Finite Group Databasebeta

← C151×#14241 #50319166

Subgroups — C151×#14241 #50319166

Order 38656.

1470 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C151C211yesmaximal, characteristic
2C2×#391×C151C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C151C211yesmaximal, characteristic
4#1446×C151C211yesmaximal, characteristic
5#1444×C151C211yesmaximal, characteristic
6#1441×C151C211yesmaximal, characteristic
7#1436×C151C212yesmaximal
8#1436×C151C212yesmaximal
9#1436×C151C212yesmaximal
10C4⋊#95×C151C212yesmaximal
11C4×#95×C151C211yesmaximal, characteristic
12C23×Q8×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2212yes—
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2212yes—
18C22×C42×C151C2211yescharacteristic
19C22×C42×C151C2212yes—
20C22×C42×C151C2211yescharacteristic
21C22×C42×C151C2211yescharacteristic
22#395×C151C418yescomplemented
23#391×C151—24no—
24C4×C4⋊C4×C151—24no—
25C2×#95×C151C2211yescharacteristic
26C2×#95×C151C2211yescharacteristic
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2212yes—
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2212yes—
33C2×#95×C151C2212yes—
34C2×#95×C151C2212yes—
35C2×#95×C151C2211yescharacteristic
36C2×#95×C151C2212yes—
37C2×#95×C151C2212yes—
38C22×Q8×C151—22no—
39C22×Q8×C151—22no—
40C22×Q8×C151—42no—
41C22×Q8×C151—42no—
42C22×Q8×C151C2×C414yes—
43C23×C4×C151C2312yes—
44C23×C4×C151C2312yes—
45C23×C4×C151C2311yescharacteristic
46C23×C4×C151C2312yes—
47C23×C4×C151C2311yescharacteristic
48C23×C4×C151C2311yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C23×C4×C151C2311yescharacteristic
51C23×C4×C151C2312yes—
52C23×C4×C151C2311yescharacteristic
53C23×C4×C151C2311yescharacteristic
54C2×C4⋊C4×C151—22no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—24no—
60C2×C4⋊C4×C151—24no—
61C2×C4⋊C4×C151—42no—
62C2×C4⋊C4×C151—42no—
63C2×C4⋊C4×C151—42no—
64C2×C4⋊C4×C151—42no—
65C2×C4⋊C4×C151C2×C414yes—
66C2×C4⋊C4×C151C2×C418yes—
67C2×C4⋊C4×C151Q814yescomplemented
68C2×C42×C151—22no—
69C2×C42×C151—22no—
70C2×C42×C151—22no—
71C2×C42×C151—22no—
72C2×C42×C151—24no—
73C2×C42×C151—24no—
74C2×C42×C151—42no—
75C2×C42×C151—42no—
76C2×C42×C151—42no—
77C2×C42×C151D414yes—
78#95×C151—22no—
79#95×C151—22no—
80#95×C151—24no—
81#95×C151—24no—
82#95×C151—22no—
83#95×C151—24no—
84#95×C151—24no—
85#95×C151—42no—
86#95×C151—42no—
87#95×C151—42no—
88#95×C151C2×C418yes—
89#95×C151C2×C414yes—
90#95×C151Q818yescomplemented
91C24×C151C2411yescharacteristic
92C2×Q8×C151—28no—
93C2×Q8×C151—48no—
94C2×Q8×C151—44no—
95C2×Q8×C151—44no—
96C2×Q8×C151—48no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—22no—
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102C22×C4×C151—22no—
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—21no—
113C22×C4×C151—22no—
114C22×C4×C151—21no—
115C22×C4×C151—21no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—21no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151C22×C414yes—
144C22×C4×C151C22×C412yes—
145C22×C4×C151C22×C412yes—
146C22×C4×C151C22×C412yes—
147C22×C4×C151C22×C414yes—
148C22×C4×C151C2×D412yes—
149C22×C4×C151C2×D412yes—
150C22×C4×C151C2×D412yes—
151C22×C4×C151C2×Q814yes—
152C22×C4×C151C2×Q812yes—
153C22×C4×C151C2×Q814yes—
154C22×C4×C151C2×Q812yes—
155C22×C4×C151C2×Q812yes—
156C22×C4×C151C2×Q814yes—
157C22×C4×C151#4112yes—
158C22×C4×C151#4112yes—
159C22×C4×C151#4112yes—
160C22×C4×C151#4114yes—
161C22×C4×C151#4112yes—
162C4⋊C4×C151—28no—
163C4⋊C4×C151—28no—
164C4⋊C4×C151—48no—
165C4⋊C4×C151—48no—
166C4⋊C4×C151—44no—
167C42×C151—28no—
168C42×C151—44no—
169C42×C151—48no—
170C42×C151—44no—
171C23×C151C23×C411yescharacteristic
172C23×C151C22×D411yescharacteristic
173C23×C151C22×Q811yescharacteristic
174C23×C151C22×Q812yes—
175C23×C151C2×#4111yescharacteristic
176C23×C151C2×#4111yescharacteristic
177C23×C151C2×#4112yes—
178C23×C151C2×#4111yescharacteristic
179C23×C151C2×#4111yescharacteristic
180C23×C151H(5,𝔽2)12yes—
181C23×C151H(5,𝔽2)12yes—
182Q8×C151—416no—
183C2×C4×C151—22no—
184C2×C4×C151—24no—
185C2×C4×C151—22no—
186C2×C4×C151—24no—
187C2×C4×C151—24no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—24no—
199C2×C4×C151—24no—
200C2×C4×C151—24no—
201C2×C4×C151—24no—
202C2×C4×C151—24no—
203C2×C4×C151—24no—
204C2×C4×C151—24no—
205C2×C4×C151—24no—
206C2×C4×C151—24no—
207C2×C4×C151—24no—
208C2×C4×C151—22no—
209C2×C4×C151—24no—
210C2×C4×C151—24no—
211C2×C4×C151—24no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—24no—
215C2×C4×C151—24no—
216C2×C4×C151—24no—
217C2×C4×C151—24no—
218C2×C4×C151—24no—
219C2×C4×C151—42no—
220C2×C4×C151—41no—
221C2×C4×C151—41no—
222C2×C4×C151—42no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—42no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151C4×D414yes—
244C2×C4×C151C4×Q818yes—
245C2×C4×C151C4×Q814yes—
246C2×C4×C151C22⋊Q814yes—
247C2×C4×C151C4⋊Q814yes—
248C22×C151C2×C4×D411yescharacteristic
249C22×C151C2×C4×Q812yes—
250C22×C151C2×C4×Q811yescharacteristic
251C22×C151C4×#4111yescharacteristic
252C22×C151#51812yes—
253C22×C151C2×C22⋊Q811yescharacteristic
254C22×C151#52511yescharacteristic
255C22×C151#52911yescharacteristic
256C22×C151C2×C4⋊Q811yescharacteristic
257C22×C151#53211yescharacteristic
258C22×C151#53312yes—
259C22×C151#53311yescharacteristic
260C22×C151#53411yescharacteristic
261C22×C151#53511yescharacteristic
262C22×C151#53812yes—
263C22×C151#55112yes—
264C22×C151#55112yes—
265C22×C151#55412yes—
266C22×C151#55412yes—
267C22×C151#55412yes—
268C22×C151#55412yes—
269C22×C151#55512yes—
270C22×C151Q8212yes—
271C4×C151—24no—
272C4×C151—24no—
273C4×C151—24no—
274C4×C151—28no—
275C4×C151—24no—
276C4×C151—42no—
277C4×C151—44no—
278C4×C151—42no—
279C4×C151—44no—
280C4×C151—42no—
281C4×C151—82no—
282C2×C151C4×C22⋊Q811yescharacteristic
283C2×C151C4×C4⋊Q811yescharacteristic
284C2×C151#232111yescharacteristic
285C2×C151#236812yes—
286C2×C151#236912yes—
287C2×C151#256411yescharacteristic
288C2×C151#256711yescharacteristic
289C2×C151#257412yes—
290C2×C151#258311yescharacteristic
291C2×C151#258612yes—
292C2×C151#261011yescharacteristic
293#14241C15111yesmaximal, characteristic, direct product factor, Sylow
294C151#1424111yescharacteristic, direct product factor, Sylow
295C2×#395C2×C15111yescharacteristic
296C2×#391C2×C15111yescharacteristic
297C2×C4×C4⋊C4C2×C15111yescharacteristic
298#1446C2×C15111yescharacteristic
299#1444C2×C15111yescharacteristic
300#1441C2×C15111yescharacteristic
301#1436C2×C15112yes—
302#1436C2×C15112yes—
303#1436C2×C15112yes—
304C4⋊#95C2×C15112yes—
305C4×#95C2×C15111yescharacteristic
306C23×Q8C22×C15111yescharacteristic
307C22×C4⋊C4C22×C15112yes—
308C22×C4⋊C4C22×C15111yescharacteristic
309C22×C4⋊C4C22×C15111yescharacteristic
310C22×C4⋊C4C22×C15111yescharacteristic
311C22×C4⋊C4C22×C15112yes—
312C22×C42C22×C15111yescharacteristic
313C22×C42C22×C15112yes—
314C22×C42C22×C15111yescharacteristic
315C22×C42C22×C15111yescharacteristic
316#395C4×C15118yescomplemented
317#391—24no—
318C4×C4⋊C4—24no—
319C2×#95C22×C15111yescharacteristic
320C2×#95C22×C15111yescharacteristic
321C2×#95C22×C15112yes—
322C2×#95C22×C15112yes—
323C2×#95C22×C15112yes—
324C2×#95C22×C15112yes—
325C2×#95C22×C15111yescharacteristic
326C2×#95C22×C15112yes—
327C2×#95C22×C15112yes—
328C2×#95C22×C15112yes—
329C2×#95C22×C15111yescharacteristic
330C2×#95C22×C15112yes—
331C2×#95C22×C15112yes—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—42no—
335C22×Q8—42no—
336C22×Q8C2×C4×C15114yes—
337C23×C4C23×C15112yes—
338C23×C4C23×C15111yescharacteristic
339C23×C4C23×C15112yes—
340C23×C4C23×C15111yescharacteristic
341C23×C4C23×C15111yescharacteristic
342C23×C4C23×C15112yes—
343C23×C4C23×C15111yescharacteristic
344C23×C4C23×C15111yescharacteristic
345C23×C4C23×C15112yes—
346C23×C4C23×C15111yescharacteristic
347C23×C4C23×C15111yescharacteristic
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4C2×C4×C15114yes—
360C2×C4⋊C4C2×C4×C15118yes—
361C2×C4⋊C4Q8×C15114yescomplemented
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—22no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42D4×C15114yes—
372#95—22no—
373#95—24no—
374#95—24no—
375#95—22no—
376#95—22no—
377#95—24no—
378#95—24no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95C2×C4×C15118yes—
383#95C2×C4×C15114yes—
384#95Q8×C15118yescomplemented
385C24C24×C15111yescharacteristic
386C2×Q8—28no—
387C2×Q8—48no—
388C2×Q8—44no—
389C2×Q8—44no—
390C2×Q8—48no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4C22×C4×C15114yes—
438C22×C4C22×C4×C15112yes—
439C22×C4C22×C4×C15112yes—
440C22×C4C22×C4×C15112yes—
441C22×C4C22×C4×C15114yes—
442C22×C4C2×D4×C15112yes—
443C22×C4C2×D4×C15112yes—
444C22×C4C2×D4×C15112yes—
445C22×C4C2×Q8×C15114yes—
446C22×C4C2×Q8×C15112yes—
447C22×C4C2×Q8×C15114yes—
448C22×C4C2×Q8×C15112yes—
449C22×C4C2×Q8×C15112yes—
450C22×C4C2×Q8×C15114yes—
451C22×C4#41×C15112yes—
452C22×C4#41×C15112yes—
453C22×C4#41×C15112yes—
454C22×C4#41×C15114yes—
455C22×C4#41×C15112yes—
456C4⋊C4—28no—
457C4⋊C4—28no—
458C4⋊C4—48no—
459C4⋊C4—48no—
460C4⋊C4—44no—
461C42—28no—
462C42—44no—
463C42—48no—
464C42—44no—
465C23C23×C4×C15111yescharacteristic
466C23C22×D4×C15111yescharacteristic
467C23C22×Q8×C15111yescharacteristic
468C23C22×Q8×C15112yes—
469C23C2×#41×C15111yescharacteristic
470C23C2×#41×C15111yescharacteristic
471C23C2×#41×C15112yes—
472C23C2×#41×C15111yescharacteristic
473C23C2×#41×C15111yescharacteristic
474C23H(5,𝔽2)×C15112yes—
475C23H(5,𝔽2)×C15112yes—
476Q8—416no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4C4×D4×C15114yes—
538C2×C4C4×Q8×C15118yes—
539C2×C4C4×Q8×C15114yes—
540C2×C4C22⋊Q8×C15114yes—
541C2×C4C4⋊Q8×C15114yes—
542C22C2×C4×D4×C15111yescharacteristic
543C22C2×C4×Q8×C15112yes—
544C22C2×C4×Q8×C15111yescharacteristic
545C22C4×#41×C15111yescharacteristic
546C22#518×C15112yes—
547C22C2×C22⋊Q8×C15111yescharacteristic
548C22#525×C15111yescharacteristic
549C22#529×C15111yescharacteristic
550C22C2×C4⋊Q8×C15111yescharacteristic
551C22#532×C15111yescharacteristic
552C22#533×C15111yescharacteristic
553C22#533×C15112yes—
554C22#534×C15111yescharacteristic
555C22#535×C15111yescharacteristic
556C22#538×C15112yes—
557C22#551×C15112yes—
558C22#551×C15112yes—
559C22#554×C15112yes—
560C22#554×C15112yes—
561C22#554×C15112yes—
562C22#554×C15112yes—
563C22#555×C15112yes—
564C22Q82×C15112yes—
565C4—28no—
566C4—24no—
567C4—24no—
568C4—24no—
569C4—24no—
570C4—42no—
571C4—42no—
572C4—44no—
573C4—44no—
574C4—42no—
575C4—82no—
576C2C4×C22⋊Q8×C15111yescharacteristic
577C2C4×C4⋊Q8×C15111yescharacteristic
578C2#2321×C15111yescharacteristic
579C2#2368×C15112yes—
580C2#2369×C15112yes—
581C2#2564×C15111yescharacteristic
582C2#2567×C15111yescharacteristic
583C2#2574×C15112yes—
584C2#2583×C15111yescharacteristic
585C2#2586×C15112yes—
586C2#2610×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
22. #395×C151C4semidirect
67. C2×C4⋊C4×C151Q8semidirect
90. #95×C151Q8semidirect
293. #14241C151direct (N × H)
294. C151#14241direct (N × H)
316. #395C4×C151semidirect
361. C2×C4⋊C4Q8×C151semidirect
384. #95Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1512
C2×#391×C1512
C2×C4×C4⋊C4×C1512
#1446×C1512
#1444×C1512
#1441×C1512
#1436×C1512
C4⋊#95×C1512
C4×#95×C1512
#14241151