Finite Group Databasebeta

← C151×#24680 #50329605

Subgroups — C151×#24680 #50329605

Order 38656.

838 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C151C211yesmaximal, characteristic
2C2×C4×SD16×C151C211yesmaximal, characteristic
3#2567×C151C211yesmaximal, characteristic, complemented
4#2354×C151C211yesmaximal, characteristic
5#2071×C151C212yesmaximal
6#2055×C151C212yesmaximal
7#1990×C151C211yesmaximal, characteristic, complemented
8#1948×C151C212yesmaximal, complemented
9#1939×C151C211yesmaximal, characteristic, complemented
10#1927×C151C212yesmaximal, complemented
11#1803×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C4×Q8×C151C2211yescharacteristic
15C2×C4×D4×C151C2211yescharacteristic
16C2×#117×C151—21no—
17#476×C151—24no—
18C4×SD16×C151—24no—
19C2×#106×C151C2211yescharacteristic
20C2×#106×C151C2212yes—
21C2×C4⋊C8×C151C2212yes—
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×#103×C151C2211yescharacteristic
24C2×#103×C151C2212yes—
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2212yes—
27C2×C4×C8×C151C2211yescharacteristic
28#395×C151—22no—
29#391×C151C2212yes—
30#390×C151C2212yes—
31#389×C151—21no—
32#389×C151—21no—
33#388×C151—22no—
34#384×C151C2211yescharacteristic
35#384×C151C2212yes—
36#380×C151—21no—
37C4×C4⋊C4×C151C2212yes—
38C4×C4⋊C4×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151—21no—
44C22×Q8×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C2×SD16×C151—22no—
48C2×SD16×C151—22no—
49C2×SD16×C151—22no—
50C22×C8×C151C2311yescharacteristic
51C22×C8×C151C2312yes—
52C22×C8×C151C2311yescharacteristic
53C4⋊Q8×C151—22no—
54C4⋊Q8×C151—22no—
55C4×Q8×C151—22no—
56C4×Q8×C151—22no—
57C4×D4×C151—22no—
58C4×D4×C151D414yes—
59#117×C151—44no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151D411yescharacteristic
67C2×C4⋊C4×C151D411yescharacteristic
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2312yes—
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C22⋊C4×C151—21no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151—22no—
75C2×C42×C151—22no—
76C2×C42×C151—21no—
77C2×C42×C151C2312yes—
78C2×C42×C151C2311yescharacteristic
79#106×C151—22no—
80#106×C151—24no—
81C4⋊C8×C151—24no—
82C4⋊C8×C151—22no—
83#103×C151—22no—
84#103×C151—24no—
85#102×C151—22no—
86#102×C151—24no—
87C4×C8×C151—22no—
88#95×C151—22no—
89#95×C151—22no—
90#95×C151—22no—
91#95×C151D412yes—
92C24×C151—21no—
93C2×Q8×C151—21no—
94C2×Q8×C151—21no—
95C2×Q8×C151—21no—
96C2×Q8×C151—21no—
97C2×Q8×C151—21no—
98C2×Q8×C151—42no—
99C2×Q8×C151—81no—
100C2×Q8×C151—81no—
101C2×Q8×C151#4112yes—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151—21no—
106C2×D4×C151—21no—
107C2×D4×C151C2×D412yes—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151—24no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—21no—
114C22×C4×C151—42no—
115C22×C4×C151—42no—
116C22×C4×C151C2×D412yes—
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151C2×D412yes—
119C22×C4×C151C2×D411yescharacteristic
120C22×C4×C151C2411yescharacteristic
121SD16×C151—28no—
122C2×C8×C151—21no—
123C2×C8×C151—21no—
124C2×C8×C151—21no—
125C2×C8×C151—22no—
126C2×C8×C151—22no—
127C2×C8×C151—22no—
128C2×C8×C151—21no—
129C2×C8×C151—21no—
130C2×C8×C151#4112yes—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—21no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—22no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—21no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—42no—
140C4⋊C4×C151—42no—
141C4⋊C4×C151—42no—
142C4⋊C4×C151—81no—
143C4⋊C4×C151—82no—
144C4⋊C4×C151—82no—
145C4⋊C4×C151SD1614yescomplemented
146C4⋊C4×C151C2×D412yes—
147C22⋊C4×C151—24no—
148C22⋊C4×C151—44no—
149C22⋊C4×C151—82no—
150C42×C151—22no—
151C42×C151—22no—
152C42×C151—42no—
153C42×C151—44no—
154C42×C151C2×D412yes—
155C42×C151#4112yes—
156C23×C151—22no—
157C23×C151—41no—
158C23×C151—41no—
159C23×C151—41no—
160C23×C151—41no—
161C23×C151—41no—
162C23×C151—41no—
163C23×C151C22×D411yescharacteristic
164Q8×C151—22no—
165Q8×C151—22no—
166Q8×C151—41no—
167Q8×C151—41no—
168Q8×C151—84no—
169D4×C151—22no—
170D4×C151—22no—
171D4×C151—41no—
172D4×C151—41no—
173C2×C4×C151—22no—
174C2×C4×C151—21no—
175C2×C4×C151—21no—
176C2×C4×C151—22no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—41no—
183C2×C4×C151—41no—
184C2×C4×C151—41no—
185C2×C4×C151—41no—
186C2×C4×C151—48no—
187C2×C4×C151—42no—
188C2×C4×C151—41no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—41no—
194C2×C4×C151—42no—
195C2×C4×C151—41no—
196C2×C4×C151#12112yes—
197C2×C4×C151#12112yes—
198C2×C4×C151C2×SD1614yes—
199C2×C4×C151C2×SD1612yes—
200C2×C4×C151#13712yes—
201C2×C4×C151C22×D411yescharacteristic
202C2×C4×C151C2×#4111yescharacteristic
203C2×C4×C151C2×#4111yescharacteristic
204C2×C4×C151C2×#4111yescharacteristic
205C2×C4×C1512−1+411yescharacteristic
206C2×C4×C1512−1+411yescharacteristic
207C8×C151—22no—
208C8×C151—42no—
209C8×C151—41no—
210C22×C151—42no—
211C22×C151—42no—
212C22×C151—42no—
213C22×C151—81no—
214C22×C151—81no—
215C22×C151—81no—
216C22×C151—81no—
217C22×C151C2×#12111yescharacteristic
218C22×C151#54711yescharacteristic
219C22×C151#54811yescharacteristic
220C22×C151C22×SD1611yescharacteristic
221C22×C151C2×#13711yescharacteristic
222C22×C151#57611yescharacteristic
223C22×C151#57711yescharacteristic
224C4×C151—24no—
225C4×C151—22no—
226C4×C151—42no—
227C4×C151—42no—
228C4×C151—42no—
229C4×C151—82no—
230C4×C151—81no—
231C4×C151—82no—
232C4×C151#46114yes—
233C4×C151#52511yescharacteristic
234C4×C151#53611yescharacteristic
235C4×C151#55211yescharacteristic
236C4×C151#55611yescharacteristic
237C2×C151—82no—
238C2×C151#241511yescharacteristic
239C2×C151C2×#46111yescharacteristic
240C2×C151#304511yescharacteristic
241C2×C151#333511yescharacteristic
242C2×C151#335711yescharacteristic
243C2×C151#336211yescharacteristic
244C2×C151#336911yescharacteristic
245#24680C15111yesmaximal, characteristic, direct product factor, Sylow
246C151#2468011yescharacteristic, direct product factor, Sylow
247C2×#476C2×C15111yescharacteristic
248C2×C4×SD16C2×C15111yescharacteristic
249#2567C2×C15111yescharacteristic, complemented
250#2354C2×C15111yescharacteristic
251#2071C2×C15112yes—
252#2055C2×C15112yes—
253#1990C2×C15111yescharacteristic, complemented
254#1948C2×C15112yescomplemented
255#1939C2×C15111yescharacteristic, complemented
256#1927C2×C15112yescomplemented
257#1803C2×C15111yescharacteristic, complemented
258C22×SD16C22×C15111yescharacteristic
259C2×C4⋊Q8C22×C15111yescharacteristic
260C2×C4×Q8C22×C15111yescharacteristic
261C2×C4×D4C22×C15111yescharacteristic
262C2×#117—21no—
263#476—24no—
264C4×SD16—24no—
265C2×#106C22×C15111yescharacteristic
266C2×#106C22×C15112yes—
267C2×C4⋊C8C22×C15112yes—
268C2×C4⋊C8C22×C15111yescharacteristic
269C2×#103C22×C15112yes—
270C2×#103C22×C15111yescharacteristic
271C2×#102C22×C15112yes—
272C2×#102C22×C15111yescharacteristic
273C2×C4×C8C22×C15111yescharacteristic
274#395—22no—
275#391C22×C15112yes—
276#390C22×C15112yes—
277#389—21no—
278#389—21no—
279#388—22no—
280#384C22×C15112yes—
281#384C22×C15111yescharacteristic
282#380—21no—
283C4×C4⋊C4C22×C15112yes—
284C4×C4⋊C4C22×C15111yescharacteristic
285#340C22×C15112yes—
286#340C22×C15112yes—
287#340C22×C15112yes—
288#336C22×C15112yes—
289C22×Q8—21no—
290C22×Q8C23×C15111yescharacteristic
291C22×D4C23×C15111yescharacteristic
292C23×C4—21no—
293C2×SD16—22no—
294C2×SD16—22no—
295C2×SD16—22no—
296C22×C8C23×C15111yescharacteristic
297C22×C8C23×C15112yes—
298C22×C8C23×C15111yescharacteristic
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×D4—22no—
304C4×D4D4×C15114yes—
305#117—44no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4D4×C15111yescharacteristic
313C2×C4⋊C4D4×C15111yescharacteristic
314C2×C4⋊C4C23×C15111yescharacteristic
315C2×C4⋊C4C23×C15112yes—
316C2×C4⋊C4C23×C15112yes—
317C2×C4⋊C4C23×C15111yescharacteristic
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C42—22no—
322C2×C42—21no—
323C2×C42C23×C15112yes—
324C2×C42C23×C15111yescharacteristic
325#106—22no—
326#106—24no—
327C4⋊C8—24no—
328C4⋊C8—22no—
329#103—24no—
330#103—22no—
331#102—22no—
332#102—24no—
333C4×C8—22no—
334#95—22no—
335#95—22no—
336#95—22no—
337#95D4×C15112yes—
338C24—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—42no—
345C2×Q8—81no—
346C2×Q8—81no—
347C2×Q8#41×C15112yes—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4C2×D4×C15112yes—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4C2×D4×C15112yes—
363C22×C4C2×D4×C15111yescharacteristic
364C22×C4C2×D4×C15112yes—
365C22×C4C2×D4×C15111yescharacteristic
366C22×C4C24×C15111yescharacteristic
367SD16—28no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8#41×C15112yes—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—81no—
389C4⋊C4—82no—
390C4⋊C4—82no—
391C4⋊C4SD16×C15114yescomplemented
392C4⋊C4C2×D4×C15112yes—
393C22⋊C4—24no—
394C22⋊C4—44no—
395C22⋊C4—82no—
396C42—22no—
397C42—22no—
398C42—42no—
399C42—44no—
400C42C2×D4×C15112yes—
401C42#41×C15112yes—
402C23—22no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23C22×D4×C15111yescharacteristic
410Q8—22no—
411Q8—22no—
412Q8—41no—
413Q8—41no—
414Q8—84no—
415D4—22no—
416D4—22no—
417D4—41no—
418D4—41no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—48no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4#121×C15112yes—
443C2×C4#121×C15112yes—
444C2×C4C2×SD16×C15114yes—
445C2×C4C2×SD16×C15112yes—
446C2×C4#137×C15112yes—
447C2×C4C22×D4×C15111yescharacteristic
448C2×C4C2×#41×C15111yescharacteristic
449C2×C4C2×#41×C15111yescharacteristic
450C2×C4C2×#41×C15111yescharacteristic
451C2×C42−1+4×C15111yescharacteristic
452C2×C42−1+4×C15111yescharacteristic
453C8—22no—
454C8—42no—
455C8—41no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22C2×#121×C15111yescharacteristic
464C22#547×C15111yescharacteristic
465C22#548×C15111yescharacteristic
466C22C22×SD16×C15111yescharacteristic
467C22C2×#137×C15111yescharacteristic
468C22#576×C15111yescharacteristic
469C22#577×C15111yescharacteristic
470C4—22no—
471C4—24no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4—82no—
477C4—81no—
478C4#461×C15114yes—
479C4#525×C15111yescharacteristic
480C4#536×C15111yescharacteristic
481C4#552×C15111yescharacteristic
482C4#556×C15111yescharacteristic
483C2—82no—
484C2#2415×C15111yescharacteristic
485C2C2×#461×C15111yescharacteristic
486C2#3045×C15111yescharacteristic
487C2#3335×C15111yescharacteristic
488C2#3357×C15111yescharacteristic
489C2#3362×C15111yescharacteristic
490C2#3369×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. #2567×C151C2semidirect
7. #1990×C151C2semidirect
8. #1948×C151C2semidirect
9. #1939×C151C2semidirect
10. #1927×C151C2semidirect
11. #1803×C151C2semidirect
145. C4⋊C4×C151SD16semidirect
245. #24680C151direct (N × H)
246. C151#24680direct (N × H)
249. #2567C2×C151semidirect
253. #1990C2×C151semidirect
254. #1948C2×C151semidirect
255. #1939C2×C151semidirect
256. #1927C2×C151semidirect
257. #1803C2×C151semidirect
391. C4⋊C4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1512
C2×C4×SD16×C1512
#2567×C1512
#2354×C1512
#2071×C1512
#2055×C1512
#1990×C1512
#1948×C1512
#1939×C1512
#1927×C1512
#1803×C1512
#24680151