Finite Group Databasebeta

← C151×#24891 #50329816

Subgroups — C151×#24891 #50329816

Order 38656.

1006 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C151C211yesmaximal, characteristic, complemented
2C2×#417×C151C211yesmaximal, characteristic, complemented
3#2407×C151C211yesmaximal, characteristic
4#2352×C151C211yesmaximal, characteristic, complemented
5#2092×C151C211yesmaximal, characteristic, complemented
6#2074×C151C211yesmaximal, characteristic, complemented
7#2035×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#1927×C151C211yesmaximal, characteristic, complemented
10#1926×C151C211yesmaximal, characteristic, complemented
11#1875×C151C211yesmaximal, characteristic, complemented
12#1870×C151C211yesmaximal, characteristic, complemented
13#1853×C151C211yesmaximal, characteristic, complemented
14#1809×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C2×C22⋊Q8×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22C22×C4⋊C4×C151C2211yescharacteristic
23#485×C151—24no—
24C2×#107×C151C2211yescharacteristic
25C2×#106×C151C2211yescharacteristic
26C2×#106×C151C2211yescharacteristic
27C2×#106×C151C2211yescharacteristic
28#417×C151—24no—
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40#394×C151—21no—
41#392×C151—21no—
42#391×C151C2211yescharacteristic
43#390×C151C2211yescharacteristic
44#388×C151—21no—
45#387×C151—21no—
46#386×C151—21no—
47#386×C151—21no—
48#385×C151—21no—
49#382×C151C2211yescharacteristic
50#380×C151C2211yescharacteristic
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C22⋊C4×C151—21no—
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C2×#41×C151—22no—
62C2×#41×C151—22no—
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—41no—
66C2×#41×C151—41no—
67C22×Q8×C151C2311yescharacteristic
68C22×D4×C151—21no—
69C22×D4×C151—21no—
70C22×D4×C151D411yescharacteristic
71C22×D4×C151C2311yescharacteristic
72C23×C4×C151—21no—
73C23×C4×C151—21no—
74C23×C4×C151C2311yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C2×M16×C151—22no—
77C2×M16×C151—22no—
78C2×M16×C151—41no—
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—41no—
85#121×C151—22no—
86#121×C151—41no—
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89#117×C151—22no—
90#117×C151—41no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—41no—
95C2×C4⋊C4×C151D411yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151D411yescharacteristic
111C2×C22⋊C4×C151D411yescharacteristic
112C2×C42×C151—21no—
113C2×C42×C151—21no—
114C2×C42×C151C2311yescharacteristic
115#107×C151—22no—
116#106×C151—22no—
117#106×C151—41no—
118#106×C151—41no—
119#103×C151—22no—
120#103×C151—22no—
121#103×C151—41no—
122#103×C151D414yescomplemented
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—22no—
126#102×C151—41no—
127C22⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—41no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138C24×C151—21no—
139C24×C151C2×D411yescharacteristic
140C24×C151C2×D411yescharacteristic
141#41×C151—28no—
142#41×C151—44no—
143#41×C151—44no—
144#41×C151—44no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151C2×D412yes—
151C2×D4×C151—22no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—41no—
158C2×D4×C151—41no—
159C2×D4×C151—42no—
160C2×D4×C151—42no—
161C2×D4×C151—42no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151—81no—
165C2×D4×C151#4112yes—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—42no—
184C22×C4×C151—42no—
185C22×C4×C151—42no—
186C22×C4×C151—42no—
187C22×C4×C151—42no—
188C22×C4×C151—81no—
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2×D411yescharacteristic
193C22×C4×C151#4112yes—
194C22×C4×C151#4112yes—
195C22×C4×C151C2411yescharacteristic
196M16×C151—44no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151C2×D412yes—
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×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—42no—
222C4⋊C4×C151—42no—
223C4⋊C4×C151C2×D412yes—
224C22⋊C4×C151—22no—
225C22⋊C4×C151—22no—
226C22⋊C4×C151—42no—
227C22⋊C4×C151—42no—
228C22⋊C4×C151—42no—
229C22⋊C4×C151—42no—
230C22⋊C4×C151—42no—
231C22⋊C4×C151—81no—
232C22⋊C4×C151—81no—
233C22⋊C4×C151—81no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—42no—
237C42×C151—81no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—22no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151—41no—
258C23×C151#12312yes—
259C23×C151C22×D411yescharacteristic
260Q8×C151—22no—
261Q8×C151—22no—
262Q8×C151—41no—
263Q8×C151—41no—
264D4×C151—22no—
265D4×C151—22no—
266D4×C151—48no—
267D4×C151—44no—
268D4×C151—41no—
269D4×C151—41no—
270D4×C151—84no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—22no—
274C2×C4×C151—22no—
275C2×C4×C151—22no—
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—22no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—48no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—84no—
313C2×C4×C151#12312yes—
314C2×C4×C151C22×D411yescharacteristic
315C2×C4×C151C2×#4111yescharacteristic
316C2×C4×C151C2×#4111yescharacteristic
317C2×C4×C151C2×#4111yescharacteristic
318C2×C4×C151H(5,𝔽2)11yescharacteristic
319C2×C4×C151H(5,𝔽2)11yescharacteristic
320C8×C151—22no—
321C8×C151—41no—
322C8×C151—41no—
323C8×C151—41no—
324C22×C151—22no—
325C22×C151—22no—
326C22×C151—22no—
327C22×C151—41no—
328C22×C151—41no—
329C22×C151—41no—
330C22×C151—41no—
331C22×C151—41no—
332C22×C151—41no—
333C22×C151—42no—
334C22×C151—41no—
335C22×C151—41no—
336C22×C151—41no—
337C22×C151—41no—
338C22×C151—42no—
339C22×C151—41no—
340C22×C151—42no—
341C22×C151—81no—
342C22×C151—81no—
343C22×C151—81no—
344C22×C151—81no—
345C22×C151C2×#12311yescharacteristic
346C22×C151D4211yescharacteristic
347C22×C151#54611yescharacteristic
348C22×C151#57511yescharacteristic
349C22×C151#57511yescharacteristic
350C22×C151#57711yescharacteristic
351C22×C151#57711yescharacteristic
352C4×C151—22no—
353C4×C151—41no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—42no—
357C4×C151—42no—
358C4×C151—81no—
359C4×C151—81no—
360C4×C151—81no—
361C4×C151—81no—
362C4×C151—81no—
363C4×C151#52511yescharacteristic
364C4×C151#53811yescharacteristic
365C4×C151#54611yescharacteristic
366C4×C151#55111yescharacteristic
367C2×C151—42no—
368C2×C151—81no—
369C2×C151—82no—
370C2×C151#241811yescharacteristic
371C2×C151#309311yescharacteristic
372C2×C151#309911yescharacteristic
373C2×C151#327111yescharacteristic
374C2×C151#327511yescharacteristic
375C2×C151#330711yescharacteristic
376C2×C151#332311yescharacteristic
377#24891C15111yesmaximal, characteristic, direct product factor, Sylow
378C151#2489111yescharacteristic, direct product factor, Sylow
379C2×#485C2×C15111yescharacteristic, complemented
380C2×#417C2×C15111yescharacteristic, complemented
381#2407C2×C15111yescharacteristic
382#2352C2×C15111yescharacteristic, complemented
383#2092C2×C15111yescharacteristic, complemented
384#2074C2×C15111yescharacteristic, complemented
385#2035C2×C15111yescharacteristic, complemented
386#2034C2×C15111yescharacteristic, complemented
387#1927C2×C15111yescharacteristic, complemented
388#1926C2×C15111yescharacteristic, complemented
389#1875C2×C15111yescharacteristic, complemented
390#1870C2×C15111yescharacteristic, complemented
391#1853C2×C15111yescharacteristic, complemented
392#1809C2×C15111yescharacteristic, complemented
393#1788C2×C15111yescharacteristic, complemented
394C22×#41C22×C15111yescharacteristic
395C22×M16C22×C15111yescharacteristic
396C2×C22⋊Q8C22×C15111yescharacteristic
397C2×#121C22×C15111yescharacteristic
398C2×C4×D4C22×C15111yescharacteristic
399C2×#117C22×C15111yescharacteristic
400C22×C4⋊C4C22×C15111yescharacteristic
401#485—24no—
402C2×#107C22×C15111yescharacteristic
403C2×#106C22×C15111yescharacteristic
404C2×#106C22×C15111yescharacteristic
405C2×#106C22×C15111yescharacteristic
406#417—24no—
407C2×#103C22×C15111yescharacteristic
408C2×#103C22×C15111yescharacteristic
409C2×#103C22×C15111yescharacteristic
410C2×#103C22×C15111yescharacteristic
411C2×#102C22×C15111yescharacteristic
412C2×#102C22×C15111yescharacteristic
413C2×#102C22×C15111yescharacteristic
414C2×#102C22×C15111yescharacteristic
415C2×C22⋊C8C22×C15111yescharacteristic
416C2×C22⋊C8C22×C15111yescharacteristic
417C2×C22⋊C8C22×C15111yescharacteristic
418#394—21no—
419#392—21no—
420#391C22×C15111yescharacteristic
421#390C22×C15111yescharacteristic
422#388—21no—
423#387—21no—
424#386—21no—
425#386—21no—
426#385—21no—
427#382C22×C15111yescharacteristic
428#380C22×C15111yescharacteristic
429#380C22×C15111yescharacteristic
430#380C22×C15111yescharacteristic
431C4×C4⋊C4C22×C15111yescharacteristic
432C4×C22⋊C4—21no—
433#340C22×C15111yescharacteristic
434#340C22×C15111yescharacteristic
435#340C22×C15111yescharacteristic
436#340C22×C15111yescharacteristic
437#336C22×C15111yescharacteristic
438#336C22×C15111yescharacteristic
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—41no—
444C2×#41—41no—
445C22×Q8C23×C15111yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4D4×C15111yescharacteristic
449C22×D4C23×C15111yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4C23×C15111yescharacteristic
453C23×C4C23×C15111yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8C23×C15111yescharacteristic
458C22×C8C23×C15111yescharacteristic
459C22×C8C23×C15111yescharacteristic
460C22×C8C23×C15111yescharacteristic
461C22⋊Q8—22no—
462C22⋊Q8—41no—
463#121—22no—
464#121—41no—
465C4×D4—22no—
466C4×D4—22no—
467#117—22no—
468#117—41no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4D4×C15111yescharacteristic
474C2×C4⋊C4C23×C15111yescharacteristic
475C2×C4⋊C4C23×C15111yescharacteristic
476C2×C4⋊C4C23×C15111yescharacteristic
477C2×C4⋊C4C23×C15111yescharacteristic
478C2×C4⋊C4C23×C15111yescharacteristic
479C2×C4⋊C4C23×C15111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4D4×C15111yescharacteristic
489C2×C22⋊C4D4×C15111yescharacteristic
490C2×C42—21no—
491C2×C42—21no—
492C2×C42C23×C15111yescharacteristic
493#107—22no—
494#106—22no—
495#106—41no—
496#106—41no—
497#103—22no—
498#103—22no—
499#103—41no—
500#103D4×C15114yescomplemented
501#102—22no—
502#102—22no—
503#102—22no—
504#102—41no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—41no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516C24—21no—
517C24C2×D4×C15111yescharacteristic
518C24C2×D4×C15111yescharacteristic
519#41—28no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C2×D4×C15112yes—
529C2×D4—22no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—81no—
543C2×D4#41×C15112yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4C2×D4×C15111yescharacteristic
568C22×C4C2×D4×C15111yescharacteristic
569C22×C4C2×D4×C15111yescharacteristic
570C22×C4C2×D4×C15111yescharacteristic
571C22×C4#41×C15112yes—
572C22×C4#41×C15112yes—
573C22×C4C24×C15111yescharacteristic
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8C2×D4×C15112yes—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4C2×D4×C15112yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C42—21no—
613C42—21no—
614C42—42no—
615C42—81no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23#123×C15112yes—
637C23C22×D4×C15111yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—41no—
641Q8—41no—
642D4—22no—
643D4—22no—
644D4—44no—
645D4—48no—
646D4—41no—
647D4—41no—
648D4—84no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—48no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—84no—
691C2×C4#123×C15112yes—
692C2×C4C22×D4×C15111yescharacteristic
693C2×C4C2×#41×C15111yescharacteristic
694C2×C4C2×#41×C15111yescharacteristic
695C2×C4C2×#41×C15111yescharacteristic
696C2×C4H(5,𝔽2)×C15111yescharacteristic
697C2×C4H(5,𝔽2)×C15111yescharacteristic
698C8—22no—
699C8—41no—
700C8—41no—
701C8—41no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—42no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—41no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22C2×#123×C15111yescharacteristic
724C22D42×C15111yescharacteristic
725C22#546×C15111yescharacteristic
726C22#575×C15111yescharacteristic
727C22#575×C15111yescharacteristic
728C22#577×C15111yescharacteristic
729C22#577×C15111yescharacteristic
730C4—22no—
731C4—41no—
732C4—42no—
733C4—42no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4#525×C15111yescharacteristic
742C4#538×C15111yescharacteristic
743C4#546×C15111yescharacteristic
744C4#551×C15111yescharacteristic
745C2—42no—
746C2—81no—
747C2—82no—
748C2#2418×C15111yescharacteristic
749C2#3093×C15111yescharacteristic
750C2#3099×C15111yescharacteristic
751C2#3271×C15111yescharacteristic
752C2#3275×C15111yescharacteristic
753C2#3307×C15111yescharacteristic
754C2#3323×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2407×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C151C2semidirect
2. C2×#417×C151C2semidirect
4. #2352×C151C2semidirect
5. #2092×C151C2semidirect
6. #2074×C151C2semidirect
7. #2035×C151C2semidirect
8. #2034×C151C2semidirect
9. #1927×C151C2semidirect
10. #1926×C151C2semidirect
11. #1875×C151C2semidirect
12. #1870×C151C2semidirect
13. #1853×C151C2semidirect
14. #1809×C151C2semidirect
15. #1788×C151C2semidirect
122. #103×C151D4semidirect
377. #24891C151direct (N × H)
378. C151#24891direct (N × H)
379. C2×#485C2×C151semidirect
380. C2×#417C2×C151semidirect
382. #2352C2×C151semidirect
383. #2092C2×C151semidirect
384. #2074C2×C151semidirect
385. #2035C2×C151semidirect
386. #2034C2×C151semidirect
387. #1927C2×C151semidirect
388. #1926C2×C151semidirect
389. #1875C2×C151semidirect
390. #1870C2×C151semidirect
391. #1853C2×C151semidirect
392. #1809C2×C151semidirect
393. #1788C2×C151semidirect
500. #103D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1512
C2×#417×C1512
#2407×C1512
#2352×C1512
#2092×C1512
#2074×C1512
#2035×C1512
#2034×C1512
#1927×C1512
#1926×C1512
#1875×C1512
#1870×C1512
#1853×C1512
#1809×C1512
#1788×C1512
#24891151