Finite Group Databasebeta

← C151×#24174 #50329099

Subgroups — C151×#24174 #50329099

Order 38656.

1078 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3512×C151C211yesmaximal, characteristic, complemented
2#3036×C151C211yesmaximal, characteristic, complemented
3C4×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic, complemented
4#2566×C151C211yesmaximal, characteristic, complemented
5#2040×C151C211yesmaximal, characteristic, complemented
6#2039×C151C211yesmaximal, characteristic, complemented
7#2006×C151C211yesmaximal, characteristic, complemented
8#2006×C151C211yesmaximal, characteristic, complemented
9#1998×C151C211yesmaximal, characteristic, complemented
10#1980×C151C211yesmaximal, characteristic, complemented
11#1883×C151C211yesmaximal, characteristic, complemented
12#1883×C151C211yesmaximal, characteristic, complemented
13#1860×C151C211yesmaximal, characteristic, complemented
14#1859×C151C211yesmaximal, characteristic, complemented
15#1806×C151C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
19#553×C151—21no—
20#553×C151—21no—
21#553×C151—22no—
22#553×C151—22no—
23#552×C151—21no—
24#552×C151—21no—
25#541×C151—21no—
26#540×C151—21no—
27#537×C151C2211yescharacteristic
28#537×C151C2211yescharacteristic
29#532×C151C2211yescharacteristic
30#529×C151—21no—
31#529×C151—21no—
32C2×#125×C151C2211yescharacteristic
33#520×C151C2211yescharacteristic
34#520×C151C2211yescharacteristic
35C4×#41×C151C2211yescharacteristic
36C2×C4×D4×C151C2211yescharacteristic
37#463×C151—21no—
38#463×C151—21no—
39#461×C151—21no—
40#459×C151—21no—
41#442×C151—21no—
42#440×C151—21no—
43C4×SD16×C151—21no—
44C4×D8×C151—21no—
45#428×C151C2211yescharacteristic
46#423×C151C2211yescharacteristic
47C2×#104×C151C2211yescharacteristic
48C2×#104×C151C2211yescharacteristic
49C2×#104×C151C2211yescharacteristic
50C2×#104×C151C2211yescharacteristic
51C2×#104×C151C2211yescharacteristic
52C2×#104×C151C2211yescharacteristic
53#418×C151C2211yescharacteristic
54#417×C151C2211yescharacteristic
55#417×C151C2211yescharacteristic
56#417×C151C2211yescharacteristic
57C4×M16×C151C2211yescharacteristic
58#396×C151—22no—
59#390×C151C2211yescharacteristic
60#390×C151C2211yescharacteristic
61#385×C151—22no—
62#384×C151C2211yescharacteristic
63#382×C151C2211yescharacteristic
64C4×C4⋊C4×C151C2211yescharacteristic
65#343×C151C2211yescharacteristic
66#343×C151C2211yescharacteristic
67#343×C151C2211yescharacteristic
68#343×C151C2211yescharacteristic
69#339×C151C2211yescharacteristic
70#339×C151C2211yescharacteristic
71C2×#41×C151C2311yescharacteristic
72C2×#41×C151C2311yescharacteristic
73C2×#41×C151C2311yescharacteristic
74C22×D4×C151C2311yescharacteristic
75C23×C4×C151—21no—
76AGL(1,ℤ/8)×C151—22no—
77AGL(1,ℤ/8)×C151—22no—
78AGL(1,ℤ/8)×C151—22no—
79AGL(1,ℤ/8)×C151—22no—
80AGL(1,ℤ/8)×C151—41no—
81AGL(1,ℤ/8)×C151—41no—
82C2×SD16×C151—21no—
83C2×SD16×C151—21no—
84C2×SD16×C151—21no—
85C2×D8×C151—21no—
86C2×D8×C151—21no—
87C2×D8×C151—21no—
88C2×M16×C151C2311yescharacteristic
89C2×M16×C151C2311yescharacteristic
90C2×M16×C151C2311yescharacteristic
91C2×M16×C151C2311yescharacteristic
92C4⋊Q8×C151D411yescharacteristic
93#127×C151D411yescharacteristic
94#126×C151—22no—
95#126×C151—22no—
96#126×C151—22no—
97#126×C151—22no—
98#125×C151—22no—
99#125×C151—22no—
100#125×C151—21no—
101#125×C151—21no—
102#125×C151—21no—
103#125×C151—21no—
104#124×C151D411yescharacteristic
105#124×C151D411yescharacteristic
106#123×C151—22no—
107#123×C151—22no—
108#123×C151—22no—
109#123×C151—22no—
110C22⋊Q8×C151—21no—
111C22⋊Q8×C151—21no—
112C22⋊Q8×C151—21no—
113C22⋊Q8×C151—21no—
114#121×C151—22no—
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—22no—
123#121×C151—22no—
124C4×Q8×C151—21no—
125C4×Q8×C151—21no—
126C4×Q8×C151D411yescharacteristic
127C4×Q8×C151D411yescharacteristic
128C4×D4×C151—22no—
129C4×D4×C151—22no—
130C4×D4×C151—21no—
131C4×D4×C151—21no—
132C4×D4×C151—21no—
133C4×D4×C151—21no—
134C4×D4×C151—22no—
135C4×D4×C151—22no—
136C4×D4×C151—21no—
137C4×D4×C151—21no—
138C4×D4×C151—21no—
139C4×D4×C151—21no—
140C4×D4×C151—21no—
141C4×D4×C151—21no—
142C4×D4×C151D411yescharacteristic
143C4×D4×C151D411yescharacteristic
144#117×C151—22no—
145#117×C151—22no—
146#117×C151—21no—
147#117×C151—21no—
148#117×C151—21no—
149#117×C151C2311yescharacteristic
150C2×C4⋊C4×C151—21no—
151C2×C4⋊C4×C151—21no—
152C2×C4⋊C4×C151—21no—
153C2×C4⋊C4×C151—22no—
154C2×C4⋊C4×C151D412yes—
155C2×C4⋊C4×C151D412yes—
156C2×C4⋊C4×C151C2311yescharacteristic
157C2×C4⋊C4×C151C2311yescharacteristic
158C2×C4⋊C4×C151C2311yescharacteristic
159C2×C22⋊C4×C151—22no—
160C2×C22⋊C4×C151—21no—
161C2×C22⋊C4×C151—22no—
162C2×C42×C151—21no—
163C2×C42×C151C2311yescharacteristic
164C2×C42×C151C2311yescharacteristic
165C2×C42×C151C2311yescharacteristic
166#107×C151—21no—
167#106×C151—21no—
168C4⋊C8×C151—21no—
169C4⋊C8×C151—21no—
170#104×C151—22no—
171#104×C151—22no—
172#104×C151—41no—
173#104×C151—41no—
174#104×C151—41no—
175#104×C151—41no—
176#103×C151—21no—
177#103×C151—21no—
178#103×C151—21no—
179#102×C151—21no—
180#102×C151—21no—
181#102×C151—21no—
182#102×C151—21no—
183#102×C151—21no—
184#97×C151—21no—
185C4×C8×C151—21no—
186#95×C151—21no—
187#95×C151—22no—
188C24×C151—21no—
189#41×C151—21no—
190#41×C151—21no—
191#41×C151—21no—
192#41×C151—21no—
193#41×C151—21no—
194#41×C151—21no—
195#41×C151—21no—
196#41×C151—21no—
197#41×C151—21no—
198#41×C151—21no—
199#41×C151—21no—
200#41×C151—21no—
201C2×Q8×C151C2×D411yescharacteristic
202C2×Q8×C151C2×D411yescharacteristic
203C2×Q8×C151C2×D411yescharacteristic
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—22no—
208C2×D4×C151—22no—
209C2×D4×C151—21no—
210C2×D4×C151—21no—
211C2×D4×C151—21no—
212C2×D4×C151—21no—
213C2×D4×C151—21no—
214C2×D4×C151—21no—
215C2×D4×C151—21no—
216C2×D4×C151C2×D411yescharacteristic
217C2×D4×C151C2×D411yescharacteristic
218C2×D4×C151C2×D411yescharacteristic
219C2×D4×C151#4112yes—
220C22×C4×C151—21no—
221C22×C4×C151—22no—
222C22×C4×C151—22no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—41no—
231C22×C4×C151—41no—
232C22×C4×C151—82no—
233C22×C4×C151C2×D412yes—
234C22×C4×C151C2×D412yes—
235C22×C4×C151C2×D411yescharacteristic
236C22×C4×C151C2×D411yescharacteristic
237C22×C4×C151C2411yescharacteristic
238SD16×C151—24no—
239SD16×C151—42no—
240SD16×C151—42no—
241D8×C151—24no—
242D8×C151—42no—
243D8×C151—42no—
244M16×C151—21no—
245M16×C151—21no—
246M16×C151—21no—
247M16×C151—21no—
248M16×C151—21no—
249M16×C151—21no—
250M16×C151—21no—
251M16×C151#4112yes—
252C2×C8×C151—21no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C4⋊C4×C151—22no—
257C4⋊C4×C151—22no—
258C4⋊C4×C151—22no—
259C4⋊C4×C151—22no—
260C4⋊C4×C151—22no—
261C4⋊C4×C151—22no—
262C4⋊C4×C151—22no—
263C4⋊C4×C151—22no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—42no—
275C4⋊C4×C151—82no—
276C4⋊C4×C151C2×D411yescharacteristic
277C4⋊C4×C151C2×D411yescharacteristic
278C22⋊C4×C151—22no—
279C22⋊C4×C151—22no—
280C22⋊C4×C151—22no—
281C22⋊C4×C151—22no—
282C22⋊C4×C151—22no—
283C22⋊C4×C151—22no—
284C22⋊C4×C151—21no—
285C22⋊C4×C151—21no—
286C22⋊C4×C151—21no—
287C22⋊C4×C151—21no—
288C22⋊C4×C151—21no—
289C22⋊C4×C151—21no—
290C22⋊C4×C151—21no—
291C22⋊C4×C151—44no—
292C22⋊C4×C151—41no—
293C22⋊C4×C151—41no—
294C22⋊C4×C151—82no—
295C42×C151—22no—
296C42×C151—22no—
297C42×C151—21no—
298C42×C151—21no—
299C42×C151—21no—
300C42×C151—21no—
301C42×C151—21no—
302C42×C151—21no—
303C42×C151—21no—
304C42×C151C2×D411yescharacteristic
305C42×C151C2×D411yescharacteristic
306C42×C151C2×D411yescharacteristic
307C42×C151C2×D411yescharacteristic
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—21no—
311C23×C151—22no—
312C23×C151—42no—
313C23×C151—42no—
314C23×C151—41no—
315C23×C151—41no—
316C23×C151C22×D411yescharacteristic
317Q8×C151—21no—
318Q8×C151—21no—
319Q8×C151—21no—
320Q8×C151—21no—
321Q8×C151—21no—
322Q8×C151—21no—
323D4×C151—21no—
324D4×C151—22no—
325D4×C151—21no—
326D4×C151—21no—
327D4×C151—21no—
328D4×C151—22no—
329D4×C151—21no—
330D4×C151—21no—
331D4×C151—41no—
332D4×C151—41no—
333D4×C151—41no—
334D4×C151—41no—
335D4×C151—41no—
336D4×C151—41no—
337D4×C151—41no—
338D4×C151—41no—
339D4×C151—81no—
340D4×C151—81no—
341D4×C151—82no—
342D4×C151—82no—
343C2×C4×C151—22no—
344C2×C4×C151—21no—
345C2×C4×C151—21no—
346C2×C4×C151—21no—
347C2×C4×C151—21no—
348C2×C4×C151—21no—
349C2×C4×C151—22no—
350C2×C4×C151—22no—
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—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—42no—
362C2×C4×C151—42no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—42no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—81no—
369C2×C4×C151—81no—
370C2×C4×C151—82no—
371C2×C4×C151—82no—
372C2×C4×C151—82no—
373C2×C4×C151—82no—
374C2×C4×C151#12011yescharacteristic
375C2×C4×C151#12011yescharacteristic
376C2×C4×C151#12011yescharacteristic
377C2×C4×C151#12011yescharacteristic
378C2×C4×C151C22×D411yescharacteristic
379C2×C4×C151C22×D411yescharacteristic
380C2×C4×C151C2×#4111yescharacteristic
381C2×C4×C151C2×#4111yescharacteristic
382C2×C4×C151H(5,𝔽2)11yescharacteristic
383C2×C4×C1512−1+411yescharacteristic
384C8×C151—22no—
385C8×C151—41no—
386C8×C151—41no—
387C8×C151—41no—
388C22×C151—21no—
389C22×C151—21no—
390C22×C151—44no—
391C22×C151—41no—
392C22×C151—41no—
393C22×C151—41no—
394C22×C151—42no—
395C22×C151—41no—
396C22×C151—41no—
397C22×C151—41no—
398C22×C151—41no—
399C22×C151—41no—
400C22×C151—41no—
401C22×C151—82no—
402C22×C151—81no—
403C22×C151—81no—
404C22×C151C2×#12011yescharacteristic
405C22×C151#54811yescharacteristic
406C22×C151#55011yescharacteristic
407C4×C151—21no—
408C4×C151—21no—
409C4×C151—21no—
410C4×C151—21no—
411C4×C151—42no—
412C4×C151—41no—
413C4×C151—41no—
414C4×C151—41no—
415C4×C151—42no—
416C4×C151—41no—
417C4×C151—42no—
418C4×C151—41no—
419C4×C151—81no—
420C4×C151—81no—
421C4×C151#52511yescharacteristic
422C4×C151#53711yescharacteristic
423C4×C151#54611yescharacteristic
424C4×C151#54711yescharacteristic
425C2×C151—21no—
426C2×C151—21no—
427C2×C151—81no—
428C2×C151—81no—
429C2×C151—81no—
430C2×C151—82no—
431C2×C151#240711yescharacteristic
432C2×C151#301811yescharacteristic
433C2×C151#302111yescharacteristic
434#24174C15111yesmaximal, characteristic, direct product factor, Sylow
435C151#2417411yescharacteristic, direct product factor, Sylow
436#3512C2×C15111yescharacteristic, complemented
437#3036C2×C15111yescharacteristic, complemented
438C4×AGL(1,ℤ/8)C2×C15111yescharacteristic, complemented
439#2566C2×C15111yescharacteristic, complemented
440#2040C2×C15111yescharacteristic, complemented
441#2039C2×C15111yescharacteristic, complemented
442#2006C2×C15111yescharacteristic, complemented
443#2006C2×C15111yescharacteristic, complemented
444#1998C2×C15111yescharacteristic, complemented
445#1980C2×C15111yescharacteristic, complemented
446#1883C2×C15111yescharacteristic, complemented
447#1883C2×C15111yescharacteristic, complemented
448#1860C2×C15111yescharacteristic, complemented
449#1859C2×C15111yescharacteristic, complemented
450#1806C2×C15111yescharacteristic, complemented
451C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
452C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
453C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
454#553—21no—
455#553—21no—
456#553—22no—
457#553—22no—
458#552—21no—
459#552—21no—
460#541—21no—
461#540—21no—
462#537C22×C15111yescharacteristic
463#537C22×C15111yescharacteristic
464#532C22×C15111yescharacteristic
465#529—21no—
466#529—21no—
467C2×#125C22×C15111yescharacteristic
468#520C22×C15111yescharacteristic
469#520C22×C15111yescharacteristic
470C4×#41C22×C15111yescharacteristic
471C2×C4×D4C22×C15111yescharacteristic
472#463—21no—
473#463—21no—
474#461—21no—
475#459—21no—
476#442—21no—
477#440—21no—
478C4×SD16—21no—
479C4×D8—21no—
480#428C22×C15111yescharacteristic
481#423C22×C15111yescharacteristic
482C2×#104C22×C15111yescharacteristic
483C2×#104C22×C15111yescharacteristic
484C2×#104C22×C15111yescharacteristic
485C2×#104C22×C15111yescharacteristic
486C2×#104C22×C15111yescharacteristic
487C2×#104C22×C15111yescharacteristic
488#418C22×C15111yescharacteristic
489#417C22×C15111yescharacteristic
490#417C22×C15111yescharacteristic
491#417C22×C15111yescharacteristic
492C4×M16C22×C15111yescharacteristic
493#396—22no—
494#390C22×C15111yescharacteristic
495#390C22×C15111yescharacteristic
496#385—22no—
497#384C22×C15111yescharacteristic
498#382C22×C15111yescharacteristic
499C4×C4⋊C4C22×C15111yescharacteristic
500#343C22×C15111yescharacteristic
501#343C22×C15111yescharacteristic
502#343C22×C15111yescharacteristic
503#343C22×C15111yescharacteristic
504#339C22×C15111yescharacteristic
505#339C22×C15111yescharacteristic
506C2×#41C23×C15111yescharacteristic
507C2×#41C23×C15111yescharacteristic
508C2×#41C23×C15111yescharacteristic
509C22×D4C23×C15111yescharacteristic
510C23×C4—21no—
511AGL(1,ℤ/8)—22no—
512AGL(1,ℤ/8)—22no—
513AGL(1,ℤ/8)—22no—
514AGL(1,ℤ/8)—22no—
515AGL(1,ℤ/8)—41no—
516AGL(1,ℤ/8)—41no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×D8—21no—
521C2×D8—21no—
522C2×D8—21no—
523C2×M16C23×C15111yescharacteristic
524C2×M16C23×C15111yescharacteristic
525C2×M16C23×C15111yescharacteristic
526C2×M16C23×C15111yescharacteristic
527C4⋊Q8D4×C15111yescharacteristic
528#127D4×C15111yescharacteristic
529#126—22no—
530#126—22no—
531#126—22no—
532#126—22no—
533#125—22no—
534#125—22no—
535#125—21no—
536#125—21no—
537#125—21no—
538#125—21no—
539#124D4×C15111yescharacteristic
540#124D4×C15111yescharacteristic
541#123—22no—
542#123—22no—
543#123—22no—
544#123—22no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549#121—22no—
550#121—22no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121—21no—
555#121—21no—
556#121—21no—
557#121—22no—
558#121—22no—
559C4×Q8—21no—
560C4×Q8—21no—
561C4×Q8D4×C15111yescharacteristic
562C4×Q8D4×C15111yescharacteristic
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—21no—
566C4×D4—21no—
567C4×D4—21no—
568C4×D4—21no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—21no—
575C4×D4—21no—
576C4×D4—21no—
577C4×D4D4×C15111yescharacteristic
578C4×D4D4×C15111yescharacteristic
579#117—22no—
580#117—22no—
581#117—21no—
582#117—21no—
583#117—21no—
584#117C23×C15111yescharacteristic
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4D4×C15112yes—
590C2×C4⋊C4D4×C15112yes—
591C2×C4⋊C4C23×C15111yescharacteristic
592C2×C4⋊C4C23×C15111yescharacteristic
593C2×C4⋊C4C23×C15111yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C42—21no—
598C2×C42C23×C15111yescharacteristic
599C2×C42C23×C15111yescharacteristic
600C2×C42C23×C15111yescharacteristic
601#107—21no—
602#106—21no—
603C4⋊C8—21no—
604C4⋊C8—21no—
605#104—22no—
606#104—22no—
607#104—41no—
608#104—41no—
609#104—41no—
610#104—41no—
611#103—21no—
612#103—21no—
613#103—21no—
614#102—21no—
615#102—21no—
616#102—21no—
617#102—21no—
618#102—21no—
619#97—21no—
620C4×C8—21no—
621#95—21no—
622#95—22no—
623C24—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636C2×Q8C2×D4×C15111yescharacteristic
637C2×Q8C2×D4×C15111yescharacteristic
638C2×Q8C2×D4×C15111yescharacteristic
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4C2×D4×C15111yescharacteristic
652C2×D4C2×D4×C15111yescharacteristic
653C2×D4C2×D4×C15111yescharacteristic
654C2×D4#41×C15112yes—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—82no—
668C22×C4C2×D4×C15112yes—
669C22×C4C2×D4×C15112yes—
670C22×C4C2×D4×C15111yescharacteristic
671C22×C4C2×D4×C15111yescharacteristic
672C22×C4C24×C15111yescharacteristic
673SD16—24no—
674SD16—42no—
675SD16—42no—
676D8—24no—
677D8—42no—
678D8—42no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16#41×C15112yes—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4—82no—
711C4⋊C4C2×D4×C15111yescharacteristic
712C4⋊C4C2×D4×C15111yescharacteristic
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—44no—
727C22⋊C4—41no—
728C22⋊C4—41no—
729C22⋊C4—82no—
730C42—22no—
731C42—22no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C42C2×D4×C15111yescharacteristic
740C42C2×D4×C15111yescharacteristic
741C42C2×D4×C15111yescharacteristic
742C42C2×D4×C15111yescharacteristic
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—42no—
748C23—42no—
749C23—41no—
750C23—41no—
751C23C22×D4×C15111yescharacteristic
752Q8—21no—
753Q8—21no—
754Q8—21no—
755Q8—21no—
756Q8—21no—
757Q8—21no—
758D4—21no—
759D4—22no—
760D4—21no—
761D4—22no—
762D4—21no—
763D4—21no—
764D4—21no—
765D4—21no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—81no—
775D4—81no—
776D4—82no—
777D4—82no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4#120×C15111yescharacteristic
810C2×C4#120×C15111yescharacteristic
811C2×C4#120×C15111yescharacteristic
812C2×C4#120×C15111yescharacteristic
813C2×C4C22×D4×C15111yescharacteristic
814C2×C4C22×D4×C15111yescharacteristic
815C2×C4C2×#41×C15111yescharacteristic
816C2×C4C2×#41×C15111yescharacteristic
817C2×C4H(5,𝔽2)×C15111yescharacteristic
818C2×C42−1+4×C15111yescharacteristic
819C8—22no—
820C8—41no—
821C8—41no—
822C8—41no—
823C22—21no—
824C22—21no—
825C22—44no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—81no—
839C22C2×#120×C15111yescharacteristic
840C22#548×C15111yescharacteristic
841C22#550×C15111yescharacteristic
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—42no—
853C4—41no—
854C4—81no—
855C4—81no—
856C4#525×C15111yescharacteristic
857C4#537×C15111yescharacteristic
858C4#546×C15111yescharacteristic
859C4#547×C15111yescharacteristic
860C2—21no—
861C2—21no—
862C2—82no—
863C2—81no—
864C2—81no—
865C2—81no—
866C2#2407×C15111yescharacteristic
867C2#3018×C15111yescharacteristic
868C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
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. #3512×C151C2semidirect
2. #3036×C151C2semidirect
3. C4×AGL(1,ℤ/8)×C151C2semidirect
4. #2566×C151C2semidirect
5. #2040×C151C2semidirect
6. #2039×C151C2semidirect
7. #2006×C151C2semidirect
8. #2006×C151C2semidirect
9. #1998×C151C2semidirect
10. #1980×C151C2semidirect
11. #1883×C151C2semidirect
12. #1883×C151C2semidirect
13. #1860×C151C2semidirect
14. #1859×C151C2semidirect
15. #1806×C151C2semidirect
434. #24174C151direct (N × H)
435. C151#24174direct (N × H)
436. #3512C2×C151semidirect
437. #3036C2×C151semidirect
438. C4×AGL(1,ℤ/8)C2×C151semidirect
439. #2566C2×C151semidirect
440. #2040C2×C151semidirect
441. #2039C2×C151semidirect
442. #2006C2×C151semidirect
443. #2006C2×C151semidirect
444. #1998C2×C151semidirect
445. #1980C2×C151semidirect
446. #1883C2×C151semidirect
447. #1883C2×C151semidirect
448. #1860C2×C151semidirect
449. #1859C2×C151semidirect
450. #1806C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3512×C1512
#3036×C1512
C4×AGL(1,ℤ/8)×C1512
#2566×C1512
#2040×C1512
#2039×C1512
#2006×C1512
#1998×C1512
#1980×C1512
#1883×C1512
#1860×C1512
#1859×C1512
#1806×C1512
#24174151