Finite Group Databasebeta

← C151×#18866 #50323791

Subgroups — C151×#18866 #50323791

Order 38656.

1020 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3519×C151C211yesmaximal, characteristic, complemented
2#3212×C151C211yesmaximal, characteristic, complemented
3#3207×C151C211yesmaximal, characteristic, complemented
4#3100×C151C211yesmaximal, characteristic, complemented
5#1646×C151C211yesmaximal, characteristic, complemented
6#1644×C151C211yesmaximal, characteristic, complemented
7#1641×C151C211yesmaximal, characteristic, complemented
8#1639×C151C211yesmaximal, characteristic, complemented
9#1624×C151C211yesmaximal, characteristic, complemented
10#1622×C151C211yesmaximal, characteristic, complemented
11#1621×C151C211yesmaximal, characteristic, complemented
12#1619×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#532×C151C2211yescharacteristic
28#532×C151C2211yescharacteristic, complemented
29#529×C151C2211yescharacteristic
30#525×C151—21no—
31C2×#121×C151—21no—
32#518×C151—21no—
33C2×C4×D4×C151C2211yescharacteristic
34#495×C151—21no—
35#493×C151C2211yescharacteristic, complemented
36#492×C151C2211yescharacteristic, complemented
37#488×C151—21no—
38#487×C151C2211yescharacteristic, complemented
39#486×C151C2211yescharacteristic, complemented
40#480×C151—21no—
41#474×C151C2211yescharacteristic
42#474×C151C2211yescharacteristic, complemented
43#463×C151—22no—
44#462×C151C2211yescharacteristic, complemented
45#461×C151C2211yescharacteristic, complemented
46#460×C151C2211yescharacteristic, complemented
47#459×C151C2211yescharacteristic
48#459×C151C2211yescharacteristic, complemented
49#459×C151C2211yescharacteristic, complemented
50#452×C151—21no—
51#449×C151—22no—
52#449×C151—21no—
53#447×C151—21no—
54C4×D8×C151—21no—
55C4×D8×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×C151—21no—
73C2×#41×C151D412yes—
74C22×D4×C151—22no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151D411yescharacteristic
78C23×C4×C151—21no—
79C2×Q16×C151—21no—
80C2×SD16×C151—21no—
81C2×SD16×C151—22no—
82C2×SD16×C151—21no—
83C2×D8×C151—21no—
84C2×D8×C151—21no—
85C2×D8×C151—21no—
86C2×D8×C151—22no—
87C4⋊Q8×C151C2311yescharacteristic
88C4⋊Q8×C151C2311yescharacteristic
89#127×C151—21no—
90#127×C151C2311yescharacteristic
91#127×C151C2311yescharacteristic
92#126×C151—22no—
93#126×C151—21no—
94#125×C151—21no—
95#125×C151D411yescharacteristic
96#124×C151—21no—
97#124×C151—22no—
98#124×C151D412yes—
99#124×C151D411yescharacteristic
100#123×C151—22no—
101#123×C151—22no—
102#123×C151—22no—
103#123×C151—21no—
104C22⋊Q8×C151—21no—
105C22⋊Q8×C151—22no—
106C22⋊Q8×C151D411yescharacteristic
107#121×C151—22no—
108#121×C151—22no—
109#121×C151—22no—
110#121×C151—22no—
111#121×C151—21no—
112#121×C151—22no—
113#121×C151—21no—
114#121×C151—21no—
115#121×C151—21no—
116#121×C151—21no—
117#121×C151—21no—
118#121×C151—21no—
119#121×C151—21no—
120#121×C151—21no—
121#121×C151D411yescharacteristic
122#120×C151—22no—
123#120×C151—22no—
124#120×C151—22no—
125C4×Q8×C151C2311yescharacteristic
126C4×D4×C151—22no—
127C4×D4×C151—22no—
128C4×D4×C151—22no—
129C4×D4×C151—21no—
130C4×D4×C151—21no—
131C4×D4×C151—21no—
132C4×D4×C151—21no—
133C4×D4×C151—21no—
134C4×D4×C151—21no—
135C4×D4×C151—21no—
136C4×D4×C151—21no—
137C4×D4×C151—21no—
138C4×D4×C151D411yescharacteristic
139C4×D4×C151D411yescharacteristic
140C4×D4×C151C2311yescharacteristic
141C4×D4×C151C2311yescharacteristic
142C4×D4×C151C2311yescharacteristic
143#117×C151—21no—
144#117×C151—21no—
145#117×C151—21no—
146C2×C4⋊C4×C151—21no—
147C2×C4⋊C4×C151D411yescharacteristic
148C2×C22⋊C4×C151—22no—
149C2×C22⋊C4×C151—22no—
150C2×C22⋊C4×C151—21no—
151C2×C42×C151C2311yescharacteristic
152#107×C151—21no—
153#107×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#102×C151—21no—
163#102×C151—21no—
164#102×C151—22no—
165#102×C151—21no—
166#102×C151—21no—
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—81no—
181#41×C151—81no—
182#41×C151—82no—
183C2×Q8×C151—21no—
184C2×Q8×C151C2×D411yescharacteristic
185C2×Q8×C151C2×D412yes—
186C2×D4×C151—22no—
187C2×D4×C151—22no—
188C2×D4×C151—22no—
189C2×D4×C151—21no—
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—22no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—41no—
201C2×D4×C151—42no—
202C2×D4×C151—42no—
203C2×D4×C151—41no—
204C2×D4×C151—81no—
205C2×D4×C151—81no—
206C2×D4×C151—84no—
207C2×D4×C151C2×D411yescharacteristic
208C2×D4×C151C2×D411yescharacteristic
209C2×D4×C151C2×D411yescharacteristic
210C2×D4×C151C2×D412yes—
211C22×C4×C151—22no—
212C22×C4×C151—22no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—22no—
219C22×C4×C151—21no—
220C22×C4×C151—41no—
221C22×C4×C151—81no—
222C22×C4×C151—81no—
223C22×C4×C151C2×D411yescharacteristic
224C22×C4×C151C2×D411yescharacteristic
225C22×C4×C151C2×D411yescharacteristic
226Q16×C151—81no—
227SD16×C151—81no—
228SD16×C151—81no—
229SD16×C151—82no—
230D8×C151—42no—
231D8×C151—42no—
232D8×C151—81no—
233D8×C151—82no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C2×C8×C151—21no—
238C2×C8×C151—21no—
239C2×C8×C151—21no—
240C4⋊C4×C151—22no—
241C4⋊C4×C151—22no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151—21no—
244C4⋊C4×C151—21no—
245C4⋊C4×C151—21no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—21no—
251C4⋊C4×C151C2×D411yescharacteristic
252C4⋊C4×C151C2×D411yescharacteristic
253C4⋊C4×C151C2×D411yescharacteristic
254C4⋊C4×C151C2×D411yescharacteristic
255C22⋊C4×C151—22no—
256C22⋊C4×C151—22no—
257C22⋊C4×C151—22no—
258C22⋊C4×C151—22no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—21no—
261C22⋊C4×C151—21no—
262C22⋊C4×C151—21no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—22no—
265C22⋊C4×C151—21no—
266C22⋊C4×C151—21no—
267C22⋊C4×C151—22no—
268C22⋊C4×C151—21no—
269C22⋊C4×C151—21no—
270C22⋊C4×C151—21no—
271C22⋊C4×C151—41no—
272C22⋊C4×C151—41no—
273C42×C151—22no—
274C42×C151—21no—
275C42×C151C2×D411yescharacteristic
276C42×C151C2×D411yescharacteristic
277C42×C151C2×D411yescharacteristic
278C42×C151C2411yescharacteristic
279C23×C151—21no—
280C23×C151—21no—
281C23×C151—21no—
282C23×C151—22no—
283C23×C151—42no—
284C23×C151—42no—
285C23×C151—44no—
286C23×C151—41no—
287C23×C151—81no—
288C23×C151—82no—
289C23×C151—82no—
290C23×C151#12011yescharacteristic
291Q8×C151—21no—
292Q8×C151—21no—
293Q8×C151—42no—
294Q8×C151—41no—
295Q8×C151—41no—
296D4×C151—21no—
297D4×C151—21no—
298D4×C151—21no—
299D4×C151—21no—
300D4×C151—21no—
301D4×C151—42no—
302D4×C151—42no—
303D4×C151—42no—
304D4×C151—44no—
305D4×C151—44no—
306D4×C151—42no—
307D4×C151—41no—
308D4×C151—41no—
309D4×C151—41no—
310D4×C151—41no—
311D4×C151—41no—
312D4×C151—41no—
313D4×C151—41no—
314D4×C151—41no—
315D4×C151—82no—
316D4×C151—82no—
317D4×C151—82no—
318D4×C151—82no—
319D4×C151—82no—
320D4×C151#13512yes—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—22no—
327C2×C4×C151—21no—
328C2×C4×C151—21no—
329C2×C4×C151—21no—
330C2×C4×C151—21no—
331C2×C4×C151—41no—
332C2×C4×C151—41no—
333C2×C4×C151—41no—
334C2×C4×C151—41no—
335C2×C4×C151—41no—
336C2×C4×C151—41no—
337C2×C4×C151—41no—
338C2×C4×C151—41no—
339C2×C4×C151—82no—
340C2×C4×C151—81no—
341C2×C4×C151—81no—
342C2×C4×C151—82no—
343C2×C4×C151—81no—
344C2×C4×C151—82no—
345C2×C4×C151—82no—
346C2×C4×C151#12011yescharacteristic
347C2×C4×C151#12011yescharacteristic
348C2×C4×C151#12011yescharacteristic
349C2×C4×C151C22×D411yescharacteristic
350C2×C4×C151C22×D411yescharacteristic
351C2×C4×C151C22×D411yescharacteristic
352C8×C151—41no—
353C8×C151—41no—
354C8×C151—41no—
355C8×C151—41no—
356C8×C151—41no—
357C8×C151—41no—
358C22×C151—21no—
359C22×C151—22no—
360C22×C151—21no—
361C22×C151—21no—
362C22×C151—41no—
363C22×C151—41no—
364C22×C151—41no—
365C22×C151—41no—
366C22×C151—42no—
367C22×C151—41no—
368C22×C151—42no—
369C22×C151—41no—
370C22×C151—42no—
371C22×C151—41no—
372C22×C151—41no—
373C22×C151—84no—
374C22×C151—81no—
375C22×C151—81no—
376C22×C151—81no—
377C22×C151—164no—
378C22×C151C2×#12011yescharacteristic
379C4×C151—21no—
380C4×C151—21no—
381C4×C151—21no—
382C4×C151—21no—
383C4×C151—41no—
384C4×C151—41no—
385C4×C151—41no—
386C4×C151—41no—
387C4×C151—41no—
388C4×C151—42no—
389C4×C151—81no—
390C4×C151C2×#13511yescharacteristic
391C4×C151#57511yescharacteristic
392C4×C151#57611yescharacteristic
393C4×C151#57611yescharacteristic
394C2×C151—41no—
395C2×C151—42no—
396C2×C151—81no—
397C2×C151—82no—
398C2×C151—81no—
399C2×C151—161no—
400C2×C151#300211yescharacteristic
401C2×C151#300811yescharacteristic
402C2×C151#301911yescharacteristic
403#18866C15111yesmaximal, characteristic, direct product factor, Sylow
404C151#1886611yescharacteristic, direct product factor, Sylow
405#3519C2×C15111yescharacteristic, complemented
406#3212C2×C15111yescharacteristic, complemented
407#3207C2×C15111yescharacteristic, complemented
408#3100C2×C15111yescharacteristic, complemented
409#1646C2×C15111yescharacteristic, complemented
410#1644C2×C15111yescharacteristic, complemented
411#1641C2×C15111yescharacteristic, complemented
412#1639C2×C15111yescharacteristic, complemented
413#1624C2×C15111yescharacteristic, complemented
414#1622C2×C15111yescharacteristic, complemented
415#1621C2×C15111yescharacteristic, complemented
416#1619C2×C15111yescharacteristic, complemented
417#1543C2×C15111yescharacteristic, complemented
418#1482C2×C15111yescharacteristic, complemented
419#1478C2×C15111yescharacteristic, complemented
420#555C22×C15111yescharacteristic
421#554C22×C15111yescharacteristic
422#553—21no—
423#553—21no—
424#550C22×C15111yescharacteristic
425#546—22no—
426#546—21no—
427D42—21no—
428D42C22×C15111yescharacteristic
429#540—21no—
430#538—22no—
431#532C22×C15111yescharacteristic
432#532C22×C15111yescharacteristic, complemented
433#529C22×C15111yescharacteristic
434#525—21no—
435C2×#121—21no—
436#518—21no—
437C2×C4×D4C22×C15111yescharacteristic
438#495—21no—
439#493C22×C15111yescharacteristic, complemented
440#492C22×C15111yescharacteristic, complemented
441#488—21no—
442#487C22×C15111yescharacteristic, complemented
443#486C22×C15111yescharacteristic, complemented
444#480—21no—
445#474C22×C15111yescharacteristic
446#474C22×C15111yescharacteristic, complemented
447#463—22no—
448#462C22×C15111yescharacteristic, complemented
449#461C22×C15111yescharacteristic, complemented
450#460C22×C15111yescharacteristic, complemented
451#459C22×C15111yescharacteristic
452#459C22×C15111yescharacteristic, complemented
453#459C22×C15111yescharacteristic, complemented
454#452—21no—
455#449—22no—
456#449—21no—
457#447—21no—
458C4×D8—21no—
459C4×D8—21no—
460#431C22×C15111yescharacteristic, complemented
461#431C22×C15111yescharacteristic, complemented
462#431C22×C15111yescharacteristic, complemented
463#333C22×C15111yescharacteristic, complemented
464#333C22×C15111yescharacteristic, complemented
465#331C22×C15111yescharacteristic, complemented
466#331C22×C15111yescharacteristic, complemented
467Q8⋊C8C22×C15111yescharacteristic, complemented
468Q8⋊C8C22×C15111yescharacteristic, complemented
469D4⋊C8C22×C15111yescharacteristic
470D4⋊C8C22×C15111yescharacteristic
471D4⋊C8C22×C15111yescharacteristic, complemented
472D4⋊C8C22×C15111yescharacteristic, complemented
473D4⋊C8C22×C15111yescharacteristic, complemented
474D4⋊C8C22×C15111yescharacteristic, complemented
475C2×#41—21no—
476C2×#41—21no—
477C2×#41D4×C15112yes—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4D4×C15111yescharacteristic
482C23×C4—21no—
483C2×Q16—21no—
484C2×SD16—22no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×D8—21no—
488C2×D8—21no—
489C2×D8—21no—
490C2×D8—22no—
491C4⋊Q8C23×C15111yescharacteristic
492C4⋊Q8C23×C15111yescharacteristic
493#127—21no—
494#127C23×C15111yescharacteristic
495#127C23×C15111yescharacteristic
496#126—22no—
497#126—21no—
498#125—21no—
499#125D4×C15111yescharacteristic
500#124—22no—
501#124—21no—
502#124D4×C15111yescharacteristic
503#124D4×C15112yes—
504#123—22no—
505#123—22no—
506#123—22no—
507#123—21no—
508C22⋊Q8—21no—
509C22⋊Q8—22no—
510C22⋊Q8D4×C15111yescharacteristic
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—21no—
516#121—22no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121D4×C15111yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529C4×Q8C23×C15111yescharacteristic
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4D4×C15111yescharacteristic
543C4×D4D4×C15111yescharacteristic
544C4×D4C23×C15111yescharacteristic
545C4×D4C23×C15111yescharacteristic
546C4×D4C23×C15111yescharacteristic
547#117—21no—
548#117—21no—
549#117—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4D4×C15111yescharacteristic
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C42C23×C15111yescharacteristic
556#107—21no—
557#107—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C15111yescharacteristic
560C4⋊C8C23×C15111yescharacteristic
561C4⋊C8C23×C15111yescharacteristic
562C4⋊C8C23×C15111yescharacteristic
563#103—22no—
564#103—21no—
565#103—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C4×C8—21no—
577C4×C8—21no—
578C4×C8C23×C15111yescharacteristic
579C4×C8C23×C15111yescharacteristic
580C24—22no—
581C24—21no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—82no—
587C2×Q8—21no—
588C2×Q8C2×D4×C15111yescharacteristic
589C2×Q8C2×D4×C15112yes—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—41no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—84no—
611C2×D4C2×D4×C15111yescharacteristic
612C2×D4C2×D4×C15111yescharacteristic
613C2×D4C2×D4×C15111yescharacteristic
614C2×D4C2×D4×C15112yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—41no—
625C22×C4—81no—
626C22×C4—81no—
627C22×C4C2×D4×C15111yescharacteristic
628C22×C4C2×D4×C15111yescharacteristic
629C22×C4C2×D4×C15111yescharacteristic
630Q16—81no—
631SD16—81no—
632SD16—81no—
633SD16—82no—
634D8—42no—
635D8—42no—
636D8—81no—
637D8—82no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4C2×D4×C15111yescharacteristic
656C4⋊C4C2×D4×C15111yescharacteristic
657C4⋊C4C2×D4×C15111yescharacteristic
658C4⋊C4C2×D4×C15111yescharacteristic
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C15111yescharacteristic
680C42C2×D4×C15111yescharacteristic
681C42C2×D4×C15111yescharacteristic
682C42C24×C15111yescharacteristic
683C23—21no—
684C23—21no—
685C23—21no—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—44no—
690C23—41no—
691C23—81no—
692C23—82no—
693C23—82no—
694C23#120×C15111yescharacteristic
695Q8—21no—
696Q8—21no—
697Q8—42no—
698Q8—41no—
699Q8—41no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—44no—
709D4—42no—
710D4—44no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—82no—
720D4—82no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4#135×C15112yes—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—81no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4#120×C15111yescharacteristic
751C2×C4#120×C15111yescharacteristic
752C2×C4#120×C15111yescharacteristic
753C2×C4C22×D4×C15111yescharacteristic
754C2×C4C22×D4×C15111yescharacteristic
755C2×C4C22×D4×C15111yescharacteristic
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—41no—
762C22—21no—
763C22—22no—
764C22—21no—
765C22—21no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—84no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—164no—
782C22C2×#120×C15111yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—42no—
793C4—81no—
794C4C2×#135×C15111yescharacteristic
795C4#575×C15111yescharacteristic
796C4#576×C15111yescharacteristic
797C4#576×C15111yescharacteristic
798C2—41no—
799C2—42no—
800C2—81no—
801C2—81no—
802C2—82no—
803C2—161no—
804C2#3002×C15111yescharacteristic
805C2#3008×C15111yescharacteristic
806C2#3019×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. #3519×C151C2semidirect
2. #3212×C151C2semidirect
3. #3207×C151C2semidirect
4. #3100×C151C2semidirect
5. #1646×C151C2semidirect
6. #1644×C151C2semidirect
7. #1641×C151C2semidirect
8. #1639×C151C2semidirect
9. #1624×C151C2semidirect
10. #1622×C151C2semidirect
11. #1621×C151C2semidirect
12. #1619×C151C2semidirect
13. #1543×C151C2semidirect
14. #1482×C151C2semidirect
15. #1478×C151C2semidirect
28. #532×C151C22semidirect
35. #493×C151C22semidirect
36. #492×C151C22semidirect
38. #487×C151C22semidirect
39. #486×C151C22semidirect
42. #474×C151C22semidirect
44. #462×C151C22semidirect
45. #461×C151C22semidirect
46. #460×C151C22semidirect
48. #459×C151C22semidirect
49. #459×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
403. #18866C151direct (N × H)
404. C151#18866direct (N × H)
405. #3519C2×C151semidirect
406. #3212C2×C151semidirect
407. #3207C2×C151semidirect
408. #3100C2×C151semidirect
409. #1646C2×C151semidirect
410. #1644C2×C151semidirect
411. #1641C2×C151semidirect
412. #1639C2×C151semidirect
413. #1624C2×C151semidirect
414. #1622C2×C151semidirect
415. #1621C2×C151semidirect
416. #1619C2×C151semidirect
417. #1543C2×C151semidirect
418. #1482C2×C151semidirect
419. #1478C2×C151semidirect
432. #532C22×C151semidirect
439. #493C22×C151semidirect
440. #492C22×C151semidirect
442. #487C22×C151semidirect
443. #486C22×C151semidirect
446. #474C22×C151semidirect
448. #462C22×C151semidirect
449. #461C22×C151semidirect
450. #460C22×C151semidirect
452. #459C22×C151semidirect
453. #459C22×C151semidirect
460. #431C22×C151semidirect
461. #431C22×C151semidirect
462. #431C22×C151semidirect
463. #333C22×C151semidirect
464. #333C22×C151semidirect
465. #331C22×C151semidirect
466. #331C22×C151semidirect
467. Q8⋊C8C22×C151semidirect
468. Q8⋊C8C22×C151semidirect
471. D4⋊C8C22×C151semidirect
472. D4⋊C8C22×C151semidirect
473. D4⋊C8C22×C151semidirect
474. 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
#3212×C1512
#3207×C1512
#3100×C1512
#1646×C1512
#1644×C1512
#1641×C1512
#1639×C1512
#1624×C1512
#1622×C1512
#1621×C1512
#1619×C1512
#1543×C1512
#1482×C1512
#1478×C1512
#18866151