Finite Group Databasebeta

← C151×#19218 #50324143

Subgroups — C151×#19218 #50324143

Order 38656.

596 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3233×C151C211yesmaximal, characteristic, complemented
2#3212×C151C211yesmaximal, characteristic
3#3167×C151C211yesmaximal, characteristic, complemented
4#2966×C151C211yesmaximal, characteristic, complemented
5#1700×C151C211yesmaximal, characteristic, complemented
6#1699×C151C211yesmaximal, characteristic, complemented
7#1698×C151C211yesmaximal, characteristic, complemented
8#1697×C151C211yesmaximal, characteristic, complemented
9#1672×C151C211yesmaximal, characteristic, complemented
10#1671×C151C211yesmaximal, characteristic, complemented
11#1666×C151C211yesmaximal, characteristic, complemented
12#1665×C151C211yesmaximal, characteristic, complemented
13#1564×C151C211yesmaximal, characteristic, complemented
14#1554×C151C211yesmaximal, characteristic, complemented
15#1553×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#532×C151C2211yescharacteristic
18#529×C151C2211yescharacteristic
19#499×C151—21no—
20#498×C151C2211yescharacteristic
21#495×C151—21no—
22#492×C151C2211yescharacteristic
23#488×C151—21no—
24#488×C151—21no—
25#487×C151C2211yescharacteristic
26#486×C151C2211yescharacteristic
27#485×C151—21no—
28#482×C151—21no—
29#477×C151C2211yescharacteristic
30#476×C151C2211yescharacteristic
31#475×C151C2211yescharacteristic
32#474×C151C2211yescharacteristic
33#465×C151—21no—
34#465×C151—21no—
35#462×C151C2211yescharacteristic
36#461×C151C2211yescharacteristic
37#460×C151C2211yescharacteristic
38#459×C151C2211yescharacteristic
39#452×C151—21no—
40#449×C151—21no—
41#446×C151C2211yescharacteristic
42C8×Q8×C151C2211yescharacteristic
43C4×SD16×C151—21no—
44C4×SD16×C151—21no—
45#436×C151C2211yescharacteristic
46#435×C151—21no—
47C8×D4×C151—21no—
48C8×D4×C151C2211yescharacteristic
49#433×C151—21no—
50#432×C151C2211yescharacteristic
51#431×C151C2211yescharacteristic
52#431×C151C2211yescharacteristic
53#405×C151—21no—
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×SD16×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×D8×C151—21no—
74C2×M16×C151—21no—
75C22×C8×C151—21no—
76C22×C8×C151D411yescharacteristic
77C22×C8×C151D411yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80C4⋊Q8×C151C2311yescharacteristic
81#127×C151C2311yescharacteristic
82#126×C151—21no—
83#125×C151—21no—
84#125×C151D411yescharacteristic
85#124×C151—21no—
86#124×C151D411yescharacteristic
87#123×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151D411yescharacteristic
91#121×C151—21no—
92#121×C151—21no—
93#121×C151D411yescharacteristic
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151C2311yescharacteristic
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151C2311yescharacteristic
101#117×C151—21no—
102#117×C151—21no—
103C2×C42×C151C2311yescharacteristic
104#107×C151—21no—
105#107×C151—21no—
106#106×C151—21no—
107#106×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110C4⋊C8×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151C2311yescharacteristic
113C4⋊C8×C151C2311yescharacteristic
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118#103×C151—21no—
119#103×C151—21no—
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
124#102×C151—21no—
125#102×C151—21no—
126#102×C151—21no—
127#102×C151—21no—
128#102×C151—21no—
129#102×C151—21no—
130C22⋊C8×C151—21no—
131C22⋊C8×C151—21no—
132C22⋊C8×C151—21no—
133C22⋊C8×C151—21no—
134C22⋊C8×C151—21no—
135#97×C151—21no—
136#97×C151—21no—
137C4×C8×C151—21no—
138C4×C8×C151—21no—
139C4×C8×C151—21no—
140C4×C8×C151D411yescharacteristic
141C4×C8×C151D411yescharacteristic
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×C151C2×D411yescharacteristic
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—41no—
155C2×D4×C151C2×D411yescharacteristic
156C22×C4×C151—21no—
157C22×C4×C151—41no—
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151C2×D411yescharacteristic
160C22×C4×C151#4111yescharacteristic
161Q16×C151—81no—
162SD16×C151—42no—
163SD16×C151—42no—
164SD16×C151—81no—
165SD16×C151—81no—
166D8×C151—81no—
167M16×C151—42no—
168C2×C8×C151—22no—
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—41no—
176C2×C8×C151—42no—
177C2×C8×C151C2×D411yescharacteristic
178C2×C8×C151C2×D411yescharacteristic
179C2×C8×C151C2×D411yescharacteristic
180C2×C8×C151C2×D411yescharacteristic
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—21no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151—41no—
193C4⋊C4×C151C2×D411yescharacteristic
194C4⋊C4×C151C2×D411yescharacteristic
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—21no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C22⋊C4×C151—41no—
203C42×C151—21no—
204C42×C151—41no—
205C42×C151C2×D411yescharacteristic
206C42×C151C2×D411yescharacteristic
207C42×C151#4111yescharacteristic
208C42×C151C2411yescharacteristic
209C23×C151—21no—
210C23×C151—41no—
211C23×C151#12111yescharacteristic
212Q8×C151—21no—
213Q8×C151—21no—
214Q8×C151—41no—
215Q8×C151—41no—
216Q8×C151—41no—
217Q8×C151—41no—
218Q8×C151—81no—
219D4×C151—21no—
220D4×C151—21no—
221D4×C151—42no—
222D4×C151—41no—
223D4×C151—41no—
224D4×C151—41no—
225D4×C151—41no—
226D4×C151—81no—
227D4×C151—82no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—82no—
242C2×C4×C151#12111yescharacteristic
243C2×C4×C151#12111yescharacteristic
244C2×C4×C151#12111yescharacteristic
245C2×C4×C151C22×D411yescharacteristic
246C2×C4×C151C22×D411yescharacteristic
247C2×C4×C151C2×#4111yescharacteristic
248C8×C151—21no—
249C8×C151—21no—
250C8×C151—21no—
251C8×C151—41no—
252C8×C151—41no—
253C8×C151—41no—
254C8×C151—41no—
255C8×C151—41no—
256C8×C151—41no—
257C8×C151#13512yes—
258C22×C151—21no—
259C22×C151—21no—
260C22×C151—21no—
261C22×C151—41no—
262C22×C151—41no—
263C22×C151—41no—
264C22×C151—81no—
265C22×C151—81no—
266C22×C151—81no—
267C22×C151C2×#12111yescharacteristic
268C4×C151—21no—
269C4×C151—21no—
270C4×C151—21no—
271C4×C151—21no—
272C4×C151—41no—
273C4×C151—41no—
274C4×C151—41no—
275C4×C151—81no—
276C4×C151—81no—
277C4×C151—81no—
278C4×C151C2×#13511yescharacteristic
279C4×C151#57511yescharacteristic
280C4×C151#57711yescharacteristic
281C4×C151#57711yescharacteristic
282C2×C151—41no—
283C2×C151—81no—
284C2×C151—161no—
285C2×C151#303511yescharacteristic
286C2×C151#305711yescharacteristic
287C2×C151#306711yescharacteristic
288#19218C15111yesmaximal, characteristic, direct product factor, Sylow
289C151#1921811yescharacteristic, direct product factor, Sylow
290#3233C2×C15111yescharacteristic, complemented
291#3212C2×C15111yescharacteristic
292#3167C2×C15111yescharacteristic, complemented
293#2966C2×C15111yescharacteristic, complemented
294#1700C2×C15111yescharacteristic, complemented
295#1699C2×C15111yescharacteristic, complemented
296#1698C2×C15111yescharacteristic, complemented
297#1697C2×C15111yescharacteristic, complemented
298#1672C2×C15111yescharacteristic, complemented
299#1671C2×C15111yescharacteristic, complemented
300#1666C2×C15111yescharacteristic, complemented
301#1665C2×C15111yescharacteristic, complemented
302#1564C2×C15111yescharacteristic, complemented
303#1554C2×C15111yescharacteristic, complemented
304#1553C2×C15111yescharacteristic, complemented
305#533C22×C15111yescharacteristic
306#532C22×C15111yescharacteristic
307#529C22×C15111yescharacteristic
308#499—21no—
309#498C22×C15111yescharacteristic
310#495—21no—
311#492C22×C15111yescharacteristic
312#488—21no—
313#488—21no—
314#487C22×C15111yescharacteristic
315#486C22×C15111yescharacteristic
316#485—21no—
317#482—21no—
318#477C22×C15111yescharacteristic
319#476C22×C15111yescharacteristic
320#475C22×C15111yescharacteristic
321#474C22×C15111yescharacteristic
322#465—21no—
323#465—21no—
324#462C22×C15111yescharacteristic
325#461C22×C15111yescharacteristic
326#460C22×C15111yescharacteristic
327#459C22×C15111yescharacteristic
328#452—21no—
329#449—21no—
330#446C22×C15111yescharacteristic
331C8×Q8C22×C15111yescharacteristic
332C4×SD16—21no—
333C4×SD16—21no—
334#436C22×C15111yescharacteristic
335#435—21no—
336C8×D4—21no—
337C8×D4C22×C15111yescharacteristic
338#433—21no—
339#432C22×C15111yescharacteristic
340#431C22×C15111yescharacteristic
341#431C22×C15111yescharacteristic
342#405—21no—
343C2×C4×C8C22×C15111yescharacteristic
344#335C22×C15111yescharacteristic
345#335C22×C15111yescharacteristic
346#334C22×C15111yescharacteristic
347#334C22×C15111yescharacteristic
348#333C22×C15111yescharacteristic
349#333C22×C15111yescharacteristic
350#332C22×C15111yescharacteristic
351#332C22×C15111yescharacteristic
352#332C22×C15111yescharacteristic
353#332C22×C15111yescharacteristic
354#331C22×C15111yescharacteristic
355#331C22×C15111yescharacteristic
356C2×#41—21no—
357C2×Q16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×D8—21no—
363C2×M16—21no—
364C22×C8—21no—
365C22×C8D4×C15111yescharacteristic
366C22×C8D4×C15111yescharacteristic
367C4⋊Q8C23×C15111yescharacteristic
368C4⋊Q8C23×C15111yescharacteristic
369C4⋊Q8C23×C15111yescharacteristic
370#127C23×C15111yescharacteristic
371#126—21no—
372#125—21no—
373#125D4×C15111yescharacteristic
374#124—21no—
375#124D4×C15111yescharacteristic
376#123—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8D4×C15111yescharacteristic
380#121—21no—
381#121—21no—
382#121D4×C15111yescharacteristic
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C15111yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C23×C15111yescharacteristic
390#117—21no—
391#117—21no—
392C2×C42C23×C15111yescharacteristic
393#107—21no—
394#107—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C23×C15111yescharacteristic
402C4⋊C8C23×C15111yescharacteristic
403C4⋊C8C23×C15111yescharacteristic
404C4⋊C8C23×C15111yescharacteristic
405C4⋊C8C23×C15111yescharacteristic
406C4⋊C8C23×C15111yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424#97—21no—
425#97—21no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8D4×C15111yescharacteristic
430C4×C8D4×C15111yescharacteristic
431C4×C8C23×C15111yescharacteristic
432C4×C8C23×C15111yescharacteristic
433#41—81no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×D4×C15111yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4C2×D4×C15111yescharacteristic
445C22×C4—21no—
446C22×C4—41no—
447C22×C4C2×D4×C15111yescharacteristic
448C22×C4C2×D4×C15111yescharacteristic
449C22×C4#41×C15111yescharacteristic
450Q16—81no—
451SD16—42no—
452SD16—42no—
453SD16—81no—
454SD16—81no—
455D8—81no—
456M16—42no—
457C2×C8—22no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—41no—
465C2×C8—42no—
466C2×C8C2×D4×C15111yescharacteristic
467C2×C8C2×D4×C15111yescharacteristic
468C2×C8C2×D4×C15111yescharacteristic
469C2×C8C2×D4×C15111yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4C2×D4×C15111yescharacteristic
483C4⋊C4C2×D4×C15111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—21no—
493C42—41no—
494C42C2×D4×C15111yescharacteristic
495C42C2×D4×C15111yescharacteristic
496C42#41×C15111yescharacteristic
497C42C24×C15111yescharacteristic
498C23—21no—
499C23—41no—
500C23#121×C15111yescharacteristic
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—81no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—82no—
531C2×C4#121×C15111yescharacteristic
532C2×C4#121×C15111yescharacteristic
533C2×C4#121×C15111yescharacteristic
534C2×C4C22×D4×C15111yescharacteristic
535C2×C4C22×D4×C15111yescharacteristic
536C2×C4C2×#41×C15111yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8#135×C15112yes—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22C2×#121×C15111yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C2×#135×C15111yescharacteristic
568C4#575×C15111yescharacteristic
569C4#577×C15111yescharacteristic
570C4#577×C15111yescharacteristic
571C2—41no—
572C2—81no—
573C2—161no—
574C2#3035×C15111yescharacteristic
575C2#3057×C15111yescharacteristic
576C2#3067×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3212×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
1. #3233×C151C2semidirect
3. #3167×C151C2semidirect
4. #2966×C151C2semidirect
5. #1700×C151C2semidirect
6. #1699×C151C2semidirect
7. #1698×C151C2semidirect
8. #1697×C151C2semidirect
9. #1672×C151C2semidirect
10. #1671×C151C2semidirect
11. #1666×C151C2semidirect
12. #1665×C151C2semidirect
13. #1564×C151C2semidirect
14. #1554×C151C2semidirect
15. #1553×C151C2semidirect
288. #19218C151direct (N × H)
289. C151#19218direct (N × H)
290. #3233C2×C151semidirect
292. #3167C2×C151semidirect
293. #2966C2×C151semidirect
294. #1700C2×C151semidirect
295. #1699C2×C151semidirect
296. #1698C2×C151semidirect
297. #1697C2×C151semidirect
298. #1672C2×C151semidirect
299. #1671C2×C151semidirect
300. #1666C2×C151semidirect
301. #1665C2×C151semidirect
302. #1564C2×C151semidirect
303. #1554C2×C151semidirect
304. #1553C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3233×C1512
#3212×C1512
#3167×C1512
#2966×C1512
#1700×C1512
#1699×C1512
#1698×C1512
#1697×C1512
#1672×C1512
#1671×C1512
#1666×C1512
#1665×C1512
#1564×C1512
#1554×C1512
#1553×C1512
#19218151