Finite Group Databasebeta

← C151×#24062 #50328987

Subgroups — C151×#24062 #50328987

Order 38656.

1352 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C151C211yesmaximal, characteristic
2C2×#482×C151C212yesmaximal, complemented
3#2296×C151C211yesmaximal, characteristic, complemented
4#2058×C151C211yesmaximal, characteristic, complemented
5#2057×C151C211yesmaximal, characteristic, complemented
6#2041×C151C211yesmaximal, characteristic, complemented
7#2041×C151C211yesmaximal, characteristic, complemented
8#1875×C151C212yesmaximal, complemented
9#1864×C151C212yesmaximal, complemented
10#1862×C151C212yesmaximal, complemented
11#1817×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151—21no—
13#532×C151—28no—
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×#127×C151C2211yescharacteristic
16C2×#124×C151—21no—
17C2×#121×C151—21no—
18C2×#121×C151C2212yes—
19C2×C4×D4×C151—21no—
20C2×C4×D4×C151C2212yes—
21C2×#117×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23C22×C42×C151C2211yescharacteristic
24#482×C151—28no—
25C2×#107×C151C2212yes—
26C2×#106×C151C2212yes—
27C2×#102×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×#102×C151C2212yes—
30C2×#102×C151C2212yes—
31C2×C22⋊C8×C151C2212yes—
32#389×C151C2211yescharacteristic
33#389×C151C2211yescharacteristic
34#389×C151C2211yescharacteristic
35#389×C151C2211yescharacteristic
36#385×C151—21no—
37#385×C151—21no—
38C4×C4⋊C4×C151—21no—
39C4×C4⋊C4×C151—21no—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43#336×C151C2211yescharacteristic
44#336×C151C2211yescharacteristic
45C2×#41×C151—28no—
46C2×#41×C151—44no—
47C2×#41×C151—44no—
48C22×Q8×C151—21no—
49C22×D4×C151—21no—
50C22×D4×C151—21no—
51C22×D4×C151—22no—
52C22×D4×C151C2312yes—
53C23×C4×C151—22no—
54C23×C4×C151D411yescharacteristic
55C23×C4×C151D411yescharacteristic
56C23×C4×C151C2311yescharacteristic
57C22×C8×C151C2312yes—
58C22×C8×C151C2312yes—
59C4⋊Q8×C151—24no—
60#127×C151—24no—
61#124×C151—28no—
62#121×C151—28no—
63#121×C151—24no—
64#121×C151D418yes—
65C4×D4×C151—28no—
66C4×D4×C151—24no—
67C4×D4×C151—24no—
68#117×C151—22no—
69#117×C151—22no—
70#117×C151—24no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C4⋊C4×C151C2312yes—
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C22⋊C4×C151—22no—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—21no—
85C2×C42×C151—21no—
86C2×C42×C151—24no—
87C2×C42×C151—21no—
88C2×C42×C151D411yescharacteristic
89C2×C42×C151D411yescharacteristic
90C2×C42×C151C2311yescharacteristic
91C2×C42×C151C2311yescharacteristic
92#107×C151—24no—
93#106×C151—24no—
94#102×C151—24no—
95#102×C151—24no—
96#102×C151—24no—
97#102×C151—24no—
98C22⋊C8×C151—24no—
99#95×C151—21no—
100#95×C151—21no—
101#95×C151—21no—
102#95×C151—21no—
103C24×C151—22no—
104C24×C151C2×D411yescharacteristic
105#41×C151—432no—
106C2×Q8×C151—24no—
107C2×Q8×C151—42no—
108C2×Q8×C151—42no—
109C2×D4×C151—24no—
110C2×D4×C151—24no—
111C2×D4×C151—28no—
112C2×D4×C151—22no—
113C2×D4×C151—22no—
114C2×D4×C151—22no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151—42no—
118C2×D4×C151—42no—
119C2×D4×C151—44no—
120C2×D4×C151—44no—
121C2×D4×C151—42no—
122C2×D4×C151—42no—
123C2×D4×C151C2×D414yes—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—22no—
130C22×C4×C151—28no—
131C22×C4×C151—22no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—41no—
139C22×C4×C151—44no—
140C22×C4×C151—44no—
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D414yes—
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2411yescharacteristic
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C2×C8×C151—22no—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—42no—
161C4⋊C4×C151—42no—
162C4⋊C4×C151—42no—
163C4⋊C4×C151—42no—
164C4⋊C4×C151C2×D414yes—
165C4⋊C4×C151#4112yescomplemented
166C4⋊C4×C151#4112yescomplemented
167C22⋊C4×C151—24no—
168C22⋊C4×C151—28no—
169C22⋊C4×C151—28no—
170C22⋊C4×C151—42no—
171C42×C151—24no—
172C42×C151—22no—
173C42×C151—22no—
174C42×C151—22no—
175C42×C151—22no—
176C42×C151—42no—
177C23×C151—21no—
178C23×C151—21no—
179C23×C151—21no—
180C23×C151—21no—
181C23×C151—21no—
182C23×C151—21no—
183C23×C151—24no—
184C23×C151—42no—
185C23×C151—42no—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151—42no—
189C23×C151—42no—
190C23×C151#12012yes—
191C23×C151C22×D411yescharacteristic
192Q8×C151—48no—
193D4×C151—24no—
194D4×C151—24no—
195D4×C151—48no—
196D4×C151—48no—
197D4×C151—416no—
198D4×C151—42no—
199D4×C151—42no—
200C2×C4×C151—28no—
201C2×C4×C151—21no—
202C2×C4×C151—21no—
203C2×C4×C151—21no—
204C2×C4×C151—21no—
205C2×C4×C151—21no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—24no—
210C2×C4×C151—24no—
211C2×C4×C151—24no—
212C2×C4×C151—21no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—44no—
218C2×C4×C151—416no—
219C2×C4×C151—41no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151#12012yes—
232C2×C4×C151#13512yes—
233C2×C4×C151AGL(1,ℤ/8)12yes—
234C2×C4×C151AGL(1,ℤ/8)12yes—
235C2×C4×C151C22×D412yes—
236C2×C4×C151C2×#4111yescharacteristic
237C2×C4×C151C2×#4111yescharacteristic
238C2×C4×C1512−1+412yes—
239C8×C151—42no—
240C8×C151—42no—
241C22×C151—22no—
242C22×C151—22no—
243C22×C151—22no—
244C22×C151—41no—
245C22×C151—41no—
246C22×C151—41no—
247C22×C151—41no—
248C22×C151—44no—
249C22×C151—44no—
250C22×C151—44no—
251C22×C151—82no—
252C22×C151—82no—
253C22×C151—82no—
254C22×C151—82no—
255C22×C151C2×#12011yescharacteristic
256C22×C151#52511yescharacteristic
257C22×C151#53611yescharacteristic
258C22×C151C2×#13511yescharacteristic
259C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C151#57511yescharacteristic
262C4×C151—22no—
263C4×C151—22no—
264C4×C151—22no—
265C4×C151—22no—
266C4×C151—42no—
267C4×C151—42no—
268C4×C151—41no—
269C4×C151—44no—
270C4×C151—81no—
271C4×C151—81no—
272C4×C151#54712yes—
273C4×C151#54712yes—
274C2×C151—42no—
275C2×C151—84no—
276C2×C151#240611yescharacteristic
277C2×C151#300211yescharacteristic
278C2×C151#300311yescharacteristic
279C2×C151#310611yescharacteristic
280C2×C151#311511yescharacteristic
281C2×C151#322811yescharacteristic
282C2×C151#323511yescharacteristic
283#24062C15111yesmaximal, characteristic, direct product factor, Sylow
284C151#2406211yescharacteristic, direct product factor, Sylow
285C2×#532C2×C15111yescharacteristic
286C2×#482C2×C15112yescomplemented
287#2296C2×C15111yescharacteristic, complemented
288#2058C2×C15111yescharacteristic, complemented
289#2057C2×C15111yescharacteristic, complemented
290#2041C2×C15111yescharacteristic, complemented
291#2041C2×C15111yescharacteristic, complemented
292#1875C2×C15112yescomplemented
293#1864C2×C15112yescomplemented
294#1862C2×C15112yescomplemented
295#1817C2×C15111yescharacteristic, complemented
296C22×#41—21no—
297#532—28no—
298C2×C4⋊Q8C22×C15111yescharacteristic
299C2×#127C22×C15111yescharacteristic
300C2×#124—21no—
301C2×#121—21no—
302C2×#121C22×C15112yes—
303C2×C4×D4—21no—
304C2×C4×D4C22×C15112yes—
305C2×#117C22×C15111yescharacteristic
306C2×#117C22×C15111yescharacteristic
307C22×C42C22×C15111yescharacteristic
308#482—28no—
309C2×#107C22×C15112yes—
310C2×#106C22×C15112yes—
311C2×#102C22×C15112yes—
312C2×#102C22×C15112yes—
313C2×#102C22×C15112yes—
314C2×#102C22×C15112yes—
315C2×C22⋊C8C22×C15112yes—
316#389C22×C15111yescharacteristic
317#389C22×C15111yescharacteristic
318#389C22×C15111yescharacteristic
319#389C22×C15111yescharacteristic
320#385—21no—
321#385—21no—
322C4×C4⋊C4—21no—
323C4×C4⋊C4—21no—
324#340C22×C15112yes—
325#340C22×C15112yes—
326#336C22×C15111yescharacteristic
327#336C22×C15111yescharacteristic
328#336C22×C15112yes—
329C2×#41—28no—
330C2×#41—44no—
331C2×#41—44no—
332C22×Q8—21no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4C23×C15112yes—
337C23×C4—22no—
338C23×C4D4×C15111yescharacteristic
339C23×C4D4×C15111yescharacteristic
340C23×C4C23×C15111yescharacteristic
341C22×C8C23×C15112yes—
342C22×C8C23×C15112yes—
343C4⋊Q8—24no—
344#127—24no—
345#124—28no—
346#121—28no—
347#121—24no—
348#121D4×C15118yes—
349C4×D4—28no—
350C4×D4—24no—
351C4×D4—24no—
352#117—22no—
353#117—22no—
354#117—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4C23×C15111yescharacteristic
361C2×C4⋊C4C23×C15111yescharacteristic
362C2×C4⋊C4C23×C15111yescharacteristic
363C2×C4⋊C4C23×C15111yescharacteristic
364C2×C4⋊C4C23×C15112yes—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C42—21no—
370C2×C42—24no—
371C2×C42—21no—
372C2×C42D4×C15111yescharacteristic
373C2×C42D4×C15111yescharacteristic
374C2×C42C23×C15111yescharacteristic
375C2×C42C23×C15111yescharacteristic
376#107—24no—
377#106—24no—
378#102—24no—
379#102—24no—
380#102—24no—
381#102—24no—
382C22⋊C8—24no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387C24—22no—
388C24C2×D4×C15111yescharacteristic
389#41—432no—
390C2×Q8—24no—
391C2×Q8—42no—
392C2×Q8—42no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—28no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—44no—
404C2×D4—44no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4C2×D4×C15114yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—28no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—41no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4C2×D4×C15111yescharacteristic
426C22×C4C2×D4×C15111yescharacteristic
427C22×C4C2×D4×C15114yes—
428C22×C4C2×D4×C15111yescharacteristic
429C22×C4C2×D4×C15111yescharacteristic
430C22×C4C2×D4×C15111yescharacteristic
431C22×C4C24×C15111yescharacteristic
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C4⋊C4—24no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4—42no—
448C4⋊C4C2×D4×C15114yes—
449C4⋊C4#41×C15112yescomplemented
450C4⋊C4#41×C15112yescomplemented
451C22⋊C4—24no—
452C22⋊C4—28no—
453C22⋊C4—28no—
454C22⋊C4—42no—
455C42—24no—
456C42—22no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—42no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—24no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23#120×C15112yes—
475C23C22×D4×C15111yescharacteristic
476Q8—48no—
477D4—24no—
478D4—24no—
479D4—48no—
480D4—48no—
481D4—416no—
482D4—42no—
483D4—42no—
484C2×C4—28no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—21no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—44no—
502C2×C4—416no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4#120×C15112yes—
516C2×C4#135×C15112yes—
517C2×C4AGL(1,ℤ/8)×C15112yes—
518C2×C4AGL(1,ℤ/8)×C15112yes—
519C2×C4C22×D4×C15112yes—
520C2×C4C2×#41×C15111yescharacteristic
521C2×C4C2×#41×C15111yescharacteristic
522C2×C42−1+4×C15112yes—
523C8—42no—
524C8—42no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—44no—
533C22—44no—
534C22—44no—
535C22—82no—
536C22—82no—
537C22—82no—
538C22—82no—
539C22C2×#120×C15111yescharacteristic
540C22#525×C15111yescharacteristic
541C22#536×C15111yescharacteristic
542C22C2×#135×C15111yescharacteristic
543C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
544C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
545C22#575×C15111yescharacteristic
546C4—22no—
547C4—22no—
548C4—22no—
549C4—22no—
550C4—42no—
551C4—42no—
552C4—41no—
553C4—44no—
554C4—81no—
555C4—81no—
556C4#547×C15112yes—
557C4#547×C15112yes—
558C2—42no—
559C2—84no—
560C2#2406×C15111yescharacteristic
561C2#3002×C15111yescharacteristic
562C2#3003×C15111yescharacteristic
563C2#3106×C15111yescharacteristic
564C2#3115×C15111yescharacteristic
565C2#3228×C15111yescharacteristic
566C2#3235×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#532×C151C2
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×#482×C151C2semidirect
3. #2296×C151C2semidirect
4. #2058×C151C2semidirect
5. #2057×C151C2semidirect
6. #2041×C151C2semidirect
7. #2041×C151C2semidirect
8. #1875×C151C2semidirect
9. #1864×C151C2semidirect
10. #1862×C151C2semidirect
11. #1817×C151C2semidirect
165. C4⋊C4×C151#41semidirect
166. C4⋊C4×C151#41semidirect
283. #24062C151direct (N × H)
284. C151#24062direct (N × H)
286. C2×#482C2×C151semidirect
287. #2296C2×C151semidirect
288. #2058C2×C151semidirect
289. #2057C2×C151semidirect
290. #2041C2×C151semidirect
291. #2041C2×C151semidirect
292. #1875C2×C151semidirect
293. #1864C2×C151semidirect
294. #1862C2×C151semidirect
295. #1817C2×C151semidirect
449. C4⋊C4#41×C151semidirect
450. C4⋊C4#41×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#532×C1512
C2×#482×C1512
#2296×C1512
#2058×C1512
#2057×C1512
#2041×C1512
#1875×C1512
#1864×C1512
#1862×C1512
#1817×C1512
#24062151