Finite Group Databasebeta

← C151×#18806 #50323731

Subgroups — C151×#18806 #50323731

Order 38656.

1180 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
1D4×#41×C151C211yesmaximal, characteristic
2#3228×C151C211yesmaximal, characteristic, complemented
3#3110×C151C211yesmaximal, characteristic, complemented
4#3107×C151C211yesmaximal, characteristic, complemented
5#1654×C151C211yesmaximal, characteristic, complemented
6#1651×C151C211yesmaximal, characteristic, complemented
7#1649×C151C211yesmaximal, characteristic, complemented
8#1647×C151C211yesmaximal, characteristic, complemented
9#1642×C151C211yesmaximal, characteristic, complemented
10#1641×C151C211yesmaximal, characteristic, complemented
11#1639×C151C211yesmaximal, characteristic, complemented
12#1639×C151C211yesmaximal, characteristic, complemented
13#1553×C151C211yesmaximal, characteristic, complemented
14#1488×C151C211yesmaximal, characteristic, complemented
15#1478×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151—21no—
17#550×C151C2211yescharacteristic
18D4×Q8×C151C2211yescharacteristic
19#548×C151—21no—
20#547×C151—21no—
21#547×C151C2211yescharacteristic
22#546×C151—22no—
23#546×C151—21no—
24D42×C151—21no—
25D42×C151C2211yescharacteristic
26#533×C151C2211yescharacteristic, complemented
27#532×C151—21no—
28#532×C151C2211yescharacteristic
29#525×C151—22no—
30#525×C151—21no—
31C4×#41×C151C2211yescharacteristic
32C2×C4×D4×C151—21no—
33C2×C4×D4×C151C2211yescharacteristic
34#500×C151C2211yescharacteristic, complemented
35#498×C151C2211yescharacteristic, complemented
36#486×C151C2211yescharacteristic, complemented
37#486×C151C2211yescharacteristic, complemented
38#485×C151—21no—
39#484×C151—21no—
40#482×C151—22no—
41#478×C151—22no—
42#475×C151C2211yescharacteristic, complemented
43#474×C151C2211yescharacteristic
44#474×C151C2211yescharacteristic, complemented
45#474×C151C2211yescharacteristic, complemented
46#462×C151C2211yescharacteristic, complemented
47#461×C151C2211yescharacteristic
48#461×C151C2211yescharacteristic, complemented
49#461×C151C2211yescharacteristic, complemented
50#452×C151—21no—
51#450×C151—21no—
52#440×C151—21no—
53#440×C151—21no—
54C4×Q16×C151—21no—
55C4×SD16×C151—21no—
56#432×C151C2211yescharacteristic, complemented
57#431×C151C2211yescharacteristic, complemented
58#431×C151C2211yescharacteristic, complemented
59#332×C151C2211yescharacteristic, complemented
60#332×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—22no—
72C2×#41×C151—22no—
73C2×#41×C151—21no—
74C2×#41×C151—21no—
75C2×#41×C151—21no—
76C2×#41×C151—44no—
77C2×#41×C151—44no—
78C2×#41×C151D411yescharacteristic
79C22×Q8×C151—21no—
80C22×D4×C151—22no—
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151D411yescharacteristic
84C23×C4×C151—22no—
85C23×C4×C151—21no—
86C2×Q16×C151—21no—
87C2×SD16×C151—21no—
88C2×SD16×C151—21no—
89C2×SD16×C151—21no—
90C4⋊Q8×C151—21no—
91C4⋊Q8×C151C2311yescharacteristic
92C4⋊Q8×C151C2311yescharacteristic
93C4⋊Q8×C151C2311yescharacteristic
94#127×C151—21no—
95#127×C151C2311yescharacteristic
96#125×C151—21no—
97#124×C151—22no—
98#124×C151—21no—
99#123×C151—22no—
100#123×C151—22no—
101#123×C151—22no—
102C22⋊Q8×C151—22no—
103C22⋊Q8×C151—22no—
104C22⋊Q8×C151—21no—
105C22⋊Q8×C151—21no—
106C22⋊Q8×C151—21no—
107C22⋊Q8×C151—21no—
108#121×C151—22no—
109#121×C151—22no—
110#121×C151—22no—
111#121×C151—21no—
112#121×C151—21no—
113#121×C151—21no—
114#121×C151—21no—
115#121×C151—21no—
116#121×C151D412yes—
117#120×C151—22no—
118#120×C151—22no—
119#120×C151—22no—
120C4×Q8×C151—21no—
121C4×Q8×C151—21no—
122C4×Q8×C151D411yescharacteristic
123C4×Q8×C151C2311yescharacteristic
124C4×D4×C151—22no—
125C4×D4×C151—22no—
126C4×D4×C151—22no—
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×C151—21no—
134C4×D4×C151D411yescharacteristic
135C4×D4×C151D411yescharacteristic
136C4×D4×C151D411yescharacteristic
137C4×D4×C151D412yes—
138C4×D4×C151C2311yescharacteristic
139C4×D4×C151C2311yescharacteristic
140C4×D4×C151C2311yescharacteristic
141#117×C151—21no—
142#117×C151—21no—
143#117×C151D411yescharacteristic
144C2×C4⋊C4×C151—21no—
145C2×C4⋊C4×C151D411yescharacteristic
146C2×C22⋊C4×C151—22no—
147C2×C22⋊C4×C151—21no—
148C2×C42×C151—21no—
149C2×C42×C151C2311yescharacteristic
150#107×C151—21no—
151#107×C151—21no—
152#107×C151—21no—
153#107×C151—22no—
154#106×C151—21no—
155#106×C151—22no—
156C4⋊C8×C151—21no—
157C4⋊C8×C151C2311yescharacteristic
158C4⋊C8×C151C2311yescharacteristic
159C4⋊C8×C151C2311yescharacteristic
160C4⋊C8×C151C2311yescharacteristic
161#103×C151—21no—
162#103×C151—21no—
163#103×C151—21no—
164#103×C151—21no—
165#103×C151—21no—
166#102×C151—21no—
167#102×C151—21no—
168#102×C151—21no—
169#102×C151—22no—
170#102×C151—22no—
171C22⋊C8×C151—21no—
172C22⋊C8×C151—21no—
173C22⋊C8×C151—21no—
174#97×C151—21no—
175C4×C8×C151—21no—
176C4×C8×C151C2311yescharacteristic
177C4×C8×C151C2311yescharacteristic
178C24×C151—22no—
179C24×C151—21no—
180#41×C151—22no—
181#41×C151—22no—
182#41×C151—48no—
183#41×C151—42no—
184#41×C151—42no—
185#41×C151—48no—
186#41×C151—42no—
187#41×C151—42no—
188#41×C151—42no—
189#41×C151—42no—
190C2×Q8×C151—22no—
191C2×Q8×C151—21no—
192C2×Q8×C151—21no—
193C2×Q8×C151—21no—
194C2×Q8×C151—42no—
195C2×Q8×C151—42no—
196C2×Q8×C151C2×D411yescharacteristic
197C2×D4×C151—21no—
198C2×D4×C151—22no—
199C2×D4×C151—22no—
200C2×D4×C151—22no—
201C2×D4×C151—22no—
202C2×D4×C151—22no—
203C2×D4×C151—22no—
204C2×D4×C151—22no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—21no—
208C2×D4×C151—41no—
209C2×D4×C151—42no—
210C2×D4×C151—48no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151C2×D411yescharacteristic
215C2×D4×C151C2×D411yescharacteristic
216C2×D4×C151C2×D411yescharacteristic
217C2×D4×C151C2×D412yes—
218C22×C4×C151—21no—
219C22×C4×C151—22no—
220C22×C4×C151—22no—
221C22×C4×C151—22no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—22no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—48no—
231C22×C4×C151—42no—
232C22×C4×C151—42no—
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151C2×D411yescharacteristic
235C22×C4×C151C2×D411yescharacteristic
236Q16×C151—42no—
237SD16×C151—42no—
238SD16×C151—42no—
239SD16×C151—42no—
240C2×C8×C151—21no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—21no—
244C2×C8×C151—21no—
245C2×C8×C151—21no—
246C4⋊C4×C151—22no—
247C4⋊C4×C151—22no—
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×C151—21no—
255C4⋊C4×C151—21no—
256C4⋊C4×C151—41no—
257C4⋊C4×C151—41no—
258C4⋊C4×C151C2×D411yescharacteristic
259C4⋊C4×C151C2×D411yescharacteristic
260C4⋊C4×C151C2×D411yescharacteristic
261C4⋊C4×C151C2×D411yescharacteristic
262C4⋊C4×C151C2×D412yes—
263C22⋊C4×C151—22no—
264C22⋊C4×C151—22no—
265C22⋊C4×C151—22no—
266C22⋊C4×C151—22no—
267C22⋊C4×C151—21no—
268C22⋊C4×C151—21no—
269C22⋊C4×C151—22no—
270C22⋊C4×C151—21no—
271C22⋊C4×C151—21no—
272C22⋊C4×C151—22no—
273C22⋊C4×C151—21no—
274C22⋊C4×C151—21no—
275C22⋊C4×C151—21no—
276C22⋊C4×C151—41no—
277C42×C151—21no—
278C42×C151—21no—
279C42×C151—21no—
280C42×C151—41no—
281C42×C151C2×D411yescharacteristic
282C42×C151C2×D411yescharacteristic
283C42×C151C2×D411yescharacteristic
284C42×C151C2411yescharacteristic
285C23×C151—21no—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—22no—
289C23×C151—42no—
290C23×C151—42no—
291C23×C151—44no—
292C23×C151—44no—
293C23×C151—81no—
294C23×C151—82no—
295C23×C151#12011yescharacteristic
296Q8×C151—21no—
297Q8×C151—44no—
298Q8×C151—41no—
299Q8×C151—41no—
300Q8×C151—41no—
301Q8×C151—41no—
302Q8×C151—41no—
303Q8×C151—41no—
304Q8×C151AGL(1,ℤ/8)12yes—
305D4×C151—24no—
306D4×C151—21no—
307D4×C151—21no—
308D4×C151—21no—
309D4×C151—21no—
310D4×C151—42no—
311D4×C151—42no—
312D4×C151—44no—
313D4×C151—44no—
314D4×C151—44no—
315D4×C151—44no—
316D4×C151—44no—
317D4×C151—41no—
318D4×C151—41no—
319D4×C151—41no—
320D4×C151—41no—
321D4×C151—82no—
322D4×C151#13512yes—
323D4×C151AGL(1,ℤ/8)12yes—
324C2×C4×C151—24no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—21no—
329C2×C4×C151—21no—
330C2×C4×C151—21no—
331C2×C4×C151—22no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—21no—
335C2×C4×C151—41no—
336C2×C4×C151—44no—
337C2×C4×C151—44no—
338C2×C4×C151—42no—
339C2×C4×C151—44no—
340C2×C4×C151—42no—
341C2×C4×C151—42no—
342C2×C4×C151—44no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—81no—
352C2×C4×C151#12011yescharacteristic
353C2×C4×C151#12011yescharacteristic
354C2×C4×C151#12011yescharacteristic
355C2×C4×C151C22×D411yescharacteristic
356C2×C4×C151C22×D411yescharacteristic
357C2×C4×C151C22×D411yescharacteristic
358C8×C151—41no—
359C8×C151—41no—
360C8×C151—41no—
361C8×C151—41no—
362C8×C151—41no—
363C8×C151—41no—
364C22×C151—21no—
365C22×C151—22no—
366C22×C151—21no—
367C22×C151—22no—
368C22×C151—21no—
369C22×C151—41no—
370C22×C151—41no—
371C22×C151—41no—
372C22×C151—41no—
373C22×C151—41no—
374C22×C151—42no—
375C22×C151—42no—
376C22×C151—41no—
377C22×C151—42no—
378C22×C151—41no—
379C22×C151—84no—
380C22×C151—88no—
381C22×C151C2×#12011yescharacteristic
382C4×C151—21no—
383C4×C151—21no—
384C4×C151—22no—
385C4×C151—21no—
386C4×C151—21no—
387C4×C151—41no—
388C4×C151—41no—
389C4×C151—42no—
390C4×C151—41no—
391C4×C151—41no—
392C4×C151—81no—
393C4×C151—81no—
394C4×C151C2×#13511yescharacteristic
395C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
396C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
397C4×C151#57511yescharacteristic
398C2×C151—41no—
399C2×C151—42no—
400C2×C151—42no—
401C2×C151—81no—
402C2×C151—82no—
403C2×C151#300211yescharacteristic
404C2×C151#300311yescharacteristic
405C2×C151#302211yescharacteristic
406#18806C15111yesmaximal, characteristic, direct product factor, Sylow
407C151#1880611yescharacteristic, direct product factor, Sylow
408D4×#41C2×C15111yescharacteristic
409#3228C2×C15111yescharacteristic, complemented
410#3110C2×C15111yescharacteristic, complemented
411#3107C2×C15111yescharacteristic, complemented
412#1654C2×C15111yescharacteristic, complemented
413#1651C2×C15111yescharacteristic, complemented
414#1649C2×C15111yescharacteristic, complemented
415#1647C2×C15111yescharacteristic, complemented
416#1642C2×C15111yescharacteristic, complemented
417#1641C2×C15111yescharacteristic, complemented
418#1639C2×C15111yescharacteristic, complemented
419#1639C2×C15111yescharacteristic, complemented
420#1553C2×C15111yescharacteristic, complemented
421#1488C2×C15111yescharacteristic, complemented
422#1478C2×C15111yescharacteristic, complemented
423C22×#41—21no—
424#550C22×C15111yescharacteristic
425D4×Q8C22×C15111yescharacteristic
426#548—21no—
427#547—21no—
428#547C22×C15111yescharacteristic
429#546—22no—
430#546—21no—
431D42—21no—
432D42C22×C15111yescharacteristic
433#533C22×C15111yescharacteristic, complemented
434#532—21no—
435#532C22×C15111yescharacteristic
436#525—22no—
437#525—21no—
438C4×#41C22×C15111yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C15111yescharacteristic
441#500C22×C15111yescharacteristic, complemented
442#498C22×C15111yescharacteristic, complemented
443#486C22×C15111yescharacteristic, complemented
444#486C22×C15111yescharacteristic, complemented
445#485—21no—
446#484—21no—
447#482—22no—
448#478—22no—
449#475C22×C15111yescharacteristic, complemented
450#474C22×C15111yescharacteristic
451#474C22×C15111yescharacteristic, complemented
452#474C22×C15111yescharacteristic, complemented
453#462C22×C15111yescharacteristic, complemented
454#461C22×C15111yescharacteristic
455#461C22×C15111yescharacteristic, complemented
456#461C22×C15111yescharacteristic, complemented
457#452—21no—
458#450—21no—
459#440—21no—
460#440—21no—
461C4×Q16—21no—
462C4×SD16—21no—
463#432C22×C15111yescharacteristic, complemented
464#431C22×C15111yescharacteristic, complemented
465#431C22×C15111yescharacteristic, complemented
466#332C22×C15111yescharacteristic, complemented
467#332C22×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—22no—
479C2×#41—22no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—44no—
484C2×#41—44no—
485C2×#41D4×C15111yescharacteristic
486C22×Q8—21no—
487C22×D4—22no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4D4×C15111yescharacteristic
491C23×C4—22no—
492C23×C4—21no—
493C2×Q16—21no—
494C2×SD16—21no—
495C2×SD16—21no—
496C2×SD16—21no—
497C4⋊Q8—21no—
498C4⋊Q8C23×C15111yescharacteristic
499C4⋊Q8C23×C15111yescharacteristic
500C4⋊Q8C23×C15111yescharacteristic
501#127—21no—
502#127C23×C15111yescharacteristic
503#125—21no—
504#124—22no—
505#124—21no—
506#123—22no—
507#123—22no—
508#123—22no—
509C22⋊Q8—22no—
510C22⋊Q8—21no—
511C22⋊Q8—22no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515#121—22no—
516#121—22no—
517#121—22no—
518#121—21no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121D4×C15112yes—
524#120—22no—
525#120—22no—
526#120—22no—
527C4×Q8—21no—
528C4×Q8—21no—
529C4×Q8D4×C15111yescharacteristic
530C4×Q8C23×C15111yescharacteristic
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4D4×C15111yescharacteristic
542C4×D4D4×C15111yescharacteristic
543C4×D4D4×C15111yescharacteristic
544C4×D4D4×C15112yes—
545C4×D4C23×C15111yescharacteristic
546C4×D4C23×C15111yescharacteristic
547C4×D4C23×C15111yescharacteristic
548#117—21no—
549#117—21no—
550#117D4×C15111yescharacteristic
551C2×C4⋊C4—21no—
552C2×C4⋊C4D4×C15111yescharacteristic
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C42—21no—
556C2×C42C23×C15111yescharacteristic
557#107—21no—
558#107—21no—
559#107—21no—
560#107—22no—
561#106—21no—
562#106—22no—
563C4⋊C8—21no—
564C4⋊C8C23×C15111yescharacteristic
565C4⋊C8C23×C15111yescharacteristic
566C4⋊C8C23×C15111yescharacteristic
567C4⋊C8C23×C15111yescharacteristic
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#103—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—22no—
577#102—22no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581#97—21no—
582C4×C8—21no—
583C4×C8C23×C15111yescharacteristic
584C4×C8C23×C15111yescharacteristic
585C24—22no—
586C24—21no—
587#41—22no—
588#41—22no—
589#41—48no—
590#41—42no—
591#41—42no—
592#41—48no—
593#41—42no—
594#41—42no—
595#41—42no—
596#41—42no—
597C2×Q8—22no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—42no—
602C2×Q8—42no—
603C2×Q8C2×D4×C15111yescharacteristic
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—41no—
616C2×D4—48no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4C2×D4×C15111yescharacteristic
622C2×D4C2×D4×C15111yescharacteristic
623C2×D4C2×D4×C15111yescharacteristic
624C2×D4C2×D4×C15112yes—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—48no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4C2×D4×C15111yescharacteristic
641C22×C4C2×D4×C15111yescharacteristic
642C22×C4C2×D4×C15111yescharacteristic
643Q16—42no—
644SD16—42no—
645SD16—42no—
646SD16—42no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4C2×D4×C15111yescharacteristic
666C4⋊C4C2×D4×C15111yescharacteristic
667C4⋊C4C2×D4×C15111yescharacteristic
668C4⋊C4C2×D4×C15111yescharacteristic
669C4⋊C4C2×D4×C15112yes—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—22no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—22no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—41no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—41no—
688C42C2×D4×C15111yescharacteristic
689C42C2×D4×C15111yescharacteristic
690C42C2×D4×C15111yescharacteristic
691C42C24×C15111yescharacteristic
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—44no—
700C23—81no—
701C23—82no—
702C23#120×C15111yescharacteristic
703Q8—21no—
704Q8—44no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711Q8AGL(1,ℤ/8)×C15112yes—
712D4—24no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—42no—
718D4—42no—
719D4—44no—
720D4—44no—
721D4—44no—
722D4—44no—
723D4—44no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—82no—
729D4#135×C15112yes—
730D4AGL(1,ℤ/8)×C15112yes—
731C2×C4—24no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—81no—
759C2×C4#120×C15111yescharacteristic
760C2×C4#120×C15111yescharacteristic
761C2×C4#120×C15111yescharacteristic
762C2×C4C22×D4×C15111yescharacteristic
763C2×C4C22×D4×C15111yescharacteristic
764C2×C4C22×D4×C15111yescharacteristic
765C8—41no—
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C22—21no—
772C22—22no—
773C22—21no—
774C22—22no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—41no—
784C22—42no—
785C22—41no—
786C22—84no—
787C22—88no—
788C22C2×#120×C15111yescharacteristic
789C4—21no—
790C4—21no—
791C4—22no—
792C4—21no—
793C4—21no—
794C4—41no—
795C4—41no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—81no—
800C4—81no—
801C4C2×#135×C15111yescharacteristic
802C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
803C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
804C4#575×C15111yescharacteristic
805C2—41no—
806C2—42no—
807C2—42no—
808C2—81no—
809C2—82no—
810C2#3002×C15111yescharacteristic
811C2#3003×C15111yescharacteristic
812C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalD4×#41×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. #3228×C151C2semidirect
3. #3110×C151C2semidirect
4. #3107×C151C2semidirect
5. #1654×C151C2semidirect
6. #1651×C151C2semidirect
7. #1649×C151C2semidirect
8. #1647×C151C2semidirect
9. #1642×C151C2semidirect
10. #1641×C151C2semidirect
11. #1639×C151C2semidirect
12. #1639×C151C2semidirect
13. #1553×C151C2semidirect
14. #1488×C151C2semidirect
15. #1478×C151C2semidirect
26. #533×C151C22semidirect
34. #500×C151C22semidirect
35. #498×C151C22semidirect
36. #486×C151C22semidirect
37. #486×C151C22semidirect
42. #475×C151C22semidirect
44. #474×C151C22semidirect
45. #474×C151C22semidirect
46. #462×C151C22semidirect
48. #461×C151C22semidirect
49. #461×C151C22semidirect
56. #432×C151C22semidirect
57. #431×C151C22semidirect
58. #431×C151C22semidirect
59. #332×C151C22semidirect
60. #332×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. #18806C151direct (N × H)
407. C151#18806direct (N × H)
409. #3228C2×C151semidirect
410. #3110C2×C151semidirect
411. #3107C2×C151semidirect
412. #1654C2×C151semidirect
413. #1651C2×C151semidirect
414. #1649C2×C151semidirect
415. #1647C2×C151semidirect
416. #1642C2×C151semidirect
417. #1641C2×C151semidirect
418. #1639C2×C151semidirect
419. #1639C2×C151semidirect
420. #1553C2×C151semidirect
421. #1488C2×C151semidirect
422. #1478C2×C151semidirect
433. #533C22×C151semidirect
441. #500C22×C151semidirect
442. #498C22×C151semidirect
443. #486C22×C151semidirect
444. #486C22×C151semidirect
449. #475C22×C151semidirect
451. #474C22×C151semidirect
452. #474C22×C151semidirect
453. #462C22×C151semidirect
455. #461C22×C151semidirect
456. #461C22×C151semidirect
463. #432C22×C151semidirect
464. #431C22×C151semidirect
465. #431C22×C151semidirect
466. #332C22×C151semidirect
467. #332C22×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
D4×#41×C1512
#3228×C1512
#3110×C1512
#3107×C1512
#1654×C1512
#1651×C1512
#1649×C1512
#1647×C1512
#1642×C1512
#1641×C1512
#1639×C1512
#1553×C1512
#1488×C1512
#1478×C1512
#18806151