Finite Group Databasebeta

← C151×#18933 #50323858

Subgroups — C151×#18933 #50323858

Order 38656.

858 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3544×C151C211yesmaximal, characteristic
2#3252×C151C211yesmaximal, characteristic, complemented
3#3233×C151C211yesmaximal, characteristic, complemented
4#3209×C151C211yesmaximal, characteristic, complemented
5#1646×C151C211yesmaximal, characteristic, complemented
6#1645×C151C211yesmaximal, characteristic, complemented
7#1644×C151C211yesmaximal, characteristic, complemented
8#1643×C151C211yesmaximal, characteristic, complemented
9#1634×C151C211yesmaximal, characteristic, complemented
10#1633×C151C211yesmaximal, characteristic, complemented
11#1632×C151C211yesmaximal, characteristic, complemented
12#1632×C151C211yesmaximal, characteristic, complemented
13#1548×C151C211yesmaximal, characteristic, complemented
14#1495×C151C211yesmaximal, characteristic, complemented
15#1482×C151C211yesmaximal, characteristic, complemented
16#563×C151—22no—
17Q82×C151C2211yescharacteristic
18#555×C151C2211yescharacteristic
19#554×C151C2211yescharacteristic
20#554×C151C2211yescharacteristic
21#552×C151—21no—
22#552×C151—21no—
23#547×C151—21no—
24#547×C151—21no—
25#544×C151—21no—
26#544×C151—21no—
27#542×C151—21no—
28#542×C151—21no—
29#536×C151—22no—
30#533×C151C2211yescharacteristic
31C2×C4⋊Q8×C151C2211yescharacteristic
32#529×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#499×C151—21no—
35#494×C151C2211yescharacteristic
36#494×C151C2211yescharacteristic
37#488×C151—21no—
38#487×C151C2211yescharacteristic
39#487×C151C2211yescharacteristic
40#485×C151—21no—
41#482×C151—21no—
42#479×C151—21no—
43#477×C151C2211yescharacteristic
44#477×C151C2211yescharacteristic
45#476×C151C2211yescharacteristic
46#476×C151C2211yescharacteristic
47#475×C151C2211yescharacteristic
48#474×C151C2211yescharacteristic
49#470×C151—21no—
50#468×C151—21no—
51#464×C151—21no—
52#462×C151—22no—
53#462×C151C2211yescharacteristic
54#461×C151C2211yescharacteristic
55#451×C151—22no—
56#431×C151C2211yescharacteristic
57#431×C151C2211yescharacteristic
58#423×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#333×C151C2211yescharacteristic
62#333×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64Q8⋊C8×C151C2211yescharacteristic
65Q8⋊C8×C151C2211yescharacteristic
66Q8⋊C8×C151C2211yescharacteristic
67D4⋊C8×C151C2211yescharacteristic
68D4⋊C8×C151C2211yescharacteristic
69D4⋊C8×C151C2211yescharacteristic
70D4⋊C8×C151C2211yescharacteristic
71C2×#41×C151—22no—
72C22×Q8×C151D412yes—
73C2×Q16×C151—22no—
74C2×Q16×C151—22no—
75C2×Q16×C151—21no—
76C2×SD16×C151—21no—
77C2×M16×C151—21no—
78C4⋊Q8×C151—22no—
79C4⋊Q8×C151—21no—
80C4⋊Q8×C151—21no—
81C4⋊Q8×C151—21no—
82C4⋊Q8×C151—21no—
83C4⋊Q8×C151—22no—
84C4⋊Q8×C151D412yes—
85C4⋊Q8×C151C2311yescharacteristic
86C4⋊Q8×C151C2311yescharacteristic
87C4⋊Q8×C151C2311yescharacteristic
88C4⋊Q8×C151C2311yescharacteristic
89#126×C151—22no—
90#126×C151—22no—
91#126×C151—21no—
92#126×C151—21no—
93#125×C151—22no—
94#125×C151—22no—
95#125×C151—21no—
96#125×C151—21no—
97#125×C151—21no—
98#125×C151D411yescharacteristic
99#125×C151D411yescharacteristic
100#124×C151—22no—
101#124×C151—22no—
102#124×C151D411yescharacteristic
103#124×C151D411yescharacteristic
104#123×C151—22no—
105#123×C151—22no—
106#123×C151—22no—
107#123×C151—22no—
108#123×C151—21no—
109#123×C151—21no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—21no—
115C22⋊Q8×C151—21no—
116C22⋊Q8×C151—22no—
117C22⋊Q8×C151—22no—
118C22⋊Q8×C151—21no—
119C22⋊Q8×C151—21no—
120C22⋊Q8×C151D411yescharacteristic
121C22⋊Q8×C151D411yescharacteristic
122#121×C151—21no—
123#121×C151—21no—
124#121×C151D411yescharacteristic
125#121×C151D411yescharacteristic
126C4×Q8×C151—21no—
127C4×Q8×C151—21no—
128C4×Q8×C151—21no—
129C4×Q8×C151—21no—
130C4×Q8×C151C2311yescharacteristic
131C4×Q8×C151C2311yescharacteristic
132C4×D4×C151—21no—
133C4×D4×C151—21no—
134C4×D4×C151—21no—
135C4×D4×C151—21no—
136C4×D4×C151C2311yescharacteristic
137C4×D4×C151C2311yescharacteristic
138#117×C151—22no—
139#117×C151—21no—
140#117×C151—21no—
141#117×C151—21no—
142#117×C151—21no—
143#117×C151—21no—
144C2×C4⋊C4×C151—21no—
145C2×C4⋊C4×C151—21no—
146C2×C4⋊C4×C151—21no—
147C2×C4⋊C4×C151—21no—
148C2×C42×C151C2311yescharacteristic
149#107×C151—21no—
150#107×C151—21no—
151#107×C151—21no—
152#106×C151—21no—
153#106×C151—21no—
154#106×C151—21no—
155C4⋊C8×C151—21no—
156C4⋊C8×C151—21no—
157C4⋊C8×C151C2311yescharacteristic
158C4⋊C8×C151C2311yescharacteristic
159C4⋊C8×C151C2311yescharacteristic
160C4⋊C8×C151C2311yescharacteristic
161#103×C151—21no—
162#103×C151—21no—
163#103×C151—22no—
164#103×C151—22no—
165#103×C151—21no—
166#103×C151—21no—
167#103×C151—21no—
168#102×C151—21no—
169#102×C151—21no—
170#102×C151—21no—
171C22⋊C8×C151—21no—
172C22⋊C8×C151—21no—
173C4×C8×C151—21no—
174C4×C8×C151C2311yescharacteristic
175C4×C8×C151C2311yescharacteristic
176#41×C151—84no—
177C2×Q8×C151—22no—
178C2×Q8×C151—22no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—82no—
182C2×Q8×C151C2×D411yescharacteristic
183C2×Q8×C151C2×D411yescharacteristic
184C2×Q8×C151C2×D412yes—
185C2×Q8×C151C2×D412yes—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—22no—
189C2×D4×C151C2×D411yescharacteristic
190C2×D4×C151C2×D411yescharacteristic
191C22×C4×C151—22no—
192C22×C4×C151—22no—
193C22×C4×C151—22no—
194C22×C4×C151—21no—
195C22×C4×C151—21no—
196C22×C4×C151C2×D411yescharacteristic
197C22×C4×C151C2×D411yescharacteristic
198C22×C4×C151C2×D411yescharacteristic
199Q16×C151—81no—
200Q16×C151—82no—
201Q16×C151—82no—
202SD16×C151—81no—
203M16×C151—81no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C4⋊C4×C151—22no—
211C4⋊C4×C151—22no—
212C4⋊C4×C151—22no—
213C4⋊C4×C151—22no—
214C4⋊C4×C151—22no—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—22no—
217C4⋊C4×C151—22no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151—21no—
233C4⋊C4×C151—21no—
234C4⋊C4×C151—41no—
235C4⋊C4×C151—41no—
236C4⋊C4×C151C2×D411yescharacteristic
237C4⋊C4×C151C2×D411yescharacteristic
238C4⋊C4×C151C2×D411yescharacteristic
239C4⋊C4×C151C2×D411yescharacteristic
240C22⋊C4×C151—22no—
241C22⋊C4×C151—22no—
242C22⋊C4×C151—22no—
243C22⋊C4×C151—22no—
244C22⋊C4×C151—21no—
245C22⋊C4×C151—21no—
246C22⋊C4×C151—21no—
247C22⋊C4×C151—21no—
248C22⋊C4×C151—21no—
249C22⋊C4×C151—21no—
250C22⋊C4×C151—21no—
251C22⋊C4×C151—21no—
252C22⋊C4×C151—21no—
253C22⋊C4×C151—21no—
254C22⋊C4×C151—41no—
255C42×C151—22no—
256C42×C151—22no—
257C42×C151—21no—
258C42×C151—21no—
259C42×C151—41no—
260C42×C151C2×D411yescharacteristic
261C42×C151C2×D411yescharacteristic
262C42×C151C2×D411yescharacteristic
263C42×C151C2411yescharacteristic
264C23×C151—21no—
265C23×C151—21no—
266C23×C151#12011yescharacteristic
267Q8×C151—21no—
268Q8×C151—21no—
269Q8×C151—21no—
270Q8×C151—21no—
271Q8×C151—42no—
272Q8×C151—42no—
273Q8×C151—42no—
274Q8×C151—41no—
275Q8×C151—41no—
276Q8×C151—82no—
277Q8×C151—82no—
278D4×C151—21no—
279D4×C151—21no—
280D4×C151—21no—
281D4×C151—21no—
282D4×C151—42no—
283D4×C151—42no—
284D4×C151—82no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—22no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—22no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—41no—
298C2×C4×C151—44no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—82no—
306C2×C4×C151—82no—
307C2×C4×C151#12011yescharacteristic
308C2×C4×C151#12011yescharacteristic
309C2×C4×C151#12011yescharacteristic
310C2×C4×C151C22×D411yescharacteristic
311C2×C4×C151C22×D411yescharacteristic
312C2×C4×C151C22×D411yescharacteristic
313C8×C151—41no—
314C8×C151—41no—
315C8×C151—41no—
316C8×C151—41no—
317C8×C151—41no—
318C8×C151—41no—
319C22×C151—21no—
320C22×C151—21no—
321C22×C151—21no—
322C22×C151—41no—
323C22×C151—41no—
324C22×C151—41no—
325C22×C151—41no—
326C22×C151—41no—
327C22×C151—41no—
328C22×C151C2×#12011yescharacteristic
329C4×C151—21no—
330C4×C151—21no—
331C4×C151—21no—
332C4×C151—21no—
333C4×C151—41no—
334C4×C151—41no—
335C4×C151—41no—
336C4×C151—41no—
337C4×C151—42no—
338C4×C151—42no—
339C4×C151—41no—
340C4×C151—41no—
341C4×C151—81no—
342C4×C151—81no—
343C4×C151#57711yescharacteristic
344C4×C151#57811yescharacteristic
345C4×C151#57811yescharacteristic
346C4×C151#57811yescharacteristic
347C2×C151—41no—
348C2×C151—81no—
349C2×C151—81no—
350C2×C151#301111yescharacteristic
351C2×C151#301311yescharacteristic
352C2×C151#301911yescharacteristic
353#18933C15111yesmaximal, characteristic, direct product factor, Sylow
354C151#1893311yescharacteristic, direct product factor, Sylow
355#3544C2×C15111yescharacteristic
356#3252C2×C15111yescharacteristic, complemented
357#3233C2×C15111yescharacteristic, complemented
358#3209C2×C15111yescharacteristic, complemented
359#1646C2×C15111yescharacteristic, complemented
360#1645C2×C15111yescharacteristic, complemented
361#1644C2×C15111yescharacteristic, complemented
362#1643C2×C15111yescharacteristic, complemented
363#1634C2×C15111yescharacteristic, complemented
364#1633C2×C15111yescharacteristic, complemented
365#1632C2×C15111yescharacteristic, complemented
366#1632C2×C15111yescharacteristic, complemented
367#1548C2×C15111yescharacteristic, complemented
368#1495C2×C15111yescharacteristic, complemented
369#1482C2×C15111yescharacteristic, complemented
370#563—22no—
371Q82C22×C15111yescharacteristic
372#555C22×C15111yescharacteristic
373#554C22×C15111yescharacteristic
374#554C22×C15111yescharacteristic
375#552—21no—
376#552—21no—
377#547—21no—
378#547—21no—
379#544—21no—
380#544—21no—
381#542—21no—
382#542—21no—
383#536—22no—
384#533C22×C15111yescharacteristic
385C2×C4⋊Q8C22×C15111yescharacteristic
386#529C22×C15111yescharacteristic
387#529C22×C15111yescharacteristic
388#499—21no—
389#494C22×C15111yescharacteristic
390#494C22×C15111yescharacteristic
391#488—21no—
392#487C22×C15111yescharacteristic
393#487C22×C15111yescharacteristic
394#485—21no—
395#482—21no—
396#479—21no—
397#477C22×C15111yescharacteristic
398#477C22×C15111yescharacteristic
399#476C22×C15111yescharacteristic
400#476C22×C15111yescharacteristic
401#475C22×C15111yescharacteristic
402#474C22×C15111yescharacteristic
403#470—21no—
404#468—21no—
405#464—21no—
406#462—22no—
407#462C22×C15111yescharacteristic
408#461C22×C15111yescharacteristic
409#451—22no—
410#431C22×C15111yescharacteristic
411#431C22×C15111yescharacteristic
412#423C22×C15111yescharacteristic
413#333C22×C15111yescharacteristic
414#333C22×C15111yescharacteristic
415#333C22×C15111yescharacteristic
416#333C22×C15111yescharacteristic
417Q8⋊C8C22×C15111yescharacteristic
418Q8⋊C8C22×C15111yescharacteristic
419Q8⋊C8C22×C15111yescharacteristic
420Q8⋊C8C22×C15111yescharacteristic
421D4⋊C8C22×C15111yescharacteristic
422D4⋊C8C22×C15111yescharacteristic
423D4⋊C8C22×C15111yescharacteristic
424D4⋊C8C22×C15111yescharacteristic
425C2×#41—22no—
426C22×Q8D4×C15112yes—
427C2×Q16—22no—
428C2×Q16—22no—
429C2×Q16—21no—
430C2×SD16—21no—
431C2×M16—21no—
432C4⋊Q8—22no—
433C4⋊Q8—22no—
434C4⋊Q8—21no—
435C4⋊Q8—21no—
436C4⋊Q8—21no—
437C4⋊Q8—21no—
438C4⋊Q8D4×C15112yes—
439C4⋊Q8C23×C15111yescharacteristic
440C4⋊Q8C23×C15111yescharacteristic
441C4⋊Q8C23×C15111yescharacteristic
442C4⋊Q8C23×C15111yescharacteristic
443#126—22no—
444#126—22no—
445#126—21no—
446#126—21no—
447#125—22no—
448#125—22no—
449#125—21no—
450#125—21no—
451#125—21no—
452#125D4×C15111yescharacteristic
453#125D4×C15111yescharacteristic
454#124—22no—
455#124—22no—
456#124D4×C15111yescharacteristic
457#124D4×C15111yescharacteristic
458#123—22no—
459#123—22no—
460#123—22no—
461#123—22no—
462#123—21no—
463#123—21no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8D4×C15111yescharacteristic
475C22⋊Q8D4×C15111yescharacteristic
476#121—21no—
477#121—21no—
478#121D4×C15111yescharacteristic
479#121D4×C15111yescharacteristic
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8—21no—
484C4×Q8C23×C15111yescharacteristic
485C4×Q8C23×C15111yescharacteristic
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4C23×C15111yescharacteristic
491C4×D4C23×C15111yescharacteristic
492#117—22no—
493#117—21no—
494#117—21no—
495#117—21no—
496#117—21no—
497#117—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C42C23×C15111yescharacteristic
503#107—21no—
504#107—21no—
505#107—21no—
506#106—21no—
507#106—21no—
508#106—21no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8C23×C15111yescharacteristic
512C4⋊C8C23×C15111yescharacteristic
513C4⋊C8C23×C15111yescharacteristic
514C4⋊C8C23×C15111yescharacteristic
515#103—22no—
516#103—22no—
517#103—21no—
518#103—21no—
519#103—21no—
520#103—21no—
521#103—21no—
522#102—21no—
523#102—21no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C4×C8—21no—
528C4×C8C23×C15111yescharacteristic
529C4×C8C23×C15111yescharacteristic
530#41—84no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—82no—
536C2×Q8C2×D4×C15111yescharacteristic
537C2×Q8C2×D4×C15111yescharacteristic
538C2×Q8C2×D4×C15112yes—
539C2×Q8C2×D4×C15112yes—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4C2×D4×C15111yescharacteristic
544C2×D4C2×D4×C15111yescharacteristic
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4C2×D4×C15111yescharacteristic
551C22×C4C2×D4×C15111yescharacteristic
552C22×C4C2×D4×C15111yescharacteristic
553Q16—81no—
554Q16—82no—
555Q16—82no—
556SD16—81no—
557M16—81no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4C2×D4×C15111yescharacteristic
591C4⋊C4C2×D4×C15111yescharacteristic
592C4⋊C4C2×D4×C15111yescharacteristic
593C4⋊C4C2×D4×C15111yescharacteristic
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—41no—
609C42—22no—
610C42—22no—
611C42—21no—
612C42—21no—
613C42—41no—
614C42C2×D4×C15111yescharacteristic
615C42C2×D4×C15111yescharacteristic
616C42C2×D4×C15111yescharacteristic
617C42C24×C15111yescharacteristic
618C23—21no—
619C23—21no—
620C23#120×C15111yescharacteristic
621Q8—21no—
622Q8—21no—
623Q8—21no—
624Q8—21no—
625Q8—42no—
626Q8—42no—
627Q8—42no—
628Q8—41no—
629Q8—41no—
630Q8—82no—
631Q8—82no—
632D4—21no—
633D4—21no—
634D4—21no—
635D4—21no—
636D4—42no—
637D4—42no—
638D4—82no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—44no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4#120×C15111yescharacteristic
662C2×C4#120×C15111yescharacteristic
663C2×C4#120×C15111yescharacteristic
664C2×C4C22×D4×C15111yescharacteristic
665C2×C4C22×D4×C15111yescharacteristic
666C2×C4C22×D4×C15111yescharacteristic
667C8—41no—
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—41no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22C2×#120×C15111yescharacteristic
683C4—21no—
684C4—21no—
685C4—21no—
686C4—21no—
687C4—41no—
688C4—41no—
689C4—41no—
690C4—41no—
691C4—42no—
692C4—42no—
693C4—41no—
694C4—41no—
695C4—81no—
696C4—81no—
697C4#577×C15111yescharacteristic
698C4#578×C15111yescharacteristic
699C4#578×C15111yescharacteristic
700C4#578×C15111yescharacteristic
701C2—41no—
702C2—81no—
703C2—81no—
704C2#3011×C15111yescharacteristic
705C2#3013×C15111yescharacteristic
706C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3544×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3252×C151C2semidirect
3. #3233×C151C2semidirect
4. #3209×C151C2semidirect
5. #1646×C151C2semidirect
6. #1645×C151C2semidirect
7. #1644×C151C2semidirect
8. #1643×C151C2semidirect
9. #1634×C151C2semidirect
10. #1633×C151C2semidirect
11. #1632×C151C2semidirect
12. #1632×C151C2semidirect
13. #1548×C151C2semidirect
14. #1495×C151C2semidirect
15. #1482×C151C2semidirect
353. #18933C151direct (N × H)
354. C151#18933direct (N × H)
356. #3252C2×C151semidirect
357. #3233C2×C151semidirect
358. #3209C2×C151semidirect
359. #1646C2×C151semidirect
360. #1645C2×C151semidirect
361. #1644C2×C151semidirect
362. #1643C2×C151semidirect
363. #1634C2×C151semidirect
364. #1633C2×C151semidirect
365. #1632C2×C151semidirect
366. #1632C2×C151semidirect
367. #1548C2×C151semidirect
368. #1495C2×C151semidirect
369. #1482C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3544×C1512
#3252×C1512
#3233×C1512
#3209×C1512
#1646×C1512
#1645×C1512
#1644×C1512
#1643×C1512
#1634×C1512
#1633×C1512
#1632×C1512
#1548×C1512
#1495×C1512
#1482×C1512
#18933151