Finite Group Databasebeta

← C151×#18971 #50323896

Subgroups — C151×#18971 #50323896

Order 38656.

874 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#3554×C151C211yesmaximal, characteristic
2#3229×C151C211yesmaximal, characteristic, complemented
3#3227×C151C211yesmaximal, characteristic, complemented
4#3218×C151C211yesmaximal, characteristic, complemented
5#1653×C151C212yesmaximal, complemented
6#1651×C151C212yesmaximal, complemented
7#1642×C151C212yesmaximal, complemented
8#1640×C151C212yesmaximal, complemented
9#1553×C151C211yesmaximal, characteristic, complemented
10#1497×C151C211yesmaximal, characteristic, complemented
11#1482×C151C211yesmaximal, characteristic, complemented
12#562×C151—22no—
13#559×C151—21no—
14#559×C151C2211yescharacteristic
15#557×C151C2211yescharacteristic
16#554×C151—21no—
17#550×C151C2211yescharacteristic
18D4×Q8×C151C2211yescharacteristic
19#548×C151—21no—
20#547×C151—21no—
21#542×C151—21no—
22#542×C151—21no—
23#540×C151—21no—
24#539×C151—22no—
25#536×C151—21no—
26#533×C151C2211yescharacteristic
27#532×C151C2211yescharacteristic
28C2×C4⋊Q8×C151C2211yescharacteristic
29#529×C151C2211yescharacteristic
30#498×C151—21no—
31#498×C151C2212yes—
32#497×C151—21no—
33#491×C151—21no—
34#487×C151—21no—
35#486×C151C2212yes—
36#483×C151—21no—
37#483×C151—21no—
38#481×C151—22no—
39#476×C151—22no—
40#475×C151C2212yes—
41#475×C151C2212yes—
42#462×C151C2212yes—
43#461×C151C2212yes—
44#451×C151—21no—
45#448×C151—21no—
46#432×C151C2211yescharacteristic
47#431×C151C2211yescharacteristic
48#431×C151C2211yescharacteristic
49#332×C151C2212yes—
50#331×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52Q8⋊C8×C151C2212yes—
53Q8⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yes—
55C2×#41×C151—21no—
56C2×#41×C151—21no—
57C22×Q8×C151—21no—
58C22×Q8×C151—21no—
59C2×Q16×C151—22no—
60C2×SD16×C151—22no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151D411yescharacteristic
67C4⋊Q8×C151D411yescharacteristic
68C4⋊Q8×C151C2312yes—
69C4⋊Q8×C151C2311yescharacteristic
70#127×C151—21no—
71#127×C151C2311yescharacteristic
72#126×C151—22no—
73#126×C151—21no—
74#125×C151—22no—
75#125×C151—21no—
76#125×C151—21no—
77#125×C151D411yescharacteristic
78#124×C151—22no—
79#124×C151—22no—
80#124×C151—21no—
81#124×C151—21no—
82#124×C151—21no—
83#124×C151D411yescharacteristic
84#123×C151—22no—
85#123×C151—22no—
86#123×C151—22no—
87#123×C151—22no—
88#123×C151—22no—
89#123×C151—22no—
90#123×C151—21no—
91C22⋊Q8×C151—22no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—22no—
94C22⋊Q8×C151—22no—
95C22⋊Q8×C151—21no—
96C22⋊Q8×C151—22no—
97C22⋊Q8×C151—21no—
98C22⋊Q8×C151D411yescharacteristic
99C22⋊Q8×C151D411yescharacteristic
100C22⋊Q8×C151D411yescharacteristic
101#121×C151—22no—
102#121×C151—22no—
103#121×C151—22no—
104#121×C151—21no—
105#121×C151—21no—
106#121×C151D411yescharacteristic
107#121×C151D412yes—
108C4×Q8×C151—21no—
109C4×Q8×C151—21no—
110C4×Q8×C151—21no—
111C4×Q8×C151C2311yescharacteristic
112C4×Q8×C151C2311yescharacteristic
113C4×Q8×C151C2311yescharacteristic
114C4×D4×C151—22no—
115C4×D4×C151—21no—
116C4×D4×C151—21no—
117C4×D4×C151—21no—
118C4×D4×C151—21no—
119C4×D4×C151—21no—
120C4×D4×C151—21no—
121C4×D4×C151D412yes—
122C4×D4×C151C2311yescharacteristic
123#117×C151—21no—
124#117×C151—21no—
125C2×C4⋊C4×C151—22no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C42×C151C2311yescharacteristic
129#106×C151—22no—
130#106×C151—22no—
131#106×C151—24no—
132C4⋊C8×C151—21no—
133C4⋊C8×C151C2312yes—
134C4⋊C8×C151C2312yes—
135#103×C151—22no—
136#103×C151—22no—
137#103×C151—22no—
138#103×C151—22no—
139#102×C151—24no—
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×D411yescharacteristic
157C2×Q8×C151C2×D411yescharacteristic
158C2×D4×C151—22no—
159C2×D4×C151—22no—
160C2×D4×C151—21no—
161C2×D4×C151—22no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151C2×D411yescharacteristic
165C2×D4×C151C2×D412yes—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
168C22×C4×C151—22no—
169C22×C4×C151—21no—
170C22×C4×C151—22no—
171C22×C4×C151—41no—
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D411yescharacteristic
174C22×C4×C151C2×D411yescharacteristic
175Q16×C151—82no—
176SD16×C151—82no—
177C2×C8×C151—22no—
178C2×C8×C151—22no—
179C2×C8×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—22no—
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—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—22no—
198C4⋊C4×C151—41no—
199C4⋊C4×C151—41no—
200C4⋊C4×C151C2×D411yescharacteristic
201C4⋊C4×C151C2×D411yescharacteristic
202C4⋊C4×C151C2×D411yescharacteristic
203C4⋊C4×C151C2×D412yes—
204C4⋊C4×C151C2×D411yescharacteristic
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—22no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—21no—
219C42×C151—22no—
220C42×C151—21no—
221C42×C151—21no—
222C42×C151—21no—
223C42×C151C2×D411yescharacteristic
224C42×C151C2×D411yescharacteristic
225C42×C151C2×D411yescharacteristic
226C42×C151C2411yescharacteristic
227C23×C151—21no—
228C23×C151—22no—
229C23×C151#12011yescharacteristic
230Q8×C151—22no—
231Q8×C151—22no—
232Q8×C151—22no—
233Q8×C151—42no—
234Q8×C151—42no—
235Q8×C151—42no—
236Q8×C151—81no—
237Q8×C151—82no—
238Q8×C151—82no—
239D4×C151—22no—
240D4×C151—42no—
241D4×C151—42no—
242D4×C151—42no—
243D4×C151—82no—
244D4×C151—81no—
245D4×C151—82no—
246D4×C151—82no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—21no—
250C2×C4×C151—22no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—41no—
258C2×C4×C151—42no—
259C2×C4×C151—42no—
260C2×C4×C151—82no—
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—42no—
279C22×C151—41no—
280C22×C151—42no—
281C22×C151—42no—
282C22×C151—41no—
283C22×C151C2×#12011yescharacteristic
284C4×C151—21no—
285C4×C151—21no—
286C4×C151—21no—
287C4×C151—21no—
288C4×C151—41no—
289C4×C151—41no—
290C4×C151—42no—
291C4×C151—41no—
292C4×C151—41no—
293C4×C151—41no—
294C4×C151—41no—
295C4×C151—41no—
296C4×C151—82no—
297C4×C151#57712yes—
298C4×C151#57712yes—
299C2×C151—41no—
300C2×C151—81no—
301C2×C151—82no—
302C2×C151#300911yescharacteristic
303C2×C151#301011yescharacteristic
304C2×C151#302211yescharacteristic
305#18971C15111yesmaximal, characteristic, direct product factor, Sylow
306C151#1897111yescharacteristic, direct product factor, Sylow
307#3554C2×C15111yescharacteristic
308#3229C2×C15111yescharacteristic, complemented
309#3227C2×C15111yescharacteristic, complemented
310#3218C2×C15111yescharacteristic, complemented
311#1653C2×C15112yescomplemented
312#1651C2×C15112yescomplemented
313#1642C2×C15112yescomplemented
314#1640C2×C15112yescomplemented
315#1553C2×C15111yescharacteristic, complemented
316#1497C2×C15111yescharacteristic, complemented
317#1482C2×C15111yescharacteristic, complemented
318#562—22no—
319#559—21no—
320#559C22×C15111yescharacteristic
321#557C22×C15111yescharacteristic
322#554—21no—
323#550C22×C15111yescharacteristic
324D4×Q8C22×C15111yescharacteristic
325#548—21no—
326#547—21no—
327#542—21no—
328#542—21no—
329#540—21no—
330#539—22no—
331#536—21no—
332#533C22×C15111yescharacteristic
333#532C22×C15111yescharacteristic
334C2×C4⋊Q8C22×C15111yescharacteristic
335#529C22×C15111yescharacteristic
336#498—21no—
337#498C22×C15112yes—
338#497—21no—
339#491—21no—
340#487—21no—
341#486C22×C15112yes—
342#483—21no—
343#483—21no—
344#481—22no—
345#476—22no—
346#475C22×C15112yes—
347#475C22×C15112yes—
348#462C22×C15112yes—
349#461C22×C15112yes—
350#451—21no—
351#448—21no—
352#432C22×C15111yescharacteristic
353#431C22×C15111yescharacteristic
354#431C22×C15111yescharacteristic
355#332C22×C15112yes—
356#331C22×C15112yes—
357Q8⋊C8C22×C15112yes—
358Q8⋊C8C22×C15112yes—
359Q8⋊C8C22×C15112yes—
360D4⋊C8C22×C15112yes—
361C2×#41—21no—
362C2×#41—21no—
363C22×Q8—21no—
364C22×Q8—21no—
365C2×Q16—22no—
366C2×SD16—22no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8D4×C15111yescharacteristic
373C4⋊Q8D4×C15111yescharacteristic
374C4⋊Q8C23×C15112yes—
375C4⋊Q8C23×C15111yescharacteristic
376#127—21no—
377#127C23×C15111yescharacteristic
378#126—22no—
379#126—21no—
380#125—22no—
381#125—21no—
382#125—21no—
383#125D4×C15111yescharacteristic
384#124—22no—
385#124—22no—
386#124—21no—
387#124—21no—
388#124—21no—
389#124D4×C15111yescharacteristic
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396#123—21no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8D4×C15111yescharacteristic
405C22⋊Q8D4×C15111yescharacteristic
406C22⋊Q8D4×C15111yescharacteristic
407#121—22no—
408#121—22no—
409#121—22no—
410#121—21no—
411#121—21no—
412#121D4×C15111yescharacteristic
413#121D4×C15112yes—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8C23×C15111yescharacteristic
418C4×Q8C23×C15111yescharacteristic
419C4×Q8C23×C15111yescharacteristic
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4D4×C15112yes—
428C4×D4C23×C15111yescharacteristic
429#117—21no—
430#117—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C42C23×C15111yescharacteristic
435#106—22no—
436#106—22no—
437#106—24no—
438C4⋊C8—21no—
439C4⋊C8C23×C15112yes—
440C4⋊C8C23×C15112yes—
441#103—22no—
442#103—22no—
443#103—22no—
444#103—22no—
445#102—24no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97—21no—
450C4×C8—21no—
451C4×C8C23×C15112yes—
452#41—82no—
453#41—82no—
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—22no—
458C2×Q8—41no—
459C2×Q8—82no—
460C2×Q8—82no—
461C2×Q8C2×D4×C15111yescharacteristic
462C2×Q8C2×D4×C15111yescharacteristic
463C2×Q8C2×D4×C15111yescharacteristic
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4C2×D4×C15111yescharacteristic
471C2×D4C2×D4×C15112yes—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—41no—
478C22×C4C2×D4×C15111yescharacteristic
479C22×C4C2×D4×C15111yescharacteristic
480C22×C4C2×D4×C15111yescharacteristic
481Q16—82no—
482SD16—82no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C2×D4×C15111yescharacteristic
507C4⋊C4C2×D4×C15111yescharacteristic
508C4⋊C4C2×D4×C15111yescharacteristic
509C4⋊C4C2×D4×C15112yes—
510C4⋊C4C2×D4×C15111yescharacteristic
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C42—22no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42C2×D4×C15111yescharacteristic
530C42C2×D4×C15111yescharacteristic
531C42C2×D4×C15111yescharacteristic
532C42C24×C15111yescharacteristic
533C23—21no—
534C23—22no—
535C23#120×C15111yescharacteristic
536Q8—22no—
537Q8—22no—
538Q8—22no—
539Q8—42no—
540Q8—42no—
541Q8—42no—
542Q8—81no—
543Q8—82no—
544Q8—82no—
545D4—22no—
546D4—42no—
547D4—42no—
548D4—42no—
549D4—82no—
550D4—81no—
551D4—82no—
552D4—82no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4#120×C15111yescharacteristic
572C2×C4#120×C15111yescharacteristic
573C2×C4#120×C15111yescharacteristic
574C2×C4C22×D4×C15111yescharacteristic
575C2×C4C22×D4×C15111yescharacteristic
576C2×C4C22×D4×C15111yescharacteristic
577C8—42no—
578C8—42no—
579C8—42no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—41no—
584C22—42no—
585C22—41no—
586C22—42no—
587C22—42no—
588C22—41no—
589C22C2×#120×C15111yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—82no—
603C4#577×C15112yes—
604C4#577×C15112yes—
605C2—41no—
606C2—81no—
607C2—82no—
608C2#3009×C15111yescharacteristic
609C2#3010×C15111yescharacteristic
610C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3554×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. #3229×C151C2semidirect
3. #3227×C151C2semidirect
4. #3218×C151C2semidirect
5. #1653×C151C2semidirect
6. #1651×C151C2semidirect
7. #1642×C151C2semidirect
8. #1640×C151C2semidirect
9. #1553×C151C2semidirect
10. #1497×C151C2semidirect
11. #1482×C151C2semidirect
305. #18971C151direct (N × H)
306. C151#18971direct (N × H)
308. #3229C2×C151semidirect
309. #3227C2×C151semidirect
310. #3218C2×C151semidirect
311. #1653C2×C151semidirect
312. #1651C2×C151semidirect
313. #1642C2×C151semidirect
314. #1640C2×C151semidirect
315. #1553C2×C151semidirect
316. #1497C2×C151semidirect
317. #1482C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3554×C1512
#3229×C1512
#3227×C1512
#3218×C1512
#1653×C1512
#1651×C1512
#1642×C1512
#1640×C1512
#1553×C1512
#1497×C1512
#1482×C1512
#18971151