Finite Group Databasebeta

← C151×#19180 #50324105

Subgroups — C151×#19180 #50324105

Order 38656.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3184×C151C211yesmaximal, characteristic, complemented
2#3106×C151C211yesmaximal, characteristic, complemented
3#3035×C151C211yesmaximal, characteristic, complemented
4#2970×C151C211yesmaximal, characteristic, complemented
5#1702×C151C211yesmaximal, characteristic, complemented
6#1698×C151C211yesmaximal, characteristic, complemented
7#1692×C151C211yesmaximal, characteristic, complemented
8#1688×C151C211yesmaximal, characteristic, complemented
9#1681×C151C211yesmaximal, characteristic, complemented
10#1677×C151C211yesmaximal, characteristic, complemented
11#1671×C151C211yesmaximal, characteristic, complemented
12#1667×C151C211yesmaximal, characteristic, complemented
13#1565×C151C211yesmaximal, characteristic, complemented
14#1553×C151C211yesmaximal, characteristic, complemented
15#1551×C151C211yesmaximal, characteristic, complemented
16C2×#135×C151—21no—
17#532×C151C2211yescharacteristic
18#532×C151C2211yescharacteristic
19C4×#41×C151C2211yescharacteristic
20#498×C151C2211yescharacteristic
21#493×C151C2211yescharacteristic
22#486×C151C2211yescharacteristic
23#486×C151C2211yescharacteristic
24#482×C151—21no—
25#477×C151C2211yescharacteristic
26#476×C151C2211yescharacteristic
27#469×C151—21no—
28#469×C151—21no—
29#464×C151—21no—
30#463×C151—21no—
31#462×C151C2211yescharacteristic
32#461×C151C2211yescharacteristic
33#460×C151C2211yescharacteristic
34#460×C151C2211yescharacteristic
35#459×C151C2211yescharacteristic
36#459×C151C2211yescharacteristic
37#449×C151—21no—
38#446×C151C2211yescharacteristic
39#446×C151C2211yescharacteristic
40#442×C151—21no—
41#442×C151—21no—
42C4×SD16×C151—21no—
43C4×D8×C151—21no—
44#435×C151—21no—
45#435×C151—21no—
46C8×D4×C151C2211yescharacteristic
47C8×D4×C151C2211yescharacteristic
48#432×C151—21no—
49#432×C151C2211yescharacteristic
50#431×C151C2211yescharacteristic
51C2×C4⋊C8×C151C2211yescharacteristic
52#416×C151—21no—
53C4×M16×C151C2211yescharacteristic
54C2×#97×C151—21no—
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#331×C151C2211yescharacteristic
64#331×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×#41×C151—21no—
69C2×#41×C151D411yescharacteristic
70#135×C151—44no—
71C2×Q16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C2×SD16×C151—21no—
75C2×D8×C151—21no—
76C2×D8×C151—21no—
77C2×D8×C151—21no—
78C2×D8×C151—21no—
79C2×M16×C151D411yescharacteristic
80C2×M16×C151D411yescharacteristic
81C22×C8×C151—21no—
82C22×C8×C151—21no—
83C22×C8×C151—21no—
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86#127×C151C2311yescharacteristic
87#127×C151C2311yescharacteristic
88#124×C151—21no—
89#124×C151—21no—
90#121×C151—21no—
91#121×C151—21no—
92#121×C151—21no—
93#121×C151—21no—
94C4×Q8×C151D411yescharacteristic
95C4×Q8×C151C2311yescharacteristic
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151D411yescharacteristic
103C4×D4×C151C2311yescharacteristic
104#117×C151—21no—
105#117×C151D411yescharacteristic
106C2×C42×C151—21no—
107C2×C42×C151C2311yescharacteristic
108#107×C151—21no—
109#106×C151—21no—
110#106×C151—21no—
111#106×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151—21no—
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
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—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133C22⋊C8×C151—21no—
134C22⋊C8×C151—21no—
135C22⋊C8×C151—21no—
136C22⋊C8×C151—21no—
137#97×C151—21no—
138#97×C151—21no—
139#97×C151—21no—
140#97×C151D411yescharacteristic
141#97×C151D411yescharacteristic
142C4×C8×C151—21no—
143C4×C8×C151C2311yescharacteristic
144C4×C8×C151C2311yescharacteristic
145#41×C151—22no—
146#41×C151—41no—
147#41×C151—42no—
148#41×C151—42no—
149#41×C151—82no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151C2×D411yescharacteristic
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—41no—
161C2×D4×C151—41no—
162C2×D4×C151C2×D411yescharacteristic
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—41no—
167C22×C4×C151—41no—
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151#4111yescharacteristic
171Q16×C151—42no—
172SD16×C151—42no—
173SD16×C151—42no—
174SD16×C151—42no—
175D8×C151—42no—
176D8×C151—42no—
177D8×C151—42no—
178D8×C151—42no—
179M16×C151—22no—
180M16×C151—41no—
181C2×C8×C151—21no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—42no—
188C2×C8×C151—42no—
189C2×C8×C151—42no—
190C2×C8×C151C2×D411yescharacteristic
191C2×C8×C151C2×D411yescharacteristic
192C2×C8×C151C2×D411yescharacteristic
193C2×C8×C151C2×D411yescharacteristic
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151C2×D411yescharacteristic
201C4⋊C4×C151C2×D411yescharacteristic
202C22⋊C4×C151—21no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151—21no—
205C22⋊C4×C151—41no—
206C22⋊C4×C151—41no—
207C22⋊C4×C151—41no—
208C22⋊C4×C151—41no—
209C42×C151—21no—
210C42×C151—21no—
211C42×C151—21no—
212C42×C151C2×D411yescharacteristic
213C42×C151C2×D411yescharacteristic
214C42×C151#4111yescharacteristic
215C42×C151C2411yescharacteristic
216C23×C151—21no—
217C23×C151—41no—
218C23×C151—41no—
219C23×C151#12111yescharacteristic
220Q8×C151—21no—
221Q8×C151—21no—
222Q8×C151—41no—
223Q8×C151—41no—
224Q8×C151—81no—
225D4×C151—21no—
226D4×C151—42no—
227D4×C151—41no—
228D4×C151—41no—
229D4×C151—41no—
230D4×C151—41no—
231D4×C151—41no—
232D4×C151—41no—
233D4×C151—41no—
234D4×C151—41no—
235D4×C151—81no—
236D4×C151—81no—
237D4×C151—82no—
238D4×C151—82no—
239D4×C151AGL(1,ℤ/8)12yes—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—41no—
248C2×C4×C151—42no—
249C2×C4×C151—41no—
250C2×C4×C151—41no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—81no—
254C2×C4×C151—82no—
255C2×C4×C151—82no—
256C2×C4×C151#12111yescharacteristic
257C2×C4×C151#12111yescharacteristic
258C2×C4×C151#12111yescharacteristic
259C2×C4×C151C22×D411yescharacteristic
260C2×C4×C151C22×D411yescharacteristic
261C2×C4×C151C2×#4111yescharacteristic
262C8×C151—21no—
263C8×C151—21no—
264C8×C151—21no—
265C8×C151—41no—
266C8×C151—41no—
267C8×C151—41no—
268C8×C151—41no—
269C8×C151—41no—
270C8×C151—41no—
271C8×C151#13512yescomplemented
272C22×C151—21no—
273C22×C151—21no—
274C22×C151—22no—
275C22×C151—21no—
276C22×C151—41no—
277C22×C151—41no—
278C22×C151—81no—
279C22×C151—81no—
280C22×C151—81no—
281C22×C151—81no—
282C22×C151—81no—
283C22×C151—81no—
284C22×C151C2×#12111yescharacteristic
285C4×C151—21no—
286C4×C151—21no—
287C4×C151—21no—
288C4×C151—21no—
289C4×C151—41no—
290C4×C151—41no—
291C4×C151—41no—
292C4×C151—81no—
293C4×C151—81no—
294C4×C151C2×#13511yescharacteristic
295C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C151#57511yescharacteristic
297C4×C151#57511yescharacteristic
298C2×C151—41no—
299C2×C151—42no—
300C2×C151—161no—
301C2×C151—161no—
302C2×C151#303511yescharacteristic
303C2×C151#305511yescharacteristic
304C2×C151#306811yescharacteristic
305#19180C15111yesmaximal, characteristic, direct product factor, Sylow
306C151#1918011yescharacteristic, direct product factor, Sylow
307#3184C2×C15111yescharacteristic, complemented
308#3106C2×C15111yescharacteristic, complemented
309#3035C2×C15111yescharacteristic, complemented
310#2970C2×C15111yescharacteristic, complemented
311#1702C2×C15111yescharacteristic, complemented
312#1698C2×C15111yescharacteristic, complemented
313#1692C2×C15111yescharacteristic, complemented
314#1688C2×C15111yescharacteristic, complemented
315#1681C2×C15111yescharacteristic, complemented
316#1677C2×C15111yescharacteristic, complemented
317#1671C2×C15111yescharacteristic, complemented
318#1667C2×C15111yescharacteristic, complemented
319#1565C2×C15111yescharacteristic, complemented
320#1553C2×C15111yescharacteristic, complemented
321#1551C2×C15111yescharacteristic, complemented
322C2×#135—21no—
323#532C22×C15111yescharacteristic
324#532C22×C15111yescharacteristic
325C4×#41C22×C15111yescharacteristic
326#498C22×C15111yescharacteristic
327#493C22×C15111yescharacteristic
328#486C22×C15111yescharacteristic
329#486C22×C15111yescharacteristic
330#482—21no—
331#477C22×C15111yescharacteristic
332#476C22×C15111yescharacteristic
333#469—21no—
334#469—21no—
335#464—21no—
336#463—21no—
337#462C22×C15111yescharacteristic
338#461C22×C15111yescharacteristic
339#460C22×C15111yescharacteristic
340#460C22×C15111yescharacteristic
341#459C22×C15111yescharacteristic
342#459C22×C15111yescharacteristic
343#449—21no—
344#446C22×C15111yescharacteristic
345#446C22×C15111yescharacteristic
346#442—21no—
347#442—21no—
348C4×SD16—21no—
349C4×D8—21no—
350#435—21no—
351#435—21no—
352C8×D4C22×C15111yescharacteristic
353C8×D4C22×C15111yescharacteristic
354#432—21no—
355#432C22×C15111yescharacteristic
356#431C22×C15111yescharacteristic
357C2×C4⋊C8C22×C15111yescharacteristic
358#416—21no—
359C4×M16C22×C15111yescharacteristic
360C2×#97—21no—
361#335C22×C15111yescharacteristic
362#335C22×C15111yescharacteristic
363#334C22×C15111yescharacteristic
364#334C22×C15111yescharacteristic
365#333C22×C15111yescharacteristic
366#333C22×C15111yescharacteristic
367#332C22×C15111yescharacteristic
368#332C22×C15111yescharacteristic
369#331C22×C15111yescharacteristic
370#331C22×C15111yescharacteristic
371#331C22×C15111yescharacteristic
372#331C22×C15111yescharacteristic
373C2×#41—21no—
374C2×#41—21no—
375C2×#41D4×C15111yescharacteristic
376#135—44no—
377C2×Q16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—21no—
384C2×D8—21no—
385C2×M16D4×C15111yescharacteristic
386C2×M16D4×C15111yescharacteristic
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390C4⋊Q8C23×C15111yescharacteristic
391C4⋊Q8C23×C15111yescharacteristic
392#127C23×C15111yescharacteristic
393#127C23×C15111yescharacteristic
394#124—21no—
395#124—21no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121—21no—
400C4×Q8D4×C15111yescharacteristic
401C4×Q8C23×C15111yescharacteristic
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4D4×C15111yescharacteristic
409C4×D4C23×C15111yescharacteristic
410#117—21no—
411#117D4×C15111yescharacteristic
412C2×C42—21no—
413C2×C42C23×C15111yescharacteristic
414#107—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8C23×C15111yescharacteristic
422C4⋊C8C23×C15111yescharacteristic
423C4⋊C8C23×C15111yescharacteristic
424C4⋊C8C23×C15111yescharacteristic
425C4⋊C8C23×C15111yescharacteristic
426C4⋊C8C23×C15111yescharacteristic
427#103—21no—
428#103—21no—
429#103—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443#97—21no—
444#97—21no—
445#97—21no—
446#97D4×C15111yescharacteristic
447#97D4×C15111yescharacteristic
448C4×C8—21no—
449C4×C8C23×C15111yescharacteristic
450C4×C8C23×C15111yescharacteristic
451#41—22no—
452#41—41no—
453#41—42no—
454#41—42no—
455#41—82no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8C2×D4×C15111yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C15111yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4C2×D4×C15111yescharacteristic
475C22×C4C2×D4×C15111yescharacteristic
476C22×C4#41×C15111yescharacteristic
477Q16—42no—
478SD16—42no—
479SD16—42no—
480SD16—42no—
481D8—42no—
482D8—42no—
483D8—42no—
484D8—42no—
485M16—22no—
486M16—41no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—42no—
495C2×C8—42no—
496C2×C8C2×D4×C15111yescharacteristic
497C2×C8C2×D4×C15111yescharacteristic
498C2×C8C2×D4×C15111yescharacteristic
499C2×C8C2×D4×C15111yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4C2×D4×C15111yescharacteristic
507C4⋊C4C2×D4×C15111yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42C2×D4×C15111yescharacteristic
519C42C2×D4×C15111yescharacteristic
520C42#41×C15111yescharacteristic
521C42C24×C15111yescharacteristic
522C23—21no—
523C23—41no—
524C23—41no—
525C23#121×C15111yescharacteristic
526Q8—21no—
527Q8—21no—
528Q8—41no—
529Q8—41no—
530Q8—81no—
531D4—21no—
532D4—42no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—81no—
542D4—81no—
543D4—82no—
544D4—82no—
545D4AGL(1,ℤ/8)×C15112yes—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—81no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4#121×C15111yescharacteristic
563C2×C4#121×C15111yescharacteristic
564C2×C4#121×C15111yescharacteristic
565C2×C4C22×D4×C15111yescharacteristic
566C2×C4C22×D4×C15111yescharacteristic
567C2×C4C2×#41×C15111yescharacteristic
568C8—21no—
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8#135×C15112yescomplemented
578C22—21no—
579C22—21no—
580C22—22no—
581C22—21no—
582C22—41no—
583C22—41no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22C2×#121×C15111yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4C2×#135×C15111yescharacteristic
601C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
602C4#575×C15111yescharacteristic
603C4#575×C15111yescharacteristic
604C2—41no—
605C2—42no—
606C2—161no—
607C2—161no—
608C2#3035×C15111yescharacteristic
609C2#3055×C15111yescharacteristic
610C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
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. #3184×C151C2semidirect
2. #3106×C151C2semidirect
3. #3035×C151C2semidirect
4. #2970×C151C2semidirect
5. #1702×C151C2semidirect
6. #1698×C151C2semidirect
7. #1692×C151C2semidirect
8. #1688×C151C2semidirect
9. #1681×C151C2semidirect
10. #1677×C151C2semidirect
11. #1671×C151C2semidirect
12. #1667×C151C2semidirect
13. #1565×C151C2semidirect
14. #1553×C151C2semidirect
15. #1551×C151C2semidirect
271. C8×C151#135semidirect
305. #19180C151direct (N × H)
306. C151#19180direct (N × H)
307. #3184C2×C151semidirect
308. #3106C2×C151semidirect
309. #3035C2×C151semidirect
310. #2970C2×C151semidirect
311. #1702C2×C151semidirect
312. #1698C2×C151semidirect
313. #1692C2×C151semidirect
314. #1688C2×C151semidirect
315. #1681C2×C151semidirect
316. #1677C2×C151semidirect
317. #1671C2×C151semidirect
318. #1667C2×C151semidirect
319. #1565C2×C151semidirect
320. #1553C2×C151semidirect
321. #1551C2×C151semidirect
577. C8#135×C151semidirect

Maximal subgroups

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

subgroupindex
#3184×C1512
#3106×C1512
#3035×C1512
#2970×C1512
#1702×C1512
#1698×C1512
#1692×C1512
#1688×C1512
#1681×C1512
#1677×C1512
#1671×C1512
#1667×C1512
#1565×C1512
#1553×C1512
#1551×C1512
#19180151