Finite Group Databasebeta

← C151×#24418 #50329343

Subgroups — C151×#24418 #50329343

Order 38656.

1386 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3486×C151C211yesmaximal, characteristic, complemented
2#3055×C151C212yesmaximal, complemented
3C2×#454×C151C211yesmaximal, characteristic, complemented
4C22×#101×C151C211yesmaximal, characteristic, complemented
5#2436×C151C211yesmaximal, characteristic, complemented
6#2038×C151C212yesmaximal, complemented
7#2003×C151C212yesmaximal, complemented
8#1888×C151C211yesmaximal, characteristic, complemented
9#1871×C151C212yesmaximal, complemented
10#1857×C151C211yesmaximal, characteristic, complemented
11#1793×C151C211yesmaximal, characteristic, complemented
12C2×2−1+4×C151C2211yescharacteristic
13C23×Q8×C151C2211yescharacteristic
14C2×AGL(1,ℤ/8)×C151C2212yes—
15C22×M16×C151C2212yes—
16D4×Q8×C151—22no—
17D4×Q8×C151—22no—
18#548×C151—22no—
19#548×C151—22no—
20#536×C151—22no—
21#536×C151C2212yes—
22C2×#124×C151C2211yescharacteristic
23C2×#124×C151C2211yescharacteristic
24#525×C151—22no—
25#525×C151C2212yes—
26C2×#121×C151C2211yescharacteristic
27#519×C151C2211yescharacteristic
28#469×C151—22no—
29#468×C151—22no—
30#466×C151—22no—
31#465×C151—22no—
32#454×C151—24no—
33#428×C151C2212yes—
34C2×#104×C151C2212yes—
35C2×#104×C151C2212yes—
36#418×C151C2212yes—
37#417×C151C2212yes—
38C2×#101×C151—24no—
39C2×#101×C151C2211yescharacteristic
40C2×#101×C151C2212yes—
41C2×#101×C151C2211yescharacteristic
42#393×C151—22no—
43#391×C151C2211yescharacteristic
44#391×C151C2211yescharacteristic
45#386×C151—22no—
46C4×C22⋊C4×C151C2211yescharacteristic
47#339×C151C2212yes—
48#339×C151C2212yes—
492−1+4×C151—22no—
502−1+4×C151—22no—
512−1+4×C151—42no—
52C2×#41×C151—22no—
53C2×#41×C151—22no—
54C2×#41×C151C2312yes—
55C22×Q8×C151—22no—
56C22×Q8×C151—22no—
57C22×Q8×C151—22no—
58C22×Q8×C151—22no—
59C22×Q8×C151—22no—
60C22×Q8×C151—42no—
61C22×Q8×C151D412yes—
62C22×Q8×C151C2311yescharacteristic
63C22×Q8×C151C2311yescharacteristic
64C22×D4×C151—21no—
65C22×D4×C151C2311yescharacteristic
66C23×C4×C151D412yes—
67C23×C4×C151C2311yescharacteristic
68AGL(1,ℤ/8)×C151—24no—
69AGL(1,ℤ/8)×C151—42no—
70C2×SD16×C151—22no—
71C2×D8×C151—22no—
72C2×M16×C151—22no—
73C2×M16×C151—24no—
74C2×M16×C151—42no—
75C2×M16×C151C2312yes—
76C2×M16×C151C2312yes—
77C22×C8×C151—22no—
78C4⋊Q8×C151—24no—
79C4⋊Q8×C151—22no—
80#124×C151—24no—
81#124×C151—22no—
82#124×C151—22no—
83#124×C151—22no—
84#124×C151—42no—
85#123×C151—24no—
86#123×C151—22no—
87C22⋊Q8×C151—22no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—24no—
90C22⋊Q8×C151—24no—
91C22⋊Q8×C151—22no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151D412yes—
94C22⋊Q8×C151D412yes—
95#121×C151—22no—
96#121×C151—22no—
97#121×C151—22no—
98#121×C151—22no—
99#121×C151D412yes—
100#121×C151D412yes—
101#120×C151—22no—
102C4×Q8×C151—22no—
103C4×Q8×C151—22no—
104C4×D4×C151—24no—
105C4×D4×C151—24no—
106C4×D4×C151—22no—
107C4×D4×C151—22no—
108#117×C151—22no—
109#117×C151C2312yes—
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C22⋊C4×C151—22no—
112C2×C22⋊C4×C151—22no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117#107×C151—22no—
118#106×C151—22no—
119#104×C151—24no—
120#104×C151—42no—
121#103×C151—22no—
122#102×C151—22no—
123#102×C151—22no—
124#102×C151—22no—
125#101×C151—24no—
126#101×C151—22no—
127#101×C151D414yescomplemented
128#95×C151—21no—
129#95×C151—22no—
130#95×C151—22no—
131C24×C151—21no—
132C24×C151C2×D411yescharacteristic
133#41×C151—22no—
134#41×C151—22no—
135#41×C151—22no—
136#41×C151—22no—
137#41×C151—44no—
138#41×C151—44no—
139#41×C151—44no—
140#41×C151—44no—
141C2×Q8×C151—22no—
142C2×Q8×C151—24no—
143C2×Q8×C151—24no—
144C2×Q8×C151—22no—
145C2×Q8×C151—21no—
146C2×Q8×C151—22no—
147C2×Q8×C151—21no—
148C2×Q8×C151—22no—
149C2×Q8×C151—22no—
150C2×Q8×C151—42no—
151C2×Q8×C151—44no—
152C2×Q8×C151—44no—
153C2×Q8×C151—44no—
154C2×Q8×C151—44no—
155C2×Q8×C151—44no—
156C2×Q8×C151—44no—
157C2×Q8×C151C2×D412yes—
158C2×Q8×C151C2×D412yes—
159C2×Q8×C151#4112yes—
160C2×D4×C151—22no—
161C2×D4×C151—22no—
162C2×D4×C151—22no—
163C2×D4×C151—22no—
164C2×D4×C151—22no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—22no—
168C2×D4×C151—44no—
169C2×D4×C151—41no—
170C2×D4×C151—41no—
171C2×D4×C151C2×D412yes—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—22no—
175C22×C4×C151—24no—
176C22×C4×C151—22no—
177C22×C4×C151—22no—
178C22×C4×C151—24no—
179C22×C4×C151—22no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—42no—
184C22×C4×C151C2×D412yes—
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2×D412yes—
187C22×C4×C151C2×D412yes—
188C22×C4×C151C2×D412yes—
189C22×C4×C151C2411yescharacteristic
190SD16×C151—44no—
191D8×C151—44no—
192M16×C151—22no—
193M16×C151—22no—
194M16×C151—22no—
195M16×C151—44no—
196M16×C151C2×D414yes—
197C2×C8×C151—22no—
198C2×C8×C151—22no—
199C2×C8×C151—44no—
200C4⋊C4×C151—22no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151—24no—
203C4⋊C4×C151—24no—
204C4⋊C4×C151—22no—
205C4⋊C4×C151—22no—
206C4⋊C4×C151—22no—
207C4⋊C4×C151C2×D412yes—
208C4⋊C4×C151C2×D412yes—
209C22⋊C4×C151—24no—
210C22⋊C4×C151—24no—
211C22⋊C4×C151—22no—
212C22⋊C4×C151—22no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—44no—
217C22⋊C4×C151—42no—
218C22⋊C4×C151—42no—
219C22⋊C4×C151—44no—
220C42×C151—24no—
221C42×C151—22no—
222C42×C151—21no—
223C42×C151—21no—
224C42×C151—22no—
225C23×C151—21no—
226C23×C151—21no—
227C23×C151—22no—
228C23×C151—22no—
229C23×C151—41no—
230C23×C151—42no—
231C23×C151—42no—
232C23×C151—41no—
233C23×C151—41no—
234C23×C151—41no—
235C23×C151#12011yescharacteristic
236C23×C151#12011yescharacteristic
237C23×C151C22×D411yescharacteristic
238Q8×C151—24no—
239Q8×C151—24no—
240Q8×C151—22no—
241Q8×C151—22no—
242Q8×C151—48no—
243Q8×C151—44no—
244Q8×C151—42no—
245Q8×C151—42no—
246D4×C151—22no—
247D4×C151—22no—
248D4×C151—44no—
249D4×C151—44no—
250D4×C151—42no—
251D4×C151—42no—
252D4×C151—44no—
253D4×C151—42no—
254D4×C151—42no—
255D4×C151—82no—
256D4×C151—82no—
257C2×C4×C151—22no—
258C2×C4×C151—21no—
259C2×C4×C151—22no—
260C2×C4×C151—21no—
261C2×C4×C151—22no—
262C2×C4×C151—22no—
263C2×C4×C151—22no—
264C2×C4×C151—22no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—22no—
269C2×C4×C151—22no—
270C2×C4×C151—22no—
271C2×C4×C151—44no—
272C2×C4×C151—44no—
273C2×C4×C151—48no—
274C2×C4×C151—42no—
275C2×C4×C151—42no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—42no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151#12012yes—
285C2×C4×C151#12114yes—
286C2×C4×C151C22×D411yescharacteristic
287C2×C4×C151C22×D412yes—
288C2×C4×C151C2×#4111yescharacteristic
289C2×C4×C151H(5,𝔽2)12yes—
290C8×C151—24no—
291C8×C151—42no—
292C22×C151—21no—
293C22×C151—21no—
294C22×C151—21no—
295C22×C151—21no—
296C22×C151—21no—
297C22×C151—21no—
298C22×C151—21no—
299C22×C151—42no—
300C22×C151—42no—
301C22×C151—42no—
302C22×C151—42no—
303C22×C151—42no—
304C22×C151—82no—
305C22×C151—82no—
306C22×C151—81no—
307C22×C151—81no—
308C22×C151—81no—
309C22×C151#45412yescomplemented
310C22×C151C2×#12011yescharacteristic
311C22×C151C2×#12111yescharacteristic
312C22×C151#53411yescharacteristic
313C4×C151—22no—
314C4×C151—24no—
315C4×C151—42no—
316C4×C151—42no—
317C4×C151—42no—
318C4×C151—42no—
319C4×C151—81no—
320C4×C151—81no—
321C4×C151—81no—
322C4×C151D4212yes—
323C4×C151#54612yes—
324C2×C151—21no—
325C2×C151—21no—
326C2×C151—22no—
327C2×C151—41no—
328C2×C151—82no—
329C2×C151—161no—
330C2×C151#241011yescharacteristic
331C2×C151C2×#45411yescharacteristic
332C2×C151#302011yescharacteristic
333#24418C15111yesmaximal, characteristic, direct product factor, Sylow
334C151#2441811yescharacteristic, direct product factor, Sylow
335#3486C2×C15111yescharacteristic, complemented
336#3055C2×C15112yescomplemented
337C2×#454C2×C15111yescharacteristic, complemented
338C22×#101C2×C15111yescharacteristic, complemented
339#2436C2×C15111yescharacteristic, complemented
340#2038C2×C15112yescomplemented
341#2003C2×C15112yescomplemented
342#1888C2×C15111yescharacteristic, complemented
343#1871C2×C15112yescomplemented
344#1857C2×C15111yescharacteristic, complemented
345#1793C2×C15111yescharacteristic, complemented
346C2×2−1+4C22×C15111yescharacteristic
347C23×Q8C22×C15111yescharacteristic
348C2×AGL(1,ℤ/8)C22×C15112yes—
349C22×M16C22×C15112yes—
350D4×Q8—22no—
351D4×Q8—22no—
352#548—22no—
353#548—22no—
354#536—22no—
355#536C22×C15112yes—
356C2×#124C22×C15111yescharacteristic
357C2×#124C22×C15111yescharacteristic
358#525—22no—
359#525C22×C15112yes—
360C2×#121C22×C15111yescharacteristic
361#519C22×C15111yescharacteristic
362#469—22no—
363#468—22no—
364#466—22no—
365#465—22no—
366#454—24no—
367#428C22×C15112yes—
368C2×#104C22×C15112yes—
369C2×#104C22×C15112yes—
370#418C22×C15112yes—
371#417C22×C15112yes—
372C2×#101—24no—
373C2×#101C22×C15111yescharacteristic
374C2×#101C22×C15112yes—
375C2×#101C22×C15111yescharacteristic
376#393—22no—
377#391C22×C15111yescharacteristic
378#391C22×C15111yescharacteristic
379#386—22no—
380C4×C22⋊C4C22×C15111yescharacteristic
381#339C22×C15112yes—
382#339C22×C15112yes—
3832−1+4—22no—
3842−1+4—22no—
3852−1+4—42no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41C23×C15112yes—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—22no—
393C22×Q8—22no—
394C22×Q8—42no—
395C22×Q8D4×C15112yes—
396C22×Q8C23×C15111yescharacteristic
397C22×Q8C23×C15111yescharacteristic
398C22×D4—21no—
399C22×D4C23×C15111yescharacteristic
400C23×C4D4×C15112yes—
401C23×C4C23×C15111yescharacteristic
402AGL(1,ℤ/8)—24no—
403AGL(1,ℤ/8)—42no—
404C2×SD16—22no—
405C2×D8—22no—
406C2×M16—22no—
407C2×M16—24no—
408C2×M16—42no—
409C2×M16C23×C15112yes—
410C2×M16C23×C15112yes—
411C22×C8—22no—
412C4⋊Q8—24no—
413C4⋊Q8—22no—
414#124—24no—
415#124—22no—
416#124—22no—
417#124—22no—
418#124—42no—
419#123—24no—
420#123—22no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8—24no—
424C22⋊Q8—24no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8D4×C15112yes—
428C22⋊Q8D4×C15112yes—
429#121—22no—
430#121—22no—
431#121—22no—
432#121—22no—
433#121D4×C15112yes—
434#121D4×C15112yes—
435#120—22no—
436C4×Q8—22no—
437C4×Q8—22no—
438C4×D4—24no—
439C4×D4—24no—
440C4×D4—22no—
441C4×D4—22no—
442#117—22no—
443#117C23×C15112yes—
444C2×C4⋊C4C23×C15111yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C42C23×C15111yescharacteristic
450C2×C42C23×C15111yescharacteristic
451#107—22no—
452#106—22no—
453#104—24no—
454#104—42no—
455#103—22no—
456#102—22no—
457#102—22no—
458#102—22no—
459#101—22no—
460#101—24no—
461#101D4×C15114yescomplemented
462#95—21no—
463#95—22no—
464#95—22no—
465C24—21no—
466C24C2×D4×C15111yescharacteristic
467#41—22no—
468#41—22no—
469#41—22no—
470#41—22no—
471#41—44no—
472#41—44no—
473#41—44no—
474#41—44no—
475C2×Q8—22no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—21no—
480C2×Q8—22no—
481C2×Q8—21no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—42no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8C2×D4×C15112yes—
492C2×Q8C2×D4×C15112yes—
493C2×Q8#41×C15112yes—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—22no—
502C2×D4—44no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4C2×D4×C15112yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—42no—
518C22×C4C2×D4×C15112yes—
519C22×C4C2×D4×C15111yescharacteristic
520C22×C4C2×D4×C15112yes—
521C22×C4C2×D4×C15112yes—
522C22×C4C2×D4×C15112yes—
523C22×C4C24×C15111yescharacteristic
524SD16—44no—
525D8—44no—
526M16—22no—
527M16—22no—
528M16—22no—
529M16—44no—
530M16C2×D4×C15114yes—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—44no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4C2×D4×C15112yes—
542C4⋊C4C2×D4×C15112yes—
543C22⋊C4—24no—
544C22⋊C4—24no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—44no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—44no—
554C42—24no—
555C42—22no—
556C42—21no—
557C42—21no—
558C42—22no—
559C23—22no—
560C23—21no—
561C23—21no—
562C23—22no—
563C23—41no—
564C23—42no—
565C23—42no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23#120×C15111yescharacteristic
570C23#120×C15111yescharacteristic
571C23C22×D4×C15111yescharacteristic
572Q8—24no—
573Q8—24no—
574Q8—22no—
575Q8—22no—
576Q8—48no—
577Q8—44no—
578Q8—42no—
579Q8—42no—
580D4—22no—
581D4—22no—
582D4—44no—
583D4—44no—
584D4—44no—
585D4—42no—
586D4—42no—
587D4—42no—
588D4—42no—
589D4—82no—
590D4—82no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—48no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4#120×C15112yes—
619C2×C4#121×C15114yes—
620C2×C4C22×D4×C15111yescharacteristic
621C2×C4C22×D4×C15112yes—
622C2×C4C2×#41×C15111yescharacteristic
623C2×C4H(5,𝔽2)×C15112yes—
624C8—24no—
625C8—42no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—82no—
639C22—82no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22#454×C15112yescomplemented
644C22C2×#120×C15111yescharacteristic
645C22C2×#121×C15111yescharacteristic
646C22#534×C15111yescharacteristic
647C4—22no—
648C4—24no—
649C4—42no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4D42×C15112yes—
657C4#546×C15112yes—
658C2—21no—
659C2—21no—
660C2—22no—
661C2—41no—
662C2—82no—
663C2—161no—
664C2#2410×C15111yescharacteristic
665C2C2×#454×C15111yescharacteristic
666C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3486×C151C2semidirect
2. #3055×C151C2semidirect
3. C2×#454×C151C2semidirect
4. C22×#101×C151C2semidirect
5. #2436×C151C2semidirect
6. #2038×C151C2semidirect
7. #2003×C151C2semidirect
8. #1888×C151C2semidirect
9. #1871×C151C2semidirect
10. #1857×C151C2semidirect
11. #1793×C151C2semidirect
127. #101×C151D4semidirect
309. C22×C151#454semidirect
333. #24418C151direct (N × H)
334. C151#24418direct (N × H)
335. #3486C2×C151semidirect
336. #3055C2×C151semidirect
337. C2×#454C2×C151semidirect
338. C22×#101C2×C151semidirect
339. #2436C2×C151semidirect
340. #2038C2×C151semidirect
341. #2003C2×C151semidirect
342. #1888C2×C151semidirect
343. #1871C2×C151semidirect
344. #1857C2×C151semidirect
345. #1793C2×C151semidirect
461. #101D4×C151semidirect
643. C22#454×C151semidirect

Maximal subgroups

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

subgroupindex
#3486×C1512
#3055×C1512
C2×#454×C1512
C22×#101×C1512
#2436×C1512
#2038×C1512
#2003×C1512
#1888×C1512
#1871×C1512
#1857×C1512
#1793×C1512
#24418151