Finite Group Databasebeta

← C151×#18947 #50323872

Subgroups — C151×#18947 #50323872

Order 38656.

902 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3548×C151C211yesmaximal, characteristic
2#3246×C151C211yesmaximal, characteristic, complemented
3#3235×C151C211yesmaximal, characteristic, complemented
4#3231×C151C211yesmaximal, characteristic, complemented
5#1654×C151C212yesmaximal, complemented
6#1647×C151C212yesmaximal, complemented
7#1635×C151C212yesmaximal, complemented
8#1635×C151C212yesmaximal, complemented
9#1552×C151C211yesmaximal, characteristic, complemented
10#1496×C151C211yesmaximal, characteristic, complemented
11#1480×C151C211yesmaximal, characteristic, complemented
12#562×C151—22no—
13#554×C151—21no—
14#554×C151—21no—
15#550×C151—21no—
16#550×C151—21no—
17#547×C151C2212yes—
18#547×C151C2212yes—
19#540×C151—22no—
20#537×C151—22no—
21#537×C151—22no—
22#533×C151C2211yescharacteristic
23#533×C151C2211yescharacteristic
24#532×C151C2211yescharacteristic
25#532×C151C2211yescharacteristic
26#501×C151—21no—
27#500×C151C2211yescharacteristic
28#498×C151C2211yescharacteristic
29#490×C151—21no—
30#487×C151C2211yescharacteristic
31#487×C151C2211yescharacteristic
32#485×C151—22no—
33#482×C151—22no—
34#479×C151—22no—
35#476×C151C2212yes—
36#476×C151C2212yes—
37#475×C151—21no—
38#474×C151C2212yes—
39#465×C151—22no—
40#461×C151C2212yes—
41#460×C151—21no—
42#432×C151C2211yescharacteristic
43#431×C151C2211yescharacteristic
44C2×C4⋊C8×C151C2211yescharacteristic
45#332×C151C2212yes—
46#332×C151C2212yes—
47D4⋊C8×C151C2212yes—
48D4⋊C8×C151C2212yes—
49D4⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
51C2×#41×C151—22no—
52C2×#41×C151—22no—
53C2×#41×C151—21no—
54C2×#41×C151—21no—
55C2×SD16×C151—22no—
56C22×C8×C151—21no—
57C4⋊Q8×C151D411yescharacteristic
58C4⋊Q8×C151D411yescharacteristic
59C4⋊Q8×C151C2311yescharacteristic
60C4⋊Q8×C151C2311yescharacteristic
61C4⋊Q8×C151C2311yescharacteristic
62C4⋊Q8×C151C2311yescharacteristic
63#127×C151—22no—
64#127×C151D411yescharacteristic
65#127×C151D411yescharacteristic
66#125×C151—22no—
67#125×C151—21no—
68#125×C151D412yes—
69#124×C151—21no—
70#124×C151—21no—
71#123×C151—24no—
72#123×C151—24no—
73C22⋊Q8×C151—24no—
74C22⋊Q8×C151—24no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151—21no—
77C22⋊Q8×C151—22no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—21no—
81#121×C151—24no—
82#121×C151—24no—
83#121×C151—24no—
84#121×C151—24no—
85#121×C151—22no—
86#121×C151—22no—
87#121×C151—21no—
88#121×C151—21no—
89#121×C151D412yes—
90#121×C151D412yes—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×D4×C151—22no—
96C4×D4×C151—22no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151C2312yes—
100C4×D4×C151C2312yes—
101#117×C151—21no—
102#117×C151D412yes—
103C2×C4⋊C4×C151—22no—
104C2×C4⋊C4×C151—22no—
105C2×C42×C151C2311yescharacteristic
106#107×C151—22no—
107#107×C151—22no—
108#106×C151—22no—
109#106×C151—22no—
110#106×C151—22no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151C2312yes—
114C4⋊C8×C151C2312yes—
115#103×C151—22no—
116#103×C151—22no—
117#103×C151—22no—
118#102×C151—22no—
119#102×C151—22no—
120#102×C151—22no—
121C22⋊C8×C151—21no—
122C22⋊C8×C151—21no—
123#97×C151—21no—
124C4×C8×C151C2311yescharacteristic
125C4×C8×C151C2311yescharacteristic
126#41×C151—81no—
127#41×C151—82no—
128#41×C151—81no—
129#41×C151—82no—
130#41×C151—84no—
131#41×C151—82no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—21no—
138C2×D4×C151—24no—
139C2×D4×C151—24no—
140C2×D4×C151—22no—
141C2×D4×C151—22no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—21no—
146C2×D4×C151C2×D412yes—
147C2×D4×C151C2×D412yes—
148C22×C4×C151—24no—
149C22×C4×C151—24no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155SD16×C151—82no—
156C2×C8×C151—21no—
157C2×C8×C151—21no—
158C2×C8×C151—22no—
159C2×C8×C151—22no—
160C2×C8×C151—81no—
161C4⋊C4×C151—24no—
162C4⋊C4×C151—24no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—41no—
174C4⋊C4×C151—41no—
175C4⋊C4×C151C2×D412yes—
176C4⋊C4×C151C2×D412yes—
177C4⋊C4×C151C2×D412yes—
178C4⋊C4×C151C2×D412yes—
179C22⋊C4×C151—24no—
180C22⋊C4×C151—24no—
181C22⋊C4×C151—22no—
182C22⋊C4×C151—22no—
183C22⋊C4×C151—22no—
184C22⋊C4×C151—22no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—41no—
187C42×C151—22no—
188C42×C151—41no—
189C42×C151C2×D411yescharacteristic
190C42×C151C2×D411yescharacteristic
191C42×C151C2×D411yescharacteristic
192C42×C151C2411yescharacteristic
193C23×C151—22no—
194C23×C151—22no—
195C23×C151#12011yescharacteristic
196Q8×C151—42no—
197Q8×C151—41no—
198Q8×C151—42no—
199Q8×C151—41no—
200Q8×C151—41no—
201Q8×C151—41no—
202Q8×C151—81no—
203Q8×C151—81no—
204D4×C151—22no—
205D4×C151—24no—
206D4×C151—22no—
207D4×C151—42no—
208D4×C151—42no—
209D4×C151—81no—
210D4×C151—81no—
211D4×C151—82no—
212D4×C151—82no—
213D4×C151—84no—
214D4×C151—84no—
215C2×C4×C151—21no—
216C2×C4×C151—22no—
217C2×C4×C151—21no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—41no—
223C2×C4×C151—42no—
224C2×C4×C151—44no—
225C2×C4×C151—42no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—84no—
229C2×C4×C151—84no—
230C2×C4×C151#12011yescharacteristic
231C2×C4×C151#12011yescharacteristic
232C2×C4×C151#12011yescharacteristic
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C22×D411yescharacteristic
235C2×C4×C151C22×D411yescharacteristic
236C8×C151—41no—
237C8×C151—41no—
238C8×C151—42no—
239C8×C151—42no—
240C22×C151—21no—
241C22×C151—21no—
242C22×C151—21no—
243C22×C151—42no—
244C22×C151—42no—
245C22×C151—42no—
246C22×C151—42no—
247C22×C151—42no—
248C22×C151—42no—
249C22×C151C2×#12011yescharacteristic
250C4×C151—21no—
251C4×C151—21no—
252C4×C151—21no—
253C4×C151—21no—
254C4×C151—42no—
255C4×C151—42no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151—81no—
259C4×C151—81no—
260C4×C151#57611yescharacteristic
261C4×C151#57712yes—
262C4×C151#57711yescharacteristic
263C2×C151—41no—
264C2×C151—82no—
265C2×C151—82no—
266C2×C151#300911yescharacteristic
267C2×C151#301211yescharacteristic
268C2×C151#302011yescharacteristic
269#18947C15111yesmaximal, characteristic, direct product factor, Sylow
270C151#1894711yescharacteristic, direct product factor, Sylow
271#3548C2×C15111yescharacteristic
272#3246C2×C15111yescharacteristic, complemented
273#3235C2×C15111yescharacteristic, complemented
274#3231C2×C15111yescharacteristic, complemented
275#1654C2×C15112yescomplemented
276#1647C2×C15112yescomplemented
277#1635C2×C15112yescomplemented
278#1635C2×C15112yescomplemented
279#1552C2×C15111yescharacteristic, complemented
280#1496C2×C15111yescharacteristic, complemented
281#1480C2×C15111yescharacteristic, complemented
282#562—22no—
283#554—21no—
284#554—21no—
285#550—21no—
286#550—21no—
287#547C22×C15112yes—
288#547C22×C15112yes—
289#540—22no—
290#537—22no—
291#537—22no—
292#533C22×C15111yescharacteristic
293#533C22×C15111yescharacteristic
294#532C22×C15111yescharacteristic
295#532C22×C15111yescharacteristic
296#501—21no—
297#500C22×C15111yescharacteristic
298#498C22×C15111yescharacteristic
299#490—21no—
300#487C22×C15111yescharacteristic
301#487C22×C15111yescharacteristic
302#485—22no—
303#482—22no—
304#479—22no—
305#476C22×C15112yes—
306#476C22×C15112yes—
307#475—21no—
308#474C22×C15112yes—
309#465—22no—
310#461C22×C15112yes—
311#460—21no—
312#432C22×C15111yescharacteristic
313#431C22×C15111yescharacteristic
314C2×C4⋊C8C22×C15111yescharacteristic
315#332C22×C15112yes—
316#332C22×C15112yes—
317D4⋊C8C22×C15112yes—
318D4⋊C8C22×C15112yes—
319D4⋊C8C22×C15112yes—
320D4⋊C8C22×C15112yes—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—21no—
324C2×#41—21no—
325C2×SD16—22no—
326C22×C8—21no—
327C4⋊Q8D4×C15111yescharacteristic
328C4⋊Q8D4×C15111yescharacteristic
329C4⋊Q8C23×C15111yescharacteristic
330C4⋊Q8C23×C15111yescharacteristic
331C4⋊Q8C23×C15111yescharacteristic
332C4⋊Q8C23×C15111yescharacteristic
333#127—22no—
334#127D4×C15111yescharacteristic
335#127D4×C15111yescharacteristic
336#125—22no—
337#125—21no—
338#125D4×C15112yes—
339#124—21no—
340#124—21no—
341#123—24no—
342#123—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351#121—24no—
352#121—24no—
353#121—24no—
354#121—24no—
355#121—22no—
356#121—22no—
357#121—21no—
358#121—21no—
359#121D4×C15112yes—
360#121D4×C15112yes—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4C23×C15112yes—
370C4×D4C23×C15112yes—
371#117—21no—
372#117D4×C15112yes—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C42C23×C15111yescharacteristic
376#107—22no—
377#107—22no—
378#106—22no—
379#106—22no—
380#106—22no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8C23×C15112yes—
384C4⋊C8C23×C15112yes—
385#103—22no—
386#103—22no—
387#103—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393#97—21no—
394C4×C8C23×C15111yescharacteristic
395C4×C8C23×C15111yescharacteristic
396#41—81no—
397#41—82no—
398#41—81no—
399#41—82no—
400#41—84no—
401#41—82no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4C2×D4×C15112yes—
417C2×D4C2×D4×C15112yes—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4C2×D4×C15111yescharacteristic
423C22×C4C2×D4×C15111yescharacteristic
424C22×C4C2×D4×C15111yescharacteristic
425SD16—82no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—81no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4C2×D4×C15112yes—
446C4⋊C4C2×D4×C15112yes—
447C4⋊C4C2×D4×C15112yes—
448C4⋊C4C2×D4×C15112yes—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—41no—
457C42—22no—
458C42—41no—
459C42C2×D4×C15111yescharacteristic
460C42C2×D4×C15111yescharacteristic
461C42C2×D4×C15111yescharacteristic
462C42C24×C15111yescharacteristic
463C23—22no—
464C23—22no—
465C23#120×C15111yescharacteristic
466Q8—42no—
467Q8—41no—
468Q8—42no—
469Q8—41no—
470Q8—41no—
471Q8—41no—
472Q8—81no—
473Q8—81no—
474D4—22no—
475D4—24no—
476D4—22no—
477D4—42no—
478D4—42no—
479D4—81no—
480D4—81no—
481D4—82no—
482D4—82no—
483D4—84no—
484D4—84no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—84no—
499C2×C4—84no—
500C2×C4#120×C15111yescharacteristic
501C2×C4#120×C15111yescharacteristic
502C2×C4#120×C15111yescharacteristic
503C2×C4C22×D4×C15111yescharacteristic
504C2×C4C22×D4×C15111yescharacteristic
505C2×C4C22×D4×C15111yescharacteristic
506C8—41no—
507C8—41no—
508C8—42no—
509C8—42no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22C2×#120×C15111yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—81no—
529C4—81no—
530C4#576×C15111yescharacteristic
531C4#577×C15112yes—
532C4#577×C15111yescharacteristic
533C2—41no—
534C2—82no—
535C2—82no—
536C2#3009×C15111yescharacteristic
537C2#3012×C15111yescharacteristic
538C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3548×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. #3246×C151C2semidirect
3. #3235×C151C2semidirect
4. #3231×C151C2semidirect
5. #1654×C151C2semidirect
6. #1647×C151C2semidirect
7. #1635×C151C2semidirect
8. #1635×C151C2semidirect
9. #1552×C151C2semidirect
10. #1496×C151C2semidirect
11. #1480×C151C2semidirect
269. #18947C151direct (N × H)
270. C151#18947direct (N × H)
272. #3246C2×C151semidirect
273. #3235C2×C151semidirect
274. #3231C2×C151semidirect
275. #1654C2×C151semidirect
276. #1647C2×C151semidirect
277. #1635C2×C151semidirect
278. #1635C2×C151semidirect
279. #1552C2×C151semidirect
280. #1496C2×C151semidirect
281. #1480C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3548×C1512
#3246×C1512
#3235×C1512
#3231×C1512
#1654×C1512
#1647×C1512
#1635×C1512
#1552×C1512
#1496×C1512
#1480×C1512
#18947151