Finite Group Databasebeta

← C151×#24652 #50329577

Subgroups — C151×#24652 #50329577

Order 38656.

896 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#462×C151C211yesmaximal, characteristic, complemented
2C2×#431×C151C211yesmaximal, characteristic
3#2857×C151C211yesmaximal, characteristic
4C4×C22⋊Q8×C151C211yesmaximal, characteristic
5#2036×C151C212yesmaximal
6#2001×C151C212yesmaximal
7#1981×C151C211yesmaximal, characteristic, complemented
8#1969×C151C212yesmaximal, complemented
9#1947×C151C211yesmaximal, characteristic, complemented
10#1933×C151C212yesmaximal, complemented
11#1803×C151C211yesmaximal, characteristic, complemented
12C22×Q16×C151C2212yes—
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C22⋊Q8×C151C2211yescharacteristic
15C2×C22⋊Q8×C151C2212yes—
16C2×C4×Q8×C151C2211yescharacteristic
17C22×C42×C151C2211yescharacteristic
18#462×C151—24no—
19#431×C151—24no—
20C2×#107×C151C2212yes—
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×#103×C151C2212yes—
24C2×#103×C151C2212yes—
25C2×#103×C151C2212yes—
26C2×#103×C151C2212yes—
27C2×C22⋊C8×C151C2212yes—
28C2×C4×C8×C151C2212yes—
29#391×C151C2212yes—
30#391×C151C2211yescharacteristic
31#389×C151—21no—
32#389×C151—21no—
33#389×C151C2211yescharacteristic
34#387×C151—21no—
35#385×C151—21no—
36#384×C151C2211yescharacteristic
37#380×C151—21no—
38#380×C151—21no—
39#380×C151C2211yescharacteristic
40C4×C4⋊C4×C151—21no—
41C4×C4⋊C4×C151C2211yescharacteristic
42C4×C22⋊C4×C151—21no—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151C2312yes—
46C22×Q8×C151C2311yescharacteristic
47C23×C4×C151D411yescharacteristic
48C23×C4×C151D411yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C2×Q16×C151—24no—
51C2×Q16×C151—24no—
52C2×Q16×C151—42no—
53C22×C8×C151C2312yes—
54C22×C8×C151C2312yes—
55C4⋊Q8×C151—22no—
56C4⋊Q8×C151—22no—
57C22⋊Q8×C151—22no—
58C22⋊Q8×C151—22no—
59C22⋊Q8×C151—42no—
60C22⋊Q8×C151—42no—
61C4×Q8×C151—22no—
62C4×Q8×C151—22no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151—21no—
70C2×C4⋊C4×C151—22no—
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C4⋊C4×C151C2312yes—
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C4⋊C4×C151C2311yescharacteristic
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151—22no—
78C2×C42×C151—22no—
79C2×C42×C151—22no—
80C2×C42×C151—21no—
81C2×C42×C151—21no—
82C2×C42×C151D411yescharacteristic
83C2×C42×C151D411yescharacteristic
84C2×C42×C151C2311yescharacteristic
85C2×C42×C151C2311yescharacteristic
86#107×C151—42no—
87C4⋊C8×C151—22no—
88C4⋊C8×C151D414yes—
89#103×C151—24no—
90#103×C151—24no—
91#103×C151—42no—
92#103×C151—42no—
93C22⋊C8×C151—24no—
94C4×C8×C151—24no—
95#95×C151—21no—
96#95×C151—21no—
97#95×C151—21no—
98#95×C151—21no—
99#95×C151—21no—
100#95×C151—22no—
101#95×C151—22no—
102C24×C151C2×D411yescharacteristic
103C2×Q8×C151—21no—
104C2×Q8×C151—21no—
105C2×Q8×C151—22no—
106C2×Q8×C151—21no—
107C2×Q8×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151—22no—
110C2×Q8×C151—21no—
111C2×Q8×C151—21no—
112C2×Q8×C151—22no—
113C2×Q8×C151—22no—
114C2×Q8×C151#4112yes—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—21no—
118C22×C4×C151—21no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—41no—
132C22×C4×C151Q1614yescomplemented
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2411yescharacteristic
139Q16×C151—48no—
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C2×C8×C151—22no—
144C2×C8×C151—22no—
145C2×C8×C151C2×D414yes—
146C4⋊C4×C151—24no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—42no—
155C4⋊C4×C151—44no—
156C4⋊C4×C151—42no—
157C4⋊C4×C151—42no—
158C4⋊C4×C151—42no—
159C4⋊C4×C151—42no—
160C4⋊C4×C151—42no—
161C4⋊C4×C151#4112yes—
162C22⋊C4×C151—24no—
163C22⋊C4×C151—42no—
164C22⋊C4×C151—44no—
165C42×C151—22no—
166C42×C151—22no—
167C42×C151—21no—
168C42×C151—21no—
169C42×C151—42no—
170C42×C151—42no—
171C42×C151C2×D412yes—
172C42×C151#4112yes—
173C23×C151—21no—
174C23×C151—21no—
175C23×C151—21no—
176C23×C151—21no—
177C23×C151—21no—
178C23×C151—21no—
179C23×C151C2×Q1612yes—
180C23×C151C22×D411yescharacteristic
181Q8×C151—22no—
182Q8×C151—22no—
183Q8×C151—41no—
184Q8×C151—41no—
185Q8×C151—42no—
186Q8×C151—42no—
187Q8×C151—42no—
188Q8×C151—42no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—21no—
193C2×C4×C151—21no—
194C2×C4×C151—21no—
195C2×C4×C151—28no—
196C2×C4×C151—21no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—21no—
200C2×C4×C151—21no—
201C2×C4×C151—44no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—41no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—41no—
216C2×C4×C151—41no—
217C2×C4×C151—42no—
218C2×C4×C151—41no—
219C2×C4×C151—41no—
220C2×C4×C151—41no—
221C2×C4×C151—42no—
222C2×C4×C151#12112yes—
223C2×C4×C151#12112yes—
224C2×C4×C151C2×Q1612yes—
225C2×C4×C151C2×Q1612yes—
226C2×C4×C151#13512yes—
227C2×C4×C151#13712yes—
228C2×C4×C151C22×D411yescharacteristic
229C2×C4×C151C2×#4111yescharacteristic
230C2×C4×C151C2×#4111yescharacteristic
231C2×C4×C151C2×#4111yescharacteristic
232C2×C4×C151H(5,𝔽2)11yescharacteristic
233C2×C4×C151H(5,𝔽2)11yescharacteristic
234C8×C151—24no—
235C8×C151—42no—
236C22×C151—22no—
237C22×C151—22no—
238C22×C151—22no—
239C22×C151—41no—
240C22×C151—41no—
241C22×C151—41no—
242C22×C151—41no—
243C22×C151C2×#12111yescharacteristic
244C22×C151#52511yescharacteristic
245C22×C151#53511yescharacteristic
246C22×C151C22×Q1611yescharacteristic
247C22×C151C2×#13511yescharacteristic
248C22×C151C2×#13711yescharacteristic
249C22×C151#57511yescharacteristic
250C4×C151—22no—
251C4×C151—22no—
252C4×C151—22no—
253C4×C151—42no—
254C4×C151—41no—
255C4×C151—42no—
256C4×C151—82no—
257C4×C151—82no—
258C4×C151—81no—
259C4×C151—81no—
260C4×C151#46714yes—
261C4×C151#54611yescharacteristic
262C4×C151#55011yescharacteristic
263C4×C151#55311yescharacteristic
264C4×C151#55511yescharacteristic
265C2×C151—42no—
266C2×C151#241411yescharacteristic
267C2×C151C2×#46711yescharacteristic
268C2×C151#305611yescharacteristic
269C2×C151#310411yescharacteristic
270C2×C151#310711yescharacteristic
271C2×C151#320911yescharacteristic
272C2×C151#321211yescharacteristic
273#24652C15111yesmaximal, characteristic, direct product factor, Sylow
274C151#2465211yescharacteristic, direct product factor, Sylow
275C2×#462C2×C15111yescharacteristic, complemented
276C2×#431C2×C15111yescharacteristic
277#2857C2×C15111yescharacteristic
278C4×C22⋊Q8C2×C15111yescharacteristic
279#2036C2×C15112yes—
280#2001C2×C15112yes—
281#1981C2×C15111yescharacteristic, complemented
282#1969C2×C15112yescomplemented
283#1947C2×C15111yescharacteristic, complemented
284#1933C2×C15112yescomplemented
285#1803C2×C15111yescharacteristic, complemented
286C22×Q16C22×C15112yes—
287C2×C4⋊Q8C22×C15111yescharacteristic
288C2×C22⋊Q8C22×C15111yescharacteristic
289C2×C22⋊Q8C22×C15112yes—
290C2×C4×Q8C22×C15111yescharacteristic
291C22×C42C22×C15111yescharacteristic
292#462—24no—
293#431—24no—
294C2×#107C22×C15112yes—
295C2×C4⋊C8C22×C15111yescharacteristic
296C2×C4⋊C8C22×C15111yescharacteristic
297C2×#103C22×C15112yes—
298C2×#103C22×C15112yes—
299C2×#103C22×C15112yes—
300C2×#103C22×C15112yes—
301C2×C22⋊C8C22×C15112yes—
302C2×C4×C8C22×C15112yes—
303#391C22×C15112yes—
304#391C22×C15111yescharacteristic
305#389—21no—
306#389—21no—
307#389C22×C15111yescharacteristic
308#387—21no—
309#385—21no—
310#384C22×C15111yescharacteristic
311#380—21no—
312#380—21no—
313#380C22×C15111yescharacteristic
314C4×C4⋊C4—21no—
315C4×C4⋊C4C22×C15111yescharacteristic
316C4×C22⋊C4—21no—
317#340C22×C15112yes—
318#340C22×C15112yes—
319C22×Q8C23×C15112yes—
320C22×Q8C23×C15111yescharacteristic
321C23×C4D4×C15111yescharacteristic
322C23×C4D4×C15111yescharacteristic
323C23×C4C23×C15111yescharacteristic
324C2×Q16—24no—
325C2×Q16—24no—
326C2×Q16—42no—
327C22×C8C23×C15112yes—
328C22×C8C23×C15112yes—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—42no—
334C22⋊Q8—42no—
335C4×Q8—22no—
336C4×Q8—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4C23×C15111yescharacteristic
346C2×C4⋊C4C23×C15112yes—
347C2×C4⋊C4C23×C15111yescharacteristic
348C2×C4⋊C4C23×C15111yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—21no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42D4×C15111yescharacteristic
357C2×C42D4×C15111yescharacteristic
358C2×C42C23×C15111yescharacteristic
359C2×C42C23×C15111yescharacteristic
360#107—42no—
361C4⋊C8—22no—
362C4⋊C8D4×C15114yes—
363#103—24no—
364#103—24no—
365#103—42no—
366#103—42no—
367C22⋊C8—24no—
368C4×C8—24no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—22no—
375#95—22no—
376C24C2×D4×C15111yescharacteristic
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8#41×C15112yes—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—41no—
406C22×C4Q16×C15114yescomplemented
407C22×C4C2×D4×C15111yescharacteristic
408C22×C4C2×D4×C15111yescharacteristic
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C2×D4×C15111yescharacteristic
411C22×C4C2×D4×C15111yescharacteristic
412C22×C4C24×C15111yescharacteristic
413Q16—48no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8C2×D4×C15114yes—
420C4⋊C4—24no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—44no—
429C4⋊C4—42no—
430C4⋊C4—42no—
431C4⋊C4—42no—
432C4⋊C4—42no—
433C4⋊C4—42no—
434C4⋊C4—42no—
435C4⋊C4#41×C15112yes—
436C22⋊C4—24no—
437C22⋊C4—44no—
438C22⋊C4—42no—
439C42—22no—
440C42—22no—
441C42—21no—
442C42—21no—
443C42—42no—
444C42—42no—
445C42C2×D4×C15112yes—
446C42#41×C15112yes—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23C2×Q16×C15112yes—
454C23C22×D4×C15111yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—41no—
458Q8—41no—
459Q8—42no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—28no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—44no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4#121×C15112yes—
497C2×C4#121×C15112yes—
498C2×C4C2×Q16×C15112yes—
499C2×C4C2×Q16×C15112yes—
500C2×C4#135×C15112yes—
501C2×C4#137×C15112yes—
502C2×C4C22×D4×C15111yescharacteristic
503C2×C4C2×#41×C15111yescharacteristic
504C2×C4C2×#41×C15111yescharacteristic
505C2×C4C2×#41×C15111yescharacteristic
506C2×C4H(5,𝔽2)×C15111yescharacteristic
507C2×C4H(5,𝔽2)×C15111yescharacteristic
508C8—24no—
509C8—42no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22C2×#121×C15111yescharacteristic
518C22#525×C15111yescharacteristic
519C22#535×C15111yescharacteristic
520C22C22×Q16×C15111yescharacteristic
521C22C2×#135×C15111yescharacteristic
522C22C2×#137×C15111yescharacteristic
523C22#575×C15111yescharacteristic
524C4—22no—
525C4—22no—
526C4—22no—
527C4—42no—
528C4—41no—
529C4—42no—
530C4—82no—
531C4—82no—
532C4—81no—
533C4—81no—
534C4#467×C15114yes—
535C4#546×C15111yescharacteristic
536C4#550×C15111yescharacteristic
537C4#553×C15111yescharacteristic
538C4#555×C15111yescharacteristic
539C2—42no—
540C2#2414×C15111yescharacteristic
541C2C2×#467×C15111yescharacteristic
542C2#3056×C15111yescharacteristic
543C2#3104×C15111yescharacteristic
544C2#3107×C15111yescharacteristic
545C2#3209×C15111yescharacteristic
546C2#3212×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
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
1. C2×#462×C151C2semidirect
7. #1981×C151C2semidirect
8. #1969×C151C2semidirect
9. #1947×C151C2semidirect
10. #1933×C151C2semidirect
11. #1803×C151C2semidirect
132. C22×C4×C151Q16semidirect
273. #24652C151direct (N × H)
274. C151#24652direct (N × H)
275. C2×#462C2×C151semidirect
281. #1981C2×C151semidirect
282. #1969C2×C151semidirect
283. #1947C2×C151semidirect
284. #1933C2×C151semidirect
285. #1803C2×C151semidirect
406. C22×C4Q16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#462×C1512
C2×#431×C1512
#2857×C1512
C4×C22⋊Q8×C1512
#2036×C1512
#2001×C1512
#1981×C1512
#1969×C1512
#1947×C1512
#1933×C1512
#1803×C1512
#24652151