Finite Group Databasebeta

← C151×#23652 #50328577

Subgroups — C151×#23652 #50328577

Order 38656.

888 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#430×C151C211yesmaximal, characteristic, complemented
2#2896×C151C211yesmaximal, characteristic
3#2896×C151C211yesmaximal, characteristic
4C2×#413×C151C211yesmaximal, characteristic
5#2082×C151C214yesmaximal, complemented
6#2081×C151C214yesmaximal, complemented
7C2×#344×C151C211yesmaximal, characteristic, complemented
8C2×#344×C151C211yesmaximal, characteristic, complemented
9C2×H(3,ℤ/4)×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151C2211yescharacteristic
11C22×M16×C151C2211yescharacteristic
12C22×M16×C151C2211yescharacteristic
13C22×M16×C151C2211yescharacteristic
14C22×M16×C151C2211yescharacteristic
15C2×#117×C151C2211yescharacteristic
16C2×#117×C151C2211yescharacteristic
17#430×C151—22no—
18#430×C151C2214yes—
19C2×#108×C151—22no—
20#419×C151C2212yes—
21#419×C151C2212yes—
22#418×C151C2212yes—
23#418×C151C2212yes—
24#417×C151—22no—
25#417×C151—22no—
26#416×C151—22no—
27#416×C151—22no—
28#413×C151—22no—
29#413×C151—22no—
30C2×#101×C151C2212yes—
31C2×#100×C151C2212yes—
32#344×C151C2214yes—
33#344×C151C2214yes—
34H(3,ℤ/4)×C151C2214yes—
35C2×#41×C151—21no—
36C2×#41×C151—21no—
37C2×#41×C151—21no—
38C2×#41×C151—21no—
39C2×#41×C151—21no—
40C2×#41×C151—21no—
41C2×#41×C151—21no—
42C2×#41×C151—21no—
43C2×#41×C151—21no—
44C2×#41×C151—21no—
45C2×#41×C151D412yes—
46C2×#41×C151D412yes—
47C22×Q8×C151C2311yescharacteristic
48C22×D4×C151—21no—
49C22×D4×C151C2311yescharacteristic
50C23×C4×C151—21no—
51C23×C4×C151C2311yescharacteristic
52C2×M16×C151—21no—
53C2×M16×C151—21no—
54C2×M16×C151—21no—
55C2×M16×C151—21no—
56C2×M16×C151—21no—
57C2×M16×C151—21no—
58C2×M16×C151—21no—
59C2×M16×C151—21no—
60C2×M16×C151—21no—
61C2×M16×C151—21no—
62C2×M16×C151—21no—
63C2×M16×C151—21no—
64C2×M16×C151—21no—
65C2×M16×C151—21no—
66C2×M16×C151—21no—
67C2×M16×C151—21no—
68C2×M16×C151—21no—
69C2×M16×C151—21no—
70C2×M16×C151—21no—
71C2×M16×C151D412yes—
72C2×M16×C151C2312yes—
73C2×M16×C151C2312yes—
74C2×M16×C151C2312yes—
75C2×M16×C151C2312yes—
76C22×C8×C151—21no—
77C22×C8×C151—21no—
78C22×C8×C151—21no—
79C22×C8×C151D412yes—
80#117×C151—21no—
81#117×C151—21no—
82#117×C151—21no—
83#117×C151—21no—
84#117×C151—21no—
85#117×C151—21no—
86#117×C151C2312yes—
87#117×C151C2312yes—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C42×C151—21no—
93C2×C42×C151—21no—
94#108×C151—28no—
95#103×C151—24no—
96#103×C151—24no—
97#102×C151—24no—
98#102×C151—24no—
99#101×C151—24no—
100#100×C151—24no—
101C24×C151—21no—
102C24×C151#4111yescharacteristic
103#41×C151—22no—
104#41×C151—22no—
105#41×C151—22no—
106#41×C151—22no—
107#41×C151—22no—
108#41×C151—22no—
109#41×C151—22no—
110#41×C151—22no—
111#41×C151—41no—
112#41×C151—41no—
113#41×C151—41no—
114#41×C151—41no—
115#41×C151—41no—
116#41×C151—41no—
117#41×C151—41no—
118#41×C151—41no—
119C2×Q8×C151—21no—
120C2×Q8×C151—21no—
121C2×Q8×C151—21no—
122C2×Q8×C151—21no—
123C2×Q8×C151—21no—
124C2×Q8×C151C2×D412yes—
125C2×D4×C151—22no—
126C2×D4×C151—22no—
127C2×D4×C151—21no—
128C2×D4×C151—21no—
129C2×D4×C151—21no—
130C2×D4×C151—21no—
131C2×D4×C151—21no—
132C2×D4×C151—41no—
133C2×D4×C151—41no—
134C2×D4×C151—41no—
135C2×D4×C151—41no—
136C2×D4×C151C2×D412yes—
137C22×C4×C151—21no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—41no—
141C22×C4×C151—41no—
142C22×C4×C151—41no—
143C22×C4×C151—41no—
144C22×C4×C151—41no—
145C22×C4×C151—41no—
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151#4111yescharacteristic
151C22×C4×C151#4111yescharacteristic
152C22×C4×C151#4111yescharacteristic
153C22×C4×C151#4111yescharacteristic
154C22×C4×C151#4111yescharacteristic
155C22×C4×C151#4111yescharacteristic
156C22×C4×C151#4111yescharacteristic
157C22×C4×C151#4111yescharacteristic
158C22×C4×C151#4111yescharacteristic
159C22×C4×C151C2411yescharacteristic
160M16×C151—22no—
161M16×C151—22no—
162M16×C151—22no—
163M16×C151—22no—
164M16×C151—22no—
165M16×C151—22no—
166M16×C151—22no—
167M16×C151—22no—
168M16×C151—22no—
169M16×C151—22no—
170M16×C151—41no—
171M16×C151—41no—
172M16×C151—41no—
173M16×C151—41no—
174M16×C151—41no—
175M16×C151—41no—
176C2×C8×C151—22no—
177C2×C8×C151—22no—
178C2×C8×C151—22no—
179C2×C8×C151—22no—
180C2×C8×C151—22no—
181C2×C8×C151—41no—
182C2×C8×C151—41no—
183C2×C8×C151—41no—
184C2×C8×C151—41no—
185C2×C8×C151—41no—
186C2×C8×C151—41no—
187C2×C8×C151C2×D414yes—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151—41no—
192C22⋊C4×C151—22no—
193C22⋊C4×C151—22no—
194C22⋊C4×C151—41no—
195C22⋊C4×C151—41no—
196C42×C151—22no—
197C42×C151—22no—
198C42×C151—41no—
199C42×C151—41no—
200C23×C151—22no—
201C23×C151—41no—
202C23×C151—41no—
203C23×C151—81no—
204C23×C151—82no—
205C23×C151#12311yescharacteristic
206C23×C151#12311yescharacteristic
207C23×C151#12411yescharacteristic
208C23×C151#12411yescharacteristic
209C23×C151#12611yescharacteristic
210C23×C151#12611yescharacteristic
211C23×C151C2×#4111yescharacteristic
212Q8×C151—22no—
213Q8×C151—22no—
214Q8×C151—41no—
215Q8×C151—41no—
216D4×C151—22no—
217D4×C151—22no—
218D4×C151—42no—
219D4×C151—42no—
220D4×C151—42no—
221D4×C151—42no—
222D4×C151—41no—
223D4×C151—41no—
224C2×C4×C151—22no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—82no—
234C2×C4×C151—82no—
235C2×C4×C151#12111yescharacteristic
236C2×C4×C151#12111yescharacteristic
237C2×C4×C151#12111yescharacteristic
238C2×C4×C151#12111yescharacteristic
239C2×C4×C151#12311yescharacteristic
240C2×C4×C151#12311yescharacteristic
241C2×C4×C151#12311yescharacteristic
242C2×C4×C151#12311yescharacteristic
243C2×C4×C151#12311yescharacteristic
244C2×C4×C151#12311yescharacteristic
245C2×C4×C151#12311yescharacteristic
246C2×C4×C151#12311yescharacteristic
247C2×C4×C151#12311yescharacteristic
248C2×C4×C151#12311yescharacteristic
249C2×C4×C151#12411yescharacteristic
250C2×C4×C151#12411yescharacteristic
251C2×C4×C151#12611yescharacteristic
252C2×C4×C151#12611yescharacteristic
253C2×C4×C151#12611yescharacteristic
254C2×C4×C151#12611yescharacteristic
255C2×C4×C151#12611yescharacteristic
256C2×C4×C151#12611yescharacteristic
257C2×C4×C151C22×D411yescharacteristic
258C2×C4×C151C22×D411yescharacteristic
259C2×C4×C151C2×#4111yescharacteristic
260C2×C4×C151C2×#4111yescharacteristic
261C2×C4×C151C2×#4111yescharacteristic
262C2×C4×C151C2×#4111yescharacteristic
263C8×C151—24no—
264C8×C151—42no—
265C8×C151—42no—
266C8×C151—42no—
267C22×C151—41no—
268C22×C151—41no—
269C22×C151—41no—
270C22×C151—41no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151—41no—
274C22×C151—42no—
275C22×C151—82no—
276C22×C151—82no—
277C22×C151—82no—
278C22×C151#39711yescharacteristic
279C22×C151#39711yescharacteristic
280C22×C151#39711yescharacteristic
281C22×C151#39711yescharacteristic
282C22×C151C2×#12311yescharacteristic
283C22×C151C2×#12411yescharacteristic
284C22×C151C2×#12611yescharacteristic
285C4×C151—42no—
286C4×C151—82no—
287C4×C151—82no—
288C4×C151#39711yescharacteristic
289C4×C151#39711yescharacteristic
290C4×C151#39711yescharacteristic
291C4×C151#39711yescharacteristic
292C4×C151C2×#12111yescharacteristic
293C4×C151C2×#12311yescharacteristic
294C4×C151C2×#12311yescharacteristic
295C4×C151C2×#12611yescharacteristic
296C2×C151—21no—
297C2×C151—21no—
298C2×C151—21no—
299C2×C151—21no—
300C2×C151—21no—
301C2×C151—21no—
302C2×C151—21no—
303C2×C151—82no—
304C2×C151C2×#39711yescharacteristic
305#23652C15111yesmaximal, characteristic, direct product factor, Sylow
306C151#2365211yescharacteristic, direct product factor, Sylow
307C2×#430C2×C15111yescharacteristic, complemented
308#2896C2×C15111yescharacteristic
309#2896C2×C15111yescharacteristic
310C2×#413C2×C15111yescharacteristic
311#2082C2×C15114yescomplemented
312#2081C2×C15114yescomplemented
313C2×#344C2×C15111yescharacteristic, complemented
314C2×#344C2×C15111yescharacteristic, complemented
315C2×H(3,ℤ/4)C2×C15111yescharacteristic, complemented
316C22×#41C22×C15111yescharacteristic
317C22×M16C22×C15111yescharacteristic
318C22×M16C22×C15111yescharacteristic
319C22×M16C22×C15111yescharacteristic
320C22×M16C22×C15111yescharacteristic
321C2×#117C22×C15111yescharacteristic
322C2×#117C22×C15111yescharacteristic
323#430—22no—
324#430C22×C15114yes—
325C2×#108—22no—
326#419C22×C15112yes—
327#419C22×C15112yes—
328#418C22×C15112yes—
329#418C22×C15112yes—
330#417—22no—
331#417—22no—
332#416—22no—
333#416—22no—
334#413—22no—
335#413—22no—
336C2×#101C22×C15112yes—
337C2×#100C22×C15112yes—
338#344C22×C15114yes—
339#344C22×C15114yes—
340H(3,ℤ/4)C22×C15114yes—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41D4×C15112yes—
352C2×#41D4×C15112yes—
353C22×Q8C23×C15111yescharacteristic
354C22×D4—21no—
355C22×D4C23×C15111yescharacteristic
356C23×C4—21no—
357C23×C4C23×C15111yescharacteristic
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16D4×C15112yes—
378C2×M16C23×C15112yes—
379C2×M16C23×C15112yes—
380C2×M16C23×C15112yes—
381C2×M16C23×C15112yes—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8D4×C15112yes—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117C23×C15112yes—
393#117C23×C15112yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C42—21no—
399C2×C42—21no—
400#108—28no—
401#103—24no—
402#103—24no—
403#102—24no—
404#102—24no—
405#101—24no—
406#100—24no—
407C24—21no—
408C24#41×C15111yescharacteristic
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—22no—
416#41—22no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423#41—41no—
424#41—41no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8C2×D4×C15112yes—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4C2×D4×C15112yes—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4C2×D4×C15111yescharacteristic
453C22×C4C2×D4×C15111yescharacteristic
454C22×C4C2×D4×C15111yescharacteristic
455C22×C4C2×D4×C15111yescharacteristic
456C22×C4#41×C15111yescharacteristic
457C22×C4#41×C15111yescharacteristic
458C22×C4#41×C15111yescharacteristic
459C22×C4#41×C15111yescharacteristic
460C22×C4#41×C15111yescharacteristic
461C22×C4#41×C15111yescharacteristic
462C22×C4#41×C15111yescharacteristic
463C22×C4#41×C15111yescharacteristic
464C22×C4#41×C15111yescharacteristic
465C22×C4C24×C15111yescharacteristic
466M16—22no—
467M16—22no—
468M16—22no—
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—41no—
477M16—41no—
478M16—41no—
479M16—41no—
480M16—41no—
481M16—41no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8C2×D4×C15114yes—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—22no—
503C42—22no—
504C42—41no—
505C42—41no—
506C23—22no—
507C23—41no—
508C23—41no—
509C23—81no—
510C23—82no—
511C23#123×C15111yescharacteristic
512C23#123×C15111yescharacteristic
513C23#124×C15111yescharacteristic
514C23#124×C15111yescharacteristic
515C23#126×C15111yescharacteristic
516C23#126×C15111yescharacteristic
517C23C2×#41×C15111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—22no—
523D4—22no—
524D4—42no—
525D4—42no—
526D4—42no—
527D4—42no—
528D4—41no—
529D4—41no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4#121×C15111yescharacteristic
542C2×C4#121×C15111yescharacteristic
543C2×C4#121×C15111yescharacteristic
544C2×C4#121×C15111yescharacteristic
545C2×C4#123×C15111yescharacteristic
546C2×C4#123×C15111yescharacteristic
547C2×C4#123×C15111yescharacteristic
548C2×C4#123×C15111yescharacteristic
549C2×C4#123×C15111yescharacteristic
550C2×C4#123×C15111yescharacteristic
551C2×C4#123×C15111yescharacteristic
552C2×C4#123×C15111yescharacteristic
553C2×C4#123×C15111yescharacteristic
554C2×C4#123×C15111yescharacteristic
555C2×C4#124×C15111yescharacteristic
556C2×C4#124×C15111yescharacteristic
557C2×C4#126×C15111yescharacteristic
558C2×C4#126×C15111yescharacteristic
559C2×C4#126×C15111yescharacteristic
560C2×C4#126×C15111yescharacteristic
561C2×C4#126×C15111yescharacteristic
562C2×C4#126×C15111yescharacteristic
563C2×C4C22×D4×C15111yescharacteristic
564C2×C4C22×D4×C15111yescharacteristic
565C2×C4C2×#41×C15111yescharacteristic
566C2×C4C2×#41×C15111yescharacteristic
567C2×C4C2×#41×C15111yescharacteristic
568C2×C4C2×#41×C15111yescharacteristic
569C8—24no—
570C8—42no—
571C8—42no—
572C8—42no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22#397×C15111yescharacteristic
585C22#397×C15111yescharacteristic
586C22#397×C15111yescharacteristic
587C22#397×C15111yescharacteristic
588C22C2×#123×C15111yescharacteristic
589C22C2×#124×C15111yescharacteristic
590C22C2×#126×C15111yescharacteristic
591C4—42no—
592C4—82no—
593C4—82no—
594C4#397×C15111yescharacteristic
595C4#397×C15111yescharacteristic
596C4#397×C15111yescharacteristic
597C4#397×C15111yescharacteristic
598C4C2×#121×C15111yescharacteristic
599C4C2×#123×C15111yescharacteristic
600C4C2×#123×C15111yescharacteristic
601C4C2×#126×C15111yescharacteristic
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—82no—
610C2C2×#397×C15111yescharacteristic
subgroupG/H
centerC4×C151#397
commutator, Frattini, cosocleC22×C4C24×C151
socleC2×C151C2×#397
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#430×C151C2semidirect
5. #2082×C151C2semidirect
6. #2081×C151C2semidirect
7. C2×#344×C151C2semidirect
8. C2×#344×C151C2semidirect
9. C2×H(3,ℤ/4)×C151C2semidirect
305. #23652C151direct (N × H)
306. C151#23652direct (N × H)
307. C2×#430C2×C151semidirect
311. #2082C2×C151semidirect
312. #2081C2×C151semidirect
313. C2×#344C2×C151semidirect
314. C2×#344C2×C151semidirect
315. C2×H(3,ℤ/4)C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#430×C1512
#2896×C1512
C2×#413×C1512
#2082×C1512
#2081×C1512
C2×#344×C1512
C2×H(3,ℤ/4)×C1512
#23652151