Finite Group Databasebeta

← C151×#10946 #50315871

Subgroups — C151×#10946 #50315871

Order 38656.

946 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#421×C151C211yesmaximal, characteristic
2C22×#104×C151C211yesmaximal, characteristic
3C2×#413×C151C211yesmaximal, characteristic
4C2×C4×M16×C151C211yesmaximal, characteristic, complemented
5C2×#344×C151C211yesmaximal, characteristic, complemented
6#1738×C151C211yesmaximal, characteristic, complemented
7C2×#339×C151C211yesmaximal, characteristic, complemented
8C22×#41×C151C2211yescharacteristic
9C22×M16×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11C22×M16×C151C2211yescharacteristic
12C22×M16×C151C2211yescharacteristic
13C2×#117×C151C2211yescharacteristic
14C22×C42×C151C2211yescharacteristic
15#421×C151—22no—
16#421×C151C414yescomplemented
17C2×#104×C151—22no—
18C2×#104×C151—22no—
19C2×#104×C151—21no—
20C2×#104×C151—21no—
21C2×#104×C151C414yescomplemented
22#413×C151—22no—
23#413×C151—22no—
24C2×#101×C151C412yescomplemented
25C2×#100×C151C412yescomplemented
26C4×M16×C151—22no—
27C4×M16×C151—22no—
28C2×#97×C151—21no—
29C2×C4×C8×C151—21no—
30#344×C151—22no—
31#341×C151—22no—
32#339×C151—22no—
33C2×#41×C151—21no—
34C2×#41×C151—21no—
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×C151C2×C412yes—
44C2×#41×C151C2×C412yes—
45C22×Q8×C151C2×C411yescharacteristic
46C22×D4×C151—21no—
47C22×D4×C151C2×C411yescharacteristic
48C23×C4×C151—21no—
49C23×C4×C151—21no—
50C23×C4×C151C2311yescharacteristic
51C2×M16×C151—21no—
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×C151C2×C412yes—
68C2×M16×C151C2×C412yes—
69C2×M16×C151C2×C412yes—
70C2×M16×C151C2×C412yes—
71C2×M16×C151D412yes—
72C2×M16×C151D412yes—
73C2×M16×C151D412yes—
74C2×M16×C151D412yes—
75C22×C8×C151—21no—
76C22×C8×C151—21no—
77C22×C8×C151—21no—
78C22×C8×C151—21no—
79#117×C151—21no—
80#117×C151—21no—
81#117×C151—21no—
82#117×C151C2×C412yes—
83C2×C4⋊C4×C151—21no—
84C2×C22⋊C4×C151—21no—
85C2×C42×C151—21no—
86C2×C42×C151—21no—
87C2×C42×C151—21no—
88C2×C42×C151—21no—
89C2×C42×C151C2×C412yes—
90C2×C42×C151D412yes—
91C2×C42×C151D411yescharacteristic
92C2×C42×C151D411yescharacteristic
93#104×C151—28no—
94#104×C151—24no—
95#104×C151—24no—
96#101×C151—24no—
97#100×C151—24no—
98#97×C151—24no—
99C4×C8×C151—24no—
100C24×C151—21no—
101C24×C151#4111yescharacteristic
102#41×C151—22no—
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—41no—
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—
118C2×Q8×C151—21no—
119C2×Q8×C151—21no—
120C2×Q8×C151—21no—
121C2×Q8×C151—21no—
122C2×Q8×C151—21no—
123C2×Q8×C151C4212yes—
124C2×D4×C151—22no—
125C2×D4×C151—22no—
126C2×D4×C151—21no—
127C2×D4×C151—21no—
128C2×D4×C151—21no—
129C2×D4×C151—21no—
130C2×D4×C151—21no—
131C2×D4×C151—41no—
132C2×D4×C151—41no—
133C2×D4×C151—41no—
134C2×D4×C151—41no—
135C2×D4×C151C4212yes—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—21no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—44no—
144C22×C4×C151—41no—
145C22×C4×C151—41no—
146C22×C4×C151—41no—
147C22×C4×C151—41no—
148C22×C4×C151—41no—
149C22×C4×C151C22×C411yescharacteristic
150C22×C4×C151C22×C411yescharacteristic
151C22×C4×C151C22×C411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151#4111yescharacteristic
159C22×C4×C151#4111yescharacteristic
160C22×C4×C151#4111yescharacteristic
161C22×C4×C151#4111yescharacteristic
162C22×C4×C151#4111yescharacteristic
163M16×C151—22no—
164M16×C151—22no—
165M16×C151—22no—
166M16×C151—22no—
167M16×C151—22no—
168M16×C151—22no—
169M16×C151—22no—
170M16×C151—22no—
171M16×C151—22no—
172M16×C151—22no—
173M16×C151—41no—
174M16×C151—41no—
175M16×C151—41no—
176M16×C151—41no—
177M16×C151C22⋊C414yes—
178M16×C151C22⋊C414yes—
179C2×C8×C151—22no—
180C2×C8×C151—22no—
181C2×C8×C151—22no—
182C2×C8×C151—22no—
183C2×C8×C151—22no—
184C2×C8×C151—22no—
185C2×C8×C151—22no—
186C2×C8×C151—22no—
187C2×C8×C151—41no—
188C2×C8×C151—41no—
189C2×C8×C151—41no—
190C2×C8×C151—41no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—41no—
193C22⋊C4×C151—22no—
194C22⋊C4×C151—41no—
195C42×C151—22no—
196C42×C151—21no—
197C42×C151—21no—
198C42×C151—22no—
199C42×C151—22no—
200C42×C151—41no—
201C42×C151C22⋊C412yes—
202C42×C151C22⋊C412yes—
203C23×C151—22no—
204C23×C151—42no—
205C23×C151—41no—
206C23×C151—41no—
207C23×C151—82no—
208C23×C151#11711yescharacteristic
209C23×C151C4×D411yescharacteristic
210C23×C151C4×D411yescharacteristic
211C23×C151#12111yescharacteristic
212C23×C151#12311yescharacteristic
213C23×C151#12411yescharacteristic
214C23×C151#12611yescharacteristic
215Q8×C151—22no—
216Q8×C151—22no—
217Q8×C151—41no—
218Q8×C151—41no—
219D4×C151—22no—
220D4×C151—22no—
221D4×C151—42no—
222D4×C151—42no—
223D4×C151—42no—
224D4×C151—42no—
225D4×C151—41no—
226D4×C151—41no—
227C2×C4×C151—24no—
228C2×C4×C151—22no—
229C2×C4×C151—22no—
230C2×C4×C151—22no—
231C2×C4×C151—44no—
232C2×C4×C151—44no—
233C2×C4×C151—42no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—82no—
242C2×C4×C151C2×C4211yescharacteristic
243C2×C4×C151C2×C22⋊C411yescharacteristic
244C2×C4×C151C2×C22⋊C411yescharacteristic
245C2×C4×C151C2×C22⋊C411yescharacteristic
246C2×C4×C151#11711yescharacteristic
247C2×C4×C151#11711yescharacteristic
248C2×C4×C151C4×D411yescharacteristic
249C2×C4×C151C4×D411yescharacteristic
250C2×C4×C151C4×D411yescharacteristic
251C2×C4×C151C4×D411yescharacteristic
252C2×C4×C151C4×D411yescharacteristic
253C2×C4×C151C4×D411yescharacteristic
254C2×C4×C151C4×D411yescharacteristic
255C2×C4×C151C4×D411yescharacteristic
256C2×C4×C151C4×D411yescharacteristic
257C2×C4×C151C4×D411yescharacteristic
258C2×C4×C151#12011yescharacteristic
259C2×C4×C151#12111yescharacteristic
260C2×C4×C151#12111yescharacteristic
261C2×C4×C151#12111yescharacteristic
262C2×C4×C151#12111yescharacteristic
263C2×C4×C151#12111yescharacteristic
264C2×C4×C151#12311yescharacteristic
265C2×C4×C151#12311yescharacteristic
266C2×C4×C151#12411yescharacteristic
267C2×C4×C151#12411yescharacteristic
268C2×C4×C151#12611yescharacteristic
269C2×C4×C151#12711yescharacteristic
270C8×C151—24no—
271C8×C151—24no—
272C8×C151—42no—
273C8×C151—42no—
274C22×C151—22no—
275C22×C151—22no—
276C22×C151—22no—
277C22×C151—41no—
278C22×C151—41no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—42no—
282C22×C151—82no—
283C22×C151—82no—
284C22×C151—82no—
285C22×C151C4×C22⋊C411yescharacteristic
286C22×C151#38611yescharacteristic
287C22×C151#38811yescharacteristic
288C22×C151#38811yescharacteristic
289C22×C151#38811yescharacteristic
290C22×C151#38811yescharacteristic
291C22×C151#39011yescharacteristic
292C4×C151—24no—
293C4×C151—42no—
294C4×C151—42no—
295C4×C151—82no—
296C4×C151C4×C22⋊C411yescharacteristic
297C4×C151C4×C22⋊C411yescharacteristic
298C4×C151#38611yescharacteristic
299C4×C151#38611yescharacteristic
300C4×C151#38811yescharacteristic
301C4×C151#38811yescharacteristic
302C4×C151#39011yescharacteristic
303C4×C151#39011yescharacteristic
304C2×C151—21no—
305C2×C151—21no—
306C2×C151—21no—
307C2×C151—21no—
308C2×C151—21no—
309C2×C151—21no—
310C2×C151—82no—
311C2×C151#143711yescharacteristic
312C2×C151#193212yes—
313#10946C15111yesmaximal, characteristic, direct product factor, Sylow
314C151#1094611yescharacteristic, direct product factor, Sylow
315C2×#421C2×C15111yescharacteristic
316C22×#104C2×C15111yescharacteristic
317C2×#413C2×C15111yescharacteristic
318C2×C4×M16C2×C15111yescharacteristic, complemented
319C2×#344C2×C15111yescharacteristic, complemented
320#1738C2×C15111yescharacteristic, complemented
321C2×#339C2×C15111yescharacteristic, complemented
322C22×#41C22×C15111yescharacteristic
323C22×M16C22×C15111yescharacteristic
324C22×M16C22×C15111yescharacteristic
325C22×M16C22×C15111yescharacteristic
326C22×M16C22×C15111yescharacteristic
327C2×#117C22×C15111yescharacteristic
328C22×C42C22×C15111yescharacteristic
329#421—22no—
330#421C4×C15114yescomplemented
331C2×#104—22no—
332C2×#104—22no—
333C2×#104—21no—
334C2×#104—21no—
335C2×#104C4×C15114yescomplemented
336#413—22no—
337#413—22no—
338C2×#101C4×C15112yescomplemented
339C2×#100C4×C15112yescomplemented
340C4×M16—22no—
341C4×M16—22no—
342C2×#97—21no—
343C2×C4×C8—21no—
344#344—22no—
345#341—22no—
346#339—22no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41C2×C4×C15112yes—
358C2×#41C2×C4×C15112yes—
359C22×Q8C2×C4×C15111yescharacteristic
360C22×D4—21no—
361C22×D4C2×C4×C15111yescharacteristic
362C23×C4—21no—
363C23×C4—21no—
364C23×C4C23×C15111yescharacteristic
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×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16C2×C4×C15112yes—
382C2×M16C2×C4×C15112yes—
383C2×M16C2×C4×C15112yes—
384C2×M16C2×C4×C15112yes—
385C2×M16D4×C15112yes—
386C2×M16D4×C15112yes—
387C2×M16D4×C15112yes—
388C2×M16D4×C15112yes—
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117C2×C4×C15112yes—
397C2×C4⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42C2×C4×C15112yes—
404C2×C42D4×C15112yes—
405C2×C42D4×C15111yescharacteristic
406C2×C42D4×C15111yescharacteristic
407#104—28no—
408#104—24no—
409#104—24no—
410#101—24no—
411#100—24no—
412#97—24no—
413C4×C8—24no—
414C24—21no—
415C24#41×C15111yescharacteristic
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—22no—
424#41—41no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431#41—41no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C42×C15112yes—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4C42×C15112yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—44no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4C22×C4×C15111yescharacteristic
464C22×C4C22×C4×C15111yescharacteristic
465C22×C4C22×C4×C15111yescharacteristic
466C22×C4C2×D4×C15111yescharacteristic
467C22×C4C2×D4×C15111yescharacteristic
468C22×C4C2×D4×C15111yescharacteristic
469C22×C4C2×D4×C15111yescharacteristic
470C22×C4C2×D4×C15111yescharacteristic
471C22×C4C2×D4×C15111yescharacteristic
472C22×C4#41×C15111yescharacteristic
473C22×C4#41×C15111yescharacteristic
474C22×C4#41×C15111yescharacteristic
475C22×C4#41×C15111yescharacteristic
476C22×C4#41×C15111yescharacteristic
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—22no—
482M16—22no—
483M16—22no—
484M16—22no—
485M16—22no—
486M16—22no—
487M16—41no—
488M16—41no—
489M16—41no—
490M16—41no—
491M16C22⋊C4×C15114yes—
492M16C22⋊C4×C15114yes—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C4⋊C4—22no—
506C4⋊C4—41no—
507C22⋊C4—22no—
508C22⋊C4—41no—
509C42—22no—
510C42—21no—
511C42—21no—
512C42—22no—
513C42—22no—
514C42—41no—
515C42C22⋊C4×C15112yes—
516C42C22⋊C4×C15112yes—
517C23—22no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—82no—
522C23#117×C15111yescharacteristic
523C23C4×D4×C15111yescharacteristic
524C23C4×D4×C15111yescharacteristic
525C23#121×C15111yescharacteristic
526C23#123×C15111yescharacteristic
527C23#124×C15111yescharacteristic
528C23#126×C15111yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533D4—22no—
534D4—22no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—41no—
540D4—41no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—82no—
556C2×C4C2×C42×C15111yescharacteristic
557C2×C4C2×C22⋊C4×C15111yescharacteristic
558C2×C4C2×C22⋊C4×C15111yescharacteristic
559C2×C4C2×C22⋊C4×C15111yescharacteristic
560C2×C4#117×C15111yescharacteristic
561C2×C4#117×C15111yescharacteristic
562C2×C4C4×D4×C15111yescharacteristic
563C2×C4C4×D4×C15111yescharacteristic
564C2×C4C4×D4×C15111yescharacteristic
565C2×C4C4×D4×C15111yescharacteristic
566C2×C4C4×D4×C15111yescharacteristic
567C2×C4C4×D4×C15111yescharacteristic
568C2×C4C4×D4×C15111yescharacteristic
569C2×C4C4×D4×C15111yescharacteristic
570C2×C4C4×D4×C15111yescharacteristic
571C2×C4C4×D4×C15111yescharacteristic
572C2×C4#120×C15111yescharacteristic
573C2×C4#121×C15111yescharacteristic
574C2×C4#121×C15111yescharacteristic
575C2×C4#121×C15111yescharacteristic
576C2×C4#121×C15111yescharacteristic
577C2×C4#121×C15111yescharacteristic
578C2×C4#123×C15111yescharacteristic
579C2×C4#123×C15111yescharacteristic
580C2×C4#124×C15111yescharacteristic
581C2×C4#124×C15111yescharacteristic
582C2×C4#126×C15111yescharacteristic
583C2×C4#127×C15111yescharacteristic
584C8—24no—
585C8—24no—
586C8—42no—
587C8—42no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—42no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22C4×C22⋊C4×C15111yescharacteristic
600C22#386×C15111yescharacteristic
601C22#388×C15111yescharacteristic
602C22#388×C15111yescharacteristic
603C22#388×C15111yescharacteristic
604C22#388×C15111yescharacteristic
605C22#390×C15111yescharacteristic
606C4—24no—
607C4—42no—
608C4—42no—
609C4—82no—
610C4C4×C22⋊C4×C15111yescharacteristic
611C4C4×C22⋊C4×C15111yescharacteristic
612C4#386×C15111yescharacteristic
613C4#386×C15111yescharacteristic
614C4#388×C15111yescharacteristic
615C4#388×C15111yescharacteristic
616C4#390×C15111yescharacteristic
617C4#390×C15111yescharacteristic
618C2—21no—
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—82no—
625C2#1437×C15111yescharacteristic
626C2#1932×C15112yes—
subgroupG/H
centerC2×C4×C151#121
commutatorC2×C4C2×C42×C151
Frattini, cosocleC23×C4C23×C151
socleC22×C151#388
prime radicalC22×#41×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C4×M16×C151C2semidirect
5. C2×#344×C151C2semidirect
6. #1738×C151C2semidirect
7. C2×#339×C151C2semidirect
16. #421×C151C4semidirect
21. C2×#104×C151C4semidirect
24. C2×#101×C151C4semidirect
25. C2×#100×C151C4semidirect
313. #10946C151direct (N × H)
314. C151#10946direct (N × H)
318. C2×C4×M16C2×C151semidirect
319. C2×#344C2×C151semidirect
320. #1738C2×C151semidirect
321. C2×#339C2×C151semidirect
330. #421C4×C151semidirect
335. C2×#104C4×C151semidirect
338. C2×#101C4×C151semidirect
339. C2×#100C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#421×C1512
C22×#104×C1512
C2×#413×C1512
C2×C4×M16×C1512
C2×#344×C1512
#1738×C1512
C2×#339×C1512
#10946151