Finite Group Databasebeta

← C151×#24636 #50329561

Subgroups — C151×#24636 #50329561

Order 38656.

888 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C151C211yesmaximal, characteristic
2C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
3#2545×C151C211yesmaximal, characteristic, complemented
4#2357×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#1958×C151C211yesmaximal, characteristic, complemented
12#1939×C151C211yesmaximal, characteristic, complemented
13#1927×C151C211yesmaximal, characteristic, complemented
14#1926×C151C211yesmaximal, characteristic, complemented
15#1805×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
24#463×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×#103×C151C2211yescharacteristic
35C2×#103×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×C4×C8×C151C2211yescharacteristic
41#396×C151—21no—
42#396×C151—21no—
43#391×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#390×C151C2211yescharacteristic
47#388×C151—21no—
48#388×C151—21no—
49#388×C151—21no—
50#388×C151—21no—
51#382×C151C2211yescharacteristic
52#381×C151—21no—
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C4⋊C4×C151C2211yescharacteristic
56C4×C22⋊C4×C151—21no—
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—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
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×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C42×C151—21no—
110C2×C42×C151—21no—
111C2×C42×C151—21no—
112C2×C42×C151C2311yescharacteristic
113C2×C42×C151C2311yescharacteristic
114C2×C42×C151C2311yescharacteristic
115#106×C151—22no—
116C4⋊C8×C151—22no—
117C4⋊C8×C151—41no—
118C4⋊C8×C151—41no—
119#103×C151—22no—
120#103×C151—22no—
121#103×C151—22no—
122#103×C151—41no—
123#103×C151—41no—
124#103×C151—41no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—22no—
128#102×C151—41no—
129C4×C8×C151—22no—
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×C151#4112yes—
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×C151C2×D412yes—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—24no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—81no—
172C22×C4×C151—81no—
173C22×C4×C151C2×D411yescharacteristic
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2411yescharacteristic
180SD16×C151—28no—
181SD16×C151—44no—
182D8×C151—44no—
183C2×C8×C151—21no—
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#4112yes—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—21no—
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—41no—
204C4⋊C4×C151—42no—
205C4⋊C4×C151—42no—
206C4⋊C4×C151—42no—
207C4⋊C4×C151C2×D412yes—
208C22⋊C4×C151—24no—
209C22⋊C4×C151—42no—
210C22⋊C4×C151—42no—
211C22⋊C4×C151—42no—
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—21no—
220C42×C151—21no—
221C42×C151—21no—
222C42×C151—21no—
223C42×C151—42no—
224C42×C151—81no—
225C42×C151—81no—
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—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
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—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—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—84no—
293C2×C4×C151#12112yes—
294C2×C4×C151#12112yes—
295C2×C4×C151#13512yes—
296C2×C4×C151C22×D411yescharacteristic
297C2×C4×C151C2×#4111yescharacteristic
298C2×C4×C151C2×#4111yescharacteristic
299C2×C4×C151C2×#4111yescharacteristic
300C2×C4×C151H(5,𝔽2)11yescharacteristic
301C2×C4×C151H(5,𝔽2)11yescharacteristic
302C8×C151—22no—
303C8×C151—41no—
304C8×C151—41no—
305C8×C151—41no—
306C22×C151—42no—
307C22×C151—42no—
308C22×C151—42no—
309C22×C151—81no—
310C22×C151—81no—
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×C151C2×#12111yescharacteristic
321C22×C151#54611yescharacteristic
322C22×C151#55011yescharacteristic
323C22×C151C2×#13511yescharacteristic
324C22×C151#57511yescharacteristic
325C22×C151#57711yescharacteristic
326C22×C151#57711yescharacteristic
327C4×C151—22no—
328C4×C151—22no—
329C4×C151—22no—
330C4×C151—42no—
331C4×C151—42no—
332C4×C151—41no—
333C4×C151—41no—
334C4×C151—41no—
335C4×C151—81no—
336C4×C151—81no—
337C4×C151—81no—
338C4×C151—81no—
339C4×C151#52511yescharacteristic
340C4×C151#53511yescharacteristic
341C4×C151#55311yescharacteristic
342C4×C151#55511yescharacteristic
343C2×C151—82no—
344C2×C151—161no—
345C2×C151#241411yescharacteristic
346C2×C151#303511yescharacteristic
347C2×C151#304211yescharacteristic
348C2×C151#330111yescharacteristic
349C2×C151#332611yescharacteristic
350C2×C151#339411yescharacteristic
351C2×C151#340111yescharacteristic
352#24636C15111yesmaximal, characteristic, direct product factor, Sylow
353C151#2463611yescharacteristic, direct product factor, Sylow
354C2×#463C2×C15111yescharacteristic
355C2×C4×SD16C2×C15111yescharacteristic, complemented
356#2545C2×C15111yescharacteristic, complemented
357#2357C2×C15111yescharacteristic, complemented
358#2055C2×C15111yescharacteristic, complemented
359#2054C2×C15111yescharacteristic
360#2013C2×C15111yescharacteristic, complemented
361#2012C2×C15111yescharacteristic
362#1983C2×C15111yescharacteristic, complemented
363#1981C2×C15111yescharacteristic, complemented
364#1958C2×C15111yescharacteristic, complemented
365#1939C2×C15111yescharacteristic, complemented
366#1927C2×C15111yescharacteristic, complemented
367#1926C2×C15111yescharacteristic, complemented
368#1805C2×C15111yescharacteristic, complemented
369C22×SD16C22×C15111yescharacteristic
370C22×SD16C22×C15111yescharacteristic
371C22×D8C22×C15111yescharacteristic
372C2×C4⋊Q8C22×C15111yescharacteristic
373C2×#124C22×C15111yescharacteristic
374C2×#124C22×C15111yescharacteristic
375C2×C4×Q8C22×C15111yescharacteristic
376C2×C4×D4C22×C15111yescharacteristic
377#463—24no—
378C4×SD16—24no—
379C2×#106C22×C15111yescharacteristic
380C2×C4⋊C8C22×C15111yescharacteristic
381C2×C4⋊C8C22×C15111yescharacteristic
382C2×C4⋊C8C22×C15111yescharacteristic
383C2×#103C22×C15111yescharacteristic
384C2×#103C22×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×C4×C8C22×C15111yescharacteristic
394#396—21no—
395#396—21no—
396#391C22×C15111yescharacteristic
397#390C22×C15111yescharacteristic
398#390C22×C15111yescharacteristic
399#390C22×C15111yescharacteristic
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#382C22×C15111yescharacteristic
405#381—21no—
406C4×C4⋊C4C22×C15111yescharacteristic
407C4×C4⋊C4C22×C15111yescharacteristic
408C4×C4⋊C4C22×C15111yescharacteristic
409C4×C22⋊C4—21no—
410#340C22×C15111yescharacteristic
411#340C22×C15111yescharacteristic
412#336C22×C15111yescharacteristic
413#336C22×C15111yescharacteristic
414C22×Q8C23×C15111yescharacteristic
415C22×Q8C23×C15111yescharacteristic
416C22×D4C23×C15111yescharacteristic
417C22×D4C23×C15111yescharacteristic
418C23×C4—21no—
419C2×SD16—22no—
420C2×SD16—22no—
421C2×SD16—22no—
422C2×SD16—22no—
423C2×SD16—41no—
424C2×SD16—41no—
425C2×D8—22no—
426C2×D8—41no—
427C2×D8—41no—
428C22×C8C23×C15111yescharacteristic
429C22×C8C23×C15111yescharacteristic
430C22×C8C23×C15111yescharacteristic
431C22×C8C23×C15111yescharacteristic
432C4⋊Q8—22no—
433C4⋊Q8—41no—
434#124—22no—
435#124—22no—
436#124—22no—
437#124—41no—
438C4×Q8—22no—
439C4×Q8—22no—
440C4×D4—22no—
441C4×D4D4×C15114yes—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4D4×C15111yescharacteristic
446C2×C4⋊C4D4×C15111yescharacteristic
447C2×C4⋊C4C23×C15111yescharacteristic
448C2×C4⋊C4C23×C15111yescharacteristic
449C2×C4⋊C4C23×C15111yescharacteristic
450C2×C4⋊C4C23×C15111yescharacteristic
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⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42C23×C15111yescharacteristic
466C2×C42C23×C15111yescharacteristic
467C2×C42C23×C15111yescharacteristic
468#106—22no—
469C4⋊C8—22no—
470C4⋊C8—41no—
471C4⋊C8—41no—
472#103—22no—
473#103—22no—
474#103—22no—
475#103—41no—
476#103—41no—
477#103—41no—
478#102—22no—
479#102—22no—
480#102—22no—
481#102—41no—
482C4×C8—22no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95D4×C15111yescharacteristic
490#95D4×C15111yescharacteristic
491C24—21no—
492C24—21no—
493C2×Q8—21no—
494C2×Q8—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#41×C15112yes—
505C2×D4—21no—
506C2×D4—21no—
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×D4C2×D4×C15112yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4C2×D4×C15111yescharacteristic
527C22×C4C2×D4×C15111yescharacteristic
528C22×C4C2×D4×C15111yescharacteristic
529C22×C4C2×D4×C15111yescharacteristic
530C22×C4C2×D4×C15111yescharacteristic
531C22×C4C2×D4×C15111yescharacteristic
532C22×C4C24×C15111yescharacteristic
533SD16—28no—
534SD16—44no—
535D8—44no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8#41×C15112yes—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—41no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4C2×D4×C15112yes—
561C22⋊C4—24no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—81no—
578C42—81no—
579C42C2×D4×C15112yes—
580C42#41×C15112yes—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C22×D4×C15111yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604D4—22no—
605D4—22no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
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—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—84no—
646C2×C4#121×C15112yes—
647C2×C4#121×C15112yes—
648C2×C4#135×C15112yes—
649C2×C4C22×D4×C15111yescharacteristic
650C2×C4C2×#41×C15111yescharacteristic
651C2×C4C2×#41×C15111yescharacteristic
652C2×C4C2×#41×C15111yescharacteristic
653C2×C4H(5,𝔽2)×C15111yescharacteristic
654C2×C4H(5,𝔽2)×C15111yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8—41no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C2×#121×C15111yescharacteristic
674C22#546×C15111yescharacteristic
675C22#550×C15111yescharacteristic
676C22C2×#135×C15111yescharacteristic
677C22#575×C15111yescharacteristic
678C22#577×C15111yescharacteristic
679C22#577×C15111yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—42no—
684C4—42no—
685C4—41no—
686C4—41no—
687C4—41no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4#525×C15111yescharacteristic
693C4#535×C15111yescharacteristic
694C4#553×C15111yescharacteristic
695C4#555×C15111yescharacteristic
696C2—82no—
697C2—161no—
698C2#2414×C15111yescharacteristic
699C2#3035×C15111yescharacteristic
700C2#3042×C15111yescharacteristic
701C2#3301×C15111yescharacteristic
702C2#3326×C15111yescharacteristic
703C2#3394×C15111yescharacteristic
704C2#3401×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×C4×SD16×C151C2semidirect
3. #2545×C151C2semidirect
4. #2357×C151C2semidirect
5. #2055×C151C2semidirect
7. #2013×C151C2semidirect
9. #1983×C151C2semidirect
10. #1981×C151C2semidirect
11. #1958×C151C2semidirect
12. #1939×C151C2semidirect
13. #1927×C151C2semidirect
14. #1926×C151C2semidirect
15. #1805×C151C2semidirect
352. #24636C151direct (N × H)
353. C151#24636direct (N × H)
355. C2×C4×SD16C2×C151semidirect
356. #2545C2×C151semidirect
357. #2357C2×C151semidirect
358. #2055C2×C151semidirect
360. #2013C2×C151semidirect
362. #1983C2×C151semidirect
363. #1981C2×C151semidirect
364. #1958C2×C151semidirect
365. #1939C2×C151semidirect
366. #1927C2×C151semidirect
367. #1926C2×C151semidirect
368. #1805C2×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×C4×SD16×C1512
#2545×C1512
#2357×C1512
#2055×C1512
#2054×C1512
#2013×C1512
#2012×C1512
#1983×C1512
#1981×C1512
#1958×C1512
#1939×C1512
#1927×C1512
#1926×C1512
#1805×C1512
#24636151