Finite Group Databasebeta

← C151×#24324 #50329249

Subgroups — C151×#24324 #50329249

Order 38656.

1008 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3504×C151C211yesmaximal, characteristic, complemented
2#3077×C151C211yesmaximal, characteristic, complemented
3C4×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic
4#2566×C151C211yesmaximal, characteristic, complemented
5#2061×C151C211yesmaximal, characteristic, complemented
6#2060×C151C211yesmaximal, characteristic, complemented
7#2027×C151C211yesmaximal, characteristic, complemented
8#2027×C151C211yesmaximal, characteristic, complemented
9#1998×C151C211yesmaximal, characteristic, complemented
10#1986×C151C211yesmaximal, characteristic, complemented
11#1883×C151C211yesmaximal, characteristic
12#1883×C151C211yesmaximal, characteristic
13#1860×C151C211yesmaximal, characteristic, complemented
14#1859×C151C211yesmaximal, characteristic, complemented
15#1806×C151C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
17#557×C151—21no—
18#557×C151—21no—
19#554×C151—21no—
20#554×C151—21no—
21#554×C151—22no—
22#554×C151—22no—
23#544×C151—21no—
24#544×C151—21no—
25#544×C151C2211yescharacteristic
26#544×C151C2211yescharacteristic
27#533×C151—21no—
28#533×C151C2211yescharacteristic
29C2×#125×C151—21no—
30C2×#125×C151C2211yescharacteristic
31#520×C151C2211yescharacteristic
32#520×C151C2211yescharacteristic
33C4×#41×C151C2211yescharacteristic
34C2×C4×D4×C151C2211yescharacteristic
35#478×C151—21no—
36#478×C151—21no—
37#476×C151—21no—
38#474×C151—21no—
39#442×C151—21no—
40#440×C151—21no—
41C4×SD16×C151—21no—
42C4×D8×C151—21no—
43#428×C151C2211yescharacteristic
44#428×C151C2211yescharacteristic
45#428×C151C2211yescharacteristic
46#423×C151C2211yescharacteristic
47C2×#104×C151C2211yescharacteristic
48C2×#104×C151C2211yescharacteristic
49#418×C151C2211yescharacteristic
50#418×C151C2211yescharacteristic
51#418×C151C2211yescharacteristic
52#417×C151C2211yescharacteristic
53C4×M16×C151C2211yescharacteristic
54#396×C151—22no—
55#390×C151C2211yescharacteristic
56#390×C151C2211yescharacteristic
57#385×C151—22no—
58#384×C151C2211yescharacteristic
59#382×C151C2211yescharacteristic
60C4×C4⋊C4×C151C2211yescharacteristic
61#343×C151C2211yescharacteristic
62#343×C151C2211yescharacteristic
63#343×C151C2211yescharacteristic
64#343×C151C2211yescharacteristic
65#339×C151C2211yescharacteristic
66#339×C151C2211yescharacteristic
67#339×C151C2211yescharacteristic
68#339×C151C2211yescharacteristic
69#339×C151C2211yescharacteristic
70#339×C151C2211yescharacteristic
71C2×#41×C151C2311yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C23×C4×C151—21no—
74AGL(1,ℤ/8)×C151—22no—
75AGL(1,ℤ/8)×C151Q814yescomplemented
76C2×SD16×C151—21no—
77C2×D8×C151—21no—
78C2×M16×C151C2311yescharacteristic
79C2×M16×C151C2311yescharacteristic
80C2×M16×C151C2311yescharacteristic
81C2×M16×C151C2311yescharacteristic
82C4⋊Q8×C151—22no—
83C4⋊Q8×C151—22no—
84C4⋊Q8×C151—21no—
85C4⋊Q8×C151—21no—
86C4⋊Q8×C151—21no—
87C4⋊Q8×C151—21no—
88C4⋊Q8×C151D411yescharacteristic
89C4⋊Q8×C151D411yescharacteristic
90#125×C151—22no—
91#125×C151—22no—
92#125×C151—22no—
93#125×C151—22no—
94#125×C151—21no—
95#125×C151—21no—
96#125×C151—21no—
97#125×C151—21no—
98#125×C151—21no—
99#125×C151—21no—
100#125×C151—21no—
101#125×C151—21no—
102#125×C151D411yescharacteristic
103#125×C151D411yescharacteristic
104C22⋊Q8×C151—22no—
105C22⋊Q8×C151—22no—
106C22⋊Q8×C151—22no—
107C22⋊Q8×C151—22no—
108C22⋊Q8×C151—22no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—21no—
111C22⋊Q8×C151—21no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C4×Q8×C151—22no—
115C4×Q8×C151—22no—
116C4×Q8×C151—21no—
117C4×Q8×C151—21no—
118C4×Q8×C151—21no—
119C4×Q8×C151—21no—
120C4×Q8×C151D411yescharacteristic
121C4×Q8×C151D411yescharacteristic
122C4×D4×C151—21no—
123C4×D4×C151—21no—
124C4×D4×C151—21no—
125C4×D4×C151—21no—
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×C151D411yescharacteristic
133C4×D4×C151D411yescharacteristic
134#117×C151—21no—
135#117×C151—21no—
136#117×C151—21no—
137#117×C151C2311yescharacteristic
138#117×C151C2311yescharacteristic
139#117×C151C2311yescharacteristic
140C2×C4⋊C4×C151—22no—
141C2×C4⋊C4×C151—22no—
142C2×C4⋊C4×C151—21no—
143C2×C4⋊C4×C151—21no—
144C2×C4⋊C4×C151—21no—
145C2×C4⋊C4×C151—22no—
146C2×C4⋊C4×C151D412yes—
147C2×C4⋊C4×C151D412yes—
148C2×C4⋊C4×C151C2311yescharacteristic
149C2×C4⋊C4×C151C2311yescharacteristic
150C2×C4⋊C4×C151C2311yescharacteristic
151C2×C22⋊C4×C151—22no—
152C2×C22⋊C4×C151—21no—
153C2×C22⋊C4×C151—22no—
154C2×C42×C151—21no—
155C2×C42×C151C2311yescharacteristic
156C2×C42×C151C2311yescharacteristic
157C2×C42×C151C2311yescharacteristic
158#107×C151—21no—
159#107×C151—21no—
160#107×C151—21no—
161#106×C151—21no—
162#106×C151—21no—
163#106×C151—21no—
164C4⋊C8×C151—21no—
165C4⋊C8×C151—21no—
166#104×C151—22no—
167#104×C151—22no—
168#103×C151—21no—
169#102×C151—21no—
170#102×C151—21no—
171#102×C151—21no—
172#102×C151—21no—
173#102×C151—21no—
174#102×C151—21no—
175#102×C151—21no—
176#97×C151—21no—
177C4×C8×C151—21no—
178#95×C151—21no—
179#95×C151—22no—
180C24×C151—21no—
181#41×C151—21no—
182#41×C151—21no—
183#41×C151C2×Q812yes—
184#41×C151#4112yes—
185C2×Q8×C151—22no—
186C2×Q8×C151—22no—
187C2×Q8×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151C2×D411yescharacteristic
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151C2×D411yescharacteristic
197C2×D4×C151C2×Q812yes—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—22no—
201C22×C4×C151—22no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—41no—
207C22×C4×C151—41no—
208C22×C4×C151—82no—
209C22×C4×C151C2×D412yes—
210C22×C4×C151C2×D412yes—
211C22×C4×C151C2×D411yescharacteristic
212C22×C4×C151C2×D411yescharacteristic
213C22×C4×C151C2411yescharacteristic
214SD16×C151—24no—
215D8×C151—24no—
216M16×C151—21no—
217M16×C151—21no—
218M16×C151—21no—
219M16×C151—21no—
220M16×C151—21no—
221M16×C151—21no—
222M16×C151—21no—
223M16×C151C2×Q812yes—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C4⋊C4×C151—22no—
229C4⋊C4×C151—22no—
230C4⋊C4×C151—22no—
231C4⋊C4×C151—22no—
232C4⋊C4×C151—22no—
233C4⋊C4×C151—22no—
234C4⋊C4×C151—22no—
235C4⋊C4×C151—22no—
236C4⋊C4×C151—21no—
237C4⋊C4×C151—21no—
238C4⋊C4×C151—22no—
239C4⋊C4×C151—22no—
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×C151—21no—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—21no—
254C4⋊C4×C151—42no—
255C4⋊C4×C151—82no—
256C4⋊C4×C151C2×D411yescharacteristic
257C4⋊C4×C151C2×D411yescharacteristic
258C4⋊C4×C151C2×D411yescharacteristic
259C4⋊C4×C151C2×D411yescharacteristic
260C4⋊C4×C151C2×D411yescharacteristic
261C4⋊C4×C151C2×D411yescharacteristic
262C22⋊C4×C151—22no—
263C22⋊C4×C151—22no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—21no—
266C22⋊C4×C151—21no—
267C22⋊C4×C151—21no—
268C22⋊C4×C151—21no—
269C22⋊C4×C151—44no—
270C22⋊C4×C151—41no—
271C22⋊C4×C151—41no—
272C22⋊C4×C151—82no—
273C42×C151—22no—
274C42×C151—22no—
275C42×C151—21no—
276C42×C151—21no—
277C42×C151—21no—
278C42×C151—21no—
279C42×C151—21no—
280C42×C151—21no—
281C42×C151—21no—
282C42×C151—21no—
283C42×C151—21no—
284C42×C151C2×D411yescharacteristic
285C42×C151C2×D411yescharacteristic
286C42×C151C2×D411yescharacteristic
287C42×C151C2×D411yescharacteristic
288C23×C151—21no—
289C23×C151—22no—
290C23×C151—42no—
291C23×C151—42no—
292C23×C151—41no—
293C23×C151—41no—
294C23×C151C22×D411yescharacteristic
295Q8×C151—21no—
296Q8×C151—81no—
297Q8×C151—81no—
298Q8×C151—82no—
299Q8×C151—82no—
300Q8×C151C22⋊Q812yes—
301D4×C151—22no—
302D4×C151—22no—
303D4×C151—22no—
304D4×C151—21no—
305D4×C151—22no—
306D4×C151—41no—
307D4×C151—41no—
308D4×C151C22⋊Q812yes—
309C2×C4×C151—21no—
310C2×C4×C151—22no—
311C2×C4×C151—22no—
312C2×C4×C151—22no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—22no—
318C2×C4×C151—22no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—42no—
326C2×C4×C151—42no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—42no—
330C2×C4×C151—41no—
331C2×C4×C151—41no—
332C2×C4×C151—81no—
333C2×C4×C151—81no—
334C2×C4×C151—82no—
335C2×C4×C151—82no—
336C2×C4×C151—82no—
337C2×C4×C151—82no—
338C2×C4×C151#12011yescharacteristic
339C2×C4×C151#12011yescharacteristic
340C2×C4×C151#12011yescharacteristic
341C2×C4×C151#12011yescharacteristic
342C2×C4×C151C22×D411yescharacteristic
343C2×C4×C151C22×D411yescharacteristic
344C2×C4×C151C22×Q811yescharacteristic
345C2×C4×C151C2×#4111yescharacteristic
346C2×C4×C1512−1+411yescharacteristic
347C2×C4×C1512−1+411yescharacteristic
348C8×C151—22no—
349C8×C151—41no—
350C8×C151—41no—
351C8×C151—41no—
352C22×C151—21no—
353C22×C151—21no—
354C22×C151—22no—
355C22×C151—44no—
356C22×C151—41no—
357C22×C151—41no—
358C22×C151—42no—
359C22×C151—82no—
360C22×C151—81no—
361C22×C151—81no—
362C22×C151C2×#12011yescharacteristic
363C22×C151#54811yescharacteristic
364C22×C151D4×Q811yescharacteristic
365C4×C151—22no—
366C4×C151—21no—
367C4×C151—21no—
368C4×C151—21no—
369C4×C151—21no—
370C4×C151—42no—
371C4×C151—42no—
372C4×C151—41no—
373C4×C151—41no—
374C4×C151—41no—
375C4×C151—42no—
376C4×C151—41no—
377C4×C151—41no—
378C4×C151—41no—
379C4×C151—81no—
380C4×C151—81no—
381C4×C151C2×C22⋊Q811yescharacteristic
382C4×C151#53611yescharacteristic
383C4×C151#54811yescharacteristic
384C4×C151D4×Q811yescharacteristic
385C2×C151—21no—
386C2×C151—21no—
387C2×C151—42no—
388C2×C151—82no—
389C2×C151#240911yescharacteristic
390C2×C151#301811yescharacteristic
391C2×C151#302111yescharacteristic
392#24324C15111yesmaximal, characteristic, direct product factor, Sylow
393C151#2432411yescharacteristic, direct product factor, Sylow
394#3504C2×C15111yescharacteristic, complemented
395#3077C2×C15111yescharacteristic, complemented
396C4×AGL(1,ℤ/8)C2×C15111yescharacteristic
397#2566C2×C15111yescharacteristic, complemented
398#2061C2×C15111yescharacteristic, complemented
399#2060C2×C15111yescharacteristic, complemented
400#2027C2×C15111yescharacteristic, complemented
401#2027C2×C15111yescharacteristic, complemented
402#1998C2×C15111yescharacteristic, complemented
403#1986C2×C15111yescharacteristic, complemented
404#1883C2×C15111yescharacteristic
405#1883C2×C15111yescharacteristic
406#1860C2×C15111yescharacteristic, complemented
407#1859C2×C15111yescharacteristic, complemented
408#1806C2×C15111yescharacteristic, complemented
409C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
410#557—21no—
411#557—21no—
412#554—21no—
413#554—21no—
414#554—22no—
415#554—22no—
416#544—21no—
417#544—21no—
418#544C22×C15111yescharacteristic
419#544C22×C15111yescharacteristic
420#533—21no—
421#533C22×C15111yescharacteristic
422C2×#125—21no—
423C2×#125C22×C15111yescharacteristic
424#520C22×C15111yescharacteristic
425#520C22×C15111yescharacteristic
426C4×#41C22×C15111yescharacteristic
427C2×C4×D4C22×C15111yescharacteristic
428#478—21no—
429#478—21no—
430#476—21no—
431#474—21no—
432#442—21no—
433#440—21no—
434C4×SD16—21no—
435C4×D8—21no—
436#428C22×C15111yescharacteristic
437#428C22×C15111yescharacteristic
438#428C22×C15111yescharacteristic
439#423C22×C15111yescharacteristic
440C2×#104C22×C15111yescharacteristic
441C2×#104C22×C15111yescharacteristic
442#418C22×C15111yescharacteristic
443#418C22×C15111yescharacteristic
444#418C22×C15111yescharacteristic
445#417C22×C15111yescharacteristic
446C4×M16C22×C15111yescharacteristic
447#396—22no—
448#390C22×C15111yescharacteristic
449#390C22×C15111yescharacteristic
450#385—22no—
451#384C22×C15111yescharacteristic
452#382C22×C15111yescharacteristic
453C4×C4⋊C4C22×C15111yescharacteristic
454#343C22×C15111yescharacteristic
455#343C22×C15111yescharacteristic
456#343C22×C15111yescharacteristic
457#343C22×C15111yescharacteristic
458#339C22×C15111yescharacteristic
459#339C22×C15111yescharacteristic
460#339C22×C15111yescharacteristic
461#339C22×C15111yescharacteristic
462#339C22×C15111yescharacteristic
463#339C22×C15111yescharacteristic
464C2×#41C23×C15111yescharacteristic
465C22×D4C23×C15111yescharacteristic
466C23×C4—21no—
467AGL(1,ℤ/8)—22no—
468AGL(1,ℤ/8)Q8×C15114yescomplemented
469C2×SD16—21no—
470C2×D8—21no—
471C2×M16C23×C15111yescharacteristic
472C2×M16C23×C15111yescharacteristic
473C2×M16C23×C15111yescharacteristic
474C2×M16C23×C15111yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8—22no—
477C4⋊Q8—21no—
478C4⋊Q8—21no—
479C4⋊Q8—21no—
480C4⋊Q8—21no—
481C4⋊Q8D4×C15111yescharacteristic
482C4⋊Q8D4×C15111yescharacteristic
483#125—22no—
484#125—22no—
485#125—22no—
486#125—22no—
487#125—21no—
488#125—21no—
489#125—21no—
490#125—21no—
491#125—21no—
492#125—21no—
493#125—21no—
494#125—21no—
495#125D4×C15111yescharacteristic
496#125D4×C15111yescharacteristic
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—21no—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8D4×C15111yescharacteristic
514C4×Q8D4×C15111yescharacteristic
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C15111yescharacteristic
526C4×D4D4×C15111yescharacteristic
527#117—21no—
528#117—21no—
529#117—21no—
530#117C23×C15111yescharacteristic
531#117C23×C15111yescharacteristic
532#117C23×C15111yescharacteristic
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4D4×C15112yes—
540C2×C4⋊C4D4×C15112yes—
541C2×C4⋊C4C23×C15111yescharacteristic
542C2×C4⋊C4C23×C15111yescharacteristic
543C2×C4⋊C4C23×C15111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C42—21no—
548C2×C42C23×C15111yescharacteristic
549C2×C42C23×C15111yescharacteristic
550C2×C42C23×C15111yescharacteristic
551#107—21no—
552#107—21no—
553#107—21no—
554#106—21no—
555#106—21no—
556#106—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559#104—22no—
560#104—22no—
561#103—21no—
562#102—21no—
563#102—21no—
564#102—21no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—21no—
569#97—21no—
570C4×C8—21no—
571#95—21no—
572#95—22no—
573C24—21no—
574#41—21no—
575#41—21no—
576#41C2×Q8×C15112yes—
577#41#41×C15112yes—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8C2×D4×C15111yescharacteristic
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4C2×D4×C15111yescharacteristic
590C2×D4C2×Q8×C15112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—82no—
602C22×C4C2×D4×C15112yes—
603C22×C4C2×D4×C15112yes—
604C22×C4C2×D4×C15111yescharacteristic
605C22×C4C2×D4×C15111yescharacteristic
606C22×C4C24×C15111yescharacteristic
607SD16—24no—
608D8—24no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16C2×Q8×C15112yes—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—42no—
648C4⋊C4—82no—
649C4⋊C4C2×D4×C15111yescharacteristic
650C4⋊C4C2×D4×C15111yescharacteristic
651C4⋊C4C2×D4×C15111yescharacteristic
652C4⋊C4C2×D4×C15111yescharacteristic
653C4⋊C4C2×D4×C15111yescharacteristic
654C4⋊C4C2×D4×C15111yescharacteristic
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—44no—
663C22⋊C4—41no—
664C22⋊C4—41no—
665C22⋊C4—82no—
666C42—22no—
667C42—22no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42C2×D4×C15111yescharacteristic
678C42C2×D4×C15111yescharacteristic
679C42C2×D4×C15111yescharacteristic
680C42C2×D4×C15111yescharacteristic
681C23—21no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23C22×D4×C15111yescharacteristic
688Q8—21no—
689Q8—81no—
690Q8—81no—
691Q8—82no—
692Q8—82no—
693Q8C22⋊Q8×C15112yes—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—21no—
698D4—22no—
699D4—41no—
700D4—41no—
701D4C22⋊Q8×C15112yes—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4#120×C15111yescharacteristic
732C2×C4#120×C15111yescharacteristic
733C2×C4#120×C15111yescharacteristic
734C2×C4#120×C15111yescharacteristic
735C2×C4C22×D4×C15111yescharacteristic
736C2×C4C22×D4×C15111yescharacteristic
737C2×C4C22×Q8×C15111yescharacteristic
738C2×C4C2×#41×C15111yescharacteristic
739C2×C42−1+4×C15111yescharacteristic
740C2×C42−1+4×C15111yescharacteristic
741C8—22no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—22no—
748C22—44no—
749C22—41no—
750C22—41no—
751C22—42no—
752C22—82no—
753C22—81no—
754C22—81no—
755C22C2×#120×C15111yescharacteristic
756C22#548×C15111yescharacteristic
757C22D4×Q8×C15111yescharacteristic
758C4—22no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—42no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—81no—
773C4—81no—
774C4C2×C22⋊Q8×C15111yescharacteristic
775C4#536×C15111yescharacteristic
776C4#548×C15111yescharacteristic
777C4D4×Q8×C15111yescharacteristic
778C2—21no—
779C2—21no—
780C2—42no—
781C2—82no—
782C2#2409×C15111yescharacteristic
783C2#3018×C15111yescharacteristic
784C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×AGL(1,ℤ/8)×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3504×C151C2semidirect
2. #3077×C151C2semidirect
4. #2566×C151C2semidirect
5. #2061×C151C2semidirect
6. #2060×C151C2semidirect
7. #2027×C151C2semidirect
8. #2027×C151C2semidirect
9. #1998×C151C2semidirect
10. #1986×C151C2semidirect
13. #1860×C151C2semidirect
14. #1859×C151C2semidirect
15. #1806×C151C2semidirect
75. AGL(1,ℤ/8)×C151Q8semidirect
392. #24324C151direct (N × H)
393. C151#24324direct (N × H)
394. #3504C2×C151semidirect
395. #3077C2×C151semidirect
397. #2566C2×C151semidirect
398. #2061C2×C151semidirect
399. #2060C2×C151semidirect
400. #2027C2×C151semidirect
401. #2027C2×C151semidirect
402. #1998C2×C151semidirect
403. #1986C2×C151semidirect
406. #1860C2×C151semidirect
407. #1859C2×C151semidirect
408. #1806C2×C151semidirect
468. AGL(1,ℤ/8)Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#3504×C1512
#3077×C1512
C4×AGL(1,ℤ/8)×C1512
#2566×C1512
#2061×C1512
#2060×C1512
#2027×C1512
#1998×C1512
#1986×C1512
#1883×C1512
#1860×C1512
#1859×C1512
#1806×C1512
#24324151