—41no—
107C2×D151—42no—
108C2×D151—41no—
109C2×D151—41no—
110C2×D151—41no—
111C2×D151—41no—
112C2×D151—41no—
113C2×D151—81no—
114C2×D151—81no—
115C2×D151—81no—
116C2×D151—82no—
117C2×D151#9911yescharacteristic
118C2×D151#9911yescharacteristic
119C4×C151—21no—
120C4×C151—41no—
121C4×C151—41no—
122C4×C151—81no—
123Dic151—21no—
124Dic151—41no—
125Dic151—81no—
126C2×C151—21no—
127C2×C151—41no—
128C2×C151—41no—
129C2×C151C2×#9911yescharacteristic
130D151—21no—
131D151—21no—
132D151—41no—
133D151—41no—
134D151—81no—
135C151#212111yescharacteristic, complemented, Sylow
136#2121—1511nomaximal, Sylow
137#534—1511no—
138C2×#100—1511no—
139C2×#99—1511no—
140#352—1511no—
141#352D15111yescharacteristic, complemented
142AΣL(1,𝔽16)—1511no—
143AΣL(1,𝔽16)—1511no—
144C22×D4—1511no—
145C22×D4—1511no—
146C2×M16—3021no—
147#123—3021no—
148#123—1511no—
149#123C2×D15111yescharacteristic
150#121—3021no—
151#121—3021no—
152#120—3021no—
153#120—1511no—
154#120—1511no—
155C2×C22⋊C4—3021no—
156C2×C22⋊C4—1511no—
157#100—3021no—
158#100—1511no—
159#100C2×D15111yescharacteristic
160#99—3021no—
161#99—1511no—
162#99C2×D15111yescharacteristic
163C24—1511no—
164C24—1511no—
165C24—1511no—
166C2×D4—3021no—
167C2×D4—3021no—
168C2×D4—3021no—
169C2×D4—3021no—
170C2×D4—6041no—
171C2×D4—6041no—
172C2×D4—6041no—
173C2×D4—6041no—
174C2×D4—1511no—
175C2×D4—1511no—
176C2×D4—1511no—
177C2×D4C22×D15111yescharacteristic
178C22×C4—3021no—
179C22×C4—6041no—
180C22×C4—1511no—
181C22×C4C4×D15111yescharacteristic, complemented
182M16—21no—
183M16—3021no—
184M16—6041no—
185C2×C8—6041no—
186C4⋊C4—21no—
187C4⋊C4—3021no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—3021no—
191C22⋊C4—3021no—
192C22⋊C4—3021no—
193C22⋊C4—3021no—
194C22⋊C4—3021no—
195C22⋊C4—6041no—
196C22⋊C4—1511no—
197C22⋊C4C4×D15111yescharacteristic, complemented
198C23—3021no—
199C23—3021no—
200C23—3021no—
201C23—3021no—
202C23—3021no—
203C23—6041no—
204C23—1511no—
205C23—1511no—
206C23—1511no—
207C23—12081no—
208C23—12081no—
209C23—12081no—
210C23C2×C4×D15111yescharacteristic
211C23D4×D15111yescharacteristic
212D4—41no—
213D4—6041no—
214D4—6042no—
215D4—6041no—
216D4—6041no—
217D4—6041no—
218D4—6041no—
219D4—12081no—
220D4—12081no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—3021no—
226C2×C4—3021no—
227C2×C4—3021no—
228C2×C4—6041no—
229C2×C4—1511no—
230C2×C4—12081no—
231C2×C4—12082no—
232C2×C4D4×D15111yescharacteristic
233C8—41no—
234C8—6041no—
235C22—21no—
236C22—21no—
237C22—41no—
238C22—41no—
239C22—3021no—
240C22—3021no—
241C22—6041no—
242C22—6041no—
243C22—6041no—
244C22—6041no—
245C22—6041no—
246C22—6042no—
247C22—6041no—
248C22—1511no—
249C22—1511no—
250C22—12081no—
251C22—12081no—
252C22—12081no—
253C22—12082no—
254C22C22⋊C4×D15111yescharacteristic
255C4—21no—
256C4—41no—
257C4—41no—
258C4—81no—
259C4—3021no—
260C4—6041no—
261C4—12081no—
262C2—21no—
263C2—41no—
264C2—41no—
265C2—3021no—
266C2—3021no—
267C2—6041no—
268C2—6041no—
269C2—12081no—
270C2#99×D15111yescharacteristic
subgroupG/H
centerC2#99×D151
commutatorC23×C151C22×C4
FrattiniC2×D4C22×D151
Fitting#352×C151C2
socleC2×C151C2×#99
prime radical#23752773C2
cosocleC2×D4×C151C23
hypercenter#352D151
hypocenterC151#2121
LCSG ▷ C23×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #100×D151C2semidirect
3. #99×D151C2semidirect
4. #23752002C2semidirect
5. #23752000C2semidirect
6. #23751998C2semidirect
7. #352×C151C2semidirect
8. C22×D604C4semidirect
12. #18012722C4semidirect
16. #18012709C4semidirect
19. C22⋊C4×D151C4semidirect
28. C23×D151C2×C4semidirect
49. C22⋊Dic151C2×C4semidirect
56. C22×C4×C151C2×C4semidirect
61. C22⋊C4×C151C2×C4semidirect
135. C151#2121semidirect
141. #352D151semidirect
181. C22×C4C4×D151semidirect
197. C22⋊C4C4×D151semidirect

Maximal subgroups

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

subgroupindex
#237527732
#100×D1512
#99×D1512
#237520022
#237520002
#237519982
#352×C1512
#2121151