Finite Group Databasebeta

← C151×#24629 #50329554

Subgroups — C151×#24629 #50329554

Order 38656.

862 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#462×C151C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C151C211yesmaximal, characteristic
3#2547×C151C211yesmaximal, characteristic
4#2355×C151C211yesmaximal, characteristic, complemented
5#2056×C151C212yesmaximal, complemented
6#2015×C151C212yesmaximal
7#1983×C151C212yesmaximal
8#1956×C151C211yesmaximal, characteristic, complemented
9#1939×C151C211yesmaximal, characteristic, complemented
10#1927×C151C212yesmaximal, complemented
11#1802×C151C211yesmaximal, characteristic
12C22×Q16×C151C2212yes—
13C22×SD16×C151C2211yescharacteristic
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×#124×C151C2212yes—
16C2×C4×Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18#462×C151—24no—
19C4×SD16×C151—24no—
20C2×#106×C151C2211yescharacteristic
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2212yes—
23C2×#103×C151C2211yescharacteristic
24C2×#103×C151C2212yes—
25C2×#103×C151C2212yes—
26C2×#103×C151C2212yes—
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2212yes—
29C2×C4×C8×C151C2211yescharacteristic
30#397×C151—22no—
31#391×C151C2212yes—
32#391×C151C2212yes—
33#387×C151—22no—
34#384×C151C2211yescharacteristic
35#382×C151—21no—
36#380×C151—21no—
37#380×C151—21no—
38C4×C4⋊C4×C151—21no—
39C4×C4⋊C4×C151C2212yes—
40C4×C4⋊C4×C151C2211yescharacteristic
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151C2312yes—
44C22×Q8×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C2×Q16×C151—24no—
48C2×Q16×C151—42no—
49C2×Q16×C151—42no—
50C2×SD16×C151—22no—
51C2×SD16×C151—22no—
52C2×SD16×C151—22no—
53C22×C8×C151C2312yes—
54C22×C8×C151C2311yescharacteristic
55C22×C8×C151C2311yescharacteristic
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151—22no—
58#124×C151—24no—
59#124×C151—42no—
60C4×Q8×C151—22no—
61C4×Q8×C151D414yes—
62C4×D4×C151—22no—
63C4×D4×C151—22no—
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×C151D411yescharacteristic
70C2×C4⋊C4×C151D411yescharacteristic
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C4⋊C4×C151C2312yes—
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C22⋊C4×C151—22no—
75C2×C22⋊C4×C151—22no—
76C2×C22⋊C4×C151—21no—
77C2×C42×C151—21no—
78C2×C42×C151—22no—
79C2×C42×C151C2312yes—
80C2×C42×C151C2311yescharacteristic
81#106×C151—22no—
82C4⋊C8×C151—22no—
83C4⋊C8×C151—42no—
84#103×C151—24no—
85#103×C151—24no—
86#103×C151—22no—
87#103×C151—42no—
88#102×C151—22no—
89#102×C151—42no—
90C4×C8×C151—22no—
91#95×C151—22no—
92#95×C151—22no—
93#95×C151—22no—
94#95×C151—22no—
95#95×C151—22no—
96#95×C151D412yes—
97C24×C151—21no—
98C2×Q8×C151—21no—
99C2×Q8×C151—22no—
100C2×Q8×C151—21no—
101C2×Q8×C151—21no—
102C2×Q8×C151—22no—
103C2×Q8×C151—22no—
104C2×Q8×C151—22no—
105C2×Q8×C151—21no—
106C2×Q8×C151—21no—
107C2×Q8×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151C2×D412yes—
110C2×D4×C151—21no—
111C2×D4×C151—21no—
112C2×D4×C151—21no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151#4112yes—
116C22×C4×C151—21no—
117C22×C4×C151—21no—
118C22×C4×C151—21no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—42no—
122C22×C4×C151—42no—
123C22×C4×C151—42no—
124C22×C4×C151C2×D412yes—
125C22×C4×C151C2×D412yes—
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2411yescharacteristic
129Q16×C151—48no—
130SD16×C151—28no—
131C2×C8×C151—21no—
132C2×C8×C151—21no—
133C2×C8×C151—21no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C2×C8×C151—21no—
137C2×C8×C151—21no—
138C2×C8×C151—22no—
139C2×C8×C151#4112yes—
140C4⋊C4×C151—24no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—42no—
149C4⋊C4×C151—42no—
150C4⋊C4×C151—42no—
151C4⋊C4×C151—81no—
152C4⋊C4×C151C2×D412yes—
153C22⋊C4×C151—44no—
154C22⋊C4×C151—44no—
155C22⋊C4×C151—42no—
156C42×C151—24no—
157C42×C151—22no—
158C42×C151—22no—
159C42×C151—82no—
160C42×C151C2×D412yes—
161C42×C151#4112yes—
162C23×C151—22no—
163C23×C151—41no—
164C23×C151—41no—
165C23×C151—41no—
166C23×C151—41no—
167C23×C151—41no—
168C23×C151—41no—
169C23×C151C22×D411yescharacteristic
170Q8×C151—22no—
171Q8×C151—22no—
172Q8×C151—41no—
173Q8×C151—41no—
174Q8×C151—42no—
175Q8×C151—42no—
176Q8×C151—42no—
177Q8×C151—42no—
178D4×C151—22no—
179D4×C151—22no—
180D4×C151—41no—
181D4×C151—41no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—41no—
193C2×C4×C151—41no—
194C2×C4×C151—41no—
195C2×C4×C151—41no—
196C2×C4×C151—42no—
197C2×C4×C151—41no—
198C2×C4×C151—42no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—42no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—42no—
205C2×C4×C151—84no—
206C2×C4×C151#12112yes—
207C2×C4×C151#12112yes—
208C2×C4×C151#13512yes—
209C2×C4×C151#13712yes—
210C2×C4×C151C22×D411yescharacteristic
211C2×C4×C151C2×#4111yescharacteristic
212C2×C4×C151C2×#4111yescharacteristic
213C2×C4×C151C2×#4111yescharacteristic
214C2×C4×C151H(5,𝔽2)11yescharacteristic
215C2×C4×C151H(5,𝔽2)11yescharacteristic
216C8×C151—22no—
217C8×C151—41no—
218C8×C151—42no—
219C22×C151—42no—
220C22×C151—42no—
221C22×C151—42no—
222C22×C151—81no—
223C22×C151—81no—
224C22×C151—81no—
225C22×C151—81no—
226C22×C151C2×#12111yescharacteristic
227C22×C151#54611yescharacteristic
228C22×C151#55011yescharacteristic
229C22×C151C2×#13511yescharacteristic
230C22×C151C2×#13711yescharacteristic
231C22×C151#57711yescharacteristic
232C22×C151#57811yescharacteristic
233C4×C151—22no—
234C4×C151—42no—
235C4×C151—42no—
236C4×C151—42no—
237C4×C151—42no—
238C4×C151—82no—
239C4×C151—82no—
240C4×C151—81no—
241C4×C151#46414yes—
242C4×C151#52511yescharacteristic
243C4×C151#53511yescharacteristic
244C4×C151#55311yescharacteristic
245C4×C151#55511yescharacteristic
246C2×C151—82no—
247C2×C151#241411yescharacteristic
248C2×C151C2×#46411yescharacteristic
249C2×C151#304611yescharacteristic
250C2×C151#330211yescharacteristic
251C2×C151#333111yescharacteristic
252C2×C151#339411yescharacteristic
253C2×C151#339811yescharacteristic
254#24629C15111yesmaximal, characteristic, direct product factor, Sylow
255C151#2462911yescharacteristic, direct product factor, Sylow
256C2×#462C2×C15111yescharacteristic, complemented
257C2×C4×SD16C2×C15111yescharacteristic
258#2547C2×C15111yescharacteristic
259#2355C2×C15111yescharacteristic, complemented
260#2056C2×C15112yescomplemented
261#2015C2×C15112yes—
262#1983C2×C15112yes—
263#1956C2×C15111yescharacteristic, complemented
264#1939C2×C15111yescharacteristic, complemented
265#1927C2×C15112yescomplemented
266#1802C2×C15111yescharacteristic
267C22×Q16C22×C15112yes—
268C22×SD16C22×C15111yescharacteristic
269C2×C4⋊Q8C22×C15111yescharacteristic
270C2×#124C22×C15112yes—
271C2×C4×Q8C22×C15111yescharacteristic
272C2×C4×D4C22×C15111yescharacteristic
273#462—24no—
274C4×SD16—24no—
275C2×#106C22×C15111yescharacteristic
276C2×C4⋊C8C22×C15111yescharacteristic
277C2×C4⋊C8C22×C15112yes—
278C2×#103C22×C15111yescharacteristic
279C2×#103C22×C15112yes—
280C2×#103C22×C15112yes—
281C2×#103C22×C15112yes—
282C2×#102C22×C15111yescharacteristic
283C2×#102C22×C15112yes—
284C2×C4×C8C22×C15111yescharacteristic
285#397—22no—
286#391C22×C15112yes—
287#391C22×C15112yes—
288#387—22no—
289#384C22×C15111yescharacteristic
290#382—21no—
291#380—21no—
292#380—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4C22×C15112yes—
295C4×C4⋊C4C22×C15111yescharacteristic
296#340C22×C15112yes—
297#336C22×C15112yes—
298C22×Q8C23×C15112yes—
299C22×Q8C23×C15111yescharacteristic
300C22×D4C23×C15111yescharacteristic
301C23×C4—21no—
302C2×Q16—24no—
303C2×Q16—42no—
304C2×Q16—42no—
305C2×SD16—22no—
306C2×SD16—22no—
307C2×SD16—22no—
308C22×C8C23×C15112yes—
309C22×C8C23×C15111yescharacteristic
310C22×C8C23×C15111yescharacteristic
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313#124—24no—
314#124—42no—
315C4×Q8—22no—
316C4×Q8D4×C15114yes—
317C4×D4—22no—
318C4×D4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4D4×C15111yescharacteristic
325C2×C4⋊C4D4×C15111yescharacteristic
326C2×C4⋊C4C23×C15111yescharacteristic
327C2×C4⋊C4C23×C15112yes—
328C2×C4⋊C4C23×C15111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C42—21no—
333C2×C42—22no—
334C2×C42C23×C15112yes—
335C2×C42C23×C15111yescharacteristic
336#106—22no—
337C4⋊C8—22no—
338C4⋊C8—42no—
339#103—22no—
340#103—24no—
341#103—24no—
342#103—42no—
343#102—22no—
344#102—42no—
345C4×C8—22no—
346#95—22no—
347#95—22no—
348#95—22no—
349#95—22no—
350#95—22no—
351#95D4×C15112yes—
352C24—21no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8C2×D4×C15112yes—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4#41×C15112yes—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4C2×D4×C15112yes—
380C22×C4C2×D4×C15112yes—
381C22×C4C2×D4×C15111yescharacteristic
382C22×C4C2×D4×C15111yescharacteristic
383C22×C4C24×C15111yescharacteristic
384Q16—48no—
385SD16—28no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—22no—
394C2×C8#41×C15112yes—
395C4⋊C4—24no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—81no—
407C4⋊C4C2×D4×C15112yes—
408C22⋊C4—44no—
409C22⋊C4—44no—
410C22⋊C4—42no—
411C42—24no—
412C42—22no—
413C42—22no—
414C42—82no—
415C42C2×D4×C15112yes—
416C42#41×C15112yes—
417C23—22no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23C22×D4×C15111yescharacteristic
425Q8—22no—
426Q8—22no—
427Q8—41no—
428Q8—41no—
429Q8—42no—
430Q8—42no—
431Q8—42no—
432Q8—42no—
433D4—22no—
434D4—22no—
435D4—41no—
436D4—41no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—84no—
461C2×C4#121×C15112yes—
462C2×C4#121×C15112yes—
463C2×C4#135×C15112yes—
464C2×C4#137×C15112yes—
465C2×C4C22×D4×C15111yescharacteristic
466C2×C4C2×#41×C15111yescharacteristic
467C2×C4C2×#41×C15111yescharacteristic
468C2×C4C2×#41×C15111yescharacteristic
469C2×C4H(5,𝔽2)×C15111yescharacteristic
470C2×C4H(5,𝔽2)×C15111yescharacteristic
471C8—22no—
472C8—42no—
473C8—41no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22C2×#121×C15111yescharacteristic
482C22#546×C15111yescharacteristic
483C22#550×C15111yescharacteristic
484C22C2×#135×C15111yescharacteristic
485C22C2×#137×C15111yescharacteristic
486C22#577×C15111yescharacteristic
487C22#578×C15111yescharacteristic
488C4—22no—
489C4—42no—
490C4—42no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—82no—
495C4—81no—
496C4#464×C15114yes—
497C4#525×C15111yescharacteristic
498C4#535×C15111yescharacteristic
499C4#553×C15111yescharacteristic
500C4#555×C15111yescharacteristic
501C2—82no—
502C2#2414×C15111yescharacteristic
503C2C2×#464×C15111yescharacteristic
504C2#3046×C15111yescharacteristic
505C2#3302×C15111yescharacteristic
506C2#3331×C15111yescharacteristic
507C2#3394×C15111yescharacteristic
508C2#3398×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#462×C151C2semidirect
4. #2355×C151C2semidirect
5. #2056×C151C2semidirect
8. #1956×C151C2semidirect
9. #1939×C151C2semidirect
10. #1927×C151C2semidirect
254. #24629C151direct (N × H)
255. C151#24629direct (N × H)
256. C2×#462C2×C151semidirect
259. #2355C2×C151semidirect
260. #2056C2×C151semidirect
263. #1956C2×C151semidirect
264. #1939C2×C151semidirect
265. #1927C2×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×C4×SD16×C1512
#2547×C1512
#2355×C1512
#2056×C1512
#2015×C1512
#1983×C1512
#1956×C1512
#1939×C1512
#1927×C1512
#1802×C1512
#24629151