Finite Group Databasebeta

← C151×#24487 #50329412

Subgroups — C151×#24487 #50329412

Order 38656.

954 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C151C211yesmaximal, characteristic, complemented
2C2×#416×C151C211yesmaximal, characteristic
3#2432×C151C211yesmaximal, characteristic
4#2346×C151C211yesmaximal, characteristic, complemented
5#2066×C151C211yesmaximal, characteristic, complemented
6#2065×C151C211yesmaximal, characteristic, complemented
7#2043×C151C211yesmaximal, characteristic, complemented
8#2042×C151C211yesmaximal, characteristic, complemented
9#1983×C151C211yesmaximal, characteristic, complemented
10#1981×C151C211yesmaximal, characteristic, complemented
11#1928×C151C211yesmaximal, characteristic, complemented
12#1925×C151C211yesmaximal, characteristic, complemented
13#1892×C151C211yesmaximal, characteristic, complemented
14#1850×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic
16C22×#41×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×#124×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22#485×C151—24no—
23C2×#107×C151C2211yescharacteristic
24C2×#106×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27#416×C151—24no—
28C2×#103×C151C2211yescharacteristic
29C2×#103×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×C22⋊C8×C151C2211yescharacteristic
41#394×C151—21no—
42#394×C151—21no—
43#391×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#389×C151C2211yescharacteristic
46#389×C151C2211yescharacteristic
47#388×C151—21no—
48#388×C151—21no—
49#385×C151—21no—
50#385×C151—21no—
51#382×C151—21no—
52#380×C151C2211yescharacteristic
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C22⋊C4×C151C2211yescharacteristic
56#376×C151—21no—
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C2×#41×C151—22no—
62C2×#41×C151—22no—
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—41no—
66C2×#41×C151—41no—
67C22×Q8×C151C2311yescharacteristic
68C22×Q8×C151C2311yescharacteristic
69C22×D4×C151—21no—
70C22×D4×C151C2311yescharacteristic
71C23×C4×C151—21no—
72C23×C4×C151C2311yescharacteristic
73C22×C8×C151—22no—
74C22×C8×C151—41no—
75C22×C8×C151—41no—
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C4⋊Q8×C151—22no—
81C4⋊Q8×C151—41no—
82#124×C151—22no—
83#124×C151—41no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151—22no—
86#117×C151—22no—
87#117×C151D414yes—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151C2311yescharacteristic
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×C151D411yescharacteristic
106C2×C22⋊C4×C151D411yescharacteristic
107C2×C42×C151—21no—
108C2×C42×C151—21no—
109C2×C42×C151—21no—
110C2×C42×C151C2311yescharacteristic
111C2×C42×C151C2311yescharacteristic
112#107×C151—22no—
113#106×C151—22no—
114C4⋊C8×C151—41no—
115C4⋊C8×C151—41no—
116#103×C151—22no—
117#103×C151—22no—
118#103×C151—22no—
119#103×C151—22no—
120#103×C151—22no—
121#103×C151—41no—
122#103×C151—41no—
123#103×C151—41no—
124#102×C151—22no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—41no—
128C22⋊C8×C151—22no—
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×C151C2×D411yescharacteristic
140#41×C151—28no—
141#41×C151—44no—
142#41×C151—44no—
143#41×C151—44no—
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—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151#4112yes—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—42no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151#4112yes—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
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—42no—
178C22×C4×C151—42no—
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D412yes—
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151#4112yes—
186C22×C4×C151C2411yescharacteristic
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—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—44no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—42no—
209C4⋊C4×C151—42no—
210C4⋊C4×C151—42no—
211C4⋊C4×C151—81no—
212C4⋊C4×C151—81no—
213C4⋊C4×C151C2×D412yes—
214C4⋊C4×C151C2×D412yes—
215C22⋊C4×C151—24no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—41no—
218C22⋊C4×C151—42no—
219C22⋊C4×C151—42no—
220C22⋊C4×C151—42no—
221C22⋊C4×C151—42no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—81no—
224C42×C151—24no—
225C42×C151—21no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—42no—
230C42×C151—42no—
231C23×C151—21no—
232C23×C151—21no—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—22no—
238C23×C151—41no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151#12112yes—
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—48no—
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—22no—
264C2×C4×C151—22no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
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—41no—
297C2×C4×C151—41no—
298C2×C4×C151#12112yes—
299C2×C4×C151#13512yes—
300C2×C4×C151C22×D411yescharacteristic
301C2×C4×C151C2×#4111yescharacteristic
302C2×C4×C151C2×#4111yescharacteristic
303C2×C4×C151C2×#4111yescharacteristic
304C2×C4×C151H(5,𝔽2)11yescharacteristic
305C2×C4×C151H(5,𝔽2)11yescharacteristic
306C8×C151—41no—
307C8×C151—41no—
308C8×C151—41no—
309C8×C151—41no—
310C22×C151—22no—
311C22×C151—22no—
312C22×C151—22no—
313C22×C151—41no—
314C22×C151—41no—
315C22×C151—41no—
316C22×C151—41no—
317C22×C151—42no—
318C22×C151—42no—
319C22×C151—42no—
320C22×C151—81no—
321C22×C151—81no—
322C22×C151—81no—
323C22×C151—81no—
324C22×C151C2×#12111yescharacteristic
325C22×C151#54611yescharacteristic
326C22×C151#54611yescharacteristic
327C22×C151C2×#13511yescharacteristic
328C22×C151#57511yescharacteristic
329C22×C151#57711yescharacteristic
330C22×C151#57811yescharacteristic
331C4×C151—22no—
332C4×C151—22no—
333C4×C151—42no—
334C4×C151—42no—
335C4×C151—42no—
336C4×C151—41no—
337C4×C151—41no—
338C4×C151—41no—
339C4×C151—81no—
340C4×C151—81no—
341C4×C151—81no—
342C4×C151—81no—
343C4×C151#52511yescharacteristic
344C4×C151#53511yescharacteristic
345C4×C151#55111yescharacteristic
346C4×C151#55111yescharacteristic
347C2×C151—42no—
348C2×C151—82no—
349C2×C151#241111yescharacteristic
350C2×C151#303511yescharacteristic
351C2×C151#304611yescharacteristic
352C2×C151#330011yescharacteristic
353C2×C151#330311yescharacteristic
354C2×C151#331511yescharacteristic
355C2×C151#332111yescharacteristic
356#24487C15111yesmaximal, characteristic, direct product factor, Sylow
357C151#2448711yescharacteristic, direct product factor, Sylow
358C2×#485C2×C15111yescharacteristic, complemented
359C2×#416C2×C15111yescharacteristic
360#2432C2×C15111yescharacteristic
361#2346C2×C15111yescharacteristic, complemented
362#2066C2×C15111yescharacteristic, complemented
363#2065C2×C15111yescharacteristic, complemented
364#2043C2×C15111yescharacteristic, complemented
365#2042C2×C15111yescharacteristic, complemented
366#1983C2×C15111yescharacteristic, complemented
367#1981C2×C15111yescharacteristic, complemented
368#1928C2×C15111yescharacteristic, complemented
369#1925C2×C15111yescharacteristic, complemented
370#1892C2×C15111yescharacteristic, complemented
371#1850C2×C15111yescharacteristic, complemented
372#1788C2×C15111yescharacteristic
373C22×#41C22×C15111yescharacteristic
374C23×C8C22×C15111yescharacteristic
375C2×C4⋊Q8C22×C15111yescharacteristic
376C2×#124C22×C15111yescharacteristic
377C2×C22⋊Q8C22×C15111yescharacteristic
378C2×#117C22×C15111yescharacteristic
379#485—24no—
380C2×#107C22×C15111yescharacteristic
381C2×#106C22×C15111yescharacteristic
382C2×C4⋊C8C22×C15111yescharacteristic
383C2×C4⋊C8C22×C15111yescharacteristic
384#416—24no—
385C2×#103C22×C15111yescharacteristic
386C2×#103C22×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×C22⋊C8C22×C15111yescharacteristic
398#394—21no—
399#394—21no—
400#391C22×C15111yescharacteristic
401#390C22×C15111yescharacteristic
402#389C22×C15111yescharacteristic
403#389C22×C15111yescharacteristic
404#388—21no—
405#388—21no—
406#385—21no—
407#385—21no—
408#382—21no—
409#380C22×C15111yescharacteristic
410C4×C4⋊C4C22×C15111yescharacteristic
411C4×C4⋊C4C22×C15111yescharacteristic
412C4×C22⋊C4C22×C15111yescharacteristic
413#376—21no—
414#340C22×C15111yescharacteristic
415#340C22×C15111yescharacteristic
416#336C22×C15111yescharacteristic
417#336C22×C15111yescharacteristic
418C2×#41—22no—
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—41no—
423C2×#41—41no—
424C22×Q8C23×C15111yescharacteristic
425C22×Q8C23×C15111yescharacteristic
426C22×D4—21no—
427C22×D4C23×C15111yescharacteristic
428C23×C4—21no—
429C23×C4C23×C15111yescharacteristic
430C22×C8—22no—
431C22×C8—41no—
432C22×C8—41no—
433C22×C8C23×C15111yescharacteristic
434C22×C8C23×C15111yescharacteristic
435C22×C8C23×C15111yescharacteristic
436C22×C8C23×C15111yescharacteristic
437C4⋊Q8—22no—
438C4⋊Q8—41no—
439#124—22no—
440#124—41no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443#117—22no—
444#117D4×C15114yes—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4C23×C15111yescharacteristic
451C2×C4⋊C4C23×C15111yescharacteristic
452C2×C4⋊C4C23×C15111yescharacteristic
453C2×C4⋊C4C23×C15111yescharacteristic
454C2×C4⋊C4C23×C15111yescharacteristic
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×C22⋊C4D4×C15111yescharacteristic
463C2×C22⋊C4D4×C15111yescharacteristic
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42C23×C15111yescharacteristic
468C2×C42C23×C15111yescharacteristic
469#107—22no—
470#106—22no—
471C4⋊C8—41no—
472C4⋊C8—41no—
473#103—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477#103—22no—
478#103—41no—
479#103—41no—
480#103—41no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102—41no—
485C22⋊C8—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95D4×C15111yescharacteristic
494#95D4×C15111yescharacteristic
495C24—21no—
496C24C2×D4×C15111yescharacteristic
497#41—28no—
498#41—44no—
499#41—44no—
500#41—44no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8#41×C15112yes—
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#41×C15112yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4C2×D4×C15111yescharacteristic
537C22×C4C2×D4×C15111yescharacteristic
538C22×C4C2×D4×C15111yescharacteristic
539C22×C4C2×D4×C15111yescharacteristic
540C22×C4C2×D4×C15112yes—
541C22×C4C2×D4×C15111yescharacteristic
542C22×C4#41×C15112yes—
543C22×C4C24×C15111yescharacteristic
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—21no—
556C2×C8—44no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—81no—
569C4⋊C4—81no—
570C4⋊C4C2×D4×C15112yes—
571C4⋊C4C2×D4×C15112yes—
572C22⋊C4—24no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—81no—
581C42—24no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—42no—
587C42—42no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23#121×C15112yes—
602C23C22×D4×C15111yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—48no—
614D4—41no—
615D4—41no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—48no—
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—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4#121×C15112yes—
656C2×C4#135×C15112yes—
657C2×C4C22×D4×C15111yescharacteristic
658C2×C4C2×#41×C15111yescharacteristic
659C2×C4C2×#41×C15111yescharacteristic
660C2×C4C2×#41×C15111yescharacteristic
661C2×C4H(5,𝔽2)×C15111yescharacteristic
662C2×C4H(5,𝔽2)×C15111yescharacteristic
663C8—41no—
664C8—41no—
665C8—41no—
666C8—41no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#121×C15111yescharacteristic
682C22#546×C15111yescharacteristic
683C22#546×C15111yescharacteristic
684C22C2×#135×C15111yescharacteristic
685C22#575×C15111yescharacteristic
686C22#577×C15111yescharacteristic
687C22#578×C15111yescharacteristic
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—41no—
694C4—41no—
695C4—41no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4#525×C15111yescharacteristic
701C4#535×C15111yescharacteristic
702C4#551×C15111yescharacteristic
703C4#551×C15111yescharacteristic
704C2—42no—
705C2—82no—
706C2#2411×C15111yescharacteristic
707C2#3035×C15111yescharacteristic
708C2#3046×C15111yescharacteristic
709C2#3300×C15111yescharacteristic
710C2#3303×C15111yescharacteristic
711C2#3315×C15111yescharacteristic
712C2#3321×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C151C2semidirect
4. #2346×C151C2semidirect
5. #2066×C151C2semidirect
6. #2065×C151C2semidirect
7. #2043×C151C2semidirect
8. #2042×C151C2semidirect
9. #1983×C151C2semidirect
10. #1981×C151C2semidirect
11. #1928×C151C2semidirect
12. #1925×C151C2semidirect
13. #1892×C151C2semidirect
14. #1850×C151C2semidirect
356. #24487C151direct (N × H)
357. C151#24487direct (N × H)
358. C2×#485C2×C151semidirect
361. #2346C2×C151semidirect
362. #2066C2×C151semidirect
363. #2065C2×C151semidirect
364. #2043C2×C151semidirect
365. #2042C2×C151semidirect
366. #1983C2×C151semidirect
367. #1981C2×C151semidirect
368. #1928C2×C151semidirect
369. #1925C2×C151semidirect
370. #1892C2×C151semidirect
371. #1850C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1512
C2×#416×C1512
#2432×C1512
#2346×C1512
#2066×C1512
#2065×C1512
#2043×C1512
#2042×C1512
#1983×C1512
#1981×C1512
#1928×C1512
#1925×C1512
#1892×C1512
#1850×C1512
#1788×C1512
#24487151