Finite Group Databasebeta

← C151×#23945 #50328870

Subgroups — C151×#23945 #50328870

Order 38656.

1382 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#542×C151C211yesmaximal, characteristic, complemented
2C2×#450×C151C211yesmaximal, characteristic, complemented
3C2×#447×C151C211yesmaximal, characteristic
4#2309×C151C211yesmaximal, characteristic, complemented
5#2023×C151C212yesmaximal, complemented
6#2012×C151C212yesmaximal, complemented
7#1880×C151C212yesmaximal, complemented
8#1879×C151C212yesmaximal, complemented
9#1875×C151C211yesmaximal, characteristic, complemented
10#1873×C151C211yesmaximal, characteristic, complemented
11#1818×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14C22×D8×C151C2212yes—
15#542×C151—24no—
16#542×C151—24no—
17C2×C4⋊Q8×C151C2211yescharacteristic, complemented
18C2×#126×C151—21no—
19C2×#124×C151—21no—
20C2×#124×C151C2211yescharacteristic, complemented
21C2×#123×C151—21no—
22C2×C22⋊Q8×C151—21no—
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×#121×C151C2211yescharacteristic
25C2×C4×Q8×C151C2211yescharacteristic, complemented
26C2×C4×D4×C151C2211yescharacteristic, complemented
27C2×#117×C151C2211yescharacteristic
28C2×#117×C151C2211yescharacteristic
29#450×C151—24no—
30#447×C151—24no—
31C2×#103×C151C2212yescomplemented
32C2×#102×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yescomplemented
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37#390×C151—21no—
38#390×C151—21no—
39#390×C151C2212yes—
40#390×C151C2212yes—
41#379×C151—21no—
42#379×C151—21no—
43#340×C151C2212yescomplemented
44#340×C151C2212yescomplemented
45#336×C151C2212yescomplemented
46#336×C151C2212yescomplemented
47C25×C151—21no—
48C22×Q8×C151—21no—
49C22×Q8×C151C2311yescharacteristic
50C22×D4×C151—24no—
51C22×D4×C151—21no—
52C22×D4×C151—21no—
53C22×D4×C151—22no—
54C22×D4×C151—22no—
55C22×D4×C151—42no—
56C22×D4×C151C2311yescharacteristic
57C22×D4×C151C2312yes—
58C23×C4×C151—21no—
59C23×C4×C151C2311yescharacteristic
60C2×SD16×C151—24no—
61C2×SD16×C151—24no—
62C2×SD16×C151—42no—
63C2×D8×C151—24no—
64C2×D8×C151—24no—
65C2×D8×C151—42no—
66C22×C8×C151C2312yes—
67C22×C8×C151C2312yes—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151—22no—
70#126×C151—28no—
71#124×C151—28no—
72#124×C151—22no—
73#124×C151—22no—
74#123×C151—28no—
75C22⋊Q8×C151—28no—
76C22⋊Q8×C151—22no—
77C22⋊Q8×C151D414yes—
78#121×C151—22no—
79#121×C151D414yes—
80C4×Q8×C151—22no—
81C4×Q8×C151—22no—
82C4×D4×C151—22no—
83C4×D4×C151—22no—
84#117×C151—22no—
85#117×C151—22no—
86#117×C151—42no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151D411yescharacteristic
91C2×C4⋊C4×C151D411yescharacteristic
92C2×C4⋊C4×C151C2312yes—
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—21no—
97C2×C22⋊C4×C151—21no—
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—22no—
100C2×C22⋊C4×C151—22no—
101C2×C22⋊C4×C151—22no—
102C2×C22⋊C4×C151—22no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151D411yescharacteristic
106C2×C22⋊C4×C151D411yescharacteristic
107C2×C42×C151—21no—
108C2×C42×C151—21no—
109C2×C42×C151C2311yescharacteristic
110C2×C42×C151C2311yescharacteristic
111#103×C151—42no—
112#102×C151—24no—
113#102×C151—24no—
114#102×C151—42no—
115C22⋊C8×C151—22no—
116C22⋊C8×C151—22no—
117C24×C151—24no—
118C24×C151—21no—
119C24×C151—22no—
120C24×C151—42no—
121C24×C151—42no—
122C24×C151—82no—
123C24×C151—82no—
124C24×C151C2×D411yescharacteristic
125C2×Q8×C151—24no—
126C2×Q8×C151—21no—
127C2×Q8×C151—22no—
128C2×Q8×C151—22no—
129C2×Q8×C151—82no—
130C2×Q8×C151C2×D412yes—
131C2×D4×C151—24no—
132C2×D4×C151—24no—
133C2×D4×C151—22no—
134C2×D4×C151—22no—
135C2×D4×C151—21no—
136C2×D4×C151—22no—
137C2×D4×C151—22no—
138C2×D4×C151—22no—
139C2×D4×C151—22no—
140C2×D4×C151—22no—
141C2×D4×C151—48no—
142C2×D4×C151—48no—
143C2×D4×C151—42no—
144C2×D4×C151—42no—
145C2×D4×C151—82no—
146C2×D4×C151C2×D412yes—
147C2×D4×C151#4114yes—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—24no—
154C22×C4×C151—22no—
155C22×C4×C151—82no—
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151C2×D411yescharacteristic
160C22×C4×C151C2×D411yescharacteristic
161C22×C4×C151C2×D412yes—
162C22×C4×C151C2×D412yes—
163C22×C4×C151C2411yescharacteristic
164SD16×C151—48no—
165D8×C151—48no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C2×C8×C151—22no—
171C2×C8×C151—22no—
172C4⋊C4×C151—24no—
173C4⋊C4×C151—24no—
174C4⋊C4×C151—24no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151C2×D412yes—
182C4⋊C4×C151C2×D412yes—
183C22⋊C4×C151—24no—
184C22⋊C4×C151—24no—
185C22⋊C4×C151—24no—
186C22⋊C4×C151—24no—
187C22⋊C4×C151—22no—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—24no—
190C22⋊C4×C151—42no—
191C22⋊C4×C151—82no—
192C22⋊C4×C151—82no—
193C22⋊C4×C151—82no—
194C22⋊C4×C151—82no—
195C42×C151—24no—
196C42×C151—21no—
197C42×C151—21no—
198C42×C151—21no—
199C42×C151—21no—
200C42×C151—42no—
201C23×C151—21no—
202C23×C151—21no—
203C23×C151—22no—
204C23×C151—22no—
205C23×C151—22no—
206C23×C151—24no—
207C23×C151—48no—
208C23×C151—42no—
209C23×C151—41no—
210C23×C151—42no—
211C23×C151—41no—
212C23×C151—42no—
213C23×C151—42no—
214C23×C151—42no—
215C23×C151—42no—
216C23×C151—42no—
217C23×C151—42no—
218C23×C151—84no—
219C23×C151—84no—
220C23×C151—88no—
221C23×C151—88no—
222C23×C151#12012yes—
223C23×C151C22×D411yescharacteristic
224Q8×C151—24no—
225Q8×C151—42no—
226Q8×C151—84no—
227D4×C151—24no—
228D4×C151—24no—
229D4×C151—24no—
230D4×C151—48no—
231D4×C151—42no—
232D4×C151—42no—
233D4×C151—42no—
234D4×C151—84no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—24no—
238C2×C4×C151—24no—
239C2×C4×C151—21no—
240C2×C4×C151—22no—
241C2×C4×C151—22no—
242C2×C4×C151—22no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—22no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—22no—
250C2×C4×C151—41no—
251C2×C4×C151—41no—
252C2×C4×C151—42no—
253C2×C4×C151—42no—
254C2×C4×C151—42no—
255C2×C4×C151—42no—
256C2×C4×C151—42no—
257C2×C4×C151—84no—
258C2×C4×C151#12012yes—
259C2×C4×C151C22×D411yescharacteristic
260C2×C4×C151C22×D411yescharacteristic
261C2×C4×C151C2×#4112yes—
262C2×C4×C151H(5,𝔽2)12yes—
263C8×C151—42no—
264C8×C151—42no—
265C22×C151—22no—
266C22×C151—22no—
267C22×C151—22no—
268C22×C151—42no—
269C22×C151—42no—
270C22×C151—44no—
271C22×C151—44no—
272C22×C151—44no—
273C22×C151—42no—
274C22×C151—42no—
275C22×C151—42no—
276C22×C151—816no—
277C22×C151—82no—
278C22×C151—82no—
279C22×C151—82no—
280C22×C151—82no—
281C22×C151—82no—
282C22×C151—82no—
283C22×C151C2×#12011yescharacteristic
284C22×C151#52511yescharacteristic
285C22×C151#53511yescharacteristic
286C22×C151#57612yes—
287C22×C151#57712yes—
288C4×C151—22no—
289C4×C151—42no—
290C4×C151—41no—
291C4×C151—41no—
292C4×C151—42no—
293C4×C151—42no—
294C4×C151—41no—
295C4×C151—41no—
296C4×C151—82no—
297C4×C151#54612yes—
298C4×C151#54612yes—
299C2×C151—42no—
300C2×C151—82no—
301C2×C151—84no—
302C2×C151#240411yescharacteristic
303C2×C151#300811yescharacteristic
304C2×C151#301011yescharacteristic
305C2×C151#311812yes—
306C2×C151#322412yes—
307#23945C15111yesmaximal, characteristic, direct product factor, Sylow
308C151#2394511yescharacteristic, direct product factor, Sylow
309C2×#542C2×C15111yescharacteristic, complemented
310C2×#450C2×C15111yescharacteristic, complemented
311C2×#447C2×C15111yescharacteristic
312#2309C2×C15111yescharacteristic, complemented
313#2023C2×C15112yescomplemented
314#2012C2×C15112yescomplemented
315#1880C2×C15112yescomplemented
316#1879C2×C15112yescomplemented
317#1875C2×C15111yescharacteristic, complemented
318#1873C2×C15111yescharacteristic, complemented
319#1818C2×C15111yescharacteristic, complemented
320C23×D4C22×C15111yescharacteristic
321C22×SD16C22×C15112yes—
322C22×D8C22×C15112yes—
323#542—24no—
324#542—24no—
325C2×C4⋊Q8C22×C15111yescharacteristic, complemented
326C2×#126—21no—
327C2×#124—21no—
328C2×#124C22×C15111yescharacteristic, complemented
329C2×#123—21no—
330C2×C22⋊Q8—21no—
331C2×C22⋊Q8C22×C15111yescharacteristic
332C2×#121C22×C15111yescharacteristic
333C2×C4×Q8C22×C15111yescharacteristic, complemented
334C2×C4×D4C22×C15111yescharacteristic, complemented
335C2×#117C22×C15111yescharacteristic
336C2×#117C22×C15111yescharacteristic
337#450—24no—
338#447—24no—
339C2×#103C22×C15112yescomplemented
340C2×#102C22×C15112yes—
341C2×#102C22×C15112yes—
342C2×#102C22×C15112yescomplemented
343C2×C22⋊C8C22×C15111yescharacteristic
344C2×C22⋊C8C22×C15111yescharacteristic
345#390—21no—
346#390—21no—
347#390C22×C15112yes—
348#390C22×C15112yes—
349#379—21no—
350#379—21no—
351#340C22×C15112yescomplemented
352#340C22×C15112yescomplemented
353#336C22×C15112yescomplemented
354#336C22×C15112yescomplemented
355C25—21no—
356C22×Q8—21no—
357C22×Q8C23×C15111yescharacteristic
358C22×D4—21no—
359C22×D4—24no—
360C22×D4—21no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—42no—
364C22×D4C23×C15112yes—
365C22×D4C23×C15111yescharacteristic
366C23×C4—21no—
367C23×C4C23×C15111yescharacteristic
368C2×SD16—24no—
369C2×SD16—24no—
370C2×SD16—42no—
371C2×D8—24no—
372C2×D8—24no—
373C2×D8—42no—
374C22×C8C23×C15112yes—
375C22×C8C23×C15112yes—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378#126—28no—
379#124—28no—
380#124—22no—
381#124—22no—
382#123—28no—
383C22⋊Q8—28no—
384C22⋊Q8—22no—
385C22⋊Q8D4×C15114yes—
386#121—22no—
387#121D4×C15114yes—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×D4—22no—
391C4×D4—22no—
392#117—22no—
393#117—22no—
394#117—42no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4D4×C15111yescharacteristic
399C2×C4⋊C4D4×C15111yescharacteristic
400C2×C4⋊C4C23×C15112yes—
401C2×C4⋊C4C23×C15111yescharacteristic
402C2×C4⋊C4C23×C15111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4D4×C15111yescharacteristic
414C2×C22⋊C4D4×C15111yescharacteristic
415C2×C42—21no—
416C2×C42—21no—
417C2×C42C23×C15111yescharacteristic
418C2×C42C23×C15111yescharacteristic
419#103—42no—
420#102—24no—
421#102—24no—
422#102—42no—
423C22⋊C8—22no—
424C22⋊C8—22no—
425C24—24no—
426C24—21no—
427C24—22no—
428C24—42no—
429C24—42no—
430C24—82no—
431C24—82no—
432C24C2×D4×C15111yescharacteristic
433C2×Q8—24no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—82no—
438C2×Q8C2×D4×C15112yes—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—48no—
450C2×D4—48no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—82no—
454C2×D4C2×D4×C15112yes—
455C2×D4#41×C15114yes—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—82no—
464C22×C4C2×D4×C15111yescharacteristic
465C22×C4C2×D4×C15111yescharacteristic
466C22×C4C2×D4×C15111yescharacteristic
467C22×C4C2×D4×C15111yescharacteristic
468C22×C4C2×D4×C15111yescharacteristic
469C22×C4C2×D4×C15112yes—
470C22×C4C2×D4×C15112yes—
471C22×C4C24×C15111yescharacteristic
472SD16—48no—
473D8—48no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4C2×D4×C15112yes—
490C4⋊C4C2×D4×C15112yes—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—24no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—24no—
498C22⋊C4—42no—
499C22⋊C4—82no—
500C22⋊C4—82no—
501C22⋊C4—82no—
502C22⋊C4—82no—
503C42—24no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—42no—
509C23—21no—
510C23—21no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—24no—
515C23—48no—
516C23—42no—
517C23—41no—
518C23—42no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—84no—
527C23—84no—
528C23—88no—
529C23—88no—
530C23#120×C15112yes—
531C23C22×D4×C15111yescharacteristic
532Q8—24no—
533Q8—42no—
534Q8—84no—
535D4—24no—
536D4—24no—
537D4—24no—
538D4—48no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—84no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—84no—
566C2×C4#120×C15112yes—
567C2×C4C22×D4×C15111yescharacteristic
568C2×C4C22×D4×C15111yescharacteristic
569C2×C4C2×#41×C15112yes—
570C2×C4H(5,𝔽2)×C15112yes—
571C8—42no—
572C8—42no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—816no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22—82no—
591C22C2×#120×C15111yescharacteristic
592C22#525×C15111yescharacteristic
593C22#535×C15111yescharacteristic
594C22#576×C15112yes—
595C22#577×C15112yes—
596C4—22no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—82no—
605C4#546×C15112yes—
606C4#546×C15112yes—
607C2—42no—
608C2—84no—
609C2—82no—
610C2#2404×C15111yescharacteristic
611C2#3008×C15111yescharacteristic
612C2#3010×C15111yescharacteristic
613C2#3118×C15112yes—
614C2#3224×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#447×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#542×C151C2semidirect
2. C2×#450×C151C2semidirect
4. #2309×C151C2semidirect
5. #2023×C151C2semidirect
6. #2012×C151C2semidirect
7. #1880×C151C2semidirect
8. #1879×C151C2semidirect
9. #1875×C151C2semidirect
10. #1873×C151C2semidirect
11. #1818×C151C2semidirect
17. C2×C4⋊Q8×C151C22semidirect
20. C2×#124×C151C22semidirect
25. C2×C4×Q8×C151C22semidirect
26. C2×C4×D4×C151C22semidirect
31. C2×#103×C151C22semidirect
34. C2×#102×C151C22semidirect
43. #340×C151C22semidirect
44. #340×C151C22semidirect
45. #336×C151C22semidirect
46. #336×C151C22semidirect
307. #23945C151direct (N × H)
308. C151#23945direct (N × H)
309. C2×#542C2×C151semidirect
310. C2×#450C2×C151semidirect
312. #2309C2×C151semidirect
313. #2023C2×C151semidirect
314. #2012C2×C151semidirect
315. #1880C2×C151semidirect
316. #1879C2×C151semidirect
317. #1875C2×C151semidirect
318. #1873C2×C151semidirect
319. #1818C2×C151semidirect
325. C2×C4⋊Q8C22×C151semidirect
328. C2×#124C22×C151semidirect
333. C2×C4×Q8C22×C151semidirect
334. C2×C4×D4C22×C151semidirect
339. C2×#103C22×C151semidirect
342. C2×#102C22×C151semidirect
351. #340C22×C151semidirect
352. #340C22×C151semidirect
353. #336C22×C151semidirect
354. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#542×C1512
C2×#450×C1512
C2×#447×C1512
#2309×C1512
#2023×C1512
#2012×C1512
#1880×C1512
#1879×C1512
#1875×C1512
#1873×C1512
#1818×C1512
#23945151