Finite Group Databasebeta

← C151×#24070 #50328995

Subgroups — C151×#24070 #50328995

Order 38656.

1130 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C151C211yesmaximal, characteristic
2C2×#482×C151C212yesmaximal, complemented
3#2316×C151C211yesmaximal, characteristic, complemented
4#2059×C151C212yesmaximal, complemented
5#2041×C151C212yesmaximal, complemented
6#1874×C151C212yesmaximal, complemented
7#1864×C151C212yesmaximal, complemented
8#1862×C151C212yesmaximal, complemented
9#1818×C151C211yesmaximal, characteristic, complemented
10#540×C151—28no—
11C2×#127×C151C2211yescharacteristic
12C2×#125×C151C2211yescharacteristic
13C2×#123×C151—22no—
14C2×#121×C151—22no—
15C2×#121×C151C2212yes—
16C2×C4×D4×C151C2212yes—
17C2×#117×C151C2211yescharacteristic
18C2×#117×C151C2211yescharacteristic
19C22×C4⋊C4×C151C2211yescharacteristic
20#482×C151—28no—
21C2×#107×C151C2212yes—
22C2×#106×C151C2212yes—
23C2×#102×C151C2212yes—
24C2×#102×C151C2212yes—
25C2×#102×C151C2212yes—
26C2×#102×C151C2212yes—
27C2×C22⋊C8×C151C2212yes—
28#389×C151—22no—
29#389×C151C2212yes—
30#389×C151C2212yes—
31#380×C151—22no—
32#340×C151C2212yes—
33#340×C151C2212yes—
34#336×C151C2211yescharacteristic
35#336×C151C2211yescharacteristic
36#336×C151C2212yes—
37C22×D4×C151—22no—
38C22×D4×C151—22no—
39C22×D4×C151C2312yes—
40C23×C4×C151—22no—
41C23×C4×C151—21no—
42C23×C4×C151C2311yescharacteristic
43C22×C8×C151C2312yes—
44C22×C8×C151C2312yes—
45#127×C151—24no—
46#125×C151—24no—
47#123×C151—216no—
48#121×C151—216no—
49#121×C151—24no—
50#121×C151D418yes—
51C4×D4×C151—24no—
52C4×D4×C151—24no—
53#117×C151—24no—
54#117×C151—24no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151D412yes—
61C2×C4⋊C4×C151C2312yes—
62C2×C4⋊C4×C151C2312yes—
63C2×C4⋊C4×C151C2312yes—
64C2×C22⋊C4×C151—22no—
65C2×C22⋊C4×C151—22no—
66C2×C22⋊C4×C151—21no—
67C2×C22⋊C4×C151D412yes—
68C2×C42×C151—21no—
69C2×C42×C151C2311yescharacteristic
70C2×C42×C151C2311yescharacteristic
71#107×C151—24no—
72#106×C151—24no—
73#102×C151—24no—
74#102×C151—24no—
75#102×C151—24no—
76#102×C151—24no—
77C22⋊C8×C151—24no—
78#95×C151—22no—
79#95×C151—22no—
80C24×C151—22no—
81C24×C151C2×D411yescharacteristic
82C2×D4×C151—28no—
83C2×D4×C151—28no—
84C2×D4×C151—22no—
85C2×D4×C151—22no—
86C2×D4×C151—22no—
87C2×D4×C151—22no—
88C2×D4×C151—22no—
89C2×D4×C151—82no—
90C2×D4×C151—82no—
91C2×D4×C151—82no—
92C2×D4×C151—82no—
93C2×D4×C151C2×D414yes—
94C22×C4×C151—22no—
95C22×C4×C151—21no—
96C22×C4×C151—21no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—24no—
100C22×C4×C151—28no—
101C22×C4×C151—22no—
102C22×C4×C151—82no—
103C22×C4×C151—82no—
104C22×C4×C151—82no—
105C22×C4×C151C2×D412yes—
106C22×C4×C151C2×D412yes—
107C22×C4×C151C2×D411yescharacteristic
108C22×C4×C151C2×D414yes—
109C22×C4×C151C2411yescharacteristic
110C2×C8×C151—22no—
111C2×C8×C151—22no—
112C2×C8×C151—22no—
113C2×C8×C151—22no—
114C2×C8×C151—22no—
115C2×C8×C151—22no—
116C4⋊C4×C151—24no—
117C4⋊C4×C151—28no—
118C4⋊C4×C151—24no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—22no—
121C4⋊C4×C151—22no—
122C4⋊C4×C151—22no—
123C4⋊C4×C151—82no—
124C4⋊C4×C151—82no—
125C4⋊C4×C151C2×D414yes—
126C4⋊C4×C151#4114yes—
127C22⋊C4×C151—28no—
128C22⋊C4×C151—24no—
129C22⋊C4×C151—28no—
130C22⋊C4×C151—42no—
131C42×C151—22no—
132C42×C151—22no—
133C42×C151—42no—
134C23×C151—21no—
135C23×C151—21no—
136C23×C151—22no—
137C23×C151—22no—
138C23×C151—24no—
139C23×C151—42no—
140C23×C151—42no—
141C23×C151—42no—
142C23×C151—42no—
143C23×C151—42no—
144C23×C151—42no—
145C23×C151#12012yes—
146C23×C151C22×D411yescharacteristic
147D4×C151—24no—
148D4×C151—24no—
149D4×C151—42no—
150D4×C151—42no—
151D4×C151—88no—
152D4×C151—88no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—24no—
156C2×C4×C151—24no—
157C2×C4×C151—22no—
158C2×C4×C151—22no—
159C2×C4×C151—24no—
160C2×C4×C151—24no—
161C2×C4×C151—22no—
162C2×C4×C151—22no—
163C2×C4×C151—22no—
164C2×C4×C151—22no—
165C2×C4×C151—42no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—42no—
169C2×C4×C151—42no—
170C2×C4×C151—42no—
171C2×C4×C151—42no—
172C2×C4×C151—84no—
173C2×C4×C151—88no—
174C2×C4×C151#12012yes—
175C2×C4×C151C22×D412yes—
176C2×C4×C151C2×#4112yes—
177C2×C4×C1512−1+411yescharacteristic
178C2×C4×C1512−1+411yescharacteristic
179C8×C151—42no—
180C8×C151—42no—
181C22×C151—22no—
182C22×C151—24no—
183C22×C151—41no—
184C22×C151—41no—
185C22×C151—42no—
186C22×C151—44no—
187C22×C151—44no—
188C22×C151—44no—
189C22×C151—82no—
190C22×C151—82no—
191C22×C151—82no—
192C22×C151—82no—
193C22×C151C2×#12011yescharacteristic
194C22×C151#52511yescharacteristic
195C22×C151#53611yescharacteristic
196C22×C151#57612yes—
197C22×C151#57712yes—
198C4×C151—22no—
199C4×C151—44no—
200C4×C151—42no—
201C4×C151—42no—
202C4×C151—44no—
203C4×C151—82no—
204C4×C151#54712yes—
205C4×C151#54712yes—
206C2×C151—42no—
207C2×C151—84no—
208C2×C151#240611yescharacteristic
209C2×C151#301212yes—
210C2×C151#312211yescharacteristic
211C2×C151#312611yescharacteristic
212C2×C151#324112yes—
213#24070C15111yesmaximal, characteristic, direct product factor, Sylow
214C151#2407011yescharacteristic, direct product factor, Sylow
215C2×#540C2×C15111yescharacteristic
216C2×#482C2×C15112yescomplemented
217#2316C2×C15111yescharacteristic, complemented
218#2059C2×C15112yescomplemented
219#2041C2×C15112yescomplemented
220#1874C2×C15112yescomplemented
221#1864C2×C15112yescomplemented
222#1862C2×C15112yescomplemented
223#1818C2×C15111yescharacteristic, complemented
224#540—28no—
225C2×#127C22×C15111yescharacteristic
226C2×#125C22×C15111yescharacteristic
227C2×#123—22no—
228C2×#121—22no—
229C2×#121C22×C15112yes—
230C2×C4×D4C22×C15112yes—
231C2×#117C22×C15111yescharacteristic
232C2×#117C22×C15111yescharacteristic
233C22×C4⋊C4C22×C15111yescharacteristic
234#482—28no—
235C2×#107C22×C15112yes—
236C2×#106C22×C15112yes—
237C2×#102C22×C15112yes—
238C2×#102C22×C15112yes—
239C2×#102C22×C15112yes—
240C2×#102C22×C15112yes—
241C2×C22⋊C8C22×C15112yes—
242#389—22no—
243#389C22×C15112yes—
244#389C22×C15112yes—
245#380—22no—
246#340C22×C15112yes—
247#340C22×C15112yes—
248#336C22×C15112yes—
249#336C22×C15111yescharacteristic
250#336C22×C15111yescharacteristic
251C22×D4—22no—
252C22×D4—22no—
253C22×D4C23×C15112yes—
254C23×C4—21no—
255C23×C4—22no—
256C23×C4C23×C15111yescharacteristic
257C22×C8C23×C15112yes—
258C22×C8C23×C15112yes—
259#127—24no—
260#125—24no—
261#123—216no—
262#121—216no—
263#121—24no—
264#121D4×C15118yes—
265C4×D4—24no—
266C4×D4—24no—
267#117—24no—
268#117—24no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4D4×C15112yes—
275C2×C4⋊C4C23×C15112yes—
276C2×C4⋊C4C23×C15112yes—
277C2×C4⋊C4C23×C15112yes—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4D4×C15112yes—
282C2×C42—21no—
283C2×C42C23×C15111yescharacteristic
284C2×C42C23×C15111yescharacteristic
285#107—24no—
286#106—24no—
287#102—24no—
288#102—24no—
289#102—24no—
290#102—24no—
291C22⋊C8—24no—
292#95—22no—
293#95—22no—
294C24—22no—
295C24C2×D4×C15111yescharacteristic
296C2×D4—28no—
297C2×D4—28no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—82no—
304C2×D4—82no—
305C2×D4—82no—
306C2×D4—82no—
307C2×D4C2×D4×C15114yes—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—24no—
314C22×C4—28no—
315C22×C4—22no—
316C22×C4—82no—
317C22×C4—82no—
318C22×C4—82no—
319C22×C4C2×D4×C15112yes—
320C22×C4C2×D4×C15112yes—
321C22×C4C2×D4×C15111yescharacteristic
322C22×C4C2×D4×C15114yes—
323C22×C4C24×C15111yescharacteristic
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C4⋊C4—24no—
331C4⋊C4—28no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—82no—
338C4⋊C4—82no—
339C4⋊C4C2×D4×C15114yes—
340C4⋊C4#41×C15114yes—
341C22⋊C4—28no—
342C22⋊C4—24no—
343C22⋊C4—28no—
344C22⋊C4—42no—
345C42—22no—
346C42—22no—
347C42—42no—
348C23—21no—
349C23—21no—
350C23—22no—
351C23—22no—
352C23—24no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23#120×C15112yes—
360C23C22×D4×C15111yescharacteristic
361D4—24no—
362D4—24no—
363D4—42no—
364D4—42no—
365D4—88no—
366D4—88no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—84no—
387C2×C4—88no—
388C2×C4#120×C15112yes—
389C2×C4C22×D4×C15112yes—
390C2×C4C2×#41×C15112yes—
391C2×C42−1+4×C15111yescharacteristic
392C2×C42−1+4×C15111yescharacteristic
393C8—42no—
394C8—42no—
395C22—22no—
396C22—24no—
397C22—41no—
398C22—41no—
399C22—42no—
400C22—44no—
401C22—44no—
402C22—44no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22—82no—
407C22C2×#120×C15111yescharacteristic
408C22#525×C15111yescharacteristic
409C22#536×C15111yescharacteristic
410C22#576×C15112yes—
411C22#577×C15112yes—
412C4—22no—
413C4—44no—
414C4—42no—
415C4—42no—
416C4—44no—
417C4—82no—
418C4#547×C15112yes—
419C4#547×C15112yes—
420C2—42no—
421C2—84no—
422C2#2406×C15111yescharacteristic
423C2#3012×C15112yes—
424C2#3122×C15111yescharacteristic
425C2#3126×C15111yescharacteristic
426C2#3241×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#540×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#482×C151C2semidirect
3. #2316×C151C2semidirect
4. #2059×C151C2semidirect
5. #2041×C151C2semidirect
6. #1874×C151C2semidirect
7. #1864×C151C2semidirect
8. #1862×C151C2semidirect
9. #1818×C151C2semidirect
213. #24070C151direct (N × H)
214. C151#24070direct (N × H)
216. C2×#482C2×C151semidirect
217. #2316C2×C151semidirect
218. #2059C2×C151semidirect
219. #2041C2×C151semidirect
220. #1874C2×C151semidirect
221. #1864C2×C151semidirect
222. #1862C2×C151semidirect
223. #1818C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C1512
C2×#482×C1512
#2316×C1512
#2059×C1512
#2041×C1512
#1874×C1512
#1864×C1512
#1862×C1512
#1818×C1512
#24070151