Finite Group Databasebeta

← C151×#24635 #50329560

Subgroups — C151×#24635 #50329560

Order 38656.

904 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×#464×C151C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
3#2544×C151C211yesmaximal, characteristic
4#2356×C151C211yesmaximal, characteristic, complemented
5#2056×C151C211yesmaximal, characteristic, complemented
6#2055×C151C211yesmaximal, characteristic, complemented
7#2015×C151C211yesmaximal, characteristic, complemented
8#2014×C151C211yesmaximal, characteristic
9#1983×C151C211yesmaximal, characteristic, complemented
10#1982×C151C211yesmaximal, characteristic
11#1958×C151C211yesmaximal, characteristic, complemented
12#1939×C151C211yesmaximal, characteristic, complemented
13#1927×C151C211yesmaximal, characteristic, complemented
14#1926×C151C211yesmaximal, characteristic, complemented
15#1804×C151C211yesmaximal, characteristic, complemented
16C22×Q16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C2×#127×C151C2211yescharacteristic
20C2×#124×C151C2211yescharacteristic
21C2×#124×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24#464×C151—24no—
25C4×SD16×C151—24no—
26C2×#106×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×C4×C8×C151C2211yescharacteristic
41#394×C151—21no—
42#394×C151—21no—
43#391×C151C2211yescharacteristic
44#391×C151C2211yescharacteristic
45#391×C151C2211yescharacteristic
46#390×C151C2211yescharacteristic
47#387×C151—21no—
48#387×C151—21no—
49#386×C151—21no—
50#386×C151—21no—
51#383×C151—21no—
52#382×C151C2211yescharacteristic
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C4⋊C4×C151C2211yescharacteristic
56#376×C151—21no—
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×Q8×C151C2311yescharacteristic
63C22×D4×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151C2311yescharacteristic
66C22×D4×C151C2311yescharacteristic
67C23×C4×C151—21no—
68C2×Q16×C151—22no—
69C2×Q16×C151—41no—
70C2×Q16×C151—41no—
71C2×SD16×C151—22no—
72C2×SD16×C151—22no—
73C2×SD16×C151—22no—
74C2×SD16×C151—22no—
75C2×SD16×C151—41no—
76C2×SD16×C151—41no—
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81#127×C151—22no—
82#127×C151—41no—
83#124×C151—22no—
84#124×C151—22no—
85#124×C151—22no—
86#124×C151—41no—
87C4×Q8×C151—22no—
88C4×Q8×C151D414yescomplemented
89C4×D4×C151—22no—
90C4×D4×C151—22no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151D411yescharacteristic
93C2×C4⋊C4×C151D411yescharacteristic
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×C42×C151—21no—
106C2×C42×C151—21no—
107C2×C42×C151—21no—
108C2×C42×C151C2311yescharacteristic
109C2×C42×C151C2311yescharacteristic
110C2×C42×C151C2311yescharacteristic
111#106×C151—22no—
112C4⋊C8×C151—22no—
113C4⋊C8×C151—41no—
114C4⋊C8×C151—41no—
115#103×C151—22no—
116#103×C151—22no—
117#103×C151—22no—
118#103×C151—41no—
119#102×C151—22no—
120#102×C151—22no—
121#102×C151—22no—
122#102×C151—41no—
123#102×C151—41no—
124#102×C151—41no—
125C4×C8×C151—22no—
126#95×C151—21no—
127#95×C151—21no—
128#95×C151—21no—
129#95×C151—21no—
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×C151D411yescharacteristic
137#95×C151D411yescharacteristic
138C24×C151—21no—
139C24×C151—21no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151C2×D412yes—
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—81no—
168C2×D4×C151—81no—
169C2×D4×C151#4112yes—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—42no—
177C22×C4×C151—81no—
178C22×C4×C151—81no—
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2411yescharacteristic
186Q16×C151—44no—
187SD16×C151—28no—
188SD16×C151—44no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151#4112yes—
201C4⋊C4×C151—24no—
202C4⋊C4×C151—22no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—41no—
211C4⋊C4×C151C2×D412yes—
212C22⋊C4×C151—42no—
213C22⋊C4×C151—42no—
214C22⋊C4×C151—42no—
215C22⋊C4×C151—42no—
216C22⋊C4×C151—42no—
217C22⋊C4×C151—81no—
218C22⋊C4×C151—81no—
219C42×C151—24no—
220C42×C151—21no—
221C42×C151—21no—
222C42×C151—21no—
223C42×C151—21no—
224C42×C151—42no—
225C42×C151—42no—
226C42×C151C2×D412yes—
227C42×C151#4112yes—
228C23×C151—22no—
229C23×C151—41no—
230C23×C151—41no—
231C23×C151—41no—
232C23×C151—41no—
233C23×C151—41no—
234C23×C151—41no—
235C23×C151—41no—
236C23×C151—41no—
237C23×C151—41no—
238C23×C151—41no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151C22×D411yescharacteristic
243Q8×C151—22no—
244Q8×C151—22no—
245Q8×C151—41no—
246Q8×C151—41no—
247Q8×C151—41no—
248Q8×C151—41no—
249Q8×C151—41no—
250Q8×C151—41no—
251D4×C151—22no—
252D4×C151—22no—
253D4×C151—41no—
254D4×C151—41no—
255D4×C151—41no—
256D4×C151—41no—
257D4×C151—41no—
258D4×C151—41no—
259D4×C151—84no—
260D4×C151—84no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—22no—
268C2×C4×C151—22no—
269C2×C4×C151—21no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
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—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—84no—
295C2×C4×C151#12112yes—
296C2×C4×C151#12112yes—
297C2×C4×C151#13512yes—
298C2×C4×C151C22×D411yescharacteristic
299C2×C4×C151C2×#4111yescharacteristic
300C2×C4×C151C2×#4111yescharacteristic
301C2×C4×C151C2×#4111yescharacteristic
302C2×C4×C151H(5,𝔽2)11yescharacteristic
303C2×C4×C151H(5,𝔽2)11yescharacteristic
304C8×C151—22no—
305C8×C151—41no—
306C8×C151—41no—
307C8×C151—41no—
308C22×C151—42no—
309C22×C151—42no—
310C22×C151—42no—
311C22×C151—81no—
312C22×C151—81no—
313C22×C151—81no—
314C22×C151—81no—
315C22×C151—81no—
316C22×C151—81no—
317C22×C151—81no—
318C22×C151—81no—
319C22×C151—81no—
320C22×C151—81no—
321C22×C151—81no—
322C22×C151C2×#12111yescharacteristic
323C22×C151#54611yescharacteristic
324C22×C151#55011yescharacteristic
325C22×C151C2×#13511yescharacteristic
326C22×C151#57511yescharacteristic
327C22×C151#57711yescharacteristic
328C22×C151#57711yescharacteristic
329C4×C151—22no—
330C4×C151—22no—
331C4×C151—22no—
332C4×C151—42no—
333C4×C151—42no—
334C4×C151—41no—
335C4×C151—41no—
336C4×C151—41no—
337C4×C151—81no—
338C4×C151—81no—
339C4×C151—81no—
340C4×C151—81no—
341C4×C151#52511yescharacteristic
342C4×C151#53511yescharacteristic
343C4×C151#55311yescharacteristic
344C4×C151#55511yescharacteristic
345C2×C151—82no—
346C2×C151—161no—
347C2×C151#241411yescharacteristic
348C2×C151#303511yescharacteristic
349C2×C151#304311yescharacteristic
350C2×C151#329611yescharacteristic
351C2×C151#332311yescharacteristic
352C2×C151#339411yescharacteristic
353C2×C151#340111yescharacteristic
354#24635C15111yesmaximal, characteristic, direct product factor, Sylow
355C151#2463511yescharacteristic, direct product factor, Sylow
356C2×#464C2×C15111yescharacteristic, complemented
357C2×C4×SD16C2×C15111yescharacteristic, complemented
358#2544C2×C15111yescharacteristic
359#2356C2×C15111yescharacteristic, complemented
360#2056C2×C15111yescharacteristic, complemented
361#2055C2×C15111yescharacteristic, complemented
362#2015C2×C15111yescharacteristic, complemented
363#2014C2×C15111yescharacteristic
364#1983C2×C15111yescharacteristic, complemented
365#1982C2×C15111yescharacteristic
366#1958C2×C15111yescharacteristic, complemented
367#1939C2×C15111yescharacteristic, complemented
368#1927C2×C15111yescharacteristic, complemented
369#1926C2×C15111yescharacteristic, complemented
370#1804C2×C15111yescharacteristic, complemented
371C22×Q16C22×C15111yescharacteristic
372C22×SD16C22×C15111yescharacteristic
373C22×SD16C22×C15111yescharacteristic
374C2×#127C22×C15111yescharacteristic
375C2×#124C22×C15111yescharacteristic
376C2×#124C22×C15111yescharacteristic
377C2×C4×Q8C22×C15111yescharacteristic
378C2×C4×D4C22×C15111yescharacteristic
379#464—24no—
380C4×SD16—24no—
381C2×#106C22×C15111yescharacteristic
382C2×C4⋊C8C22×C15111yescharacteristic
383C2×C4⋊C8C22×C15111yescharacteristic
384C2×C4⋊C8C22×C15111yescharacteristic
385C2×#103C22×C15111yescharacteristic
386C2×#103C22×C15111yescharacteristic
387C2×#103C22×C15111yescharacteristic
388C2×#103C22×C15111yescharacteristic
389C2×#102C22×C15111yescharacteristic
390C2×#102C22×C15111yescharacteristic
391C2×#102C22×C15111yescharacteristic
392C2×#102C22×C15111yescharacteristic
393C2×#102C22×C15111yescharacteristic
394C2×#102C22×C15111yescharacteristic
395C2×C4×C8C22×C15111yescharacteristic
396#394—21no—
397#394—21no—
398#391C22×C15111yescharacteristic
399#391C22×C15111yescharacteristic
400#391C22×C15111yescharacteristic
401#390C22×C15111yescharacteristic
402#387—21no—
403#387—21no—
404#386—21no—
405#386—21no—
406#383—21no—
407#382C22×C15111yescharacteristic
408C4×C4⋊C4C22×C15111yescharacteristic
409C4×C4⋊C4C22×C15111yescharacteristic
410C4×C4⋊C4C22×C15111yescharacteristic
411#376—21no—
412#340C22×C15111yescharacteristic
413#340C22×C15111yescharacteristic
414#336C22×C15111yescharacteristic
415#336C22×C15111yescharacteristic
416C22×Q8C23×C15111yescharacteristic
417C22×Q8C23×C15111yescharacteristic
418C22×D4—21no—
419C22×D4—21no—
420C22×D4C23×C15111yescharacteristic
421C22×D4C23×C15111yescharacteristic
422C23×C4—21no—
423C2×Q16—22no—
424C2×Q16—41no—
425C2×Q16—41no—
426C2×SD16—22no—
427C2×SD16—22no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—41no—
431C2×SD16—41no—
432C22×C8C23×C15111yescharacteristic
433C22×C8C23×C15111yescharacteristic
434C22×C8C23×C15111yescharacteristic
435C22×C8C23×C15111yescharacteristic
436#127—22no—
437#127—41no—
438#124—22no—
439#124—22no—
440#124—22no—
441#124—41no—
442C4×Q8—22no—
443C4×Q8D4×C15114yescomplemented
444C4×D4—22no—
445C4×D4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4D4×C15111yescharacteristic
448C2×C4⋊C4D4×C15111yescharacteristic
449C2×C4⋊C4C23×C15111yescharacteristic
450C2×C4⋊C4C23×C15111yescharacteristic
451C2×C4⋊C4C23×C15111yescharacteristic
452C2×C4⋊C4C23×C15111yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42C23×C15111yescharacteristic
464C2×C42C23×C15111yescharacteristic
465C2×C42C23×C15111yescharacteristic
466#106—22no—
467C4⋊C8—22no—
468C4⋊C8—41no—
469C4⋊C8—41no—
470#103—22no—
471#103—22no—
472#103—22no—
473#103—41no—
474#102—22no—
475#102—22no—
476#102—22no—
477#102—41no—
478#102—41no—
479#102—41no—
480C4×C8—22no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95D4×C15111yescharacteristic
492#95D4×C15111yescharacteristic
493C24—21no—
494C24—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8C2×D4×C15112yes—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4#41×C15112yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×D4×C15111yescharacteristic
535C22×C4C2×D4×C15111yescharacteristic
536C22×C4C2×D4×C15111yescharacteristic
537C22×C4C2×D4×C15111yescharacteristic
538C22×C4C2×D4×C15111yescharacteristic
539C22×C4C2×D4×C15111yescharacteristic
540C22×C4C24×C15111yescharacteristic
541Q16—44no—
542SD16—28no—
543SD16—44no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8#41×C15112yes—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—41no—
566C4⋊C4C2×D4×C15112yes—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C42—24no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42C2×D4×C15112yes—
582C42#41×C15112yes—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23C22×D4×C15111yescharacteristic
598Q8—22no—
599Q8—22no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—84no—
615D4—84no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
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—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4#121×C15112yes—
651C2×C4#121×C15112yes—
652C2×C4#135×C15112yes—
653C2×C4C22×D4×C15111yescharacteristic
654C2×C4C2×#41×C15111yescharacteristic
655C2×C4C2×#41×C15111yescharacteristic
656C2×C4C2×#41×C15111yescharacteristic
657C2×C4H(5,𝔽2)×C15111yescharacteristic
658C2×C4H(5,𝔽2)×C15111yescharacteristic
659C8—22no—
660C8—41no—
661C8—41no—
662C8—41no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×#121×C15111yescharacteristic
678C22#546×C15111yescharacteristic
679C22#550×C15111yescharacteristic
680C22C2×#135×C15111yescharacteristic
681C22#575×C15111yescharacteristic
682C22#577×C15111yescharacteristic
683C22#577×C15111yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—42no—
688C4—42no—
689C4—41no—
690C4—41no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4#525×C15111yescharacteristic
697C4#535×C15111yescharacteristic
698C4#553×C15111yescharacteristic
699C4#555×C15111yescharacteristic
700C2—82no—
701C2—161no—
702C2#2414×C15111yescharacteristic
703C2#3035×C15111yescharacteristic
704C2#3043×C15111yescharacteristic
705C2#3296×C15111yescharacteristic
706C2#3323×C15111yescharacteristic
707C2#3394×C15111yescharacteristic
708C2#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 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#464×C151C2semidirect
2. C2×C4×SD16×C151C2semidirect
4. #2356×C151C2semidirect
5. #2056×C151C2semidirect
6. #2055×C151C2semidirect
7. #2015×C151C2semidirect
9. #1983×C151C2semidirect
11. #1958×C151C2semidirect
12. #1939×C151C2semidirect
13. #1927×C151C2semidirect
14. #1926×C151C2semidirect
15. #1804×C151C2semidirect
88. C4×Q8×C151D4semidirect
354. #24635C151direct (N × H)
355. C151#24635direct (N × H)
356. C2×#464C2×C151semidirect
357. C2×C4×SD16C2×C151semidirect
359. #2356C2×C151semidirect
360. #2056C2×C151semidirect
361. #2055C2×C151semidirect
362. #2015C2×C151semidirect
364. #1983C2×C151semidirect
366. #1958C2×C151semidirect
367. #1939C2×C151semidirect
368. #1927C2×C151semidirect
369. #1926C2×C151semidirect
370. #1804C2×C151semidirect
443. C4×Q8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#464×C1512
C2×C4×SD16×C1512
#2544×C1512
#2356×C1512
#2056×C1512
#2055×C1512
#2015×C1512
#2014×C1512
#1983×C1512
#1982×C1512
#1958×C1512
#1939×C1512
#1927×C1512
#1926×C1512
#1804×C1512
#24635151