Finite Group Databasebeta

← C151×#24067 #50328992

Subgroups — C151×#24067 #50328992

Order 38656.

1176 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C151C211yesmaximal, characteristic
2C2×#484×C151C211yesmaximal, characteristic, complemented
3C2×#481×C151C211yesmaximal, characteristic
4C2×#389×C151C211yesmaximal, characteristic, complemented
5#2059×C151C212yesmaximal, complemented
6#2042×C151C212yesmaximal, complemented
7#1874×C151C211yesmaximal, characteristic
8#1872×C151C211yesmaximal, characteristic, complemented
9#1865×C151C212yesmaximal, complemented
10#1862×C151C212yesmaximal, complemented
11#1817×C151C211yesmaximal, characteristic, complemented
12#529×C151—24no—
13#529×C151—24no—
14C2×#126×C151—21no—
15C2×#125×C151C2211yescharacteristic
16C2×#124×C151C2211yescharacteristic
17C2×#123×C151—21no—
18C2×C22⋊Q8×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151—21no—
22C2×C4×D4×C151C2211yescharacteristic
23C2×#117×C151—21no—
24C22×C4⋊C4×C151—21no—
25C22×C4⋊C4×C151C2211yescharacteristic
26C22×C4⋊C4×C151C2211yescharacteristic
27C22×C42×C151C2211yescharacteristic
28#484×C151—24no—
29#481×C151—24no—
30C2×#107×C151C2212yes—
31C2×#106×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#103×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×#102×C151C2212yes—
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38#389×C151—21no—
39#389×C151—21no—
40#389×C151C2212yes—
41#389×C151C2212yes—
42C2×#95×C151—21no—
43#340×C151C2212yes—
44#340×C151C2212yes—
45#336×C151C2212yes—
46#336×C151C2212yes—
47C22×Q8×C151C2311yescharacteristic
48C22×D4×C151—21no—
49C22×D4×C151C2311yescharacteristic
50C23×C4×C151—21no—
51C23×C4×C151—21no—
52C23×C4×C151—21no—
53C23×C4×C151D411yescharacteristic
54C23×C4×C151D411yescharacteristic
55C23×C4×C151C2311yescharacteristic
56C22×C8×C151C2312yes—
57C22×C8×C151C2312yes—
58#126×C151—28no—
59#125×C151—22no—
60#125×C151—22no—
61#124×C151—22no—
62#124×C151—22no—
63#123×C151—28no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151D414yes—
66#121×C151—22no—
67#121×C151D414yes—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×D4×C151—28no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73#117×C151—28no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—24no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—44no—
86C2×C4⋊C4×C151C2312yes—
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2312yes—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151—21no—
95C2×C42×C151—22no—
96C2×C42×C151—22no—
97C2×C42×C151—21no—
98C2×C42×C151D411yescharacteristic
99C2×C42×C151D411yescharacteristic
100C2×C42×C151C2311yescharacteristic
101C2×C42×C151C2311yescharacteristic
102#107×C151—24no—
103#106×C151—24no—
104#103×C151—24no—
105#103×C151—24no—
106#102×C151—24no—
107#102×C151—24no—
108C22⋊C8×C151—22no—
109C22⋊C8×C151—22no—
110#95×C151—22no—
111#95×C151—22no—
112C24×C151—21no—
113C24×C151C2×D411yescharacteristic
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151C2×D412yes—
118C2×D4×C151—24no—
119C2×D4×C151—21no—
120C2×D4×C151—22no—
121C2×D4×C151—22no—
122C2×D4×C151—42no—
123C2×D4×C151—42no—
124C2×D4×C151C2×D412yes—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—24no—
128C22×C4×C151—24no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—41no—
140C22×C4×C151—42no—
141C22×C4×C151—42no—
142C22×C4×C151—42no—
143C22×C4×C151—42no—
144C22×C4×C151—42no—
145C22×C4×C151—42no—
146C22×C4×C151—42no—
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D412yes—
152C22×C4×C151C2×D412yes—
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2411yescharacteristic
155C2×C8×C151—22no—
156C2×C8×C151—22no—
157C2×C8×C151—22no—
158C2×C8×C151—22no—
159C2×C8×C151—22no—
160C2×C8×C151—22no—
161C4⋊C4×C151—24no—
162C4⋊C4×C151—24no—
163C4⋊C4×C151—24no—
164C4⋊C4×C151—24no—
165C4⋊C4×C151—24no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—44no—
172C4⋊C4×C151—42no—
173C4⋊C4×C151—44no—
174C4⋊C4×C151C2×D412yes—
175C4⋊C4×C151C2×D412yes—
176C4⋊C4×C151#4114yes—
177C22⋊C4×C151—24no—
178C22⋊C4×C151—24no—
179C22⋊C4×C151—24no—
180C22⋊C4×C151—24no—
181C22⋊C4×C151—24no—
182C42×C151—24no—
183C42×C151—22no—
184C42×C151—22no—
185C42×C151—21no—
186C42×C151—21no—
187C42×C151—21no—
188C42×C151—21no—
189C23×C151—21no—
190C23×C151—21no—
191C23×C151—21no—
192C23×C151—21no—
193C23×C151—22no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151—41no—
198C23×C151—41no—
199C23×C151—41no—
200C23×C151#12012yes—
201C23×C151#13512yes—
202C23×C151#13712yes—
203C23×C151C22×D411yescharacteristic
204Q8×C151—24no—
205Q8×C151—42no—
206D4×C151—24no—
207D4×C151—48no—
208D4×C151—42no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—24no—
214C2×C4×C151—24no—
215C2×C4×C151—22no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—24no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—44no—
229C2×C4×C151—48no—
230C2×C4×C151—48no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—42no—
234C2×C4×C151—41no—
235C2×C4×C151—42no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—44no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151—84no—
244C2×C4×C151#12012yes—
245C2×C4×C151AGL(1,ℤ/8)12yes—
246C2×C4×C151C22×D411yescharacteristic
247C2×C4×C151C22×D411yescharacteristic
248C2×C4×C151C2×#4112yes—
249C2×C4×C1512−1+412yes—
250C8×C151—42no—
251C8×C151—42no—
252C22×C151—22no—
253C22×C151—22no—
254C22×C151—22no—
255C22×C151—22no—
256C22×C151—22no—
257C22×C151—22no—
258C22×C151—42no—
259C22×C151—42no—
260C22×C151—42no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151—81no—
264C22×C151—81no—
265C22×C151#45214yes—
266C22×C151C2×#12011yescharacteristic
267C22×C151#52511yescharacteristic
268C22×C151#53611yescharacteristic
269C22×C151C2×#13511yescharacteristic
270C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C151C2×#13711yescharacteristic
272C22×C151#57511yescharacteristic
273C4×C151—22no—
274C4×C151—22no—
275C4×C151—44no—
276C4×C151—42no—
277C4×C151—41no—
278C4×C151—41no—
279C4×C151—42no—
280C4×C151—41no—
281C4×C151—42no—
282C4×C151—82no—
283C4×C151#54712yes—
284C4×C151#54712yes—
285C2×C151—24no—
286C2×C151—82no—
287C2×C151#240611yescharacteristic
288C2×C151C2×#45211yescharacteristic
289C2×C151#300611yescharacteristic
290C2×C151#310511yescharacteristic
291C2×C151#311711yescharacteristic
292C2×C151#323211yescharacteristic
293C2×C151#323911yescharacteristic
294#24067C15111yesmaximal, characteristic, direct product factor, Sylow
295C151#2406711yescharacteristic, direct product factor, Sylow
296C2×#529C2×C15111yescharacteristic
297C2×#484C2×C15111yescharacteristic, complemented
298C2×#481C2×C15111yescharacteristic
299C2×#389C2×C15111yescharacteristic, complemented
300#2059C2×C15112yescomplemented
301#2042C2×C15112yescomplemented
302#1874C2×C15111yescharacteristic
303#1872C2×C15111yescharacteristic, complemented
304#1865C2×C15112yescomplemented
305#1862C2×C15112yescomplemented
306#1817C2×C15111yescharacteristic, complemented
307#529—24no—
308#529—24no—
309C2×#126—21no—
310C2×#125C22×C15111yescharacteristic
311C2×#124C22×C15111yescharacteristic
312C2×#123—21no—
313C2×C22⋊Q8C22×C15111yescharacteristic
314C2×#121C22×C15111yescharacteristic
315C2×C4×Q8C22×C15111yescharacteristic
316C2×C4×D4—21no—
317C2×C4×D4C22×C15111yescharacteristic
318C2×#117—21no—
319C22×C4⋊C4—21no—
320C22×C4⋊C4C22×C15111yescharacteristic
321C22×C4⋊C4C22×C15111yescharacteristic
322C22×C42C22×C15111yescharacteristic
323#484—24no—
324#481—24no—
325C2×#107C22×C15112yes—
326C2×#106C22×C15112yes—
327C2×#103C22×C15112yes—
328C2×#103C22×C15112yes—
329C2×#102C22×C15112yes—
330C2×#102C22×C15112yes—
331C2×C22⋊C8C22×C15111yescharacteristic
332C2×C22⋊C8C22×C15111yescharacteristic
333#389—21no—
334#389—21no—
335#389C22×C15112yes—
336#389C22×C15112yes—
337C2×#95—21no—
338#340C22×C15112yes—
339#340C22×C15112yes—
340#336C22×C15112yes—
341#336C22×C15112yes—
342C22×Q8C23×C15111yescharacteristic
343C22×D4—21no—
344C22×D4C23×C15111yescharacteristic
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4D4×C15111yescharacteristic
349C23×C4D4×C15111yescharacteristic
350C23×C4C23×C15111yescharacteristic
351C22×C8C23×C15112yes—
352C22×C8C23×C15112yes—
353#126—28no—
354#125—22no—
355#125—22no—
356#124—22no—
357#124—22no—
358#123—28no—
359C22⋊Q8—22no—
360C22⋊Q8D4×C15114yes—
361#121—22no—
362#121D4×C15114yes—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×D4—28no—
366C4×D4—22no—
367C4×D4—22no—
368#117—28no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4C23×C15112yes—
382C2×C4⋊C4C23×C15112yes—
383C2×C4⋊C4C23×C15111yescharacteristic
384C2×C4⋊C4C23×C15111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C42—21no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42D4×C15111yescharacteristic
394C2×C42D4×C15111yescharacteristic
395C2×C42C23×C15111yescharacteristic
396C2×C42C23×C15111yescharacteristic
397#107—24no—
398#106—24no—
399#103—24no—
400#103—24no—
401#102—24no—
402#102—24no—
403C22⋊C8—22no—
404C22⋊C8—22no—
405#95—22no—
406#95—22no—
407C24—21no—
408C24C2×D4×C15111yescharacteristic
409C2×Q8—21no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8C2×D4×C15112yes—
413C2×D4—24no—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4C2×D4×C15112yes—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—41no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15111yescharacteristic
444C22×C4C2×D4×C15111yescharacteristic
445C22×C4C2×D4×C15111yescharacteristic
446C22×C4C2×D4×C15112yes—
447C22×C4C2×D4×C15112yes—
448C22×C4C2×D4×C15111yescharacteristic
449C22×C4C24×C15111yescharacteristic
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—44no—
467C4⋊C4—42no—
468C4⋊C4—44no—
469C4⋊C4C2×D4×C15112yes—
470C4⋊C4C2×D4×C15112yes—
471C4⋊C4#41×C15114yes—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C42—24no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23#120×C15112yes—
496C23#135×C15112yes—
497C23#137×C15112yes—
498C23C22×D4×C15111yescharacteristic
499Q8—24no—
500Q8—42no—
501D4—24no—
502D4—48no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—44no—
524C2×C4—48no—
525C2×C4—48no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—84no—
539C2×C4#120×C15112yes—
540C2×C4AGL(1,ℤ/8)×C15112yes—
541C2×C4C22×D4×C15111yescharacteristic
542C2×C4C22×D4×C15111yescharacteristic
543C2×C4C2×#41×C15112yes—
544C2×C42−1+4×C15112yes—
545C8—42no—
546C8—42no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22#452×C15114yes—
561C22C2×#120×C15111yescharacteristic
562C22#525×C15111yescharacteristic
563C22#536×C15111yescharacteristic
564C22C2×#135×C15111yescharacteristic
565C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
566C22C2×#137×C15111yescharacteristic
567C22#575×C15111yescharacteristic
568C4—22no—
569C4—22no—
570C4—44no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—42no—
575C4—41no—
576C4—42no—
577C4—82no—
578C4#547×C15112yes—
579C4#547×C15112yes—
580C2—24no—
581C2—82no—
582C2#2406×C15111yescharacteristic
583C2C2×#452×C15111yescharacteristic
584C2#3006×C15111yescharacteristic
585C2#3105×C15111yescharacteristic
586C2#3117×C15111yescharacteristic
587C2#3232×C15111yescharacteristic
588C2#3239×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#484×C151C2semidirect
4. C2×#389×C151C2semidirect
5. #2059×C151C2semidirect
6. #2042×C151C2semidirect
8. #1872×C151C2semidirect
9. #1865×C151C2semidirect
10. #1862×C151C2semidirect
11. #1817×C151C2semidirect
294. #24067C151direct (N × H)
295. C151#24067direct (N × H)
297. C2×#484C2×C151semidirect
299. C2×#389C2×C151semidirect
300. #2059C2×C151semidirect
301. #2042C2×C151semidirect
303. #1872C2×C151semidirect
304. #1865C2×C151semidirect
305. #1862C2×C151semidirect
306. #1817C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#529×C1512
C2×#484×C1512
C2×#481×C1512
C2×#389×C1512
#2059×C1512
#2042×C1512
#1874×C1512
#1872×C1512
#1865×C1512
#1862×C1512
#1817×C1512
#24067151