Finite Group Databasebeta

← C151×#18467 #50323392

Subgroups — C151×#18467 #50323392

Order 38656.

890 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3561×C151C211yesmaximal, characteristic
2#3236×C151C211yesmaximal, characteristic, complemented
3#3232×C151C211yesmaximal, characteristic, complemented
4#2820×C151C211yesmaximal, characteristic, complemented
5#1618×C151C212yesmaximal, complemented
6#1614×C151C212yesmaximal, complemented
7#1612×C151C212yesmaximal, complemented
8#1608×C151C212yesmaximal, complemented
9#1518×C151C211yesmaximal, characteristic, complemented
10#1512×C151C211yesmaximal, characteristic, complemented
11#1469×C151C211yesmaximal, characteristic, complemented
12#563×C151—21no—
13#562×C151—21no—
14#556×C151—21no—
15#551×C151—22no—
16D4×Q8×C151—21no—
17#548×C151—21no—
18#546×C151—21no—
19#543×C151C2212yes—
20#542×C151—21no—
21#542×C151—22no—
22#538×C151C2212yes—
23#536×C151—21no—
24#533×C151C2211yescharacteristic
25#529×C151C2211yescharacteristic
26C2×#125×C151C2211yescharacteristic
27C2×#124×C151C2211yescharacteristic
28#501×C151—21no—
29#499×C151—21no—
30#491×C151—21no—
31#488×C151—21no—
32#484×C151C2211yescharacteristic
33#484×C151C2212yes—
34#483×C151C2211yescharacteristic
35#483×C151C2212yes—
36#481×C151C2211yescharacteristic
37#480×C151C2211yescharacteristic
38#479×C151—21no—
39#479×C151—22no—
40#478×C151—21no—
41#432×C151C2211yescharacteristic
42#431×C151C2211yescharacteristic
43#399×C151C2212yes—
44#397×C151C2212yes—
45#396×C151—22no—
46#395×C151—21no—
47#394×C151—21no—
48#382×C151C2211yescharacteristic
49#328×C151C2212yes—
50#328×C151C2212yes—
51#328×C151C2212yes—
52#327×C151C2212yes—
53#323×C151C2212yes—
54#323×C151C2212yes—
55C2×#41×C151—21no—
56C22×Q8×C151—21no—
57C22×Q8×C151D411yescharacteristic
58C22×D4×C151D411yescharacteristic
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151D411yescharacteristic
62C4⋊Q8×C151D411yescharacteristic
63#126×C151—22no—
64#126×C151—22no—
65#126×C151—22no—
66#126×C151—21no—
67#125×C151—21no—
68#125×C151—21no—
69#125×C151—21no—
70#125×C151—21no—
71#125×C151—21no—
72#125×C151D411yescharacteristic
73#124×C151—21no—
74#124×C151—22no—
75#124×C151—21no—
76#124×C151—21no—
77#124×C151—21no—
78#124×C151—21no—
79#124×C151—22no—
80#124×C151D411yescharacteristic
81#123×C151—22no—
82#123×C151—22no—
83#123×C151—22no—
84#123×C151—21no—
85#123×C151—22no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151—22no—
91C22⋊Q8×C151—22no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—22no—
94C22⋊Q8×C151—22no—
95C22⋊Q8×C151C2311yescharacteristic
96C22⋊Q8×C151C2312yes—
97#121×C151—21no—
98#121×C151—22no—
99#121×C151—22no—
100#121×C151C2311yescharacteristic
101#120×C151—22no—
102C4×Q8×C151—21no—
103C4×Q8×C151—21no—
104C4×Q8×C151D411yescharacteristic
105C4×Q8×C151D412yes—
106C4×D4×C151—21no—
107C4×D4×C151—22no—
108C4×D4×C151—21no—
109C4×D4×C151—22no—
110C4×D4×C151D411yescharacteristic
111#117×C151—22no—
112#117×C151—21no—
113#117×C151—21no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—21no—
117C2×C4⋊C4×C151—22no—
118C2×C4⋊C4×C151C2311yescharacteristic
119C2×C4⋊C4×C151C2311yescharacteristic
120C2×C22⋊C4×C151—22no—
121C2×C22⋊C4×C151—22no—
122C2×C22⋊C4×C151—22no—
123C2×C22⋊C4×C151D412yes—
124C2×C22⋊C4×C151C2312yes—
125C2×C42×C151C2311yescharacteristic
126#107×C151—21no—
127#107×C151—21no—
128#107×C151—22no—
129#106×C151—21no—
130#106×C151—21no—
131#106×C151—22no—
132C4⋊C8×C151—21no—
133C4⋊C8×C151—21no—
134#103×C151—21no—
135#103×C151—22no—
136#103×C151—21no—
137#103×C151—22no—
138#102×C151—21no—
139#102×C151—21no—
140C22⋊C8×C151C2311yescharacteristic
141C22⋊C8×C151C2311yescharacteristic
142C22⋊C8×C151C2312yes—
143#97×C151—21no—
144C4×C8×C151—21no—
145#95×C151—21no—
146#95×C151—22no—
147#95×C151C2312yes—
148C24×C151C2×D412yes—
149#41×C151—82no—
150C2×Q8×C151—22no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—81no—
155C2×Q8×C151—82no—
156C2×Q8×C151C2×D411yescharacteristic
157C2×Q8×C151C2×D412yes—
158C2×D4×C151—21no—
159C2×D4×C151—22no—
160C2×D4×C151—22no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—81no—
164C2×D4×C151C2×D411yescharacteristic
165C22×C4×C151—22no—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
168C22×C4×C151—21no—
169C22×C4×C151—22no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D412yes—
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2411yescharacteristic
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—22no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—22no—
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—22no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151—41no—
198C4⋊C4×C151—41no—
199C4⋊C4×C151—41no—
200C4⋊C4×C151—81no—
201C4⋊C4×C151—82no—
202C4⋊C4×C151C2×D411yescharacteristic
203C4⋊C4×C151C2×D411yescharacteristic
204C4⋊C4×C151C2×D412yes—
205C22⋊C4×C151—22no—
206C22⋊C4×C151—22no—
207C22⋊C4×C151—22no—
208C22⋊C4×C151—22no—
209C22⋊C4×C151—22no—
210C22⋊C4×C151—21no—
211C22⋊C4×C151—22no—
212C22⋊C4×C151—22no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—21no—
215C22⋊C4×C151—21no—
216C22⋊C4×C151—21no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—21no—
220C22⋊C4×C151—82no—
221C22⋊C4×C151—82no—
222C42×C151—22no—
223C42×C151—22no—
224C42×C151—21no—
225C42×C151C2×D411yescharacteristic
226C42×C151C2×D411yescharacteristic
227C42×C151C2×D411yescharacteristic
228C42×C151C2×D411yescharacteristic
229C23×C151—22no—
230C23×C151—21no—
231C23×C151—22no—
232C23×C151—22no—
233C23×C151—42no—
234C23×C151—42no—
235C23×C151C22×D411yescharacteristic
236Q8×C151—41no—
237Q8×C151—42no—
238Q8×C151—42no—
239Q8×C151—42no—
240Q8×C151—81no—
241Q8×C151—82no—
242D4×C151—41no—
243D4×C151—42no—
244D4×C151—41no—
245D4×C151—41no—
246D4×C151—81no—
247D4×C151—82no—
248D4×C151—82no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—22no—
252C2×C4×C151—22no—
253C2×C4×C151—21no—
254C2×C4×C151—22no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—42no—
260C2×C4×C151—42no—
261C2×C4×C151—42no—
262C2×C4×C151—42no—
263C2×C4×C151—42no—
264C2×C4×C151—41no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—42no—
268C2×C4×C151—41no—
269C2×C4×C151—82no—
270C2×C4×C151—82no—
271C2×C4×C151—82no—
272C2×C4×C151#12011yescharacteristic
273C2×C4×C151#12011yescharacteristic
274C2×C4×C151#12011yescharacteristic
275C2×C4×C151#12011yescharacteristic
276C2×C4×C151C22×D411yescharacteristic
277C2×C4×C151C22×D411yescharacteristic
278C8×C151—41no—
279C8×C151—41no—
280C8×C151—42no—
281C22×C151—21no—
282C22×C151—21no—
283C22×C151—41no—
284C22×C151—42no—
285C22×C151—41no—
286C22×C151—42no—
287C22×C151—42no—
288C22×C151—41no—
289C22×C151—82no—
290C22×C151—82no—
291C22×C151C2×#12011yescharacteristic
292C22×C151#57711yescharacteristic
293C22×C151#57811yescharacteristic
294C4×C151—21no—
295C4×C151—21no—
296C4×C151—21no—
297C4×C151—21no—
298C4×C151—21no—
299C4×C151—21no—
300C4×C151—41no—
301C4×C151—41no—
302C4×C151—42no—
303C4×C151—42no—
304C4×C151—41no—
305C4×C151—42no—
306C4×C151—82no—
307C4×C151—81no—
308C4×C151—81no—
309C2×C151—21no—
310C2×C151—21no—
311C2×C151—81no—
312C2×C151—82no—
313C2×C151#301311yescharacteristic
314C2×C151#301911yescharacteristic
315C2×C151#302811yescharacteristic
316#18467C15111yesmaximal, characteristic, direct product factor, Sylow
317C151#1846711yescharacteristic, direct product factor, Sylow
318#3561C2×C15111yescharacteristic
319#3236C2×C15111yescharacteristic, complemented
320#3232C2×C15111yescharacteristic, complemented
321#2820C2×C15111yescharacteristic, complemented
322#1618C2×C15112yescomplemented
323#1614C2×C15112yescomplemented
324#1612C2×C15112yescomplemented
325#1608C2×C15112yescomplemented
326#1518C2×C15111yescharacteristic, complemented
327#1512C2×C15111yescharacteristic, complemented
328#1469C2×C15111yescharacteristic, complemented
329#563—21no—
330#562—21no—
331#556—21no—
332#551—22no—
333D4×Q8—21no—
334#548—21no—
335#546—21no—
336#543C22×C15112yes—
337#542—21no—
338#542—22no—
339#538C22×C15112yes—
340#536—21no—
341#533C22×C15111yescharacteristic
342#529C22×C15111yescharacteristic
343C2×#125C22×C15111yescharacteristic
344C2×#124C22×C15111yescharacteristic
345#501—21no—
346#499—21no—
347#491—21no—
348#488—21no—
349#484C22×C15111yescharacteristic
350#484C22×C15112yes—
351#483C22×C15111yescharacteristic
352#483C22×C15112yes—
353#481C22×C15111yescharacteristic
354#480C22×C15111yescharacteristic
355#479—21no—
356#479—22no—
357#478—21no—
358#432C22×C15111yescharacteristic
359#431C22×C15111yescharacteristic
360#399C22×C15112yes—
361#397C22×C15112yes—
362#396—22no—
363#395—21no—
364#394—21no—
365#382C22×C15111yescharacteristic
366#328C22×C15112yes—
367#328C22×C15112yes—
368#328C22×C15112yes—
369#327C22×C15112yes—
370#323C22×C15112yes—
371#323C22×C15112yes—
372C2×#41—21no—
373C22×Q8—21no—
374C22×Q8D4×C15111yescharacteristic
375C22×D4D4×C15111yescharacteristic
376C4⋊Q8—21no—
377C4⋊Q8—22no—
378C4⋊Q8D4×C15111yescharacteristic
379C4⋊Q8D4×C15111yescharacteristic
380#126—22no—
381#126—22no—
382#126—22no—
383#126—21no—
384#125—21no—
385#125—21no—
386#125—21no—
387#125—21no—
388#125—21no—
389#125D4×C15111yescharacteristic
390#124—21no—
391#124—22no—
392#124—22no—
393#124—21no—
394#124—21no—
395#124—21no—
396#124—21no—
397#124D4×C15111yescharacteristic
398#123—22no—
399#123—22no—
400#123—22no—
401#123—21no—
402#123—22no—
403C22⋊Q8—22no—
404C22⋊Q8—21no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—21no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8C23×C15111yescharacteristic
413C22⋊Q8C23×C15112yes—
414#121—21no—
415#121—22no—
416#121—22no—
417#121C23×C15111yescharacteristic
418#120—22no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8D4×C15111yescharacteristic
422C4×Q8D4×C15112yes—
423C4×D4—21no—
424C4×D4—22no—
425C4×D4—21no—
426C4×D4—22no—
427C4×D4D4×C15111yescharacteristic
428#117—22no—
429#117—21no—
430#117—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4C23×C15111yescharacteristic
436C2×C4⋊C4C23×C15111yescharacteristic
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4D4×C15112yes—
441C2×C22⋊C4C23×C15112yes—
442C2×C42C23×C15111yescharacteristic
443#107—21no—
444#107—21no—
445#107—22no—
446#106—21no—
447#106—21no—
448#106—22no—
449C4⋊C8—21no—
450C4⋊C8—21no—
451#103—21no—
452#103—22no—
453#103—21no—
454#103—22no—
455#102—21no—
456#102—21no—
457C22⋊C8C23×C15112yes—
458C22⋊C8C23×C15111yescharacteristic
459C22⋊C8C23×C15111yescharacteristic
460#97—21no—
461C4×C8—21no—
462#95—21no—
463#95—22no—
464#95C23×C15112yes—
465C24C2×D4×C15112yes—
466#41—82no—
467C2×Q8—22no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—81no—
472C2×Q8—82no—
473C2×Q8C2×D4×C15111yescharacteristic
474C2×Q8C2×D4×C15112yes—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—81no—
481C2×D4C2×D4×C15111yescharacteristic
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4C2×D4×C15111yescharacteristic
490C22×C4C2×D4×C15112yes—
491C22×C4C2×D4×C15111yescharacteristic
492C22×C4C24×C15111yescharacteristic
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—81no—
518C4⋊C4—82no—
519C4⋊C4C2×D4×C15111yescharacteristic
520C4⋊C4C2×D4×C15111yescharacteristic
521C4⋊C4C2×D4×C15112yes—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—82no—
538C22⋊C4—82no—
539C42—22no—
540C42—22no—
541C42—21no—
542C42C2×D4×C15111yescharacteristic
543C42C2×D4×C15111yescharacteristic
544C42C2×D4×C15111yescharacteristic
545C42C2×D4×C15111yescharacteristic
546C23—22no—
547C23—21no—
548C23—22no—
549C23—22no—
550C23—42no—
551C23—42no—
552C23C22×D4×C15111yescharacteristic
553Q8—41no—
554Q8—42no—
555Q8—42no—
556Q8—42no—
557Q8—81no—
558Q8—82no—
559D4—41no—
560D4—42no—
561D4—41no—
562D4—41no—
563D4—81no—
564D4—82no—
565D4—82no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4#120×C15111yescharacteristic
590C2×C4#120×C15111yescharacteristic
591C2×C4#120×C15111yescharacteristic
592C2×C4#120×C15111yescharacteristic
593C2×C4C22×D4×C15111yescharacteristic
594C2×C4C22×D4×C15111yescharacteristic
595C8—41no—
596C8—41no—
597C8—42no—
598C22—21no—
599C22—21no—
600C22—41no—
601C22—42no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—41no—
606C22—82no—
607C22—82no—
608C22C2×#120×C15111yescharacteristic
609C22#577×C15111yescharacteristic
610C22#578×C15111yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—42no—
620C4—42no—
621C4—41no—
622C4—42no—
623C4—82no—
624C4—81no—
625C4—81no—
626C2—21no—
627C2—21no—
628C2—82no—
629C2—81no—
630C2#3013×C15111yescharacteristic
631C2#3019×C15111yescharacteristic
632C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3561×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #3236×C151C2semidirect
3. #3232×C151C2semidirect
4. #2820×C151C2semidirect
5. #1618×C151C2semidirect
6. #1614×C151C2semidirect
7. #1612×C151C2semidirect
8. #1608×C151C2semidirect
9. #1518×C151C2semidirect
10. #1512×C151C2semidirect
11. #1469×C151C2semidirect
316. #18467C151direct (N × H)
317. C151#18467direct (N × H)
319. #3236C2×C151semidirect
320. #3232C2×C151semidirect
321. #2820C2×C151semidirect
322. #1618C2×C151semidirect
323. #1614C2×C151semidirect
324. #1612C2×C151semidirect
325. #1608C2×C151semidirect
326. #1518C2×C151semidirect
327. #1512C2×C151semidirect
328. #1469C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3561×C1512
#3236×C1512
#3232×C1512
#2820×C1512
#1618×C1512
#1614×C1512
#1612×C1512
#1608×C1512
#1518×C1512
#1512×C1512
#1469×C1512
#18467151