Finite Group Databasebeta

← C151×#19237 #50324162

Subgroups — C151×#19237 #50324162

Order 38656.

674 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3245×C151C211yesmaximal, characteristic
2#3206×C151C211yesmaximal, characteristic, complemented
3#3141×C151C211yesmaximal, characteristic, complemented
4#2935×C151C211yesmaximal, characteristic, complemented
5#1701×C151C212yesmaximal, complemented
6#1699×C151C212yesmaximal, complemented
7#1681×C151C212yesmaximal, complemented
8#1679×C151C212yesmaximal, complemented
9#1565×C151C211yesmaximal, characteristic, complemented
10#1540×C151C211yesmaximal, characteristic, complemented
11C2×#332×C151C211yesmaximal, characteristic, complemented
12C2×#131×C151—21no—
13#532×C151C2211yescharacteristic
14#532×C151C2211yescharacteristic
15C2×C4⋊Q8×C151C2211yescharacteristic
16#492×C151—21no—
17#489×C151—22no—
18#487×C151—21no—
19#487×C151C2212yes—
20#486×C151C2212yes—
21#474×C151—21no—
22#474×C151C2212yes—
23#466×C151—22no—
24#461×C151C2212yes—
25#461×C151C2212yes—
26#459×C151—21no—
27#459×C151C2212yes—
28#448×C151—22no—
29#436×C151C2212yes—
30#435×C151—22no—
31C8×D4×C151C2212yes—
32#431×C151C2211yescharacteristic
33C2×C4⋊C8×C151C2211yescharacteristic
34C2×C4⋊C8×C151C2211yescharacteristic
35#417×C151—21no—
36#417×C151—21no—
37#408×C151—21no—
38C4×M16×C151C2211yescharacteristic
39#335×C151C2212yes—
40#334×C151C2212yes—
41#332×C151C2211yescharacteristic
42#332×C151C2212yes—
43#332×C151C2211yescharacteristic
44#332×C151C2212yes—
45#331×C151C2211yescharacteristic
46#331×C151C2211yescharacteristic
47C2×#41×C151—21no—
48C2×#41×C151—21no—
49C22×Q8×C151—21no—
50C2×SD16×C151—22no—
51C2×SD16×C151—22no—
52C2×D8×C151—22no—
53#131×C151—44no—
54C2×M16×C151—22no—
55C2×M16×C151D411yescharacteristic
56C2×M16×C151D411yescharacteristic
57C22×C8×C151—21no—
58C22×C8×C151—21no—
59C22×C8×C151—22no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151D411yescharacteristic
64C4⋊Q8×C151C2312yes—
65C4⋊Q8×C151C2311yescharacteristic
66#127×C151D411yescharacteristic
67#127×C151C2311yescharacteristic
68#124×C151—21no—
69#124×C151—21no—
70#121×C151—21no—
71#121×C151—21no—
72#121×C151—21no—
73#121×C151D412yes—
74C4×D4×C151—21no—
75C4×D4×C151—21no—
76C4×D4×C151—21no—
77C4×D4×C151C2312yes—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C42×C151C2311yescharacteristic
81#107×C151—22no—
82C4⋊C8×C151—21no—
83C4⋊C8×C151—21no—
84C4⋊C8×C151C2311yescharacteristic
85C4⋊C8×C151C2311yescharacteristic
86C4⋊C8×C151C2312yes—
87C4⋊C8×C151C2311yescharacteristic
88C4⋊C8×C151C2311yescharacteristic
89#103×C151—22no—
90#103×C151—22no—
91#103×C151—22no—
92#103×C151—22no—
93#102×C151—22no—
94#102×C151—22no—
95#102×C151—22no—
96#102×C151—22no—
97C22⋊C8×C151—21no—
98C22⋊C8×C151—22no—
99C22⋊C8×C151—22no—
100#97×C151D412yes—
101C4×C8×C151—21no—
102C4×C8×C151C2312yes—
103#41×C151—42no—
104#41×C151—42no—
105#41×C151—42no—
106#41×C151—42no—
107C2×Q8×C151—21no—
108C2×Q8×C151—21no—
109C2×Q8×C151—22no—
110C2×Q8×C151—41no—
111C2×Q8×C151—81no—
112C2×Q8×C151—81no—
113C2×D4×C151—22no—
114C2×D4×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151—21no—
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—41no—
120C2×D4×C151C2×D412yes—
121C22×C4×C151—22no—
122C22×C4×C151—41no—
123C22×C4×C151—41no—
124C22×C4×C151C2×D411yescharacteristic
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151#4111yescharacteristic
127SD16×C151—82no—
128SD16×C151—82no—
129D8×C151—82no—
130M16×C151—22no—
131M16×C151—22no—
132M16×C151—44no—
133C2×C8×C151—21no—
134C2×C8×C151—21no—
135C2×C8×C151—21no—
136C2×C8×C151—21no—
137C2×C8×C151—22no—
138C2×C8×C151—44no—
139C2×C8×C151—42no—
140C2×C8×C151—81no—
141C2×C8×C151C2×D412yes—
142C2×C8×C151C2×D412yes—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—41no—
149C4⋊C4×C151—41no—
150C4⋊C4×C151C2×D412yes—
151C22⋊C4×C151—22no—
152C22⋊C4×C151—22no—
153C22⋊C4×C151—41no—
154C22⋊C4×C151—41no—
155C42×C151C2×D411yescharacteristic
156C42×C151C2×D411yescharacteristic
157C42×C151#4111yescharacteristic
158C42×C151C2411yescharacteristic
159C23×C151—22no—
160C23×C151—41no—
161C23×C151#12111yescharacteristic
162Q8×C151—42no—
163Q8×C151—41no—
164Q8×C151—41no—
165Q8×C151—42no—
166Q8×C151—42no—
167Q8×C151—82no—
168D4×C151—22no—
169D4×C151—22no—
170D4×C151—44no—
171D4×C151—41no—
172D4×C151—41no—
173D4×C151—41no—
174D4×C151—41no—
175D4×C151—42no—
176D4×C151—81no—
177D4×C151—81no—
178D4×C151—82no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151—22no—
182C2×C4×C151—41no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—41no—
187C2×C4×C151—82no—
188C2×C4×C151—82no—
189C2×C4×C151#12111yescharacteristic
190C2×C4×C151#12111yescharacteristic
191C2×C4×C151#12111yescharacteristic
192C2×C4×C151#13512yes—
193C2×C4×C151AGL(1,ℤ/8)12yes—
194C2×C4×C151C22×D411yescharacteristic
195C2×C4×C151C22×D411yescharacteristic
196C2×C4×C151C2×#4111yescharacteristic
197C8×C151—22no—
198C8×C151—22no—
199C8×C151—41no—
200C8×C151—41no—
201C8×C151—42no—
202C8×C151—41no—
203C8×C151—41no—
204C22×C151—21no—
205C22×C151—21no—
206C22×C151—42no—
207C22×C151—42no—
208C22×C151—42no—
209C22×C151—81no—
210C22×C151—81no—
211C22×C151—81no—
212C22×C151#46312yes—
213C22×C151C2×#12111yescharacteristic
214C4×C151—21no—
215C4×C151—21no—
216C4×C151—21no—
217C4×C151—42no—
218C4×C151—81no—
219C4×C151—82no—
220C4×C151#46312yes—
221C4×C151C2×#13511yescharacteristic
222C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
223C4×C151#57611yescharacteristic
224C4×C151#57711yescharacteristic
225C2×C151—22no—
226C2×C151—82no—
227C2×C151—161no—
228C2×C151C2×#46311yescharacteristic
229C2×C151#306211yescharacteristic
230C2×C151#306911yescharacteristic
231#19237C15111yesmaximal, characteristic, direct product factor, Sylow
232C151#1923711yescharacteristic, direct product factor, Sylow
233#3245C2×C15111yescharacteristic
234#3206C2×C15111yescharacteristic, complemented
235#3141C2×C15111yescharacteristic, complemented
236#2935C2×C15111yescharacteristic, complemented
237#1701C2×C15112yescomplemented
238#1699C2×C15112yescomplemented
239#1681C2×C15112yescomplemented
240#1679C2×C15112yescomplemented
241#1565C2×C15111yescharacteristic, complemented
242#1540C2×C15111yescharacteristic, complemented
243C2×#332C2×C15111yescharacteristic, complemented
244C2×#131—21no—
245#532C22×C15111yescharacteristic
246#532C22×C15111yescharacteristic
247C2×C4⋊Q8C22×C15111yescharacteristic
248#492—21no—
249#489—22no—
250#487—21no—
251#487C22×C15112yes—
252#486C22×C15112yes—
253#474—21no—
254#474C22×C15112yes—
255#466—22no—
256#461C22×C15112yes—
257#461C22×C15112yes—
258#459—21no—
259#459C22×C15112yes—
260#448—22no—
261#436C22×C15112yes—
262#435—22no—
263C8×D4C22×C15112yes—
264#431C22×C15111yescharacteristic
265C2×C4⋊C8C22×C15111yescharacteristic
266C2×C4⋊C8C22×C15111yescharacteristic
267#417—21no—
268#417—21no—
269#408—21no—
270C4×M16C22×C15111yescharacteristic
271#335C22×C15112yes—
272#334C22×C15112yes—
273#332C22×C15112yes—
274#332C22×C15112yes—
275#332C22×C15111yescharacteristic
276#332C22×C15111yescharacteristic
277#331C22×C15111yescharacteristic
278#331C22×C15111yescharacteristic
279C2×#41—21no—
280C2×#41—21no—
281C22×Q8—21no—
282C2×SD16—22no—
283C2×SD16—22no—
284C2×D8—22no—
285#131—44no—
286C2×M16—22no—
287C2×M16D4×C15111yescharacteristic
288C2×M16D4×C15111yescharacteristic
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—22no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8D4×C15111yescharacteristic
296C4⋊Q8C23×C15112yes—
297C4⋊Q8C23×C15111yescharacteristic
298#127D4×C15111yescharacteristic
299#127C23×C15111yescharacteristic
300#124—21no—
301#124—21no—
302#121—21no—
303#121—21no—
304#121—21no—
305#121D4×C15112yes—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4C23×C15112yes—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C42C23×C15111yescharacteristic
313#107—22no—
314C4⋊C8—21no—
315C4⋊C8—21no—
316C4⋊C8C23×C15111yescharacteristic
317C4⋊C8C23×C15111yescharacteristic
318C4⋊C8C23×C15111yescharacteristic
319C4⋊C8C23×C15111yescharacteristic
320C4⋊C8C23×C15112yes—
321#103—22no—
322#103—22no—
323#103—22no—
324#103—22no—
325#102—22no—
326#102—22no—
327#102—22no—
328#102—22no—
329C22⋊C8—21no—
330C22⋊C8—22no—
331C22⋊C8—22no—
332#97D4×C15112yes—
333C4×C8—21no—
334C4×C8C23×C15112yes—
335#41—42no—
336#41—42no—
337#41—42no—
338#41—42no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—41no—
343C2×Q8—81no—
344C2×Q8—81no—
345C2×D4—22no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4C2×D4×C15112yes—
353C22×C4—22no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4C2×D4×C15111yescharacteristic
357C22×C4C2×D4×C15111yescharacteristic
358C22×C4#41×C15111yescharacteristic
359SD16—82no—
360SD16—82no—
361D8—82no—
362M16—22no—
363M16—22no—
364M16—44no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—44no—
371C2×C8—42no—
372C2×C8—81no—
373C2×C8C2×D4×C15112yes—
374C2×C8C2×D4×C15112yes—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4C2×D4×C15112yes—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C42C2×D4×C15111yescharacteristic
388C42C2×D4×C15111yescharacteristic
389C42#41×C15111yescharacteristic
390C42C24×C15111yescharacteristic
391C23—22no—
392C23—41no—
393C23#121×C15111yescharacteristic
394Q8—42no—
395Q8—41no—
396Q8—41no—
397Q8—42no—
398Q8—42no—
399Q8—82no—
400D4—22no—
401D4—22no—
402D4—44no—
403D4—42no—
404D4—41no—
405D4—41no—
406D4—41no—
407D4—41no—
408D4—81no—
409D4—81no—
410D4—82no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4#121×C15111yescharacteristic
422C2×C4#121×C15111yescharacteristic
423C2×C4#121×C15111yescharacteristic
424C2×C4#135×C15112yes—
425C2×C4AGL(1,ℤ/8)×C15112yes—
426C2×C4C22×D4×C15111yescharacteristic
427C2×C4C22×D4×C15111yescharacteristic
428C2×C4C2×#41×C15111yescharacteristic
429C8—22no—
430C8—22no—
431C8—41no—
432C8—41no—
433C8—42no—
434C8—41no—
435C8—41no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22#463×C15112yes—
445C22C2×#121×C15111yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—81no—
451C4—82no—
452C4#463×C15112yes—
453C4C2×#135×C15111yescharacteristic
454C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
455C4#576×C15111yescharacteristic
456C4#577×C15111yescharacteristic
457C2—22no—
458C2—82no—
459C2—161no—
460C2C2×#463×C15111yescharacteristic
461C2#3062×C15111yescharacteristic
462C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3245×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3206×C151C2semidirect
3. #3141×C151C2semidirect
4. #2935×C151C2semidirect
5. #1701×C151C2semidirect
6. #1699×C151C2semidirect
7. #1681×C151C2semidirect
8. #1679×C151C2semidirect
9. #1565×C151C2semidirect
10. #1540×C151C2semidirect
11. C2×#332×C151C2semidirect
231. #19237C151direct (N × H)
232. C151#19237direct (N × H)
234. #3206C2×C151semidirect
235. #3141C2×C151semidirect
236. #2935C2×C151semidirect
237. #1701C2×C151semidirect
238. #1699C2×C151semidirect
239. #1681C2×C151semidirect
240. #1679C2×C151semidirect
241. #1565C2×C151semidirect
242. #1540C2×C151semidirect
243. C2×#332C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3245×C1512
#3206×C1512
#3141×C1512
#2935×C1512
#1701×C1512
#1699×C1512
#1681×C1512
#1679×C1512
#1565×C1512
#1540×C1512
C2×#332×C1512
#19237151