Finite Group Databasebeta

← C151×#18794 #50323719

Subgroups — C151×#18794 #50323719

Order 38656.

1214 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#41×C151C211yesmaximal, characteristic, complemented
2#3207×C151C211yesmaximal, characteristic, complemented
3#3109×C151C211yesmaximal, characteristic, complemented
4#3106×C151C211yesmaximal, characteristic, complemented
5#1637×C151C211yesmaximal, characteristic, complemented
6#1635×C151C211yesmaximal, characteristic, complemented
7#1631×C151C211yesmaximal, characteristic, complemented
8#1629×C151C211yesmaximal, characteristic, complemented
9#1627×C151C211yesmaximal, characteristic, complemented
10#1625×C151C211yesmaximal, characteristic, complemented
11#1621×C151C211yesmaximal, characteristic, complemented
12#1619×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#532×C151—21no—
27#532×C151C2211yescharacteristic
28#532×C151C2211yescharacteristic, complemented
29#525×C151—22no—
30#525×C151—21no—
31C4×#41×C151C2211yescharacteristic
32C2×C4×D4×C151—21no—
33C2×C4×D4×C151C2211yescharacteristic
34#493×C151C2211yescharacteristic, complemented
35#492×C151C2211yescharacteristic, complemented
36#487×C151C2211yescharacteristic, complemented
37#486×C151C2211yescharacteristic, complemented
38#482×C151—21no—
39#481×C151—21no—
40#477×C151C2211yescharacteristic, complemented
41#476×C151C2211yescharacteristic
42#476×C151C2211yescharacteristic, complemented
43#476×C151C2211yescharacteristic, complemented
44#463×C151—22no—
45#460×C151C2211yescharacteristic, complemented
46#459×C151C2211yescharacteristic
47#459×C151C2211yescharacteristic, complemented
48#459×C151C2211yescharacteristic, complemented
49#449×C151—21no—
50#449×C151—22no—
51#447×C151—21no—
52#442×C151—21no—
53#442×C151—21no—
54C4×SD16×C151—21no—
55C4×D8×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—21no—
77C2×#41×C151—44no—
78C2×#41×C151—44no—
79C2×#41×C151D411yescharacteristic
80C22×Q8×C151—21no—
81C22×D4×C151—22no—
82C22×D4×C151—21no—
83C22×D4×C151—21no—
84C22×D4×C151D411yescharacteristic
85C23×C4×C151—22no—
86C23×C4×C151—21no—
87C2×SD16×C151—22no—
88C2×SD16×C151—21no—
89C2×D8×C151—21no—
90C2×D8×C151—21no—
91C2×D8×C151—21no—
92C2×D8×C151—22no—
93C4⋊Q8×C151—21no—
94C4⋊Q8×C151C2311yescharacteristic
95C4⋊Q8×C151C2311yescharacteristic
96#127×C151—21no—
97#127×C151C2311yescharacteristic
98#127×C151C2311yescharacteristic
99#124×C151—22no—
100#124×C151—21no—
101#124×C151—21no—
102#123×C151—22no—
103#123×C151—22no—
104#123×C151—22no—
105C22⋊Q8×C151—22no—
106C22⋊Q8×C151—22no—
107C22⋊Q8×C151—21no—
108C22⋊Q8×C151—21no—
109#121×C151—22no—
110#121×C151—22no—
111#121×C151—22no—
112#121×C151—21no—
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×C151D412yes—
120#120×C151—22no—
121#120×C151—22no—
122#120×C151—22no—
123C4×Q8×C151D411yescharacteristic
124C4×Q8×C151C2311yescharacteristic
125C4×D4×C151—22no—
126C4×D4×C151—22no—
127C4×D4×C151—22no—
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×C151—21no—
135C4×D4×C151—21no—
136C4×D4×C151—21no—
137C4×D4×C151D411yescharacteristic
138C4×D4×C151D411yescharacteristic
139C4×D4×C151D411yescharacteristic
140C4×D4×C151D412yes—
141C4×D4×C151C2311yescharacteristic
142C4×D4×C151C2311yescharacteristic
143C4×D4×C151C2311yescharacteristic
144#117×C151—21no—
145#117×C151D411yescharacteristic
146C2×C4⋊C4×C151—21no—
147C2×C4⋊C4×C151D411yescharacteristic
148C2×C22⋊C4×C151—22no—
149C2×C22⋊C4×C151—21no—
150C2×C42×C151—21no—
151C2×C42×C151C2311yescharacteristic
152#107×C151—21no—
153#106×C151—21no—
154#106×C151—21no—
155#106×C151—21no—
156C4⋊C8×C151—21no—
157C4⋊C8×C151C2311yescharacteristic
158C4⋊C8×C151C2311yescharacteristic
159C4⋊C8×C151C2311yescharacteristic
160C4⋊C8×C151C2311yescharacteristic
161#103×C151—22no—
162#103×C151—21no—
163#102×C151—21no—
164#102×C151—21no—
165#102×C151—21no—
166#102×C151—21no—
167#102×C151—21no—
168#102×C151—21no—
169#102×C151—21no—
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—
190#41×C151—82no—
191C2×Q8×C151—22no—
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—21no—
209C2×D4×C151—21no—
210C2×D4×C151—21no—
211C2×D4×C151—41no—
212C2×D4×C151—42no—
213C2×D4×C151—48no—
214C2×D4×C151—42no—
215C2×D4×C151—42no—
216C2×D4×C151—42no—
217C2×D4×C151—41no—
218C2×D4×C151C2×D411yescharacteristic
219C2×D4×C151C2×D411yescharacteristic
220C2×D4×C151C2×D411yescharacteristic
221C2×D4×C151C2×D412yes—
222C22×C4×C151—21no—
223C22×C4×C151—22no—
224C22×C4×C151—22no—
225C22×C4×C151—22no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—22no—
229C22×C4×C151—21no—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—48no—
235C22×C4×C151—42no—
236C22×C4×C151—42no—
237C22×C4×C151—41no—
238C22×C4×C151C2×D411yescharacteristic
239C22×C4×C151C2×D411yescharacteristic
240C22×C4×C151C2×D411yescharacteristic
241SD16×C151—42no—
242SD16×C151—82no—
243D8×C151—42no—
244D8×C151—42no—
245D8×C151—42no—
246D8×C151—82no—
247C2×C8×C151—21no—
248C2×C8×C151—21no—
249C2×C8×C151—21no—
250C2×C8×C151—21no—
251C2×C8×C151—21no—
252C2×C8×C151—21no—
253C4⋊C4×C151—22no—
254C4⋊C4×C151—22no—
255C4⋊C4×C151—21no—
256C4⋊C4×C151—21no—
257C4⋊C4×C151—21no—
258C4⋊C4×C151—21no—
259C4⋊C4×C151—21no—
260C4⋊C4×C151—21no—
261C4⋊C4×C151C2×D412yes—
262C4⋊C4×C151C2×D411yescharacteristic
263C4⋊C4×C151C2×D411yescharacteristic
264C4⋊C4×C151C2×D411yescharacteristic
265C4⋊C4×C151C2×D411yescharacteristic
266C22⋊C4×C151—22no—
267C22⋊C4×C151—22no—
268C22⋊C4×C151—22no—
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—22no—
276C22⋊C4×C151—21no—
277C22⋊C4×C151—21no—
278C22⋊C4×C151—21no—
279C22⋊C4×C151—41no—
280C22⋊C4×C151—41no—
281C42×C151—21no—
282C42×C151—21no—
283C42×C151—21no—
284C42×C151C2×D411yescharacteristic
285C42×C151C2×D411yescharacteristic
286C42×C151C2×D411yescharacteristic
287C42×C151C2411yescharacteristic
288C23×C151—21no—
289C23×C151—21no—
290C23×C151—21no—
291C23×C151—22no—
292C23×C151—42no—
293C23×C151—42no—
294C23×C151—44no—
295C23×C151—44no—
296C23×C151—41no—
297C23×C151—81no—
298C23×C151—82no—
299C23×C151#12011yescharacteristic
300Q8×C151—21no—
301Q8×C151—44no—
302Q8×C151—42no—
303Q8×C151—41no—
304Q8×C151—41no—
305Q8×C151AGL(1,ℤ/8)12yes—
306D4×C151—24no—
307D4×C151—21no—
308D4×C151—21no—
309D4×C151—21no—
310D4×C151—21no—
311D4×C151—42no—
312D4×C151—42no—
313D4×C151—44no—
314D4×C151—42no—
315D4×C151—44no—
316D4×C151—44no—
317D4×C151—44no—
318D4×C151—44no—
319D4×C151—41no—
320D4×C151—41no—
321D4×C151—41no—
322D4×C151—41no—
323D4×C151—41no—
324D4×C151—41no—
325D4×C151—41no—
326D4×C151—41no—
327D4×C151—82no—
328D4×C151—82no—
329D4×C151#13512yes—
330D4×C151AGL(1,ℤ/8)12yes—
331C2×C4×C151—24no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—21no—
335C2×C4×C151—21no—
336C2×C4×C151—21no—
337C2×C4×C151—21no—
338C2×C4×C151—22no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—21no—
342C2×C4×C151—41no—
343C2×C4×C151—44no—
344C2×C4×C151—44no—
345C2×C4×C151—42no—
346C2×C4×C151—44no—
347C2×C4×C151—42no—
348C2×C4×C151—42no—
349C2×C4×C151—44no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—81no—
358C2×C4×C151—82no—
359C2×C4×C151#12011yescharacteristic
360C2×C4×C151#12011yescharacteristic
361C2×C4×C151#12011yescharacteristic
362C2×C4×C151C22×D411yescharacteristic
363C2×C4×C151C22×D411yescharacteristic
364C2×C4×C151C22×D411yescharacteristic
365C8×C151—41no—
366C8×C151—41no—
367C8×C151—41no—
368C8×C151—41no—
369C8×C151—41no—
370C8×C151—41no—
371C22×C151—21no—
372C22×C151—22no—
373C22×C151—21no—
374C22×C151—22no—
375C22×C151—21no—
376C22×C151—41no—
377C22×C151—41no—
378C22×C151—41no—
379C22×C151—41no—
380C22×C151—41no—
381C22×C151—42no—
382C22×C151—42no—
383C22×C151—41no—
384C22×C151—42no—
385C22×C151—41no—
386C22×C151—84no—
387C22×C151—88no—
388C22×C151—81no—
389C22×C151—81no—
390C22×C151—81no—
391C22×C151C2×#12011yescharacteristic
392C4×C151—21no—
393C4×C151—21no—
394C4×C151—22no—
395C4×C151—21no—
396C4×C151—21no—
397C4×C151—41no—
398C4×C151—41no—
399C4×C151—42no—
400C4×C151—41no—
401C4×C151—41no—
402C4×C151—81no—
403C4×C151C2×#13511yescharacteristic
404C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
405C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
406C4×C151#57511yescharacteristic
407C2×C151—41no—
408C2×C151—42no—
409C2×C151—42no—
410C2×C151—81no—
411C2×C151—82no—
412C2×C151—161no—
413C2×C151#300211yescharacteristic
414C2×C151#300311yescharacteristic
415C2×C151#302111yescharacteristic
416#18794C15111yesmaximal, characteristic, direct product factor, Sylow
417C151#1879411yescharacteristic, direct product factor, Sylow
418D4×#41C2×C15111yescharacteristic, complemented
419#3207C2×C15111yescharacteristic, complemented
420#3109C2×C15111yescharacteristic, complemented
421#3106C2×C15111yescharacteristic, complemented
422#1637C2×C15111yescharacteristic, complemented
423#1635C2×C15111yescharacteristic, complemented
424#1631C2×C15111yescharacteristic, complemented
425#1629C2×C15111yescharacteristic, complemented
426#1627C2×C15111yescharacteristic, complemented
427#1625C2×C15111yescharacteristic, complemented
428#1621C2×C15111yescharacteristic, complemented
429#1619C2×C15111yescharacteristic, complemented
430#1553C2×C15111yescharacteristic, complemented
431#1488C2×C15111yescharacteristic, complemented
432#1478C2×C15111yescharacteristic, complemented
433C22×#41—21no—
434#550C22×C15111yescharacteristic
435D4×Q8C22×C15111yescharacteristic
436#548—21no—
437#547—21no—
438#547C22×C15111yescharacteristic
439#546—22no—
440#546—21no—
441D42—21no—
442D42C22×C15111yescharacteristic
443#532—21no—
444#532C22×C15111yescharacteristic
445#532C22×C15111yescharacteristic, complemented
446#525—22no—
447#525—21no—
448C4×#41C22×C15111yescharacteristic
449C2×C4×D4—21no—
450C2×C4×D4C22×C15111yescharacteristic
451#493C22×C15111yescharacteristic, complemented
452#492C22×C15111yescharacteristic, complemented
453#487C22×C15111yescharacteristic, complemented
454#486C22×C15111yescharacteristic, complemented
455#482—21no—
456#481—21no—
457#477C22×C15111yescharacteristic, complemented
458#476C22×C15111yescharacteristic
459#476C22×C15111yescharacteristic, complemented
460#476C22×C15111yescharacteristic, complemented
461#463—22no—
462#460C22×C15111yescharacteristic, complemented
463#459C22×C15111yescharacteristic
464#459C22×C15111yescharacteristic, complemented
465#459C22×C15111yescharacteristic, complemented
466#449—21no—
467#449—22no—
468#447—21no—
469#442—21no—
470#442—21no—
471C4×SD16—21no—
472C4×D8—21no—
473#432C22×C15111yescharacteristic, complemented
474#431C22×C15111yescharacteristic, complemented
475#431C22×C15111yescharacteristic, complemented
476#332C22×C15111yescharacteristic, complemented
477#332C22×C15111yescharacteristic, complemented
478#331C22×C15111yescharacteristic, complemented
479#331C22×C15111yescharacteristic, complemented
480Q8⋊C8C22×C15111yescharacteristic, complemented
481Q8⋊C8C22×C15111yescharacteristic, complemented
482D4⋊C8C22×C15111yescharacteristic
483D4⋊C8C22×C15111yescharacteristic
484D4⋊C8C22×C15111yescharacteristic, complemented
485D4⋊C8C22×C15111yescharacteristic, complemented
486D4⋊C8C22×C15111yescharacteristic, complemented
487D4⋊C8C22×C15111yescharacteristic, complemented
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—44no—
495C2×#41—44no—
496C2×#41D4×C15111yescharacteristic
497C22×Q8—21no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4D4×C15111yescharacteristic
502C23×C4—22no—
503C23×C4—21no—
504C2×SD16—21no—
505C2×SD16—22no—
506C2×D8—21no—
507C2×D8—21no—
508C2×D8—21no—
509C2×D8—22no—
510C4⋊Q8—21no—
511C4⋊Q8C23×C15111yescharacteristic
512C4⋊Q8C23×C15111yescharacteristic
513#127—21no—
514#127C23×C15111yescharacteristic
515#127C23×C15111yescharacteristic
516#124—22no—
517#124—21no—
518#124—21no—
519#123—22no—
520#123—22no—
521#123—22no—
522C22⋊Q8—22no—
523C22⋊Q8—21no—
524C22⋊Q8—22no—
525C22⋊Q8—21no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121—21no—
530#121—21no—
531#121—21no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121—21no—
536#121D4×C15112yes—
537#120—22no—
538#120—22no—
539#120—22no—
540C4×Q8D4×C15111yescharacteristic
541C4×Q8C23×C15111yescharacteristic
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4D4×C15111yescharacteristic
555C4×D4D4×C15111yescharacteristic
556C4×D4D4×C15111yescharacteristic
557C4×D4D4×C15112yes—
558C4×D4C23×C15111yescharacteristic
559C4×D4C23×C15111yescharacteristic
560C4×D4C23×C15111yescharacteristic
561#117—21no—
562#117D4×C15111yescharacteristic
563C2×C4⋊C4—21no—
564C2×C4⋊C4D4×C15111yescharacteristic
565C2×C22⋊C4—22no—
566C2×C22⋊C4—21no—
567C2×C42—21no—
568C2×C42C23×C15111yescharacteristic
569#107—21no—
570#106—21no—
571#106—21no—
572#106—21no—
573C4⋊C8—21no—
574C4⋊C8C23×C15111yescharacteristic
575C4⋊C8C23×C15111yescharacteristic
576C4⋊C8C23×C15111yescharacteristic
577C4⋊C8C23×C15111yescharacteristic
578#103—21no—
579#103—22no—
580#102—21no—
581#102—21no—
582#102—21no—
583#102—21no—
584#102—21no—
585#102—21no—
586#102—21no—
587#102—22no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591#97—21no—
592C4×C8—21no—
593C4×C8C23×C15111yescharacteristic
594C4×C8C23×C15111yescharacteristic
595C24—22no—
596C24—21no—
597#41—22no—
598#41—22no—
599#41—48no—
600#41—42no—
601#41—42no—
602#41—48no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—82no—
608C2×Q8—22no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—42no—
612C2×Q8—42no—
613C2×Q8C2×D4×C15111yescharacteristic
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—48no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—41no—
635C2×D4C2×D4×C15111yescharacteristic
636C2×D4C2×D4×C15111yescharacteristic
637C2×D4C2×D4×C15111yescharacteristic
638C2×D4C2×D4×C15112yes—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—22no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—48no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—41no—
655C22×C4C2×D4×C15111yescharacteristic
656C22×C4C2×D4×C15111yescharacteristic
657C22×C4C2×D4×C15111yescharacteristic
658SD16—42no—
659SD16—82no—
660D8—42no—
661D8—42no—
662D8—42no—
663D8—82no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4C2×D4×C15112yes—
679C4⋊C4C2×D4×C15111yescharacteristic
680C4⋊C4C2×D4×C15111yescharacteristic
681C4⋊C4C2×D4×C15111yescharacteristic
682C4⋊C4C2×D4×C15111yescharacteristic
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—22no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—22no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42C2×D4×C15111yescharacteristic
702C42C2×D4×C15111yescharacteristic
703C42C2×D4×C15111yescharacteristic
704C42C24×C15111yescharacteristic
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—42no—
710C23—42no—
711C23—44no—
712C23—44no—
713C23—41no—
714C23—81no—
715C23—82no—
716C23#120×C15111yescharacteristic
717Q8—21no—
718Q8—44no—
719Q8—42no—
720Q8—41no—
721Q8—41no—
722Q8AGL(1,ℤ/8)×C15112yes—
723D4—24no—
724D4—21no—
725D4—21no—
726D4—21no—
727D4—21no—
728D4—42no—
729D4—42no—
730D4—44no—
731D4—42no—
732D4—44no—
733D4—44no—
734D4—44no—
735D4—44no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—82no—
745D4—82no—
746D4#135×C15112yes—
747D4AGL(1,ℤ/8)×C15112yes—
748C2×C4—24no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4#120×C15111yescharacteristic
777C2×C4#120×C15111yescharacteristic
778C2×C4#120×C15111yescharacteristic
779C2×C4C22×D4×C15111yescharacteristic
780C2×C4C22×D4×C15111yescharacteristic
781C2×C4C22×D4×C15111yescharacteristic
782C8—41no—
783C8—41no—
784C8—41no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—21no—
789C22—22no—
790C22—21no—
791C22—22no—
792C22—21no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—42no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—84no—
804C22—88no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22C2×#120×C15111yescharacteristic
809C4—21no—
810C4—21no—
811C4—22no—
812C4—21no—
813C4—21no—
814C4—41no—
815C4—41no—
816C4—42no—
817C4—41no—
818C4—41no—
819C4—81no—
820C4C2×#135×C15111yescharacteristic
821C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
822C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
823C4#575×C15111yescharacteristic
824C2—41no—
825C2—42no—
826C2—42no—
827C2—81no—
828C2—82no—
829C2—161no—
830C2#3002×C15111yescharacteristic
831C2#3003×C15111yescharacteristic
832C2#3021×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. D4×#41×C151C2semidirect
2. #3207×C151C2semidirect
3. #3109×C151C2semidirect
4. #3106×C151C2semidirect
5. #1637×C151C2semidirect
6. #1635×C151C2semidirect
7. #1631×C151C2semidirect
8. #1629×C151C2semidirect
9. #1627×C151C2semidirect
10. #1625×C151C2semidirect
11. #1621×C151C2semidirect
12. #1619×C151C2semidirect
13. #1553×C151C2semidirect
14. #1488×C151C2semidirect
15. #1478×C151C2semidirect
28. #532×C151C22semidirect
34. #493×C151C22semidirect
35. #492×C151C22semidirect
36. #487×C151C22semidirect
37. #486×C151C22semidirect
40. #477×C151C22semidirect
42. #476×C151C22semidirect
43. #476×C151C22semidirect
45. #460×C151C22semidirect
47. #459×C151C22semidirect
48. #459×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
416. #18794C151direct (N × H)
417. C151#18794direct (N × H)
418. D4×#41C2×C151semidirect
419. #3207C2×C151semidirect
420. #3109C2×C151semidirect
421. #3106C2×C151semidirect
422. #1637C2×C151semidirect
423. #1635C2×C151semidirect
424. #1631C2×C151semidirect
425. #1629C2×C151semidirect
426. #1627C2×C151semidirect
427. #1625C2×C151semidirect
428. #1621C2×C151semidirect
429. #1619C2×C151semidirect
430. #1553C2×C151semidirect
431. #1488C2×C151semidirect
432. #1478C2×C151semidirect
445. #532C22×C151semidirect
451. #493C22×C151semidirect
452. #492C22×C151semidirect
453. #487C22×C151semidirect
454. #486C22×C151semidirect
457. #477C22×C151semidirect
459. #476C22×C151semidirect
460. #476C22×C151semidirect
462. #460C22×C151semidirect
464. #459C22×C151semidirect
465. #459C22×C151semidirect
473. #432C22×C151semidirect
474. #431C22×C151semidirect
475. #431C22×C151semidirect
476. #332C22×C151semidirect
477. #332C22×C151semidirect
478. #331C22×C151semidirect
479. #331C22×C151semidirect
480. Q8⋊C8C22×C151semidirect
481. Q8⋊C8C22×C151semidirect
484. D4⋊C8C22×C151semidirect
485. D4⋊C8C22×C151semidirect
486. D4⋊C8C22×C151semidirect
487. 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
#3207×C1512
#3109×C1512
#3106×C1512
#1637×C1512
#1635×C1512
#1631×C1512
#1629×C1512
#1627×C1512
#1625×C1512
#1621×C1512
#1619×C1512
#1553×C1512
#1488×C1512
#1478×C1512
#18794151