Finite Group Databasebeta

← C151×#18867 #50323792

Subgroups — C151×#18867 #50323792

Order 38656.

986 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3519×C151C211yesmaximal, characteristic
2#3233×C151C211yesmaximal, characteristic, complemented
3#3210×C151C211yesmaximal, characteristic, complemented
4#3101×C151C211yesmaximal, characteristic, complemented
5#1646×C151C211yesmaximal, characteristic, complemented
6#1643×C151C211yesmaximal, characteristic, complemented
7#1642×C151C211yesmaximal, characteristic, complemented
8#1639×C151C211yesmaximal, characteristic, complemented
9#1634×C151C211yesmaximal, characteristic, complemented
10#1632×C151C211yesmaximal, characteristic, complemented
11#1631×C151C211yesmaximal, characteristic, complemented
12#1629×C151C211yesmaximal, characteristic, complemented
13#1543×C151C211yesmaximal, characteristic, complemented
14#1482×C151C211yesmaximal, characteristic, complemented
15#1478×C151C211yesmaximal, characteristic, complemented
16#555×C151C2211yescharacteristic
17#554×C151C2211yescharacteristic
18#553×C151—21no—
19#553×C151—21no—
20#550×C151C2211yescharacteristic
21#546×C151—22no—
22#546×C151—21no—
23D42×C151—21no—
24D42×C151C2211yescharacteristic
25#540×C151—21no—
26#538×C151—22no—
27#533×C151C2211yescharacteristic, complemented
28#532×C151C2211yescharacteristic
29#529×C151C2211yescharacteristic
30#525×C151—21no—
31C2×#121×C151—21no—
32#518×C151—21no—
33C2×C4×D4×C151C2211yescharacteristic
34#499×C151—21no—
35#494×C151C2211yescharacteristic, complemented
36#492×C151C2211yescharacteristic, complemented
37#488×C151—21no—
38#487×C151C2211yescharacteristic, complemented
39#486×C151C2211yescharacteristic, complemented
40#485×C151—21no—
41#483×C151—21no—
42#482×C151—21no—
43#477×C151C2211yescharacteristic, complemented
44#476×C151C2211yescharacteristic
45#476×C151C2211yescharacteristic, complemented
46#476×C151C2211yescharacteristic, complemented
47#475×C151C2211yescharacteristic, complemented
48#474×C151C2211yescharacteristic, complemented
49#464×C151—22no—
50#461×C151C2211yescharacteristic
51#461×C151C2211yescharacteristic, complemented
52#452×C151—22no—
53#450×C151—21no—
54C4×SD16×C151—21no—
55C4×SD16×C151—21no—
56#431×C151C2211yescharacteristic, complemented
57#431×C151C2211yescharacteristic, complemented
58#431×C151C2211yescharacteristic, complemented
59#333×C151C2211yescharacteristic, complemented
60#333×C151C2211yescharacteristic, complemented
61#331×C151C2211yescharacteristic, complemented
62#331×C151C2211yescharacteristic, complemented
63Q8⋊C8×C151C2211yescharacteristic, complemented
64Q8⋊C8×C151C2211yescharacteristic, complemented
65D4⋊C8×C151C2211yescharacteristic
66D4⋊C8×C151C2211yescharacteristic
67D4⋊C8×C151C2211yescharacteristic, complemented
68D4⋊C8×C151C2211yescharacteristic, complemented
69D4⋊C8×C151C2211yescharacteristic, complemented
70D4⋊C8×C151C2211yescharacteristic, complemented
71C2×#41×C151—21no—
72C2×#41×C151D412yes—
73C22×D4×C151—22no—
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151D411yescharacteristic
77C23×C4×C151—21no—
78C2×Q16×C151—22no—
79C2×SD16×C151—21no—
80C2×SD16×C151—21no—
81C2×SD16×C151—22no—
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85#127×C151—21no—
86#127×C151C2311yescharacteristic
87#126×C151—22no—
88#126×C151—21no—
89#125×C151—21no—
90#125×C151—21no—
91#125×C151D411yescharacteristic
92#124×C151—22no—
93#124×C151D412yes—
94#124×C151D411yescharacteristic
95#123×C151—22no—
96#123×C151—22no—
97#123×C151—22no—
98#123×C151—21no—
99C22⋊Q8×C151—21no—
100C22⋊Q8×C151—21no—
101C22⋊Q8×C151—21no—
102C22⋊Q8×C151—22no—
103C22⋊Q8×C151D411yescharacteristic
104#121×C151—22no—
105#121×C151—22no—
106#121×C151—22no—
107#121×C151—22no—
108#121×C151—21no—
109#121×C151—22no—
110#121×C151—21no—
111#121×C151—21no—
112#121×C151—21no—
113#121×C151—21no—
114#121×C151—21no—
115#121×C151—21no—
116#121×C151D411yescharacteristic
117#120×C151—22no—
118#120×C151—22no—
119#120×C151—22no—
120C4×Q8×C151—21no—
121C4×Q8×C151—21no—
122C4×Q8×C151C2311yescharacteristic
123C4×D4×C151—22no—
124C4×D4×C151—22no—
125C4×D4×C151—22no—
126C4×D4×C151—21no—
127C4×D4×C151—21no—
128C4×D4×C151—21no—
129C4×D4×C151—21no—
130C4×D4×C151—21no—
131C4×D4×C151—21no—
132C4×D4×C151—21no—
133C4×D4×C151D411yescharacteristic
134C4×D4×C151D411yescharacteristic
135C4×D4×C151C2311yescharacteristic
136C4×D4×C151C2311yescharacteristic
137C4×D4×C151C2311yescharacteristic
138#117×C151—21no—
139#117×C151—21no—
140#117×C151—21no—
141#117×C151—21no—
142C2×C4⋊C4×C151—21no—
143C2×C4⋊C4×C151D411yescharacteristic
144C2×C22⋊C4×C151—22no—
145C2×C22⋊C4×C151—22no—
146C2×C22⋊C4×C151—21no—
147C2×C42×C151C2311yescharacteristic
148#107×C151—21no—
149#107×C151—21no—
150#106×C151—21no—
151#106×C151—21no—
152#106×C151—21no—
153#106×C151—21no—
154C4⋊C8×C151—21no—
155C4⋊C8×C151C2311yescharacteristic
156C4⋊C8×C151C2311yescharacteristic
157C4⋊C8×C151C2311yescharacteristic
158C4⋊C8×C151C2311yescharacteristic
159#103×C151—21no—
160#103×C151—21no—
161#103×C151—22no—
162#103×C151—21no—
163#103×C151—21no—
164#102×C151—21no—
165#102×C151—21no—
166#102×C151—22no—
167#102×C151—21no—
168#102×C151—21no—
169C22⋊C8×C151—21no—
170C22⋊C8×C151—21no—
171C22⋊C8×C151—21no—
172C4×C8×C151—21no—
173C4×C8×C151—21no—
174C4×C8×C151C2311yescharacteristic
175C4×C8×C151C2311yescharacteristic
176C24×C151—22no—
177C24×C151—21no—
178#41×C151—81no—
179#41×C151—81no—
180#41×C151—82no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151C2×D411yescharacteristic
184C2×Q8×C151C2×D412yes—
185C2×D4×C151—22no—
186C2×D4×C151—22no—
187C2×D4×C151—22no—
188C2×D4×C151—21no—
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—41no—
197C2×D4×C151—42no—
198C2×D4×C151—42no—
199C2×D4×C151—81no—
200C2×D4×C151—81no—
201C2×D4×C151—84no—
202C2×D4×C151C2×D411yescharacteristic
203C2×D4×C151C2×D411yescharacteristic
204C2×D4×C151C2×D411yescharacteristic
205C2×D4×C151C2×D412yes—
206C22×C4×C151—22no—
207C22×C4×C151—22no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—22no—
214C22×C4×C151—21no—
215C22×C4×C151—81no—
216C22×C4×C151—81no—
217C22×C4×C151C2×D411yescharacteristic
218C22×C4×C151C2×D411yescharacteristic
219C22×C4×C151C2×D411yescharacteristic
220Q16×C151—82no—
221SD16×C151—42no—
222SD16×C151—42no—
223SD16×C151—82no—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C4⋊C4×C151—22no—
231C4⋊C4×C151—22no—
232C4⋊C4×C151—21no—
233C4⋊C4×C151—21no—
234C4⋊C4×C151—21no—
235C4⋊C4×C151—21no—
236C4⋊C4×C151—21no—
237C4⋊C4×C151—21no—
238C4⋊C4×C151—21no—
239C4⋊C4×C151—21no—
240C4⋊C4×C151—21no—
241C4⋊C4×C151—21no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151—41no—
244C4⋊C4×C151—41no—
245C4⋊C4×C151C2×D411yescharacteristic
246C4⋊C4×C151C2×D411yescharacteristic
247C4⋊C4×C151C2×D411yescharacteristic
248C4⋊C4×C151C2×D411yescharacteristic
249C22⋊C4×C151—22no—
250C22⋊C4×C151—22no—
251C22⋊C4×C151—22no—
252C22⋊C4×C151—22no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151—21no—
255C22⋊C4×C151—21no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—22no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—21no—
261C22⋊C4×C151—22no—
262C22⋊C4×C151—21no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—41no—
266C42×C151—22no—
267C42×C151—21no—
268C42×C151—41no—
269C42×C151C2×D411yescharacteristic
270C42×C151C2×D411yescharacteristic
271C42×C151C2×D411yescharacteristic
272C42×C151C2411yescharacteristic
273C23×C151—21no—
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—22no—
277C23×C151—42no—
278C23×C151—42no—
279C23×C151—44no—
280C23×C151—81no—
281C23×C151—82no—
282C23×C151—82no—
283C23×C151#12011yescharacteristic
284Q8×C151—21no—
285Q8×C151—21no—
286Q8×C151—42no—
287Q8×C151—42no—
288Q8×C151—41no—
289Q8×C151—41no—
290D4×C151—21no—
291D4×C151—21no—
292D4×C151—21no—
293D4×C151—21no—
294D4×C151—21no—
295D4×C151—42no—
296D4×C151—42no—
297D4×C151—44no—
298D4×C151—44no—
299D4×C151—42no—
300D4×C151—41no—
301D4×C151—41no—
302D4×C151—41no—
303D4×C151—41no—
304D4×C151—82no—
305D4×C151—82no—
306D4×C151—82no—
307D4×C151—82no—
308D4×C151#13512yes—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—22no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—82no—
329C2×C4×C151—81no—
330C2×C4×C151—81no—
331C2×C4×C151—81no—
332C2×C4×C151—82no—
333C2×C4×C151—82no—
334C2×C4×C151#12011yescharacteristic
335C2×C4×C151#12011yescharacteristic
336C2×C4×C151#12011yescharacteristic
337C2×C4×C151C22×D411yescharacteristic
338C2×C4×C151C22×D411yescharacteristic
339C2×C4×C151C22×D411yescharacteristic
340C8×C151—41no—
341C8×C151—41no—
342C8×C151—41no—
343C8×C151—41no—
344C8×C151—41no—
345C8×C151—41no—
346C22×C151—21no—
347C22×C151—22no—
348C22×C151—21no—
349C22×C151—21no—
350C22×C151—41no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151—41no—
354C22×C151—42no—
355C22×C151—41no—
356C22×C151—42no—
357C22×C151—41no—
358C22×C151—42no—
359C22×C151—41no—
360C22×C151—41no—
361C22×C151—84no—
362C22×C151—164no—
363C22×C151C2×#12011yescharacteristic
364C4×C151—21no—
365C4×C151—21no—
366C4×C151—21no—
367C4×C151—21no—
368C4×C151—41no—
369C4×C151—41no—
370C4×C151—41no—
371C4×C151—41no—
372C4×C151—41no—
373C4×C151—42no—
374C4×C151—81no—
375C4×C151—81no—
376C4×C151C2×#13511yescharacteristic
377C4×C151#57511yescharacteristic
378C4×C151#57711yescharacteristic
379C4×C151#57711yescharacteristic
380C2×C151—41no—
381C2×C151—42no—
382C2×C151—81no—
383C2×C151—82no—
384C2×C151—81no—
385C2×C151#300211yescharacteristic
386C2×C151#300911yescharacteristic
387C2×C151#301911yescharacteristic
388#18867C15111yesmaximal, characteristic, direct product factor, Sylow
389C151#1886711yescharacteristic, direct product factor, Sylow
390#3519C2×C15111yescharacteristic
391#3233C2×C15111yescharacteristic, complemented
392#3210C2×C15111yescharacteristic, complemented
393#3101C2×C15111yescharacteristic, complemented
394#1646C2×C15111yescharacteristic, complemented
395#1643C2×C15111yescharacteristic, complemented
396#1642C2×C15111yescharacteristic, complemented
397#1639C2×C15111yescharacteristic, complemented
398#1634C2×C15111yescharacteristic, complemented
399#1632C2×C15111yescharacteristic, complemented
400#1631C2×C15111yescharacteristic, complemented
401#1629C2×C15111yescharacteristic, complemented
402#1543C2×C15111yescharacteristic, complemented
403#1482C2×C15111yescharacteristic, complemented
404#1478C2×C15111yescharacteristic, complemented
405#555C22×C15111yescharacteristic
406#554C22×C15111yescharacteristic
407#553—21no—
408#553—21no—
409#550C22×C15111yescharacteristic
410#546—22no—
411#546—21no—
412D42—21no—
413D42C22×C15111yescharacteristic
414#540—21no—
415#538—22no—
416#533C22×C15111yescharacteristic, complemented
417#532C22×C15111yescharacteristic
418#529C22×C15111yescharacteristic
419#525—21no—
420C2×#121—21no—
421#518—21no—
422C2×C4×D4C22×C15111yescharacteristic
423#499—21no—
424#494C22×C15111yescharacteristic, complemented
425#492C22×C15111yescharacteristic, complemented
426#488—21no—
427#487C22×C15111yescharacteristic, complemented
428#486C22×C15111yescharacteristic, complemented
429#485—21no—
430#483—21no—
431#482—21no—
432#477C22×C15111yescharacteristic, complemented
433#476C22×C15111yescharacteristic
434#476C22×C15111yescharacteristic, complemented
435#476C22×C15111yescharacteristic, complemented
436#475C22×C15111yescharacteristic, complemented
437#474C22×C15111yescharacteristic, complemented
438#464—22no—
439#461C22×C15111yescharacteristic
440#461C22×C15111yescharacteristic, complemented
441#452—22no—
442#450—21no—
443C4×SD16—21no—
444C4×SD16—21no—
445#431C22×C15111yescharacteristic, complemented
446#431C22×C15111yescharacteristic, complemented
447#431C22×C15111yescharacteristic, complemented
448#333C22×C15111yescharacteristic, complemented
449#333C22×C15111yescharacteristic, complemented
450#331C22×C15111yescharacteristic, complemented
451#331C22×C15111yescharacteristic, complemented
452Q8⋊C8C22×C15111yescharacteristic, complemented
453Q8⋊C8C22×C15111yescharacteristic, complemented
454D4⋊C8C22×C15111yescharacteristic
455D4⋊C8C22×C15111yescharacteristic
456D4⋊C8C22×C15111yescharacteristic, complemented
457D4⋊C8C22×C15111yescharacteristic, complemented
458D4⋊C8C22×C15111yescharacteristic, complemented
459D4⋊C8C22×C15111yescharacteristic, complemented
460C2×#41—21no—
461C2×#41D4×C15112yes—
462C22×D4—22no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4D4×C15111yescharacteristic
466C23×C4—21no—
467C2×Q16—22no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—22no—
471C4⋊Q8C23×C15111yescharacteristic
472C4⋊Q8C23×C15111yescharacteristic
473C4⋊Q8C23×C15111yescharacteristic
474#127—21no—
475#127C23×C15111yescharacteristic
476#126—22no—
477#126—21no—
478#125—21no—
479#125—21no—
480#125D4×C15111yescharacteristic
481#124—22no—
482#124D4×C15111yescharacteristic
483#124D4×C15112yes—
484#123—22no—
485#123—22no—
486#123—22no—
487#123—21no—
488C22⋊Q8—21no—
489C22⋊Q8—22no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8D4×C15111yescharacteristic
493#121—22no—
494#121—22no—
495#121—22no—
496#121—22no—
497#121—21no—
498#121—22no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121D4×C15111yescharacteristic
506#120—22no—
507#120—22no—
508#120—22no—
509C4×Q8—21no—
510C4×Q8—21no—
511C4×Q8C23×C15111yescharacteristic
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4D4×C15111yescharacteristic
523C4×D4D4×C15111yescharacteristic
524C4×D4C23×C15111yescharacteristic
525C4×D4C23×C15111yescharacteristic
526C4×D4C23×C15111yescharacteristic
527#117—21no—
528#117—21no—
529#117—21no—
530#117—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4D4×C15111yescharacteristic
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—21no—
536C2×C42C23×C15111yescharacteristic
537#107—21no—
538#107—21no—
539#106—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543C4⋊C8—21no—
544C4⋊C8C23×C15111yescharacteristic
545C4⋊C8C23×C15111yescharacteristic
546C4⋊C8C23×C15111yescharacteristic
547C4⋊C8C23×C15111yescharacteristic
548#103—22no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#102—21no—
554#102—21no—
555#102—22no—
556#102—21no—
557#102—21no—
558C22⋊C8—21no—
559C22⋊C8—21no—
560C22⋊C8—21no—
561C4×C8—21no—
562C4×C8—21no—
563C4×C8C23×C15111yescharacteristic
564C4×C8C23×C15111yescharacteristic
565C24—22no—
566C24—21no—
567#41—81no—
568#41—81no—
569#41—82no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8C2×D4×C15111yescharacteristic
573C2×Q8C2×D4×C15112yes—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—41no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—84no—
591C2×D4C2×D4×C15111yescharacteristic
592C2×D4C2×D4×C15111yescharacteristic
593C2×D4C2×D4×C15111yescharacteristic
594C2×D4C2×D4×C15112yes—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4C2×D4×C15111yescharacteristic
607C22×C4C2×D4×C15111yescharacteristic
608C22×C4C2×D4×C15111yescharacteristic
609Q16—82no—
610SD16—42no—
611SD16—42no—
612SD16—82no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4C2×D4×C15111yescharacteristic
635C4⋊C4C2×D4×C15111yescharacteristic
636C4⋊C4C2×D4×C15111yescharacteristic
637C4⋊C4C2×D4×C15111yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C15111yescharacteristic
659C42C2×D4×C15111yescharacteristic
660C42C2×D4×C15111yescharacteristic
661C42C24×C15111yescharacteristic
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—44no—
669C23—81no—
670C23—82no—
671C23—82no—
672C23#120×C15111yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—42no—
676Q8—42no—
677Q8—41no—
678Q8—41no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—42no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—82no—
694D4—82no—
695D4—82no—
696D4—82no—
697D4#135×C15112yes—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—82no—
720C2×C4—81no—
721C2×C4—82no—
722C2×C4—82no—
723C2×C4#120×C15111yescharacteristic
724C2×C4#120×C15111yescharacteristic
725C2×C4#120×C15111yescharacteristic
726C2×C4C22×D4×C15111yescharacteristic
727C2×C4C22×D4×C15111yescharacteristic
728C2×C4C22×D4×C15111yescharacteristic
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C8—41no—
735C22—21no—
736C22—22no—
737C22—21no—
738C22—21no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—42no—
748C22—41no—
749C22—41no—
750C22—84no—
751C22—164no—
752C22C2×#120×C15111yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—42no—
763C4—81no—
764C4—81no—
765C4C2×#135×C15111yescharacteristic
766C4#575×C15111yescharacteristic
767C4#577×C15111yescharacteristic
768C4#577×C15111yescharacteristic
769C2—41no—
770C2—42no—
771C2—81no—
772C2—81no—
773C2—82no—
774C2#3002×C15111yescharacteristic
775C2#3009×C15111yescharacteristic
776C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3519×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. #3233×C151C2semidirect
3. #3210×C151C2semidirect
4. #3101×C151C2semidirect
5. #1646×C151C2semidirect
6. #1643×C151C2semidirect
7. #1642×C151C2semidirect
8. #1639×C151C2semidirect
9. #1634×C151C2semidirect
10. #1632×C151C2semidirect
11. #1631×C151C2semidirect
12. #1629×C151C2semidirect
13. #1543×C151C2semidirect
14. #1482×C151C2semidirect
15. #1478×C151C2semidirect
27. #533×C151C22semidirect
35. #494×C151C22semidirect
36. #492×C151C22semidirect
38. #487×C151C22semidirect
39. #486×C151C22semidirect
43. #477×C151C22semidirect
45. #476×C151C22semidirect
46. #476×C151C22semidirect
47. #475×C151C22semidirect
48. #474×C151C22semidirect
51. #461×C151C22semidirect
56. #431×C151C22semidirect
57. #431×C151C22semidirect
58. #431×C151C22semidirect
59. #333×C151C22semidirect
60. #333×C151C22semidirect
61. #331×C151C22semidirect
62. #331×C151C22semidirect
63. Q8⋊C8×C151C22semidirect
64. Q8⋊C8×C151C22semidirect
67. D4⋊C8×C151C22semidirect
68. D4⋊C8×C151C22semidirect
69. D4⋊C8×C151C22semidirect
70. D4⋊C8×C151C22semidirect
388. #18867C151direct (N × H)
389. C151#18867direct (N × H)
391. #3233C2×C151semidirect
392. #3210C2×C151semidirect
393. #3101C2×C151semidirect
394. #1646C2×C151semidirect
395. #1643C2×C151semidirect
396. #1642C2×C151semidirect
397. #1639C2×C151semidirect
398. #1634C2×C151semidirect
399. #1632C2×C151semidirect
400. #1631C2×C151semidirect
401. #1629C2×C151semidirect
402. #1543C2×C151semidirect
403. #1482C2×C151semidirect
404. #1478C2×C151semidirect
416. #533C22×C151semidirect
424. #494C22×C151semidirect
425. #492C22×C151semidirect
427. #487C22×C151semidirect
428. #486C22×C151semidirect
432. #477C22×C151semidirect
434. #476C22×C151semidirect
435. #476C22×C151semidirect
436. #475C22×C151semidirect
437. #474C22×C151semidirect
440. #461C22×C151semidirect
445. #431C22×C151semidirect
446. #431C22×C151semidirect
447. #431C22×C151semidirect
448. #333C22×C151semidirect
449. #333C22×C151semidirect
450. #331C22×C151semidirect
451. #331C22×C151semidirect
452. Q8⋊C8C22×C151semidirect
453. Q8⋊C8C22×C151semidirect
456. D4⋊C8C22×C151semidirect
457. D4⋊C8C22×C151semidirect
458. D4⋊C8C22×C151semidirect
459. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3519×C1512
#3233×C1512
#3210×C1512
#3101×C1512
#1646×C1512
#1643×C1512
#1642×C1512
#1639×C1512
#1634×C1512
#1632×C1512
#1631×C1512
#1629×C1512
#1543×C1512
#1482×C1512
#1478×C1512
#18867151