Finite Group Databasebeta

← C151×#19308 #50324233

Subgroups — C151×#19308 #50324233

Order 38656.

632 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3182×C151C211yesmaximal, characteristic
2#3113×C151C211yesmaximal, characteristic, complemented
3#3037×C151C211yesmaximal, characteristic
4Q8×M16×C151C211yesmaximal, characteristic, complemented
5#1702×C151C211yesmaximal, characteristic, complemented
6#1700×C151C211yesmaximal, characteristic, complemented
7#1694×C151C211yesmaximal, characteristic, complemented
8#1686×C151C211yesmaximal, characteristic, complemented
9#1682×C151C211yesmaximal, characteristic, complemented
10#1680×C151C211yesmaximal, characteristic, complemented
11#1674×C151C211yesmaximal, characteristic, complemented
12#1666×C151C211yesmaximal, characteristic, complemented
13#1569×C151C211yesmaximal, characteristic, complemented
14#1561×C151C211yesmaximal, characteristic, complemented
15#1557×C151C211yesmaximal, characteristic
16C2×#137×C151—21no—
17#533×C151C2211yescharacteristic
18#532×C151C2211yescharacteristic
19C2×C4×Q8×C151C2211yescharacteristic
20#500×C151C2211yescharacteristic
21#492×C151C2211yescharacteristic
22#487×C151C2211yescharacteristic
23#486×C151C2211yescharacteristic
24#483×C151—21no—
25#475×C151C2211yescharacteristic
26#475×C151C2211yescharacteristic
27#468×C151—21no—
28#468×C151—21no—
29#464×C151—21no—
30#464×C151—21no—
31#462×C151C2211yescharacteristic
32#462×C151C2211yescharacteristic
33#462×C151C2211yescharacteristic
34#462×C151C2211yescharacteristic
35#460×C151C2211yescharacteristic
36#460×C151C2211yescharacteristic
37#451×C151—21no—
38#446×C151—21no—
39#446×C151—21no—
40#446×C151C2211yescharacteristic
41#446×C151C2211yescharacteristic
42C8×Q8×C151C2211yescharacteristic
43C8×Q8×C151C2211yescharacteristic
44#441×C151—21no—
45#441×C151—21no—
46#440×C151—21no—
47#440×C151—21no—
48#432×C151C2211yescharacteristic
49#423×C151—21no—
50#423×C151C2211yescharacteristic
51#423×C151C2211yescharacteristic
52#417×C151—21no—
53C4×M16×C151—21no—
54C4×M16×C151C2211yescharacteristic
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62#332×C151C2211yescharacteristic
63#332×C151C2211yescharacteristic
64#332×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C22×Q8×C151D411yescharacteristic
69#137×C151—44no—
70C2×Q16×C151—21no—
71C2×Q16×C151—21no—
72C2×Q16×C151—21no—
73C2×Q16×C151—21no—
74C2×SD16×C151—21no—
75C2×SD16×C151—21no—
76C2×SD16×C151—21no—
77C2×SD16×C151—21no—
78C2×M16×C151—21no—
79C2×M16×C151—21no—
80C2×M16×C151D411yescharacteristic
81C2×M16×C151D411yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85#127×C151C2311yescharacteristic
86#125×C151—21no—
87#124×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—21no—
90#121×C151—21no—
91#121×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151D411yescharacteristic
97C4×Q8×C151D411yescharacteristic
98C4×Q8×C151C2311yescharacteristic
99C4×Q8×C151C2311yescharacteristic
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102#117×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151D411yescharacteristic
105C2×C42×C151—21no—
106C2×C42×C151C2311yescharacteristic
107#107×C151—21no—
108#107×C151—21no—
109#106×C151—21no—
110#106×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151—21no—
115C4⋊C8×C151—21no—
116C4⋊C8×C151—21no—
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
122C4⋊C8×C151C2311yescharacteristic
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—21no—
128#103×C151—21no—
129#103×C151—21no—
130#103×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151—21no—
135C22⋊C8×C151—21no—
136#97×C151—21no—
137#97×C151—21no—
138#97×C151—21no—
139#97×C151D411yescharacteristic
140#97×C151D411yescharacteristic
141C4×C8×C151—21no—
142C4×C8×C151—21no—
143C4×C8×C151C2311yescharacteristic
144C4×C8×C151C2311yescharacteristic
145#41×C151—42no—
146#41×C151—42no—
147C2×Q8×C151—21no—
148C2×Q8×C151—22no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—41no—
153C2×Q8×C151C2×D411yescharacteristic
154C2×Q8×C151C2×D411yescharacteristic
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—41no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—41no—
162C22×C4×C151C2×D411yescharacteristic
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151#4111yescharacteristic
165Q16×C151—42no—
166Q16×C151—42no—
167Q16×C151—42no—
168Q16×C151—42no—
169SD16×C151—42no—
170SD16×C151—42no—
171SD16×C151—42no—
172SD16×C151—42no—
173M16×C151—22no—
174M16×C151—41no—
175M16×C151—42no—
176M16×C151—42no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—21no—
183C2×C8×C151C2×D411yescharacteristic
184C2×C8×C151C2×D411yescharacteristic
185C2×C8×C151C2×D411yescharacteristic
186C2×C8×C151C2×D411yescharacteristic
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—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—41no—
199C4⋊C4×C151—41no—
200C4⋊C4×C151C2×D411yescharacteristic
201C4⋊C4×C151C2×D411yescharacteristic
202C22⋊C4×C151—41no—
203C22⋊C4×C151—41no—
204C22⋊C4×C151—41no—
205C42×C151—21no—
206C42×C151—21no—
207C42×C151—21no—
208C42×C151—21no—
209C42×C151—41no—
210C42×C151C2×D411yescharacteristic
211C42×C151C2×D411yescharacteristic
212C42×C151#4111yescharacteristic
213C42×C151C2411yescharacteristic
214C23×C151—41no—
215C23×C151#12111yescharacteristic
216Q8×C151—21no—
217Q8×C151—21no—
218Q8×C151—21no—
219Q8×C151—42no—
220Q8×C151—41no—
221Q8×C151—41no—
222Q8×C151—41no—
223Q8×C151—41no—
224Q8×C151—41no—
225Q8×C151—41no—
226Q8×C151AGL(1,ℤ/8)12yes—
227D4×C151—41no—
228D4×C151—41no—
229D4×C151—41no—
230D4×C151—41no—
231D4×C151—81no—
232D4×C151—82no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—41no—
242C2×C4×C151—42no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—82no—
247C2×C4×C151—81no—
248C2×C4×C151#12111yescharacteristic
249C2×C4×C151#12111yescharacteristic
250C2×C4×C151#12111yescharacteristic
251C2×C4×C151C22×D411yescharacteristic
252C2×C4×C151C22×D411yescharacteristic
253C2×C4×C151C2×#4111yescharacteristic
254C8×C151—21no—
255C8×C151—21no—
256C8×C151—21no—
257C8×C151—41no—
258C8×C151—41no—
259C8×C151—41no—
260C8×C151—41no—
261C8×C151—41no—
262C8×C151—41no—
263C8×C151#13712yescomplemented
264C22×C151—21no—
265C22×C151—21no—
266C22×C151—21no—
267C22×C151—81no—
268C22×C151—81no—
269C22×C151—81no—
270C22×C151C2×#12111yescharacteristic
271C4×C151—21no—
272C4×C151—21no—
273C4×C151—22no—
274C4×C151—21no—
275C4×C151—21no—
276C4×C151—41no—
277C4×C151—41no—
278C4×C151—41no—
279C4×C151—81no—
280C4×C151—81no—
281C4×C151—81no—
282C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
283C4×C151C2×#13711yescharacteristic
284C4×C151#57511yescharacteristic
285C4×C151#57511yescharacteristic
286C2×C151—41no—
287C2×C151—161no—
288C2×C151#303711yescharacteristic
289C2×C151#305511yescharacteristic
290C2×C151#306911yescharacteristic
291#19308C15111yesmaximal, characteristic, direct product factor, Sylow
292C151#1930811yescharacteristic, direct product factor, Sylow
293#3182C2×C15111yescharacteristic
294#3113C2×C15111yescharacteristic, complemented
295#3037C2×C15111yescharacteristic
296Q8×M16C2×C15111yescharacteristic, complemented
297#1702C2×C15111yescharacteristic, complemented
298#1700C2×C15111yescharacteristic, complemented
299#1694C2×C15111yescharacteristic, complemented
300#1686C2×C15111yescharacteristic, complemented
301#1682C2×C15111yescharacteristic, complemented
302#1680C2×C15111yescharacteristic, complemented
303#1674C2×C15111yescharacteristic, complemented
304#1666C2×C15111yescharacteristic, complemented
305#1569C2×C15111yescharacteristic, complemented
306#1561C2×C15111yescharacteristic, complemented
307#1557C2×C15111yescharacteristic
308C2×#137—21no—
309#533C22×C15111yescharacteristic
310#532C22×C15111yescharacteristic
311C2×C4×Q8C22×C15111yescharacteristic
312#500C22×C15111yescharacteristic
313#492C22×C15111yescharacteristic
314#487C22×C15111yescharacteristic
315#486C22×C15111yescharacteristic
316#483—21no—
317#475C22×C15111yescharacteristic
318#475C22×C15111yescharacteristic
319#468—21no—
320#468—21no—
321#464—21no—
322#464—21no—
323#462C22×C15111yescharacteristic
324#462C22×C15111yescharacteristic
325#462C22×C15111yescharacteristic
326#462C22×C15111yescharacteristic
327#460C22×C15111yescharacteristic
328#460C22×C15111yescharacteristic
329#451—21no—
330#446—21no—
331#446—21no—
332#446C22×C15111yescharacteristic
333#446C22×C15111yescharacteristic
334C8×Q8C22×C15111yescharacteristic
335C8×Q8C22×C15111yescharacteristic
336#441—21no—
337#441—21no—
338#440—21no—
339#440—21no—
340#432C22×C15111yescharacteristic
341#423—21no—
342#423C22×C15111yescharacteristic
343#423C22×C15111yescharacteristic
344#417—21no—
345C4×M16—21no—
346C4×M16C22×C15111yescharacteristic
347#335C22×C15111yescharacteristic
348#335C22×C15111yescharacteristic
349#334C22×C15111yescharacteristic
350#334C22×C15111yescharacteristic
351#332C22×C15111yescharacteristic
352#332C22×C15111yescharacteristic
353#332C22×C15111yescharacteristic
354#332C22×C15111yescharacteristic
355#332C22×C15111yescharacteristic
356#332C22×C15111yescharacteristic
357#331C22×C15111yescharacteristic
358#331C22×C15111yescharacteristic
359C2×#41—21no—
360C22×Q8D4×C15111yescharacteristic
361#137—44no—
362C2×Q16—21no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16D4×C15111yescharacteristic
373C2×M16D4×C15111yescharacteristic
374C4⋊Q8C23×C15111yescharacteristic
375C4⋊Q8C23×C15111yescharacteristic
376C4⋊Q8C23×C15111yescharacteristic
377#127C23×C15111yescharacteristic
378#125—21no—
379#124—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382#121—21no—
383#121—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8D4×C15111yescharacteristic
389C4×Q8D4×C15111yescharacteristic
390C4×Q8C23×C15111yescharacteristic
391C4×Q8C23×C15111yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394#117—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4D4×C15111yescharacteristic
397C2×C42—21no—
398C2×C42C23×C15111yescharacteristic
399#107—21no—
400#107—21no—
401#106—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8C23×C15111yescharacteristic
410C4⋊C8C23×C15111yescharacteristic
411C4⋊C8C23×C15111yescharacteristic
412C4⋊C8C23×C15111yescharacteristic
413C4⋊C8C23×C15111yescharacteristic
414C4⋊C8C23×C15111yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427C22⋊C8—21no—
428#97—21no—
429#97—21no—
430#97—21no—
431#97D4×C15111yescharacteristic
432#97D4×C15111yescharacteristic
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C15111yescharacteristic
436C4×C8C23×C15111yescharacteristic
437#41—42no—
438#41—42no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8C2×D4×C15111yescharacteristic
446C2×Q8C2×D4×C15111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4C2×D4×C15111yescharacteristic
455C22×C4C2×D4×C15111yescharacteristic
456C22×C4#41×C15111yescharacteristic
457Q16—42no—
458Q16—42no—
459Q16—42no—
460Q16—42no—
461SD16—42no—
462SD16—42no—
463SD16—42no—
464SD16—42no—
465M16—22no—
466M16—41no—
467M16—42no—
468M16—42no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C2×D4×C15111yescharacteristic
476C2×C8C2×D4×C15111yescharacteristic
477C2×C8C2×D4×C15111yescharacteristic
478C2×C8C2×D4×C15111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C15111yescharacteristic
493C4⋊C4C2×D4×C15111yescharacteristic
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C2×D4×C15111yescharacteristic
503C42C2×D4×C15111yescharacteristic
504C42#41×C15111yescharacteristic
505C42C24×C15111yescharacteristic
506C23—41no—
507C23#121×C15111yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—42no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8AGL(1,ℤ/8)×C15112yes—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—82no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—81no—
540C2×C4#121×C15111yescharacteristic
541C2×C4#121×C15111yescharacteristic
542C2×C4#121×C15111yescharacteristic
543C2×C4C22×D4×C15111yescharacteristic
544C2×C4C22×D4×C15111yescharacteristic
545C2×C4C2×#41×C15111yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8#137×C15112yescomplemented
556C22—21no—
557C22—21no—
558C22—21no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22C2×#121×C15111yescharacteristic
563C4—21no—
564C4—21no—
565C4—22no—
566C4—21no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
575C4C2×#137×C15111yescharacteristic
576C4#575×C15111yescharacteristic
577C4#575×C15111yescharacteristic
578C2—41no—
579C2—161no—
580C2#3037×C15111yescharacteristic
581C2#3055×C15111yescharacteristic
582C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
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. #3113×C151C2semidirect
4. Q8×M16×C151C2semidirect
5. #1702×C151C2semidirect
6. #1700×C151C2semidirect
7. #1694×C151C2semidirect
8. #1686×C151C2semidirect
9. #1682×C151C2semidirect
10. #1680×C151C2semidirect
11. #1674×C151C2semidirect
12. #1666×C151C2semidirect
13. #1569×C151C2semidirect
14. #1561×C151C2semidirect
263. C8×C151#137semidirect
291. #19308C151direct (N × H)
292. C151#19308direct (N × H)
294. #3113C2×C151semidirect
296. Q8×M16C2×C151semidirect
297. #1702C2×C151semidirect
298. #1700C2×C151semidirect
299. #1694C2×C151semidirect
300. #1686C2×C151semidirect
301. #1682C2×C151semidirect
302. #1680C2×C151semidirect
303. #1674C2×C151semidirect
304. #1666C2×C151semidirect
305. #1569C2×C151semidirect
306. #1561C2×C151semidirect
555. C8#137×C151semidirect

Maximal subgroups

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

subgroupindex
#3182×C1512
#3113×C1512
#3037×C1512
Q8×M16×C1512
#1702×C1512
#1700×C1512
#1694×C1512
#1686×C1512
#1682×C1512
#1680×C1512
#1674×C1512
#1666×C1512
#1569×C1512
#1561×C1512
#1557×C1512
#19308151