Finite Group Databasebeta

← C151×#24177 #50329102

Subgroups — C151×#24177 #50329102

Order 38656.

1070 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3507×C151C211yesmaximal, characteristic, complemented
2#3077×C151C211yesmaximal, characteristic, complemented
3#3036×C151C211yesmaximal, characteristic
4C4×#124×C151C211yesmaximal, characteristic, complemented
5#2038×C151C212yesmaximal, complemented
6#2003×C151C212yesmaximal, complemented
7#1994×C151C211yesmaximal, characteristic, complemented
8#1962×C151C211yesmaximal, characteristic, complemented
9#1883×C151C212yesmaximal, complemented
10#1860×C151C212yesmaximal, complemented
11#1801×C151C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C151C2212yes—
13#559×C151—21no—
14#557×C151—21no—
15#556×C151—21no—
16#556×C151—22no—
17#554×C151—21no—
18#552×C151—22no—
19#539×C151—22no—
20#536×C151C2212yes—
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23#529×C151—22no—
24C2×#124×C151C2211yescharacteristic
25#520×C151C2212yes—
26C2×C4×Q8×C151C2211yescharacteristic
27C2×C4×D4×C151C2211yescharacteristic
28#478×C151—22no—
29#476×C151—21no—
30#474×C151—21no—
31#463×C151—22no—
32#461×C151—21no—
33#459×C151—21no—
34#428×C151C2212yes—
35#423×C151C2211yescharacteristic
36#423×C151C2211yescharacteristic
37C2×#104×C151C2212yes—
38C2×#104×C151C2212yes—
39#418×C151C2212yes—
40#417×C151C2212yes—
41C2×#101×C151C2212yes—
42#391×C151C2211yescharacteristic
43#390×C151C2211yescharacteristic
44#388×C151—22no—
45#382×C151C2211yescharacteristic
46C4×C22⋊C4×C151—22no—
47C43×C151C2211yescharacteristic
48#343×C151C2212yes—
49#339×C151C2212yes—
50#339×C151C2212yes—
51C2×#41×C151C2312yes—
52C22×Q8×C151C2311yescharacteristic
53C22×D4×C151C2311yescharacteristic
54C23×C4×C151—21no—
55AGL(1,ℤ/8)×C151—24no—
56AGL(1,ℤ/8)×C151—42no—
57C2×SD16×C151—22no—
58C2×D8×C151—22no—
59C2×M16×C151C2312yes—
60C2×M16×C151C2312yes—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151D411yescharacteristic
63C4⋊Q8×C151D411yescharacteristic
64C4⋊Q8×C151D411yescharacteristic
65#127×C151D411yescharacteristic
66#126×C151—24no—
67#126×C151—24no—
68#125×C151—22no—
69#125×C151—24no—
70#125×C151D412yes—
71#124×C151—22no—
72#124×C151—22no—
73#124×C151—22no—
74#124×C151—22no—
75#124×C151D412yes—
76#123×C151—24no—
77#123×C151—24no—
78C22⋊Q8×C151—24no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—21no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—22no—
83#121×C151—21no—
84#121×C151—21no—
85C4×Q8×C151—22no—
86C4×Q8×C151—21no—
87C4×Q8×C151—21no—
88C4×Q8×C151—21no—
89C4×Q8×C151—21no—
90C4×Q8×C151—21no—
91C4×Q8×C151—21no—
92C4×Q8×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151—22no—
95C4×D4×C151—24no—
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102#117×C151—24no—
103#117×C151—22no—
104#117×C151C2312yes—
105C2×C4⋊C4×C151—22no—
106C2×C4⋊C4×C151D412yes—
107C2×C4⋊C4×C151C2311yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C22⋊C4×C151—22no—
110C2×C22⋊C4×C151—22no—
111C2×C22⋊C4×C151—21no—
112C2×C42×C151—21no—
113C2×C42×C151—21no—
114C2×C42×C151D412yes—
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118#107×C151—22no—
119#106×C151—22no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151—21no—
123C4⋊C8×C151—21no—
124#104×C151—24no—
125#104×C151—42no—
126#103×C151—22no—
127#102×C151—22no—
128#102×C151—22no—
129#102×C151—22no—
130#101×C151—42no—
131#95×C151—22no—
132#95×C151—22no—
133C24×C151—21no—
134#41×C151—22no—
135#41×C151—22no—
136#41×C151—22no—
137#41×C151—22no—
138C2×Q8×C151—21no—
139C2×Q8×C151—21no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151C2×D412yes—
147C2×D4×C151—22no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151C2×D412yes—
156C2×D4×C151#4112yes—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—24no—
160C22×C4×C151—22no—
161C22×C4×C151—21no—
162C22×C4×C151—44no—
163C22×C4×C151—41no—
164C22×C4×C151—41no—
165C22×C4×C151C2×D412yes—
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2×D412yes—
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2411yescharacteristic
170SD16×C151—44no—
171D8×C151—44no—
172M16×C151—22no—
173M16×C151—22no—
174M16×C151—22no—
175M16×C151—22no—
176C2×C8×C151—22no—
177C2×C8×C151—22no—
178C4⋊C4×C151—24no—
179C4⋊C4×C151—24no—
180C4⋊C4×C151—24no—
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—22no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151C2×D412yes—
194C4⋊C4×C151C2×D412yes—
195C22⋊C4×C151—28no—
196C22⋊C4×C151—24no—
197C22⋊C4×C151—24no—
198C22⋊C4×C151—24no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—22no—
201C22⋊C4×C151—22no—
202C22⋊C4×C151—44no—
203C22⋊C4×C151—41no—
204C22⋊C4×C151—41no—
205C42×C151—24no—
206C42×C151—22no—
207C42×C151—22no—
208C42×C151—22no—
209C42×C151—21no—
210C42×C151—21no—
211C42×C151—21no—
212C42×C151—42no—
213C42×C151—42no—
214C42×C151C2×D411yescharacteristic
215C42×C151C2×D411yescharacteristic
216C42×C151C2×D411yescharacteristic
217C42×C151C2×D411yescharacteristic
218C42×C151#4112yes—
219C23×C151—22no—
220C23×C151—22no—
221C23×C151—42no—
222C23×C151—42no—
223C23×C151—41no—
224C23×C151—41no—
225C23×C151C22×D411yescharacteristic
226Q8×C151—22no—
227Q8×C151—22no—
228Q8×C151—41no—
229Q8×C151—41no—
230Q8×C151—41no—
231Q8×C151—41no—
232Q8×C151—42no—
233Q8×C151—81no—
234D4×C151—22no—
235D4×C151—22no—
236D4×C151—22no—
237D4×C151—22no—
238D4×C151—42no—
239D4×C151—42no—
240D4×C151—41no—
241D4×C151—41no—
242D4×C151—42no—
243D4×C151—81no—
244C2×C4×C151—22no—
245C2×C4×C151—22no—
246C2×C4×C151—22no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—22no—
250C2×C4×C151—22no—
251C2×C4×C151—22no—
252C2×C4×C151—22no—
253C2×C4×C151—22no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—42no—
260C2×C4×C151—42no—
261C2×C4×C151—42no—
262C2×C4×C151—42no—
263C2×C4×C151—41no—
264C2×C4×C151—82no—
265C2×C4×C151—84no—
266C2×C4×C151—82no—
267C2×C4×C151#12011yescharacteristic
268C2×C4×C151#12011yescharacteristic
269C2×C4×C151#12011yescharacteristic
270C2×C4×C151#12011yescharacteristic
271C2×C4×C151C22×D411yescharacteristic
272C2×C4×C151C22×D411yescharacteristic
273C2×C4×C151C2×#4111yescharacteristic
274C2×C4×C151C2×#4111yescharacteristic
275C2×C4×C151H(5,𝔽2)11yescharacteristic
276C2×C4×C1512−1+411yescharacteristic
277C8×C151—42no—
278C8×C151—42no—
279C22×C151—21no—
280C22×C151—21no—
281C22×C151—44no—
282C22×C151—42no—
283C22×C151—42no—
284C22×C151—42no—
285C22×C151—42no—
286C22×C151—82no—
287C22×C151—81no—
288C22×C151—81no—
289C22×C151C2×#12011yescharacteristic
290C22×C151#52511yescharacteristic
291C22×C151#53711yescharacteristic
292C4×C151—21no—
293C4×C151—21no—
294C4×C151—21no—
295C4×C151—42no—
296C4×C151—42no—
297C4×C151—42no—
298C4×C151—42no—
299C4×C151—42no—
300C4×C151—42no—
301C4×C151—42no—
302C4×C151—81no—
303C4×C151#45412yes—
304C4×C151#54611yescharacteristic
305C4×C151#54711yescharacteristic
306C4×C151#54811yescharacteristic
307C4×C151#55011yescharacteristic
308C2×C151—21no—
309C2×C151—21no—
310C2×C151—82no—
311C2×C151—82no—
312C2×C151#240711yescharacteristic
313C2×C151C2×#45411yescharacteristic
314C2×C151#301811yescharacteristic
315#24177C15111yesmaximal, characteristic, direct product factor, Sylow
316C151#2417711yescharacteristic, direct product factor, Sylow
317#3507C2×C15111yescharacteristic, complemented
318#3077C2×C15111yescharacteristic, complemented
319#3036C2×C15111yescharacteristic
320C4×#124C2×C15111yescharacteristic, complemented
321#2038C2×C15112yescomplemented
322#2003C2×C15112yescomplemented
323#1994C2×C15111yescharacteristic, complemented
324#1962C2×C15111yescharacteristic, complemented
325#1883C2×C15112yescomplemented
326#1860C2×C15112yescomplemented
327#1801C2×C15111yescharacteristic, complemented
328C2×AGL(1,ℤ/8)C22×C15112yes—
329#559—21no—
330#557—21no—
331#556—21no—
332#556—22no—
333#554—21no—
334#552—22no—
335#539—22no—
336#536C22×C15112yes—
337#533C22×C15111yescharacteristic
338#532C22×C15111yescharacteristic
339#529—22no—
340C2×#124C22×C15111yescharacteristic
341#520C22×C15112yes—
342C2×C4×Q8C22×C15111yescharacteristic
343C2×C4×D4C22×C15111yescharacteristic
344#478—22no—
345#476—21no—
346#474—21no—
347#463—22no—
348#461—21no—
349#459—21no—
350#428C22×C15112yes—
351#423C22×C15111yescharacteristic
352#423C22×C15111yescharacteristic
353C2×#104C22×C15112yes—
354C2×#104C22×C15112yes—
355#418C22×C15112yes—
356#417C22×C15112yes—
357C2×#101C22×C15112yes—
358#391C22×C15111yescharacteristic
359#390C22×C15111yescharacteristic
360#388—22no—
361#382C22×C15111yescharacteristic
362C4×C22⋊C4—22no—
363C43C22×C15111yescharacteristic
364#343C22×C15112yes—
365#339C22×C15112yes—
366#339C22×C15112yes—
367C2×#41C23×C15112yes—
368C22×Q8C23×C15111yescharacteristic
369C22×D4C23×C15111yescharacteristic
370C23×C4—21no—
371AGL(1,ℤ/8)—24no—
372AGL(1,ℤ/8)—42no—
373C2×SD16—22no—
374C2×D8—22no—
375C2×M16C23×C15112yes—
376C2×M16C23×C15112yes—
377C4⋊Q8—22no—
378C4⋊Q8D4×C15111yescharacteristic
379C4⋊Q8D4×C15111yescharacteristic
380C4⋊Q8D4×C15111yescharacteristic
381#127D4×C15111yescharacteristic
382#126—24no—
383#126—24no—
384#125—22no—
385#125—24no—
386#125D4×C15112yes—
387#124—22no—
388#124—22no—
389#124—22no—
390#124—22no—
391#124D4×C15112yes—
392#123—24no—
393#123—24no—
394C22⋊Q8—24no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399#121—21no—
400#121—21no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—24no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418#117—24no—
419#117—22no—
420#117C23×C15112yes—
421C2×C4⋊C4—22no—
422C2×C4⋊C4D4×C15112yes—
423C2×C4⋊C4C23×C15111yescharacteristic
424C2×C4⋊C4C23×C15111yescharacteristic
425C2×C22⋊C4—22no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—22no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42D4×C15112yes—
431C2×C42C23×C15111yescharacteristic
432C2×C42C23×C15111yescharacteristic
433C2×C42C23×C15111yescharacteristic
434#107—22no—
435#106—22no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440#104—24no—
441#104—42no—
442#103—22no—
443#102—22no—
444#102—22no—
445#102—22no—
446#101—42no—
447#95—22no—
448#95—22no—
449C24—21no—
450#41—22no—
451#41—22no—
452#41—22no—
453#41—22no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C15112yes—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4C2×D4×C15112yes—
472C2×D4#41×C15112yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—44no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4C2×D4×C15112yes—
482C22×C4C2×D4×C15111yescharacteristic
483C22×C4C2×D4×C15112yes—
484C22×C4C2×D4×C15111yescharacteristic
485C22×C4C24×C15111yescharacteristic
486SD16—44no—
487D8—44no—
488M16—22no—
489M16—22no—
490M16—22no—
491M16—22no—
492C2×C8—22no—
493C2×C8—22no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4C2×D4×C15112yes—
510C4⋊C4C2×D4×C15112yes—
511C22⋊C4—28no—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—44no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—24no—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—42no—
529C42—42no—
530C42C2×D4×C15111yescharacteristic
531C42C2×D4×C15111yescharacteristic
532C42C2×D4×C15111yescharacteristic
533C42C2×D4×C15111yescharacteristic
534C42#41×C15112yes—
535C23—22no—
536C23—22no—
537C23—42no—
538C23—42no—
539C23—41no—
540C23—41no—
541C23C22×D4×C15111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—42no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549Q8—81no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4—22no—
554D4—42no—
555D4—42no—
556D4—42no—
557D4—41no—
558D4—41no—
559D4—81no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—82no—
581C2×C4—84no—
582C2×C4—82no—
583C2×C4#120×C15111yescharacteristic
584C2×C4#120×C15111yescharacteristic
585C2×C4#120×C15111yescharacteristic
586C2×C4#120×C15111yescharacteristic
587C2×C4C22×D4×C15111yescharacteristic
588C2×C4C22×D4×C15111yescharacteristic
589C2×C4C2×#41×C15111yescharacteristic
590C2×C4C2×#41×C15111yescharacteristic
591C2×C4H(5,𝔽2)×C15111yescharacteristic
592C2×C42−1+4×C15111yescharacteristic
593C8—42no—
594C8—42no—
595C22—21no—
596C22—21no—
597C22—44no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—82no—
603C22—81no—
604C22—81no—
605C22C2×#120×C15111yescharacteristic
606C22#525×C15111yescharacteristic
607C22#537×C15111yescharacteristic
608C4—21no—
609C4—21no—
610C4—21no—
611C4—42no—
612C4—42no—
613C4—42no—
614C4—42no—
615C4—42no—
616C4—42no—
617C4—42no—
618C4—81no—
619C4#454×C15112yes—
620C4#546×C15111yescharacteristic
621C4#547×C15111yescharacteristic
622C4#548×C15111yescharacteristic
623C4#550×C15111yescharacteristic
624C2—21no—
625C2—21no—
626C2—82no—
627C2—82no—
628C2#2407×C15111yescharacteristic
629C2C2×#454×C15111yescharacteristic
630C2#3018×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3036×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3507×C151C2semidirect
2. #3077×C151C2semidirect
4. C4×#124×C151C2semidirect
5. #2038×C151C2semidirect
6. #2003×C151C2semidirect
7. #1994×C151C2semidirect
8. #1962×C151C2semidirect
9. #1883×C151C2semidirect
10. #1860×C151C2semidirect
11. #1801×C151C2semidirect
315. #24177C151direct (N × H)
316. C151#24177direct (N × H)
317. #3507C2×C151semidirect
318. #3077C2×C151semidirect
320. C4×#124C2×C151semidirect
321. #2038C2×C151semidirect
322. #2003C2×C151semidirect
323. #1994C2×C151semidirect
324. #1962C2×C151semidirect
325. #1883C2×C151semidirect
326. #1860C2×C151semidirect
327. #1801C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3507×C1512
#3077×C1512
#3036×C1512
C4×#124×C1512
#2038×C1512
#2003×C1512
#1994×C1512
#1962×C1512
#1883×C1512
#1860×C1512
#1801×C1512
#24177151