Finite Group Databasebeta

← C151×#24232 #50329157

Subgroups — C151×#24232 #50329157

Order 38656.

1488 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3498×C151C211yesmaximal, characteristic
2#3037×C151C211yesmaximal, characteristic, complemented
3C2×#455×C151C212yesmaximal, complemented
4C4×#137×C151C211yesmaximal, characteristic, complemented
5#2548×C151C211yesmaximal, characteristic, complemented
6#2037×C151C212yesmaximal, complemented
7#2004×C151C212yesmaximal, complemented
8#1980×C151C211yesmaximal, characteristic, complemented
9#1965×C151C211yesmaximal, characteristic, complemented
10#1806×C151C211yesmaximal, characteristic, complemented
11#1792×C151C212yesmaximal, complemented
12C2×H(5,𝔽2)×C151C2212yes—
13C2×#137×C151C2211yescharacteristic
14C2×#137×C151C2212yescomplemented
15#550×C151—21no—
16#550×C151—21no—
17D42×C151—22no—
18D42×C151—22no—
19D42×C151—21no—
20D42×C151—21no—
21#535×C151—22no—
22#535×C151C2212yes—
23#532×C151—21no—
24#532×C151C2211yescharacteristic
25C2×#127×C151—21no—
26C2×#127×C151C2211yescharacteristic
27C2×#124×C151C2212yescomplemented
28C4×#41×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic, complemented
30#464×C151—22no—
31#462×C151—21no—
32#460×C151—21no—
33#455×C151—28no—
34#441×C151—21no—
35#440×C151—21no—
36C4×Q16×C151—21no—
37C4×SD16×C151—21no—
38#428×C151C2211yescharacteristic, complemented
39#423×C151C2211yescharacteristic, complemented
40C2×#104×C151C2212yes—
41C2×#104×C151C2212yescomplemented
42C2×#104×C151C2212yescomplemented
43#419×C151C2211yescharacteristic, complemented
44#417×C151C2211yescharacteristic
45#417×C151C2212yescomplemented
46C2×#100×C151C2212yescomplemented
47C2×#100×C151C2212yescomplemented
48C4×M16×C151C2211yescharacteristic, complemented
49#394×C151—22no—
50#390×C151—22no—
51#390×C151C2212yescomplemented
52C4×C4⋊C4×C151C2211yescharacteristic, complemented
53#339×C151C2212yescomplemented
54H(5,𝔽2)×C151—24no—
55H(5,𝔽2)×C151—24no—
56H(5,𝔽2)×C151—42no—
57H(5,𝔽2)×C151—42no—
58C2×#41×C151—22no—
59C2×#41×C151—22no—
60C2×#41×C151C2312yes—
61C2×#41×C151C2311yescharacteristic
62C22×Q8×C151C2311yescharacteristic
63C22×D4×C151—22no—
64C22×D4×C151—22no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—24no—
68C22×D4×C151D412yes—
69C22×D4×C151D412yes—
70C22×D4×C151C2312yes—
71#137×C151—22no—
72#137×C151—24no—
73#137×C151—42no—
74#137×C151D414yescomplemented
75C2×Q16×C151—21no—
76C2×Q16×C151—22no—
77C2×SD16×C151—21no—
78C2×SD16×C151—22no—
79C2×M16×C151C2312yes—
80C2×M16×C151C2311yescharacteristic
81C2×M16×C151C2311yescharacteristic
82C4⋊Q8×C151D411yescharacteristic
83#127×C151—22no—
84#127×C151—22no—
85#127×C151—22no—
86#127×C151—21no—
87#127×C151—21no—
88#127×C151—21no—
89#127×C151—21no—
90#127×C151D411yescharacteristic
91#124×C151—22no—
92#124×C151—24no—
93#124×C151—42no—
94#124×C151D412yes—
95#121×C151—22no—
96#121×C151—22no—
97#121×C151—24no—
98#121×C151—24no—
99#121×C151—21no—
100#121×C151—21no—
101#121×C151—22no—
102#121×C151—22no—
103#120×C151—24no—
104#120×C151—24no—
105#120×C151—24no—
106C4×Q8×C151—21no—
107C4×Q8×C151—21no—
108C4×Q8×C151—21no—
109C4×Q8×C151—21no—
110C4×Q8×C151D411yescharacteristic
111C4×Q8×C151D411yescharacteristic
112C4×D4×C151—22no—
113C4×D4×C151—22no—
114C4×D4×C151—21no—
115C4×D4×C151—21no—
116C4×D4×C151—21no—
117C4×D4×C151—21no—
118C4×D4×C151D411yescharacteristic
119C4×D4×C151D411yescharacteristic
120#117×C151—21no—
121#117×C151C2311yescharacteristic
122C2×C4⋊C4×C151—21no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151C2311yescharacteristic
125C2×C22⋊C4×C151—24no—
126C2×C22⋊C4×C151—24no—
127C2×C42×C151—21no—
128C2×C42×C151—21no—
129C2×C42×C151C2312yes—
130C2×C42×C151C2311yescharacteristic
131#107×C151—21no—
132#106×C151—21no—
133C4⋊C8×C151—21no—
134C4⋊C8×C151—21no—
135#104×C151—24no—
136#104×C151—24no—
137#104×C151—42no—
138#103×C151—21no—
139#103×C151—21no—
140#103×C151—21no—
141#103×C151—22no—
142#102×C151—21no—
143#102×C151—22no—
144#100×C151—24no—
145#100×C151—42no—
146#97×C151—21no—
147C4×C8×C151—21no—
148#95×C151—21no—
149C24×C151—24no—
150C24×C151C2×D414yes—
151#41×C151—21no—
152#41×C151—21no—
153#41×C151—22no—
154#41×C151—22no—
155#41×C151—22no—
156#41×C151—22no—
157#41×C151—44no—
158#41×C151—44no—
159#41×C151—44no—
160#41×C151—44no—
161#41×C151C2×D412yes—
162#41×C151#4112yes—
163C2×Q8×C151—21no—
164C2×Q8×C151—21no—
165C2×Q8×C151—21no—
166C2×Q8×C151—21no—
167C2×Q8×C151—21no—
168C2×Q8×C151C2×D412yes—
169C2×Q8×C151C2×D411yescharacteristic
170C2×Q8×C151C2×D412yescomplemented
171C2×D4×C151—21no—
172C2×D4×C151—24no—
173C2×D4×C151—24no—
174C2×D4×C151—22no—
175C2×D4×C151—24no—
176C2×D4×C151—24no—
177C2×D4×C151—22no—
178C2×D4×C151—22no—
179C2×D4×C151—21no—
180C2×D4×C151—21no—
181C2×D4×C151—22no—
182C2×D4×C151—22no—
183C2×D4×C151—22no—
184C2×D4×C151—22no—
185C2×D4×C151—22no—
186C2×D4×C151—22no—
187C2×D4×C151—22no—
188C2×D4×C151—22no—
189C2×D4×C151—44no—
190C2×D4×C151—44no—
191C2×D4×C151—44no—
192C2×D4×C151—48no—
193C2×D4×C151—48no—
194C2×D4×C151—44no—
195C2×D4×C151—44no—
196C2×D4×C151—84no—
197C2×D4×C151—84no—
198C2×D4×C151—82no—
199C2×D4×C151C2×D412yes—
200C2×D4×C151C2×D411yescharacteristic
201C22×C4×C151—21no—
202C22×C4×C151—24no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—22no—
207C22×C4×C151—22no—
208C22×C4×C151—21no—
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151C2411yescharacteristic
212Q16×C151—24no—
213Q16×C151—44no—
214SD16×C151—24no—
215SD16×C151—44no—
216M16×C151—21no—
217M16×C151—22no—
218M16×C151—21no—
219M16×C151—22no—
220M16×C151—21no—
221M16×C151C2×D412yescomplemented
222C2×C8×C151—21no—
223C2×C8×C151—21no—
224C2×C8×C151—22no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—42no—
232C4⋊C4×C151—41no—
233C4⋊C4×C151—41no—
234C4⋊C4×C151C2×D411yescharacteristic
235C4⋊C4×C151C2×D411yescharacteristic
236C22⋊C4×C151—24no—
237C22⋊C4×C151—24no—
238C22⋊C4×C151—21no—
239C22⋊C4×C151—21no—
240C22⋊C4×C151—21no—
241C22⋊C4×C151—22no—
242C22⋊C4×C151—22no—
243C22⋊C4×C151—48no—
244C22⋊C4×C151—84no—
245C42×C151—21no—
246C42×C151—21no—
247C42×C151—21no—
248C42×C151—22no—
249C42×C151—22no—
250C42×C151—41no—
251C42×C151—41no—
252C42×C151C2×D411yescharacteristic
253C42×C151C2×D411yescharacteristic
254C42×C151C2×D411yescharacteristic
255C42×C151C2×D411yescharacteristic
256C23×C151—21no—
257C23×C151—22no—
258C23×C151—24no—
259C23×C151—24no—
260C23×C151—24no—
261C23×C151—48no—
262C23×C151—44no—
263C23×C151—44no—
264C23×C151—84no—
265C23×C151—84no—
266C23×C151C22×D411yescharacteristic
267Q8×C151—21no—
268Q8×C151—22no—
269Q8×C151—22no—
270Q8×C151—22no—
271Q8×C151—22no—
272Q8×C151—41no—
273Q8×C151—41no—
274Q8×C151#12112yes—
275D4×C151—22no—
276D4×C151—22no—
277D4×C151—21no—
278D4×C151—22no—
279D4×C151—22no—
280D4×C151—48no—
281D4×C151—44no—
282D4×C151—42no—
283D4×C151—48no—
284D4×C151—42no—
285D4×C151—42no—
286D4×C151—42no—
287D4×C151—42no—
288D4×C151—42no—
289D4×C151—42no—
290D4×C151—44no—
291D4×C151—42no—
292D4×C151—82no—
293D4×C151—82no—
294D4×C151—84no—
295D4×C151—84no—
296D4×C151#12112yes—
297C2×C4×C151—21no—
298C2×C4×C151—22no—
299C2×C4×C151—22no—
300C2×C4×C151—22no—
301C2×C4×C151—22no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—22no—
305C2×C4×C151—41no—
306C2×C4×C151—48no—
307C2×C4×C151—42no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—42no—
311C2×C4×C151—42no—
312C2×C4×C151—42no—
313C2×C4×C151—42no—
314C2×C4×C151—42no—
315C2×C4×C151—42no—
316C2×C4×C151—41no—
317C2×C4×C151—42no—
318C2×C4×C151#12011yescharacteristic
319C2×C4×C151#12011yescharacteristic
320C2×C4×C151#12011yescharacteristic
321C2×C4×C151#12011yescharacteristic
322C2×C4×C151C22×D411yescharacteristic
323C2×C4×C151C22×D411yescharacteristic
324C2×C4×C151C22×D411yescharacteristic
325C2×C4×C151C2×#4111yescharacteristic
326C2×C4×C151H(5,𝔽2)11yescharacteristic
327C2×C4×C151H(5,𝔽2)11yescharacteristic
328C8×C151—22no—
329C8×C151—41no—
330C8×C151—42no—
331C22×C151—21no—
332C22×C151—21no—
333C22×C151—22no—
334C22×C151—41no—
335C22×C151—41no—
336C22×C151—42no—
337C22×C151—44no—
338C22×C151—44no—
339C22×C151—42no—
340C22×C151—44no—
341C22×C151—42no—
342C22×C151—84no—
343C22×C151—84no—
344C22×C151—168no—
345C22×C151C2×#12011yescharacteristic
346C22×C151D4211yescharacteristic
347C22×C151#54611yescharacteristic
348C4×C151—22no—
349C4×C151—21no—
350C4×C151—21no—
351C4×C151—21no—
352C4×C151—42no—
353C4×C151—42no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—82no—
357C4×C151—81no—
358C4×C151#45512yescomplemented
359C4×C151C2×#12111yescharacteristic
360C4×C151#53511yescharacteristic
361C4×C151D4211yescharacteristic
362C4×C151#54611yescharacteristic
363C2×C151—21no—
364C2×C151—21no—
365C2×C151—42no—
366C2×C151—84no—
367C2×C151—82no—
368C2×C151#240811yescharacteristic
369C2×C151C2×#45511yescharacteristic
370C2×C151#301911yescharacteristic
371#24232C15111yesmaximal, characteristic, direct product factor, Sylow
372C151#2423211yescharacteristic, direct product factor, Sylow
373#3498C2×C15111yescharacteristic
374#3037C2×C15111yescharacteristic, complemented
375C2×#455C2×C15112yescomplemented
376C4×#137C2×C15111yescharacteristic, complemented
377#2548C2×C15111yescharacteristic, complemented
378#2037C2×C15112yescomplemented
379#2004C2×C15112yescomplemented
380#1980C2×C15111yescharacteristic, complemented
381#1965C2×C15111yescharacteristic, complemented
382#1806C2×C15111yescharacteristic, complemented
383#1792C2×C15112yescomplemented
384C2×H(5,𝔽2)C22×C15112yes—
385C2×#137C22×C15111yescharacteristic
386C2×#137C22×C15112yescomplemented
387#550—21no—
388#550—21no—
389D42—22no—
390D42—22no—
391D42—21no—
392D42—21no—
393#535—22no—
394#535C22×C15112yes—
395#532—21no—
396#532C22×C15111yescharacteristic
397C2×#127—21no—
398C2×#127C22×C15111yescharacteristic
399C2×#124C22×C15112yescomplemented
400C4×#41C22×C15111yescharacteristic
401C2×C4×Q8C22×C15111yescharacteristic, complemented
402#464—22no—
403#462—21no—
404#460—21no—
405#455—28no—
406#441—21no—
407#440—21no—
408C4×Q16—21no—
409C4×SD16—21no—
410#428C22×C15111yescharacteristic, complemented
411#423C22×C15111yescharacteristic, complemented
412C2×#104C22×C15112yes—
413C2×#104C22×C15112yescomplemented
414C2×#104C22×C15112yescomplemented
415#419C22×C15111yescharacteristic, complemented
416#417C22×C15111yescharacteristic
417#417C22×C15112yescomplemented
418C2×#100C22×C15112yescomplemented
419C2×#100C22×C15112yescomplemented
420C4×M16C22×C15111yescharacteristic, complemented
421#394—22no—
422#390—22no—
423#390C22×C15112yescomplemented
424C4×C4⋊C4C22×C15111yescharacteristic, complemented
425#339C22×C15112yescomplemented
426H(5,𝔽2)—24no—
427H(5,𝔽2)—24no—
428H(5,𝔽2)—42no—
429H(5,𝔽2)—42no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41C23×C15112yes—
433C2×#41C23×C15111yescharacteristic
434C22×Q8C23×C15111yescharacteristic
435C22×D4—24no—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4D4×C15112yes—
441C22×D4D4×C15112yes—
442C22×D4C23×C15112yes—
443#137—22no—
444#137—24no—
445#137—42no—
446#137D4×C15114yescomplemented
447C2×Q16—21no—
448C2×Q16—22no—
449C2×SD16—21no—
450C2×SD16—22no—
451C2×M16C23×C15112yes—
452C2×M16C23×C15111yescharacteristic
453C2×M16C23×C15111yescharacteristic
454C4⋊Q8D4×C15111yescharacteristic
455#127—22no—
456#127—22no—
457#127—22no—
458#127—21no—
459#127—21no—
460#127—21no—
461#127—21no—
462#127D4×C15111yescharacteristic
463#124—22no—
464#124—24no—
465#124—42no—
466#124D4×C15112yes—
467#121—22no—
468#121—22no—
469#121—24no—
470#121—24no—
471#121—21no—
472#121—21no—
473#121—22no—
474#121—22no—
475#120—24no—
476#120—24no—
477#120—24no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8D4×C15111yescharacteristic
483C4×Q8D4×C15111yescharacteristic
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4D4×C15111yescharacteristic
491C4×D4D4×C15111yescharacteristic
492#117—21no—
493#117C23×C15111yescharacteristic
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4C23×C15111yescharacteristic
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42C23×C15112yes—
502C2×C42C23×C15111yescharacteristic
503#107—21no—
504#106—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507#104—24no—
508#104—24no—
509#104—42no—
510#103—21no—
511#103—22no—
512#103—21no—
513#103—21no—
514#102—21no—
515#102—22no—
516#100—24no—
517#100—42no—
518#97—21no—
519C4×C8—21no—
520#95—21no—
521C24—24no—
522C24C2×D4×C15114yes—
523#41—21no—
524#41—21no—
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
529#41—44no—
530#41—44no—
531#41—44no—
532#41—44no—
533#41C2×D4×C15112yes—
534#41#41×C15112yes—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8C2×D4×C15112yes—
541C2×Q8C2×D4×C15111yescharacteristic
542C2×Q8C2×D4×C15112yescomplemented
543C2×D4—21no—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—22no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—48no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—84no—
569C2×D4—84no—
570C2×D4—82no—
571C2×D4C2×D4×C15112yes—
572C2×D4C2×D4×C15111yescharacteristic
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4C2×D4×C15111yescharacteristic
582C22×C4C2×D4×C15111yescharacteristic
583C22×C4C24×C15111yescharacteristic
584Q16—24no—
585Q16—44no—
586SD16—24no—
587SD16—44no—
588M16—21no—
589M16—22no—
590M16—21no—
591M16—22no—
592M16—21no—
593M16C2×D4×C15112yescomplemented
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4C2×D4×C15111yescharacteristic
607C4⋊C4C2×D4×C15111yescharacteristic
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—48no—
616C22⋊C4—84no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—22no—
621C42—22no—
622C42—41no—
623C42—41no—
624C42C2×D4×C15111yescharacteristic
625C42C2×D4×C15111yescharacteristic
626C42C2×D4×C15111yescharacteristic
627C42C2×D4×C15111yescharacteristic
628C23—21no—
629C23—24no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—48no—
634C23—44no—
635C23—44no—
636C23—84no—
637C23—84no—
638C23C22×D4×C15111yescharacteristic
639Q8—21no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—41no—
645Q8—41no—
646Q8#121×C15112yes—
647D4—22no—
648D4—22no—
649D4—21no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—44no—
654D4—42no—
655D4—48no—
656D4—42no—
657D4—42no—
658D4—44no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—82no—
665D4—82no—
666D4—84no—
667D4—84no—
668D4#121×C15112yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—48no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4#120×C15111yescharacteristic
691C2×C4#120×C15111yescharacteristic
692C2×C4#120×C15111yescharacteristic
693C2×C4#120×C15111yescharacteristic
694C2×C4C22×D4×C15111yescharacteristic
695C2×C4C22×D4×C15111yescharacteristic
696C2×C4C22×D4×C15111yescharacteristic
697C2×C4C2×#41×C15111yescharacteristic
698C2×C4H(5,𝔽2)×C15111yescharacteristic
699C2×C4H(5,𝔽2)×C15111yescharacteristic
700C8—22no—
701C8—41no—
702C8—42no—
703C22—21no—
704C22—21no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—44no—
710C22—44no—
711C22—42no—
712C22—44no—
713C22—42no—
714C22—84no—
715C22—84no—
716C22—168no—
717C22C2×#120×C15111yescharacteristic
718C22D42×C15111yescharacteristic
719C22#546×C15111yescharacteristic
720C4—22no—
721C4—21no—
722C4—21no—
723C4—21no—
724C4—42no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—82no—
729C4—81no—
730C4#455×C15112yescomplemented
731C4C2×#121×C15111yescharacteristic
732C4#535×C15111yescharacteristic
733C4D42×C15111yescharacteristic
734C4#546×C15111yescharacteristic
735C2—21no—
736C2—21no—
737C2—42no—
738C2—84no—
739C2—82no—
740C2#2408×C15111yescharacteristic
741C2C2×#455×C15111yescharacteristic
742C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3498×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
2. #3037×C151C2semidirect
3. C2×#455×C151C2semidirect
4. C4×#137×C151C2semidirect
5. #2548×C151C2semidirect
6. #2037×C151C2semidirect
7. #2004×C151C2semidirect
8. #1980×C151C2semidirect
9. #1965×C151C2semidirect
10. #1806×C151C2semidirect
11. #1792×C151C2semidirect
14. C2×#137×C151C22semidirect
27. C2×#124×C151C22semidirect
29. C2×C4×Q8×C151C22semidirect
38. #428×C151C22semidirect
39. #423×C151C22semidirect
41. C2×#104×C151C22semidirect
42. C2×#104×C151C22semidirect
43. #419×C151C22semidirect
45. #417×C151C22semidirect
46. C2×#100×C151C22semidirect
47. C2×#100×C151C22semidirect
48. C4×M16×C151C22semidirect
51. #390×C151C22semidirect
52. C4×C4⋊C4×C151C22semidirect
53. #339×C151C22semidirect
74. #137×C151D4semidirect
170. C2×Q8×C151C2×D4semidirect
221. M16×C151C2×D4semidirect
358. C4×C151#455semidirect
371. #24232C151direct (N × H)
372. C151#24232direct (N × H)
374. #3037C2×C151semidirect
375. C2×#455C2×C151semidirect
376. C4×#137C2×C151semidirect
377. #2548C2×C151semidirect
378. #2037C2×C151semidirect
379. #2004C2×C151semidirect
380. #1980C2×C151semidirect
381. #1965C2×C151semidirect
382. #1806C2×C151semidirect
383. #1792C2×C151semidirect
386. C2×#137C22×C151semidirect
399. C2×#124C22×C151semidirect
401. C2×C4×Q8C22×C151semidirect
410. #428C22×C151semidirect
411. #423C22×C151semidirect
413. C2×#104C22×C151semidirect
414. C2×#104C22×C151semidirect
415. #419C22×C151semidirect
417. #417C22×C151semidirect
418. C2×#100C22×C151semidirect
419. C2×#100C22×C151semidirect
420. C4×M16C22×C151semidirect
423. #390C22×C151semidirect
424. C4×C4⋊C4C22×C151semidirect
425. #339C22×C151semidirect
446. #137D4×C151semidirect
542. C2×Q8C2×D4×C151semidirect
593. M16C2×D4×C151semidirect
730. C4#455×C151semidirect

Maximal subgroups

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

subgroupindex
#3498×C1512
#3037×C1512
C2×#455×C1512
C4×#137×C1512
#2548×C1512
#2037×C1512
#2004×C1512
#1980×C1512
#1965×C1512
#1806×C1512
#1792×C1512
#24232151