Finite Group Databasebeta

← C151×#24504 #50329429

Subgroups — C151×#24504 #50329429

Order 38656.

1058 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×#449×C151C211yesmaximal, characteristic
2C2×#431×C151C211yesmaximal, characteristic, complemented
3#2854×C151C211yesmaximal, characteristic, complemented
4#2297×C151C211yesmaximal, characteristic, complemented
5#2068×C151C211yesmaximal, characteristic, complemented
6#2065×C151C211yesmaximal, characteristic, complemented
7#2055×C151C211yesmaximal, characteristic, complemented
8#2054×C151C211yesmaximal, characteristic, complemented
9#1970×C151C211yesmaximal, characteristic, complemented
10#1968×C151C211yesmaximal, characteristic, complemented
11#1934×C151C211yesmaximal, characteristic, complemented
12#1933×C151C211yesmaximal, characteristic, complemented
13#1875×C151C211yesmaximal, characteristic, complemented
14#1854×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C2×#123×C151—21no—
20C2×#121×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22C22×C42×C151C2211yescharacteristic
23#449×C151—24no—
24#431×C151—24no—
25C2×#107×C151C2211yescharacteristic
26C2×#106×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C4×C8×C151C2211yescharacteristic
40C2×C4×C8×C151C2211yescharacteristic
41#391×C151C2211yescharacteristic
42#391×C151C2211yescharacteristic
43#390×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#390×C151C2211yescharacteristic
47#389×C151C2211yescharacteristic
48#389×C151C2211yescharacteristic
49#388×C151—21no—
50#388×C151—21no—
51#386×C151—21no—
52#386×C151—21no—
53#386×C151—21no—
54#380×C151C2211yescharacteristic
55C4×C22⋊C4×C151—21no—
56C4×C22⋊C4×C151—21no—
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×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×C151C2311yescharacteristic
71C22×D4×C151C2311yescharacteristic
72C23×C4×C151—21no—
73C23×C4×C151D411yescharacteristic
74C23×C4×C151D411yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C2×SD16×C151—22no—
77C2×SD16×C151—22no—
78C2×SD16×C151—41no—
79C2×D8×C151—22no—
80C2×D8×C151—22no—
81C2×D8×C151—41no—
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86#123×C151—44no—
87#121×C151—22no—
88#121×C151—22no—
89#117×C151—41no—
90#117×C151—41no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
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×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C42×C151—22no—
110C2×C42×C151—22no—
111C2×C42×C151—21no—
112C2×C42×C151D411yescharacteristic
113C2×C42×C151D411yescharacteristic
114C2×C42×C151C2311yescharacteristic
115C2×C42×C151C2311yescharacteristic
116#107×C151—41no—
117#106×C151—41no—
118C4⋊C8×C151—22no—
119C4⋊C8×C151—22no—
120#103×C151—22no—
121#103×C151—22no—
122#103×C151—41no—
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—41no—
126#102×C151—41no—
127#102×C151—41no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151D414yes—
130C4×C8×C151—22no—
131C4×C8×C151—22no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151—21no—
139C24×C151—21no—
140C24×C151—21no—
141C24×C151C2×D411yescharacteristic
142#41×C151—44no—
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—24no—
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—21no—
164C2×D4×C151—42no—
165C2×D4×C151—42no—
166C2×D4×C151—42no—
167C2×D4×C151—42no—
168C2×D4×C151—42no—
169C2×D4×C151#4112yes—
170C22×C4×C151—22no—
171C22×C4×C151—22no—
172C22×C4×C151—22no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—24no—
178C22×C4×C151—22no—
179C22×C4×C151—21no—
180C22×C4×C151—22no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—41no—
187C22×C4×C151—42no—
188C22×C4×C151—42no—
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D412yes—
192C22×C4×C151C2×D411yescharacteristic
193C22×C4×C151C2×D411yescharacteristic
194C22×C4×C151C2×D411yescharacteristic
195C22×C4×C151#4112yes—
196C22×C4×C151C2411yescharacteristic
197SD16×C151—44no—
198D8×C151—44no—
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×C151—21no—
209C2×C8×C151C2×D412yes—
210C2×C8×C151C2×D412yes—
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—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—42no—
225C22⋊C4×C151—42no—
226C22⋊C4×C151—42no—
227C22⋊C4×C151—42no—
228C22⋊C4×C151—42no—
229C22⋊C4×C151—42no—
230C22⋊C4×C151—42no—
231C22⋊C4×C151—42no—
232C22⋊C4×C151—42no—
233C22⋊C4×C151—42no—
234C42×C151—22no—
235C42×C151—22no—
236C42×C151—21no—
237C42×C151—21no—
238C42×C151—21no—
239C42×C151—21no—
240C42×C151—42no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—22no—
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—41no—
261C23×C151#12112yes—
262C23×C151C22×D411yescharacteristic
263Q8×C151—22no—
264Q8×C151—22no—
265Q8×C151—41no—
266Q8×C151—41no—
267D4×C151—22no—
268D4×C151—22no—
269D4×C151—48no—
270D4×C151—41no—
271D4×C151—41no—
272D4×C151—41no—
273D4×C151—41no—
274D4×C151—41no—
275D4×C151—41no—
276D4×C151—84no—
277C2×C4×C151—28no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—22no—
287C2×C4×C151—22no—
288C2×C4×C151—22no—
289C2×C4×C151—22no—
290C2×C4×C151—21no—
291C2×C4×C151—22no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—44no—
295C2×C4×C151—48no—
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—41no—
313C2×C4×C151#12112yes—
314C2×C4×C151#13512yes—
315C2×C4×C151#13512yes—
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—22no—
324C8×C151—22no—
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#52511yescharacteristic
350C22×C151#53511yescharacteristic
351C22×C151C2×#13511yescharacteristic
352C22×C151C2×#13511yescharacteristic
353C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C151#57511yescharacteristic
355C4×C151—22no—
356C4×C151—22no—
357C4×C151—22no—
358C4×C151—22no—
359C4×C151—42no—
360C4×C151—41no—
361C4×C151—81no—
362C4×C151—81no—
363C4×C151—81no—
364C4×C151—81no—
365C4×C151—81no—
366C4×C151#54611yescharacteristic
367C4×C151#54611yescharacteristic
368C4×C151#55111yescharacteristic
369C4×C151#55111yescharacteristic
370C2×C151—42no—
371C2×C151—82no—
372C2×C151—161no—
373C2×C151#241111yescharacteristic
374C2×C151#305011yescharacteristic
375C2×C151#305511yescharacteristic
376C2×C151#310211yescharacteristic
377C2×C151#310611yescharacteristic
378C2×C151#320711yescharacteristic
379C2×C151#321211yescharacteristic
380#24504C15111yesmaximal, characteristic, direct product factor, Sylow
381C151#2450411yescharacteristic, direct product factor, Sylow
382C2×#449C2×C15111yescharacteristic
383C2×#431C2×C15111yescharacteristic, complemented
384#2854C2×C15111yescharacteristic, complemented
385#2297C2×C15111yescharacteristic, complemented
386#2068C2×C15111yescharacteristic, complemented
387#2065C2×C15111yescharacteristic, complemented
388#2055C2×C15111yescharacteristic, complemented
389#2054C2×C15111yescharacteristic, complemented
390#1970C2×C15111yescharacteristic, complemented
391#1968C2×C15111yescharacteristic, complemented
392#1934C2×C15111yescharacteristic, complemented
393#1933C2×C15111yescharacteristic, complemented
394#1875C2×C15111yescharacteristic, complemented
395#1854C2×C15111yescharacteristic, complemented
396#1788C2×C15111yescharacteristic, complemented
397C22×#41C22×C15111yescharacteristic
398C22×SD16C22×C15111yescharacteristic
399C22×D8C22×C15111yescharacteristic
400C2×#123—21no—
401C2×#121C22×C15111yescharacteristic
402C2×#117C22×C15111yescharacteristic
403C22×C42C22×C15111yescharacteristic
404#449—24no—
405#431—24no—
406C2×#107C22×C15111yescharacteristic
407C2×#106C22×C15111yescharacteristic
408C2×C4⋊C8C22×C15111yescharacteristic
409C2×C4⋊C8C22×C15111yescharacteristic
410C2×#103C22×C15111yescharacteristic
411C2×#103C22×C15111yescharacteristic
412C2×#103C22×C15111yescharacteristic
413C2×#102C22×C15111yescharacteristic
414C2×#102C22×C15111yescharacteristic
415C2×#102C22×C15111yescharacteristic
416C2×#102C22×C15111yescharacteristic
417C2×#102C22×C15111yescharacteristic
418C2×C22⋊C8C22×C15111yescharacteristic
419C2×C22⋊C8C22×C15111yescharacteristic
420C2×C4×C8C22×C15111yescharacteristic
421C2×C4×C8C22×C15111yescharacteristic
422#391C22×C15111yescharacteristic
423#391C22×C15111yescharacteristic
424#390C22×C15111yescharacteristic
425#390C22×C15111yescharacteristic
426#390C22×C15111yescharacteristic
427#390C22×C15111yescharacteristic
428#389C22×C15111yescharacteristic
429#389C22×C15111yescharacteristic
430#388—21no—
431#388—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#380C22×C15111yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438#340C22×C15111yescharacteristic
439#340C22×C15111yescharacteristic
440#340C22×C15111yescharacteristic
441#340C22×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×D4C23×C15111yescharacteristic
452C22×D4C23×C15111yescharacteristic
453C23×C4—21no—
454C23×C4D4×C15111yescharacteristic
455C23×C4D4×C15111yescharacteristic
456C23×C4C23×C15111yescharacteristic
457C2×SD16—22no—
458C2×SD16—22no—
459C2×SD16—41no—
460C2×D8—22no—
461C2×D8—22no—
462C2×D8—41no—
463C22×C8C23×C15111yescharacteristic
464C22×C8C23×C15111yescharacteristic
465C22×C8C23×C15111yescharacteristic
466C22×C8C23×C15111yescharacteristic
467#123—44no—
468#121—22no—
469#121—22no—
470#117—41no—
471#117—41no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4C23×C15111yescharacteristic
475C2×C4⋊C4C23×C15111yescharacteristic
476C2×C4⋊C4C23×C15111yescharacteristic
477C2×C4⋊C4C23×C15111yescharacteristic
478C2×C4⋊C4C23×C15111yescharacteristic
479C2×C22⋊C4—21no—
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⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—21no—
493C2×C42D4×C15111yescharacteristic
494C2×C42D4×C15111yescharacteristic
495C2×C42C23×C15111yescharacteristic
496C2×C42C23×C15111yescharacteristic
497#107—41no—
498#106—41no—
499C4⋊C8—22no—
500C4⋊C8—22no—
501#103—22no—
502#103—22no—
503#103—41no—
504#102—22no—
505#102—22no—
506#102—41no—
507#102—41no—
508#102—41no—
509C22⋊C8—22no—
510C22⋊C8D4×C15114yes—
511C4×C8—22no—
512C4×C8—22no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520C24—21no—
521C24—21no—
522C24C2×D4×C15111yescharacteristic
523#41—44no—
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—24no—
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—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4#41×C15112yes—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—41no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4C2×D4×C15111yescharacteristic
571C22×C4C2×D4×C15111yescharacteristic
572C22×C4C2×D4×C15112yes—
573C22×C4C2×D4×C15111yescharacteristic
574C22×C4C2×D4×C15111yescharacteristic
575C22×C4C2×D4×C15111yescharacteristic
576C22×C4#41×C15112yes—
577C22×C4C24×C15111yescharacteristic
578SD16—44no—
579D8—44no—
580C2×C8—21no—
581C2×C8—21no—
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×C8C2×D4×C15112yes—
591C2×C8C2×D4×C15112yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C42—22no—
616C42—22no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—42no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
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—41no—
642C23#121×C15112yes—
643C23C22×D4×C15111yescharacteristic
644Q8—22no—
645Q8—22no—
646Q8—41no—
647Q8—41no—
648D4—22no—
649D4—22no—
650D4—48no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—84no—
658C2×C4—28no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—44no—
676C2×C4—48no—
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—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4#121×C15112yes—
695C2×C4#135×C15112yes—
696C2×C4#135×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—22no—
705C8—22no—
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#525×C15111yescharacteristic
731C22#535×C15111yescharacteristic
732C22C2×#135×C15111yescharacteristic
733C22C2×#135×C15111yescharacteristic
734C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
735C22#575×C15111yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—41no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4#546×C15111yescharacteristic
748C4#546×C15111yescharacteristic
749C4#551×C15111yescharacteristic
750C4#551×C15111yescharacteristic
751C2—42no—
752C2—82no—
753C2—161no—
754C2#2411×C15111yescharacteristic
755C2#3050×C15111yescharacteristic
756C2#3055×C15111yescharacteristic
757C2#3102×C15111yescharacteristic
758C2#3106×C15111yescharacteristic
759C2#3207×C15111yescharacteristic
760C2#3212×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#449×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#431×C151C2semidirect
3. #2854×C151C2semidirect
4. #2297×C151C2semidirect
5. #2068×C151C2semidirect
6. #2065×C151C2semidirect
7. #2055×C151C2semidirect
8. #2054×C151C2semidirect
9. #1970×C151C2semidirect
10. #1968×C151C2semidirect
11. #1934×C151C2semidirect
12. #1933×C151C2semidirect
13. #1875×C151C2semidirect
14. #1854×C151C2semidirect
15. #1788×C151C2semidirect
380. #24504C151direct (N × H)
381. C151#24504direct (N × H)
383. C2×#431C2×C151semidirect
384. #2854C2×C151semidirect
385. #2297C2×C151semidirect
386. #2068C2×C151semidirect
387. #2065C2×C151semidirect
388. #2055C2×C151semidirect
389. #2054C2×C151semidirect
390. #1970C2×C151semidirect
391. #1968C2×C151semidirect
392. #1934C2×C151semidirect
393. #1933C2×C151semidirect
394. #1875C2×C151semidirect
395. #1854C2×C151semidirect
396. #1788C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1512
C2×#431×C1512
#2854×C1512
#2297×C1512
#2068×C1512
#2065×C1512
#2055×C1512
#2054×C1512
#1970×C1512
#1968×C1512
#1934×C1512
#1933×C1512
#1875×C1512
#1854×C1512
#1788×C1512
#24504151