Finite Group Databasebeta

← C151×#24966 #50329891

Subgroups — C151×#24966 #50329891

Order 38656.

854 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2537×C151C211yesmaximal, characteristic
2#2354×C151C211yesmaximal, characteristic, complemented
3#2077×C151C212yesmaximal, complemented
4#2034×C151C212yesmaximal, complemented
5#1954×C151C211yesmaximal, characteristic, complemented
6#1948×C151C211yesmaximal, characteristic, complemented
7#1875×C151C212yesmaximal, complemented
8#1834×C151C211yesmaximal, characteristic, complemented
9#1825×C151C212yesmaximal, complemented
10#1802×C151C211yesmaximal, characteristic, complemented
11C4×#102×C151C211yesmaximal, characteristic, complemented
12C2×#121×C151—21no—
13C2×#121×C151C2212yes—
14C2×C4×D4×C151C2211yescharacteristic
15C2×C4×D4×C151C2211yescharacteristic
16C2×#117×C151C2212yes—
17C2×#106×C151C2212yes—
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#102×C151C2211yescharacteristic
20C2×#102×C151C2211yescharacteristic
21C2×#102×C151C2212yes—
22C2×C22⋊C8×C151C2212yes—
23C2×C22⋊C8×C151C2212yes—
24C2×C4×C8×C151C2211yescharacteristic
25#394×C151—22no—
26#390×C151—21no—
27#388×C151—22no—
28#384×C151C2211yescharacteristic
29#384×C151C2211yescharacteristic
30#380×C151—21no—
31#380×C151C2212yes—
32#380×C151C2212yes—
33C4×C4⋊C4×C151—21no—
34C4×C4⋊C4×C151C2211yescharacteristic
35#340×C151C2211yescharacteristic
36#340×C151C2212yes—
37#340×C151C2212yes—
38#340×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41C22×D4×C151—22no—
42C22×D4×C151D411yescharacteristic
43C22×D4×C151C2311yescharacteristic
44C23×C4×C151—21no—
45C23×C4×C151C2312yes—
46C22×C8×C151C2311yescharacteristic
47C22×C8×C151C2311yescharacteristic
48C22×C8×C151C2312yes—
49#121×C151—24no—
50#121×C151—42no—
51#121×C151—44no—
52C4×D4×C151—22no—
53C4×D4×C151—22no—
54C4×D4×C151—22no—
55C4×D4×C151—22no—
56#117×C151—24no—
57#117×C151—42no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151D411yescharacteristic
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2312yes—
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C22⋊C4×C151—22no—
69C2×C22⋊C4×C151—21no—
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151D412yes—
74C2×C42×C151—21no—
75C2×C42×C151—22no—
76C2×C42×C151C2311yescharacteristic
77#106×C151—42no—
78C4⋊C8×C151—22no—
79#102×C151—22no—
80#102×C151—22no—
81#102×C151—42no—
82C22⋊C8×C151—42no—
83C22⋊C8×C151—42no—
84C4×C8×C151—22no—
85#95×C151—22no—
86#95×C151—21no—
87#95×C151—22no—
88C24×C151—21no—
89C24×C151C2×D412yes—
90C2×D4×C151—22no—
91C2×D4×C151—22no—
92C2×D4×C151—22no—
93C2×D4×C151—21no—
94C2×D4×C151—21no—
95C2×D4×C151—21no—
96C2×D4×C151—21no—
97C2×D4×C151—21no—
98C2×D4×C151—44no—
99C2×D4×C151—44no—
100C2×D4×C151—82no—
101C2×D4×C151#4112yes—
102C22×C4×C151—21no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—21no—
110C22×C4×C151—21no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—42no—
114C22×C4×C151—42no—
115C22×C4×C151—42no—
116C22×C4×C151C2×D412yes—
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2411yescharacteristic
120C2×C8×C151—21no—
121C2×C8×C151—21no—
122C2×C8×C151—21no—
123C2×C8×C151—21no—
124C2×C8×C151—22no—
125C2×C8×C151—21no—
126C2×C8×C151—21no—
127C2×C8×C151—22no—
128C2×C8×C151—22no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—21no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—42no—
140C4⋊C4×C151—42no—
141C4⋊C4×C151—81no—
142C4⋊C4×C151—81no—
143C4⋊C4×C151#4112yes—
144C22⋊C4×C151—24no—
145C22⋊C4×C151—44no—
146C22⋊C4×C151—44no—
147C22⋊C4×C151—44no—
148C22⋊C4×C151—42no—
149C22⋊C4×C151—82no—
150C42×C151—44no—
151C42×C151—42no—
152C42×C151#4112yes—
153C42×C151#4112yes—
154C23×C151—22no—
155C23×C151—22no—
156C23×C151—22no—
157C23×C151—22no—
158C23×C151—22no—
159C23×C151—22no—
160C23×C151—22no—
161C23×C151—22no—
162C23×C151—41no—
163C23×C151—41no—
164C23×C151—41no—
165C23×C151—41no—
166C23×C151—41no—
167C23×C151—41no—
168C23×C151C22×D411yescharacteristic
169D4×C151—22no—
170D4×C151—22no—
171D4×C151—41no—
172D4×C151—41no—
173D4×C151—44no—
174D4×C151—88no—
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—41no—
182C2×C4×C151—41no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—41no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—41no—
191C2×C4×C151—41no—
192C2×C4×C151—41no—
193C2×C4×C151—41no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—41no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—84no—
200C2×C4×C151#12312yes—
201C2×C4×C151#12312yes—
202C2×C4×C151#13512yes—
203C2×C4×C151AGL(1,ℤ/8)12yes—
204C2×C4×C151C2×#4111yescharacteristic
205C2×C4×C151C2×#4111yescharacteristic
206C2×C4×C151C2×#4111yescharacteristic
207C2×C4×C151C2×#4111yescharacteristic
208C2×C4×C151H(5,𝔽2)11yescharacteristic
209C2×C4×C151H(5,𝔽2)11yescharacteristic
210C8×C151—42no—
211C8×C151—41no—
212C8×C151—41no—
213C22×C151—42no—
214C22×C151—42no—
215C22×C151—42no—
216C22×C151—42no—
217C22×C151—42no—
218C22×C151—42no—
219C22×C151—42no—
220C22×C151—42no—
221C22×C151—42no—
222C22×C151—42no—
223C22×C151—81no—
224C22×C151—81no—
225C22×C151—81no—
226C22×C151—81no—
227C22×C151C2×#12311yescharacteristic
228C22×C151#54611yescharacteristic
229C22×C151#54611yescharacteristic
230C22×C151C2×#13511yescharacteristic
231C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
232C22×C151#57711yescharacteristic
233C22×C151#57711yescharacteristic
234C4×C151—22no—
235C4×C151—42no—
236C4×C151—42no—
237C4×C151—82no—
238C4×C151—81no—
239C4×C151—81no—
240C4×C151—82no—
241C4×C151#48214yes—
242C4×C151#52911yescharacteristic
243C4×C151#54011yescharacteristic
244C4×C151#55311yescharacteristic
245C4×C151#55511yescharacteristic
246C2×C151—82no—
247C2×C151—82no—
248C2×C151#242011yescharacteristic
249C2×C151C2×#48211yescharacteristic
250C2×C151#309911yescharacteristic
251C2×C151#330311yescharacteristic
252C2×C151#330311yescharacteristic
253C2×C151#332411yescharacteristic
254C2×C151#333211yescharacteristic
255#24966C15111yesmaximal, characteristic, direct product factor, Sylow
256C151#2496611yescharacteristic, direct product factor, Sylow
257#2537C2×C15111yescharacteristic
258#2354C2×C15111yescharacteristic, complemented
259#2077C2×C15112yescomplemented
260#2034C2×C15112yescomplemented
261#1954C2×C15111yescharacteristic, complemented
262#1948C2×C15111yescharacteristic, complemented
263#1875C2×C15112yescomplemented
264#1834C2×C15111yescharacteristic, complemented
265#1825C2×C15112yescomplemented
266#1802C2×C15111yescharacteristic, complemented
267C4×#102C2×C15111yescharacteristic, complemented
268C2×#121—21no—
269C2×#121C22×C15112yes—
270C2×C4×D4C22×C15111yescharacteristic
271C2×C4×D4C22×C15111yescharacteristic
272C2×#117C22×C15112yes—
273C2×#106C22×C15112yes—
274C2×C4⋊C8C22×C15111yescharacteristic
275C2×#102C22×C15111yescharacteristic
276C2×#102C22×C15111yescharacteristic
277C2×#102C22×C15112yes—
278C2×C22⋊C8C22×C15112yes—
279C2×C22⋊C8C22×C15112yes—
280C2×C4×C8C22×C15111yescharacteristic
281#394—22no—
282#390—21no—
283#388—22no—
284#384C22×C15111yescharacteristic
285#384C22×C15111yescharacteristic
286#380—21no—
287#380C22×C15112yes—
288#380C22×C15112yes—
289C4×C4⋊C4—21no—
290C4×C4⋊C4C22×C15111yescharacteristic
291#340C22×C15112yes—
292#340C22×C15111yescharacteristic
293#340C22×C15112yes—
294#340C22×C15111yescharacteristic
295#340C22×C15112yes—
296#340C22×C15112yes—
297C22×D4—22no—
298C22×D4D4×C15111yescharacteristic
299C22×D4C23×C15111yescharacteristic
300C23×C4—21no—
301C23×C4C23×C15112yes—
302C22×C8C23×C15111yescharacteristic
303C22×C8C23×C15111yescharacteristic
304C22×C8C23×C15112yes—
305#121—24no—
306#121—42no—
307#121—44no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—22no—
312#117—24no—
313#117—42no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4D4×C15111yescharacteristic
319C2×C4⋊C4C23×C15112yes—
320C2×C4⋊C4C23×C15111yescharacteristic
321C2×C4⋊C4C23×C15112yes—
322C2×C4⋊C4C23×C15111yescharacteristic
323C2×C4⋊C4C23×C15111yescharacteristic
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4D4×C15112yes—
330C2×C42—22no—
331C2×C42—21no—
332C2×C42C23×C15111yescharacteristic
333#106—42no—
334C4⋊C8—22no—
335#102—22no—
336#102—22no—
337#102—42no—
338C22⋊C8—42no—
339C22⋊C8—42no—
340C4×C8—22no—
341#95—22no—
342#95—21no—
343#95—22no—
344C24—21no—
345C24C2×D4×C15112yes—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—44no—
355C2×D4—44no—
356C2×D4—82no—
357C2×D4#41×C15112yes—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4C2×D4×C15112yes—
373C22×C4C2×D4×C15111yescharacteristic
374C22×C4C2×D4×C15111yescharacteristic
375C22×C4C24×C15111yescharacteristic
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—22no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—22no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4—81no—
398C4⋊C4—81no—
399C4⋊C4#41×C15112yes—
400C22⋊C4—24no—
401C22⋊C4—44no—
402C22⋊C4—44no—
403C22⋊C4—44no—
404C22⋊C4—42no—
405C22⋊C4—82no—
406C42—44no—
407C42—42no—
408C42#41×C15112yes—
409C42#41×C15112yes—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—22no—
415C23—22no—
416C23—22no—
417C23—22no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23C22×D4×C15111yescharacteristic
425D4—22no—
426D4—22no—
427D4—44no—
428D4—41no—
429D4—41no—
430D4—88no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—84no—
456C2×C4#123×C15112yes—
457C2×C4#123×C15112yes—
458C2×C4#135×C15112yes—
459C2×C4AGL(1,ℤ/8)×C15112yes—
460C2×C4C2×#41×C15111yescharacteristic
461C2×C4C2×#41×C15111yescharacteristic
462C2×C4C2×#41×C15111yescharacteristic
463C2×C4C2×#41×C15111yescharacteristic
464C2×C4H(5,𝔽2)×C15111yescharacteristic
465C2×C4H(5,𝔽2)×C15111yescharacteristic
466C8—42no—
467C8—41no—
468C8—41no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C2×#123×C15111yescharacteristic
484C22#546×C15111yescharacteristic
485C22#546×C15111yescharacteristic
486C22C2×#135×C15111yescharacteristic
487C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
488C22#577×C15111yescharacteristic
489C22#577×C15111yescharacteristic
490C4—22no—
491C4—42no—
492C4—42no—
493C4—81no—
494C4—82no—
495C4—82no—
496C4—81no—
497C4#482×C15114yes—
498C4#529×C15111yescharacteristic
499C4#540×C15111yescharacteristic
500C4#553×C15111yescharacteristic
501C4#555×C15111yescharacteristic
502C2—82no—
503C2—82no—
504C2#2420×C15111yescharacteristic
505C2C2×#482×C15111yescharacteristic
506C2#3099×C15111yescharacteristic
507C2#3303×C15111yescharacteristic
508C2#3303×C15111yescharacteristic
509C2#3324×C15111yescharacteristic
510C2#3332×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2537×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2354×C151C2semidirect
3. #2077×C151C2semidirect
4. #2034×C151C2semidirect
5. #1954×C151C2semidirect
6. #1948×C151C2semidirect
7. #1875×C151C2semidirect
8. #1834×C151C2semidirect
9. #1825×C151C2semidirect
10. #1802×C151C2semidirect
11. C4×#102×C151C2semidirect
255. #24966C151direct (N × H)
256. C151#24966direct (N × H)
258. #2354C2×C151semidirect
259. #2077C2×C151semidirect
260. #2034C2×C151semidirect
261. #1954C2×C151semidirect
262. #1948C2×C151semidirect
263. #1875C2×C151semidirect
264. #1834C2×C151semidirect
265. #1825C2×C151semidirect
266. #1802C2×C151semidirect
267. C4×#102C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2537×C1512
#2354×C1512
#2077×C1512
#2034×C1512
#1954×C1512
#1948×C1512
#1875×C1512
#1834×C1512
#1825×C1512
#1802×C1512
C4×#102×C1512
#24966151