Finite Group Databasebeta

← C151×#24679 #50329604

Subgroups — C151×#24679 #50329604

Order 38656.

794 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#477×C151C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C151C211yesmaximal, characteristic
3#2563×C151C211yesmaximal, characteristic
4#2355×C151C211yesmaximal, characteristic, complemented
5#2074×C151C212yesmaximal, complemented
6#2055×C151C212yesmaximal
7#1990×C151C211yesmaximal, characteristic, complemented
8#1949×C151C212yesmaximal, complemented
9#1939×C151C211yesmaximal, characteristic, complemented
10#1925×C151C212yesmaximal
11#1802×C151C211yesmaximal, characteristic
12C22×SD16×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C4×Q8×C151C2211yescharacteristic
15C2×C4×D4×C151C2211yescharacteristic
16#477×C151—24no—
17C4×SD16×C151—24no—
18C2×#107×C151C2212yes—
19C2×#106×C151C2211yescharacteristic
20C2×C4⋊C8×C151C2212yes—
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×#103×C151C2211yescharacteristic
23C2×#103×C151C2212yes—
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2212yes—
26C2×C4×C8×C151C2211yescharacteristic
27#393×C151—22no—
28#391×C151C2212yes—
29#390×C151C2212yes—
30#387×C151—22no—
31#384×C151C2211yescharacteristic
32#382×C151—21no—
33#382×C151C2212yes—
34#380×C151—21no—
35#380×C151—21no—
36C4×C4⋊C4×C151—21no—
37C4×C4⋊C4×C151C2212yes—
38C4×C4⋊C4×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151—21no—
44C22×Q8×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C2×SD16×C151—22no—
48C2×SD16×C151—22no—
49C2×SD16×C151—22no—
50C22×C8×C151C2311yescharacteristic
51C22×C8×C151C2312yes—
52C22×C8×C151C2311yescharacteristic
53C4⋊Q8×C151—22no—
54C4⋊Q8×C151—22no—
55C4×Q8×C151—22no—
56C4×Q8×C151D414yes—
57C4×D4×C151—22no—
58C4×D4×C151—22no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151D411yescharacteristic
64C2×C4⋊C4×C151D411yescharacteristic
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2312yes—
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C22⋊C4×C151—21no—
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151—22no—
72C2×C42×C151—21no—
73C2×C42×C151—22no—
74C2×C42×C151C2312yes—
75C2×C42×C151C2311yescharacteristic
76#107×C151—24no—
77#106×C151—22no—
78C4⋊C8×C151—24no—
79C4⋊C8×C151—22no—
80#103×C151—22no—
81#103×C151—24no—
82#102×C151—24no—
83#102×C151—22no—
84C4×C8×C151—22no—
85#95×C151—22no—
86#95×C151—22no—
87#95×C151—22no—
88#95×C151—22no—
89#95×C151—22no—
90#95×C151D412yes—
91C24×C151—21no—
92C2×Q8×C151—21no—
93C2×Q8×C151—21no—
94C2×Q8×C151—21no—
95C2×Q8×C151—21no—
96C2×Q8×C151—21no—
97C2×Q8×C151—42no—
98C2×Q8×C151—81no—
99C2×Q8×C151—81no—
100C2×Q8×C151C2×D412yes—
101C2×D4×C151—21no—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151—21no—
106C2×D4×C151#4112yes—
107C22×C4×C151—21no—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—42no—
113C22×C4×C151—42no—
114C22×C4×C151—42no—
115C22×C4×C151C2×D412yes—
116C22×C4×C151C2×D412yes—
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2411yescharacteristic
120SD16×C151—28no—
121C2×C8×C151—21no—
122C2×C8×C151—21no—
123C2×C8×C151—21no—
124C2×C8×C151—22no—
125C2×C8×C151—22no—
126C2×C8×C151—22no—
127C2×C8×C151—21no—
128C2×C8×C151—21no—
129C2×C8×C151#4112yes—
130C4⋊C4×C151—24no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—21no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—42no—
141C4⋊C4×C151—42no—
142C4⋊C4×C151—81no—
143C4⋊C4×C151C2×D412yes—
144C22⋊C4×C151—42no—
145C22⋊C4×C151—82no—
146C22⋊C4×C151—82no—
147C42×C151—24no—
148C42×C151—22no—
149C42×C151—22no—
150C42×C151—82no—
151C42×C151C2×D412yes—
152C42×C151#4112yes—
153C23×C151—22no—
154C23×C151—41no—
155C23×C151—41no—
156C23×C151—41no—
157C23×C151—41no—
158C23×C151—41no—
159C23×C151—41no—
160C23×C151C22×D411yescharacteristic
161Q8×C151—22no—
162Q8×C151—22no—
163Q8×C151—41no—
164Q8×C151—41no—
165Q8×C151—84no—
166D4×C151—22no—
167D4×C151—22no—
168D4×C151—41no—
169D4×C151—41no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—41no—
181C2×C4×C151—41no—
182C2×C4×C151—41no—
183C2×C4×C151—41no—
184C2×C4×C151—42no—
185C2×C4×C151—41no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—41no—
189C2×C4×C151—41no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—84no—
194C2×C4×C151#12112yes—
195C2×C4×C151#12112yes—
196C2×C4×C151#13512yes—
197C2×C4×C151#13712yes—
198C2×C4×C151C22×D411yescharacteristic
199C2×C4×C151C2×#4111yescharacteristic
200C2×C4×C151C2×#4111yescharacteristic
201C2×C4×C151C2×#4111yescharacteristic
202C2×C4×C1512−1+411yescharacteristic
203C2×C4×C1512−1+411yescharacteristic
204C8×C151—22no—
205C8×C151—42no—
206C8×C151—41no—
207C22×C151—42no—
208C22×C151—42no—
209C22×C151—42no—
210C22×C151—81no—
211C22×C151—81no—
212C22×C151—81no—
213C22×C151—81no—
214C22×C151C2×#12111yescharacteristic
215C22×C151#54711yescharacteristic
216C22×C151#54811yescharacteristic
217C22×C151C2×#13511yescharacteristic
218C22×C151C2×#13711yescharacteristic
219C22×C151#57611yescharacteristic
220C22×C151#57711yescharacteristic
221C4×C151—22no—
222C4×C151—42no—
223C4×C151—42no—
224C4×C151—42no—
225C4×C151—42no—
226C4×C151—82no—
227C4×C151—81no—
228C4×C151—82no—
229C4×C151#46414yes—
230C4×C151#52511yescharacteristic
231C4×C151#53611yescharacteristic
232C4×C151#55211yescharacteristic
233C4×C151#55611yescharacteristic
234C2×C151—82no—
235C2×C151#241511yescharacteristic
236C2×C151C2×#46411yescharacteristic
237C2×C151#304511yescharacteristic
238C2×C151#334011yescharacteristic
239C2×C151#335711yescharacteristic
240C2×C151#336111yescharacteristic
241C2×C151#337211yescharacteristic
242#24679C15111yesmaximal, characteristic, direct product factor, Sylow
243C151#2467911yescharacteristic, direct product factor, Sylow
244C2×#477C2×C15111yescharacteristic, complemented
245C2×C4×SD16C2×C15111yescharacteristic
246#2563C2×C15111yescharacteristic
247#2355C2×C15111yescharacteristic, complemented
248#2074C2×C15112yescomplemented
249#2055C2×C15112yes—
250#1990C2×C15111yescharacteristic, complemented
251#1949C2×C15112yescomplemented
252#1939C2×C15111yescharacteristic, complemented
253#1925C2×C15112yes—
254#1802C2×C15111yescharacteristic
255C22×SD16C22×C15111yescharacteristic
256C2×C4⋊Q8C22×C15111yescharacteristic
257C2×C4×Q8C22×C15111yescharacteristic
258C2×C4×D4C22×C15111yescharacteristic
259#477—24no—
260C4×SD16—24no—
261C2×#107C22×C15112yes—
262C2×#106C22×C15111yescharacteristic
263C2×C4⋊C8C22×C15111yescharacteristic
264C2×C4⋊C8C22×C15112yes—
265C2×#103C22×C15112yes—
266C2×#103C22×C15111yescharacteristic
267C2×#102C22×C15112yes—
268C2×#102C22×C15111yescharacteristic
269C2×C4×C8C22×C15111yescharacteristic
270#393—22no—
271#391C22×C15112yes—
272#390C22×C15112yes—
273#387—22no—
274#384C22×C15111yescharacteristic
275#382—21no—
276#382C22×C15112yes—
277#380—21no—
278#380—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4C22×C15112yes—
281C4×C4⋊C4C22×C15111yescharacteristic
282#340C22×C15112yes—
283#340C22×C15112yes—
284#340C22×C15112yes—
285#336C22×C15112yes—
286C22×Q8—21no—
287C22×Q8C23×C15111yescharacteristic
288C22×D4C23×C15111yescharacteristic
289C23×C4—21no—
290C2×SD16—22no—
291C2×SD16—22no—
292C2×SD16—22no—
293C22×C8C23×C15111yescharacteristic
294C22×C8C23×C15112yes—
295C22×C8C23×C15111yescharacteristic
296C4⋊Q8—22no—
297C4⋊Q8—22no—
298C4×Q8—22no—
299C4×Q8D4×C15114yes—
300C4×D4—22no—
301C4×D4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4D4×C15111yescharacteristic
307C2×C4⋊C4D4×C15111yescharacteristic
308C2×C4⋊C4C23×C15111yescharacteristic
309C2×C4⋊C4C23×C15112yes—
310C2×C4⋊C4C23×C15112yes—
311C2×C4⋊C4C23×C15111yescharacteristic
312C2×C22⋊C4—21no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C42—21no—
316C2×C42—22no—
317C2×C42C23×C15112yes—
318C2×C42C23×C15111yescharacteristic
319#107—24no—
320#106—22no—
321C4⋊C8—24no—
322C4⋊C8—22no—
323#103—22no—
324#103—24no—
325#102—24no—
326#102—22no—
327C4×C8—22no—
328#95—22no—
329#95—22no—
330#95—22no—
331#95—22no—
332#95—22no—
333#95D4×C15112yes—
334C24—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C2×Q8—81no—
342C2×Q8—81no—
343C2×Q8C2×D4×C15112yes—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4#41×C15112yes—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4C2×D4×C15112yes—
359C22×C4C2×D4×C15112yes—
360C22×C4C2×D4×C15111yescharacteristic
361C22×C4C2×D4×C15111yescharacteristic
362C22×C4C24×C15111yescharacteristic
363SD16—28no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8#41×C15112yes—
373C4⋊C4—24no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—81no—
386C4⋊C4C2×D4×C15112yes—
387C22⋊C4—42no—
388C22⋊C4—82no—
389C22⋊C4—82no—
390C42—24no—
391C42—22no—
392C42—22no—
393C42—82no—
394C42C2×D4×C15112yes—
395C42#41×C15112yes—
396C23—22no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23C22×D4×C15111yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—84no—
409D4—22no—
410D4—22no—
411D4—41no—
412D4—41no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—84no—
437C2×C4#121×C15112yes—
438C2×C4#121×C15112yes—
439C2×C4#135×C15112yes—
440C2×C4#137×C15112yes—
441C2×C4C22×D4×C15111yescharacteristic
442C2×C4C2×#41×C15111yescharacteristic
443C2×C4C2×#41×C15111yescharacteristic
444C2×C4C2×#41×C15111yescharacteristic
445C2×C42−1+4×C15111yescharacteristic
446C2×C42−1+4×C15111yescharacteristic
447C8—22no—
448C8—42no—
449C8—41no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22C2×#121×C15111yescharacteristic
458C22#547×C15111yescharacteristic
459C22#548×C15111yescharacteristic
460C22C2×#135×C15111yescharacteristic
461C22C2×#137×C15111yescharacteristic
462C22#576×C15111yescharacteristic
463C22#577×C15111yescharacteristic
464C4—22no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4—81no—
471C4—82no—
472C4#464×C15114yes—
473C4#525×C15111yescharacteristic
474C4#536×C15111yescharacteristic
475C4#552×C15111yescharacteristic
476C4#556×C15111yescharacteristic
477C2—82no—
478C2#2415×C15111yescharacteristic
479C2C2×#464×C15111yescharacteristic
480C2#3045×C15111yescharacteristic
481C2#3340×C15111yescharacteristic
482C2#3357×C15111yescharacteristic
483C2#3361×C15111yescharacteristic
484C2#3372×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#477×C151C2semidirect
4. #2355×C151C2semidirect
5. #2074×C151C2semidirect
7. #1990×C151C2semidirect
8. #1949×C151C2semidirect
9. #1939×C151C2semidirect
242. #24679C151direct (N × H)
243. C151#24679direct (N × H)
244. C2×#477C2×C151semidirect
247. #2355C2×C151semidirect
248. #2074C2×C151semidirect
250. #1990C2×C151semidirect
251. #1949C2×C151semidirect
252. #1939C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#477×C1512
C2×C4×SD16×C1512
#2563×C1512
#2355×C1512
#2074×C1512
#2055×C1512
#1990×C1512
#1949×C1512
#1939×C1512
#1925×C1512
#1802×C1512
#24679151