Finite Group Databasebeta

← C151×#24630 #50329555

Subgroups — C151×#24630 #50329555

Order 38656.

906 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C151C211yesmaximal, characteristic
2C2×C4×SD16×C151C211yesmaximal, characteristic
3#2546×C151C211yesmaximal, characteristic, complemented
4#2354×C151C211yesmaximal, characteristic
5#2055×C151C212yesmaximal
6#2013×C151C212yesmaximal
7#1981×C151C212yesmaximal, complemented
8#1956×C151C211yesmaximal, characteristic, complemented
9#1939×C151C211yesmaximal, characteristic, complemented
10#1927×C151C212yesmaximal, complemented
11#1803×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×C4⋊Q8×C151C2212yes—
16C2×C4×Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18C2×#117×C151—21no—
19#461×C151—24no—
20C4×SD16×C151—24no—
21C2×#106×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2212yes—
24C2×#103×C151C2211yescharacteristic
25C2×#103×C151C2212yes—
26C2×#103×C151C2212yes—
27C2×#103×C151C2212yes—
28C2×#103×C151C2212yes—
29C2×#102×C151C2211yescharacteristic
30C2×C4×C8×C151C2211yescharacteristic
31#398×C151—22no—
32#391×C151C2212yes—
33#390×C151C2212yes—
34#389×C151—21no—
35#389×C151—21no—
36#388×C151—22no—
37#384×C151C2211yescharacteristic
38#380×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×SD16×C151—22no—
48C2×SD16×C151—24no—
49C2×SD16×C151—22no—
50C2×SD16×C151—22no—
51C2×SD16×C151—42no—
52C2×SD16×C151—42no—
53C22×C8×C151C2312yes—
54C22×C8×C151C2311yescharacteristic
55C22×C8×C151C2311yescharacteristic
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151—24no—
59C4⋊Q8×C151—42no—
60C4×Q8×C151—22no—
61C4×Q8×C151—22no—
62C4×D4×C151—22no—
63C4×D4×C151D414yes—
64#117×C151—44no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151—21no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151D411yescharacteristic
73C2×C4⋊C4×C151D411yescharacteristic
74C2×C4⋊C4×C151C2311yescharacteristic
75C2×C4⋊C4×C151C2312yes—
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C22⋊C4×C151—21no—
78C2×C22⋊C4×C151—22no—
79C2×C22⋊C4×C151—22no—
80C2×C42×C151—22no—
81C2×C42×C151—21no—
82C2×C42×C151C2312yes—
83C2×C42×C151C2311yescharacteristic
84#106×C151—22no—
85C4⋊C8×C151—22no—
86C4⋊C8×C151—42no—
87#103×C151—24no—
88#103×C151—22no—
89#103×C151—24no—
90#103×C151—42no—
91#103×C151—42no—
92#102×C151—22no—
93C4×C8×C151—22no—
94#95×C151—22no—
95#95×C151—22no—
96#95×C151—22no—
97#95×C151D412yes—
98C24×C151—21no—
99C2×Q8×C151—21no—
100C2×Q8×C151—21no—
101C2×Q8×C151—22no—
102C2×Q8×C151—21no—
103C2×Q8×C151—21no—
104C2×Q8×C151—22no—
105C2×Q8×C151—22no—
106C2×Q8×C151—22no—
107C2×Q8×C151—21no—
108C2×Q8×C151—22no—
109C2×Q8×C151—22no—
110C2×Q8×C151#4112yes—
111C2×D4×C151—21no—
112C2×D4×C151—21no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151C2×D412yes—
117C22×C4×C151—21no—
118C22×C4×C151—21no—
119C22×C4×C151—24no—
120C22×C4×C151—21no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—42no—
124C22×C4×C151—42no—
125C22×C4×C151C2×D412yes—
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151C2×D412yes—
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2411yescharacteristic
130SD16×C151—28no—
131SD16×C151—48no—
132C2×C8×C151—21no—
133C2×C8×C151—21no—
134C2×C8×C151—21no—
135C2×C8×C151—22no—
136C2×C8×C151—21no—
137C2×C8×C151—22no—
138C2×C8×C151—21no—
139C2×C8×C151—22no—
140C2×C8×C151#4112yes—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—44no—
148C4⋊C4×C151—44no—
149C4⋊C4×C151—42no—
150C4⋊C4×C151—42no—
151C4⋊C4×C151—42no—
152C4⋊C4×C151—42no—
153C4⋊C4×C151—81no—
154C4⋊C4×C151SD1614yescomplemented
155C4⋊C4×C151C2×D412yes—
156C22⋊C4×C151—24no—
157C22⋊C4×C151—44no—
158C22⋊C4×C151—82no—
159C42×C151—22no—
160C42×C151—22no—
161C42×C151—42no—
162C42×C151—44no—
163C42×C151C2×D412yes—
164C42×C151#4112yes—
165C23×C151—22no—
166C23×C151—41no—
167C23×C151—41no—
168C23×C151—41no—
169C23×C151—41no—
170C23×C151—41no—
171C23×C151—41no—
172C23×C151C22×D411yescharacteristic
173Q8×C151—22no—
174Q8×C151—22no—
175Q8×C151—41no—
176Q8×C151—41no—
177Q8×C151—42no—
178Q8×C151—42no—
179Q8×C151—42no—
180Q8×C151—42no—
181D4×C151—22no—
182D4×C151—22no—
183D4×C151—41no—
184D4×C151—41no—
185C2×C4×C151—22no—
186C2×C4×C151—21no—
187C2×C4×C151—22no—
188C2×C4×C151—21no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—41no—
195C2×C4×C151—41no—
196C2×C4×C151—41no—
197C2×C4×C151—41no—
198C2×C4×C151—48no—
199C2×C4×C151—42no—
200C2×C4×C151—41no—
201C2×C4×C151—42no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151#12112yes—
209C2×C4×C151#12112yes—
210C2×C4×C151C2×SD1614yes—
211C2×C4×C151C2×SD1612yes—
212C2×C4×C151#13712yes—
213C2×C4×C151C22×D411yescharacteristic
214C2×C4×C151C2×#4111yescharacteristic
215C2×C4×C151C2×#4111yescharacteristic
216C2×C4×C151C2×#4111yescharacteristic
217C2×C4×C151H(5,𝔽2)11yescharacteristic
218C2×C4×C151H(5,𝔽2)11yescharacteristic
219C8×C151—22no—
220C8×C151—41no—
221C8×C151—42no—
222C22×C151—42no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—81no—
226C22×C151—81no—
227C22×C151—81no—
228C22×C151—81no—
229C22×C151C2×#12111yescharacteristic
230C22×C151#54611yescharacteristic
231C22×C151#55011yescharacteristic
232C22×C151C22×SD1611yescharacteristic
233C22×C151C2×#13711yescharacteristic
234C22×C151#57711yescharacteristic
235C22×C151#57811yescharacteristic
236C4×C151—24no—
237C4×C151—22no—
238C4×C151—42no—
239C4×C151—42no—
240C4×C151—42no—
241C4×C151—82no—
242C4×C151—82no—
243C4×C151—81no—
244C4×C151#46114yes—
245C4×C151#52511yescharacteristic
246C4×C151#53511yescharacteristic
247C4×C151#55311yescharacteristic
248C4×C151#55511yescharacteristic
249C2×C151—82no—
250C2×C151#241411yescharacteristic
251C2×C151C2×#46111yescharacteristic
252C2×C151#304611yescharacteristic
253C2×C151#329811yescharacteristic
254C2×C151#332911yescharacteristic
255C2×C151#339211yescharacteristic
256C2×C151#339811yescharacteristic
257#24630C15111yesmaximal, characteristic, direct product factor, Sylow
258C151#2463011yescharacteristic, direct product factor, Sylow
259C2×#461C2×C15111yescharacteristic
260C2×C4×SD16C2×C15111yescharacteristic
261#2546C2×C15111yescharacteristic, complemented
262#2354C2×C15111yescharacteristic
263#2055C2×C15112yes—
264#2013C2×C15112yes—
265#1981C2×C15112yescomplemented
266#1956C2×C15111yescharacteristic, complemented
267#1939C2×C15111yescharacteristic, complemented
268#1927C2×C15112yescomplemented
269#1803C2×C15111yescharacteristic, complemented
270C22×SD16C22×C15111yescharacteristic
271C22×SD16C22×C15112yes—
272C2×C4⋊Q8C22×C15111yescharacteristic
273C2×C4⋊Q8C22×C15112yes—
274C2×C4×Q8C22×C15111yescharacteristic
275C2×C4×D4C22×C15111yescharacteristic
276C2×#117—21no—
277#461—24no—
278C4×SD16—24no—
279C2×#106C22×C15111yescharacteristic
280C2×C4⋊C8C22×C15111yescharacteristic
281C2×C4⋊C8C22×C15112yes—
282C2×#103C22×C15111yescharacteristic
283C2×#103C22×C15112yes—
284C2×#103C22×C15112yes—
285C2×#103C22×C15112yes—
286C2×#103C22×C15112yes—
287C2×#102C22×C15111yescharacteristic
288C2×C4×C8C22×C15111yescharacteristic
289#398—22no—
290#391C22×C15112yes—
291#390C22×C15112yes—
292#389—21no—
293#389—21no—
294#388—22no—
295#384C22×C15111yescharacteristic
296#380—21no—
297C4×C4⋊C4C22×C15112yes—
298C4×C4⋊C4C22×C15111yescharacteristic
299#340C22×C15112yes—
300#336C22×C15112yes—
301C22×Q8C23×C15112yes—
302C22×Q8C23×C15111yescharacteristic
303C22×D4C23×C15111yescharacteristic
304C23×C4—21no—
305C2×SD16—22no—
306C2×SD16—22no—
307C2×SD16—24no—
308C2×SD16—22no—
309C2×SD16—42no—
310C2×SD16—42no—
311C22×C8C23×C15112yes—
312C22×C8C23×C15111yescharacteristic
313C22×C8C23×C15111yescharacteristic
314C4⋊Q8—24no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—42no—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×D4—22no—
321C4×D4D4×C15114yes—
322#117—44no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4D4×C15111yescharacteristic
331C2×C4⋊C4D4×C15111yescharacteristic
332C2×C4⋊C4C23×C15111yescharacteristic
333C2×C4⋊C4C23×C15112yes—
334C2×C4⋊C4C23×C15111yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C42—22no—
339C2×C42—21no—
340C2×C42C23×C15112yes—
341C2×C42C23×C15111yescharacteristic
342#106—22no—
343C4⋊C8—22no—
344C4⋊C8—42no—
345#103—24no—
346#103—22no—
347#103—24no—
348#103—42no—
349#103—42no—
350#102—22no—
351C4×C8—22no—
352#95—22no—
353#95—22no—
354#95—22no—
355#95D4×C15112yes—
356C24—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8#41×C15112yes—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4C2×D4×C15112yes—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—24no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4C2×D4×C15112yes—
384C22×C4C2×D4×C15111yescharacteristic
385C22×C4C2×D4×C15112yes—
386C22×C4C2×D4×C15111yescharacteristic
387C22×C4C24×C15111yescharacteristic
388SD16—28no—
389SD16—48no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—22no—
394C2×C8—21no—
395C2×C8—22no—
396C2×C8—21no—
397C2×C8—22no—
398C2×C8#41×C15112yes—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—44no—
406C4⋊C4—44no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—81no—
412C4⋊C4SD16×C15114yescomplemented
413C4⋊C4C2×D4×C15112yes—
414C22⋊C4—24no—
415C22⋊C4—44no—
416C22⋊C4—82no—
417C42—22no—
418C42—22no—
419C42—42no—
420C42—44no—
421C42C2×D4×C15112yes—
422C42#41×C15112yes—
423C23—22no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23C22×D4×C15111yescharacteristic
431Q8—22no—
432Q8—22no—
433Q8—41no—
434Q8—41no—
435Q8—42no—
436Q8—42no—
437Q8—42no—
438Q8—42no—
439D4—22no—
440D4—22no—
441D4—41no—
442D4—41no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—48no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4#121×C15112yes—
467C2×C4#121×C15112yes—
468C2×C4C2×SD16×C15114yes—
469C2×C4C2×SD16×C15112yes—
470C2×C4#137×C15112yes—
471C2×C4C22×D4×C15111yescharacteristic
472C2×C4C2×#41×C15111yescharacteristic
473C2×C4C2×#41×C15111yescharacteristic
474C2×C4C2×#41×C15111yescharacteristic
475C2×C4H(5,𝔽2)×C15111yescharacteristic
476C2×C4H(5,𝔽2)×C15111yescharacteristic
477C8—22no—
478C8—42no—
479C8—41no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22C2×#121×C15111yescharacteristic
488C22#546×C15111yescharacteristic
489C22#550×C15111yescharacteristic
490C22C22×SD16×C15111yescharacteristic
491C22C2×#137×C15111yescharacteristic
492C22#577×C15111yescharacteristic
493C22#578×C15111yescharacteristic
494C4—24no—
495C4—22no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—82no—
500C4—82no—
501C4—81no—
502C4#461×C15114yes—
503C4#525×C15111yescharacteristic
504C4#535×C15111yescharacteristic
505C4#553×C15111yescharacteristic
506C4#555×C15111yescharacteristic
507C2—82no—
508C2#2414×C15111yescharacteristic
509C2C2×#461×C15111yescharacteristic
510C2#3046×C15111yescharacteristic
511C2#3298×C15111yescharacteristic
512C2#3329×C15111yescharacteristic
513C2#3392×C15111yescharacteristic
514C2#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
3. #2546×C151C2semidirect
7. #1981×C151C2semidirect
8. #1956×C151C2semidirect
9. #1939×C151C2semidirect
10. #1927×C151C2semidirect
11. #1803×C151C2semidirect
154. C4⋊C4×C151SD16semidirect
257. #24630C151direct (N × H)
258. C151#24630direct (N × H)
261. #2546C2×C151semidirect
265. #1981C2×C151semidirect
266. #1956C2×C151semidirect
267. #1939C2×C151semidirect
268. #1927C2×C151semidirect
269. #1803C2×C151semidirect
412. C4⋊C4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1512
C2×C4×SD16×C1512
#2546×C1512
#2354×C1512
#2055×C1512
#2013×C1512
#1981×C1512
#1956×C1512
#1939×C1512
#1927×C1512
#1803×C1512
#24630151