Finite Group Databasebeta

← C151×#24982 #50329907

Subgroups — C151×#24982 #50329907

Order 38656.

862 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
1#2537×C151C211yesmaximal, characteristic
2#2352×C151C211yesmaximal, characteristic, complemented
3#2077×C151C211yesmaximal, characteristic, complemented
4#2077×C151C211yesmaximal, characteristic, complemented
5#2034×C151C211yesmaximal, characteristic, complemented
6#2034×C151C211yesmaximal, characteristic, complemented
7#1955×C151C211yesmaximal, characteristic, complemented
8#1948×C151C211yesmaximal, characteristic, complemented
9#1875×C151C211yesmaximal, characteristic, complemented
10#1874×C151C211yesmaximal, characteristic, complemented
11#1836×C151C211yesmaximal, characteristic, complemented
12#1825×C151C211yesmaximal, characteristic, complemented
13#1823×C151C211yesmaximal, characteristic, complemented
14#1804×C151C211yesmaximal, characteristic, complemented
15#1762×C151C211yesmaximal, characteristic, complemented
16C2×#121×C151—21no—
17C2×#121×C151C2211yescharacteristic
18C2×#121×C151C2211yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22C22×C4⋊C4×C151C2211yescharacteristic
23C2×#106×C151C2211yescharacteristic
24C2×#106×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2211yescharacteristic
29C2×#102×C151C2211yescharacteristic
30C2×C22⋊C8×C151C2211yescharacteristic
31C2×C22⋊C8×C151C2211yescharacteristic
32C2×C22⋊C8×C151C2211yescharacteristic
33C2×C22⋊C8×C151C2211yescharacteristic
34C2×#97×C151C2211yescharacteristic
35#394×C151—21no—
36#394×C151—21no—
37#388×C151—21no—
38#387×C151—21no—
39#386×C151—21no—
40#384×C151C2211yescharacteristic
41#382×C151C2211yescharacteristic
42#380×C151—21no—
43#380×C151C2211yescharacteristic
44#380×C151C2211yescharacteristic
45#380×C151C2211yescharacteristic
46#380×C151C2211yescharacteristic
47C4×C4⋊C4×C151C2211yescharacteristic
48C4×C22⋊C4×C151—21no—
49#340×C151C2211yescharacteristic
50#340×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59C22×D4×C151—21no—
60C22×D4×C151—21no—
61C22×D4×C151D411yescharacteristic
62C22×D4×C151C2311yescharacteristic
63C23×C4×C151—21no—
64C23×C4×C151—21no—
65C23×C4×C151C2311yescharacteristic
66C23×C4×C151C2311yescharacteristic
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71#121×C151—22no—
72#121×C151—22no—
73#121×C151—41no—
74#121×C151—41no—
75#121×C151—44no—
76C4×D4×C151—22no—
77C4×D4×C151—22no—
78C4×D4×C151—22no—
79C4×D4×C151—22no—
80#117×C151—22no—
81#117×C151—41no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—41no—
87C2×C4⋊C4×C151D411yescharacteristic
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C4⋊C4×C151C2311yescharacteristic
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C4⋊C4×C151C2311yescharacteristic
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—21no—
97C2×C22⋊C4×C151—21no—
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×C151D411yescharacteristic
104C2×C22⋊C4×C151D411yescharacteristic
105C2×C42×C151—21no—
106C2×C42×C151—21no—
107C2×C42×C151C2311yescharacteristic
108#106×C151—41no—
109#106×C151—41no—
110C4⋊C8×C151—22no—
111#102×C151—22no—
112#102×C151—22no—
113#102×C151—41no—
114#102×C151—41no—
115C22⋊C8×C151—41no—
116C22⋊C8×C151—41no—
117C22⋊C8×C151—41no—
118C22⋊C8×C151—41no—
119#97×C151—22no—
120#95×C151—21no—
121#95×C151—21no—
122#95×C151—21no—
123#95×C151—21no—
124#95×C151—21no—
125#95×C151—21no—
126#95×C151—21no—
127C24×C151—21no—
128C24×C151C2×D411yescharacteristic
129C24×C151C2×D411yescharacteristic
130C2×D4×C151—22no—
131C2×D4×C151—22no—
132C2×D4×C151—21no—
133C2×D4×C151—21no—
134C2×D4×C151—21no—
135C2×D4×C151—21no—
136C2×D4×C151—21no—
137C2×D4×C151—41no—
138C2×D4×C151—42no—
139C2×D4×C151—42no—
140C2×D4×C151—42no—
141C2×D4×C151—42no—
142C2×D4×C151—81no—
143C2×D4×C151—81no—
144C2×D4×C151#4112yes—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
148C22×C4×C151—21no—
149C22×C4×C151—21no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—42no—
165C22×C4×C151—42no—
166C22×C4×C151—42no—
167C22×C4×C151—42no—
168C22×C4×C151—42no—
169C22×C4×C151—81no—
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D411yescharacteristic
174C22×C4×C151C2411yescharacteristic
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—42no—
202C4⋊C4×C151—42no—
203C4⋊C4×C151—81no—
204C4⋊C4×C151#4112yes—
205C22⋊C4×C151—22no—
206C22⋊C4×C151—22no—
207C22⋊C4×C151—42no—
208C22⋊C4×C151—42no—
209C22⋊C4×C151—42no—
210C22⋊C4×C151—42no—
211C22⋊C4×C151—42no—
212C22⋊C4×C151—42no—
213C22⋊C4×C151—42no—
214C22⋊C4×C151—81no—
215C42×C151—42no—
216C42×C151—81no—
217C42×C151#4112yes—
218C42×C151#4112yes—
219C23×C151—21no—
220C23×C151—21no—
221C23×C151—21no—
222C23×C151—21no—
223C23×C151—21no—
224C23×C151—21no—
225C23×C151—21no—
226C23×C151—22no—
227C23×C151—21no—
228C23×C151—21no—
229C23×C151—21no—
230C23×C151—21no—
231C23×C151—21no—
232C23×C151—21no—
233C23×C151—41no—
234C23×C151—41no—
235C23×C151—41no—
236C23×C151—41no—
237C23×C151—41no—
238C23×C151—41no—
239C23×C151AGL(1,ℤ/8)12yes—
240C23×C151C22×D411yescharacteristic
241D4×C151—22no—
242D4×C151—22no—
243D4×C151—44no—
244D4×C151—41no—
245D4×C151—41no—
246D4×C151—84no—
247D4×C151—84no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—21no—
255C2×C4×C151—22no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—41no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—41no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—84no—
288C2×C4×C151—84no—
289C2×C4×C151#12312yes—
290C2×C4×C151#12312yes—
291C2×C4×C151C2×#4111yescharacteristic
292C2×C4×C151C2×#4111yescharacteristic
293C2×C4×C151C2×#4111yescharacteristic
294C2×C4×C151C2×#4111yescharacteristic
295C2×C4×C151H(5,𝔽2)11yescharacteristic
296C2×C4×C151H(5,𝔽2)11yescharacteristic
297C8×C151—41no—
298C8×C151—41no—
299C8×C151—41no—
300C8×C151—41no—
301C22×C151—22no—
302C22×C151—22no—
303C22×C151—22no—
304C22×C151—41no—
305C22×C151—41no—
306C22×C151—41no—
307C22×C151—41no—
308C22×C151—41no—
309C22×C151—41no—
310C22×C151—41no—
311C22×C151—42no—
312C22×C151—41no—
313C22×C151—41no—
314C22×C151—42no—
315C22×C151—41no—
316C22×C151—42no—
317C22×C151—41no—
318C22×C151—81no—
319C22×C151—81no—
320C22×C151—81no—
321C22×C151—81no—
322C22×C151C2×#12311yescharacteristic
323C22×C151#54611yescharacteristic
324C22×C151#54611yescharacteristic
325C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C151#57511yescharacteristic
327C22×C151#57711yescharacteristic
328C22×C151#57711yescharacteristic
329C4×C151—22no—
330C4×C151—22no—
331C4×C151—41no—
332C4×C151—41no—
333C4×C151—42no—
334C4×C151—81no—
335C4×C151—81no—
336C4×C151—81no—
337C4×C151—81no—
338C4×C151—81no—
339C4×C151—81no—
340C4×C151#52911yescharacteristic
341C4×C151#54011yescharacteristic
342C4×C151#55311yescharacteristic
343C4×C151#55511yescharacteristic
344C2×C151—42no—
345C2×C151—81no—
346C2×C151—82no—
347C2×C151#242011yescharacteristic
348C2×C151#309411yescharacteristic
349C2×C151#309911yescharacteristic
350C2×C151#330611yescharacteristic
351C2×C151#330711yescharacteristic
352C2×C151#331011yescharacteristic
353C2×C151#332111yescharacteristic
354#24982C15111yesmaximal, characteristic, direct product factor, Sylow
355C151#2498211yescharacteristic, direct product factor, Sylow
356#2537C2×C15111yescharacteristic
357#2352C2×C15111yescharacteristic, complemented
358#2077C2×C15111yescharacteristic, complemented
359#2077C2×C15111yescharacteristic, complemented
360#2034C2×C15111yescharacteristic, complemented
361#2034C2×C15111yescharacteristic, complemented
362#1955C2×C15111yescharacteristic, complemented
363#1948C2×C15111yescharacteristic, complemented
364#1875C2×C15111yescharacteristic, complemented
365#1874C2×C15111yescharacteristic, complemented
366#1836C2×C15111yescharacteristic, complemented
367#1825C2×C15111yescharacteristic, complemented
368#1823C2×C15111yescharacteristic, complemented
369#1804C2×C15111yescharacteristic, complemented
370#1762C2×C15111yescharacteristic, complemented
371C2×#121—21no—
372C2×#121C22×C15111yescharacteristic
373C2×#121C22×C15111yescharacteristic
374C2×C4×D4C22×C15111yescharacteristic
375C2×C4×D4C22×C15111yescharacteristic
376C2×#117C22×C15111yescharacteristic
377C22×C4⋊C4C22×C15111yescharacteristic
378C2×#106C22×C15111yescharacteristic
379C2×#106C22×C15111yescharacteristic
380C2×C4⋊C8C22×C15111yescharacteristic
381C2×#102C22×C15111yescharacteristic
382C2×#102C22×C15111yescharacteristic
383C2×#102C22×C15111yescharacteristic
384C2×#102C22×C15111yescharacteristic
385C2×C22⋊C8C22×C15111yescharacteristic
386C2×C22⋊C8C22×C15111yescharacteristic
387C2×C22⋊C8C22×C15111yescharacteristic
388C2×C22⋊C8C22×C15111yescharacteristic
389C2×#97C22×C15111yescharacteristic
390#394—21no—
391#394—21no—
392#388—21no—
393#387—21no—
394#386—21no—
395#384C22×C15111yescharacteristic
396#382C22×C15111yescharacteristic
397#380—21no—
398#380C22×C15111yescharacteristic
399#380C22×C15111yescharacteristic
400#380C22×C15111yescharacteristic
401#380C22×C15111yescharacteristic
402C4×C4⋊C4C22×C15111yescharacteristic
403C4×C22⋊C4—21no—
404#340C22×C15111yescharacteristic
405#340C22×C15111yescharacteristic
406#340C22×C15111yescharacteristic
407#340C22×C15111yescharacteristic
408#340C22×C15111yescharacteristic
409#340C22×C15111yescharacteristic
410#340C22×C15111yescharacteristic
411#340C22×C15111yescharacteristic
412#340C22×C15111yescharacteristic
413#340C22×C15111yescharacteristic
414C22×D4—21no—
415C22×D4—21no—
416C22×D4D4×C15111yescharacteristic
417C22×D4C23×C15111yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4C23×C15111yescharacteristic
421C23×C4C23×C15111yescharacteristic
422C22×C8C23×C15111yescharacteristic
423C22×C8C23×C15111yescharacteristic
424C22×C8C23×C15111yescharacteristic
425C22×C8C23×C15111yescharacteristic
426#121—22no—
427#121—22no—
428#121—41no—
429#121—41no—
430#121—44no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435#117—22no—
436#117—41no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4D4×C15111yescharacteristic
443C2×C4⋊C4C23×C15111yescharacteristic
444C2×C4⋊C4C23×C15111yescharacteristic
445C2×C4⋊C4C23×C15111yescharacteristic
446C2×C4⋊C4C23×C15111yescharacteristic
447C2×C4⋊C4C23×C15111yescharacteristic
448C2×C4⋊C4C23×C15111yescharacteristic
449C2×C4⋊C4C23×C15111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C15111yescharacteristic
459C2×C22⋊C4D4×C15111yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C15111yescharacteristic
463#106—41no—
464#106—41no—
465C4⋊C8—22no—
466#102—22no—
467#102—22no—
468#102—41no—
469#102—41no—
470C22⋊C8—41no—
471C22⋊C8—41no—
472C22⋊C8—41no—
473C22⋊C8—41no—
474#97—22no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482C24—21no—
483C24C2×D4×C15111yescharacteristic
484C24C2×D4×C15111yescharacteristic
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—41no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4#41×C15112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4C2×D4×C15111yescharacteristic
526C22×C4C2×D4×C15111yescharacteristic
527C22×C4C2×D4×C15111yescharacteristic
528C22×C4C2×D4×C15111yescharacteristic
529C22×C4C24×C15111yescharacteristic
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—81no—
559C4⋊C4#41×C15112yes—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C42—42no—
571C42—81no—
572C42#41×C15112yes—
573C42#41×C15112yes—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23AGL(1,ℤ/8)×C15112yes—
595C23C22×D4×C15111yescharacteristic
596D4—22no—
597D4—22no—
598D4—44no—
599D4—41no—
600D4—41no—
601D4—84no—
602D4—84no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—84no—
643C2×C4—84no—
644C2×C4#123×C15112yes—
645C2×C4#123×C15112yes—
646C2×C4C2×#41×C15111yescharacteristic
647C2×C4C2×#41×C15111yescharacteristic
648C2×C4C2×#41×C15111yescharacteristic
649C2×C4C2×#41×C15111yescharacteristic
650C2×C4H(5,𝔽2)×C15111yescharacteristic
651C2×C4H(5,𝔽2)×C15111yescharacteristic
652C8—41no—
653C8—41no—
654C8—41no—
655C8—41no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—41no—
666C22—41no—
667C22—42no—
668C22—41no—
669C22—42no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×#123×C15111yescharacteristic
678C22#546×C15111yescharacteristic
679C22#546×C15111yescharacteristic
680C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
681C22#575×C15111yescharacteristic
682C22#577×C15111yescharacteristic
683C22#577×C15111yescharacteristic
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—42no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4#529×C15111yescharacteristic
696C4#540×C15111yescharacteristic
697C4#553×C15111yescharacteristic
698C4#555×C15111yescharacteristic
699C2—42no—
700C2—81no—
701C2—82no—
702C2#2420×C15111yescharacteristic
703C2#3094×C15111yescharacteristic
704C2#3099×C15111yescharacteristic
705C2#3306×C15111yescharacteristic
706C2#3307×C15111yescharacteristic
707C2#3310×C15111yescharacteristic
708C2#3321×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2537×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
2. #2352×C151C2semidirect
3. #2077×C151C2semidirect
4. #2077×C151C2semidirect
5. #2034×C151C2semidirect
6. #2034×C151C2semidirect
7. #1955×C151C2semidirect
8. #1948×C151C2semidirect
9. #1875×C151C2semidirect
10. #1874×C151C2semidirect
11. #1836×C151C2semidirect
12. #1825×C151C2semidirect
13. #1823×C151C2semidirect
14. #1804×C151C2semidirect
15. #1762×C151C2semidirect
354. #24982C151direct (N × H)
355. C151#24982direct (N × H)
357. #2352C2×C151semidirect
358. #2077C2×C151semidirect
359. #2077C2×C151semidirect
360. #2034C2×C151semidirect
361. #2034C2×C151semidirect
362. #1955C2×C151semidirect
363. #1948C2×C151semidirect
364. #1875C2×C151semidirect
365. #1874C2×C151semidirect
366. #1836C2×C151semidirect
367. #1825C2×C151semidirect
368. #1823C2×C151semidirect
369. #1804C2×C151semidirect
370. #1762C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2537×C1512
#2352×C1512
#2077×C1512
#2034×C1512
#1955×C1512
#1948×C1512
#1875×C1512
#1874×C1512
#1836×C1512
#1825×C1512
#1823×C1512
#1804×C1512
#1762×C1512
#24982151