Finite Group Databasebeta

← C151×#24227 #50329152

Subgroups — C151×#24227 #50329152

Order 38656.

1378 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3497×C151C211yesmaximal, characteristic, complemented
2#3036×C151C212yesmaximal, complemented
3C2×#454×C151C212yesmaximal, complemented
4#2326×C151C211yesmaximal, characteristic, complemented
5#2039×C151C212yesmaximal, complemented
6#2006×C151C212yesmaximal, complemented
7#1963×C151C212yesmaximal, complemented
8#1801×C151C211yesmaximal, characteristic, complemented
9#1793×C151C212yesmaximal, complemented
10C2×2−1+4×C151C2212yes—
11C2×AGL(1,ℤ/8)×C151C2214yes—
12#550×C151—22no—
13D4×Q8×C151—22no—
14#548×C151—24no—
15#537×C151—22no—
16#537×C151C2212yes—
17#532×C151—22no—
18#532×C151C2212yes—
19C2×#124×C151C2211yescharacteristic
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22#463×C151—24no—
23#461×C151—22no—
24#459×C151—22no—
25#454×C151—28no—
26#423×C151C2212yes—
27C2×#104×C151C2214yes—
28C2×#104×C151C2214yes—
29#417×C151C2214yes—
30C2×#101×C151C2212yes—
31#391×C151C2211yescharacteristic
32#390×C151C2211yescharacteristic
33#388×C151—22no—
34#385×C151—22no—
35#384×C151C2211yescharacteristic
36#376×C151C2211yescharacteristic
37#343×C151C2212yes—
382−1+4×C151—24no—
392−1+4×C151—24no—
402−1+4×C151—44no—
41C2×#41×C151—24no—
42C2×#41×C151—24no—
43C2×#41×C151C2314yes—
44C22×Q8×C151—24no—
45C22×Q8×C151C2311yescharacteristic
46C22×D4×C151C2311yescharacteristic
47C23×C4×C151—21no—
48AGL(1,ℤ/8)×C151—28no—
49AGL(1,ℤ/8)×C151—44no—
50C2×SD16×C151—24no—
51C2×D8×C151—24no—
52C2×M16×C151C2314yes—
53C4⋊Q8×C151—22no—
54C4⋊Q8×C151D412yes—
55#127×C151—22no—
56#127×C151D412yes—
57#124×C151—24no—
58#124×C151—22no—
59#124×C151D414yes—
60#124×C151D414yescomplemented
61C22⋊Q8×C151—28no—
62C22⋊Q8×C151—24no—
63#121×C151—28no—
64#121×C151—24no—
65#121×C151—22no—
66#121×C151—24no—
67#121×C151—22no—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×D4×C151—24no—
71C4×D4×C151—24no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74C4×D4×C151—22no—
75C4×D4×C151—22no—
76C2×C4⋊C4×C151—22no—
77C2×C4⋊C4×C151D412yes—
78C2×C4⋊C4×C151C2311yescharacteristic
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—21no—
82C2×C22⋊C4×C151—22no—
83C2×C42×C151D412yes—
84C2×C42×C151C2311yescharacteristic
85C2×C42×C151C2311yescharacteristic
86C2×C42×C151C2311yescharacteristic
87C4⋊C8×C151—22no—
88C4⋊C8×C151—22no—
89#104×C151—28no—
90#104×C151—44no—
91#103×C151—24no—
92#102×C151—24no—
93#101×C151—24no—
94#95×C151—21no—
95#95×C151—21no—
96#95×C151—22no—
97C24×C151—21no—
98#41×C151—24no—
99#41×C151—24no—
100#41×C151—24no—
101#41×C151—24no—
102#41×C151—48no—
103#41×C151—48no—
104#41×C151—48no—
105#41×C151—48no—
106C2×Q8×C151—24no—
107C2×Q8×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151—48no—
110C2×Q8×C151—48no—
111C2×Q8×C151C2×D414yes—
112C2×Q8×C151C2×D412yes—
113C2×Q8×C151#4112yes—
114C2×D4×C151—24no—
115C2×D4×C151—24no—
116C2×D4×C151—24no—
117C2×D4×C151—22no—
118C2×D4×C151—22no—
119C2×D4×C151—22no—
120C2×D4×C151—21no—
121C2×D4×C151—22no—
122C2×D4×C151C2×D414yes—
123C2×D4×C151C2×D412yes—
124C22×C4×C151—28no—
125C22×C4×C151—21no—
126C22×C4×C151—24no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—42no—
130C22×C4×C151—82no—
131C22×C4×C151C2×D412yes—
132C22×C4×C151C2×D412yes—
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2411yescharacteristic
136SD16×C151—48no—
137D8×C151—48no—
138M16×C151—24no—
139M16×C151—24no—
140C2×C8×C151—24no—
141C4⋊C4×C151—24no—
142C4⋊C4×C151—24no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—82no—
148C22⋊C4×C151—28no—
149C22⋊C4×C151—24no—
150C22⋊C4×C151—24no—
151C22⋊C4×C151—28no—
152C22⋊C4×C151—41no—
153C22⋊C4×C151—41no—
154C22⋊C4×C151—82no—
155C42×C151—22no—
156C42×C151—22no—
157C42×C151—21no—
158C42×C151—22no—
159C42×C151C2×D412yes—
160C42×C151C2×D412yes—
161C42×C151C2×D412yes—
162C23×C151—24no—
163C23×C151—22no—
164C23×C151—42no—
165C23×C151—42no—
166C23×C151—41no—
167C23×C151—41no—
168C23×C151C22×D411yescharacteristic
169Q8×C151—24no—
170Q8×C151—24no—
171Q8×C151—24no—
172Q8×C151—24no—
173Q8×C151—48no—
174D4×C151—24no—
175D4×C151—24no—
176D4×C151—24no—
177D4×C151—48no—
178D4×C151—44no—
179D4×C151—44no—
180D4×C151—44no—
181D4×C151—42no—
182D4×C151—82no—
183D4×C151—84no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—24no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—41no—
190C2×C4×C151—41no—
191C2×C4×C151—416no—
192C2×C4×C151—41no—
193C2×C4×C151—41no—
194C2×C4×C151—44no—
195C2×C4×C151—44no—
196C2×C4×C151—42no—
197C2×C4×C151—41no—
198C2×C4×C151—42no—
199C2×C4×C151—41no—
200C2×C4×C151—41no—
201C2×C4×C151—41no—
202C2×C4×C151—84no—
203C2×C4×C151#12011yescharacteristic
204C2×C4×C151#12011yescharacteristic
205C2×C4×C151#12012yes—
206C2×C4×C151#12114yes—
207C2×C4×C151C22×D411yescharacteristic
208C2×C4×C151C22×D412yes—
209C2×C4×C151C2×#4111yescharacteristic
210C2×C4×C151H(5,𝔽2)12yes—
211C8×C151—44no—
212C22×C151—21no—
213C22×C151—21no—
214C22×C151—44no—
215C22×C151—44no—
216C22×C151—42no—
217C22×C151—44no—
218C22×C151—44no—
219C22×C151—82no—
220C22×C151—81no—
221C22×C151—81no—
222C22×C151C2×#12011yescharacteristic
223C22×C151C2×#12111yescharacteristic
224C22×C151#53511yescharacteristic
225C4×C151—24no—
226C4×C151—21no—
227C4×C151—21no—
228C4×C151—22no—
229C4×C151—42no—
230C4×C151—44no—
231C4×C151—42no—
232C4×C151—81no—
233C4×C151—81no—
234C4×C151D4212yes—
235C4×C151#54612yes—
236C2×C151—21no—
237C2×C151—21no—
238C2×C151—84no—
239C2×C151—82no—
240C2×C151#240811yescharacteristic
241C2×C151#302011yescharacteristic
242C2×C151#302111yescharacteristic
243#24227C15111yesmaximal, characteristic, direct product factor, Sylow
244C151#2422711yescharacteristic, direct product factor, Sylow
245#3497C2×C15111yescharacteristic, complemented
246#3036C2×C15112yescomplemented
247C2×#454C2×C15112yescomplemented
248#2326C2×C15111yescharacteristic, complemented
249#2039C2×C15112yescomplemented
250#2006C2×C15112yescomplemented
251#1963C2×C15112yescomplemented
252#1801C2×C15111yescharacteristic, complemented
253#1793C2×C15112yescomplemented
254C2×2−1+4C22×C15112yes—
255C2×AGL(1,ℤ/8)C22×C15114yes—
256#550—22no—
257D4×Q8—22no—
258#548—24no—
259#537—22no—
260#537C22×C15112yes—
261#532—22no—
262#532C22×C15112yes—
263C2×#124C22×C15111yescharacteristic
264C2×C4×Q8C22×C15111yescharacteristic
265C2×C4×D4C22×C15111yescharacteristic
266#463—24no—
267#461—22no—
268#459—22no—
269#454—28no—
270#423C22×C15112yes—
271C2×#104C22×C15114yes—
272C2×#104C22×C15114yes—
273#417C22×C15114yes—
274C2×#101C22×C15112yes—
275#391C22×C15111yescharacteristic
276#390C22×C15111yescharacteristic
277#388—22no—
278#385—22no—
279#384C22×C15111yescharacteristic
280#376C22×C15111yescharacteristic
281#343C22×C15112yes—
2822−1+4—24no—
2832−1+4—24no—
2842−1+4—44no—
285C2×#41—24no—
286C2×#41—24no—
287C2×#41C23×C15114yes—
288C22×Q8—24no—
289C22×Q8C23×C15111yescharacteristic
290C22×D4C23×C15111yescharacteristic
291C23×C4—21no—
292AGL(1,ℤ/8)—28no—
293AGL(1,ℤ/8)—44no—
294C2×SD16—24no—
295C2×D8—24no—
296C2×M16C23×C15114yes—
297C4⋊Q8—22no—
298C4⋊Q8D4×C15112yes—
299#127—22no—
300#127D4×C15112yes—
301#124—24no—
302#124—22no—
303#124D4×C15114yes—
304#124D4×C15114yescomplemented
305C22⋊Q8—28no—
306C22⋊Q8—24no—
307#121—28no—
308#121—24no—
309#121—22no—
310#121—24no—
311#121—22no—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×D4—24no—
315C4×D4—24no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4D4×C15112yes—
322C2×C4⋊C4C23×C15111yescharacteristic
323C2×C4⋊C4C23×C15111yescharacteristic
324C2×C22⋊C4—22no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—22no—
327C2×C42D4×C15112yes—
328C2×C42C23×C15111yescharacteristic
329C2×C42C23×C15111yescharacteristic
330C2×C42C23×C15111yescharacteristic
331C4⋊C8—22no—
332C4⋊C8—22no—
333#104—28no—
334#104—44no—
335#103—24no—
336#102—24no—
337#101—24no—
338#95—21no—
339#95—21no—
340#95—22no—
341C24—21no—
342#41—24no—
343#41—24no—
344#41—24no—
345#41—24no—
346#41—48no—
347#41—48no—
348#41—48no—
349#41—48no—
350C2×Q8—24no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—48no—
354C2×Q8—48no—
355C2×Q8C2×D4×C15114yes—
356C2×Q8C2×D4×C15112yes—
357C2×Q8#41×C15112yes—
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—24no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4C2×D4×C15114yes—
367C2×D4C2×D4×C15112yes—
368C22×C4—28no—
369C22×C4—21no—
370C22×C4—24no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—42no—
374C22×C4—82no—
375C22×C4C2×D4×C15112yes—
376C22×C4C2×D4×C15112yes—
377C22×C4C2×D4×C15111yescharacteristic
378C22×C4C2×D4×C15111yescharacteristic
379C22×C4C24×C15111yescharacteristic
380SD16—48no—
381D8—48no—
382M16—24no—
383M16—24no—
384C2×C8—24no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—82no—
392C22⋊C4—28no—
393C22⋊C4—24no—
394C22⋊C4—24no—
395C22⋊C4—28no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—82no—
399C42—22no—
400C42—22no—
401C42—21no—
402C42—22no—
403C42C2×D4×C15112yes—
404C42C2×D4×C15112yes—
405C42C2×D4×C15112yes—
406C23—24no—
407C23—22no—
408C23—42no—
409C23—42no—
410C23—41no—
411C23—41no—
412C23C22×D4×C15111yescharacteristic
413Q8—24no—
414Q8—24no—
415Q8—24no—
416Q8—24no—
417Q8—48no—
418D4—24no—
419D4—24no—
420D4—24no—
421D4—48no—
422D4—44no—
423D4—44no—
424D4—44no—
425D4—42no—
426D4—82no—
427D4—84no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—416no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—84no—
447C2×C4#120×C15111yescharacteristic
448C2×C4#120×C15111yescharacteristic
449C2×C4#120×C15112yes—
450C2×C4#121×C15114yes—
451C2×C4C22×D4×C15111yescharacteristic
452C2×C4C22×D4×C15112yes—
453C2×C4C2×#41×C15111yescharacteristic
454C2×C4H(5,𝔽2)×C15112yes—
455C8—44no—
456C22—21no—
457C22—21no—
458C22—44no—
459C22—44no—
460C22—42no—
461C22—44no—
462C22—44no—
463C22—82no—
464C22—81no—
465C22—81no—
466C22C2×#120×C15111yescharacteristic
467C22C2×#121×C15111yescharacteristic
468C22#535×C15111yescharacteristic
469C4—24no—
470C4—21no—
471C4—21no—
472C4—22no—
473C4—42no—
474C4—44no—
475C4—42no—
476C4—81no—
477C4—81no—
478C4D42×C15112yes—
479C4#546×C15112yes—
480C2—21no—
481C2—21no—
482C2—82no—
483C2—84no—
484C2#2408×C15111yescharacteristic
485C2#3020×C15111yescharacteristic
486C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3497×C151C2semidirect
2. #3036×C151C2semidirect
3. C2×#454×C151C2semidirect
4. #2326×C151C2semidirect
5. #2039×C151C2semidirect
6. #2006×C151C2semidirect
7. #1963×C151C2semidirect
8. #1801×C151C2semidirect
9. #1793×C151C2semidirect
60. #124×C151D4semidirect
243. #24227C151direct (N × H)
244. C151#24227direct (N × H)
245. #3497C2×C151semidirect
246. #3036C2×C151semidirect
247. C2×#454C2×C151semidirect
248. #2326C2×C151semidirect
249. #2039C2×C151semidirect
250. #2006C2×C151semidirect
251. #1963C2×C151semidirect
252. #1801C2×C151semidirect
253. #1793C2×C151semidirect
304. #124D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3497×C1512
#3036×C1512
C2×#454×C1512
#2326×C1512
#2039×C1512
#2006×C1512
#1963×C1512
#1801×C1512
#1793×C1512
#24227151