Finite Group Databasebeta

← C151×#24148 #50329073

Subgroups — C151×#24148 #50329073

Order 38656.

1102 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3510×C151C211yesmaximal, characteristic, complemented
2#3077×C151C211yesmaximal, characteristic, complemented
3C4×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic, complemented
4#2544×C151C211yesmaximal, characteristic, complemented
5#2038×C151C211yesmaximal, characteristic, complemented
6#2037×C151C211yesmaximal, characteristic, complemented
7#2003×C151C211yesmaximal, characteristic, complemented
8#2002×C151C211yesmaximal, characteristic
9#1986×C151C211yesmaximal, characteristic, complemented
10#1967×C151C211yesmaximal, characteristic, complemented
11#1888×C151C211yesmaximal, characteristic, complemented
12#1887×C151C211yesmaximal, characteristic, complemented
13#1857×C151C211yesmaximal, characteristic, complemented
14#1856×C151C211yesmaximal, characteristic, complemented
15#1806×C151C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
17#559×C151—21no—
18#559×C151—21no—
19#556×C151—21no—
20#556×C151—21no—
21#551×C151—22no—
22#551×C151—22no—
23#542×C151—21no—
24#542×C151—21no—
25#536×C151C2211yescharacteristic
26#535×C151C2211yescharacteristic
27#533×C151C2211yescharacteristic
28C2×#127×C151C2211yescharacteristic
29#529×C151—21no—
30#529×C151—21no—
31C2×#124×C151C2211yescharacteristic
32C2×#124×C151C2211yescharacteristic
33#519×C151C2211yescharacteristic
34#518×C151C2211yescharacteristic
35C4×#41×C151C2211yescharacteristic
36C2×C4×D4×C151C2211yescharacteristic
37#478×C151—21no—
38#478×C151—21no—
39#476×C151—21no—
40#474×C151—21no—
41#442×C151—21no—
42#440×C151—21no—
43C4×SD16×C151—21no—
44C4×D8×C151—21no—
45#428×C151C2211yescharacteristic
46#428×C151C2211yescharacteristic
47#428×C151C2211yescharacteristic
48#423×C151C2211yescharacteristic
49C2×#104×C151C2211yescharacteristic
50C2×#104×C151C2211yescharacteristic
51#418×C151C2211yescharacteristic
52#418×C151C2211yescharacteristic
53#418×C151C2211yescharacteristic
54#417×C151C2211yescharacteristic
55C2×#101×C151C2211yescharacteristic
56C2×#101×C151C2211yescharacteristic
57C2×#100×C151C2211yescharacteristic
58C2×#100×C151C2211yescharacteristic
59C4×M16×C151C2211yescharacteristic
60#394×C151—22no—
61#391×C151C2211yescharacteristic
62#390×C151C2211yescharacteristic
63#386×C151—22no—
64C4×C4⋊C4×C151C2211yescharacteristic
65#339×C151C2211yescharacteristic
66#339×C151C2211yescharacteristic
67#339×C151C2211yescharacteristic
68#339×C151C2211yescharacteristic
69#339×C151C2211yescharacteristic
70#339×C151C2211yescharacteristic
71C2×#41×C151C2311yescharacteristic
72C22×Q8×C151C2311yescharacteristic
73C22×D4×C151—22no—
74C22×D4×C151C2311yescharacteristic
75C22×D4×C151C2311yescharacteristic
76C23×C4×C151—21no—
77AGL(1,ℤ/8)×C151—22no—
78AGL(1,ℤ/8)×C151—22no—
79C2×SD16×C151—21no—
80C2×D8×C151—21no—
81C2×M16×C151C2311yescharacteristic
82C2×M16×C151C2311yescharacteristic
83C2×M16×C151C2311yescharacteristic
84C2×M16×C151C2311yescharacteristic
85C4⋊Q8×C151—21no—
86C4⋊Q8×C151D411yescharacteristic, complemented
87C4⋊Q8×C151D411yescharacteristic, complemented
88#127×C151—21no—
89#127×C151—22no—
90#127×C151—41no—
91#126×C151—22no—
92#126×C151—22no—
93#126×C151—22no—
94#126×C151—22no—
95#125×C151D411yescharacteristic, complemented
96#125×C151D411yescharacteristic, complemented
97#124×C151—22no—
98#124×C151—22no—
99#124×C151—21no—
100#124×C151—22no—
101#124×C151—21no—
102#124×C151—21no—
103#124×C151—21no—
104#124×C151—21no—
105#124×C151—21no—
106#124×C151—41no—
107#123×C151—22no—
108#123×C151—22no—
109#123×C151—22no—
110#123×C151—22no—
111#123×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—21no—
115C22⋊Q8×C151—21no—
116C22⋊Q8×C151—21no—
117C22⋊Q8×C151—21no—
118#121×C151—21no—
119#121×C151—21no—
120#120×C151—22no—
121C4×Q8×C151—21no—
122C4×Q8×C151—21no—
123C4×Q8×C151—21no—
124C4×Q8×C151—21no—
125C4×Q8×C151—21no—
126C4×Q8×C151—21no—
127C4×Q8×C151D411yescharacteristic, complemented
128C4×Q8×C151D411yescharacteristic, complemented
129C4×D4×C151—22no—
130C4×D4×C151—22no—
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×C151—21no—
138C4×D4×C151—21no—
139C4×D4×C151—21no—
140C4×D4×C151—21no—
141C4×D4×C151D411yescharacteristic, complemented
142C4×D4×C151D411yescharacteristic, complemented
143#117×C151—22no—
144#117×C151—22no—
145#117×C151—22no—
146#117×C151—21no—
147#117×C151C2311yescharacteristic
148#117×C151C2311yescharacteristic
149#117×C151C2311yescharacteristic
150C2×C4⋊C4×C151—21no—
151C2×C4⋊C4×C151C2311yescharacteristic
152C2×C22⋊C4×C151—22no—
153C2×C22⋊C4×C151—21no—
154C2×C22⋊C4×C151—22no—
155C2×C22⋊C4×C151—22no—
156C2×C22⋊C4×C151D412yes—
157C2×C22⋊C4×C151D412yes—
158C2×C42×C151—21no—
159C2×C42×C151C2311yescharacteristic
160C2×C42×C151C2311yescharacteristic
161C2×C42×C151C2311yescharacteristic
162#107×C151—21no—
163#107×C151—21no—
164#107×C151—21no—
165#106×C151—21no—
166#106×C151—21no—
167#106×C151—21no—
168C4⋊C8×C151—21no—
169C4⋊C8×C151—21no—
170#104×C151—41no—
171#104×C151—41no—
172#103×C151—21no—
173#102×C151—21no—
174#102×C151—21no—
175#102×C151—21no—
176#102×C151—21no—
177#102×C151—21no—
178#102×C151—21no—
179#102×C151—21no—
180#101×C151—22no—
181#101×C151—41no—
182#100×C151—22no—
183#100×C151—41no—
184#97×C151—21no—
185C4×C8×C151—21no—
186#95×C151—21no—
187#95×C151—22no—
188C24×C151—21no—
189C24×C151C2×D412yes—
190#41×C151—21no—
191#41×C151—21no—
192#41×C151—21no—
193#41×C151—21no—
194C2×Q8×C151—21no—
195C2×Q8×C151—21no—
196C2×Q8×C151—21no—
197C2×Q8×C151—21no—
198C2×Q8×C151—21no—
199C2×Q8×C151—21no—
200C2×Q8×C151—21no—
201C2×Q8×C151—21no—
202C2×Q8×C151C2×D411yescharacteristic
203C2×D4×C151—21no—
204C2×D4×C151—22no—
205C2×D4×C151—22no—
206C2×D4×C151—21no—
207C2×D4×C151—21no—
208C2×D4×C151—21no—
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×C151—21no—
217C2×D4×C151—44no—
218C2×D4×C151—44no—
219C2×D4×C151—82no—
220C2×D4×C151C2×D411yescharacteristic
221C2×D4×C151#4112yes—
222C22×C4×C151—21no—
223C22×C4×C151—22no—
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—41no—
231C22×C4×C151—41no—
232C22×C4×C151—82no—
233C22×C4×C151C2×D412yes—
234C22×C4×C151C2×D411yescharacteristic
235C22×C4×C151C2×D411yescharacteristic
236C22×C4×C151C2411yescharacteristic
237SD16×C151—24no—
238D8×C151—24no—
239M16×C151—21no—
240M16×C151—21no—
241M16×C151—21no—
242M16×C151—21no—
243M16×C151—21no—
244M16×C151—21no—
245M16×C151—21no—
246M16×C151#4112yes—
247C2×C8×C151—21no—
248C2×C8×C151—21no—
249C2×C8×C151—21no—
250C2×C8×C151—21no—
251C4⋊C4×C151—22no—
252C4⋊C4×C151—22no—
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×C151—21no—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—42no—
266C4⋊C4×C151C2×D411yescharacteristic
267C4⋊C4×C151C2×D411yescharacteristic
268C4⋊C4×C151C2×D411yescharacteristic
269C4⋊C4×C151C2×D411yescharacteristic
270C4⋊C4×C151C2×D411yescharacteristic
271C4⋊C4×C151C2×D411yescharacteristic
272C22⋊C4×C151—22no—
273C22⋊C4×C151—22no—
274C22⋊C4×C151—22no—
275C22⋊C4×C151—22no—
276C22⋊C4×C151—22no—
277C22⋊C4×C151—22no—
278C22⋊C4×C151—21no—
279C22⋊C4×C151—21no—
280C22⋊C4×C151—21no—
281C22⋊C4×C151—22no—
282C22⋊C4×C151—22no—
283C22⋊C4×C151—22no—
284C22⋊C4×C151—22no—
285C22⋊C4×C151—21no—
286C22⋊C4×C151—21no—
287C22⋊C4×C151—44no—
288C22⋊C4×C151—41no—
289C22⋊C4×C151—41no—
290C22⋊C4×C151—82no—
291C42×C151—22no—
292C42×C151—22no—
293C42×C151—21no—
294C42×C151—21no—
295C42×C151—21no—
296C42×C151—21no—
297C42×C151—21no—
298C42×C151—21no—
299C42×C151—21no—
300C42×C151—21no—
301C42×C151—21no—
302C42×C151C2×D411yescharacteristic
303C42×C151C2×D411yescharacteristic
304C42×C151C2×D411yescharacteristic
305C42×C151C2×D411yescharacteristic
306C23×C151—22no—
307C23×C151—21no—
308C23×C151—22no—
309C23×C151—22no—
310C23×C151—22no—
311C23×C151—42no—
312C23×C151—42no—
313C23×C151—42no—
314C23×C151—42no—
315C23×C151—41no—
316C23×C151—41no—
317C23×C151C22×D411yescharacteristic
318Q8×C151—21no—
319Q8×C151—21no—
320Q8×C151—41no—
321Q8×C151—41no—
322Q8×C151—41no—
323Q8×C151—41no—
324Q8×C151—81no—
325Q8×C151—81no—
326D4×C151—21no—
327D4×C151—22no—
328D4×C151—21no—
329D4×C151—22no—
330D4×C151—41no—
331D4×C151—41no—
332D4×C151—41no—
333D4×C151—41no—
334D4×C151—41no—
335D4×C151—41no—
336D4×C151—41no—
337D4×C151—41no—
338D4×C151—82no—
339D4×C151—82no—
340D4×C151—88no—
341C2×C4×C151—22no—
342C2×C4×C151—22no—
343C2×C4×C151—21no—
344C2×C4×C151—21no—
345C2×C4×C151—21no—
346C2×C4×C151—21no—
347C2×C4×C151—21no—
348C2×C4×C151—21no—
349C2×C4×C151—21no—
350C2×C4×C151—22no—
351C2×C4×C151—22no—
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—42no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—81no—
364C2×C4×C151—81no—
365C2×C4×C151—82no—
366C2×C4×C151—82no—
367C2×C4×C151—82no—
368C2×C4×C151—82no—
369C2×C4×C151#12011yescharacteristic
370C2×C4×C151#12011yescharacteristic
371C2×C4×C151#12011yescharacteristic
372C2×C4×C151#12011yescharacteristic
373C2×C4×C151C22×D411yescharacteristic
374C2×C4×C151C22×D411yescharacteristic
375C2×C4×C151C2×#4111yescharacteristic
376C2×C4×C151C2×#4111yescharacteristic
377C2×C4×C151H(5,𝔽2)11yescharacteristic
378C2×C4×C1512−1+411yescharacteristic
379C8×C151—22no—
380C8×C151—41no—
381C8×C151—41no—
382C8×C151—41no—
383C22×C151—21no—
384C22×C151—21no—
385C22×C151—44no—
386C22×C151—41no—
387C22×C151—42no—
388C22×C151—42no—
389C22×C151—41no—
390C22×C151—42no—
391C22×C151—41no—
392C22×C151—42no—
393C22×C151—82no—
394C22×C151—82no—
395C22×C151—82no—
396C22×C151—81no—
397C22×C151—81no—
398C22×C151C2×#12011yescharacteristic
399C22×C151#54611yescharacteristic
400C22×C151#54711yescharacteristic
401C4×C151—21no—
402C4×C151—21no—
403C4×C151—21no—
404C4×C151—21no—
405C4×C151—42no—
406C4×C151—42no—
407C4×C151—41no—
408C4×C151—41no—
409C4×C151—41no—
410C4×C151—41no—
411C4×C151—41no—
412C4×C151—41no—
413C4×C151—41no—
414C4×C151—81no—
415C4×C151—81no—
416C4×C151#52511yescharacteristic
417C4×C151#53711yescharacteristic
418C4×C151#54811yescharacteristic
419C4×C151#55011yescharacteristic
420C2×C151—21no—
421C2×C151—21no—
422C2×C151—81no—
423C2×C151—82no—
424C2×C151—82no—
425C2×C151#240711yescharacteristic
426C2×C151#301811yescharacteristic
427C2×C151#302111yescharacteristic
428#24148C15111yesmaximal, characteristic, direct product factor, Sylow
429C151#2414811yescharacteristic, direct product factor, Sylow
430#3510C2×C15111yescharacteristic, complemented
431#3077C2×C15111yescharacteristic, complemented
432C4×AGL(1,ℤ/8)C2×C15111yescharacteristic, complemented
433#2544C2×C15111yescharacteristic, complemented
434#2038C2×C15111yescharacteristic, complemented
435#2037C2×C15111yescharacteristic, complemented
436#2003C2×C15111yescharacteristic, complemented
437#2002C2×C15111yescharacteristic
438#1986C2×C15111yescharacteristic, complemented
439#1967C2×C15111yescharacteristic, complemented
440#1888C2×C15111yescharacteristic, complemented
441#1887C2×C15111yescharacteristic, complemented
442#1857C2×C15111yescharacteristic, complemented
443#1856C2×C15111yescharacteristic, complemented
444#1806C2×C15111yescharacteristic, complemented
445C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
446#559—21no—
447#559—21no—
448#556—21no—
449#556—21no—
450#551—22no—
451#551—22no—
452#542—21no—
453#542—21no—
454#536C22×C15111yescharacteristic
455#535C22×C15111yescharacteristic
456#533C22×C15111yescharacteristic
457C2×#127C22×C15111yescharacteristic
458#529—21no—
459#529—21no—
460C2×#124C22×C15111yescharacteristic
461C2×#124C22×C15111yescharacteristic
462#519C22×C15111yescharacteristic
463#518C22×C15111yescharacteristic
464C4×#41C22×C15111yescharacteristic
465C2×C4×D4C22×C15111yescharacteristic
466#478—21no—
467#478—21no—
468#476—21no—
469#474—21no—
470#442—21no—
471#440—21no—
472C4×SD16—21no—
473C4×D8—21no—
474#428C22×C15111yescharacteristic
475#428C22×C15111yescharacteristic
476#428C22×C15111yescharacteristic
477#423C22×C15111yescharacteristic
478C2×#104C22×C15111yescharacteristic
479C2×#104C22×C15111yescharacteristic
480#418C22×C15111yescharacteristic
481#418C22×C15111yescharacteristic
482#418C22×C15111yescharacteristic
483#417C22×C15111yescharacteristic
484C2×#101C22×C15111yescharacteristic
485C2×#101C22×C15111yescharacteristic
486C2×#100C22×C15111yescharacteristic
487C2×#100C22×C15111yescharacteristic
488C4×M16C22×C15111yescharacteristic
489#394—22no—
490#391C22×C15111yescharacteristic
491#390C22×C15111yescharacteristic
492#386—22no—
493C4×C4⋊C4C22×C15111yescharacteristic
494#339C22×C15111yescharacteristic
495#339C22×C15111yescharacteristic
496#339C22×C15111yescharacteristic
497#339C22×C15111yescharacteristic
498#339C22×C15111yescharacteristic
499#339C22×C15111yescharacteristic
500C2×#41C23×C15111yescharacteristic
501C22×Q8C23×C15111yescharacteristic
502C22×D4—22no—
503C22×D4C23×C15111yescharacteristic
504C22×D4C23×C15111yescharacteristic
505C23×C4—21no—
506AGL(1,ℤ/8)—22no—
507AGL(1,ℤ/8)—22no—
508C2×SD16—21no—
509C2×D8—21no—
510C2×M16C23×C15111yescharacteristic
511C2×M16C23×C15111yescharacteristic
512C2×M16C23×C15111yescharacteristic
513C2×M16C23×C15111yescharacteristic
514C4⋊Q8—21no—
515C4⋊Q8D4×C15111yescharacteristic, complemented
516C4⋊Q8D4×C15111yescharacteristic, complemented
517#127—21no—
518#127—22no—
519#127—41no—
520#126—22no—
521#126—22no—
522#126—22no—
523#126—22no—
524#125D4×C15111yescharacteristic, complemented
525#125D4×C15111yescharacteristic, complemented
526#124—22no—
527#124—22no—
528#124—21no—
529#124—21no—
530#124—22no—
531#124—21no—
532#124—21no—
533#124—21no—
534#124—21no—
535#124—41no—
536#123—22no—
537#123—22no—
538#123—22no—
539#123—22no—
540#123—22no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547#121—21no—
548#121—21no—
549#120—22no—
550C4×Q8—21no—
551C4×Q8—21no—
552C4×Q8—21no—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8—21no—
556C4×Q8D4×C15111yescharacteristic, complemented
557C4×Q8D4×C15111yescharacteristic, complemented
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—21no—
567C4×D4—21no—
568C4×D4—21no—
569C4×D4—21no—
570C4×D4D4×C15111yescharacteristic, complemented
571C4×D4D4×C15111yescharacteristic, complemented
572#117—22no—
573#117—22no—
574#117—22no—
575#117—21no—
576#117C23×C15111yescharacteristic
577#117C23×C15111yescharacteristic
578#117C23×C15111yescharacteristic
579C2×C4⋊C4—21no—
580C2×C4⋊C4C23×C15111yescharacteristic
581C2×C22⋊C4—22no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4D4×C15112yes—
586C2×C22⋊C4D4×C15112yes—
587C2×C42—21no—
588C2×C42C23×C15111yescharacteristic
589C2×C42C23×C15111yescharacteristic
590C2×C42C23×C15111yescharacteristic
591#107—21no—
592#107—21no—
593#107—21no—
594#106—21no—
595#106—21no—
596#106—21no—
597C4⋊C8—21no—
598C4⋊C8—21no—
599#104—41no—
600#104—41no—
601#103—21no—
602#102—21no—
603#102—21no—
604#102—21no—
605#102—21no—
606#102—21no—
607#102—21no—
608#102—21no—
609#101—22no—
610#101—41no—
611#100—22no—
612#100—41no—
613#97—21no—
614C4×C8—21no—
615#95—21no—
616#95—22no—
617C24—21no—
618C24C2×D4×C15112yes—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8C2×D4×C15111yescharacteristic
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—44no—
647C2×D4—44no—
648C2×D4—82no—
649C2×D4C2×D4×C15111yescharacteristic
650C2×D4#41×C15112yes—
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—82no—
662C22×C4C2×D4×C15112yes—
663C22×C4C2×D4×C15111yescharacteristic
664C22×C4C2×D4×C15111yescharacteristic
665C22×C4C24×C15111yescharacteristic
666SD16—24no—
667D8—24no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16#41×C15112yes—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—42no—
695C4⋊C4C2×D4×C15111yescharacteristic
696C4⋊C4C2×D4×C15111yescharacteristic
697C4⋊C4C2×D4×C15111yescharacteristic
698C4⋊C4C2×D4×C15111yescharacteristic
699C4⋊C4C2×D4×C15111yescharacteristic
700C4⋊C4C2×D4×C15111yescharacteristic
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—44no—
717C22⋊C4—41no—
718C22⋊C4—41no—
719C22⋊C4—82no—
720C42—22no—
721C42—22no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42C2×D4×C15111yescharacteristic
732C42C2×D4×C15111yescharacteristic
733C42C2×D4×C15111yescharacteristic
734C42C2×D4×C15111yescharacteristic
735C23—22no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—41no—
745C23—41no—
746C23C22×D4×C15111yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—81no—
754Q8—81no—
755D4—21no—
756D4—22no—
757D4—21no—
758D4—22no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—82no—
768D4—82no—
769D4—88no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—82no—
795C2×C4—82no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4#120×C15111yescharacteristic
799C2×C4#120×C15111yescharacteristic
800C2×C4#120×C15111yescharacteristic
801C2×C4#120×C15111yescharacteristic
802C2×C4C22×D4×C15111yescharacteristic
803C2×C4C22×D4×C15111yescharacteristic
804C2×C4C2×#41×C15111yescharacteristic
805C2×C4C2×#41×C15111yescharacteristic
806C2×C4H(5,𝔽2)×C15111yescharacteristic
807C2×C42−1+4×C15111yescharacteristic
808C8—22no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—21no—
813C22—21no—
814C22—44no—
815C22—41no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—81no—
826C22—81no—
827C22C2×#120×C15111yescharacteristic
828C22#546×C15111yescharacteristic
829C22#547×C15111yescharacteristic
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—42no—
835C4—42no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—81no—
844C4—81no—
845C4#525×C15111yescharacteristic
846C4#537×C15111yescharacteristic
847C4#548×C15111yescharacteristic
848C4#550×C15111yescharacteristic
849C2—21no—
850C2—21no—
851C2—82no—
852C2—82no—
853C2—81no—
854C2#2407×C15111yescharacteristic
855C2#3018×C15111yescharacteristic
856C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2002×C151C2
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. #3510×C151C2semidirect
2. #3077×C151C2semidirect
3. C4×AGL(1,ℤ/8)×C151C2semidirect
4. #2544×C151C2semidirect
5. #2038×C151C2semidirect
6. #2037×C151C2semidirect
7. #2003×C151C2semidirect
9. #1986×C151C2semidirect
10. #1967×C151C2semidirect
11. #1888×C151C2semidirect
12. #1887×C151C2semidirect
13. #1857×C151C2semidirect
14. #1856×C151C2semidirect
15. #1806×C151C2semidirect
86. C4⋊Q8×C151D4semidirect
87. C4⋊Q8×C151D4semidirect
95. #125×C151D4semidirect
96. #125×C151D4semidirect
127. C4×Q8×C151D4semidirect
128. C4×Q8×C151D4semidirect
141. C4×D4×C151D4semidirect
142. C4×D4×C151D4semidirect
428. #24148C151direct (N × H)
429. C151#24148direct (N × H)
430. #3510C2×C151semidirect
431. #3077C2×C151semidirect
432. C4×AGL(1,ℤ/8)C2×C151semidirect
433. #2544C2×C151semidirect
434. #2038C2×C151semidirect
435. #2037C2×C151semidirect
436. #2003C2×C151semidirect
438. #1986C2×C151semidirect
439. #1967C2×C151semidirect
440. #1888C2×C151semidirect
441. #1887C2×C151semidirect
442. #1857C2×C151semidirect
443. #1856C2×C151semidirect
444. #1806C2×C151semidirect
515. C4⋊Q8D4×C151semidirect
516. C4⋊Q8D4×C151semidirect
524. #125D4×C151semidirect
525. #125D4×C151semidirect
556. C4×Q8D4×C151semidirect
557. C4×Q8D4×C151semidirect
570. C4×D4D4×C151semidirect
571. C4×D4D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3510×C1512
#3077×C1512
C4×AGL(1,ℤ/8)×C1512
#2544×C1512
#2038×C1512
#2037×C1512
#2003×C1512
#2002×C1512
#1986×C1512
#1967×C1512
#1888×C1512
#1887×C1512
#1857×C1512
#1856×C1512
#1806×C1512
#24148151