Finite Group Databasebeta

← C151×#19547 #50324472

Subgroups — C151×#19547 #50324472

Order 38656.

552 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3238×C151C211yesmaximal, characteristic
2#3233×C151C211yesmaximal, characteristic
3#3230×C151C211yesmaximal, characteristic, complemented
4#2993×C151C211yesmaximal, characteristic
5#1704×C151C211yesmaximal, characteristic, complemented
6#1703×C151C211yesmaximal, characteristic, complemented
7#1696×C151C211yesmaximal, characteristic, complemented
8#1695×C151C211yesmaximal, characteristic, complemented
9#1684×C151C211yesmaximal, characteristic, complemented
10#1683×C151C211yesmaximal, characteristic, complemented
11#1676×C151C211yesmaximal, characteristic, complemented
12#1675×C151C211yesmaximal, characteristic, complemented
13#1572×C151C211yesmaximal, characteristic, complemented
14#1559×C151C211yesmaximal, characteristic, complemented
15#1548×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17C2×C4⋊Q8×C151C2211yescharacteristic
18#529×C151C2211yescharacteristic
19#501×C151—21no—
20#500×C151C2211yescharacteristic
21#500×C151C2211yescharacteristic
22#499×C151—21no—
23#489×C151—21no—
24#488×C151—21no—
25#487×C151C2211yescharacteristic
26#487×C151C2211yescharacteristic
27#485×C151—21no—
28#484×C151—21no—
29#484×C151—21no—
30#483×C151—21no—
31#482×C151—21no—
32#480×C151—21no—
33#477×C151—21no—
34#477×C151—21no—
35#477×C151C2211yescharacteristic
36#477×C151C2211yescharacteristic
37#477×C151C2211yescharacteristic
38#476×C151C2211yescharacteristic
39#476×C151C2211yescharacteristic
40#476×C151C2211yescharacteristic
41#475×C151C2211yescharacteristic
42#474×C151C2211yescharacteristic
43#446×C151C2211yescharacteristic
44C8×Q8×C151C2211yescharacteristic
45#436×C151—21no—
46#436×C151C2211yescharacteristic
47#435×C151—21no—
48C8×D4×C151C2211yescharacteristic
49#433×C151—21no—
50#432×C151C2211yescharacteristic
51#431×C151C2211yescharacteristic
52#431×C151C2211yescharacteristic
53#424×C151—21no—
54#423×C151C2211yescharacteristic
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#333×C151C2211yescharacteristic
62#333×C151C2211yescharacteristic
63#333×C151C2211yescharacteristic
64#333×C151C2211yescharacteristic
65#332×C151C2211yescharacteristic
66#332×C151C2211yescharacteristic
67C22×Q8×C151—21no—
68C2×M16×C151—21no—
69C2×M16×C151—21no—
70C22×C8×C151—21no—
71C4⋊Q8×C151—21no—
72C4⋊Q8×C151—21no—
73C4⋊Q8×C151—21no—
74C4⋊Q8×C151C2311yescharacteristic
75C4⋊Q8×C151C2311yescharacteristic
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78#126×C151—21no—
79#125×C151—21no—
80#125×C151D411yescharacteristic
81#124×C151D411yescharacteristic
82#123×C151—21no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151D411yescharacteristic
86#121×C151D411yescharacteristic
87C4×Q8×C151—21no—
88C4×Q8×C151—21no—
89C4×Q8×C151C2311yescharacteristic
90C4×D4×C151—21no—
91C4×D4×C151C2311yescharacteristic
92#117×C151—21no—
93#117×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C42×C151C2311yescharacteristic
97#107×C151—21no—
98#107×C151—21no—
99#107×C151—21no—
100#107×C151—21no—
101#107×C151—21no—
102#107×C151—21no—
103#107×C151—21no—
104#107×C151—21no—
105#106×C151—21no—
106#106×C151—21no—
107#106×C151—21no—
108#106×C151—21no—
109C4⋊C8×C151—21no—
110C4⋊C8×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151D411yescharacteristic
113C4⋊C8×C151D411yescharacteristic
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—21no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132C22⋊C8×C151—21no—
133C22⋊C8×C151—21no—
134C22⋊C8×C151—21no—
135C22⋊C8×C151—21no—
136C22⋊C8×C151D411yescharacteristic
137C22⋊C8×C151D411yescharacteristic
138#97×C151—21no—
139#97×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—41no—
149C2×Q8×C151—82no—
150C2×Q8×C151C2×D411yescharacteristic
151C2×D4×C151—21no—
152C2×D4×C151C2×D411yescharacteristic
153C22×C4×C151—21no—
154C22×C4×C151—41no—
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151#4111yescharacteristic
158M16×C151—81no—
159M16×C151—81no—
160C2×C8×C151—21no—
161C2×C8×C151—21no—
162C2×C8×C151—21no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—81no—
167C2×C8×C151C2×D411yescharacteristic
168C2×C8×C151C2×D411yescharacteristic
169C2×C8×C151C2×D411yescharacteristic
170C2×C8×C151C2×D411yescharacteristic
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—41no—
184C4⋊C4×C151—41no—
185C4⋊C4×C151—41no—
186C4⋊C4×C151—41no—
187C4⋊C4×C151C2×D411yescharacteristic
188C4⋊C4×C151C2×D411yescharacteristic
189C22⋊C4×C151—21no—
190C22⋊C4×C151—21no—
191C22⋊C4×C151—21no—
192C22⋊C4×C151—21no—
193C22⋊C4×C151—21no—
194C22⋊C4×C151—41no—
195C42×C151—21no—
196C42×C151—41no—
197C42×C151C2×D411yescharacteristic
198C42×C151C2×D411yescharacteristic
199C42×C151#4111yescharacteristic
200C42×C151C2411yescharacteristic
201C23×C151—21no—
202C23×C151#12111yescharacteristic
203Q8×C151—21no—
204Q8×C151—21no—
205Q8×C151—41no—
206Q8×C151—41no—
207Q8×C151—81no—
208Q8×C151—81no—
209Q8×C151—81no—
210Q8×C151—82no—
211D4×C151—21no—
212D4×C151—21no—
213D4×C151—81no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—41no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—82no—
229C2×C4×C151#12111yescharacteristic
230C2×C4×C151#12111yescharacteristic
231C2×C4×C151#12111yescharacteristic
232C2×C4×C151C22×D411yescharacteristic
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C2×#4111yescharacteristic
235C8×C151—21no—
236C8×C151—21no—
237C8×C151—21no—
238C8×C151—21no—
239C8×C151—41no—
240C8×C151—41no—
241C8×C151—41no—
242C8×C151—41no—
243C8×C151—41no—
244C8×C151—41no—
245C22×C151—21no—
246C22×C151—21no—
247C22×C151—21no—
248C22×C151—41no—
249C22×C151—41no—
250C22×C151—41no—
251C22×C151C2×#12111yescharacteristic
252C4×C151—21no—
253C4×C151—21no—
254C4×C151—21no—
255C4×C151—21no—
256C4×C151—41no—
257C4×C151—41no—
258C4×C151—41no—
259C4×C151—81no—
260C4×C151—81no—
261C4×C151—81no—
262C4×C151—81no—
263C4×C151#57711yescharacteristic
264C4×C151#57811yescharacteristic
265C4×C151#57811yescharacteristic
266C4×C151#57811yescharacteristic
267C2×C151—41no—
268C2×C151—81no—
269C2×C151#304611yescharacteristic
270C2×C151#305911yescharacteristic
271C2×C151#306811yescharacteristic
272#19547C15111yesmaximal, characteristic, direct product factor, Sylow
273C151#1954711yescharacteristic, direct product factor, Sylow
274#3238C2×C15111yescharacteristic
275#3233C2×C15111yescharacteristic
276#3230C2×C15111yescharacteristic, complemented
277#2993C2×C15111yescharacteristic
278#1704C2×C15111yescharacteristic, complemented
279#1703C2×C15111yescharacteristic, complemented
280#1696C2×C15111yescharacteristic, complemented
281#1695C2×C15111yescharacteristic, complemented
282#1684C2×C15111yescharacteristic, complemented
283#1683C2×C15111yescharacteristic, complemented
284#1676C2×C15111yescharacteristic, complemented
285#1675C2×C15111yescharacteristic, complemented
286#1572C2×C15111yescharacteristic, complemented
287#1559C2×C15111yescharacteristic, complemented
288#1548C2×C15111yescharacteristic, complemented
289#533C22×C15111yescharacteristic
290C2×C4⋊Q8C22×C15111yescharacteristic
291#529C22×C15111yescharacteristic
292#501—21no—
293#500C22×C15111yescharacteristic
294#500C22×C15111yescharacteristic
295#499—21no—
296#489—21no—
297#488—21no—
298#487C22×C15111yescharacteristic
299#487C22×C15111yescharacteristic
300#485—21no—
301#484—21no—
302#484—21no—
303#483—21no—
304#482—21no—
305#480—21no—
306#477—21no—
307#477—21no—
308#477C22×C15111yescharacteristic
309#477C22×C15111yescharacteristic
310#477C22×C15111yescharacteristic
311#476C22×C15111yescharacteristic
312#476C22×C15111yescharacteristic
313#476C22×C15111yescharacteristic
314#475C22×C15111yescharacteristic
315#474C22×C15111yescharacteristic
316#446C22×C15111yescharacteristic
317C8×Q8C22×C15111yescharacteristic
318#436—21no—
319#436C22×C15111yescharacteristic
320#435—21no—
321C8×D4C22×C15111yescharacteristic
322#433—21no—
323#432C22×C15111yescharacteristic
324#431C22×C15111yescharacteristic
325#431C22×C15111yescharacteristic
326#424—21no—
327#423C22×C15111yescharacteristic
328#335C22×C15111yescharacteristic
329#335C22×C15111yescharacteristic
330#334C22×C15111yescharacteristic
331#334C22×C15111yescharacteristic
332#333C22×C15111yescharacteristic
333#333C22×C15111yescharacteristic
334#333C22×C15111yescharacteristic
335#333C22×C15111yescharacteristic
336#333C22×C15111yescharacteristic
337#333C22×C15111yescharacteristic
338#332C22×C15111yescharacteristic
339#332C22×C15111yescharacteristic
340C22×Q8—21no—
341C2×M16—21no—
342C2×M16—21no—
343C22×C8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8C23×C15111yescharacteristic
348C4⋊Q8C23×C15111yescharacteristic
349C4⋊Q8C23×C15111yescharacteristic
350C4⋊Q8C23×C15111yescharacteristic
351#126—21no—
352#125—21no—
353#125D4×C15111yescharacteristic
354#124D4×C15111yescharacteristic
355#123—21no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8D4×C15111yescharacteristic
359#121D4×C15111yescharacteristic
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8C23×C15111yescharacteristic
363C4×D4—21no—
364C4×D4C23×C15111yescharacteristic
365#117—21no—
366#117—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C42C23×C15111yescharacteristic
370#107—21no—
371#107—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#106—21no—
379#106—21no—
380#106—21no—
381#106—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8D4×C15111yescharacteristic
386C4⋊C8D4×C15111yescharacteristic
387C4⋊C8C23×C15111yescharacteristic
388C4⋊C8C23×C15111yescharacteristic
389C4⋊C8C23×C15111yescharacteristic
390C4⋊C8C23×C15111yescharacteristic
391C4⋊C8C23×C15111yescharacteristic
392C4⋊C8C23×C15111yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#102—21no—
402#102—21no—
403#102—21no—
404#102—21no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8D4×C15111yescharacteristic
410C22⋊C8D4×C15111yescharacteristic
411#97—21no—
412#97—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8C23×C15111yescharacteristic
416C4×C8C23×C15111yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—41no—
422C2×Q8—82no—
423C2×Q8C2×D4×C15111yescharacteristic
424C2×D4—21no—
425C2×D4C2×D4×C15111yescharacteristic
426C22×C4—21no—
427C22×C4—41no—
428C22×C4C2×D4×C15111yescharacteristic
429C22×C4C2×D4×C15111yescharacteristic
430C22×C4#41×C15111yescharacteristic
431M16—81no—
432M16—81no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—81no—
440C2×C8C2×D4×C15111yescharacteristic
441C2×C8C2×D4×C15111yescharacteristic
442C2×C8C2×D4×C15111yescharacteristic
443C2×C8C2×D4×C15111yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4C2×D4×C15111yescharacteristic
461C4⋊C4C2×D4×C15111yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—41no—
468C42—21no—
469C42—41no—
470C42C2×D4×C15111yescharacteristic
471C42C2×D4×C15111yescharacteristic
472C42#41×C15111yescharacteristic
473C42C24×C15111yescharacteristic
474C23—21no—
475C23#121×C15111yescharacteristic
476Q8—21no—
477Q8—21no—
478Q8—41no—
479Q8—41no—
480Q8—81no—
481Q8—81no—
482Q8—81no—
483Q8—82no—
484D4—21no—
485D4—21no—
486D4—81no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—82no—
502C2×C4#121×C15111yescharacteristic
503C2×C4#121×C15111yescharacteristic
504C2×C4#121×C15111yescharacteristic
505C2×C4C22×D4×C15111yescharacteristic
506C2×C4C22×D4×C15111yescharacteristic
507C2×C4C2×#41×C15111yescharacteristic
508C8—21no—
509C8—21no—
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—41no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22C2×#121×C15111yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4—81no—
536C4#577×C15111yescharacteristic
537C4#578×C15111yescharacteristic
538C4#578×C15111yescharacteristic
539C4#578×C15111yescharacteristic
540C2—41no—
541C2—81no—
542C2#3046×C15111yescharacteristic
543C2#3059×C15111yescharacteristic
544C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#121×C151D4
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
3. #3230×C151C2semidirect
5. #1704×C151C2semidirect
6. #1703×C151C2semidirect
7. #1696×C151C2semidirect
8. #1695×C151C2semidirect
9. #1684×C151C2semidirect
10. #1683×C151C2semidirect
11. #1676×C151C2semidirect
12. #1675×C151C2semidirect
13. #1572×C151C2semidirect
14. #1559×C151C2semidirect
15. #1548×C151C2semidirect
272. #19547C151direct (N × H)
273. C151#19547direct (N × H)
276. #3230C2×C151semidirect
278. #1704C2×C151semidirect
279. #1703C2×C151semidirect
280. #1696C2×C151semidirect
281. #1695C2×C151semidirect
282. #1684C2×C151semidirect
283. #1683C2×C151semidirect
284. #1676C2×C151semidirect
285. #1675C2×C151semidirect
286. #1572C2×C151semidirect
287. #1559C2×C151semidirect
288. #1548C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3238×C1512
#3233×C1512
#3230×C1512
#2993×C1512
#1704×C1512
#1703×C1512
#1696×C1512
#1695×C1512
#1684×C1512
#1683×C1512
#1676×C1512
#1675×C1512
#1572×C1512
#1559×C1512
#1548×C1512
#19547151