Finite Group Databasebeta

← C151×#24194 #50329119

Subgroups — C151×#24194 #50329119

Order 38656.

1138 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C151C211yesmaximal, characteristic
2C2×#464×C151C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
4#2581×C151C211yesmaximal, characteristic, complemented
5#2042×C151C211yesmaximal, characteristic, complemented
6#2041×C151C211yesmaximal, characteristic
7#2015×C151C211yesmaximal, characteristic, complemented
8#2014×C151C211yesmaximal, characteristic
9#1984×C151C211yesmaximal, characteristic, complemented
10#1958×C151C211yesmaximal, characteristic, complemented
11#1878×C151C211yesmaximal, characteristic, complemented
12#1877×C151C211yesmaximal, characteristic, complemented
13#1865×C151C211yesmaximal, characteristic, complemented
14#1864×C151C211yesmaximal, characteristic, complemented
15#1804×C151C211yesmaximal, characteristic, complemented
16C22×Q16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19#559×C151—24no—
20#559×C151—24no—
21C2×#127×C151C2211yescharacteristic
22C2×#124×C151—21no—
23C2×#124×C151C2211yescharacteristic
24C2×#124×C151C2211yescharacteristic
25C2×#123×C151—21no—
26C2×#123×C151—21no—
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30C2×C4×D4×C151—21no—
31C2×C4×D4×C151C2211yescharacteristic
32C2×C4×D4×C151C2211yescharacteristic
33#464×C151—24no—
34C4×SD16×C151—24no—
35C2×#106×C151C2211yescharacteristic
36C2×C4⋊C8×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×C4×C8×C151C2211yescharacteristic
48#400×C151—21no—
49#395×C151—21no—
50#391×C151C2211yescharacteristic
51#391×C151C2211yescharacteristic
52#389×C151C2211yescharacteristic
53#389×C151C2211yescharacteristic
54#387×C151—21no—
55#387×C151—21no—
56#382×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151D411yescharacteristic
64C22×Q8×C151C2311yescharacteristic
65C22×Q8×C151C2311yescharacteristic
66C22×D4×C151—21no—
67C22×D4×C151—21no—
68C22×D4×C151C2311yescharacteristic
69C22×D4×C151C2311yescharacteristic
70C23×C4×C151—21no—
71C23×C4×C151—21no—
72C2×Q16×C151—22no—
73C2×Q16×C151—22no—
74C2×Q16×C151—41no—
75C2×SD16×C151—22no—
76C2×SD16×C151—22no—
77C2×SD16×C151—22no—
78C2×SD16×C151—22no—
79C2×SD16×C151—22no—
80C2×SD16×C151—41no—
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85#127×C151—22no—
86#127×C151—22no—
87#124×C151—28no—
88#124×C151—22no—
89#124×C151—22no—
90#124×C151—22no—
91#124×C151D414yes—
92#123×C151—28no—
93#123×C151—28no—
94C4×Q8×C151—22no—
95C4×Q8×C151—22no—
96C4×Q8×C151—22no—
97C4×Q8×C151—22no—
98C4×Q8×C151—22no—
99C4×Q8×C151—22no—
100C4×D4×C151—28no—
101C4×D4×C151—22no—
102C4×D4×C151—22no—
103C4×D4×C151—22no—
104C4×D4×C151D414yes—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151D411yescharacteristic
110C2×C4⋊C4×C151D411yescharacteristic
111C2×C4⋊C4×C151D411yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C42×C151—21no—
123C2×C42×C151—21no—
124C2×C42×C151C2311yescharacteristic
125C2×C42×C151C2311yescharacteristic
126C2×C42×C151C2311yescharacteristic
127#106×C151—22no—
128C4⋊C8×C151—22no—
129#103×C151—22no—
130#103×C151—22no—
131#103×C151—22no—
132#103×C151—41no—
133#102×C151—22no—
134#102×C151—22no—
135#102×C151—22no—
136#102×C151—41no—
137#102×C151—41no—
138#102×C151—41no—
139C4×C8×C151—22no—
140#95×C151—21no—
141#95×C151—21no—
142#95×C151—21no—
143#95×C151—21no—
144#95×C151—21no—
145#95×C151—21no—
146#95×C151—21no—
147#95×C151—21no—
148C24×C151—21no—
149C24×C151—21no—
150C2×Q8×C151—22no—
151C2×Q8×C151—22no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C2×Q8×C151—21no—
158C2×Q8×C151—21no—
159C2×Q8×C151—21no—
160C2×Q8×C151—21no—
161C2×Q8×C151—21no—
162C2×Q8×C151—41no—
163C2×Q8×C151C2×D412yes—
164C2×Q8×C151#4112yes—
165C2×D4×C151—24no—
166C2×D4×C151—24no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—21no—
171C2×D4×C151—21no—
172C2×D4×C151—21no—
173C2×D4×C151—21no—
174C2×D4×C151—21no—
175C2×D4×C151—21no—
176C2×D4×C151—21no—
177C2×D4×C151—42no—
178C2×D4×C151—42no—
179C2×D4×C151—81no—
180C2×D4×C151—81no—
181C2×D4×C151C2×D412yes—
182C2×D4×C151C2×D412yes—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—24no—
187C22×C4×C151—24no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—81no—
192C22×C4×C151—81no—
193C22×C4×C151—81no—
194C22×C4×C151—81no—
195C22×C4×C151C2×D411yescharacteristic
196C22×C4×C151C2×D411yescharacteristic
197C22×C4×C151C2×D411yescharacteristic
198C22×C4×C151C2×D411yescharacteristic
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2411yescharacteristic
202Q16×C151—44no—
203SD16×C151—28no—
204SD16×C151—44no—
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—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151#4112yes—
217C4⋊C4×C151—24no—
218C4⋊C4×C151—22no—
219C4⋊C4×C151—22no—
220C4⋊C4×C151—22no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—42no—
229C4⋊C4×C151—42no—
230C4⋊C4×C151—42no—
231C4⋊C4×C151C2×D412yes—
232C22⋊C4×C151—24no—
233C22⋊C4×C151—24no—
234C22⋊C4×C151—24no—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—24no—
237C22⋊C4×C151—24no—
238C42×C151—24no—
239C42×C151—21no—
240C42×C151—21no—
241C42×C151—21no—
242C42×C151—21no—
243C42×C151—42no—
244C42×C151C2×D412yes—
245C42×C151C2×D412yes—
246C23×C151—22no—
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×C151C22×D411yescharacteristic
261Q8×C151—22no—
262Q8×C151—22no—
263Q8×C151—22no—
264Q8×C151—22no—
265Q8×C151—44no—
266Q8×C151—41no—
267Q8×C151—41no—
268Q8×C151—41no—
269Q8×C151—41no—
270D4×C151—22no—
271D4×C151—22no—
272D4×C151—22no—
273D4×C151—22no—
274D4×C151—48no—
275D4×C151—41no—
276D4×C151—41no—
277D4×C151—41no—
278D4×C151—41no—
279D4×C151—84no—
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—21no—
287C2×C4×C151—22no—
288C2×C4×C151—21no—
289C2×C4×C151—22no—
290C2×C4×C151—21no—
291C2×C4×C151—22no—
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—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—84no—
314C2×C4×C151—84no—
315C2×C4×C151#12012yes—
316C2×C4×C151#12012yes—
317C2×C4×C151#13512yes—
318C2×C4×C151C22×D411yescharacteristic
319C2×C4×C151C22×D411yescharacteristic
320C2×C4×C151C2×#4111yescharacteristic
321C2×C4×C151C2×#4111yescharacteristic
322C2×C4×C151H(5,𝔽2)11yescharacteristic
323C2×C4×C1512−1+411yescharacteristic
324C8×C151—22no—
325C8×C151—41no—
326C8×C151—41no—
327C8×C151—41no—
328C22×C151—42no—
329C22×C151—42no—
330C22×C151—42no—
331C22×C151—42no—
332C22×C151—42no—
333C22×C151—42no—
334C22×C151—81no—
335C22×C151—81no—
336C22×C151—81no—
337C22×C151—81no—
338C22×C151—81no—
339C22×C151—81no—
340C22×C151—81no—
341C22×C151—81no—
342C22×C151C2×#12011yescharacteristic
343C22×C151#54811yescharacteristic
344C22×C151#55011yescharacteristic
345C22×C151C2×#13511yescharacteristic
346C22×C151#57511yescharacteristic
347C22×C151#57711yescharacteristic
348C22×C151#57711yescharacteristic
349C4×C151—22no—
350C4×C151—22no—
351C4×C151—22no—
352C4×C151—42no—
353C4×C151—42no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—41no—
357C4×C151—42no—
358C4×C151—81no—
359C4×C151—81no—
360C4×C151—81no—
361C4×C151#52511yescharacteristic
362C4×C151#53711yescharacteristic
363C4×C151#54611yescharacteristic
364C4×C151#54711yescharacteristic
365C2×C151—82no—
366C2×C151—82no—
367C2×C151#240711yescharacteristic
368C2×C151#300211yescharacteristic
369C2×C151#300911yescharacteristic
370C2×C151#336511yescharacteristic
371C2×C151#337111yescharacteristic
372C2×C151#339411yescharacteristic
373C2×C151#340111yescharacteristic
374#24194C15111yesmaximal, characteristic, direct product factor, Sylow
375C151#2419411yescharacteristic, direct product factor, Sylow
376C2×#559C2×C15111yescharacteristic
377C2×#464C2×C15111yescharacteristic, complemented
378C2×C4×SD16C2×C15111yescharacteristic, complemented
379#2581C2×C15111yescharacteristic, complemented
380#2042C2×C15111yescharacteristic, complemented
381#2041C2×C15111yescharacteristic
382#2015C2×C15111yescharacteristic, complemented
383#2014C2×C15111yescharacteristic
384#1984C2×C15111yescharacteristic, complemented
385#1958C2×C15111yescharacteristic, complemented
386#1878C2×C15111yescharacteristic, complemented
387#1877C2×C15111yescharacteristic, complemented
388#1865C2×C15111yescharacteristic, complemented
389#1864C2×C15111yescharacteristic, complemented
390#1804C2×C15111yescharacteristic, complemented
391C22×Q16C22×C15111yescharacteristic
392C22×SD16C22×C15111yescharacteristic
393C22×SD16C22×C15111yescharacteristic
394#559—24no—
395#559—24no—
396C2×#127C22×C15111yescharacteristic
397C2×#124—21no—
398C2×#124C22×C15111yescharacteristic
399C2×#124C22×C15111yescharacteristic
400C2×#123—21no—
401C2×#123—21no—
402C2×C4×Q8C22×C15111yescharacteristic
403C2×C4×Q8C22×C15111yescharacteristic
404C2×C4×Q8C22×C15111yescharacteristic
405C2×C4×D4—21no—
406C2×C4×D4C22×C15111yescharacteristic
407C2×C4×D4C22×C15111yescharacteristic
408#464—24no—
409C4×SD16—24no—
410C2×#106C22×C15111yescharacteristic
411C2×C4⋊C8C22×C15111yescharacteristic
412C2×#103C22×C15111yescharacteristic
413C2×#103C22×C15111yescharacteristic
414C2×#103C22×C15111yescharacteristic
415C2×#103C22×C15111yescharacteristic
416C2×#102C22×C15111yescharacteristic
417C2×#102C22×C15111yescharacteristic
418C2×#102C22×C15111yescharacteristic
419C2×#102C22×C15111yescharacteristic
420C2×#102C22×C15111yescharacteristic
421C2×#102C22×C15111yescharacteristic
422C2×C4×C8C22×C15111yescharacteristic
423#400—21no—
424#395—21no—
425#391C22×C15111yescharacteristic
426#391C22×C15111yescharacteristic
427#389C22×C15111yescharacteristic
428#389C22×C15111yescharacteristic
429#387—21no—
430#387—21no—
431#382C22×C15111yescharacteristic
432#340C22×C15111yescharacteristic
433#340C22×C15111yescharacteristic
434#336C22×C15111yescharacteristic
435#336C22×C15111yescharacteristic
436#336C22×C15111yescharacteristic
437#336C22×C15111yescharacteristic
438C22×Q8D4×C15111yescharacteristic
439C22×Q8C23×C15111yescharacteristic
440C22×Q8C23×C15111yescharacteristic
441C22×D4—21no—
442C22×D4—21no—
443C22×D4C23×C15111yescharacteristic
444C22×D4C23×C15111yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C2×Q16—22no—
448C2×Q16—22no—
449C2×Q16—41no—
450C2×SD16—22no—
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—41no—
456C22×C8C23×C15111yescharacteristic
457C22×C8C23×C15111yescharacteristic
458C22×C8C23×C15111yescharacteristic
459C22×C8C23×C15111yescharacteristic
460#127—22no—
461#127—22no—
462#124—28no—
463#124—22no—
464#124—22no—
465#124—22no—
466#124D4×C15114yes—
467#123—28no—
468#123—28no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—22no—
475C4×D4—28no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4D4×C15114yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4D4×C15111yescharacteristic
485C2×C4⋊C4D4×C15111yescharacteristic
486C2×C4⋊C4D4×C15111yescharacteristic
487C2×C4⋊C4C23×C15111yescharacteristic
488C2×C4⋊C4C23×C15111yescharacteristic
489C2×C4⋊C4C23×C15111yescharacteristic
490C2×C4⋊C4C23×C15111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42C23×C15111yescharacteristic
500C2×C42C23×C15111yescharacteristic
501C2×C42C23×C15111yescharacteristic
502#106—22no—
503C4⋊C8—22no—
504#103—22no—
505#103—22no—
506#103—22no—
507#103—41no—
508#102—22no—
509#102—22no—
510#102—22no—
511#102—41no—
512#102—41no—
513#102—41no—
514C4×C8—22no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523C24—21no—
524C24—21no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—41no—
538C2×Q8C2×D4×C15112yes—
539C2×Q8#41×C15112yes—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4C2×D4×C15112yes—
557C2×D4C2×D4×C15112yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4—81no—
569C22×C4—81no—
570C22×C4C2×D4×C15111yescharacteristic
571C22×C4C2×D4×C15111yescharacteristic
572C22×C4C2×D4×C15111yescharacteristic
573C22×C4C2×D4×C15111yescharacteristic
574C22×C4C2×D4×C15111yescharacteristic
575C22×C4C2×D4×C15111yescharacteristic
576C22×C4C24×C15111yescharacteristic
577Q16—44no—
578SD16—28no—
579SD16—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×C8—21no—
591C2×C8#41×C15112yes—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
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⋊C4—42no—
606C4⋊C4C2×D4×C15112yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C42—24no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—42no—
619C42C2×D4×C15112yes—
620C42C2×D4×C15112yes—
621C23—22no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23C22×D4×C15111yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—44no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—48no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
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—84no—
689C2×C4—84no—
690C2×C4#120×C15112yes—
691C2×C4#120×C15112yes—
692C2×C4#135×C15112yes—
693C2×C4C22×D4×C15111yescharacteristic
694C2×C4C22×D4×C15111yescharacteristic
695C2×C4C2×#41×C15111yescharacteristic
696C2×C4C2×#41×C15111yescharacteristic
697C2×C4H(5,𝔽2)×C15111yescharacteristic
698C2×C42−1+4×C15111yescharacteristic
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C2×#120×C15111yescharacteristic
718C22#548×C15111yescharacteristic
719C22#550×C15111yescharacteristic
720C22C2×#135×C15111yescharacteristic
721C22#575×C15111yescharacteristic
722C22#577×C15111yescharacteristic
723C22#577×C15111yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—42no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4#525×C15111yescharacteristic
737C4#537×C15111yescharacteristic
738C4#546×C15111yescharacteristic
739C4#547×C15111yescharacteristic
740C2—82no—
741C2—82no—
742C2#2407×C15111yescharacteristic
743C2#3002×C15111yescharacteristic
744C2#3009×C15111yescharacteristic
745C2#3365×C15111yescharacteristic
746C2#3371×C15111yescharacteristic
747C2#3394×C15111yescharacteristic
748C2#3401×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#127×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#464×C151C2semidirect
3. C2×C4×SD16×C151C2semidirect
4. #2581×C151C2semidirect
5. #2042×C151C2semidirect
7. #2015×C151C2semidirect
9. #1984×C151C2semidirect
10. #1958×C151C2semidirect
11. #1878×C151C2semidirect
12. #1877×C151C2semidirect
13. #1865×C151C2semidirect
14. #1864×C151C2semidirect
15. #1804×C151C2semidirect
374. #24194C151direct (N × H)
375. C151#24194direct (N × H)
377. C2×#464C2×C151semidirect
378. C2×C4×SD16C2×C151semidirect
379. #2581C2×C151semidirect
380. #2042C2×C151semidirect
382. #2015C2×C151semidirect
384. #1984C2×C151semidirect
385. #1958C2×C151semidirect
386. #1878C2×C151semidirect
387. #1877C2×C151semidirect
388. #1865C2×C151semidirect
389. #1864C2×C151semidirect
390. #1804C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#559×C1512
C2×#464×C1512
C2×C4×SD16×C1512
#2581×C1512
#2042×C1512
#2041×C1512
#2015×C1512
#2014×C1512
#1984×C1512
#1958×C1512
#1878×C1512
#1877×C1512
#1865×C1512
#1864×C1512
#1804×C1512
#24194151