Finite Group Databasebeta

← C151×#24640 #50329565

Subgroups — C151×#24640 #50329565

Order 38656.

918 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C151C211yesmaximal, characteristic
2C2×#440×C151C211yesmaximal, characteristic, complemented
3#2545×C151C211yesmaximal, characteristic, complemented
4#2354×C151C211yesmaximal, characteristic, complemented
5#2055×C151C211yesmaximal, characteristic, complemented
6#2054×C151C211yesmaximal, characteristic
7#2013×C151C211yesmaximal, characteristic, complemented
8#2012×C151C211yesmaximal, characteristic
9#1983×C151C211yesmaximal, characteristic, complemented
10#1981×C151C211yesmaximal, characteristic, complemented
11#1959×C151C211yesmaximal, characteristic, complemented
12#1940×C151C211yesmaximal, characteristic, complemented
13#1928×C151C211yesmaximal, characteristic, complemented
14#1925×C151C211yesmaximal, characteristic, complemented
15#1803×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C2×C4⋊Q8×C151C2211yescharacteristic
20C2×#124×C151C2211yescharacteristic
21C2×#124×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×#117×C151—21no—
25#463×C151—24no—
26#440×C151—24no—
27C2×#107×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#103×C151C2211yescharacteristic
35C2×#103×C151C2211yescharacteristic
36C2×#103×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#97×C151C2211yescharacteristic
42#396×C151—21no—
43#396×C151—21no—
44#391×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#390×C151C2211yescharacteristic
47#390×C151C2211yescharacteristic
48#388×C151—21no—
49#388×C151—21no—
50#388×C151—21no—
51#388×C151—21no—
52#384×C151C2211yescharacteristic
53#380×C151—21no—
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C4⋊C4×C151C2211yescharacteristic
56C4×C4⋊C4×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×Q8×C151C2311yescharacteristic
63C22×D4×C151C2311yescharacteristic
64C22×D4×C151C2311yescharacteristic
65C23×C4×C151—21no—
66C2×SD16×C151—22no—
67C2×SD16×C151—22no—
68C2×SD16×C151—22no—
69C2×SD16×C151—22no—
70C2×SD16×C151—41no—
71C2×SD16×C151—41no—
72C2×D8×C151—22no—
73C2×D8×C151—41no—
74C2×D8×C151—41no—
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C4⋊Q8×C151—22no—
80C4⋊Q8×C151—41no—
81#124×C151—22no—
82#124×C151—22no—
83#124×C151—22no—
84#124×C151—41no—
85C4×Q8×C151—22no—
86C4×Q8×C151—22no—
87C4×D4×C151—22no—
88C4×D4×C151D414yes—
89#117×C151—44no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151D411yescharacteristic
96C2×C4⋊C4×C151D411yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
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×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C42×C151—21no—
113C2×C42×C151—21no—
114C2×C42×C151—21no—
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118#107×C151—22no—
119C4⋊C8×C151—22no—
120C4⋊C8×C151—41no—
121C4⋊C8×C151—41no—
122#103×C151—22no—
123#103×C151—22no—
124#103×C151—22no—
125#103×C151—41no—
126#103×C151—41no—
127#103×C151—41no—
128#102×C151—22no—
129#102×C151—22no—
130#102×C151—22no—
131#102×C151—41no—
132#97×C151—22no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151D411yescharacteristic
138#95×C151D411yescharacteristic
139C24×C151—21no—
140C24×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×C151—21no—
152C2×Q8×C151#4112yes—
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×C151C2×D412yes—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—24no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—42no—
173C22×C4×C151—42no—
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2411yescharacteristic
181SD16×C151—28no—
182SD16×C151—44no—
183D8×C151—44no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
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#4112yes—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—41no—
205C4⋊C4×C151—42no—
206C4⋊C4×C151—42no—
207C4⋊C4×C151—42no—
208C4⋊C4×C151—42no—
209C4⋊C4×C151—81no—
210C4⋊C4×C151C2×D412yes—
211C22⋊C4×C151—24no—
212C22⋊C4×C151—42no—
213C22⋊C4×C151—42no—
214C22⋊C4×C151—42no—
215C22⋊C4×C151—42no—
216C22⋊C4×C151—42no—
217C22⋊C4×C151—42no—
218C22⋊C4×C151—42no—
219C22⋊C4×C151—42no—
220C22⋊C4×C151—81no—
221C22⋊C4×C151—81no—
222C42×C151—21no—
223C42×C151—21no—
224C42×C151—21no—
225C42×C151—21no—
226C42×C151—42no—
227C42×C151—42no—
228C42×C151—42no—
229C42×C151C2×D412yes—
230C42×C151#4112yes—
231C23×C151—22no—
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×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151C22×D411yescharacteristic
246Q8×C151—22no—
247Q8×C151—22no—
248Q8×C151—41no—
249Q8×C151—41no—
250Q8×C151—41no—
251Q8×C151—41no—
252Q8×C151—41no—
253Q8×C151—41no—
254D4×C151—22no—
255D4×C151—22no—
256D4×C151—41no—
257D4×C151—41no—
258D4×C151—41no—
259D4×C151—41no—
260D4×C151—41no—
261D4×C151—41no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—22no—
269C2×C4×C151—22no—
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—21no—
279C2×C4×C151—48no—
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—41no—
295C2×C4×C151—41no—
296C2×C4×C151#12112yes—
297C2×C4×C151#12112yes—
298C2×C4×C151AGL(1,ℤ/8)12yes—
299C2×C4×C151C22×D411yescharacteristic
300C2×C4×C151C2×#4111yescharacteristic
301C2×C4×C151C2×#4111yescharacteristic
302C2×C4×C151C2×#4111yescharacteristic
303C2×C4×C151H(5,𝔽2)11yescharacteristic
304C2×C4×C151H(5,𝔽2)11yescharacteristic
305C8×C151—22no—
306C8×C151—41no—
307C8×C151—41no—
308C8×C151—41no—
309C22×C151—42no—
310C22×C151—42no—
311C22×C151—42no—
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×C151—81no—
323C22×C151C2×#12111yescharacteristic
324C22×C151#54611yescharacteristic
325C22×C151#55011yescharacteristic
326C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C151#57511yescharacteristic
328C22×C151#57711yescharacteristic
329C22×C151#57811yescharacteristic
330C4×C151—22no—
331C4×C151—22no—
332C4×C151—22no—
333C4×C151—42no—
334C4×C151—42no—
335C4×C151—41no—
336C4×C151—41no—
337C4×C151—41no—
338C4×C151—81no—
339C4×C151—81no—
340C4×C151—81no—
341C4×C151—81no—
342C4×C151#52511yescharacteristic
343C4×C151#53511yescharacteristic
344C4×C151#55311yescharacteristic
345C4×C151#55511yescharacteristic
346C2×C151—82no—
347C2×C151—161no—
348C2×C151#241411yescharacteristic
349C2×C151#303611yescharacteristic
350C2×C151#304611yescharacteristic
351C2×C151#330811yescharacteristic
352C2×C151#332111yescharacteristic
353C2×C151#339711yescharacteristic
354C2×C151#340211yescharacteristic
355#24640C15111yesmaximal, characteristic, direct product factor, Sylow
356C151#2464011yescharacteristic, direct product factor, Sylow
357C2×#463C2×C15111yescharacteristic
358C2×#440C2×C15111yescharacteristic, complemented
359#2545C2×C15111yescharacteristic, complemented
360#2354C2×C15111yescharacteristic, complemented
361#2055C2×C15111yescharacteristic, complemented
362#2054C2×C15111yescharacteristic
363#2013C2×C15111yescharacteristic, complemented
364#2012C2×C15111yescharacteristic
365#1983C2×C15111yescharacteristic, complemented
366#1981C2×C15111yescharacteristic, complemented
367#1959C2×C15111yescharacteristic, complemented
368#1940C2×C15111yescharacteristic, complemented
369#1928C2×C15111yescharacteristic, complemented
370#1925C2×C15111yescharacteristic, complemented
371#1803C2×C15111yescharacteristic, complemented
372C22×SD16C22×C15111yescharacteristic
373C22×SD16C22×C15111yescharacteristic
374C22×D8C22×C15111yescharacteristic
375C2×C4⋊Q8C22×C15111yescharacteristic
376C2×#124C22×C15111yescharacteristic
377C2×#124C22×C15111yescharacteristic
378C2×C4×Q8C22×C15111yescharacteristic
379C2×C4×D4C22×C15111yescharacteristic
380C2×#117—21no—
381#463—24no—
382#440—24no—
383C2×#107C22×C15111yescharacteristic
384C2×C4⋊C8C22×C15111yescharacteristic
385C2×C4⋊C8C22×C15111yescharacteristic
386C2×C4⋊C8C22×C15111yescharacteristic
387C2×#103C22×C15111yescharacteristic
388C2×#103C22×C15111yescharacteristic
389C2×#103C22×C15111yescharacteristic
390C2×#103C22×C15111yescharacteristic
391C2×#103C22×C15111yescharacteristic
392C2×#103C22×C15111yescharacteristic
393C2×#102C22×C15111yescharacteristic
394C2×#102C22×C15111yescharacteristic
395C2×#102C22×C15111yescharacteristic
396C2×#102C22×C15111yescharacteristic
397C2×#97C22×C15111yescharacteristic
398#396—21no—
399#396—21no—
400#391C22×C15111yescharacteristic
401#390C22×C15111yescharacteristic
402#390C22×C15111yescharacteristic
403#390C22×C15111yescharacteristic
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#384C22×C15111yescharacteristic
409#380—21no—
410C4×C4⋊C4C22×C15111yescharacteristic
411C4×C4⋊C4C22×C15111yescharacteristic
412C4×C4⋊C4C22×C15111yescharacteristic
413#340C22×C15111yescharacteristic
414#340C22×C15111yescharacteristic
415#336C22×C15111yescharacteristic
416#336C22×C15111yescharacteristic
417C22×Q8C23×C15111yescharacteristic
418C22×Q8C23×C15111yescharacteristic
419C22×D4C23×C15111yescharacteristic
420C22×D4C23×C15111yescharacteristic
421C23×C4—21no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—22no—
426C2×SD16—41no—
427C2×SD16—41no—
428C2×D8—22no—
429C2×D8—41no—
430C2×D8—41no—
431C22×C8C23×C15111yescharacteristic
432C22×C8C23×C15111yescharacteristic
433C22×C8C23×C15111yescharacteristic
434C22×C8C23×C15111yescharacteristic
435C4⋊Q8—22no—
436C4⋊Q8—41no—
437#124—22no—
438#124—22no—
439#124—22no—
440#124—41no—
441C4×Q8—22no—
442C4×Q8—22no—
443C4×D4—22no—
444C4×D4D4×C15114yes—
445#117—44no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4D4×C15111yescharacteristic
452C2×C4⋊C4D4×C15111yescharacteristic
453C2×C4⋊C4C23×C15111yescharacteristic
454C2×C4⋊C4C23×C15111yescharacteristic
455C2×C4⋊C4C23×C15111yescharacteristic
456C2×C4⋊C4C23×C15111yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C23×C15111yescharacteristic
472C2×C42C23×C15111yescharacteristic
473C2×C42C23×C15111yescharacteristic
474#107—22no—
475C4⋊C8—22no—
476C4⋊C8—41no—
477C4⋊C8—41no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—41no—
482#103—41no—
483#103—41no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—41no—
488#97—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95D4×C15111yescharacteristic
494#95D4×C15111yescharacteristic
495C24—21no—
496C24—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×Q8—21no—
507C2×Q8—21no—
508C2×Q8#41×C15112yes—
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—21no—
519C2×D4—21no—
520C2×D4C2×D4×C15112yes—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4C2×D4×C15111yescharacteristic
531C22×C4C2×D4×C15111yescharacteristic
532C22×C4C2×D4×C15111yescharacteristic
533C22×C4C2×D4×C15111yescharacteristic
534C22×C4C2×D4×C15111yescharacteristic
535C22×C4C2×D4×C15111yescharacteristic
536C22×C4C24×C15111yescharacteristic
537SD16—28no—
538SD16—44no—
539D8—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8#41×C15112yes—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—41no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—81no—
566C4⋊C4C2×D4×C15112yes—
567C22⋊C4—24no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—42no—
583C42—42no—
584C42—42no—
585C42C2×D4×C15112yes—
586C42#41×C15112yes—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23C22×D4×C15111yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610D4—22no—
611D4—22no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—48no—
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—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4#121×C15112yes—
653C2×C4#121×C15112yes—
654C2×C4AGL(1,ℤ/8)×C15112yes—
655C2×C4C22×D4×C15111yescharacteristic
656C2×C4C2×#41×C15111yescharacteristic
657C2×C4C2×#41×C15111yescharacteristic
658C2×C4C2×#41×C15111yescharacteristic
659C2×C4H(5,𝔽2)×C15111yescharacteristic
660C2×C4H(5,𝔽2)×C15111yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×#121×C15111yescharacteristic
680C22#546×C15111yescharacteristic
681C22#550×C15111yescharacteristic
682C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
683C22#575×C15111yescharacteristic
684C22#577×C15111yescharacteristic
685C22#578×C15111yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4#525×C15111yescharacteristic
699C4#535×C15111yescharacteristic
700C4#553×C15111yescharacteristic
701C4#555×C15111yescharacteristic
702C2—82no—
703C2—161no—
704C2#2414×C15111yescharacteristic
705C2#3036×C15111yescharacteristic
706C2#3046×C15111yescharacteristic
707C2#3308×C15111yescharacteristic
708C2#3321×C15111yescharacteristic
709C2#3397×C15111yescharacteristic
710C2#3402×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×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
2. C2×#440×C151C2semidirect
3. #2545×C151C2semidirect
4. #2354×C151C2semidirect
5. #2055×C151C2semidirect
7. #2013×C151C2semidirect
9. #1983×C151C2semidirect
10. #1981×C151C2semidirect
11. #1959×C151C2semidirect
12. #1940×C151C2semidirect
13. #1928×C151C2semidirect
14. #1925×C151C2semidirect
15. #1803×C151C2semidirect
355. #24640C151direct (N × H)
356. C151#24640direct (N × H)
358. C2×#440C2×C151semidirect
359. #2545C2×C151semidirect
360. #2354C2×C151semidirect
361. #2055C2×C151semidirect
363. #2013C2×C151semidirect
365. #1983C2×C151semidirect
366. #1981C2×C151semidirect
367. #1959C2×C151semidirect
368. #1940C2×C151semidirect
369. #1928C2×C151semidirect
370. #1925C2×C151semidirect
371. #1803C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1512
C2×#440×C1512
#2545×C1512
#2354×C1512
#2055×C1512
#2054×C1512
#2013×C1512
#2012×C1512
#1983×C1512
#1981×C1512
#1959×C1512
#1940×C1512
#1928×C1512
#1925×C1512
#1803×C1512
#24640151