Finite Group Databasebeta

← C151×#24374 #50329299

Subgroups — C151×#24374 #50329299

Order 38656.

1396 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C151C211yesmaximal, characteristic
2C2×#462×C151C212yesmaximal, complemented
3C2×#452×C151C211yesmaximal, characteristic
4#2434×C151C211yesmaximal, characteristic, complemented
5#2341×C151C211yesmaximal, characteristic
6#2055×C151C212yesmaximal, complemented
7#2013×C151C212yesmaximal, complemented
8#1894×C151C211yesmaximal, characteristic, complemented
9#1878×C151C212yesmaximal, complemented
10#1851×C151C211yesmaximal, characteristic, complemented
11#1787×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2211yescharacteristic
13C23×Q8×C151C2211yescharacteristic
14C2×#137×C151—24no—
15C2×#137×C151—28no—
16C22×Q16×C151C2211yescharacteristic
17C22×Q16×C151C2212yes—
18C22×SD16×C151C2212yes—
19C22×SD16×C151C2211yescharacteristic
20C22×M16×C151C2211yescharacteristic
21C2×C4⋊Q8×C151C2212yes—
22C2×C22⋊Q8×C151C2211yescharacteristic
23C2×C4×Q8×C151C2212yes—
24#462×C151—28no—
25#452×C151—24no—
26C2×C4⋊C8×C151C2212yes—
27C2×#103×C151C2211yescharacteristic
28C2×#103×C151C2212yes—
29C2×#103×C151C2212yes—
30C2×#103×C151C2212yes—
31C2×#102×C151C2211yescharacteristic
32C2×C22⋊C8×C151C2211yescharacteristic
33#395×C151—21no—
34#395×C151—21no—
35#391×C151C2212yes—
36#390×C151—22no—
37#390×C151C2212yes—
38#385×C151—22no—
39#380×C151—21no—
40#380×C151C2211yescharacteristic
41C4×C22⋊C4×C151—21no—
42C4×C22⋊C4×C151C2211yescharacteristic
43#340×C151C2212yes—
44#336×C151C2212yes—
45C2×#41×C151—22no—
46C2×#41×C151—24no—
47C2×#41×C151—42no—
48C2×#41×C151D414yes—
49C22×Q8×C151—22no—
50C22×Q8×C151—24no—
51C22×Q8×C151—22no—
52C22×Q8×C151—21no—
53C22×Q8×C151—42no—
54C22×Q8×C151C2311yescharacteristic
55C22×Q8×C151C2312yes—
56C22×Q8×C151C2311yescharacteristic
57C22×D4×C151—21no—
58C22×D4×C151C2311yescharacteristic
59C23×C4×C151—21no—
60C23×C4×C151—21no—
61C23×C4×C151C2311yescharacteristic
62#137×C151—232no—
63C2×Q16×C151—24no—
64C2×Q16×C151—24no—
65C2×Q16×C151—22no—
66C2×Q16×C151—24no—
67C2×Q16×C151D418yes—
68C2×SD16×C151—24no—
69C2×SD16×C151—22no—
70C2×SD16×C151—24no—
71C2×SD16×C151—24no—
72C2×SD16×C151—42no—
73C2×M16×C151—22no—
74C2×M16×C151—24no—
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2312yes—
78C4⋊Q8×C151—24no—
79C4⋊Q8×C151—42no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—22no—
82C4×Q8×C151—24no—
83C4×Q8×C151—42no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—22no—
86C2×C4⋊C4×C151—22no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2312yes—
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151—22no—
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151D412yes—
95C2×C42×C151—22no—
96C2×C42×C151C2312yes—
97C4⋊C8×C151—24no—
98#103×C151—24no—
99#103×C151—22no—
100#103×C151—24no—
101#103×C151—42no—
102#102×C151—22no—
103C22⋊C8×C151—22no—
104#95×C151—21no—
105#95×C151—22no—
106#95×C151—22no—
107#95×C151D411yescharacteristic
108#95×C151D411yescharacteristic
109C24×C151—21no—
110C24×C151C2×D411yescharacteristic
111#41×C151—28no—
112#41×C151—44no—
113#41×C151—48no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—28no—
118C2×Q8×C151—22no—
119C2×Q8×C151—22no—
120C2×Q8×C151—22no—
121C2×Q8×C151—21no—
122C2×Q8×C151—22no—
123C2×Q8×C151—21no—
124C2×Q8×C151—22no—
125C2×Q8×C151—22no—
126C2×Q8×C151—44no—
127C2×Q8×C151—48no—
128C2×Q8×C151—44no—
129C2×Q8×C151—42no—
130C2×Q8×C151C2×D414yes—
131C2×Q8×C151C2×D412yes—
132C2×Q8×C151C2×D414yes—
133C2×D4×C151—24no—
134C2×D4×C151—22no—
135C2×D4×C151—21no—
136C2×D4×C151—22no—
137C2×D4×C151—44no—
138C2×D4×C151C2×D412yes—
139C22×C4×C151—21no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—24no—
144C22×C4×C151—21no—
145C22×C4×C151—22no—
146C22×C4×C151—21no—
147C22×C4×C151—44no—
148C22×C4×C151—44no—
149C22×C4×C151—42no—
150C22×C4×C151C2×D412yes—
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D412yes—
153C22×C4×C151C2×D412yes—
154C22×C4×C151#4112yes—
155C22×C4×C151C2411yescharacteristic
156Q16×C151—216no—
157Q16×C151—44no—
158SD16×C151—216no—
159SD16×C151—44no—
160M16×C151—28no—
161C2×C8×C151—22no—
162C2×C8×C151—22no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151C2×D414yes—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—44no—
173C4⋊C4×C151—44no—
174C4⋊C4×C151—44no—
175C4⋊C4×C151—42no—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—42no—
178C22⋊C4×C151—44no—
179C22⋊C4×C151—82no—
180C22⋊C4×C151—81no—
181C42×C151—22no—
182C42×C151—22no—
183C42×C151—44no—
184C23×C151—22no—
185C23×C151—22no—
186C23×C151—21no—
187C23×C151—21no—
188C23×C151—22no—
189C23×C151—42no—
190C23×C151—42no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151#12112yes—
194C23×C151C22×D411yescharacteristic
195Q8×C151—22no—
196Q8×C151—24no—
197Q8×C151—24no—
198Q8×C151—24no—
199Q8×C151—48no—
200Q8×C151—42no—
201Q8×C151—42no—
202Q8×C151—41no—
203Q8×C151—41no—
204Q8×C151—42no—
205Q8×C151#12014yes—
206D4×C151—22no—
207D4×C151—22no—
208D4×C151—48no—
209D4×C151—42no—
210C2×C4×C151—22no—
211C2×C4×C151—24no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—24no—
218C2×C4×C151—24no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—48no—
223C2×C4×C151—48no—
224C2×C4×C151—42no—
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—41no—
233C2×C4×C151—41no—
234C2×C4×C151#12112yes—
235C2×C4×C151#13714yescomplemented
236C2×C4×C151C22×D411yescharacteristic
237C2×C4×C151C22×D412yes—
238C2×C4×C151C2×#4111yescharacteristic
239C2×C4×C151H(5,𝔽2)12yes—
240C8×C151—24no—
241C8×C151—41no—
242C8×C151—41no—
243C22×C151—22no—
244C22×C151—22no—
245C22×C151—22no—
246C22×C151—42no—
247C22×C151—42no—
248C22×C151—42no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—82no—
252C22×C151—82no—
253C22×C151C2×#12111yescharacteristic
254C22×C151D4212yes—
255C22×C151C2×#13712yes—
256C22×C151#57711yescharacteristic
257C22×C151#57811yescharacteristic
258C4×C151—22no—
259C4×C151—24no—
260C4×C151—24no—
261C4×C151—44no—
262C4×C151—42no—
263C4×C151—81no—
264C4×C151—82no—
265C4×C151—81no—
266C4×C151C2×#12011yescharacteristic
267C4×C151#53411yescharacteristic
268C4×C151#54612yes—
269C2×C151—42no—
270C2×C151—82no—
271C2×C151#241011yescharacteristic
272C2×C151#303911yescharacteristic
273C2×C151#304611yescharacteristic
274C2×C151#327012yes—
275C2×C151#327812yes—
276#24374C15111yesmaximal, characteristic, direct product factor, Sylow
277C151#2437411yescharacteristic, direct product factor, Sylow
278C22×#137C2×C15111yescharacteristic
279C2×#462C2×C15112yescomplemented
280C2×#452C2×C15111yescharacteristic
281#2434C2×C15111yescharacteristic, complemented
282#2341C2×C15111yescharacteristic
283#2055C2×C15112yescomplemented
284#2013C2×C15112yescomplemented
285#1894C2×C15111yescharacteristic, complemented
286#1878C2×C15112yescomplemented
287#1851C2×C15111yescharacteristic, complemented
288#1787C2×C15111yescharacteristic, complemented
289C22×#41C22×C15111yescharacteristic
290C23×Q8C22×C15111yescharacteristic
291C2×#137—24no—
292C2×#137—28no—
293C22×Q16C22×C15111yescharacteristic
294C22×Q16C22×C15112yes—
295C22×SD16C22×C15112yes—
296C22×SD16C22×C15111yescharacteristic
297C22×M16C22×C15111yescharacteristic
298C2×C4⋊Q8C22×C15112yes—
299C2×C22⋊Q8C22×C15111yescharacteristic
300C2×C4×Q8C22×C15112yes—
301#462—28no—
302#452—24no—
303C2×C4⋊C8C22×C15112yes—
304C2×#103C22×C15112yes—
305C2×#103C22×C15111yescharacteristic
306C2×#103C22×C15112yes—
307C2×#103C22×C15112yes—
308C2×#102C22×C15111yescharacteristic
309C2×C22⋊C8C22×C15111yescharacteristic
310#395—21no—
311#395—21no—
312#391C22×C15112yes—
313#390—22no—
314#390C22×C15112yes—
315#385—22no—
316#380—21no—
317#380C22×C15111yescharacteristic
318C4×C22⋊C4—21no—
319C4×C22⋊C4C22×C15111yescharacteristic
320#340C22×C15112yes—
321#336C22×C15112yes—
322C2×#41—22no—
323C2×#41—24no—
324C2×#41—42no—
325C2×#41D4×C15114yes—
326C22×Q8—21no—
327C22×Q8—24no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—42no—
331C22×Q8C23×C15111yescharacteristic
332C22×Q8C23×C15112yes—
333C22×Q8C23×C15111yescharacteristic
334C22×D4—21no—
335C22×D4C23×C15111yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4C23×C15111yescharacteristic
339#137—232no—
340C2×Q16—24no—
341C2×Q16—24no—
342C2×Q16—22no—
343C2×Q16—24no—
344C2×Q16D4×C15118yes—
345C2×SD16—24no—
346C2×SD16—24no—
347C2×SD16—22no—
348C2×SD16—24no—
349C2×SD16—42no—
350C2×M16—22no—
351C2×M16—24no—
352C22×C8C23×C15111yescharacteristic
353C22×C8C23×C15111yescharacteristic
354C22×C8C23×C15112yes—
355C4⋊Q8—24no—
356C4⋊Q8—42no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C4×Q8—24no—
360C4×Q8—42no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4C23×C15112yes—
366C2×C4⋊C4C23×C15111yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4D4×C15112yes—
372C2×C42—22no—
373C2×C42C23×C15112yes—
374C4⋊C8—24no—
375#103—22no—
376#103—24no—
377#103—24no—
378#103—42no—
379#102—22no—
380C22⋊C8—22no—
381#95—21no—
382#95—22no—
383#95—22no—
384#95D4×C15111yescharacteristic
385#95D4×C15111yescharacteristic
386C24—21no—
387C24C2×D4×C15111yescharacteristic
388#41—28no—
389#41—44no—
390#41—48no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—28no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—21no—
399C2×Q8—22no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—44no—
404C2×Q8—48no—
405C2×Q8—44no—
406C2×Q8—42no—
407C2×Q8C2×D4×C15114yes—
408C2×Q8C2×D4×C15112yes—
409C2×Q8C2×D4×C15114yes—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—44no—
415C2×D4C2×D4×C15112yes—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—42no—
427C22×C4C2×D4×C15112yes—
428C22×C4C2×D4×C15111yescharacteristic
429C22×C4C2×D4×C15112yes—
430C22×C4C2×D4×C15112yes—
431C22×C4#41×C15112yes—
432C22×C4C24×C15111yescharacteristic
433Q16—216no—
434Q16—44no—
435SD16—216no—
436SD16—44no—
437M16—28no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8C2×D4×C15114yes—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—44no—
450C4⋊C4—44no—
451C4⋊C4—44no—
452C4⋊C4—42no—
453C22⋊C4—24no—
454C22⋊C4—42no—
455C22⋊C4—44no—
456C22⋊C4—82no—
457C22⋊C4—81no—
458C42—22no—
459C42—22no—
460C42—44no—
461C23—22no—
462C23—22no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23#121×C15112yes—
471C23C22×D4×C15111yescharacteristic
472Q8—22no—
473Q8—24no—
474Q8—24no—
475Q8—24no—
476Q8—48no—
477Q8—42no—
478Q8—42no—
479Q8—41no—
480Q8—41no—
481Q8—42no—
482Q8#120×C15114yes—
483D4—22no—
484D4—22no—
485D4—48no—
486D4—42no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—48no—
500C2×C4—48no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4#121×C15112yes—
512C2×C4#137×C15114yescomplemented
513C2×C4C22×D4×C15111yescharacteristic
514C2×C4C22×D4×C15112yes—
515C2×C4C2×#41×C15111yescharacteristic
516C2×C4H(5,𝔽2)×C15112yes—
517C8—24no—
518C8—41no—
519C8—41no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—82no—
529C22—82no—
530C22C2×#121×C15111yescharacteristic
531C22D42×C15112yes—
532C22C2×#137×C15112yes—
533C22#577×C15111yescharacteristic
534C22#578×C15111yescharacteristic
535C4—22no—
536C4—24no—
537C4—24no—
538C4—44no—
539C4—42no—
540C4—81no—
541C4—82no—
542C4—81no—
543C4C2×#120×C15111yescharacteristic
544C4#534×C15111yescharacteristic
545C4#546×C15112yes—
546C2—42no—
547C2—82no—
548C2#2410×C15111yescharacteristic
549C2#3039×C15111yescharacteristic
550C2#3046×C15111yescharacteristic
551C2#3270×C15112yes—
552C2#3278×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#462×C151C2semidirect
4. #2434×C151C2semidirect
6. #2055×C151C2semidirect
7. #2013×C151C2semidirect
8. #1894×C151C2semidirect
9. #1878×C151C2semidirect
10. #1851×C151C2semidirect
11. #1787×C151C2semidirect
235. C2×C4×C151#137semidirect
276. #24374C151direct (N × H)
277. C151#24374direct (N × H)
279. C2×#462C2×C151semidirect
281. #2434C2×C151semidirect
283. #2055C2×C151semidirect
284. #2013C2×C151semidirect
285. #1894C2×C151semidirect
286. #1878C2×C151semidirect
287. #1851C2×C151semidirect
288. #1787C2×C151semidirect
512. C2×C4#137×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1512
C2×#462×C1512
C2×#452×C1512
#2434×C1512
#2341×C1512
#2055×C1512
#2013×C1512
#1894×C1512
#1878×C1512
#1851×C1512
#1787×C1512
#24374151