Finite Group Databasebeta

← C151×#24045 #50328970

Subgroups — C151×#24045 #50328970

Order 38656.

1410 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C151C211yesmaximal, characteristic
2C2×#481×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic, complemented
4#2486×C151C211yesmaximal, characteristic, complemented
5#2041×C151C212yesmaximal, complemented
6#2034×C151C212yesmaximal, complemented
7#1895×C151C211yesmaximal, characteristic, complemented
8#1870×C151C211yesmaximal, characteristic, complemented
9#1865×C151C212yesmaximal, complemented
10#1788×C151C211yesmaximal, characteristic, complemented
11#1788×C151C212yesmaximal, complemented
12C22×#41×C151C2211yescharacteristic
13C22×#41×C151C2211yescharacteristic
14C22×M16×C151C2211yescharacteristic
15#550×C151—24no—
16#550×C151—24no—
17C2×#127×C151—21no—
18C2×#127×C151C2211yescharacteristic
19C2×#123×C151—21no—
20C2×#121×C151—21no—
21C2×#121×C151—21no—
22C2×#121×C151C2211yescharacteristic
23C2×#121×C151C2211yescharacteristic
24C2×C4×Q8×C151C2211yescharacteristic
25C2×C4×D4×C151—21no—
26C2×C4×D4×C151C2211yescharacteristic
27C22×C4⋊C4×C151C2211yescharacteristic
28#481×C151—24no—
29C2×#106×C151C2212yes—
30#417×C151—24no—
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×#102×C151C2212yes—
36C2×#102×C151C2212yes—
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2212yes—
39#398×C151—21no—
40#397×C151—21no—
41#389×C151C2212yes—
42#381×C151—21no—
43#380×C151C2211yescharacteristic
44#380×C151C2212yes—
45#340×C151C2212yes—
46#336×C151C2212yes—
47C2×#41×C151—22no—
48C2×#41×C151—22no—
49C2×#41×C151—22no—
50C2×#41×C151—24no—
51C2×#41×C151—24no—
52C2×#41×C151—42no—
53C2×#41×C151—42no—
54C2×#41×C151D414yes—
55C22×Q8×C151C2311yescharacteristic
56C22×D4×C151—21no—
57C22×D4×C151—21no—
58C22×D4×C151—21no—
59C22×D4×C151—21no—
60C22×D4×C151—21no—
61C22×D4×C151—21no—
62C22×D4×C151D411yescharacteristic
63C22×D4×C151C2311yescharacteristic
64C22×D4×C151C2311yescharacteristic
65C23×C4×C151—21no—
66C23×C4×C151—21no—
67C23×C4×C151—21no—
68C23×C4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C2×M16×C151—22no—
71C2×M16×C151—42no—
72C22×C8×C151C2312yes—
73C22×C8×C151C2312yes—
74#127×C151—28no—
75#127×C151—22no—
76#127×C151—22no—
77#123×C151—44no—
78#121×C151—28no—
79#121×C151—28no—
80#121×C151—22no—
81#121×C151—22no—
82#121×C151—22no—
83#121×C151D414yes—
84C4×Q8×C151—22no—
85C4×Q8×C151—22no—
86C4×D4×C151—28no—
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—22no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—22no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151D411yescharacteristic
95C2×C4⋊C4×C151C2312yes—
96C2×C4⋊C4×C151C2312yes—
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—22no—
102C2×C22⋊C4×C151D411yescharacteristic
103C2×C22⋊C4×C151D411yescharacteristic
104C2×C42×C151—21no—
105C2×C42×C151C2311yescharacteristic
106#106×C151—24no—
107#103×C151—24no—
108#103×C151—24no—
109#102×C151—24no—
110#102×C151—24no—
111#102×C151—42no—
112#102×C151—42no—
113C22⋊C8×C151—22no—
114C22⋊C8×C151—42no—
115#95×C151—22no—
116#95×C151—21no—
117#95×C151—22no—
118C24×C151—21no—
119C24×C151—21no—
120C24×C151C2×D411yescharacteristic
121C24×C151C2×D411yescharacteristic
122#41×C151—28no—
123#41×C151—44no—
124#41×C151—48no—
125#41×C151—48no—
126#41×C151—44no—
127#41×C151—44no—
128C2×Q8×C151—21no—
129C2×Q8×C151—22no—
130C2×Q8×C151C2×D412yes—
131C2×Q8×C151#4114yes—
132C2×D4×C151—24no—
133C2×D4×C151—24no—
134C2×D4×C151—22no—
135C2×D4×C151—24no—
136C2×D4×C151—24no—
137C2×D4×C151—24no—
138C2×D4×C151—24no—
139C2×D4×C151—22no—
140C2×D4×C151—21no—
141C2×D4×C151—21no—
142C2×D4×C151—22no—
143C2×D4×C151—22no—
144C2×D4×C151—22no—
145C2×D4×C151—22no—
146C2×D4×C151—41no—
147C2×D4×C151—44no—
148C2×D4×C151—44no—
149C2×D4×C151—42no—
150C2×D4×C151—42no—
151C2×D4×C151—82no—
152C2×D4×C151—82no—
153C2×D4×C151—82no—
154C2×D4×C151C2×D412yes—
155C2×D4×C151C2×D412yes—
156C22×C4×C151—21no—
157C22×C4×C151—22no—
158C22×C4×C151—22no—
159C22×C4×C151—24no—
160C22×C4×C151—21no—
161C22×C4×C151—24no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—22no—
165C22×C4×C151—22no—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
168C22×C4×C151—44no—
169C22×C4×C151—44no—
170C22×C4×C151—42no—
171C22×C4×C151—42no—
172C22×C4×C151—42no—
173C22×C4×C151C2×D411yescharacteristic
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D412yes—
177C22×C4×C151C2×D412yes—
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2411yescharacteristic
180M16×C151—44no—
181C2×C8×C151—22no—
182C2×C8×C151—22no—
183C2×C8×C151—22no—
184C2×C8×C151—22no—
185C2×C8×C151—22no—
186C2×C8×C151—22no—
187C4⋊C4×C151—24no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—22no—
194C4⋊C4×C151—42no—
195C4⋊C4×C151—44no—
196C4⋊C4×C151C2×D412yes—
197C22⋊C4×C151—24no—
198C22⋊C4×C151—22no—
199C22⋊C4×C151—24no—
200C22⋊C4×C151—22no—
201C22⋊C4×C151—42no—
202C22⋊C4×C151—44no—
203C42×C151—24no—
204C42×C151—21no—
205C42×C151—21no—
206C23×C151—22no—
207C23×C151—21no—
208C23×C151—21no—
209C23×C151—22no—
210C23×C151—22no—
211C23×C151—22no—
212C23×C151—21no—
213C23×C151—22no—
214C23×C151—21no—
215C23×C151—21no—
216C23×C151—22no—
217C23×C151—42no—
218C23×C151—42no—
219C23×C151—41no—
220C23×C151—41no—
221C23×C151—41no—
222C23×C151—41no—
223C23×C151—42no—
224C23×C151—42no—
225C23×C151#12012yes—
226C23×C151C22×D411yescharacteristic
227Q8×C151—22no—
228Q8×C151—24no—
229Q8×C151#12314yescomplemented
230D4×C151—22no—
231D4×C151—22no—
232D4×C151—24no—
233D4×C151—48no—
234D4×C151—44no—
235D4×C151—48no—
236D4×C151—48no—
237D4×C151—41no—
238D4×C151—41no—
239D4×C151—42no—
240D4×C151—84no—
241D4×C151—84no—
242D4×C151—84no—
243C2×C4×C151—22no—
244C2×C4×C151—21no—
245C2×C4×C151—24no—
246C2×C4×C151—22no—
247C2×C4×C151—21no—
248C2×C4×C151—22no—
249C2×C4×C151—22no—
250C2×C4×C151—24no—
251C2×C4×C151—21no—
252C2×C4×C151—22no—
253C2×C4×C151—21no—
254C2×C4×C151—22no—
255C2×C4×C151—22no—
256C2×C4×C151—48no—
257C2×C4×C151—48no—
258C2×C4×C151—42no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—42no—
262C2×C4×C151—42no—
263C2×C4×C151—42no—
264C2×C4×C151—42no—
265C2×C4×C151—42no—
266C2×C4×C151—42no—
267C2×C4×C151—42no—
268C2×C4×C151—84no—
269C2×C4×C151#12012yes—
270C2×C4×C151AGL(1,ℤ/8)12yes—
271C2×C4×C151C22×D411yescharacteristic
272C2×C4×C151C22×D411yescharacteristic
273C2×C4×C151C2×#4112yes—
274C2×C4×C151H(5,𝔽2)12yes—
275C8×C151—42no—
276C8×C151—42no—
277C22×C151—22no—
278C22×C151—22no—
279C22×C151—22no—
280C22×C151—42no—
281C22×C151—42no—
282C22×C151—42no—
283C22×C151—42no—
284C22×C151—42no—
285C22×C151—41no—
286C22×C151—41no—
287C22×C151—42no—
288C22×C151—42no—
289C22×C151—41no—
290C22×C151—42no—
291C22×C151—42no—
292C22×C151—42no—
293C22×C151—82no—
294C22×C151—82no—
295C22×C151—82no—
296C22×C151—82no—
297C22×C151C2×#12011yescharacteristic
298C22×C151#54612yes—
299C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C151#57511yescharacteristic
301C22×C151#57712yes—
302C4×C151—22no—
303C4×C151—24no—
304C4×C151—22no—
305C4×C151—41no—
306C4×C151—41no—
307C4×C151—42no—
308C4×C151—82no—
309C4×C151—82no—
310C4×C151C2×#12311yescharacteristic
311C4×C151#53411yescharacteristic
312C4×C151#54612yes—
313C2×C151—42no—
314C2×C151—81no—
315C2×C151—82no—
316C2×C151—82no—
317C2×C151#240511yescharacteristic
318C2×C151#300611yescharacteristic
319C2×C151#300911yescharacteristic
320C2×C151#331712yes—
321C2×C151#333212yes—
322#24045C15111yesmaximal, characteristic, direct product factor, Sylow
323C151#2404511yescharacteristic, direct product factor, Sylow
324C2×#550C2×C15111yescharacteristic
325C2×#481C2×C15111yescharacteristic, complemented
326C2×#417C2×C15111yescharacteristic, complemented
327#2486C2×C15111yescharacteristic, complemented
328#2041C2×C15112yescomplemented
329#2034C2×C15112yescomplemented
330#1895C2×C15111yescharacteristic, complemented
331#1870C2×C15111yescharacteristic, complemented
332#1865C2×C15112yescomplemented
333#1788C2×C15112yescomplemented
334#1788C2×C15111yescharacteristic, complemented
335C22×#41C22×C15111yescharacteristic
336C22×#41C22×C15111yescharacteristic
337C22×M16C22×C15111yescharacteristic
338#550—24no—
339#550—24no—
340C2×#127—21no—
341C2×#127C22×C15111yescharacteristic
342C2×#123—21no—
343C2×#121—21no—
344C2×#121—21no—
345C2×#121C22×C15111yescharacteristic
346C2×#121C22×C15111yescharacteristic
347C2×C4×Q8C22×C15111yescharacteristic
348C2×C4×D4—21no—
349C2×C4×D4C22×C15111yescharacteristic
350C22×C4⋊C4C22×C15111yescharacteristic
351#481—24no—
352C2×#106C22×C15112yes—
353#417—24no—
354C2×#103C22×C15112yes—
355C2×#103C22×C15112yes—
356C2×#102C22×C15112yes—
357C2×#102C22×C15112yes—
358C2×#102C22×C15112yes—
359C2×#102C22×C15112yes—
360C2×C22⋊C8C22×C15111yescharacteristic
361C2×C22⋊C8C22×C15112yes—
362#398—21no—
363#397—21no—
364#389C22×C15112yes—
365#381—21no—
366#380C22×C15111yescharacteristic
367#380C22×C15112yes—
368#340C22×C15112yes—
369#336C22×C15112yes—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—24no—
374C2×#41—24no—
375C2×#41—42no—
376C2×#41—42no—
377C2×#41D4×C15114yes—
378C22×Q8C23×C15111yescharacteristic
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—21no—
384C22×D4—21no—
385C22×D4D4×C15111yescharacteristic
386C22×D4C23×C15111yescharacteristic
387C22×D4C23×C15111yescharacteristic
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—21no—
391C23×C4C23×C15111yescharacteristic
392C23×C4C23×C15111yescharacteristic
393C2×M16—22no—
394C2×M16—42no—
395C22×C8C23×C15112yes—
396C22×C8C23×C15112yes—
397#127—28no—
398#127—22no—
399#127—22no—
400#123—44no—
401#121—28no—
402#121—28no—
403#121—22no—
404#121—22no—
405#121—22no—
406#121D4×C15114yes—
407C4×Q8—22no—
408C4×Q8—22no—
409C4×D4—28no—
410C4×D4—22no—
411C4×D4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4D4×C15111yescharacteristic
418C2×C4⋊C4C23×C15112yes—
419C2×C4⋊C4C23×C15112yes—
420C2×C4⋊C4C23×C15111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4D4×C15111yescharacteristic
426C2×C22⋊C4D4×C15111yescharacteristic
427C2×C42—21no—
428C2×C42C23×C15111yescharacteristic
429#106—24no—
430#103—24no—
431#103—24no—
432#102—24no—
433#102—24no—
434#102—42no—
435#102—42no—
436C22⋊C8—22no—
437C22⋊C8—42no—
438#95—22no—
439#95—21no—
440#95—22no—
441C24—21no—
442C24—21no—
443C24C2×D4×C15111yescharacteristic
444C24C2×D4×C15111yescharacteristic
445#41—28no—
446#41—44no—
447#41—48no—
448#41—48no—
449#41—44no—
450#41—44no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8C2×D4×C15112yes—
454C2×Q8#41×C15114yes—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—22no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—41no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—82no—
475C2×D4—82no—
476C2×D4—82no—
477C2×D4C2×D4×C15112yes—
478C2×D4C2×D4×C15112yes—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4C2×D4×C15111yescharacteristic
497C22×C4C2×D4×C15111yescharacteristic
498C22×C4C2×D4×C15111yescharacteristic
499C22×C4C2×D4×C15112yes—
500C22×C4C2×D4×C15112yes—
501C22×C4C2×D4×C15111yescharacteristic
502C22×C4C24×C15111yescharacteristic
503M16—44no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C4⋊C4—24no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—42no—
518C4⋊C4—44no—
519C4⋊C4C2×D4×C15112yes—
520C22⋊C4—24no—
521C22⋊C4—22no—
522C22⋊C4—24no—
523C22⋊C4—22no—
524C22⋊C4—42no—
525C22⋊C4—44no—
526C42—24no—
527C42—21no—
528C42—21no—
529C23—22no—
530C23—21no—
531C23—21no—
532C23—22no—
533C23—21no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—21no—
538C23—21no—
539C23—22no—
540C23—42no—
541C23—42no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—42no—
548C23#120×C15112yes—
549C23C22×D4×C15111yescharacteristic
550Q8—22no—
551Q8—24no—
552Q8#123×C15114yescomplemented
553D4—22no—
554D4—22no—
555D4—24no—
556D4—44no—
557D4—48no—
558D4—48no—
559D4—48no—
560D4—41no—
561D4—41no—
562D4—42no—
563D4—84no—
564D4—84no—
565D4—84no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—48no—
580C2×C4—48no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—84no—
592C2×C4#120×C15112yes—
593C2×C4AGL(1,ℤ/8)×C15112yes—
594C2×C4C22×D4×C15111yescharacteristic
595C2×C4C22×D4×C15111yescharacteristic
596C2×C4C2×#41×C15112yes—
597C2×C4H(5,𝔽2)×C15112yes—
598C8—42no—
599C8—42no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—41no—
608C22—41no—
609C22—42no—
610C22—42no—
611C22—41no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—82no—
617C22—82no—
618C22—82no—
619C22—82no—
620C22C2×#120×C15111yescharacteristic
621C22#546×C15112yes—
622C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
623C22#575×C15111yescharacteristic
624C22#577×C15112yes—
625C4—22no—
626C4—24no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—42no—
631C4—82no—
632C4—82no—
633C4C2×#123×C15111yescharacteristic
634C4#534×C15111yescharacteristic
635C4#546×C15112yes—
636C2—42no—
637C2—81no—
638C2—82no—
639C2—82no—
640C2#2405×C15111yescharacteristic
641C2#3006×C15111yescharacteristic
642C2#3009×C15111yescharacteristic
643C2#3317×C15112yes—
644C2#3332×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#550×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#481×C151C2semidirect
3. C2×#417×C151C2semidirect
4. #2486×C151C2semidirect
5. #2041×C151C2semidirect
6. #2034×C151C2semidirect
7. #1895×C151C2semidirect
8. #1870×C151C2semidirect
9. #1865×C151C2semidirect
10. #1788×C151C2semidirect
11. #1788×C151C2semidirect
229. Q8×C151#123semidirect
322. #24045C151direct (N × H)
323. C151#24045direct (N × H)
325. C2×#481C2×C151semidirect
326. C2×#417C2×C151semidirect
327. #2486C2×C151semidirect
328. #2041C2×C151semidirect
329. #2034C2×C151semidirect
330. #1895C2×C151semidirect
331. #1870C2×C151semidirect
332. #1865C2×C151semidirect
333. #1788C2×C151semidirect
334. #1788C2×C151semidirect
552. Q8#123×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1512
C2×#481×C1512
C2×#417×C1512
#2486×C1512
#2041×C1512
#2034×C1512
#1895×C1512
#1870×C1512
#1865×C1512
#1788×C1512
#24045151