Finite Group Databasebeta

← C151×#24488 #50329413

Subgroups — C151×#24488 #50329413

Order 38656.

1050 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C151C211yesmaximal, characteristic, complemented
2C2×#417×C151C211yesmaximal, characteristic, complemented
3#2431×C151C211yesmaximal, characteristic
4#2344×C151C211yesmaximal, characteristic, complemented
5#2066×C151C211yesmaximal, characteristic, complemented
6#2065×C151C211yesmaximal, characteristic, complemented
7#2042×C151C211yesmaximal, characteristic, complemented
8#2041×C151C211yesmaximal, characteristic, complemented
9#1983×C151C211yesmaximal, characteristic, complemented
10#1982×C151C211yesmaximal, characteristic, complemented
11#1927×C151C211yesmaximal, characteristic, complemented
12#1926×C151C211yesmaximal, characteristic, complemented
13#1895×C151C211yesmaximal, characteristic, complemented
14#1851×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C2×#127×C151C2211yescharacteristic
19C2×#124×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×#117×C151—21no—
22C22×C4⋊C4×C151C2211yescharacteristic
23#481×C151—24no—
24C2×#106×C151C2211yescharacteristic
25C2×#106×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C4⋊C8×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×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×C22⋊C8×C151C2211yescharacteristic
42#392×C151—21no—
43#392×C151—21no—
44#391×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#389×C151C2211yescharacteristic
47#389×C151C2211yescharacteristic
48#387×C151—21no—
49#387×C151—21no—
50#386×C151—21no—
51#386×C151—21no—
52#381×C151—21no—
53#380×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C4⋊C4×C151C2211yescharacteristic
56C4×C22⋊C4×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×C151—21no—
71C22×D4×C151—21no—
72C22×D4×C151C2311yescharacteristic
73C22×D4×C151C2311yescharacteristic
74C23×C4×C151—21no—
75C23×C4×C151—21no—
76C23×C4×C151C2311yescharacteristic
77C2×M16×C151—22no—
78C2×M16×C151—41no—
79C2×M16×C151—41no—
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84#127×C151—22no—
85#127×C151—41no—
86#124×C151—22no—
87#124×C151—41no—
88#121×C151—22no—
89#121×C151—22no—
90#117×C151—44no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—22no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151D414yescomplemented
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C22⋊C4×C151—21no—
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×C151D411yescharacteristic
108C2×C22⋊C4×C151D411yescharacteristic
109C2×C42×C151—21no—
110C2×C42×C151—21no—
111C2×C42×C151C2311yescharacteristic
112C2×C42×C151C2311yescharacteristic
113#106×C151—22no—
114#106×C151—22no—
115C4⋊C8×C151—41no—
116C4⋊C8×C151—41no—
117#103×C151—22no—
118#103×C151—22no—
119#103×C151—22no—
120#103×C151—41no—
121#102×C151—22no—
122#102×C151—22no—
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—22no—
126#102×C151—41no—
127#102×C151—41no—
128#102×C151—41no—
129C22⋊C8×C151—22no—
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×C151D411yescharacteristic
138#95×C151D411yescharacteristic
139C24×C151—21no—
140C24×C151—21no—
141C24×C151C2×D411yescharacteristic
142#41×C151—28no—
143#41×C151—44no—
144#41×C151—44no—
145#41×C151—44no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151#4112yes—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—42no—
164C2×D4×C151—42no—
165C2×D4×C151—42no—
166C2×D4×C151—42no—
167C2×D4×C151—42no—
168C2×D4×C151—42no—
169C2×D4×C151—42no—
170C2×D4×C151—42no—
171C2×D4×C151—81no—
172C2×D4×C151—81no—
173C2×D4×C151—81no—
174C2×D4×C151—81no—
175C2×D4×C151#4112yes—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—24no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—42no—
188C22×C4×C151—42no—
189C22×C4×C151—42no—
190C22×C4×C151—42no—
191C22×C4×C151—42no—
192C22×C4×C151C2×D411yescharacteristic
193C22×C4×C151C2×D411yescharacteristic
194C22×C4×C151C2×D411yescharacteristic
195C22×C4×C151C2×D411yescharacteristic
196C22×C4×C151C2×D412yes—
197C22×C4×C151C2×D411yescharacteristic
198C22×C4×C151#4112yes—
199C22×C4×C151C2411yescharacteristic
200M16×C151—44no—
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×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C4⋊C4×C151—24no—
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—21no—
222C4⋊C4×C151—42no—
223C4⋊C4×C151—42no—
224C4⋊C4×C151C2×D412yes—
225C4⋊C4×C151C2×D412yes—
226C22⋊C4×C151—22no—
227C22⋊C4×C151—41no—
228C22⋊C4×C151—42no—
229C22⋊C4×C151—42no—
230C22⋊C4×C151—42no—
231C22⋊C4×C151—42no—
232C22⋊C4×C151—81no—
233C22⋊C4×C151—81no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151—21no—
238C42×C151—42no—
239C42×C151—42no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—22no—
247C23×C151—41no—
248C23×C151—41no—
249C23×C151—41no—
250C23×C151—41no—
251C23×C151—41no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151—41no—
258C23×C151—41no—
259C23×C151—41no—
260C23×C151#12112yes—
261C23×C151C22×D411yescharacteristic
262Q8×C151—22no—
263Q8×C151—22no—
264Q8×C151—41no—
265Q8×C151—41no—
266D4×C151—22no—
267D4×C151—22no—
268D4×C151—48no—
269D4×C151—41no—
270D4×C151—41no—
271D4×C151—41no—
272D4×C151—41no—
273D4×C151—41no—
274D4×C151—41no—
275D4×C151—84no—
276D4×C151—84no—
277D4×C151—84no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—22no—
283C2×C4×C151—22no—
284C2×C4×C151—22no—
285C2×C4×C151—22no—
286C2×C4×C151—22no—
287C2×C4×C151—22no—
288C2×C4×C151—22no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—48no—
299C2×C4×C151—48no—
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—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151#12112yes—
316C2×C4×C151AGL(1,ℤ/8)12yes—
317C2×C4×C151C22×D411yescharacteristic
318C2×C4×C151C2×#4111yescharacteristic
319C2×C4×C151C2×#4111yescharacteristic
320C2×C4×C151C2×#4111yescharacteristic
321C2×C4×C151H(5,𝔽2)11yescharacteristic
322C2×C4×C151H(5,𝔽2)11yescharacteristic
323C8×C151—41no—
324C8×C151—41no—
325C8×C151—41no—
326C8×C151—41no—
327C22×C151—22no—
328C22×C151—22no—
329C22×C151—22no—
330C22×C151—41no—
331C22×C151—41no—
332C22×C151—41no—
333C22×C151—41no—
334C22×C151—42no—
335C22×C151—42no—
336C22×C151—42no—
337C22×C151—81no—
338C22×C151—81no—
339C22×C151—81no—
340C22×C151—81no—
341C22×C151—81no—
342C22×C151—81no—
343C22×C151—81no—
344C22×C151—81no—
345C22×C151—81no—
346C22×C151—81no—
347C22×C151—81no—
348C22×C151C2×#12111yescharacteristic
349C22×C151#54611yescharacteristic
350C22×C151#54611yescharacteristic
351C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C151#57511yescharacteristic
353C22×C151#57711yescharacteristic
354C22×C151#57711yescharacteristic
355C4×C151—22no—
356C4×C151—22no—
357C4×C151—41no—
358C4×C151—42no—
359C4×C151—42no—
360C4×C151—42no—
361C4×C151—41no—
362C4×C151—41no—
363C4×C151—81no—
364C4×C151—81no—
365C4×C151—81no—
366C4×C151#52511yescharacteristic
367C4×C151#53511yescharacteristic
368C4×C151#55111yescharacteristic
369C4×C151#55111yescharacteristic
370C2×C151—42no—
371C2×C151—82no—
372C2×C151—161no—
373C2×C151#241111yescharacteristic
374C2×C151#303611yescharacteristic
375C2×C151#304311yescharacteristic
376C2×C151#330611yescharacteristic
377C2×C151#331711yescharacteristic
378C2×C151#332311yescharacteristic
379C2×C151#333211yescharacteristic
380#24488C15111yesmaximal, characteristic, direct product factor, Sylow
381C151#2448811yescharacteristic, direct product factor, Sylow
382C2×#481C2×C15111yescharacteristic, complemented
383C2×#417C2×C15111yescharacteristic, complemented
384#2431C2×C15111yescharacteristic
385#2344C2×C15111yescharacteristic, complemented
386#2066C2×C15111yescharacteristic, complemented
387#2065C2×C15111yescharacteristic, complemented
388#2042C2×C15111yescharacteristic, complemented
389#2041C2×C15111yescharacteristic, complemented
390#1983C2×C15111yescharacteristic, complemented
391#1982C2×C15111yescharacteristic, complemented
392#1927C2×C15111yescharacteristic, complemented
393#1926C2×C15111yescharacteristic, complemented
394#1895C2×C15111yescharacteristic, complemented
395#1851C2×C15111yescharacteristic, complemented
396#1788C2×C15111yescharacteristic, complemented
397C22×#41C22×C15111yescharacteristic
398C22×M16C22×C15111yescharacteristic
399C2×#127C22×C15111yescharacteristic
400C2×#124C22×C15111yescharacteristic
401C2×#121C22×C15111yescharacteristic
402C2×#117—21no—
403C22×C4⋊C4C22×C15111yescharacteristic
404#481—24no—
405C2×#106C22×C15111yescharacteristic
406C2×#106C22×C15111yescharacteristic
407C2×C4⋊C8C22×C15111yescharacteristic
408C2×C4⋊C8C22×C15111yescharacteristic
409#417—24no—
410C2×#103C22×C15111yescharacteristic
411C2×#103C22×C15111yescharacteristic
412C2×#103C22×C15111yescharacteristic
413C2×#103C22×C15111yescharacteristic
414C2×#102C22×C15111yescharacteristic
415C2×#102C22×C15111yescharacteristic
416C2×#102C22×C15111yescharacteristic
417C2×#102C22×C15111yescharacteristic
418C2×#102C22×C15111yescharacteristic
419C2×#102C22×C15111yescharacteristic
420C2×#102C22×C15111yescharacteristic
421C2×#102C22×C15111yescharacteristic
422C2×C22⋊C8C22×C15111yescharacteristic
423#392—21no—
424#392—21no—
425#391C22×C15111yescharacteristic
426#390C22×C15111yescharacteristic
427#389C22×C15111yescharacteristic
428#389C22×C15111yescharacteristic
429#387—21no—
430#387—21no—
431#386—21no—
432#386—21no—
433#381—21no—
434#380C22×C15111yescharacteristic
435C4×C4⋊C4C22×C15111yescharacteristic
436C4×C4⋊C4C22×C15111yescharacteristic
437C4×C22⋊C4C22×C15111yescharacteristic
438#340C22×C15111yescharacteristic
439#340C22×C15111yescharacteristic
440#336C22×C15111yescharacteristic
441#336C22×C15111yescharacteristic
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—41no—
447C2×#41—41no—
448C22×Q8C23×C15111yescharacteristic
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C23×C15111yescharacteristic
454C22×D4C23×C15111yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4C23×C15111yescharacteristic
458C2×M16—22no—
459C2×M16—41no—
460C2×M16—41no—
461C22×C8C23×C15111yescharacteristic
462C22×C8C23×C15111yescharacteristic
463C22×C8C23×C15111yescharacteristic
464C22×C8C23×C15111yescharacteristic
465#127—22no—
466#127—41no—
467#124—22no—
468#124—41no—
469#121—22no—
470#121—22no—
471#117—44no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4D4×C15114yescomplemented
477C2×C4⋊C4C23×C15111yescharacteristic
478C2×C4⋊C4C23×C15111yescharacteristic
479C2×C4⋊C4C23×C15111yescharacteristic
480C2×C4⋊C4C23×C15111yescharacteristic
481C2×C4⋊C4C23×C15111yescharacteristic
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
493C2×C42C23×C15111yescharacteristic
494#106—22no—
495#106—22no—
496C4⋊C8—41no—
497C4⋊C8—41no—
498#103—22no—
499#103—22no—
500#103—22no—
501#103—41no—
502#102—22no—
503#102—22no—
504#102—22no—
505#102—22no—
506#102—22no—
507#102—41no—
508#102—41no—
509#102—41no—
510C22⋊C8—22no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95D4×C15111yescharacteristic
519#95D4×C15111yescharacteristic
520C24—21no—
521C24—21no—
522C24C2×D4×C15111yescharacteristic
523#41—28no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8#41×C15112yes—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4#41×C15112yes—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4C2×D4×C15111yescharacteristic
574C22×C4C2×D4×C15111yescharacteristic
575C22×C4C2×D4×C15111yescharacteristic
576C22×C4C2×D4×C15111yescharacteristic
577C22×C4C2×D4×C15112yes—
578C22×C4C2×D4×C15111yescharacteristic
579C22×C4#41×C15112yes—
580C22×C4C24×C15111yescharacteristic
581M16—44no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C4⋊C4—24no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4C2×D4×C15112yes—
606C4⋊C4C2×D4×C15112yes—
607C22⋊C4—22no—
608C22⋊C4—41no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—42no—
620C42—42no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23#121×C15112yes—
642C23C22×D4×C15111yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—41no—
646Q8—41no—
647D4—22no—
648D4—22no—
649D4—48no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657D4—84no—
658D4—84no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—48no—
680C2×C4—48no—
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—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4#121×C15112yes—
697C2×C4AGL(1,ℤ/8)×C15112yes—
698C2×C4C22×D4×C15111yescharacteristic
699C2×C4C2×#41×C15111yescharacteristic
700C2×C4C2×#41×C15111yescharacteristic
701C2×C4C2×#41×C15111yescharacteristic
702C2×C4H(5,𝔽2)×C15111yescharacteristic
703C2×C4H(5,𝔽2)×C15111yescharacteristic
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22C2×#121×C15111yescharacteristic
730C22#546×C15111yescharacteristic
731C22#546×C15111yescharacteristic
732C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
733C22#575×C15111yescharacteristic
734C22#577×C15111yescharacteristic
735C22#577×C15111yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4#525×C15111yescharacteristic
748C4#535×C15111yescharacteristic
749C4#551×C15111yescharacteristic
750C4#551×C15111yescharacteristic
751C2—42no—
752C2—82no—
753C2—161no—
754C2#2411×C15111yescharacteristic
755C2#3036×C15111yescharacteristic
756C2#3043×C15111yescharacteristic
757C2#3306×C15111yescharacteristic
758C2#3317×C15111yescharacteristic
759C2#3323×C15111yescharacteristic
760C2#3332×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2431×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#481×C151C2semidirect
2. C2×#417×C151C2semidirect
4. #2344×C151C2semidirect
5. #2066×C151C2semidirect
6. #2065×C151C2semidirect
7. #2042×C151C2semidirect
8. #2041×C151C2semidirect
9. #1983×C151C2semidirect
10. #1982×C151C2semidirect
11. #1927×C151C2semidirect
12. #1926×C151C2semidirect
13. #1895×C151C2semidirect
14. #1851×C151C2semidirect
15. #1788×C151C2semidirect
95. C2×C4⋊C4×C151D4semidirect
380. #24488C151direct (N × H)
381. C151#24488direct (N × H)
382. C2×#481C2×C151semidirect
383. C2×#417C2×C151semidirect
385. #2344C2×C151semidirect
386. #2066C2×C151semidirect
387. #2065C2×C151semidirect
388. #2042C2×C151semidirect
389. #2041C2×C151semidirect
390. #1983C2×C151semidirect
391. #1982C2×C151semidirect
392. #1927C2×C151semidirect
393. #1926C2×C151semidirect
394. #1895C2×C151semidirect
395. #1851C2×C151semidirect
396. #1788C2×C151semidirect
476. C2×C4⋊C4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1512
C2×#417×C1512
#2431×C1512
#2344×C1512
#2066×C1512
#2065×C1512
#2042×C1512
#2041×C1512
#1983×C1512
#1982×C1512
#1927×C1512
#1926×C1512
#1895×C1512
#1851×C1512
#1788×C1512
#24488151