Finite Group Databasebeta

← C151×#19575 #50324500

Subgroups — C151×#19575 #50324500

Order 38656.

568 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3249×C151C211yesmaximal, characteristic, complemented
2#3228×C151C211yesmaximal, characteristic
3#3216×C151C211yesmaximal, characteristic
4#2986×C151C211yesmaximal, characteristic, complemented
5#1702×C151C211yesmaximal, characteristic, complemented
6#1698×C151C211yesmaximal, characteristic, complemented
7#1694×C151C211yesmaximal, characteristic, complemented
8#1692×C151C211yesmaximal, characteristic, complemented
9#1682×C151C211yesmaximal, characteristic, complemented
10#1678×C151C211yesmaximal, characteristic, complemented
11#1674×C151C211yesmaximal, characteristic, complemented
12#1672×C151C211yesmaximal, characteristic, complemented
13#1573×C151C211yesmaximal, characteristic, complemented
14#1554×C151C211yesmaximal, characteristic, complemented
15#1540×C151C211yesmaximal, characteristic
16#533×C151C2211yescharacteristic
17#533×C151C2211yescharacteristic
18#532×C151C2211yescharacteristic
19#500×C151C2211yescharacteristic
20#498×C151C2211yescharacteristic
21#497×C151—21no—
22#489×C151—21no—
23#486×C151C2211yescharacteristic
24#486×C151C2211yescharacteristic
25#482×C151—21no—
26#482×C151—21no—
27#478×C151—21no—
28#478×C151—21no—
29#477×C151—21no—
30#477×C151C2211yescharacteristic
31#477×C151C2211yescharacteristic
32#467×C151—21no—
33#467×C151—21no—
34#462×C151—21no—
35#462×C151C2211yescharacteristic
36#462×C151C2211yescharacteristic
37#462×C151C2211yescharacteristic
38#462×C151C2211yescharacteristic
39#460×C151C2211yescharacteristic
40#460×C151C2211yescharacteristic
41#452×C151—21no—
42#452×C151—21no—
43#446×C151—21no—
44#446×C151C2211yescharacteristic
45#446×C151C2211yescharacteristic
46C8×Q8×C151—21no—
47C8×Q8×C151C2211yescharacteristic
48C8×Q8×C151C2211yescharacteristic
49#433×C151—21no—
50#433×C151—21no—
51#432×C151C2211yescharacteristic
52#431×C151C2211yescharacteristic
53#431×C151C2211yescharacteristic
54C2×C4⋊C8×C151C2211yescharacteristic
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62#332×C151C2211yescharacteristic
63#332×C151C2211yescharacteristic
64#332×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×Q16×C151—21no—
69C2×Q16×C151—21no—
70C2×Q16×C151—21no—
71C2×Q16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C22×C8×C151—21no—
75C4⋊Q8×C151D411yescharacteristic
76C4⋊Q8×C151D411yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80#127×C151C2311yescharacteristic
81#125×C151—21no—
82#125×C151—21no—
83#124×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151D411yescharacteristic
88C22⋊Q8×C151D411yescharacteristic
89#121×C151—21no—
90#121×C151—21no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151C2311yescharacteristic
95C4×Q8×C151C2311yescharacteristic
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98#117×C151—21no—
99#117×C151—21no—
100C2×C42×C151C2311yescharacteristic
101#107×C151—21no—
102#107×C151—21no—
103#107×C151—21no—
104#107×C151—21no—
105#106×C151—21no—
106#106×C151—21no—
107C4⋊C8×C151—21no—
108C4⋊C8×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#102×C151—21no—
127#102×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×C151D411yescharacteristic
135C22⋊C8×C151D411yescharacteristic
136#97×C151—21no—
137#97×C151—21no—
138#97×C151—21no—
139C4×C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—81no—
145#41×C151—81no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151C2×D411yescharacteristic
151C2×Q8×C151C2×D411yescharacteristic
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—41no—
156C22×C4×C151—41no—
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151#4111yescharacteristic
160Q16×C151—81no—
161Q16×C151—81no—
162Q16×C151—81no—
163Q16×C151—81no—
164SD16×C151—81no—
165SD16×C151—81no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—81no—
173C2×C8×C151C2×D411yescharacteristic
174C2×C8×C151C2×D411yescharacteristic
175C2×C8×C151C2×D411yescharacteristic
176C2×C8×C151C2×D411yescharacteristic
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—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151C2×D411yescharacteristic
193C4⋊C4×C151C2×D411yescharacteristic
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—41no—
197C22⋊C4×C151—41no—
198C22⋊C4×C151—41no—
199C42×C151—21no—
200C42×C151—21no—
201C42×C151—41no—
202C42×C151C2×D411yescharacteristic
203C42×C151C2×D411yescharacteristic
204C42×C151#4111yescharacteristic
205C42×C151C2411yescharacteristic
206C23×C151—41no—
207C23×C151#12111yescharacteristic
208Q8×C151—21no—
209Q8×C151—21no—
210Q8×C151—21no—
211Q8×C151—21no—
212Q8×C151—42no—
213Q8×C151—41no—
214Q8×C151—41no—
215Q8×C151—41no—
216Q8×C151—41no—
217Q8×C151—81no—
218D4×C151—41no—
219D4×C151—41no—
220D4×C151—41no—
221D4×C151—41no—
222D4×C151—81no—
223D4×C151—82no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—82no—
237C2×C4×C151#12111yescharacteristic
238C2×C4×C151#12111yescharacteristic
239C2×C4×C151#12111yescharacteristic
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151C2×#4111yescharacteristic
243C8×C151—21no—
244C8×C151—21no—
245C8×C151—21no—
246C8×C151—21no—
247C8×C151—41no—
248C8×C151—41no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151—41no—
252C8×C151—41no—
253C22×C151—21no—
254C22×C151—21no—
255C22×C151—21no—
256C22×C151—81no—
257C22×C151—81no—
258C22×C151—81no—
259C22×C151C2×#12111yescharacteristic
260C4×C151—21no—
261C4×C151—21no—
262C4×C151—21no—
263C4×C151—21no—
264C4×C151—41no—
265C4×C151—41no—
266C4×C151—41no—
267C4×C151—41no—
268C4×C151—81no—
269C4×C151—81no—
270C4×C151—81no—
271C4×C151#57611yescharacteristic
272C4×C151#57711yescharacteristic
273C4×C151#57811yescharacteristic
274C4×C151#57811yescharacteristic
275C2×C151—41no—
276C2×C151—161no—
277C2×C151#304411yescharacteristic
278C2×C151#306211yescharacteristic
279C2×C151#306711yescharacteristic
280#19575C15111yesmaximal, characteristic, direct product factor, Sylow
281C151#1957511yescharacteristic, direct product factor, Sylow
282#3249C2×C15111yescharacteristic, complemented
283#3228C2×C15111yescharacteristic
284#3216C2×C15111yescharacteristic
285#2986C2×C15111yescharacteristic, complemented
286#1702C2×C15111yescharacteristic, complemented
287#1698C2×C15111yescharacteristic, complemented
288#1694C2×C15111yescharacteristic, complemented
289#1692C2×C15111yescharacteristic, complemented
290#1682C2×C15111yescharacteristic, complemented
291#1678C2×C15111yescharacteristic, complemented
292#1674C2×C15111yescharacteristic, complemented
293#1672C2×C15111yescharacteristic, complemented
294#1573C2×C15111yescharacteristic, complemented
295#1554C2×C15111yescharacteristic, complemented
296#1540C2×C15111yescharacteristic
297#533C22×C15111yescharacteristic
298#533C22×C15111yescharacteristic
299#532C22×C15111yescharacteristic
300#500C22×C15111yescharacteristic
301#498C22×C15111yescharacteristic
302#497—21no—
303#489—21no—
304#486C22×C15111yescharacteristic
305#486C22×C15111yescharacteristic
306#482—21no—
307#482—21no—
308#478—21no—
309#478—21no—
310#477—21no—
311#477C22×C15111yescharacteristic
312#477C22×C15111yescharacteristic
313#467—21no—
314#467—21no—
315#462—21no—
316#462C22×C15111yescharacteristic
317#462C22×C15111yescharacteristic
318#462C22×C15111yescharacteristic
319#462C22×C15111yescharacteristic
320#460C22×C15111yescharacteristic
321#460C22×C15111yescharacteristic
322#452—21no—
323#452—21no—
324#446—21no—
325#446C22×C15111yescharacteristic
326#446C22×C15111yescharacteristic
327C8×Q8—21no—
328C8×Q8C22×C15111yescharacteristic
329C8×Q8C22×C15111yescharacteristic
330#433—21no—
331#433—21no—
332#432C22×C15111yescharacteristic
333#431C22×C15111yescharacteristic
334#431C22×C15111yescharacteristic
335C2×C4⋊C8C22×C15111yescharacteristic
336#335C22×C15111yescharacteristic
337#335C22×C15111yescharacteristic
338#334C22×C15111yescharacteristic
339#334C22×C15111yescharacteristic
340#333C22×C15111yescharacteristic
341#333C22×C15111yescharacteristic
342#332C22×C15111yescharacteristic
343#332C22×C15111yescharacteristic
344#332C22×C15111yescharacteristic
345#332C22×C15111yescharacteristic
346#331C22×C15111yescharacteristic
347#331C22×C15111yescharacteristic
348C2×#41—21no—
349C2×Q16—21no—
350C2×Q16—21no—
351C2×Q16—21no—
352C2×Q16—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C22×C8—21no—
356C4⋊Q8D4×C15111yescharacteristic
357C4⋊Q8D4×C15111yescharacteristic
358C4⋊Q8C23×C15111yescharacteristic
359C4⋊Q8C23×C15111yescharacteristic
360C4⋊Q8C23×C15111yescharacteristic
361#127C23×C15111yescharacteristic
362#125—21no—
363#125—21no—
364#124—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8D4×C15111yescharacteristic
369C22⋊Q8D4×C15111yescharacteristic
370#121—21no—
371#121—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C15111yescharacteristic
376C4×Q8C23×C15111yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379#117—21no—
380#117—21no—
381C2×C42C23×C15111yescharacteristic
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#106—21no—
387#106—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8D4×C15111yescharacteristic
394C4⋊C8D4×C15111yescharacteristic
395C4⋊C8C23×C15111yescharacteristic
396C4⋊C8C23×C15111yescharacteristic
397C4⋊C8C23×C15111yescharacteristic
398C4⋊C8C23×C15111yescharacteristic
399C4⋊C8C23×C15111yescharacteristic
400C4⋊C8C23×C15111yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8D4×C15111yescharacteristic
416C22⋊C8D4×C15111yescharacteristic
417#97—21no—
418#97—21no—
419#97—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8C23×C15111yescharacteristic
424C4×C8C23×C15111yescharacteristic
425#41—81no—
426#41—81no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C2×D4×C15111yescharacteristic
432C2×Q8C2×D4×C15111yescharacteristic
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—41no—
437C22×C4—41no—
438C22×C4C2×D4×C15111yescharacteristic
439C22×C4C2×D4×C15111yescharacteristic
440C22×C4#41×C15111yescharacteristic
441Q16—81no—
442Q16—81no—
443Q16—81no—
444Q16—81no—
445SD16—81no—
446SD16—81no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—81no—
454C2×C8C2×D4×C15111yescharacteristic
455C2×C8C2×D4×C15111yescharacteristic
456C2×C8C2×D4×C15111yescharacteristic
457C2×C8C2×D4×C15111yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C15111yescharacteristic
474C4⋊C4C2×D4×C15111yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42C2×D4×C15111yescharacteristic
484C42C2×D4×C15111yescharacteristic
485C42#41×C15111yescharacteristic
486C42C24×C15111yescharacteristic
487C23—41no—
488C23#121×C15111yescharacteristic
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—42no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—81no—
504D4—82no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4#121×C15111yescharacteristic
519C2×C4#121×C15111yescharacteristic
520C2×C4#121×C15111yescharacteristic
521C2×C4C22×D4×C15111yescharacteristic
522C2×C4C22×D4×C15111yescharacteristic
523C2×C4C2×#41×C15111yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22C2×#121×C15111yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4#576×C15111yescharacteristic
553C4#577×C15111yescharacteristic
554C4#578×C15111yescharacteristic
555C4#578×C15111yescharacteristic
556C2—41no—
557C2—161no—
558C2#3044×C15111yescharacteristic
559C2#3062×C15111yescharacteristic
560C2#3067×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
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
1. #3249×C151C2semidirect
4. #2986×C151C2semidirect
5. #1702×C151C2semidirect
6. #1698×C151C2semidirect
7. #1694×C151C2semidirect
8. #1692×C151C2semidirect
9. #1682×C151C2semidirect
10. #1678×C151C2semidirect
11. #1674×C151C2semidirect
12. #1672×C151C2semidirect
13. #1573×C151C2semidirect
14. #1554×C151C2semidirect
280. #19575C151direct (N × H)
281. C151#19575direct (N × H)
282. #3249C2×C151semidirect
285. #2986C2×C151semidirect
286. #1702C2×C151semidirect
287. #1698C2×C151semidirect
288. #1694C2×C151semidirect
289. #1692C2×C151semidirect
290. #1682C2×C151semidirect
291. #1678C2×C151semidirect
292. #1674C2×C151semidirect
293. #1672C2×C151semidirect
294. #1573C2×C151semidirect
295. #1554C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3249×C1512
#3228×C1512
#3216×C1512
#2986×C1512
#1702×C1512
#1698×C1512
#1694×C1512
#1692×C1512
#1682×C1512
#1678×C1512
#1674×C1512
#1672×C1512
#1573×C1512
#1554×C1512
#1540×C1512
#19575151