Finite Group Databasebeta

← C151×#18955 #50323880

Subgroups — C151×#18955 #50323880

Order 38656.

938 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3546×C151C211yesmaximal, characteristic
2#3238×C151C211yesmaximal, characteristic, complemented
3#3227×C151C211yesmaximal, characteristic, complemented
4#3206×C151C211yesmaximal, characteristic, complemented
5#1638×C151C212yesmaximal, complemented
6#1635×C151C212yesmaximal, complemented
7#1631×C151C212yesmaximal, complemented
8#1629×C151C212yesmaximal, complemented
9#1553×C151C211yesmaximal, characteristic, complemented
10#1496×C151C211yesmaximal, characteristic, complemented
11#1482×C151C211yesmaximal, characteristic, complemented
12#560×C151—22no—
13#556×C151C2211yescharacteristic
14#553×C151—21no—
15#550×C151—21no—
16#550×C151C2211yescharacteristic
17#547×C151C2211yescharacteristic
18#546×C151—21no—
19#546×C151—21no—
20D42×C151C2211yescharacteristic
21#542×C151—21no—
22#538×C151—22no—
23#537×C151—21no—
24#535×C151—21no—
25#535×C151—21no—
26#532×C151C2211yescharacteristic
27#532×C151C2211yescharacteristic
28C2×C4⋊Q8×C151C2211yescharacteristic, complemented
29#529×C151C2211yescharacteristic
30#501×C151—21no—
31#498×C151—21no—
32#492×C151C2212yes—
33#489×C151—21no—
34#487×C151C2212yescomplemented
35#486×C151—21no—
36#483×C151—21no—
37#481×C151—21no—
38#481×C151—21no—
39#480×C151—21no—
40#477×C151C2212yescomplemented
41#476×C151C2212yes—
42#476×C151C2212yes—
43#476×C151C2212yescomplemented
44#461×C151—22no—
45#448×C151—22no—
46#432×C151C2211yescharacteristic, complemented
47#431×C151C2211yescharacteristic, complemented
48#431×C151C2211yescharacteristic, complemented
49#332×C151C2212yescomplemented
50#331×C151C2212yes—
51Q8⋊C8×C151C2212yescomplemented
52D4⋊C8×C151C2212yes—
53D4⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yescomplemented
55C2×#41×C151—21no—
56C2×#41×C151—21no—
57C2×#41×C151—21no—
58C2×#41×C151—21no—
59C22×Q8×C151—21no—
60C22×D4×C151—21no—
61C22×D4×C151—21no—
62C2×SD16×C151—24no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151D411yescharacteristic
67C4⋊Q8×C151C2312yes—
68C4⋊Q8×C151C2311yescharacteristic
69#127×C151—22no—
70#127×C151—21no—
71#127×C151D411yescharacteristic
72#127×C151C2311yescharacteristic
73#126×C151—22no—
74#126×C151—22no—
75#126×C151—21no—
76#125×C151D411yescharacteristic
77#124×C151—22no—
78#124×C151—21no—
79#124×C151—21no—
80#124×C151—21no—
81#124×C151D411yescharacteristic
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—21no—
89C22⋊Q8×C151D411yescharacteristic
90#121×C151—22no—
91#121×C151—22no—
92#121×C151—22no—
93#121×C151—22no—
94#121×C151—22no—
95#121×C151—21no—
96#121×C151—22no—
97#121×C151—21no—
98#121×C151—21no—
99#121×C151—21no—
100#121×C151—21no—
101#121×C151—21no—
102#121×C151D412yes—
103#121×C151D411yescharacteristic
104#121×C151D411yescharacteristic
105#121×C151D411yescharacteristic
106#120×C151—22no—
107#120×C151—22no—
108#120×C151—22no—
109#120×C151—22no—
110C4×Q8×C151—21no—
111C4×Q8×C151C2311yescharacteristic
112C4×D4×C151—22no—
113C4×D4×C151—21no—
114C4×D4×C151—21no—
115C4×D4×C151—21no—
116C4×D4×C151—21no—
117C4×D4×C151D412yes—
118C4×D4×C151C2311yescharacteristic
119C4×D4×C151C2311yescharacteristic
120C4×D4×C151C2311yescharacteristic
121#117×C151—21no—
122#117×C151—21no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C22⋊C4×C151—22no—
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—
146C24×C151—22no—
147#41×C151—82no—
148#41×C151—82no—
149#41×C151—82no—
150#41×C151—82no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—22no—
154C2×Q8×C151—41no—
155C2×Q8×C151—82no—
156C2×Q8×C151C2×D411yescharacteristic
157C2×D4×C151—22no—
158C2×D4×C151—22no—
159C2×D4×C151—22no—
160C2×D4×C151—22no—
161C2×D4×C151—22no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—22no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—82no—
171C2×D4×C151—82no—
172C2×D4×C151C2×D411yescharacteristic
173C2×D4×C151C2×D411yescharacteristic
174C2×D4×C151C2×D411yescharacteristic
175C2×D4×C151C2×D412yes—
176C22×C4×C151—22no—
177C22×C4×C151—22no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—22no—
182C22×C4×C151—41no—
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186SD16×C151—84no—
187C2×C8×C151—22no—
188C2×C8×C151—22no—
189C2×C8×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
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—22no—
199C4⋊C4×C151—22no—
200C4⋊C4×C151—41no—
201C4⋊C4×C151—41no—
202C4⋊C4×C151C2×D412yes—
203C4⋊C4×C151C2×D411yescharacteristic
204C4⋊C4×C151C2×D411yescharacteristic
205C4⋊C4×C151C2×D411yescharacteristic
206C4⋊C4×C151C2×D411yescharacteristic
207C22⋊C4×C151—22no—
208C22⋊C4×C151—22no—
209C22⋊C4×C151—22no—
210C22⋊C4×C151—22no—
211C22⋊C4×C151—22no—
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—22no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151—21no—
221C22⋊C4×C151—21no—
222C22⋊C4×C151—21no—
223C42×C151—22no—
224C42×C151—21no—
225C42×C151C2×D411yescharacteristic
226C42×C151C2×D411yescharacteristic
227C42×C151C2×D411yescharacteristic
228C42×C151C2411yescharacteristic
229C23×C151—21no—
230C23×C151—21no—
231C23×C151—22no—
232C23×C151—21no—
233C23×C151—82no—
234C23×C151—82no—
235C23×C151—82no—
236C23×C151#12011yescharacteristic
237Q8×C151—22no—
238Q8×C151—44no—
239Q8×C151—42no—
240Q8×C151—81no—
241Q8×C151—82no—
242D4×C151—22no—
243D4×C151—22no—
244D4×C151—22no—
245D4×C151—42no—
246D4×C151—42no—
247D4×C151—42no—
248D4×C151—81no—
249D4×C151—81no—
250D4×C151—81no—
251D4×C151—81no—
252D4×C151—82no—
253D4×C151—81no—
254D4×C151—82no—
255D4×C151—82no—
256D4×C151—82no—
257D4×C151—82no—
258D4×C151—82no—
259C2×C4×C151—22no—
260C2×C4×C151—22no—
261C2×C4×C151—21no—
262C2×C4×C151—22no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—41no—
268C2×C4×C151—42no—
269C2×C4×C151—42no—
270C2×C4×C151—42no—
271C2×C4×C151—42no—
272C2×C4×C151—82no—
273C2×C4×C151—82no—
274C2×C4×C151—82no—
275C2×C4×C151—82no—
276C2×C4×C151#12011yescharacteristic
277C2×C4×C151#12011yescharacteristic
278C2×C4×C151#12011yescharacteristic
279C2×C4×C151C22×D411yescharacteristic
280C2×C4×C151C22×D411yescharacteristic
281C2×C4×C151C22×D411yescharacteristic
282C8×C151—42no—
283C8×C151—42no—
284C8×C151—42no—
285C22×C151—21no—
286C22×C151—21no—
287C22×C151—21no—
288C22×C151—41no—
289C22×C151—41no—
290C22×C151—41no—
291C22×C151—41no—
292C22×C151—42no—
293C22×C151—42no—
294C22×C151—41no—
295C22×C151—41no—
296C22×C151—42no—
297C22×C151—41no—
298C22×C151—41no—
299C22×C151—41no—
300C22×C151—164no—
301C22×C151C2×#12011yescharacteristic
302C4×C151—21no—
303C4×C151—21no—
304C4×C151—21no—
305C4×C151—21no—
306C4×C151—41no—
307C4×C151—41no—
308C4×C151—41no—
309C4×C151—41no—
310C4×C151—42no—
311C4×C151—41no—
312C4×C151—82no—
313C4×C151#57712yes—
314C4×C151#57712yes—
315C2×C151—41no—
316C2×C151—81no—
317C2×C151—82no—
318C2×C151—81no—
319C2×C151—81no—
320C2×C151#300911yescharacteristic
321C2×C151#300911yescharacteristic
322C2×C151#302111yescharacteristic
323#18955C15111yesmaximal, characteristic, direct product factor, Sylow
324C151#1895511yescharacteristic, direct product factor, Sylow
325#3546C2×C15111yescharacteristic
326#3238C2×C15111yescharacteristic, complemented
327#3227C2×C15111yescharacteristic, complemented
328#3206C2×C15111yescharacteristic, complemented
329#1638C2×C15112yescomplemented
330#1635C2×C15112yescomplemented
331#1631C2×C15112yescomplemented
332#1629C2×C15112yescomplemented
333#1553C2×C15111yescharacteristic, complemented
334#1496C2×C15111yescharacteristic, complemented
335#1482C2×C15111yescharacteristic, complemented
336#560—22no—
337#556C22×C15111yescharacteristic
338#553—21no—
339#550—21no—
340#550C22×C15111yescharacteristic
341#547C22×C15111yescharacteristic
342#546—21no—
343#546—21no—
344D42C22×C15111yescharacteristic
345#542—21no—
346#538—22no—
347#537—21no—
348#535—21no—
349#535—21no—
350#532C22×C15111yescharacteristic
351#532C22×C15111yescharacteristic
352C2×C4⋊Q8C22×C15111yescharacteristic, complemented
353#529C22×C15111yescharacteristic
354#501—21no—
355#498—21no—
356#492C22×C15112yes—
357#489—21no—
358#487C22×C15112yescomplemented
359#486—21no—
360#483—21no—
361#481—21no—
362#481—21no—
363#480—21no—
364#477C22×C15112yescomplemented
365#476C22×C15112yes—
366#476C22×C15112yes—
367#476C22×C15112yescomplemented
368#461—22no—
369#448—22no—
370#432C22×C15111yescharacteristic, complemented
371#431C22×C15111yescharacteristic, complemented
372#431C22×C15111yescharacteristic, complemented
373#332C22×C15112yescomplemented
374#331C22×C15112yes—
375Q8⋊C8C22×C15112yescomplemented
376D4⋊C8C22×C15112yes—
377D4⋊C8C22×C15112yes—
378D4⋊C8C22×C15112yescomplemented
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41—21no—
383C22×Q8—21no—
384C22×D4—21no—
385C22×D4—21no—
386C2×SD16—24no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8D4×C15111yescharacteristic
391C4⋊Q8C23×C15112yes—
392C4⋊Q8C23×C15111yescharacteristic
393#127—22no—
394#127—21no—
395#127D4×C15111yescharacteristic
396#127C23×C15111yescharacteristic
397#126—22no—
398#126—22no—
399#126—21no—
400#125D4×C15111yescharacteristic
401#124—22no—
402#124—21no—
403#124—21no—
404#124—21no—
405#124D4×C15111yescharacteristic
406#123—22no—
407#123—22no—
408#123—21no—
409#123—22no—
410C22⋊Q8—22no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8D4×C15111yescharacteristic
414#121—22no—
415#121—22no—
416#121—22no—
417#121—22no—
418#121—22no—
419#121—21no—
420#121—22no—
421#121—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—21no—
426#121D4×C15111yescharacteristic
427#121D4×C15111yescharacteristic
428#121D4×C15111yescharacteristic
429#121D4×C15112yes—
430#120—22no—
431#120—22no—
432#120—22no—
433#120—22no—
434C4×Q8—21no—
435C4×Q8C23×C15111yescharacteristic
436C4×D4—22no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4D4×C15112yes—
442C4×D4C23×C15111yescharacteristic
443C4×D4C23×C15111yescharacteristic
444C4×D4C23×C15111yescharacteristic
445#117—21no—
446#117—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C42C23×C15111yescharacteristic
452#107—22no—
453#106—22no—
454#106—22no—
455#106—22no—
456C4⋊C8—21no—
457C4⋊C8C23×C15112yes—
458C4⋊C8C23×C15112yes—
459#103—22no—
460#103—24no—
461#102—22no—
462#102—22no—
463#102—22no—
464C22⋊C8—21no—
465C22⋊C8—21no—
466C22⋊C8—21no—
467#97—21no—
468C4×C8—21no—
469C4×C8C23×C15112yes—
470C24—22no—
471#41—82no—
472#41—82no—
473#41—82no—
474#41—82no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—22no—
478C2×Q8—41no—
479C2×Q8—82no—
480C2×Q8C2×D4×C15111yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—82no—
495C2×D4—82no—
496C2×D4C2×D4×C15111yescharacteristic
497C2×D4C2×D4×C15111yescharacteristic
498C2×D4C2×D4×C15111yescharacteristic
499C2×D4C2×D4×C15112yes—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—41no—
507C22×C4C2×D4×C15111yescharacteristic
508C22×C4C2×D4×C15111yescharacteristic
509C22×C4C2×D4×C15111yescharacteristic
510SD16—84no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4C2×D4×C15112yes—
527C4⋊C4C2×D4×C15111yescharacteristic
528C4⋊C4C2×D4×C15111yescharacteristic
529C4⋊C4C2×D4×C15111yescharacteristic
530C4⋊C4C2×D4×C15111yescharacteristic
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C42—22no—
548C42—21no—
549C42C2×D4×C15111yescharacteristic
550C42C2×D4×C15111yescharacteristic
551C42C2×D4×C15111yescharacteristic
552C42C24×C15111yescharacteristic
553C23—21no—
554C23—21no—
555C23—22no—
556C23—21no—
557C23—82no—
558C23—82no—
559C23—82no—
560C23#120×C15111yescharacteristic
561Q8—22no—
562Q8—44no—
563Q8—42no—
564Q8—81no—
565Q8—82no—
566D4—22no—
567D4—22no—
568D4—22no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—81no—
573D4—81no—
574D4—81no—
575D4—81no—
576D4—82no—
577D4—81no—
578D4—82no—
579D4—82no—
580D4—82no—
581D4—82no—
582D4—82no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4#120×C15111yescharacteristic
601C2×C4#120×C15111yescharacteristic
602C2×C4#120×C15111yescharacteristic
603C2×C4C22×D4×C15111yescharacteristic
604C2×C4C22×D4×C15111yescharacteristic
605C2×C4C22×D4×C15111yescharacteristic
606C8—42no—
607C8—42no—
608C8—42no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—164no—
625C22C2×#120×C15111yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—82no—
637C4#577×C15112yes—
638C4#577×C15112yes—
639C2—41no—
640C2—81no—
641C2—81no—
642C2—82no—
643C2—81no—
644C2#3009×C15111yescharacteristic
645C2#3009×C15111yescharacteristic
646C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3546×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. #3206×C151C2semidirect
5. #1638×C151C2semidirect
6. #1635×C151C2semidirect
7. #1631×C151C2semidirect
8. #1629×C151C2semidirect
9. #1553×C151C2semidirect
10. #1496×C151C2semidirect
11. #1482×C151C2semidirect
28. C2×C4⋊Q8×C151C22semidirect
34. #487×C151C22semidirect
40. #477×C151C22semidirect
43. #476×C151C22semidirect
46. #432×C151C22semidirect
47. #431×C151C22semidirect
48. #431×C151C22semidirect
49. #332×C151C22semidirect
51. Q8⋊C8×C151C22semidirect
54. D4⋊C8×C151C22semidirect
323. #18955C151direct (N × H)
324. C151#18955direct (N × H)
326. #3238C2×C151semidirect
327. #3227C2×C151semidirect
328. #3206C2×C151semidirect
329. #1638C2×C151semidirect
330. #1635C2×C151semidirect
331. #1631C2×C151semidirect
332. #1629C2×C151semidirect
333. #1553C2×C151semidirect
334. #1496C2×C151semidirect
335. #1482C2×C151semidirect
352. C2×C4⋊Q8C22×C151semidirect
358. #487C22×C151semidirect
364. #477C22×C151semidirect
367. #476C22×C151semidirect
370. #432C22×C151semidirect
371. #431C22×C151semidirect
372. #431C22×C151semidirect
373. #332C22×C151semidirect
375. Q8⋊C8C22×C151semidirect
378. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3546×C1512
#3238×C1512
#3227×C1512
#3206×C1512
#1638×C1512
#1635×C1512
#1631×C1512
#1629×C1512
#1553×C1512
#1496×C1512
#1482×C1512
#18955151