Finite Group Databasebeta

← C151×#19010 #50323935

Subgroups — C151×#19010 #50323935

Order 38656.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3529×C151C211yesmaximal, characteristic, complemented
2#3219×C151C211yesmaximal, characteristic, complemented
3#3214×C151C211yesmaximal, characteristic, complemented
4#3180×C151C211yesmaximal, characteristic, complemented
5#1664×C151C211yesmaximal, characteristic, complemented
6#1662×C151C211yesmaximal, characteristic, complemented
7#1661×C151C211yesmaximal, characteristic, complemented
8#1659×C151C211yesmaximal, characteristic, complemented
9#1657×C151C211yesmaximal, characteristic, complemented
10#1656×C151C211yesmaximal, characteristic, complemented
11#1656×C151C211yesmaximal, characteristic, complemented
12#1655×C151C211yesmaximal, characteristic, complemented
13#1535×C151C211yesmaximal, characteristic, complemented
14#1532×C151C211yesmaximal, characteristic, complemented
15#1530×C151C211yesmaximal, characteristic, complemented
16#563×C151—21no—
17#563×C151C2211yescharacteristic
18#562×C151—21no—
19#562×C151—21no—
20#562×C151C2211yescharacteristic
21#562×C151C2211yescharacteristic
22H(3,𝔽4)×C151C2211yescharacteristic
23#560×C151—21no—
24#560×C151—21no—
25#560×C151—21no—
26#532×C151—21no—
27#532×C151C2211yescharacteristic
28#532×C151C2211yescharacteristic, complemented
29#529×C151—21no—
30#529×C151—21no—
31#529×C151C2211yescharacteristic
32#529×C151C2211yescharacteristic
33#525×C151—21no—
34#525×C151—21no—
35#525×C151—21no—
36#501×C151C2211yescharacteristic, complemented
37#497×C151C2211yescharacteristic
38#496×C151C2211yescharacteristic
39#496×C151C2211yescharacteristic
40#496×C151C2211yescharacteristic
41#496×C151C2211yescharacteristic, complemented
42#491×C151C2211yescharacteristic, complemented
43#490×C151C2211yescharacteristic, complemented
44#490×C151C2211yescharacteristic, complemented
45#489×C151C2211yescharacteristic
46#489×C151C2211yescharacteristic
47#489×C151C2211yescharacteristic, complemented
48#466×C151—21no—
49#465×C151—21no—
50#464×C151—21no—
51#463×C151—21no—
52#461×C151—21no—
53#459×C151—21no—
54#452×C151—21no—
55#449×C151—21no—
56#449×C151—21no—
57#449×C151—21no—
58#442×C151—21no—
59#440×C151—21no—
60#432×C151C2211yescharacteristic, complemented
61#432×C151C2211yescharacteristic, complemented
62C2×#97×C151C2211yescharacteristic, complemented
63#330×C151C2211yescharacteristic, complemented
64#330×C151C2211yescharacteristic, complemented
65#330×C151C2211yescharacteristic, complemented
66#330×C151C2211yescharacteristic, complemented
67#329×C151C2211yescharacteristic
68#329×C151C2211yescharacteristic
69#329×C151C2211yescharacteristic
70#329×C151C2211yescharacteristic
71#329×C151C2211yescharacteristic
72#329×C151C2211yescharacteristic
73#329×C151C2211yescharacteristic, complemented
74#329×C151C2211yescharacteristic, complemented
75C2×#41×C151—21no—
76C2×#41×C151—21no—
77C2×#41×C151D411yescharacteristic
78C2×#41×C151D411yescharacteristic
79C23×C4×C151—21no—
80C2×Q16×C151—21no—
81C2×SD16×C151—21no—
82C2×SD16×C151—21no—
83C2×SD16×C151—21no—
84C2×SD16×C151—21no—
85C2×SD16×C151—21no—
86C2×D8×C151—21no—
87C2×D8×C151—21no—
88C2×D8×C151—21no—
89C2×D8×C151—21no—
90C22×C8×C151—21no—
91C4⋊Q8×C151—21no—
92C4⋊Q8×C151D411yescharacteristic
93C4⋊Q8×C151C2311yescharacteristic
94#127×C151—21no—
95#127×C151D411yescharacteristic
96#127×C151C2311yescharacteristic
97#126×C151—21no—
98#126×C151—21no—
99#126×C151—21no—
100#126×C151—21no—
101#126×C151—21no—
102#126×C151—21no—
103#125×C151—21no—
104#125×C151—21no—
105#125×C151C2311yescharacteristic
106#125×C151C2311yescharacteristic
107#124×C151—21no—
108#124×C151—21no—
109#124×C151—21no—
110#124×C151—21no—
111#124×C151—21no—
112#124×C151C2311yescharacteristic
113#124×C151C2311yescharacteristic
114#124×C151C2311yescharacteristic
115#124×C151C2311yescharacteristic
116#123×C151—21no—
117#123×C151—21no—
118#123×C151—21no—
119#123×C151—21no—
120#123×C151—21no—
121#123×C151—21no—
122#123×C151—21no—
123#123×C151—21no—
124#123×C151—21no—
125#123×C151—21no—
126#123×C151—21no—
127#123×C151—21no—
128C22⋊Q8×C151—21no—
129C22⋊Q8×C151—21no—
130C22⋊Q8×C151—21no—
131C22⋊Q8×C151—21no—
132C22⋊Q8×C151—21no—
133C22⋊Q8×C151—21no—
134C22⋊Q8×C151—21no—
135C22⋊Q8×C151—21no—
136C22⋊Q8×C151D411yescharacteristic
137C22⋊Q8×C151D411yescharacteristic
138#121×C151—21no—
139#121×C151—21no—
140#121×C151—21no—
141#121×C151—21no—
142#121×C151—21no—
143#121×C151—21no—
144#121×C151—21no—
145#121×C151—21no—
146#121×C151—21no—
147#121×C151—21no—
148#121×C151—21no—
149#121×C151—21no—
150#121×C151—21no—
151#121×C151—21no—
152#121×C151—21no—
153#121×C151—21no—
154#121×C151D411yescharacteristic
155#121×C151D411yescharacteristic
156#120×C151—21no—
157#120×C151—21no—
158#120×C151—21no—
159#120×C151—21no—
160#120×C151—21no—
161#120×C151—21no—
162C4×Q8×C151D411yescharacteristic
163C4×Q8×C151D411yescharacteristic
164C4×D4×C151—21no—
165C4×D4×C151—21no—
166C4×D4×C151—21no—
167C4×D4×C151—21no—
168C4×D4×C151—21no—
169C4×D4×C151—21no—
170C4×D4×C151—21no—
171C4×D4×C151—21no—
172C4×D4×C151—21no—
173C4×D4×C151—21no—
174C4×D4×C151D411yescharacteristic
175C4×D4×C151D411yescharacteristic
176#117×C151—21no—
177#117×C151—21no—
178#117×C151—21no—
179C2×C42×C151—21no—
180C2×C42×C151C2311yescharacteristic
181#107×C151—21no—
182#106×C151—21no—
183C4⋊C8×C151—21no—
184C4⋊C8×C151—21no—
185#103×C151—21no—
186#103×C151—21no—
187#103×C151—21no—
188#103×C151—21no—
189#103×C151—21no—
190#102×C151—21no—
191#102×C151—21no—
192#102×C151—21no—
193#102×C151—21no—
194#102×C151—21no—
195#102×C151—21no—
196#102×C151—21no—
197C22⋊C8×C151—21no—
198C22⋊C8×C151—21no—
199#97×C151—21no—
200#97×C151C2311yescharacteristic
201#97×C151C2311yescharacteristic
202#97×C151C2311yescharacteristic
203#97×C151C2311yescharacteristic
204#97×C151C2311yescharacteristic
205#97×C151C2311yescharacteristic
206C24×C151—21no—
207#41×C151—81no—
208#41×C151—81no—
209#41×C151—82no—
210#41×C151—81no—
211#41×C151—81no—
212C2×Q8×C151—21no—
213C2×Q8×C151—21no—
214C2×Q8×C151C2×D411yescharacteristic
215C2×Q8×C151C2×D411yescharacteristic
216C2×Q8×C151C2×D411yescharacteristic
217C2×Q8×C151C2×D411yescharacteristic
218C2×D4×C151—21no—
219C2×D4×C151—21no—
220C2×D4×C151—21no—
221C2×D4×C151—21no—
222C2×D4×C151—21no—
223C2×D4×C151—21no—
224C2×D4×C151—21no—
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—21no—
228C2×D4×C151—21no—
229C2×D4×C151—21no—
230C2×D4×C151—21no—
231C2×D4×C151—21no—
232C2×D4×C151—21no—
233C2×D4×C151—21no—
234C2×D4×C151—41no—
235C2×D4×C151C2×D411yescharacteristic
236C2×D4×C151C2×D411yescharacteristic
237C2×D4×C151C2×D411yescharacteristic
238C2×D4×C151C2×D411yescharacteristic
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—41no—
249C22×C4×C151—82no—
250C22×C4×C151C2×D411yescharacteristic
251C22×C4×C151C2×D411yescharacteristic
252C22×C4×C151C2×D411yescharacteristic
253Q16×C151—81no—
254SD16×C151—42no—
255SD16×C151—81no—
256SD16×C151—81no—
257SD16×C151—81no—
258SD16×C151—81no—
259D8×C151—42no—
260D8×C151—81no—
261D8×C151—81no—
262D8×C151—81no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C2×C8×C151—21no—
269C2×C8×C151—42no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—21no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151—21no—
284C4⋊C4×C151—21no—
285C4⋊C4×C151—21no—
286C4⋊C4×C151—21no—
287C4⋊C4×C151—21no—
288C4⋊C4×C151C2×D411yescharacteristic
289C4⋊C4×C151C2×D411yescharacteristic
290C4⋊C4×C151C2×D411yescharacteristic
291C4⋊C4×C151C2×D411yescharacteristic
292C22⋊C4×C151—21no—
293C22⋊C4×C151—21no—
294C22⋊C4×C151—21no—
295C22⋊C4×C151—21no—
296C22⋊C4×C151—21no—
297C22⋊C4×C151—21no—
298C22⋊C4×C151—21no—
299C22⋊C4×C151—21no—
300C22⋊C4×C151—21no—
301C22⋊C4×C151—21no—
302C22⋊C4×C151—21no—
303C22⋊C4×C151—21no—
304C22⋊C4×C151—21no—
305C22⋊C4×C151—21no—
306C22⋊C4×C151—21no—
307C22⋊C4×C151—21no—
308C22⋊C4×C151—21no—
309C22⋊C4×C151—21no—
310C22⋊C4×C151—21no—
311C22⋊C4×C151—21no—
312C22⋊C4×C151—21no—
313C22⋊C4×C151—21no—
314C22⋊C4×C151—21no—
315C22⋊C4×C151—21no—
316C22⋊C4×C151—41no—
317C22⋊C4×C151—41no—
318C42×C151—21no—
319C42×C151—21no—
320C42×C151—21no—
321C42×C151—21no—
322C42×C151C2×D411yescharacteristic
323C42×C151C2×D411yescharacteristic
324C42×C151C2×D411yescharacteristic
325C42×C151C2411yescharacteristic
326C23×C151—21no—
327C23×C151—21no—
328C23×C151—21no—
329C23×C151—21no—
330C23×C151—41no—
331C23×C151—81no—
332C23×C151—81no—
333C23×C151—81no—
334C23×C151#12011yescharacteristic
335Q8×C151—41no—
336Q8×C151—41no—
337Q8×C151—41no—
338Q8×C151—41no—
339Q8×C151—41no—
340Q8×C151—41no—
341Q8×C151—81no—
342D4×C151—41no—
343D4×C151—41no—
344D4×C151—41no—
345D4×C151—41no—
346D4×C151—41no—
347D4×C151—41no—
348D4×C151—41no—
349D4×C151—41no—
350D4×C151—41no—
351D4×C151—41no—
352D4×C151—81no—
353D4×C151—81no—
354D4×C151—81no—
355D4×C151—81no—
356D4×C151—81no—
357D4×C151—81no—
358D4×C151—81no—
359D4×C151—81no—
360D4×C151—81no—
361D4×C151—81no—
362D4×C151—81no—
363D4×C151—81no—
364D4×C151—81no—
365D4×C151—82no—
366C2×C4×C151—21no—
367C2×C4×C151—21no—
368C2×C4×C151—21no—
369C2×C4×C151—21no—
370C2×C4×C151—21no—
371C2×C4×C151—21no—
372C2×C4×C151—21no—
373C2×C4×C151—21no—
374C2×C4×C151—41no—
375C2×C4×C151—41no—
376C2×C4×C151—41no—
377C2×C4×C151—42no—
378C2×C4×C151—42no—
379C2×C4×C151—42no—
380C2×C4×C151—42no—
381C2×C4×C151—41no—
382C2×C4×C151—82no—
383C2×C4×C151—81no—
384C2×C4×C151—81no—
385C2×C4×C151—81no—
386C2×C4×C151—81no—
387C2×C4×C151—81no—
388C2×C4×C151#12011yescharacteristic
389C2×C4×C151#12011yescharacteristic
390C2×C4×C151#12011yescharacteristic
391C2×C4×C151C22×D411yescharacteristic
392C2×C4×C151C22×D411yescharacteristic
393C2×C4×C151C22×D411yescharacteristic
394C8×C151—22no—
395C8×C151—41no—
396C8×C151—41no—
397C8×C151—41no—
398C8×C151—41no—
399C8×C151—41no—
400C22×C151—21no—
401C22×C151—21no—
402C22×C151—21no—
403C22×C151—41no—
404C22×C151—41no—
405C22×C151—41no—
406C22×C151—41no—
407C22×C151—41no—
408C22×C151—41no—
409C22×C151—41no—
410C22×C151—41no—
411C22×C151—41no—
412C22×C151—41no—
413C22×C151—41no—
414C22×C151—41no—
415C22×C151—84no—
416C22×C151—81no—
417C22×C151—81no—
418C22×C151—81no—
419C22×C151C2×#12011yescharacteristic
420C4×C151—21no—
421C4×C151—21no—
422C4×C151—21no—
423C4×C151—21no—
424C4×C151—21no—
425C4×C151—21no—
426C4×C151—41no—
427C4×C151—41no—
428C4×C151—41no—
429C4×C151—41no—
430C4×C151—41no—
431C4×C151—41no—
432C4×C151—41no—
433C4×C151—41no—
434C4×C151—81no—
435C2×C151—41no—
436C2×C151—81no—
437C2×C151—81no—
438C2×C151—81no—
439C2×C151—81no—
440C2×C151—161no—
441C2×C151#301811yescharacteristic
442C2×C151#301911yescharacteristic
443C2×C151#302111yescharacteristic
444#19010C15111yesmaximal, characteristic, direct product factor, Sylow
445C151#1901011yescharacteristic, direct product factor, Sylow
446#3529C2×C15111yescharacteristic, complemented
447#3219C2×C15111yescharacteristic, complemented
448#3214C2×C15111yescharacteristic, complemented
449#3180C2×C15111yescharacteristic, complemented
450#1664C2×C15111yescharacteristic, complemented
451#1662C2×C15111yescharacteristic, complemented
452#1661C2×C15111yescharacteristic, complemented
453#1659C2×C15111yescharacteristic, complemented
454#1657C2×C15111yescharacteristic, complemented
455#1656C2×C15111yescharacteristic, complemented
456#1656C2×C15111yescharacteristic, complemented
457#1655C2×C15111yescharacteristic, complemented
458#1535C2×C15111yescharacteristic, complemented
459#1532C2×C15111yescharacteristic, complemented
460#1530C2×C15111yescharacteristic, complemented
461#563—21no—
462#563C22×C15111yescharacteristic
463#562—21no—
464#562—21no—
465#562C22×C15111yescharacteristic
466#562C22×C15111yescharacteristic
467H(3,𝔽4)C22×C15111yescharacteristic
468#560—21no—
469#560—21no—
470#560—21no—
471#532—21no—
472#532C22×C15111yescharacteristic
473#532C22×C15111yescharacteristic, complemented
474#529—21no—
475#529—21no—
476#529C22×C15111yescharacteristic
477#529C22×C15111yescharacteristic
478#525—21no—
479#525—21no—
480#525—21no—
481#501C22×C15111yescharacteristic, complemented
482#497C22×C15111yescharacteristic
483#496C22×C15111yescharacteristic
484#496C22×C15111yescharacteristic
485#496C22×C15111yescharacteristic
486#496C22×C15111yescharacteristic, complemented
487#491C22×C15111yescharacteristic, complemented
488#490C22×C15111yescharacteristic, complemented
489#490C22×C15111yescharacteristic, complemented
490#489C22×C15111yescharacteristic
491#489C22×C15111yescharacteristic
492#489C22×C15111yescharacteristic, complemented
493#466—21no—
494#465—21no—
495#464—21no—
496#463—21no—
497#461—21no—
498#459—21no—
499#452—21no—
500#449—21no—
501#449—21no—
502#449—21no—
503#442—21no—
504#440—21no—
505#432C22×C15111yescharacteristic, complemented
506#432C22×C15111yescharacteristic, complemented
507C2×#97C22×C15111yescharacteristic, complemented
508#330C22×C15111yescharacteristic, complemented
509#330C22×C15111yescharacteristic, complemented
510#330C22×C15111yescharacteristic, complemented
511#330C22×C15111yescharacteristic, complemented
512#329C22×C15111yescharacteristic
513#329C22×C15111yescharacteristic
514#329C22×C15111yescharacteristic
515#329C22×C15111yescharacteristic
516#329C22×C15111yescharacteristic
517#329C22×C15111yescharacteristic
518#329C22×C15111yescharacteristic, complemented
519#329C22×C15111yescharacteristic, complemented
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C15111yescharacteristic
523C2×#41D4×C15111yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C15111yescharacteristic
538C4⋊Q8C23×C15111yescharacteristic
539#127—21no—
540#127D4×C15111yescharacteristic
541#127C23×C15111yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C15111yescharacteristic
551#125C23×C15111yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C15111yescharacteristic
558#124C23×C15111yescharacteristic
559#124C23×C15111yescharacteristic
560#124C23×C15111yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C15111yescharacteristic
582C22⋊Q8D4×C15111yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C15111yescharacteristic
600#121D4×C15111yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C15111yescharacteristic
608C4×Q8D4×C15111yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C15111yescharacteristic
620C4×D4D4×C15111yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C15111yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C15111yescharacteristic
646#97C23×C15111yescharacteristic
647#97C23×C15111yescharacteristic
648#97C23×C15111yescharacteristic
649#97C23×C15111yescharacteristic
650#97C23×C15111yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C15111yescharacteristic
660C2×Q8C2×D4×C15111yescharacteristic
661C2×Q8C2×D4×C15111yescharacteristic
662C2×Q8C2×D4×C15111yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4C2×D4×C15111yescharacteristic
681C2×D4C2×D4×C15111yescharacteristic
682C2×D4C2×D4×C15111yescharacteristic
683C2×D4C2×D4×C15111yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4—82no—
695C22×C4C2×D4×C15111yescharacteristic
696C22×C4C2×D4×C15111yescharacteristic
697C22×C4C2×D4×C15111yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C15111yescharacteristic
734C4⋊C4C2×D4×C15111yescharacteristic
735C4⋊C4C2×D4×C15111yescharacteristic
736C4⋊C4C2×D4×C15111yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C15111yescharacteristic
768C42C2×D4×C15111yescharacteristic
769C42C2×D4×C15111yescharacteristic
770C42C24×C15111yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C15111yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C15111yescharacteristic
834C2×C4#120×C15111yescharacteristic
835C2×C4#120×C15111yescharacteristic
836C2×C4C22×D4×C15111yescharacteristic
837C2×C4C22×D4×C15111yescharacteristic
838C2×C4C22×D4×C15111yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C15111yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2#3018×C15111yescharacteristic
887C2#3019×C15111yescharacteristic
888C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3529×C151C2semidirect
2. #3219×C151C2semidirect
3. #3214×C151C2semidirect
4. #3180×C151C2semidirect
5. #1664×C151C2semidirect
6. #1662×C151C2semidirect
7. #1661×C151C2semidirect
8. #1659×C151C2semidirect
9. #1657×C151C2semidirect
10. #1656×C151C2semidirect
11. #1656×C151C2semidirect
12. #1655×C151C2semidirect
13. #1535×C151C2semidirect
14. #1532×C151C2semidirect
15. #1530×C151C2semidirect
28. #532×C151C22semidirect
36. #501×C151C22semidirect
41. #496×C151C22semidirect
42. #491×C151C22semidirect
43. #490×C151C22semidirect
44. #490×C151C22semidirect
47. #489×C151C22semidirect
60. #432×C151C22semidirect
61. #432×C151C22semidirect
62. C2×#97×C151C22semidirect
63. #330×C151C22semidirect
64. #330×C151C22semidirect
65. #330×C151C22semidirect
66. #330×C151C22semidirect
73. #329×C151C22semidirect
74. #329×C151C22semidirect
444. #19010C151direct (N × H)
445. C151#19010direct (N × H)
446. #3529C2×C151semidirect
447. #3219C2×C151semidirect
448. #3214C2×C151semidirect
449. #3180C2×C151semidirect
450. #1664C2×C151semidirect
451. #1662C2×C151semidirect
452. #1661C2×C151semidirect
453. #1659C2×C151semidirect
454. #1657C2×C151semidirect
455. #1656C2×C151semidirect
456. #1656C2×C151semidirect
457. #1655C2×C151semidirect
458. #1535C2×C151semidirect
459. #1532C2×C151semidirect
460. #1530C2×C151semidirect
473. #532C22×C151semidirect
481. #501C22×C151semidirect
486. #496C22×C151semidirect
487. #491C22×C151semidirect
488. #490C22×C151semidirect
489. #490C22×C151semidirect
492. #489C22×C151semidirect
505. #432C22×C151semidirect
506. #432C22×C151semidirect
507. C2×#97C22×C151semidirect
508. #330C22×C151semidirect
509. #330C22×C151semidirect
510. #330C22×C151semidirect
511. #330C22×C151semidirect
518. #329C22×C151semidirect
519. #329C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3529×C1512
#3219×C1512
#3214×C1512
#3180×C1512
#1664×C1512
#1662×C1512
#1661×C1512
#1659×C1512
#1657×C1512
#1656×C1512
#1655×C1512
#1535×C1512
#1532×C1512
#1530×C1512
#19010151