Finite Group Databasebeta

← C151×#18957 #50323882

Subgroups — C151×#18957 #50323882

Order 38656.

874 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3547×C151C211yesmaximal, characteristic
2#3238×C151C211yesmaximal, characteristic, complemented
3#3227×C151C211yesmaximal, characteristic, complemented
4#3209×C151C211yesmaximal, characteristic, complemented
5#1637×C151C212yesmaximal, complemented
6#1635×C151C212yesmaximal, complemented
7#1634×C151C212yesmaximal, complemented
8#1632×C151C212yesmaximal, complemented
9#1554×C151C211yesmaximal, characteristic, complemented
10#1496×C151C211yesmaximal, characteristic, complemented
11#1482×C151C211yesmaximal, characteristic, complemented
12#562×C151—22no—
13#555×C151—21no—
14#555×C151C2211yescharacteristic
15#554×C151C2211yescharacteristic
16#553×C151—21no—
17#552×C151—21no—
18D4×Q8×C151C2211yescharacteristic
19#548×C151—21no—
20#547×C151C2211yescharacteristic
21#544×C151—21no—
22#542×C151—22no—
23#540×C151—21no—
24#537×C151—21no—
25#536×C151—21no—
26#533×C151C2211yescharacteristic
27#532×C151C2211yescharacteristic
28C2×C4⋊Q8×C151C2211yescharacteristic
29#529×C151C2211yescharacteristic
30#501×C151—21no—
31#498×C151—21no—
32#494×C151C2212yes—
33#489×C151—21no—
34#487×C151C2212yes—
35#486×C151—21no—
36#483×C151—21no—
37#481×C151—21no—
38#481×C151—21no—
39#480×C151—21no—
40#477×C151C2212yes—
41#476×C151C2212yes—
42#476×C151C2212yes—
43#476×C151C2212yes—
44#462×C151—22no—
45#451×C151—22no—
46#432×C151C2211yescharacteristic
47#431×C151C2211yescharacteristic
48#431×C151C2211yescharacteristic
49#333×C151C2212yes—
50#332×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52D4⋊C8×C151C2212yes—
53D4⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yes—
55C2×#41×C151—21no—
56C2×#41×C151—21no—
57C22×Q8×C151—21no—
58C22×Q8×C151—21no—
59C2×Q16×C151—24no—
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151D411yescharacteristic
66C4⋊Q8×C151C2312yes—
67C4⋊Q8×C151C2311yescharacteristic
68C4⋊Q8×C151C2311yescharacteristic
69#127×C151D411yescharacteristic
70#126×C151—22no—
71#126×C151—21no—
72#125×C151—22no—
73#125×C151—21no—
74#125×C151—21no—
75#125×C151D411yescharacteristic
76#124×C151—22no—
77#124×C151—22no—
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—22no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—22no—
92C22⋊Q8×C151—21no—
93C22⋊Q8×C151—22no—
94C22⋊Q8×C151D412yes—
95C22⋊Q8×C151D411yescharacteristic
96#121×C151—22no—
97#121×C151—22no—
98#121×C151—22no—
99#121×C151—22no—
100#121×C151—21no—
101#121×C151—21no—
102#121×C151—21no—
103#121×C151—21no—
104#121×C151D411yescharacteristic
105#121×C151D411yescharacteristic
106#121×C151D411yescharacteristic
107C4×Q8×C151—21no—
108C4×Q8×C151D412yes—
109C4×Q8×C151C2311yescharacteristic
110C4×D4×C151—22no—
111C4×D4×C151—21no—
112C4×D4×C151—21no—
113C4×D4×C151—21no—
114C4×D4×C151—21no—
115C4×D4×C151C2311yescharacteristic
116C4×D4×C151C2311yescharacteristic
117C4×D4×C151C2311yescharacteristic
118#117×C151—22no—
119#117×C151—21no—
120#117×C151—21no—
121#117×C151—21no—
122#117×C151—21no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C42×C151C2311yescharacteristic
128#107×C151—22no—
129#106×C151—22no—
130#106×C151—22no—
131#106×C151—22no—
132C4⋊C8×C151—21no—
133C4⋊C8×C151C2312yes—
134C4⋊C8×C151C2312yes—
135#103×C151—24no—
136#103×C151—22no—
137#102×C151—22no—
138#102×C151—22no—
139#102×C151—22no—
140C22⋊C8×C151—21no—
141C22⋊C8×C151—21no—
142C22⋊C8×C151—21no—
143#97×C151—21no—
144C4×C8×C151—21no—
145C4×C8×C151C2312yes—
146#41×C151—82no—
147#41×C151—82no—
148C2×Q8×C151—22no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—22no—
152C2×Q8×C151—41no—
153C2×Q8×C151—82no—
154C2×Q8×C151—82no—
155C2×Q8×C151C2×D411yescharacteristic
156C2×Q8×C151C2×D412yes—
157C2×D4×C151—22no—
158C2×D4×C151—22no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151C2×D411yescharacteristic
165C2×D4×C151C2×D411yescharacteristic
166C2×D4×C151C2×D411yescharacteristic
167C22×C4×C151—22no—
168C22×C4×C151—22no—
169C22×C4×C151—22no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—41no—
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D411yescharacteristic
177Q16×C151—84no—
178C2×C8×C151—22no—
179C2×C8×C151—22no—
180C2×C8×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—41no—
198C4⋊C4×C151—41no—
199C4⋊C4×C151C2×D412yes—
200C4⋊C4×C151C2×D411yescharacteristic
201C4⋊C4×C151C2×D411yescharacteristic
202C4⋊C4×C151C2×D411yescharacteristic
203C4⋊C4×C151C2×D411yescharacteristic
204C22⋊C4×C151—22no—
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—21no—
212C22⋊C4×C151—21no—
213C22⋊C4×C151—21no—
214C22⋊C4×C151—21no—
215C22⋊C4×C151—21no—
216C22⋊C4×C151—21no—
217C22⋊C4×C151—21no—
218C22⋊C4×C151—21no—
219C42×C151—22no—
220C42×C151—22no—
221C42×C151—21no—
222C42×C151C2×D411yescharacteristic
223C42×C151C2×D411yescharacteristic
224C42×C151C2×D411yescharacteristic
225C42×C151C2411yescharacteristic
226C23×C151—21no—
227C23×C151—21no—
228C23×C151—21no—
229C23×C151#12011yescharacteristic
230Q8×C151—22no—
231Q8×C151—42no—
232Q8×C151—44no—
233Q8×C151—42no—
234Q8×C151—81no—
235Q8×C151—82no—
236Q8×C151—82no—
237D4×C151—22no—
238D4×C151—22no—
239D4×C151—22no—
240D4×C151—81no—
241D4×C151—81no—
242D4×C151—81no—
243D4×C151—81no—
244D4×C151—81no—
245D4×C151—82no—
246D4×C151—82no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—22no—
252C2×C4×C151—21no—
253C2×C4×C151—22no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—41no—
257C2×C4×C151—42no—
258C2×C4×C151—42no—
259C2×C4×C151—42no—
260C2×C4×C151—42no—
261C2×C4×C151—82no—
262C2×C4×C151—82no—
263C2×C4×C151—82no—
264C2×C4×C151—82no—
265C2×C4×C151#12011yescharacteristic
266C2×C4×C151#12011yescharacteristic
267C2×C4×C151#12011yescharacteristic
268C2×C4×C151C22×D411yescharacteristic
269C2×C4×C151C22×D411yescharacteristic
270C2×C4×C151C22×D411yescharacteristic
271C8×C151—42no—
272C8×C151—42no—
273C8×C151—42no—
274C22×C151—21no—
275C22×C151—21no—
276C22×C151—21no—
277C22×C151—41no—
278C22×C151—41no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—41no—
282C22×C151—41no—
283C22×C151—41no—
284C22×C151—41no—
285C22×C151—41no—
286C22×C151C2×#12011yescharacteristic
287C4×C151—21no—
288C4×C151—21no—
289C4×C151—21no—
290C4×C151—21no—
291C4×C151—41no—
292C4×C151—41no—
293C4×C151—42no—
294C4×C151—41no—
295C4×C151—41no—
296C4×C151—41no—
297C4×C151—42no—
298C4×C151—82no—
299C4×C151#57712yes—
300C4×C151#57812yes—
301C2×C151—41no—
302C2×C151—81no—
303C2×C151—81no—
304C2×C151—81no—
305C2×C151#300911yescharacteristic
306C2×C151#301111yescharacteristic
307C2×C151#302111yescharacteristic
308#18957C15111yesmaximal, characteristic, direct product factor, Sylow
309C151#1895711yescharacteristic, direct product factor, Sylow
310#3547C2×C15111yescharacteristic
311#3238C2×C15111yescharacteristic, complemented
312#3227C2×C15111yescharacteristic, complemented
313#3209C2×C15111yescharacteristic, complemented
314#1637C2×C15112yescomplemented
315#1635C2×C15112yescomplemented
316#1634C2×C15112yescomplemented
317#1632C2×C15112yescomplemented
318#1554C2×C15111yescharacteristic, complemented
319#1496C2×C15111yescharacteristic, complemented
320#1482C2×C15111yescharacteristic, complemented
321#562—22no—
322#555—21no—
323#555C22×C15111yescharacteristic
324#554C22×C15111yescharacteristic
325#553—21no—
326#552—21no—
327D4×Q8C22×C15111yescharacteristic
328#548—21no—
329#547C22×C15111yescharacteristic
330#544—21no—
331#542—22no—
332#540—21no—
333#537—21no—
334#536—21no—
335#533C22×C15111yescharacteristic
336#532C22×C15111yescharacteristic
337C2×C4⋊Q8C22×C15111yescharacteristic
338#529C22×C15111yescharacteristic
339#501—21no—
340#498—21no—
341#494C22×C15112yes—
342#489—21no—
343#487C22×C15112yes—
344#486—21no—
345#483—21no—
346#481—21no—
347#481—21no—
348#480—21no—
349#477C22×C15112yes—
350#476C22×C15112yes—
351#476C22×C15112yes—
352#476C22×C15112yes—
353#462—22no—
354#451—22no—
355#432C22×C15111yescharacteristic
356#431C22×C15111yescharacteristic
357#431C22×C15111yescharacteristic
358#333C22×C15112yes—
359#332C22×C15112yes—
360Q8⋊C8C22×C15112yes—
361D4⋊C8C22×C15112yes—
362D4⋊C8C22×C15112yes—
363D4⋊C8C22×C15112yes—
364C2×#41—21no—
365C2×#41—21no—
366C22×Q8—21no—
367C22×Q8—21no—
368C2×Q16—24no—
369C4⋊Q8—22no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8D4×C15111yescharacteristic
375C4⋊Q8C23×C15112yes—
376C4⋊Q8C23×C15111yescharacteristic
377C4⋊Q8C23×C15111yescharacteristic
378#127D4×C15111yescharacteristic
379#126—22no—
380#126—21no—
381#125—22no—
382#125—21no—
383#125—21no—
384#125D4×C15111yescharacteristic
385#124—22no—
386#124—22no—
387#124—22no—
388#124—21no—
389#124D4×C15111yescharacteristic
390#123—22no—
391#123—22no—
392#123—22no—
393#123—21no—
394#123—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8D4×C15111yescharacteristic
404C22⋊Q8D4×C15112yes—
405#121—22no—
406#121—22no—
407#121—22no—
408#121—22no—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121D4×C15111yescharacteristic
414#121D4×C15111yescharacteristic
415#121D4×C15111yescharacteristic
416C4×Q8—21no—
417C4×Q8D4×C15112yes—
418C4×Q8C23×C15111yescharacteristic
419C4×D4—22no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4C23×C15111yescharacteristic
425C4×D4C23×C15111yescharacteristic
426C4×D4C23×C15111yescharacteristic
427#117—22no—
428#117—21no—
429#117—21no—
430#117—21no—
431#117—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C42C23×C15111yescharacteristic
437#107—22no—
438#106—22no—
439#106—22no—
440#106—22no—
441C4⋊C8—21no—
442C4⋊C8C23×C15112yes—
443C4⋊C8C23×C15112yes—
444#103—22no—
445#103—24no—
446#102—22no—
447#102—22no—
448#102—22no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452#97—21no—
453C4×C8—21no—
454C4×C8C23×C15112yes—
455#41—82no—
456#41—82no—
457C2×Q8—22no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—41no—
462C2×Q8—82no—
463C2×Q8—82no—
464C2×Q8C2×D4×C15111yescharacteristic
465C2×Q8C2×D4×C15112yes—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4C2×D4×C15111yescharacteristic
474C2×D4C2×D4×C15111yescharacteristic
475C2×D4C2×D4×C15111yescharacteristic
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4C2×D4×C15111yescharacteristic
484C22×C4C2×D4×C15111yescharacteristic
485C22×C4C2×D4×C15111yescharacteristic
486Q16—84no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4C2×D4×C15112yes—
509C4⋊C4C2×D4×C15111yescharacteristic
510C4⋊C4C2×D4×C15111yescharacteristic
511C4⋊C4C2×D4×C15111yescharacteristic
512C4⋊C4C2×D4×C15111yescharacteristic
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C42—22no—
529C42—22no—
530C42—21no—
531C42C2×D4×C15111yescharacteristic
532C42C2×D4×C15111yescharacteristic
533C42C2×D4×C15111yescharacteristic
534C42C24×C15111yescharacteristic
535C23—21no—
536C23—21no—
537C23—21no—
538C23#120×C15111yescharacteristic
539Q8—22no—
540Q8—42no—
541Q8—44no—
542Q8—42no—
543Q8—81no—
544Q8—82no—
545Q8—82no—
546D4—22no—
547D4—22no—
548D4—22no—
549D4—81no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4#120×C15111yescharacteristic
575C2×C4#120×C15111yescharacteristic
576C2×C4#120×C15111yescharacteristic
577C2×C4C22×D4×C15111yescharacteristic
578C2×C4C22×D4×C15111yescharacteristic
579C2×C4C22×D4×C15111yescharacteristic
580C8—42no—
581C8—42no—
582C8—42no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C2×#120×C15111yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—42no—
607C4—82no—
608C4#577×C15112yes—
609C4#578×C15112yes—
610C2—41no—
611C2—81no—
612C2—81no—
613C2—81no—
614C2#3009×C15111yescharacteristic
615C2#3011×C15111yescharacteristic
616C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3547×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
2. #3238×C151C2semidirect
3. #3227×C151C2semidirect
4. #3209×C151C2semidirect
5. #1637×C151C2semidirect
6. #1635×C151C2semidirect
7. #1634×C151C2semidirect
8. #1632×C151C2semidirect
9. #1554×C151C2semidirect
10. #1496×C151C2semidirect
11. #1482×C151C2semidirect
308. #18957C151direct (N × H)
309. C151#18957direct (N × H)
311. #3238C2×C151semidirect
312. #3227C2×C151semidirect
313. #3209C2×C151semidirect
314. #1637C2×C151semidirect
315. #1635C2×C151semidirect
316. #1634C2×C151semidirect
317. #1632C2×C151semidirect
318. #1554C2×C151semidirect
319. #1496C2×C151semidirect
320. #1482C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3547×C1512
#3238×C1512
#3227×C1512
#3209×C1512
#1637×C1512
#1635×C1512
#1634×C1512
#1632×C1512
#1554×C1512
#1496×C1512
#1482×C1512
#18957151