Finite Group Databasebeta

← C151×#18959 #50323884

Subgroups — C151×#18959 #50323884

Order 38656.

874 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3554×C151C211yesmaximal, characteristic
2#3238×C151C211yesmaximal, characteristic, complemented
3#3230×C151C211yesmaximal, characteristic, complemented
4#3206×C151C211yesmaximal, characteristic, complemented
5#1637×C151C212yesmaximal, complemented
6#1636×C151C212yesmaximal, complemented
7#1631×C151C212yesmaximal, complemented
8#1630×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#501×C151—21no—
31#500×C151—21no—
32#492×C151C2212yes—
33#489×C151—21no—
34#487×C151—21no—
35#487×C151C2212yes—
36#484×C151—21no—
37#484×C151—21no—
38#483×C151—21no—
39#480×C151—21no—
40#477×C151C2212yes—
41#477×C151C2212yes—
42#477×C151C2212yes—
43#476×C151C2212yes—
44#461×C151—22no—
45#448×C151—22no—
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×SD16×C151—24no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151D411yescharacteristic
66C4⋊Q8×C151D411yescharacteristic
67C4⋊Q8×C151C2312yes—
68C4⋊Q8×C151C2311yescharacteristic
69#127×C151—21no—
70#127×C151C2311yescharacteristic
71#126×C151—22no—
72#126×C151—21no—
73#125×C151—22no—
74#125×C151—21no—
75#125×C151—21no—
76#125×C151D411yescharacteristic
77#124×C151—22no—
78#124×C151—22no—
79#124×C151—21no—
80#124×C151—21no—
81#124×C151—21no—
82#124×C151D411yescharacteristic
83#123×C151—22no—
84#123×C151—22no—
85#123×C151—22no—
86#123×C151—22no—
87#123×C151—22no—
88#123×C151—22no—
89#123×C151—21no—
90C22⋊Q8×C151—22no—
91C22⋊Q8×C151—22no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—22no—
94C22⋊Q8×C151—21no—
95C22⋊Q8×C151—22no—
96C22⋊Q8×C151—21no—
97C22⋊Q8×C151D411yescharacteristic
98C22⋊Q8×C151D411yescharacteristic
99C22⋊Q8×C151D411yescharacteristic
100#121×C151—22no—
101#121×C151—22no—
102#121×C151—22no—
103#121×C151—21no—
104#121×C151—21no—
105#121×C151D412yes—
106#121×C151D411yescharacteristic
107C4×Q8×C151—21no—
108C4×Q8×C151—21no—
109C4×Q8×C151—21no—
110C4×Q8×C151C2311yescharacteristic
111C4×Q8×C151C2311yescharacteristic
112C4×Q8×C151C2311yescharacteristic
113C4×D4×C151—22no—
114C4×D4×C151—21no—
115C4×D4×C151—21no—
116C4×D4×C151—21no—
117C4×D4×C151—21no—
118C4×D4×C151—21no—
119C4×D4×C151—21no—
120C4×D4×C151D412yes—
121C4×D4×C151C2311yescharacteristic
122#117×C151—21no—
123#117×C151—21no—
124C2×C4⋊C4×C151—22no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C42×C151C2311yescharacteristic
128#107×C151—22no—
129#107×C151—22no—
130#107×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#103×C151—22no—
138#103×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×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
175SD16×C151—84no—
176C2×C8×C151—22no—
177C2×C8×C151—22no—
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—21no—
190C4⋊C4×C151—21no—
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—21no—
210C22⋊C4×C151—21no—
211C22⋊C4×C151—21no—
212C22⋊C4×C151—21no—
213C22⋊C4×C151—21no—
214C22⋊C4×C151—21no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—21no—
218C42×C151—22no—
219C42×C151—21no—
220C42×C151—21no—
221C42×C151—21no—
222C42×C151C2×D411yescharacteristic
223C42×C151C2×D411yescharacteristic
224C42×C151C2×D411yescharacteristic
225C42×C151C2411yescharacteristic
226C23×C151—21no—
227C23×C151—22no—
228C23×C151#12011yescharacteristic
229Q8×C151—22no—
230Q8×C151—22no—
231Q8×C151—22no—
232Q8×C151—44no—
233Q8×C151—42no—
234Q8×C151—81no—
235Q8×C151—82no—
236Q8×C151—82no—
237D4×C151—22no—
238D4×C151—42no—
239D4×C151—42no—
240D4×C151—42no—
241D4×C151—82no—
242D4×C151—81no—
243D4×C151—82no—
244D4×C151—82no—
245C2×C4×C151—22no—
246C2×C4×C151—22no—
247C2×C4×C151—21no—
248C2×C4×C151—22no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—21no—
255C2×C4×C151—41no—
256C2×C4×C151—42no—
257C2×C4×C151—42no—
258C2×C4×C151—82no—
259C2×C4×C151—82no—
260C2×C4×C151—82no—
261C2×C4×C151—82no—
262C2×C4×C151—82no—
263C2×C4×C151#12011yescharacteristic
264C2×C4×C151#12011yescharacteristic
265C2×C4×C151#12011yescharacteristic
266C2×C4×C151C22×D411yescharacteristic
267C2×C4×C151C22×D411yescharacteristic
268C2×C4×C151C22×D411yescharacteristic
269C8×C151—42no—
270C8×C151—42no—
271C8×C151—42no—
272C22×C151—21no—
273C22×C151—21no—
274C22×C151—21no—
275C22×C151—41no—
276C22×C151—42no—
277C22×C151—41no—
278C22×C151—42no—
279C22×C151—42no—
280C22×C151—41no—
281C22×C151C2×#12011yescharacteristic
282C4×C151—21no—
283C4×C151—21no—
284C4×C151—21no—
285C4×C151—21no—
286C4×C151—41no—
287C4×C151—41no—
288C4×C151—42no—
289C4×C151—41no—
290C4×C151—41no—
291C4×C151—41no—
292C4×C151—41no—
293C4×C151—41no—
294C4×C151—82no—
295C4×C151#57712yes—
296C4×C151#57812yes—
297C2×C151—41no—
298C2×C151—81no—
299C2×C151—82no—
300C2×C151#300911yescharacteristic
301C2×C151#301111yescharacteristic
302C2×C151#302111yescharacteristic
303#18959C15111yesmaximal, characteristic, direct product factor, Sylow
304C151#1895911yescharacteristic, direct product factor, Sylow
305#3554C2×C15111yescharacteristic
306#3238C2×C15111yescharacteristic, complemented
307#3230C2×C15111yescharacteristic, complemented
308#3206C2×C15111yescharacteristic, complemented
309#1637C2×C15112yescomplemented
310#1636C2×C15112yescomplemented
311#1631C2×C15112yescomplemented
312#1630C2×C15112yescomplemented
313#1553C2×C15111yescharacteristic, complemented
314#1497C2×C15111yescharacteristic, complemented
315#1482C2×C15111yescharacteristic, complemented
316#562—22no—
317#559—21no—
318#559C22×C15111yescharacteristic
319#557C22×C15111yescharacteristic
320#554—21no—
321#550C22×C15111yescharacteristic
322D4×Q8C22×C15111yescharacteristic
323#548—21no—
324#547—21no—
325#542—21no—
326#542—21no—
327#540—21no—
328#539—22no—
329#536—21no—
330#533C22×C15111yescharacteristic
331#532C22×C15111yescharacteristic
332C2×C4⋊Q8C22×C15111yescharacteristic
333#529C22×C15111yescharacteristic
334#501—21no—
335#500—21no—
336#492C22×C15112yes—
337#489—21no—
338#487—21no—
339#487C22×C15112yes—
340#484—21no—
341#484—21no—
342#483—21no—
343#480—21no—
344#477C22×C15112yes—
345#477C22×C15112yes—
346#477C22×C15112yes—
347#476C22×C15112yes—
348#461—22no—
349#448—22no—
350#432C22×C15111yescharacteristic
351#431C22×C15111yescharacteristic
352#431C22×C15111yescharacteristic
353#332C22×C15112yes—
354#331C22×C15112yes—
355Q8⋊C8C22×C15112yes—
356Q8⋊C8C22×C15112yes—
357Q8⋊C8C22×C15112yes—
358D4⋊C8C22×C15112yes—
359C2×#41—21no—
360C2×#41—21no—
361C22×Q8—21no—
362C22×Q8—21no—
363C2×SD16—24no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8D4×C15111yescharacteristic
370C4⋊Q8D4×C15111yescharacteristic
371C4⋊Q8C23×C15112yes—
372C4⋊Q8C23×C15111yescharacteristic
373#127—21no—
374#127C23×C15111yescharacteristic
375#126—22no—
376#126—21no—
377#125—22no—
378#125—21no—
379#125—21no—
380#125D4×C15111yescharacteristic
381#124—22no—
382#124—22no—
383#124—21no—
384#124—21no—
385#124—21no—
386#124D4×C15111yescharacteristic
387#123—22no—
388#123—22no—
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—21no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8D4×C15111yescharacteristic
402C22⋊Q8D4×C15111yescharacteristic
403C22⋊Q8D4×C15111yescharacteristic
404#121—22no—
405#121—22no—
406#121—22no—
407#121—21no—
408#121—21no—
409#121D4×C15111yescharacteristic
410#121D4×C15112yes—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8C23×C15111yescharacteristic
415C4×Q8C23×C15111yescharacteristic
416C4×Q8C23×C15111yescharacteristic
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4D4×C15112yes—
425C4×D4C23×C15111yescharacteristic
426#117—21no—
427#117—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C42C23×C15111yescharacteristic
432#107—22no—
433#107—22no—
434#107—22no—
435#106—22no—
436C4⋊C8—21no—
437C4⋊C8C23×C15112yes—
438C4⋊C8C23×C15112yes—
439#103—22no—
440#103—22no—
441#103—22no—
442#103—24no—
443#102—22no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447#97—21no—
448C4×C8—21no—
449C4×C8C23×C15112yes—
450#41—82no—
451#41—82no—
452C2×Q8—22no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—41no—
457C2×Q8—82no—
458C2×Q8—82no—
459C2×Q8C2×D4×C15111yescharacteristic
460C2×Q8C2×D4×C15111yescharacteristic
461C2×Q8C2×D4×C15111yescharacteristic
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4C2×D4×C15111yescharacteristic
469C2×D4C2×D4×C15112yes—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—41no—
476C22×C4C2×D4×C15111yescharacteristic
477C22×C4C2×D4×C15111yescharacteristic
478C22×C4C2×D4×C15111yescharacteristic
479SD16—84no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
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—22no—
500C4⋊C4—22no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C15112yes—
504C4⋊C4C2×D4×C15111yescharacteristic
505C4⋊C4C2×D4×C15111yescharacteristic
506C4⋊C4C2×D4×C15111yescharacteristic
507C4⋊C4C2×D4×C15111yescharacteristic
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C42—22no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42C2×D4×C15111yescharacteristic
527C42C2×D4×C15111yescharacteristic
528C42C2×D4×C15111yescharacteristic
529C42C24×C15111yescharacteristic
530C23—21no—
531C23—22no—
532C23#120×C15111yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—44no—
537Q8—42no—
538Q8—81no—
539Q8—82no—
540Q8—82no—
541D4—22no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—82no—
546D4—81no—
547D4—82no—
548D4—82no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4#120×C15111yescharacteristic
568C2×C4#120×C15111yescharacteristic
569C2×C4#120×C15111yescharacteristic
570C2×C4C22×D4×C15111yescharacteristic
571C2×C4C22×D4×C15111yescharacteristic
572C2×C4C22×D4×C15111yescharacteristic
573C8—42no—
574C8—42no—
575C8—42no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—42no—
581C22—41no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22C2×#120×C15111yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—82no—
599C4#577×C15112yes—
600C4#578×C15112yes—
601C2—41no—
602C2—81no—
603C2—82no—
604C2#3009×C15111yescharacteristic
605C2#3011×C15111yescharacteristic
606C2#3021×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. #3238×C151C2semidirect
3. #3230×C151C2semidirect
4. #3206×C151C2semidirect
5. #1637×C151C2semidirect
6. #1636×C151C2semidirect
7. #1631×C151C2semidirect
8. #1630×C151C2semidirect
9. #1553×C151C2semidirect
10. #1497×C151C2semidirect
11. #1482×C151C2semidirect
303. #18959C151direct (N × H)
304. C151#18959direct (N × H)
306. #3238C2×C151semidirect
307. #3230C2×C151semidirect
308. #3206C2×C151semidirect
309. #1637C2×C151semidirect
310. #1636C2×C151semidirect
311. #1631C2×C151semidirect
312. #1630C2×C151semidirect
313. #1553C2×C151semidirect
314. #1497C2×C151semidirect
315. #1482C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3554×C1512
#3238×C1512
#3230×C1512
#3206×C1512
#1637×C1512
#1636×C1512
#1631×C1512
#1630×C1512
#1553×C1512
#1497×C1512
#1482×C1512
#18959151