Finite Group Databasebeta

← C151×#18810 #50323735

Subgroups — C151×#18810 #50323735

Order 38656.

1042 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3519×C151C211yesmaximal, characteristic, complemented
2#3251×C151C211yesmaximal, characteristic, complemented
3#3207×C151C211yesmaximal, characteristic, complemented
4#3036×C151C211yesmaximal, characteristic, complemented
5#1646×C151C211yesmaximal, characteristic, complemented
6#1643×C151C211yesmaximal, characteristic, complemented
7#1642×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#1560×C151C211yesmaximal, characteristic, complemented
14#1495×C151C211yesmaximal, characteristic, complemented
15#1486×C151C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C151—21no—
17#555×C151C2211yescharacteristic
18#554×C151C2211yescharacteristic
19#553×C151—21no—
20#553×C151—21no—
21#550×C151C2211yescharacteristic
22#546×C151—22no—
23#546×C151—21no—
24D42×C151—21no—
25D42×C151C2211yescharacteristic
26#540×C151—21no—
27#538×C151—22no—
28#532×C151C2211yescharacteristic
29#532×C151C2211yescharacteristic, complemented
30#529×C151C2211yescharacteristic
31#525×C151—21no—
32C2×#121×C151—21no—
33#518×C151—21no—
34C2×C4×D4×C151C2211yescharacteristic
35#493×C151C2211yescharacteristic, complemented
36#492×C151C2211yescharacteristic, complemented
37#487×C151C2211yescharacteristic, complemented
38#486×C151C2211yescharacteristic, complemented
39#478×C151—21no—
40#475×C151C2211yescharacteristic, complemented
41#474×C151C2211yescharacteristic, complemented
42#469×C151—21no—
43#468×C151—21no—
44#463×C151—22no—
45#463×C151—21no—
46#463×C151—21no—
47#463×C151—21no—
48#461×C151C2211yescharacteristic
49#461×C151C2211yescharacteristic, complemented
50#460×C151C2211yescharacteristic, complemented
51#459×C151C2211yescharacteristic
52#459×C151C2211yescharacteristic, complemented
53#459×C151C2211yescharacteristic, complemented
54#449×C151—22no—
55#431×C151C2211yescharacteristic, complemented
56#423×C151C2211yescharacteristic, complemented
57#423×C151C2211yescharacteristic, complemented
58#417×C151—21no—
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—
79AGL(1,ℤ/8)×C151—44no—
80C2×SD16×C151—21no—
81C2×SD16×C151—21no—
82C2×SD16×C151—22no—
83C2×SD16×C151—21no—
84C2×D8×C151—21no—
85C2×D8×C151—21no—
86C2×D8×C151—22no—
87C2×D8×C151—21no—
88C2×M16×C151—21no—
89C2×M16×C151—21no—
90C4⋊Q8×C151C2311yescharacteristic
91C4⋊Q8×C151C2311yescharacteristic
92#127×C151—21no—
93#127×C151C2311yescharacteristic
94#127×C151C2311yescharacteristic
95#126×C151—22no—
96#126×C151—21no—
97#125×C151—21no—
98#125×C151D411yescharacteristic
99#124×C151—21no—
100#124×C151—22no—
101#124×C151D411yescharacteristic
102#124×C151D412yes—
103#123×C151—22no—
104#123×C151—22no—
105#123×C151—22no—
106#123×C151—21no—
107C22⋊Q8×C151—21no—
108C22⋊Q8×C151—22no—
109C22⋊Q8×C151D411yescharacteristic
110#121×C151—22no—
111#121×C151—22no—
112#121×C151—22no—
113#121×C151—22no—
114#121×C151—21no—
115#121×C151—22no—
116#121×C151—21no—
117#121×C151—21no—
118#121×C151—21no—
119#121×C151—21no—
120#121×C151—21no—
121#121×C151—21no—
122#121×C151—21no—
123#121×C151—21no—
124#121×C151D411yescharacteristic
125#120×C151—22no—
126#120×C151—22no—
127#120×C151—22no—
128C4×Q8×C151C2311yescharacteristic
129C4×D4×C151—22no—
130C4×D4×C151—22no—
131C4×D4×C151—22no—
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×C151—21no—
139C4×D4×C151—21no—
140C4×D4×C151—21no—
141C4×D4×C151D411yescharacteristic
142C4×D4×C151D411yescharacteristic
143C4×D4×C151C2311yescharacteristic
144C4×D4×C151C2311yescharacteristic
145C4×D4×C151C2311yescharacteristic
146#117×C151—21no—
147#117×C151—21no—
148#117×C151—21no—
149C2×C4⋊C4×C151—21no—
150C2×C4⋊C4×C151D411yescharacteristic
151C2×C22⋊C4×C151—22no—
152C2×C22⋊C4×C151—22no—
153C2×C22⋊C4×C151—21no—
154C2×C42×C151C2311yescharacteristic
155#107×C151—21no—
156#106×C151—21no—
157C4⋊C8×C151—21no—
158C4⋊C8×C151—21no—
159C4⋊C8×C151—21no—
160C4⋊C8×C151C2311yescharacteristic
161C4⋊C8×C151C2311yescharacteristic
162C4⋊C8×C151C2311yescharacteristic
163C4⋊C8×C151C2311yescharacteristic
164#103×C151—21no—
165#103×C151—21no—
166#103×C151—22no—
167#103×C151—21no—
168#102×C151—22no—
169#102×C151—21no—
170#102×C151—21no—
171#102×C151—21no—
172#102×C151—21no—
173#102×C151—21no—
174C22⋊C8×C151—21no—
175C4×C8×C151C2311yescharacteristic
176C4×C8×C151C2311yescharacteristic
177C24×C151—22no—
178C24×C151—21no—
179#41×C151—42no—
180#41×C151—42no—
181#41×C151—81no—
182#41×C151—81no—
183#41×C151—82no—
184C2×Q8×C151—21no—
185C2×Q8×C151C2×D411yescharacteristic
186C2×Q8×C151C2×D412yes—
187C2×D4×C151—22no—
188C2×D4×C151—22no—
189C2×D4×C151—22no—
190C2×D4×C151—21no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—22no—
194C2×D4×C151—22no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—41no—
202C2×D4×C151—42no—
203C2×D4×C151—42no—
204C2×D4×C151—41no—
205C2×D4×C151—81no—
206C2×D4×C151—81no—
207C2×D4×C151—84no—
208C2×D4×C151C2×D411yescharacteristic
209C2×D4×C151C2×D411yescharacteristic
210C2×D4×C151C2×D411yescharacteristic
211C2×D4×C151C2×D412yes—
212C22×C4×C151—22no—
213C22×C4×C151—22no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—22no—
220C22×C4×C151—21no—
221C22×C4×C151—41no—
222C22×C4×C151—81no—
223C22×C4×C151—81no—
224C22×C4×C151C2×D411yescharacteristic
225C22×C4×C151C2×D411yescharacteristic
226C22×C4×C151C2×D411yescharacteristic
227SD16×C151—42no—
228SD16×C151—42no—
229SD16×C151—81no—
230SD16×C151—82no—
231D8×C151—42no—
232D8×C151—42no—
233D8×C151—81no—
234D8×C151—82no—
235M16×C151—42no—
236M16×C151—81no—
237C2×C8×C151—21no—
238C2×C8×C151—21no—
239C2×C8×C151—21no—
240C2×C8×C151—21no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C4⋊C4×C151—22no—
244C4⋊C4×C151—22no—
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×C151—21no—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—21no—
254C4⋊C4×C151C2×D411yescharacteristic
255C4⋊C4×C151C2×D411yescharacteristic
256C4⋊C4×C151C2×D411yescharacteristic
257C4⋊C4×C151C2×D411yescharacteristic
258C22⋊C4×C151—22no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—22no—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—21no—
266C22⋊C4×C151—21no—
267C22⋊C4×C151—22no—
268C22⋊C4×C151—21no—
269C22⋊C4×C151—21no—
270C22⋊C4×C151—22no—
271C22⋊C4×C151—21no—
272C22⋊C4×C151—21no—
273C22⋊C4×C151—21no—
274C22⋊C4×C151—41no—
275C22⋊C4×C151—41no—
276C42×C151—22no—
277C42×C151—21no—
278C42×C151C2×D411yescharacteristic
279C42×C151C2×D411yescharacteristic
280C42×C151C2×D411yescharacteristic
281C42×C151C2411yescharacteristic
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—22no—
286C23×C151—42no—
287C23×C151—42no—
288C23×C151—44no—
289C23×C151—41no—
290C23×C151—81no—
291C23×C151—82no—
292C23×C151—82no—
293C23×C151#12011yescharacteristic
294Q8×C151—21no—
295Q8×C151—21no—
296Q8×C151—42no—
297Q8×C151—41no—
298Q8×C151—41no—
299D4×C151—21no—
300D4×C151—21no—
301D4×C151—21no—
302D4×C151—21no—
303D4×C151—21no—
304D4×C151—42no—
305D4×C151—42no—
306D4×C151—42no—
307D4×C151—44no—
308D4×C151—44no—
309D4×C151—42no—
310D4×C151—41no—
311D4×C151—41no—
312D4×C151—41no—
313D4×C151—41no—
314D4×C151—41no—
315D4×C151—41no—
316D4×C151—41no—
317D4×C151—41no—
318D4×C151—82no—
319D4×C151—82no—
320D4×C151—82no—
321D4×C151—82no—
322D4×C151—82no—
323D4×C151AGL(1,ℤ/8)12yes—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—21no—
329C2×C4×C151—22no—
330C2×C4×C151—21no—
331C2×C4×C151—21no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—41no—
335C2×C4×C151—41no—
336C2×C4×C151—41no—
337C2×C4×C151—41no—
338C2×C4×C151—41no—
339C2×C4×C151—41no—
340C2×C4×C151—41no—
341C2×C4×C151—41no—
342C2×C4×C151—82no—
343C2×C4×C151—81no—
344C2×C4×C151—81no—
345C2×C4×C151—82no—
346C2×C4×C151—81no—
347C2×C4×C151—82no—
348C2×C4×C151—82no—
349C2×C4×C151#12011yescharacteristic
350C2×C4×C151#12011yescharacteristic
351C2×C4×C151#12011yescharacteristic
352C2×C4×C151C22×D411yescharacteristic
353C2×C4×C151C22×D411yescharacteristic
354C2×C4×C151C22×D411yescharacteristic
355C8×C151—41no—
356C8×C151—41no—
357C8×C151—41no—
358C8×C151—41no—
359C8×C151—41no—
360C8×C151—41no—
361C22×C151—21no—
362C22×C151—22no—
363C22×C151—21no—
364C22×C151—21no—
365C22×C151—41no—
366C22×C151—41no—
367C22×C151—41no—
368C22×C151—41no—
369C22×C151—42no—
370C22×C151—41no—
371C22×C151—42no—
372C22×C151—41no—
373C22×C151—42no—
374C22×C151—41no—
375C22×C151—41no—
376C22×C151—84no—
377C22×C151—81no—
378C22×C151—81no—
379C22×C151—81no—
380C22×C151—164no—
381C22×C151C2×#12011yescharacteristic
382C4×C151—21no—
383C4×C151—21no—
384C4×C151—21no—
385C4×C151—21no—
386C4×C151—41no—
387C4×C151—41no—
388C4×C151—41no—
389C4×C151—41no—
390C4×C151—41no—
391C4×C151—42no—
392C4×C151—81no—
393C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
394C4×C151#57511yescharacteristic
395C4×C151#57611yescharacteristic
396C4×C151#57711yescharacteristic
397C2×C151—41no—
398C2×C151—42no—
399C2×C151—81no—
400C2×C151—82no—
401C2×C151—81no—
402C2×C151—161no—
403C2×C151#300611yescharacteristic
404C2×C151#301211yescharacteristic
405C2×C151#301911yescharacteristic
406#18810C15111yesmaximal, characteristic, direct product factor, Sylow
407C151#1881011yescharacteristic, direct product factor, Sylow
408#3519C2×C15111yescharacteristic, complemented
409#3251C2×C15111yescharacteristic, complemented
410#3207C2×C15111yescharacteristic, complemented
411#3036C2×C15111yescharacteristic, complemented
412#1646C2×C15111yescharacteristic, complemented
413#1643C2×C15111yescharacteristic, complemented
414#1642C2×C15111yescharacteristic, complemented
415#1639C2×C15111yescharacteristic, complemented
416#1624C2×C15111yescharacteristic, complemented
417#1622C2×C15111yescharacteristic, complemented
418#1621C2×C15111yescharacteristic, complemented
419#1619C2×C15111yescharacteristic, complemented
420#1560C2×C15111yescharacteristic, complemented
421#1495C2×C15111yescharacteristic, complemented
422#1486C2×C15111yescharacteristic, complemented
423C2×AGL(1,ℤ/8)—21no—
424#555C22×C15111yescharacteristic
425#554C22×C15111yescharacteristic
426#553—21no—
427#553—21no—
428#550C22×C15111yescharacteristic
429#546—22no—
430#546—21no—
431D42—21no—
432D42C22×C15111yescharacteristic
433#540—21no—
434#538—22no—
435#532C22×C15111yescharacteristic
436#532C22×C15111yescharacteristic, complemented
437#529C22×C15111yescharacteristic
438#525—21no—
439C2×#121—21no—
440#518—21no—
441C2×C4×D4C22×C15111yescharacteristic
442#493C22×C15111yescharacteristic, complemented
443#492C22×C15111yescharacteristic, complemented
444#487C22×C15111yescharacteristic, complemented
445#486C22×C15111yescharacteristic, complemented
446#478—21no—
447#475C22×C15111yescharacteristic, complemented
448#474C22×C15111yescharacteristic, complemented
449#469—21no—
450#468—21no—
451#463—22no—
452#463—21no—
453#463—21no—
454#463—21no—
455#461C22×C15111yescharacteristic
456#461C22×C15111yescharacteristic, complemented
457#460C22×C15111yescharacteristic, complemented
458#459C22×C15111yescharacteristic
459#459C22×C15111yescharacteristic, complemented
460#459C22×C15111yescharacteristic, complemented
461#449—22no—
462#431C22×C15111yescharacteristic, complemented
463#423C22×C15111yescharacteristic, complemented
464#423C22×C15111yescharacteristic, complemented
465#417—21no—
466#333C22×C15111yescharacteristic, complemented
467#333C22×C15111yescharacteristic, complemented
468#331C22×C15111yescharacteristic, complemented
469#331C22×C15111yescharacteristic, complemented
470Q8⋊C8C22×C15111yescharacteristic, complemented
471Q8⋊C8C22×C15111yescharacteristic, complemented
472D4⋊C8C22×C15111yescharacteristic
473D4⋊C8C22×C15111yescharacteristic
474D4⋊C8C22×C15111yescharacteristic, complemented
475D4⋊C8C22×C15111yescharacteristic, complemented
476D4⋊C8C22×C15111yescharacteristic, complemented
477D4⋊C8C22×C15111yescharacteristic, complemented
478C2×#41—21no—
479C2×#41—21no—
480C2×#41D4×C15112yes—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4D4×C15111yescharacteristic
485C23×C4—21no—
486AGL(1,ℤ/8)—44no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×SD16—21no—
491C2×D8—21no—
492C2×D8—21no—
493C2×D8—22no—
494C2×D8—21no—
495C2×M16—21no—
496C2×M16—21no—
497C4⋊Q8C23×C15111yescharacteristic
498C4⋊Q8C23×C15111yescharacteristic
499#127—21no—
500#127C23×C15111yescharacteristic
501#127C23×C15111yescharacteristic
502#126—22no—
503#126—21no—
504#125—21no—
505#125D4×C15111yescharacteristic
506#124—22no—
507#124—21no—
508#124D4×C15111yescharacteristic
509#124D4×C15112yes—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—21no—
514C22⋊Q8—21no—
515C22⋊Q8—22no—
516C22⋊Q8D4×C15111yescharacteristic
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121D4×C15111yescharacteristic
532#120—22no—
533#120—22no—
534#120—22no—
535C4×Q8C23×C15111yescharacteristic
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4D4×C15111yescharacteristic
549C4×D4D4×C15111yescharacteristic
550C4×D4C23×C15111yescharacteristic
551C4×D4C23×C15111yescharacteristic
552C4×D4C23×C15111yescharacteristic
553#117—21no—
554#117—21no—
555#117—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C15111yescharacteristic
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C42C23×C15111yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8—21no—
567C4⋊C8C23×C15111yescharacteristic
568C4⋊C8C23×C15111yescharacteristic
569C4⋊C8C23×C15111yescharacteristic
570C4⋊C8C23×C15111yescharacteristic
571#103—22no—
572#103—21no—
573#103—21no—
574#103—21no—
575#102—22no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581C22⋊C8—21no—
582C4×C8C23×C15111yescharacteristic
583C4×C8C23×C15111yescharacteristic
584C24—22no—
585C24—21no—
586#41—42no—
587#41—42no—
588#41—81no—
589#41—81no—
590#41—82no—
591C2×Q8—21no—
592C2×Q8C2×D4×C15111yescharacteristic
593C2×Q8C2×D4×C15112yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—41no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—84no—
615C2×D4C2×D4×C15111yescharacteristic
616C2×D4C2×D4×C15111yescharacteristic
617C2×D4C2×D4×C15111yescharacteristic
618C2×D4C2×D4×C15112yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4C2×D4×C15111yescharacteristic
632C22×C4C2×D4×C15111yescharacteristic
633C22×C4C2×D4×C15111yescharacteristic
634SD16—42no—
635SD16—42no—
636SD16—81no—
637SD16—82no—
638D8—42no—
639D8—42no—
640D8—81no—
641D8—82no—
642M16—42no—
643M16—81no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4C2×D4×C15111yescharacteristic
662C4⋊C4C2×D4×C15111yescharacteristic
663C4⋊C4C2×D4×C15111yescharacteristic
664C4⋊C4C2×D4×C15111yescharacteristic
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—22no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C42—22no—
684C42—21no—
685C42C2×D4×C15111yescharacteristic
686C42C2×D4×C15111yescharacteristic
687C42C2×D4×C15111yescharacteristic
688C42C24×C15111yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—41no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23#120×C15111yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—42no—
704Q8—41no—
705Q8—41no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—44no—
715D4—42no—
716D4—44no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—82no—
726D4—82no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4AGL(1,ℤ/8)×C15112yes—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—81no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4#120×C15111yescharacteristic
757C2×C4#120×C15111yescharacteristic
758C2×C4#120×C15111yescharacteristic
759C2×C4C22×D4×C15111yescharacteristic
760C2×C4C22×D4×C15111yescharacteristic
761C2×C4C22×D4×C15111yescharacteristic
762C8—41no—
763C8—41no—
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C22—21no—
769C22—22no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—84no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—164no—
788C22C2×#120×C15111yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
801C4#575×C15111yescharacteristic
802C4#576×C15111yescharacteristic
803C4#577×C15111yescharacteristic
804C2—41no—
805C2—42no—
806C2—81no—
807C2—81no—
808C2—82no—
809C2—161no—
810C2#3006×C15111yescharacteristic
811C2#3012×C15111yescharacteristic
812C2#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. #3251×C151C2semidirect
3. #3207×C151C2semidirect
4. #3036×C151C2semidirect
5. #1646×C151C2semidirect
6. #1643×C151C2semidirect
7. #1642×C151C2semidirect
8. #1639×C151C2semidirect
9. #1624×C151C2semidirect
10. #1622×C151C2semidirect
11. #1621×C151C2semidirect
12. #1619×C151C2semidirect
13. #1560×C151C2semidirect
14. #1495×C151C2semidirect
15. #1486×C151C2semidirect
29. #532×C151C22semidirect
35. #493×C151C22semidirect
36. #492×C151C22semidirect
37. #487×C151C22semidirect
38. #486×C151C22semidirect
40. #475×C151C22semidirect
41. #474×C151C22semidirect
49. #461×C151C22semidirect
50. #460×C151C22semidirect
52. #459×C151C22semidirect
53. #459×C151C22semidirect
55. #431×C151C22semidirect
56. #423×C151C22semidirect
57. #423×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
406. #18810C151direct (N × H)
407. C151#18810direct (N × H)
408. #3519C2×C151semidirect
409. #3251C2×C151semidirect
410. #3207C2×C151semidirect
411. #3036C2×C151semidirect
412. #1646C2×C151semidirect
413. #1643C2×C151semidirect
414. #1642C2×C151semidirect
415. #1639C2×C151semidirect
416. #1624C2×C151semidirect
417. #1622C2×C151semidirect
418. #1621C2×C151semidirect
419. #1619C2×C151semidirect
420. #1560C2×C151semidirect
421. #1495C2×C151semidirect
422. #1486C2×C151semidirect
436. #532C22×C151semidirect
442. #493C22×C151semidirect
443. #492C22×C151semidirect
444. #487C22×C151semidirect
445. #486C22×C151semidirect
447. #475C22×C151semidirect
448. #474C22×C151semidirect
456. #461C22×C151semidirect
457. #460C22×C151semidirect
459. #459C22×C151semidirect
460. #459C22×C151semidirect
462. #431C22×C151semidirect
463. #423C22×C151semidirect
464. #423C22×C151semidirect
466. #333C22×C151semidirect
467. #333C22×C151semidirect
468. #331C22×C151semidirect
469. #331C22×C151semidirect
470. Q8⋊C8C22×C151semidirect
471. Q8⋊C8C22×C151semidirect
474. D4⋊C8C22×C151semidirect
475. D4⋊C8C22×C151semidirect
476. D4⋊C8C22×C151semidirect
477. 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
#3251×C1512
#3207×C1512
#3036×C1512
#1646×C1512
#1643×C1512
#1642×C1512
#1639×C1512
#1624×C1512
#1622×C1512
#1621×C1512
#1619×C1512
#1560×C1512
#1495×C1512
#1486×C1512
#18810151