Finite Group Databasebeta

← C151×#18788 #50323713

Subgroups — C151×#18788 #50323713

Order 38656.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#41×C151C211yesmaximal, characteristic, complemented
2#3208×C151C211yesmaximal, characteristic, complemented
3#3038×C151C211yesmaximal, characteristic
4C2×#460×C151C211yesmaximal, characteristic, complemented
5#1627×C151C212yesmaximal, complemented
6#1626×C151C212yesmaximal, complemented
7#1623×C151C212yesmaximal, complemented
8#1622×C151C212yesmaximal, complemented
9#1550×C151C211yesmaximal, characteristic, complemented
10#1487×C151C211yesmaximal, characteristic, complemented
11#1477×C151C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C151—21no—
13C22×SD16×C151—21no—
14Q82×C151C2211yescharacteristic, complemented
15#557×C151—21no—
16#557×C151C2211yescharacteristic, complemented
17#554×C151—22no—
18#554×C151—21no—
19#554×C151—21no—
20#554×C151C2211yescharacteristic, complemented
21D4×Q8×C151—21no—
22D4×Q8×C151C2211yescharacteristic, complemented
23#533×C151—22no—
24#533×C151—21no—
25#533×C151—21no—
26#533×C151C2211yescharacteristic
27C2×#127×C151C2211yescharacteristic
28C4×#41×C151—21no—
29C4×#41×C151C2211yescharacteristic
30C2×C4×Q8×C151—21no—
31C2×C4×Q8×C151C2211yescharacteristic
32#492×C151C2212yes—
33#486×C151C2212yes—
34#460×C151—22no—
35#460×C151—21no—
36#460×C151—21no—
37#460×C151—21no—
38#460×C151C2212yes—
39#460×C151C2212yes—
40#460×C151C2212yes—
41#459×C151—21no—
42#459×C151C2212yes—
43#450×C151—22no—
44#431×C151C2211yescharacteristic
45#423×C151C2211yescharacteristic
46C2×C4⋊C8×C151C2211yescharacteristic
47#418×C151—21no—
48C2×#102×C151—21no—
49#333×C151C2212yescomplemented
50#332×C151C2212yescomplemented
51Q8⋊C8×C151C2212yescomplemented
52Q8⋊C8×C151C2212yescomplemented
53Q8⋊C8×C151C2212yescomplemented
54D4⋊C8×C151C2212yescomplemented
55C2×#41×C151D411yescharacteristic
56C22×Q8×C151—21no—
57C22×Q8×C151D411yescharacteristic
58C22×D4×C151—21no—
59C22×D4×C151—21no—
60C22×D4×C151—21no—
61AGL(1,ℤ/8)×C151—44no—
62C2×SD16×C151—22no—
63C2×SD16×C151—22no—
64C2×SD16×C151—22no—
65C2×SD16×C151—24no—
66C2×SD16×C151—44no—
67C2×D8×C151—22no—
68C2×M16×C151—21no—
69C22×C8×C151—21no—
70C4⋊Q8×C151—22no—
71C4⋊Q8×C151—21no—
72C4⋊Q8×C151—21no—
73C4⋊Q8×C151—21no—
74C4⋊Q8×C151—21no—
75C4⋊Q8×C151—22no—
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78#127×C151—21no—
79#127×C151—21no—
80#127×C151—21no—
81#127×C151C2312yes—
82#125×C151—22no—
83#125×C151—22no—
84#125×C151—22no—
85#125×C151—21no—
86#125×C151—21no—
87#125×C151—21no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—22no—
90C22⋊Q8×C151—22no—
91C22⋊Q8×C151—22no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—21no—
94C22⋊Q8×C151—22no—
95C22⋊Q8×C151—21no—
96C22⋊Q8×C151—21no—
97C22⋊Q8×C151—22no—
98C22⋊Q8×C151D412yes—
99C4×Q8×C151—22no—
100C4×Q8×C151—22no—
101C4×Q8×C151—22no—
102C4×Q8×C151—21no—
103C4×Q8×C151—21no—
104C4×Q8×C151—21no—
105C4×Q8×C151—21no—
106C4×Q8×C151—21no—
107C4×Q8×C151—21no—
108C4×Q8×C151—21no—
109C4×Q8×C151D411yescharacteristic
110C4×Q8×C151D411yescharacteristic
111C4×Q8×C151D411yescharacteristic
112C4×Q8×C151D412yes—
113C4×Q8×C151C2311yescharacteristic
114C4×Q8×C151C2311yescharacteristic
115C4×Q8×C151C2311yescharacteristic
116C4×D4×C151—22no—
117C4×D4×C151—22no—
118C4×D4×C151—21no—
119C4×D4×C151—21no—
120C4×D4×C151—21no—
121C4×D4×C151—21no—
122C4×D4×C151D411yescharacteristic
123C4×D4×C151C2311yescharacteristic
124#117×C151—22no—
125#117×C151—21no—
126#117×C151—21no—
127#117×C151D411yescharacteristic
128C2×C4⋊C4×C151—22no—
129C2×C4⋊C4×C151—21no—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151D411yescharacteristic
132C2×C42×C151—22no—
133C2×C42×C151—21no—
134C2×C42×C151—21no—
135C2×C42×C151C2311yescharacteristic
136C4⋊C8×C151—21no—
137C4⋊C8×C151—21no—
138C4⋊C8×C151—21no—
139C4⋊C8×C151C2312yes—
140C4⋊C8×C151C2312yes—
141#102×C151—22no—
142#102×C151—22no—
143#102×C151—22no—
144#102×C151—22no—
145#102×C151—24no—
146C22⋊C8×C151—21no—
147C4×C8×C151C2312yes—
148C24×C151—41no—
149#41×C151—22no—
150#41×C151SD1614yescomplemented
151C2×Q8×C151—22no—
152C2×Q8×C151—22no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—22no—
156C2×Q8×C151—41no—
157C2×Q8×C151—42no—
158C2×Q8×C151—42no—
159C2×Q8×C151C2×D411yescharacteristic
160C2×Q8×C151C2×D411yescharacteristic
161C2×Q8×C151C2×D411yescharacteristic
162C2×Q8×C151C2×D412yes—
163C2×D4×C151—21no—
164C2×D4×C151—22no—
165C2×D4×C151—22no—
166C2×D4×C151—22no—
167C2×D4×C151—42no—
168C2×D4×C151—42no—
169C2×D4×C151—41no—
170C2×D4×C151—41no—
171C2×D4×C151—41no—
172C2×D4×C151—42no—
173C2×D4×C151—42no—
174C2×D4×C151—82no—
175C2×D4×C151C2×D411yescharacteristic
176C22×C4×C151—21no—
177C22×C4×C151—22no—
178C22×C4×C151—21no—
179C22×C4×C151—22no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186SD16×C151—44no—
187SD16×C151—44no—
188SD16×C151—44no—
189SD16×C151—84no—
190D8×C151—44no—
191M16×C151—42no—
192C2×C8×C151—22no—
193C2×C8×C151—22no—
194C2×C8×C151—22no—
195C2×C8×C151—42no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—22no—
198C4⋊C4×C151—22no—
199C4⋊C4×C151—22no—
200C4⋊C4×C151—22no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151—22no—
203C4⋊C4×C151—22no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—22no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—22no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—21no—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151C2×D411yescharacteristic
217C4⋊C4×C151C2×D411yescharacteristic
218C4⋊C4×C151C2×D411yescharacteristic
219C4⋊C4×C151C2×D411yescharacteristic
220C4⋊C4×C151C2×D412yes—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—22no—
223C22⋊C4×C151—22no—
224C22⋊C4×C151—21no—
225C22⋊C4×C151—21no—
226C22⋊C4×C151—21no—
227C42×C151—22no—
228C42×C151—22no—
229C42×C151—21no—
230C42×C151—22no—
231C42×C151—21no—
232C42×C151—21no—
233C42×C151—21no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151C2×D411yescharacteristic
238C42×C151C2×D411yescharacteristic
239C42×C151C2×D411yescharacteristic
240C42×C151C2411yescharacteristic
241C23×C151—21no—
242C23×C151—42no—
243C23×C151—82no—
244C23×C151—82no—
245C23×C151—82no—
246C23×C151#12011yescharacteristic
247Q8×C151—21no—
248Q8×C151—21no—
249Q8×C151—21no—
250Q8×C151—21no—
251Q8×C151—42no—
252Q8×C151—42no—
253Q8×C151—44no—
254Q8×C151—41no—
255Q8×C151—41no—
256Q8×C151—82no—
257Q8×C151C2×SD1612yescomplemented
258Q8×C151AGL(1,ℤ/8)12yescomplemented
259D4×C151—24no—
260D4×C151—21no—
261D4×C151—44no—
262D4×C151—42no—
263D4×C151—42no—
264D4×C151—42no—
265D4×C151—42no—
266D4×C151—82no—
267D4×C151—82no—
268D4×C151—82no—
269D4×C151C2×SD1612yescomplemented
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—24no—
275C2×C4×C151—21no—
276C2×C4×C151—22no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—22no—
281C2×C4×C151—21no—
282C2×C4×C151—41no—
283C2×C4×C151—42no—
284C2×C4×C151—44no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—81no—
288C2×C4×C151—81no—
289C2×C4×C151—82no—
290C2×C4×C151#12011yescharacteristic
291C2×C4×C151#12011yescharacteristic
292C2×C4×C151#12011yescharacteristic
293C2×C4×C151C2×SD1612yes—
294C2×C4×C151#13712yes—
295C2×C4×C151C22×D411yescharacteristic
296C2×C4×C151C22×D411yescharacteristic
297C2×C4×C151C22×D411yescharacteristic
298C8×C151—42no—
299C8×C151—42no—
300C8×C151—42no—
301C22×C151—21no—
302C22×C151—21no—
303C22×C151—22no—
304C22×C151—41no—
305C22×C151—41no—
306C22×C151—82no—
307C22×C151—82no—
308C22×C151—82no—
309C22×C151—164no—
310C22×C151#44812yes—
311C22×C151C2×#12011yescharacteristic
312C4×C151—22no—
313C4×C151—21no—
314C4×C151—22no—
315C4×C151—21no—
316C4×C151—21no—
317C4×C151—41no—
318C4×C151—42no—
319C4×C151—41no—
320C4×C151—41no—
321C4×C151—42no—
322C4×C151—41no—
323C4×C151—41no—
324C4×C151#44812yes—
325C4×C151C22×SD1611yescharacteristic
326C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
327C4×C151C2×#13711yescharacteristic
328C4×C151#57511yescharacteristic
329C2×C151—22no—
330C2×C151—42no—
331C2×C151—162no—
332C2×C151C2×#44811yescharacteristic
333C2×C151#300611yescharacteristic
334C2×C151#302111yescharacteristic
335#18788C15111yesmaximal, characteristic, direct product factor, Sylow
336C151#1878811yescharacteristic, direct product factor, Sylow
337Q8×#41C2×C15111yescharacteristic, complemented
338#3208C2×C15111yescharacteristic, complemented
339#3038C2×C15111yescharacteristic
340C2×#460C2×C15111yescharacteristic, complemented
341#1627C2×C15112yescomplemented
342#1626C2×C15112yescomplemented
343#1623C2×C15112yescomplemented
344#1622C2×C15112yescomplemented
345#1550C2×C15111yescharacteristic, complemented
346#1487C2×C15111yescharacteristic, complemented
347#1477C2×C15111yescharacteristic, complemented
348C2×AGL(1,ℤ/8)—21no—
349C22×SD16—21no—
350Q82C22×C15111yescharacteristic, complemented
351#557—21no—
352#557C22×C15111yescharacteristic, complemented
353#554—22no—
354#554—21no—
355#554—21no—
356#554C22×C15111yescharacteristic, complemented
357D4×Q8—21no—
358D4×Q8C22×C15111yescharacteristic, complemented
359#533—22no—
360#533—21no—
361#533—21no—
362#533C22×C15111yescharacteristic
363C2×#127C22×C15111yescharacteristic
364C4×#41—21no—
365C4×#41C22×C15111yescharacteristic
366C2×C4×Q8—21no—
367C2×C4×Q8C22×C15111yescharacteristic
368#492C22×C15112yes—
369#486C22×C15112yes—
370#460—22no—
371#460—21no—
372#460—21no—
373#460—21no—
374#460C22×C15112yes—
375#460C22×C15112yes—
376#460C22×C15112yes—
377#459—21no—
378#459C22×C15112yes—
379#450—22no—
380#431C22×C15111yescharacteristic
381#423C22×C15111yescharacteristic
382C2×C4⋊C8C22×C15111yescharacteristic
383#418—21no—
384C2×#102—21no—
385#333C22×C15112yescomplemented
386#332C22×C15112yescomplemented
387Q8⋊C8C22×C15112yescomplemented
388Q8⋊C8C22×C15112yescomplemented
389Q8⋊C8C22×C15112yescomplemented
390D4⋊C8C22×C15112yescomplemented
391C2×#41D4×C15111yescharacteristic
392C22×Q8—21no—
393C22×Q8D4×C15111yescharacteristic
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397AGL(1,ℤ/8)—44no—
398C2×SD16—22no—
399C2×SD16—22no—
400C2×SD16—22no—
401C2×SD16—24no—
402C2×SD16—44no—
403C2×D8—22no—
404C2×M16—21no—
405C22×C8—21no—
406C4⋊Q8—22no—
407C4⋊Q8—21no—
408C4⋊Q8—22no—
409C4⋊Q8—21no—
410C4⋊Q8—21no—
411C4⋊Q8—21no—
412C4⋊Q8C23×C15111yescharacteristic
413C4⋊Q8C23×C15111yescharacteristic
414#127—21no—
415#127—21no—
416#127—21no—
417#127C23×C15112yes—
418#125—22no—
419#125—22no—
420#125—22no—
421#125—21no—
422#125—21no—
423#125—21no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—21no—
430C22⋊Q8—22no—
431C22⋊Q8—21no—
432C22⋊Q8—21no—
433C22⋊Q8—22no—
434C22⋊Q8D4×C15112yes—
435C4×Q8—22no—
436C4×Q8—22no—
437C4×Q8—22no—
438C4×Q8—21no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8—21no—
444C4×Q8—21no—
445C4×Q8D4×C15111yescharacteristic
446C4×Q8D4×C15111yescharacteristic
447C4×Q8D4×C15111yescharacteristic
448C4×Q8D4×C15112yes—
449C4×Q8C23×C15111yescharacteristic
450C4×Q8C23×C15111yescharacteristic
451C4×Q8C23×C15111yescharacteristic
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—21no—
458C4×D4D4×C15111yescharacteristic
459C4×D4C23×C15111yescharacteristic
460#117—22no—
461#117—21no—
462#117—21no—
463#117D4×C15111yescharacteristic
464C2×C4⋊C4—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4D4×C15111yescharacteristic
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C23×C15111yescharacteristic
472C4⋊C8—21no—
473C4⋊C8—21no—
474C4⋊C8—21no—
475C4⋊C8C23×C15112yes—
476C4⋊C8C23×C15112yes—
477#102—22no—
478#102—22no—
479#102—22no—
480#102—22no—
481#102—24no—
482C22⋊C8—21no—
483C4×C8C23×C15112yes—
484C24—41no—
485#41—22no—
486#41SD16×C15114yescomplemented
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—22no—
492C2×Q8—41no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8C2×D4×C15111yescharacteristic
496C2×Q8C2×D4×C15111yescharacteristic
497C2×Q8C2×D4×C15111yescharacteristic
498C2×Q8C2×D4×C15112yes—
499C2×D4—21no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—82no—
511C2×D4C2×D4×C15111yescharacteristic
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4C2×D4×C15111yescharacteristic
520C22×C4C2×D4×C15111yescharacteristic
521C22×C4C2×D4×C15111yescharacteristic
522SD16—44no—
523SD16—44no—
524SD16—44no—
525SD16—84no—
526D8—44no—
527M16—42no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—42no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4C2×D4×C15111yescharacteristic
553C4⋊C4C2×D4×C15111yescharacteristic
554C4⋊C4C2×D4×C15111yescharacteristic
555C4⋊C4C2×D4×C15111yescharacteristic
556C4⋊C4C2×D4×C15112yes—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C42—22no—
564C42—22no—
565C42—21no—
566C42—22no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42C2×D4×C15111yescharacteristic
574C42C2×D4×C15111yescharacteristic
575C42C2×D4×C15111yescharacteristic
576C42C24×C15111yescharacteristic
577C23—21no—
578C23—42no—
579C23—82no—
580C23—82no—
581C23—82no—
582C23#120×C15111yescharacteristic
583Q8—21no—
584Q8—21no—
585Q8—21no—
586Q8—21no—
587Q8—42no—
588Q8—42no—
589Q8—44no—
590Q8—41no—
591Q8—41no—
592Q8—82no—
593Q8C2×SD16×C15112yescomplemented
594Q8AGL(1,ℤ/8)×C15112yescomplemented
595D4—24no—
596D4—21no—
597D4—44no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—82no—
603D4—82no—
604D4—82no—
605D4C2×SD16×C15112yescomplemented
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—24no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—44no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4—82no—
626C2×C4#120×C15111yescharacteristic
627C2×C4#120×C15111yescharacteristic
628C2×C4#120×C15111yescharacteristic
629C2×C4C2×SD16×C15112yes—
630C2×C4#137×C15112yes—
631C2×C4C22×D4×C15111yescharacteristic
632C2×C4C22×D4×C15111yescharacteristic
633C2×C4C22×D4×C15111yescharacteristic
634C8—42no—
635C8—42no—
636C8—42no—
637C22—21no—
638C22—21no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—82no—
643C22—82no—
644C22—82no—
645C22—164no—
646C22#448×C15112yes—
647C22C2×#120×C15111yescharacteristic
648C4—22no—
649C4—21no—
650C4—22no—
651C4—21no—
652C4—21no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—41no—
660C4#448×C15112yes—
661C4C22×SD16×C15111yescharacteristic
662C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
663C4C2×#137×C15111yescharacteristic
664C4#575×C15111yescharacteristic
665C2—22no—
666C2—42no—
667C2—162no—
668C2C2×#448×C15111yescharacteristic
669C2#3006×C15111yescharacteristic
670C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3038×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
1. Q8×#41×C151C2semidirect
2. #3208×C151C2semidirect
4. C2×#460×C151C2semidirect
5. #1627×C151C2semidirect
6. #1626×C151C2semidirect
7. #1623×C151C2semidirect
8. #1622×C151C2semidirect
9. #1550×C151C2semidirect
10. #1487×C151C2semidirect
11. #1477×C151C2semidirect
14. Q82×C151C22semidirect
16. #557×C151C22semidirect
20. #554×C151C22semidirect
22. D4×Q8×C151C22semidirect
49. #333×C151C22semidirect
50. #332×C151C22semidirect
51. Q8⋊C8×C151C22semidirect
52. Q8⋊C8×C151C22semidirect
53. Q8⋊C8×C151C22semidirect
54. D4⋊C8×C151C22semidirect
150. #41×C151SD16semidirect
257. Q8×C151C2×SD16semidirect
258. Q8×C151AGL(1,ℤ/8)semidirect
269. D4×C151C2×SD16semidirect
335. #18788C151direct (N × H)
336. C151#18788direct (N × H)
337. Q8×#41C2×C151semidirect
338. #3208C2×C151semidirect
340. C2×#460C2×C151semidirect
341. #1627C2×C151semidirect
342. #1626C2×C151semidirect
343. #1623C2×C151semidirect
344. #1622C2×C151semidirect
345. #1550C2×C151semidirect
346. #1487C2×C151semidirect
347. #1477C2×C151semidirect
350. Q82C22×C151semidirect
352. #557C22×C151semidirect
356. #554C22×C151semidirect
358. D4×Q8C22×C151semidirect
385. #333C22×C151semidirect
386. #332C22×C151semidirect
387. Q8⋊C8C22×C151semidirect
388. Q8⋊C8C22×C151semidirect
389. Q8⋊C8C22×C151semidirect
390. D4⋊C8C22×C151semidirect
486. #41SD16×C151semidirect
593. Q8C2×SD16×C151semidirect
594. Q8AGL(1,ℤ/8)×C151semidirect
605. D4C2×SD16×C151semidirect

Maximal subgroups

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

subgroupindex
Q8×#41×C1512
#3208×C1512
#3038×C1512
C2×#460×C1512
#1627×C1512
#1626×C1512
#1623×C1512
#1622×C1512
#1550×C1512
#1487×C1512
#1477×C1512
#18788151