Finite Group Databasebeta

← C2×#1314×C151 #50316342

Subgroups — C2×#1314×C151 #50316342

Order 38656.

682 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C151C211yesmaximal, characteristic
2C2×C22⋊C16×C151C212yesmaximal, complemented
3#1314×C151C214yesmaximal, direct product factor
4C24×C4×C151C411yescharacteristic
5C23×C8×C151C411yescharacteristic
6C23×C8×C151C2211yescharacteristic
7C22×C16×C151—22no—
8C2×C22⋊C8×C151—22no—
9C2×C22⋊C8×C151—22no—
10C2×C22⋊C8×C151C412yes—
11C2×C22⋊C8×C151C2212yes—
12C22⋊C16×C151—22no—
13C22⋊C16×C151C2214yescomplemented
14C25×C151C811yescharacteristic
15C23×C4×C151—21no—
16C23×C4×C151—21no—
17C23×C4×C151—21no—
18C23×C4×C151—21no—
19C23×C4×C151—42no—
20C23×C4×C151—42no—
21C23×C4×C151C811yescharacteristic
22C23×C4×C151C812yes—
23C23×C4×C151C2×C411yescharacteristic
24C23×C4×C151C2×C412yes—
25C22×C8×C151—21no—
26C22×C8×C151—21no—
27C22×C8×C151—42no—
28C22×C8×C151—42no—
29C22×C8×C151C2×C412yes—
30C22×C8×C151C2×C411yescharacteristic
31C22×C8×C151D412yes—
32C22×C8×C151D412yes—
33C22×C8×C151C2311yescharacteristic
34C2×C16×C151—24no—
35C2×C16×C151—44no—
36C22⋊C8×C151—24no—
37C22⋊C8×C151—24no—
38C24×C151—21no—
39C24×C151—21no—
40C24×C151—22no—
41C24×C151—42no—
42C24×C151—42no—
43C24×C151C1614yescomplemented
44C24×C151C2×C811yescharacteristic
45C24×C151C2×C812yes—
46C22×C4×C151—22no—
47C22×C4×C151—22no—
48C22×C4×C151—21no—
49C22×C4×C151—21no—
50C22×C4×C151—22no—
51C22×C4×C151—22no—
52C22×C4×C151—22no—
53C22×C4×C151—22no—
54C22×C4×C151—44no—
55C22×C4×C151—44no—
56C22×C4×C151—42no—
57C22×C4×C151—42no—
58C22×C4×C151—44no—
59C22×C4×C151—42no—
60C22×C4×C151—42no—
61C22×C4×C151—42no—
62C22×C4×C151—42no—
63C22×C4×C151—42no—
64C22×C4×C151C22⋊C411yescharacteristic
65C22×C4×C151C22⋊C411yescharacteristic
66C22×C4×C151C2×C811yescharacteristic
67C22×C4×C151C2×C812yes—
68C22×C4×C151M1611yescharacteristic
69C22×C4×C151M1611yescharacteristic
70C22×C4×C151C22×C411yescharacteristic
71C2×C8×C151—24no—
72C2×C8×C151—22no—
73C2×C8×C151—41no—
74C2×C8×C151—42no—
75C2×C8×C151—41no—
76C2×C8×C151—42no—
77C2×C8×C151—42no—
78C2×C8×C151—42no—
79C2×C8×C151C22⋊C412yes—
80C2×C8×C151C2×D412yes—
81C16×C151—44no—
82C23×C151—22no—
83C23×C151—22no—
84C23×C151—24no—
85C23×C151—24no—
86C23×C151—22no—
87C23×C151—22no—
88C23×C151—48no—
89C23×C151—42no—
90C23×C151—42no—
91C23×C151—48no—
92C23×C151—42no—
93C23×C151—42no—
94C23×C151—42no—
95C23×C151—42no—
96C23×C151C22⋊C811yescharacteristic
97C23×C151C22⋊C811yescharacteristic
98C23×C151C2×C1612yes—
99C23×C151C2×C1614yescomplemented
100C23×C151M3212yes—
101C23×C151C22×C811yescharacteristic
102C2×C4×C151—22no—
103C2×C4×C151—22no—
104C2×C4×C151—22no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—22no—
110C2×C4×C151—44no—
111C2×C4×C151—44no—
112C2×C4×C151—42no—
113C2×C4×C151—42no—
114C2×C4×C151—44no—
115C2×C4×C151—42no—
116C2×C4×C151—42no—
117C2×C4×C151—42no—
118C2×C4×C151C22⋊C811yescharacteristic
119C2×C4×C151C22⋊C811yescharacteristic
120C2×C4×C151#9912yes—
121C2×C4×C151#10012yes—
122C2×C4×C151C2×C22⋊C411yescharacteristic
123C2×C4×C151C2×M1611yescharacteristic
124C8×C151—22no—
125C8×C151—22no—
126C8×C151—42no—
127C22×C151—24no—
128C22×C151—24no—
129C22×C151—21no—
130C22×C151—21no—
131C22×C151—21no—
132C22×C151—21no—
133C22×C151—24no—
134C22×C151—44no—
135C22×C151—48no—
136C22×C151—44no—
137C22×C151—48no—
138C22×C151—42no—
139C22×C151—42no—
140C22×C151#32312yes—
141C22×C151C22⋊C1612yes—
142C22×C151C22⋊C1612yes—
143C22×C151#34912yes—
144C22×C151C2×C22⋊C811yescharacteristic
145C22×C151C22×C1611yescharacteristic
146C22×C151C2×M3211yescharacteristic
147C4×C151—21no—
148C4×C151—21no—
149C4×C151—42no—
150C4×C151#32312yes—
151C4×C151C2×#9911yescharacteristic
152C4×C151C2×#10011yescharacteristic
153C2×C151—22no—
154C2×C151—21no—
155C2×C151—21no—
156C2×C151—44no—
157C2×C151#131414yesdirect product factor
158C2×C151C2×#32311yescharacteristic
159C2×C151C2×C22⋊C1611yescharacteristic
160C2×C151C2×#34911yescharacteristic
161C2×#1314C15111yesmaximal, characteristic, direct product factor, Sylow
162C151C2×#131411yescharacteristic, direct product factor, Sylow
163C22×C22⋊C8C2×C15111yescharacteristic
164C2×C22⋊C16C2×C15112yescomplemented
165#1314C2×C15114yesdirect product factor
166C24×C4C4×C15111yescharacteristic
167C23×C8C4×C15111yescharacteristic
168C23×C8C22×C15111yescharacteristic
169C22×C16—22no—
170C2×C22⋊C8—22no—
171C2×C22⋊C8—22no—
172C2×C22⋊C8C4×C15112yes—
173C2×C22⋊C8C22×C15112yes—
174C22⋊C16—22no—
175C22⋊C16C22×C15114yescomplemented
176C25C8×C15111yescharacteristic
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—42no—
182C23×C4—42no—
183C23×C4C8×C15111yescharacteristic
184C23×C4C8×C15112yes—
185C23×C4C2×C4×C15111yescharacteristic
186C23×C4C2×C4×C15112yes—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—42no—
190C22×C8—42no—
191C22×C8C2×C4×C15112yes—
192C22×C8C2×C4×C15111yescharacteristic
193C22×C8D4×C15112yes—
194C22×C8D4×C15112yes—
195C22×C8C23×C15111yescharacteristic
196C2×C16—24no—
197C2×C16—44no—
198C22⋊C8—24no—
199C22⋊C8—24no—
200C24—21no—
201C24—21no—
202C24—22no—
203C24—42no—
204C24—42no—
205C24C16×C15114yescomplemented
206C24C2×C8×C15111yescharacteristic
207C24C2×C8×C15112yes—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—44no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—44no—
220C22×C4—44no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4C22⋊C4×C15111yescharacteristic
227C22×C4C22⋊C4×C15111yescharacteristic
228C22×C4C2×C8×C15111yescharacteristic
229C22×C4C2×C8×C15112yes—
230C22×C4M16×C15111yescharacteristic
231C22×C4M16×C15111yescharacteristic
232C22×C4C22×C4×C15111yescharacteristic
233C2×C8—24no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—42no—
237C2×C8—41no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8C22⋊C4×C15112yes—
242C2×C8C2×D4×C15112yes—
243C16—44no—
244C23—22no—
245C23—22no—
246C23—24no—
247C23—24no—
248C23—22no—
249C23—22no—
250C23—42no—
251C23—48no—
252C23—42no—
253C23—42no—
254C23—48no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23C22⋊C8×C15111yescharacteristic
259C23C22⋊C8×C15111yescharacteristic
260C23C2×C16×C15112yes—
261C23C2×C16×C15114yescomplemented
262C23M32×C15112yes—
263C23C22×C8×C15111yescharacteristic
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—42no—
280C2×C4C22⋊C8×C15111yescharacteristic
281C2×C4C22⋊C8×C15111yescharacteristic
282C2×C4#99×C15112yes—
283C2×C4#100×C15112yes—
284C2×C4C2×C22⋊C4×C15111yescharacteristic
285C2×C4C2×M16×C15111yescharacteristic
286C8—22no—
287C8—22no—
288C8—42no—
289C22—24no—
290C22—24no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—24no—
296C22—44no—
297C22—48no—
298C22—44no—
299C22—48no—
300C22—42no—
301C22—42no—
302C22#323×C15112yes—
303C22C22⋊C16×C15112yes—
304C22C22⋊C16×C15112yes—
305C22#349×C15112yes—
306C22C2×C22⋊C8×C15111yescharacteristic
307C22C22×C16×C15111yescharacteristic
308C22C2×M32×C15111yescharacteristic
309C4—21no—
310C4—21no—
311C4—42no—
312C4#323×C15112yes—
313C4C2×#99×C15111yescharacteristic
314C4C2×#100×C15111yescharacteristic
315C2—22no—
316C2—21no—
317C2—21no—
318C2—44no—
319C2#1314×C15114yesdirect product factor
320C2C2×#323×C15111yescharacteristic
321C2C2×C22⋊C16×C15111yescharacteristic
322C2C2×#349×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C22⋊C4
commutatorC22C22×C16×C151
Frattini, cosocleC22×C8C23×C151
socleC23×C151C22⋊C8
prime radicalC25×C151C8
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ C23×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C16×C151C2semidirect
3. #1314×C151C2direct (N × H)
13. C22⋊C16×C151C22semidirect
43. C24×C151C16semidirect
99. C23×C151C2×C16semidirect
157. C2×C151#1314direct (N × H)
161. C2×#1314C151direct (N × H)
162. C151C2×#1314direct (N × H)
164. C2×C22⋊C16C2×C151semidirect
165. #1314C2×C151direct (N × H)
175. C22⋊C16C22×C151semidirect
205. C24C16×C151semidirect
261. C23C2×C16×C151semidirect
319. C2#1314×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C1512
C2×C22⋊C16×C1512
#1314×C1512
C2×#1314151