Finite Group Databasebeta

← C151×#19011 #50323936

Subgroups — C151×#19011 #50323936

Order 38656.

886 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3529×C151C211yesmaximal, characteristic
2#3240×C151C211yesmaximal, characteristic, complemented
3#3216×C151C211yesmaximal, characteristic, complemented
4#3181×C151C211yesmaximal, characteristic, complemented
5#1664×C151C211yesmaximal, characteristic, complemented
6#1662×C151C211yesmaximal, characteristic, complemented
7#1661×C151C211yesmaximal, characteristic, complemented
8#1661×C151C211yesmaximal, characteristic, complemented
9#1661×C151C211yesmaximal, characteristic, complemented
10#1660×C151C211yesmaximal, characteristic, complemented
11#1659×C151C211yesmaximal, characteristic, complemented
12#1659×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#533×C151C2211yescharacteristic, complemented
27#532×C151—21no—
28#532×C151C2211yescharacteristic
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#501×C151C2211yescharacteristic, complemented
38#501×C151C2211yescharacteristic, complemented
39#497×C151C2211yescharacteristic
40#497×C151C2211yescharacteristic
41#497×C151C2211yescharacteristic, complemented
42#491×C151C2211yescharacteristic, complemented
43#489×C151C2211yescharacteristic
44#489×C151C2211yescharacteristic
45#489×C151C2211yescharacteristic
46#489×C151C2211yescharacteristic
47#489×C151C2211yescharacteristic, complemented
48#485×C151—21no—
49#482×C151—21no—
50#479×C151—21no—
51#478×C151—21no—
52#467×C151—21no—
53#465×C151—21no—
54#462×C151—21no—
55#460×C151—21no—
56#452×C151—21no—
57#452×C151—21no—
58#441×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×C151D411yescharacteristic
77C2×#41×C151D411yescharacteristic
78C23×C4×C151—21no—
79C2×Q16×C151—21no—
80C2×Q16×C151—21no—
81C2×Q16×C151—21no—
82C2×SD16×C151—21no—
83C2×SD16×C151—21no—
84C2×SD16×C151—21no—
85C22×C8×C151—21no—
86C4⋊Q8×C151—21no—
87C4⋊Q8×C151D411yescharacteristic
88C4⋊Q8×C151C2311yescharacteristic
89C4⋊Q8×C151C2311yescharacteristic
90#127×C151—21no—
91#127×C151D411yescharacteristic
92#126×C151—21no—
93#126×C151—21no—
94#126×C151—21no—
95#126×C151—21no—
96#126×C151—21no—
97#126×C151—21no—
98#125×C151—21no—
99#125×C151—21no—
100#125×C151—21no—
101#125×C151C2311yescharacteristic
102#125×C151C2311yescharacteristic
103#124×C151—21no—
104#124×C151—21no—
105#124×C151—21no—
106#124×C151—21no—
107#124×C151C2311yescharacteristic
108#124×C151C2311yescharacteristic
109#124×C151C2311yescharacteristic
110#124×C151C2311yescharacteristic
111#123×C151—21no—
112#123×C151—21no—
113#123×C151—21no—
114#123×C151—21no—
115#123×C151—21no—
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—
123C22⋊Q8×C151—21no—
124C22⋊Q8×C151—21no—
125C22⋊Q8×C151—21no—
126C22⋊Q8×C151—21no—
127C22⋊Q8×C151—21no—
128C22⋊Q8×C151—21no—
129C22⋊Q8×C151—21no—
130C22⋊Q8×C151—21no—
131C22⋊Q8×C151—21no—
132C22⋊Q8×C151—21no—
133C22⋊Q8×C151D411yescharacteristic
134C22⋊Q8×C151D411yescharacteristic
135#121×C151—21no—
136#121×C151—21no—
137#121×C151—21no—
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×C151D411yescharacteristic
150#121×C151D411yescharacteristic
151#120×C151—21no—
152#120×C151—21no—
153#120×C151—21no—
154#120×C151—21no—
155#120×C151—21no—
156#120×C151—21no—
157C4×Q8×C151—21no—
158C4×Q8×C151—21no—
159C4×Q8×C151D411yescharacteristic
160C4×Q8×C151D411yescharacteristic
161C4×D4×C151—21no—
162C4×D4×C151—21no—
163C4×D4×C151—21no—
164C4×D4×C151—21no—
165C4×D4×C151—21no—
166C4×D4×C151—21no—
167C4×D4×C151—21no—
168C4×D4×C151—21no—
169C4×D4×C151D411yescharacteristic
170C4×D4×C151D411yescharacteristic
171#117×C151—21no—
172#117×C151—21no—
173#117×C151—21no—
174#117×C151—21no—
175C2×C42×C151—21no—
176C2×C42×C151C2311yescharacteristic
177#107×C151—21no—
178#107×C151—21no—
179#107×C151—21no—
180#106×C151—21no—
181#106×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#103×C151—21no—
191#103×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—
210C2×Q8×C151—21no—
211C2×Q8×C151—21no—
212C2×Q8×C151—21no—
213C2×Q8×C151C2×D411yescharacteristic
214C2×Q8×C151C2×D411yescharacteristic
215C2×Q8×C151C2×D411yescharacteristic
216C2×Q8×C151C2×D411yescharacteristic
217C2×D4×C151—21no—
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×C151C2×D411yescharacteristic
231C2×D4×C151C2×D411yescharacteristic
232C2×D4×C151C2×D411yescharacteristic
233C2×D4×C151C2×D411yescharacteristic
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—82no—
244C22×C4×C151C2×D411yescharacteristic
245C22×C4×C151C2×D411yescharacteristic
246C22×C4×C151C2×D411yescharacteristic
247Q16×C151—42no—
248Q16×C151—81no—
249Q16×C151—81no—
250SD16×C151—42no—
251SD16×C151—81no—
252SD16×C151—81no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—42no—
260C4⋊C4×C151—21no—
261C4⋊C4×C151—21no—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
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—41no—
281C4⋊C4×C151—41no—
282C4⋊C4×C151C2×D411yescharacteristic
283C4⋊C4×C151C2×D411yescharacteristic
284C4⋊C4×C151C2×D411yescharacteristic
285C4⋊C4×C151C2×D411yescharacteristic
286C22⋊C4×C151—21no—
287C22⋊C4×C151—21no—
288C22⋊C4×C151—21no—
289C22⋊C4×C151—21no—
290C22⋊C4×C151—21no—
291C22⋊C4×C151—21no—
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—41no—
311C42×C151—21no—
312C42×C151—21no—
313C42×C151—21no—
314C42×C151—21no—
315C42×C151—41no—
316C42×C151C2×D411yescharacteristic
317C42×C151C2×D411yescharacteristic
318C42×C151C2×D411yescharacteristic
319C42×C151C2411yescharacteristic
320C23×C151—21no—
321C23×C151—21no—
322C23×C151—21no—
323C23×C151—21no—
324C23×C151—81no—
325C23×C151—81no—
326C23×C151—81no—
327C23×C151#12011yescharacteristic
328Q8×C151—41no—
329Q8×C151—41no—
330Q8×C151—41no—
331Q8×C151—41no—
332Q8×C151—41no—
333Q8×C151—41no—
334Q8×C151—41no—
335Q8×C151—41no—
336Q8×C151—81no—
337D4×C151—41no—
338D4×C151—41no—
339D4×C151—41no—
340D4×C151—41no—
341D4×C151—81no—
342D4×C151—81no—
343D4×C151—81no—
344D4×C151—81no—
345D4×C151—81no—
346D4×C151—81no—
347D4×C151—81no—
348D4×C151—81no—
349D4×C151—81no—
350D4×C151—81no—
351D4×C151—81no—
352D4×C151—81no—
353D4×C151—81no—
354C2×C4×C151—21no—
355C2×C4×C151—21no—
356C2×C4×C151—21no—
357C2×C4×C151—21no—
358C2×C4×C151—21no—
359C2×C4×C151—21no—
360C2×C4×C151—21no—
361C2×C4×C151—21no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—42no—
366C2×C4×C151—42no—
367C2×C4×C151—42no—
368C2×C4×C151—42no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151—81no—
372C2×C4×C151—81no—
373C2×C4×C151—81no—
374C2×C4×C151—81no—
375C2×C4×C151—81no—
376C2×C4×C151#12011yescharacteristic
377C2×C4×C151#12011yescharacteristic
378C2×C4×C151#12011yescharacteristic
379C2×C4×C151C22×D411yescharacteristic
380C2×C4×C151C22×D411yescharacteristic
381C2×C4×C151C22×D411yescharacteristic
382C8×C151—22no—
383C8×C151—41no—
384C8×C151—41no—
385C8×C151—41no—
386C8×C151—41no—
387C8×C151—41no—
388C22×C151—21no—
389C22×C151—21no—
390C22×C151—21no—
391C22×C151—41no—
392C22×C151—41no—
393C22×C151—41no—
394C22×C151—41no—
395C22×C151—41no—
396C22×C151—41no—
397C22×C151—41no—
398C22×C151—41no—
399C22×C151—41no—
400C22×C151—41no—
401C22×C151—41no—
402C22×C151—41no—
403C22×C151—84no—
404C22×C151C2×#12011yescharacteristic
405C4×C151—21no—
406C4×C151—21no—
407C4×C151—21no—
408C4×C151—21no—
409C4×C151—21no—
410C4×C151—21no—
411C4×C151—41no—
412C4×C151—41no—
413C4×C151—41no—
414C4×C151—41no—
415C4×C151—41no—
416C4×C151—41no—
417C4×C151—41no—
418C4×C151—41no—
419C4×C151—81no—
420C4×C151—81no—
421C2×C151—41no—
422C2×C151—81no—
423C2×C151—81no—
424C2×C151—81no—
425C2×C151—81no—
426C2×C151#301811yescharacteristic
427C2×C151#301911yescharacteristic
428C2×C151#302211yescharacteristic
429#19011C15111yesmaximal, characteristic, direct product factor, Sylow
430C151#1901111yescharacteristic, direct product factor, Sylow
431#3529C2×C15111yescharacteristic
432#3240C2×C15111yescharacteristic, complemented
433#3216C2×C15111yescharacteristic, complemented
434#3181C2×C15111yescharacteristic, complemented
435#1664C2×C15111yescharacteristic, complemented
436#1662C2×C15111yescharacteristic, complemented
437#1661C2×C15111yescharacteristic, complemented
438#1661C2×C15111yescharacteristic, complemented
439#1661C2×C15111yescharacteristic, complemented
440#1660C2×C15111yescharacteristic, complemented
441#1659C2×C15111yescharacteristic, complemented
442#1659C2×C15111yescharacteristic, complemented
443#1535C2×C15111yescharacteristic, complemented
444#1532C2×C15111yescharacteristic, complemented
445#1530C2×C15111yescharacteristic, complemented
446#563—21no—
447#563C22×C15111yescharacteristic
448#562—21no—
449#562—21no—
450#562C22×C15111yescharacteristic
451#562C22×C15111yescharacteristic
452H(3,𝔽4)C22×C15111yescharacteristic
453#560—21no—
454#560—21no—
455#560—21no—
456#533C22×C15111yescharacteristic, complemented
457#532—21no—
458#532C22×C15111yescharacteristic
459#529—21no—
460#529—21no—
461#529C22×C15111yescharacteristic
462#529C22×C15111yescharacteristic
463#525—21no—
464#525—21no—
465#525—21no—
466#501C22×C15111yescharacteristic, complemented
467#501C22×C15111yescharacteristic, complemented
468#501C22×C15111yescharacteristic, complemented
469#497C22×C15111yescharacteristic
470#497C22×C15111yescharacteristic
471#497C22×C15111yescharacteristic, complemented
472#491C22×C15111yescharacteristic, complemented
473#489C22×C15111yescharacteristic
474#489C22×C15111yescharacteristic
475#489C22×C15111yescharacteristic
476#489C22×C15111yescharacteristic
477#489C22×C15111yescharacteristic, complemented
478#485—21no—
479#482—21no—
480#479—21no—
481#478—21no—
482#467—21no—
483#465—21no—
484#462—21no—
485#460—21no—
486#452—21no—
487#452—21no—
488#441—21no—
489#440—21no—
490#432C22×C15111yescharacteristic, complemented
491#432C22×C15111yescharacteristic, complemented
492C2×#97C22×C15111yescharacteristic, complemented
493#330C22×C15111yescharacteristic, complemented
494#330C22×C15111yescharacteristic, complemented
495#330C22×C15111yescharacteristic, complemented
496#330C22×C15111yescharacteristic, complemented
497#329C22×C15111yescharacteristic
498#329C22×C15111yescharacteristic
499#329C22×C15111yescharacteristic
500#329C22×C15111yescharacteristic
501#329C22×C15111yescharacteristic
502#329C22×C15111yescharacteristic
503#329C22×C15111yescharacteristic, complemented
504#329C22×C15111yescharacteristic, complemented
505C2×#41—21no—
506C2×#41D4×C15111yescharacteristic
507C2×#41D4×C15111yescharacteristic
508C23×C4—21no—
509C2×Q16—21no—
510C2×Q16—21no—
511C2×Q16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16—21no—
515C22×C8—21no—
516C4⋊Q8—21no—
517C4⋊Q8D4×C15111yescharacteristic
518C4⋊Q8C23×C15111yescharacteristic
519C4⋊Q8C23×C15111yescharacteristic
520#127—21no—
521#127D4×C15111yescharacteristic
522#126—21no—
523#126—21no—
524#126—21no—
525#126—21no—
526#126—21no—
527#126—21no—
528#125—21no—
529#125—21no—
530#125—21no—
531#125C23×C15111yescharacteristic
532#125C23×C15111yescharacteristic
533#124—21no—
534#124—21no—
535#124—21no—
536#124—21no—
537#124C23×C15111yescharacteristic
538#124C23×C15111yescharacteristic
539#124C23×C15111yescharacteristic
540#124C23×C15111yescharacteristic
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545#123—21no—
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8D4×C15111yescharacteristic
564C22⋊Q8D4×C15111yescharacteristic
565#121—21no—
566#121—21no—
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121D4×C15111yescharacteristic
580#121D4×C15111yescharacteristic
581#120—21no—
582#120—21no—
583#120—21no—
584#120—21no—
585#120—21no—
586#120—21no—
587C4×Q8—21no—
588C4×Q8—21no—
589C4×Q8D4×C15111yescharacteristic
590C4×Q8D4×C15111yescharacteristic
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4D4×C15111yescharacteristic
600C4×D4D4×C15111yescharacteristic
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605C2×C42—21no—
606C2×C42C23×C15111yescharacteristic
607#107—21no—
608#107—21no—
609#107—21no—
610#106—21no—
611#106—21no—
612#106—21no—
613C4⋊C8—21no—
614C4⋊C8—21no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#103—21no—
621#103—21no—
622#102—21no—
623#102—21no—
624#102—21no—
625#102—21no—
626#102—21no—
627C22⋊C8—21no—
628C22⋊C8—21no—
629#97—21no—
630#97C23×C15111yescharacteristic
631#97C23×C15111yescharacteristic
632#97C23×C15111yescharacteristic
633#97C23×C15111yescharacteristic
634#97C23×C15111yescharacteristic
635#97C23×C15111yescharacteristic
636C24—21no—
637#41—81no—
638#41—81no—
639#41—82no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C15111yescharacteristic
644C2×Q8C2×D4×C15111yescharacteristic
645C2×Q8C2×D4×C15111yescharacteristic
646C2×Q8C2×D4×C15111yescharacteristic
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4C2×D4×C15111yescharacteristic
661C2×D4C2×D4×C15111yescharacteristic
662C2×D4C2×D4×C15111yescharacteristic
663C2×D4C2×D4×C15111yescharacteristic
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—82no—
674C22×C4C2×D4×C15111yescharacteristic
675C22×C4C2×D4×C15111yescharacteristic
676C22×C4C2×D4×C15111yescharacteristic
677Q16—42no—
678Q16—81no—
679Q16—81no—
680SD16—42no—
681SD16—81no—
682SD16—81no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—41no—
711C4⋊C4—41no—
712C4⋊C4C2×D4×C15111yescharacteristic
713C4⋊C4C2×D4×C15111yescharacteristic
714C4⋊C4C2×D4×C15111yescharacteristic
715C4⋊C4C2×D4×C15111yescharacteristic
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—41no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—41no—
746C42C2×D4×C15111yescharacteristic
747C42C2×D4×C15111yescharacteristic
748C42C2×D4×C15111yescharacteristic
749C42C24×C15111yescharacteristic
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—81no—
755C23—81no—
756C23—81no—
757C23#120×C15111yescharacteristic
758Q8—41no—
759Q8—41no—
760Q8—41no—
761Q8—41no—
762Q8—41no—
763Q8—41no—
764Q8—41no—
765Q8—41no—
766Q8—81no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—81no—
772D4—81no—
773D4—81no—
774D4—81no—
775D4—81no—
776D4—81no—
777D4—81no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783D4—81no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4#120×C15111yescharacteristic
807C2×C4#120×C15111yescharacteristic
808C2×C4#120×C15111yescharacteristic
809C2×C4C22×D4×C15111yescharacteristic
810C2×C4C22×D4×C15111yescharacteristic
811C2×C4C22×D4×C15111yescharacteristic
812C8—22no—
813C8—41no—
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—84no—
834C22C2×#120×C15111yescharacteristic
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—81no—
850C4—81no—
851C2—41no—
852C2—81no—
853C2—81no—
854C2—81no—
855C2—81no—
856C2#3018×C15111yescharacteristic
857C2#3019×C15111yescharacteristic
858C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3529×C151C2
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
2. #3240×C151C2semidirect
3. #3216×C151C2semidirect
4. #3181×C151C2semidirect
5. #1664×C151C2semidirect
6. #1662×C151C2semidirect
7. #1661×C151C2semidirect
8. #1661×C151C2semidirect
9. #1661×C151C2semidirect
10. #1660×C151C2semidirect
11. #1659×C151C2semidirect
12. #1659×C151C2semidirect
13. #1535×C151C2semidirect
14. #1532×C151C2semidirect
15. #1530×C151C2semidirect
26. #533×C151C22semidirect
36. #501×C151C22semidirect
37. #501×C151C22semidirect
38. #501×C151C22semidirect
41. #497×C151C22semidirect
42. #491×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
429. #19011C151direct (N × H)
430. C151#19011direct (N × H)
432. #3240C2×C151semidirect
433. #3216C2×C151semidirect
434. #3181C2×C151semidirect
435. #1664C2×C151semidirect
436. #1662C2×C151semidirect
437. #1661C2×C151semidirect
438. #1661C2×C151semidirect
439. #1661C2×C151semidirect
440. #1660C2×C151semidirect
441. #1659C2×C151semidirect
442. #1659C2×C151semidirect
443. #1535C2×C151semidirect
444. #1532C2×C151semidirect
445. #1530C2×C151semidirect
456. #533C22×C151semidirect
466. #501C22×C151semidirect
467. #501C22×C151semidirect
468. #501C22×C151semidirect
471. #497C22×C151semidirect
472. #491C22×C151semidirect
477. #489C22×C151semidirect
490. #432C22×C151semidirect
491. #432C22×C151semidirect
492. C2×#97C22×C151semidirect
493. #330C22×C151semidirect
494. #330C22×C151semidirect
495. #330C22×C151semidirect
496. #330C22×C151semidirect
503. #329C22×C151semidirect
504. #329C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3529×C1512
#3240×C1512
#3216×C1512
#3181×C1512
#1664×C1512
#1662×C1512
#1661×C1512
#1660×C1512
#1659×C1512
#1535×C1512
#1532×C1512
#1530×C1512
#19011151