Finite Group Databasebeta

← C151×#8024 #50312949

Subgroups — C151×#8024 #50312949

Order 38656.

1014 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C151C211yesmaximal, characteristic
2#2280×C151C211yesmaximal, characteristic
3C2×#381×C151C211yesmaximal, characteristic
4#1294×C151C214yesmaximal, complemented
5C24×C4×C151C2211yescharacteristic
6C23×C8×C151—21no—
7C2×#117×C151C412yescomplemented
8C22×C22⋊C4×C151—21no—
9C2×C22⋊C8×C151—21no—
10C2×C22⋊C8×C151—22no—
11C2×C22⋊C8×C151C414yescomplemented
12C2×C22⋊C8×C151C2212yes—
13#381×C151—22no—
14#381×C151—21no—
15#381×C151C414yescomplemented
16#380×C151C412yescomplemented
17#380×C151C2212yes—
18#379×C151—21no—
19C4×C22⋊C4×C151—21no—
20C4×C22⋊C4×C151—21no—
21C2×#95×C151—21no—
22C2×#95×C151C2212yes—
23C25×C151D411yescharacteristic
24C23×C4×C151—22no—
25C23×C4×C151—44no—
26C23×C4×C151C2×C411yescharacteristic
27C23×C4×C151C2×C411yescharacteristic
28C23×C4×C151C2×C412yes—
29C23×C4×C151C2×C412yes—
30C23×C4×C151D411yescharacteristic
31C23×C4×C151D411yescharacteristic
32C23×C4×C151D412yes—
33C23×C4×C151D411yescharacteristic
34C23×C4×C151Q812yes—
35C23×C4×C151C2311yescharacteristic
36C22×C8×C151—24no—
37C22×C8×C151—22no—
38C22×C8×C151—44no—
39#117×C151—44no—
40C2×C4⋊C4×C151C2×C414yes—
41C2×C22⋊C4×C151—22no—
42C2×C22⋊C4×C151—22no—
43C2×C22⋊C4×C151—24no—
44C2×C22⋊C4×C151—22no—
45C2×C22⋊C4×C151—44no—
46C2×C42×C151—22no—
47C22⋊C8×C151—24no—
48C22⋊C8×C151—22no—
49C22⋊C8×C151C2×C414yes—
50#95×C151—24no—
51#95×C151—22no—
52#95×C151—22no—
53#95×C151—22no—
54#95×C151C2×C414yes—
55C24×C151—24no—
56C24×C151—24no—
57C24×C151—42no—
58C24×C151C22⋊C411yescharacteristic
59C24×C151C22⋊C412yes—
60C24×C151C22⋊C411yescharacteristic
61C24×C151C4⋊C412yes—
62C24×C151C2×D411yescharacteristic
63C22×C4×C151—24no—
64C22×C4×C151—24no—
65C22×C4×C151—24no—
66C22×C4×C151—24no—
67C22×C4×C151—44no—
68C22×C4×C151—44no—
69C22×C4×C151—42no—
70C22×C4×C151—44no—
71C22×C4×C151—42no—
72C22×C4×C151—42no—
73C22×C4×C151—44no—
74C22×C4×C151—42no—
75C22×C4×C151—44no—
76C22×C4×C151—44no—
77C22×C4×C151—44no—
78C22×C4×C151C4212yes—
79C22×C4×C151C4212yes—
80C22×C4×C151C22⋊C411yescharacteristic
81C22×C4×C151C22⋊C411yescharacteristic
82C22×C4×C151C22⋊C412yes—
83C22×C4×C151C22⋊C412yes—
84C22×C4×C151C22⋊C412yes—
85C22×C4×C151C4⋊C412yes—
86C22×C4×C151C4⋊C412yes—
87C22×C4×C151C4⋊C412yes—
88C22×C4×C151C4⋊C412yes—
89C22×C4×C151C4⋊C412yes—
90C22×C4×C151C22×C411yescharacteristic
91C22×C4×C151C22×C411yescharacteristic
92C22×C4×C151C22×C411yescharacteristic
93C22×C4×C151C2×D411yescharacteristic
94C22×C4×C151C2×D411yescharacteristic
95C22×C4×C151C2×Q811yescharacteristic
96C2×C8×C151—24no—
97C2×C8×C151—48no—
98C2×C8×C151—44no—
99C4⋊C4×C151—44no—
100C22⋊C4×C151—44no—
101C22⋊C4×C151—48no—
102C22⋊C4×C151—44no—
103C22⋊C4×C151—44no—
104C42×C151—44no—
105C23×C151—22no—
106C23×C151—22no—
107C23×C151—22no—
108C23×C151—22no—
109C23×C151—24no—
110C23×C151—24no—
111C23×C151—22no—
112C23×C151—24no—
113C23×C151—22no—
114C23×C151—22no—
115C23×C151—24no—
116C23×C151—42no—
117C23×C151—42no—
118C23×C151—416no—
119C23×C151#9512yes—
120C23×C151#9512yes—
121C23×C151#9914yes—
122C23×C151C2×C22⋊C411yescharacteristic
123C23×C151C2×C22⋊C411yescharacteristic
124C23×C151C2×C4⋊C411yescharacteristic
125C23×C151#13514yes—
126C2×C4×C151—24no—
127C2×C4×C151—24no—
128C2×C4×C151—24no—
129C2×C4×C151—24no—
130C2×C4×C151—22no—
131C2×C4×C151—22no—
132C2×C4×C151—22no—
133C2×C4×C151—22no—
134C2×C4×C151—42no—
135C2×C4×C151—42no—
136C2×C4×C151—42no—
137C2×C4×C151—42no—
138C2×C4×C151—42no—
139C2×C4×C151—42no—
140C2×C4×C151—41no—
141C2×C4×C151—41no—
142C2×C4×C151—41no—
143C2×C4×C151—41no—
144C2×C4×C151—44no—
145C2×C4×C151—44no—
146C2×C4×C151—44no—
147C2×C4×C151—44no—
148C2×C4×C151—44no—
149C2×C4×C151—44no—
150C2×C4×C151—88no—
151C2×C4×C151#9512yes—
152C2×C4×C151#9512yes—
153C2×C4×C151C2×C4211yescharacteristic
154C2×C4×C151C2×C22⋊C411yescharacteristic
155C2×C4×C151C2×C4⋊C411yescharacteristic
156C2×C4×C151C2×C4⋊C411yescharacteristic
157C8×C151—44no—
158C22×C151—21no—
159C22×C151—22no—
160C22×C151—21no—
161C22×C151—22no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—28no—
165C22×C151—28no—
166C22×C151—22no—
167C22×C151—22no—
168C22×C151—22no—
169C22×C151—48no—
170C22×C151—48no—
171C22×C151—44no—
172C22×C151#34214yes—
173C22×C151C2×#9511yescharacteristic
174C22×C151C2×#9912yes—
175C22×C151#41612yes—
176C22×C151#41612yes—
177C22×C151#42112yes—
178C22×C151#42712yes—
179C4×C151—21no—
180C4×C151—22no—
181C4×C151—22no—
182C4×C151—21no—
183C4×C151—21no—
184C4×C151—21no—
185C4×C151—84no—
186C4×C151—84no—
187C2×C151—22no—
188C2×C151—24no—
189C2×C151—22no—
190C2×C151—42no—
191C2×C151#151614yes—
192C2×C151#173311yescharacteristic
193C2×C151#173511yescharacteristic
194C2×C151C2×#34211yescharacteristic
195#8024C15111yesmaximal, characteristic, direct product factor, Sylow
196C151#802411yescharacteristic, direct product factor, Sylow
197C22×C22⋊C8C2×C15111yescharacteristic
198#2280C2×C15111yescharacteristic
199C2×#381C2×C15111yescharacteristic
200#1294C2×C15114yescomplemented
201C24×C4C22×C15111yescharacteristic
202C23×C8—21no—
203C2×#117C4×C15112yescomplemented
204C22×C22⋊C4—21no—
205C2×C22⋊C8—21no—
206C2×C22⋊C8—22no—
207C2×C22⋊C8C4×C15114yescomplemented
208C2×C22⋊C8C22×C15112yes—
209#381—22no—
210#381—21no—
211#381C4×C15114yescomplemented
212#380C4×C15112yescomplemented
213#380C22×C15112yes—
214#379—21no—
215C4×C22⋊C4—21no—
216C4×C22⋊C4—21no—
217C2×#95—21no—
218C2×#95C22×C15112yes—
219C25D4×C15111yescharacteristic
220C23×C4—22no—
221C23×C4—44no—
222C23×C4C2×C4×C15111yescharacteristic
223C23×C4C2×C4×C15112yes—
224C23×C4C2×C4×C15111yescharacteristic
225C23×C4C2×C4×C15112yes—
226C23×C4D4×C15111yescharacteristic
227C23×C4D4×C15111yescharacteristic
228C23×C4D4×C15111yescharacteristic
229C23×C4D4×C15112yes—
230C23×C4Q8×C15112yes—
231C23×C4C23×C15111yescharacteristic
232C22×C8—24no—
233C22×C8—22no—
234C22×C8—44no—
235#117—44no—
236C2×C4⋊C4C2×C4×C15114yes—
237C2×C22⋊C4—24no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—44no—
242C2×C42—22no—
243C22⋊C8—24no—
244C22⋊C8—22no—
245C22⋊C8C2×C4×C15114yes—
246#95—24no—
247#95—22no—
248#95—22no—
249#95—22no—
250#95C2×C4×C15114yes—
251C24—24no—
252C24—24no—
253C24—42no—
254C24C22⋊C4×C15111yescharacteristic
255C24C22⋊C4×C15112yes—
256C24C22⋊C4×C15111yescharacteristic
257C24C4⋊C4×C15112yes—
258C24C2×D4×C15111yescharacteristic
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—44no—
264C22×C4—44no—
265C22×C4—42no—
266C22×C4—44no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—44no—
270C22×C4—42no—
271C22×C4—44no—
272C22×C4—44no—
273C22×C4—44no—
274C22×C4C42×C15112yes—
275C22×C4C42×C15112yes—
276C22×C4C22⋊C4×C15111yescharacteristic
277C22×C4C22⋊C4×C15111yescharacteristic
278C22×C4C22⋊C4×C15112yes—
279C22×C4C22⋊C4×C15112yes—
280C22×C4C22⋊C4×C15112yes—
281C22×C4C4⋊C4×C15112yes—
282C22×C4C4⋊C4×C15112yes—
283C22×C4C4⋊C4×C15112yes—
284C22×C4C4⋊C4×C15112yes—
285C22×C4C4⋊C4×C15112yes—
286C22×C4C22×C4×C15111yescharacteristic
287C22×C4C22×C4×C15111yescharacteristic
288C22×C4C22×C4×C15111yescharacteristic
289C22×C4C2×D4×C15111yescharacteristic
290C22×C4C2×D4×C15111yescharacteristic
291C22×C4C2×Q8×C15111yescharacteristic
292C2×C8—24no—
293C2×C8—48no—
294C2×C8—44no—
295C4⋊C4—44no—
296C22⋊C4—48no—
297C22⋊C4—44no—
298C22⋊C4—44no—
299C22⋊C4—44no—
300C42—44no—
301C23—22no—
302C23—22no—
303C23—22no—
304C23—22no—
305C23—24no—
306C23—24no—
307C23—22no—
308C23—24no—
309C23—22no—
310C23—22no—
311C23—24no—
312C23—42no—
313C23—42no—
314C23—416no—
315C23#95×C15112yes—
316C23#95×C15112yes—
317C23#99×C15114yes—
318C23C2×C22⋊C4×C15111yescharacteristic
319C23C2×C22⋊C4×C15111yescharacteristic
320C23C2×C4⋊C4×C15111yescharacteristic
321C23#135×C15114yes—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—88no—
347C2×C4#95×C15112yes—
348C2×C4#95×C15112yes—
349C2×C4C2×C42×C15111yescharacteristic
350C2×C4C2×C22⋊C4×C15111yescharacteristic
351C2×C4C2×C4⋊C4×C15111yescharacteristic
352C2×C4C2×C4⋊C4×C15111yescharacteristic
353C8—44no—
354C22—21no—
355C22—22no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—21no—
360C22—28no—
361C22—28no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—48no—
366C22—48no—
367C22—44no—
368C22#342×C15114yes—
369C22C2×#95×C15111yescharacteristic
370C22C2×#99×C15112yes—
371C22#416×C15112yes—
372C22#416×C15112yes—
373C22#421×C15112yes—
374C22#427×C15112yes—
375C4—21no—
376C4—22no—
377C4—22no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—84no—
382C4—84no—
383C2—22no—
384C2—24no—
385C2—22no—
386C2—42no—
387C2#1516×C15114yes—
388C2#1733×C15111yescharacteristic
389C2#1735×C15111yescharacteristic
390C2C2×#342×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC2×C4C2×C42×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC25×C151D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1294×C151C2semidirect
7. C2×#117×C151C4semidirect
11. C2×C22⋊C8×C151C4semidirect
15. #381×C151C4semidirect
16. #380×C151C4semidirect
195. #8024C151direct (N × H)
196. C151#8024direct (N × H)
200. #1294C2×C151semidirect
203. C2×#117C4×C151semidirect
207. C2×C22⋊C8C4×C151semidirect
211. #381C4×C151semidirect
212. #380C4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C1512
#2280×C1512
C2×#381×C1512
#1294×C1512
#8024151