Finite Group Databasebeta

← C151×#24195 #50329120

Subgroups — C151×#24195 #50329120

Order 38656.

1074 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C151C211yesmaximal, characteristic
2C2×#464×C151C211yesmaximal, characteristic
3C2×C4×Q16×C151C211yesmaximal, characteristic, complemented
4#2581×C151C211yesmaximal, characteristic, complemented
5#2043×C151C211yesmaximal, characteristic, complemented
6#2042×C151C211yesmaximal, characteristic
7#2016×C151C211yesmaximal, characteristic, complemented
8#2015×C151C211yesmaximal, characteristic
9#1984×C151C211yesmaximal, characteristic, complemented
10#1958×C151C211yesmaximal, characteristic
11#1878×C151C211yesmaximal, characteristic, complemented
12#1877×C151C211yesmaximal, characteristic
13#1863×C151C211yesmaximal, characteristic, complemented
14#1862×C151C211yesmaximal, characteristic
15#1805×C151C211yesmaximal, characteristic, complemented
16C22×Q16×C151C2211yescharacteristic
17C22×Q16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19#556×C151—24no—
20#556×C151—24no—
21C2×C4⋊Q8×C151C2211yescharacteristic
22C2×#126×C151—21no—
23C2×#126×C151—21no—
24C2×#124×C151C2211yescharacteristic
25C2×#124×C151C2211yescharacteristic
26C2×C22⋊Q8×C151—21no—
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30C2×C4×Q8×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×#117×C151—21no—
33#464×C151—24no—
34C4×Q16×C151—24no—
35C2×#107×C151C2211yescharacteristic
36C2×C4⋊C8×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×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×Q8×C151C2311yescharacteristic
67C22×D4×C151C2311yescharacteristic
68C23×C4×C151—21no—
69C2×Q16×C151—22no—
70C2×Q16×C151—22no—
71C2×Q16×C151—22no—
72C2×Q16×C151—22no—
73C2×Q16×C151—22no—
74C2×Q16×C151—41no—
75C2×SD16×C151—22no—
76C2×SD16×C151—22no—
77C2×SD16×C151—41no—
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C4⋊Q8×C151—22no—
83C4⋊Q8×C151—22no—
84#126×C151—28no—
85#126×C151—28no—
86#124×C151—22no—
87#124×C151—22no—
88#124×C151—22no—
89#124×C151D414yes—
90C22⋊Q8×C151—28no—
91C4×Q8×C151—22no—
92C4×Q8×C151—22no—
93C4×Q8×C151—22no—
94C4×Q8×C151—22no—
95C4×Q8×C151—22no—
96C4×Q8×C151—22no—
97C4×Q8×C151—22no—
98C4×Q8×C151D414yes—
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101#117×C151—28no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—21no—
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×C42×C151—21no—
122C2×C42×C151—21no—
123C2×C42×C151—21no—
124C2×C42×C151C2311yescharacteristic
125C2×C42×C151C2311yescharacteristic
126C2×C42×C151C2311yescharacteristic
127#107×C151—22no—
128C4⋊C8×C151—22no—
129#103×C151—22no—
130#103×C151—22no—
131#103×C151—22no—
132#103×C151—22no—
133#103×C151—41no—
134#103×C151—41no—
135#103×C151—41no—
136#102×C151—22no—
137#102×C151—22no—
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—
149C2×Q8×C151—22no—
150C2×Q8×C151—22no—
151C2×Q8×C151—21no—
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—21no—
163C2×Q8×C151—21no—
164C2×Q8×C151—21no—
165C2×Q8×C151—21no—
166C2×Q8×C151—41no—
167C2×Q8×C151C2×D412yes—
168C2×Q8×C151C2×D412yes—
169C2×Q8×C151#4112yes—
170C2×D4×C151—21no—
171C2×D4×C151—21no—
172C2×D4×C151—21no—
173C2×D4×C151—21no—
174C2×D4×C151—21no—
175C2×D4×C151C2×D412yes—
176C22×C4×C151—24no—
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—21no—
184C22×C4×C151—42no—
185C22×C4×C151—42no—
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2411yescharacteristic
193Q16×C151—28no—
194Q16×C151—44no—
195SD16×C151—44no—
196C2×C8×C151—21no—
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#4112yes—
208C4⋊C4×C151—24no—
209C4⋊C4×C151—24no—
210C4⋊C4×C151—24no—
211C4⋊C4×C151—24no—
212C4⋊C4×C151—22no—
213C4⋊C4×C151—22no—
214C4⋊C4×C151—22no—
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×C151—42no—
225C4⋊C4×C151C2×D412yes—
226C22⋊C4×C151—24no—
227C22⋊C4×C151—24no—
228C22⋊C4×C151—24no—
229C22⋊C4×C151—24no—
230C22⋊C4×C151—24no—
231C42×C151—24no—
232C42×C151—24no—
233C42×C151—21no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151—42no—
238C42×C151C2×D412yes—
239C42×C151C2×D412yes—
240C23×C151—22no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151C22×D411yescharacteristic
248Q8×C151—22no—
249Q8×C151—22no—
250Q8×C151—22no—
251Q8×C151—22no—
252Q8×C151—22no—
253Q8×C151—22no—
254Q8×C151—44no—
255Q8×C151—41no—
256Q8×C151—41no—
257Q8×C151—41no—
258Q8×C151—41no—
259Q8×C151—41no—
260Q8×C151—41no—
261D4×C151—22no—
262D4×C151—22no—
263D4×C151—41no—
264D4×C151—41no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—22no—
273C2×C4×C151—22no—
274C2×C4×C151—21no—
275C2×C4×C151—22no—
276C2×C4×C151—21no—
277C2×C4×C151—22no—
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—48no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
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#12012yes—
303C2×C4×C151#12012yes—
304C2×C4×C151#13512yes—
305C2×C4×C151C22×D411yescharacteristic
306C2×C4×C151C22×D411yescharacteristic
307C2×C4×C151C2×#4111yescharacteristic
308C2×C4×C151C2×#4111yescharacteristic
309C2×C4×C151H(5,𝔽2)11yescharacteristic
310C2×C4×C1512−1+411yescharacteristic
311C8×C151—22no—
312C8×C151—41no—
313C8×C151—41no—
314C8×C151—41no—
315C22×C151—42no—
316C22×C151—42no—
317C22×C151—42no—
318C22×C151—81no—
319C22×C151—81no—
320C22×C151—81no—
321C22×C151—81no—
322C22×C151C2×#12011yescharacteristic
323C22×C151#54811yescharacteristic
324C22×C151#55011yescharacteristic
325C22×C151C2×#13511yescharacteristic
326C22×C151#57511yescharacteristic
327C22×C151#57811yescharacteristic
328C22×C151#57811yescharacteristic
329C4×C151—22no—
330C4×C151—22no—
331C4×C151—22no—
332C4×C151—42no—
333C4×C151—42no—
334C4×C151—42no—
335C4×C151—41no—
336C4×C151—42no—
337C4×C151—41no—
338C4×C151—41no—
339C4×C151—81no—
340C4×C151—81no—
341C4×C151—81no—
342C4×C151#52511yescharacteristic
343C4×C151#53711yescharacteristic
344C4×C151#54611yescharacteristic
345C4×C151#54711yescharacteristic
346C2×C151—82no—
347C2×C151#240711yescharacteristic
348C2×C151#300211yescharacteristic
349C2×C151#301111yescharacteristic
350C2×C151#336411yescharacteristic
351C2×C151#337711yescharacteristic
352C2×C151#339311yescharacteristic
353C2×C151#340211yescharacteristic
354#24195C15111yesmaximal, characteristic, direct product factor, Sylow
355C151#2419511yescharacteristic, direct product factor, Sylow
356C2×#556C2×C15111yescharacteristic
357C2×#464C2×C15111yescharacteristic
358C2×C4×Q16C2×C15111yescharacteristic, complemented
359#2581C2×C15111yescharacteristic, complemented
360#2043C2×C15111yescharacteristic, complemented
361#2042C2×C15111yescharacteristic
362#2016C2×C15111yescharacteristic, complemented
363#2015C2×C15111yescharacteristic
364#1984C2×C15111yescharacteristic, complemented
365#1958C2×C15111yescharacteristic
366#1878C2×C15111yescharacteristic, complemented
367#1877C2×C15111yescharacteristic
368#1863C2×C15111yescharacteristic, complemented
369#1862C2×C15111yescharacteristic
370#1805C2×C15111yescharacteristic, complemented
371C22×Q16C22×C15111yescharacteristic
372C22×Q16C22×C15111yescharacteristic
373C22×SD16C22×C15111yescharacteristic
374#556—24no—
375#556—24no—
376C2×C4⋊Q8C22×C15111yescharacteristic
377C2×#126—21no—
378C2×#126—21no—
379C2×#124C22×C15111yescharacteristic
380C2×#124C22×C15111yescharacteristic
381C2×C22⋊Q8—21no—
382C2×C4×Q8C22×C15111yescharacteristic
383C2×C4×Q8C22×C15111yescharacteristic
384C2×C4×Q8C22×C15111yescharacteristic
385C2×C4×Q8C22×C15111yescharacteristic
386C2×C4×D4C22×C15111yescharacteristic
387C2×#117—21no—
388#464—24no—
389C4×Q16—24no—
390C2×#107C22×C15111yescharacteristic
391C2×C4⋊C8C22×C15111yescharacteristic
392C2×#103C22×C15111yescharacteristic
393C2×#103C22×C15111yescharacteristic
394C2×#103C22×C15111yescharacteristic
395C2×#103C22×C15111yescharacteristic
396C2×#103C22×C15111yescharacteristic
397C2×#103C22×C15111yescharacteristic
398C2×#103C22×C15111yescharacteristic
399C2×#102C22×C15111yescharacteristic
400C2×#102C22×C15111yescharacteristic
401C2×#102C22×C15111yescharacteristic
402C2×C4×C8C22×C15111yescharacteristic
403#400—21no—
404#395—21no—
405#391C22×C15111yescharacteristic
406#391C22×C15111yescharacteristic
407#389C22×C15111yescharacteristic
408#389C22×C15111yescharacteristic
409#387—21no—
410#387—21no—
411#382C22×C15111yescharacteristic
412#340C22×C15111yescharacteristic
413#340C22×C15111yescharacteristic
414#336C22×C15111yescharacteristic
415#336C22×C15111yescharacteristic
416#336C22×C15111yescharacteristic
417#336C22×C15111yescharacteristic
418C22×Q8D4×C15111yescharacteristic
419C22×Q8C23×C15111yescharacteristic
420C22×Q8C23×C15111yescharacteristic
421C22×Q8C23×C15111yescharacteristic
422C22×D4C23×C15111yescharacteristic
423C23×C4—21no—
424C2×Q16—22no—
425C2×Q16—22no—
426C2×Q16—22no—
427C2×Q16—22no—
428C2×Q16—22no—
429C2×Q16—41no—
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—41no—
433C22×C8C23×C15111yescharacteristic
434C22×C8C23×C15111yescharacteristic
435C22×C8C23×C15111yescharacteristic
436C22×C8C23×C15111yescharacteristic
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439#126—28no—
440#126—28no—
441#124—22no—
442#124—22no—
443#124—22no—
444#124D4×C15114yes—
445C22⋊Q8—28no—
446C4×Q8—22no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8—22no—
453C4×Q8D4×C15114yes—
454C4×D4—22no—
455C4×D4—22no—
456#117—28no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4D4×C15111yescharacteristic
465C2×C4⋊C4D4×C15111yescharacteristic
466C2×C4⋊C4D4×C15111yescharacteristic
467C2×C4⋊C4C23×C15111yescharacteristic
468C2×C4⋊C4C23×C15111yescharacteristic
469C2×C4⋊C4C23×C15111yescharacteristic
470C2×C4⋊C4C23×C15111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C23×C15111yescharacteristic
480C2×C42C23×C15111yescharacteristic
481C2×C42C23×C15111yescharacteristic
482#107—22no—
483C4⋊C8—22no—
484#103—22no—
485#103—22no—
486#103—22no—
487#103—22no—
488#103—41no—
489#103—41no—
490#103—41no—
491#102—22no—
492#102—22no—
493#102—41no—
494C4×C8—22no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503C24—21no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—41no—
522C2×Q8C2×D4×C15112yes—
523C2×Q8C2×D4×C15112yes—
524C2×Q8#41×C15112yes—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4C2×D4×C15112yes—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4C2×D4×C15111yescharacteristic
542C22×C4C2×D4×C15111yescharacteristic
543C22×C4C2×D4×C15111yescharacteristic
544C22×C4C2×D4×C15111yescharacteristic
545C22×C4C2×D4×C15111yescharacteristic
546C22×C4C2×D4×C15111yescharacteristic
547C22×C4C24×C15111yescharacteristic
548Q16—28no—
549Q16—44no—
550SD16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8#41×C15112yes—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4C2×D4×C15112yes—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C42—24no—
587C42—24no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—42no—
593C42C2×D4×C15112yes—
594C42C2×D4×C15112yes—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23C22×D4×C15111yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—22no—
606Q8—22no—
607Q8—22no—
608Q8—22no—
609Q8—44no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616D4—22no—
617D4—22no—
618D4—41no—
619D4—41no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—48no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4#120×C15112yes—
658C2×C4#120×C15112yes—
659C2×C4#135×C15112yes—
660C2×C4C22×D4×C15111yescharacteristic
661C2×C4C22×D4×C15111yescharacteristic
662C2×C4C2×#41×C15111yescharacteristic
663C2×C4C2×#41×C15111yescharacteristic
664C2×C4H(5,𝔽2)×C15111yescharacteristic
665C2×C42−1+4×C15111yescharacteristic
666C8—22no—
667C8—41no—
668C8—41no—
669C8—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×#120×C15111yescharacteristic
678C22#548×C15111yescharacteristic
679C22#550×C15111yescharacteristic
680C22C2×#135×C15111yescharacteristic
681C22#575×C15111yescharacteristic
682C22#578×C15111yescharacteristic
683C22#578×C15111yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—41no—
691C4—42no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4#525×C15111yescharacteristic
698C4#537×C15111yescharacteristic
699C4#546×C15111yescharacteristic
700C4#547×C15111yescharacteristic
701C2—82no—
702C2#2407×C15111yescharacteristic
703C2#3002×C15111yescharacteristic
704C2#3011×C15111yescharacteristic
705C2#3364×C15111yescharacteristic
706C2#3377×C15111yescharacteristic
707C2#3393×C15111yescharacteristic
708C2#3402×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
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
3. C2×C4×Q16×C151C2semidirect
4. #2581×C151C2semidirect
5. #2043×C151C2semidirect
7. #2016×C151C2semidirect
9. #1984×C151C2semidirect
11. #1878×C151C2semidirect
13. #1863×C151C2semidirect
15. #1805×C151C2semidirect
354. #24195C151direct (N × H)
355. C151#24195direct (N × H)
358. C2×C4×Q16C2×C151semidirect
359. #2581C2×C151semidirect
360. #2043C2×C151semidirect
362. #2016C2×C151semidirect
364. #1984C2×C151semidirect
366. #1878C2×C151semidirect
368. #1863C2×C151semidirect
370. #1805C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#556×C1512
C2×#464×C1512
C2×C4×Q16×C1512
#2581×C1512
#2043×C1512
#2042×C1512
#2016×C1512
#2015×C1512
#1984×C1512
#1958×C1512
#1878×C1512
#1877×C1512
#1863×C1512
#1862×C1512
#1805×C1512
#24195151