Finite Group Databasebeta

← C151×#18729 #50323654

Subgroups — C151×#18729 #50323654

Order 38656.

940 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3550×C151C211yesmaximal, characteristic, complemented
2#3208×C151C211yesmaximal, characteristic, complemented
3#3205×C151C211yesmaximal, characteristic
4#3138×C151C211yesmaximal, characteristic, complemented
5#1628×C151C214yesmaximal, complemented
6#1627×C151C214yesmaximal, complemented
7#1544×C151C211yesmaximal, characteristic, complemented
8#1485×C151C211yesmaximal, characteristic, complemented
9#1484×C151C211yesmaximal, characteristic, complemented
10#563×C151—22no—
11#559×C151—21no—
12Q82×C151—21no—
13#556×C151—21no—
14#556×C151C2212yescomplemented
15D4×Q8×C151—21no—
16D4×Q8×C151C2212yescomplemented
17#542×C151—22no—
18#542×C151—22no—
19#536×C151—22no—
20#533×C151C2211yescharacteristic
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23C2×#127×C151C2211yescharacteristic
24#493×C151—21no—
25#492×C151—21no—
26#490×C151—22no—
27#486×C151—21no—
28#486×C151—21no—
29#486×C151C2212yes—
30#486×C151C2212yes—
31#460×C151C2214yes—
32#459×C151C2214yes—
33#450×C151—22no—
34#447×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#418×C151—22no—
38C4×M16×C151C2211yescharacteristic
39#332×C151C2212yescomplemented
40#332×C151C2212yescomplemented
41Q8⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yescomplemented
43C2×#41×C151—21no—
44C22×Q8×C151—22no—
45C22×D4×C151—21no—
46C22×D4×C151—21no—
47C22×D4×C151—21no—
48C2×SD16×C151—24no—
49C2×D8×C151—24no—
50C2×M16×C151—21no—
51C4⋊Q8×C151—24no—
52C4⋊Q8×C151—22no—
53C4⋊Q8×C151—22no—
54C4⋊Q8×C151D411yescharacteristic
55C4⋊Q8×C151D411yescharacteristic
56C4⋊Q8×C151D411yescharacteristic
57C4⋊Q8×C151C2311yescharacteristic
58C4⋊Q8×C151C2311yescharacteristic
59#127×C151—21no—
60#127×C151—21no—
61#127×C151—21no—
62#127×C151D411yescharacteristic
63#127×C151C2312yes—
64#126×C151—24no—
65#126×C151—24no—
66#125×C151—21no—
67#125×C151D412yes—
68#124×C151—24no—
69#124×C151—22no—
70#124×C151—22no—
71#124×C151—21no—
72#123×C151—24no—
73#123×C151—24no—
74C22⋊Q8×C151—24no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151—21no—
77C22⋊Q8×C151—21no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151—24no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151D412yes—
82#121×C151—21no—
83#121×C151D412yes—
84C4×Q8×C151—22no—
85C4×Q8×C151—22no—
86C4×Q8×C151—21no—
87C4×Q8×C151—21no—
88C4×Q8×C151—21no—
89C4×Q8×C151C2312yes—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—21no—
93C4×D4×C151C2312yes—
94#117×C151—21no—
95#117×C151—22no—
96#117×C151D412yes—
97C2×C42×C151C2311yescharacteristic
98C4⋊C8×C151C2312yes—
99C4⋊C8×C151C2312yes—
100#102×C151—24no—
101#102×C151—24no—
102#102×C151—24no—
103#102×C151—24no—
104C22⋊C8×C151—21no—
105C22⋊C8×C151—21no—
106#97×C151—21no—
107C4×C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110C24×C151—41no—
111#41×C151—82no—
112C2×Q8×C151—24no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—21no—
117C2×Q8×C151—84no—
118C2×Q8×C151C2×D412yes—
119C2×D4×C151—22no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—22no—
123C2×D4×C151—22no—
124C2×D4×C151—22no—
125C2×D4×C151—44no—
126C2×D4×C151—41no—
127C2×D4×C151—41no—
128C2×D4×C151—41no—
129C2×D4×C151—82no—
130C2×D4×C151—82no—
131C2×D4×C151C2×D412yes—
132C22×C4×C151—24no—
133C22×C4×C151—22no—
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137SD16×C151—84no—
138D8×C151—84no—
139M16×C151—42no—
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C4⋊C4×C151—24no—
144C4⋊C4×C151—24no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151C2×D412yes—
156C4⋊C4×C151C2×D412yes—
157C4⋊C4×C151C2×D412yes—
158C4⋊C4×C151C2×D412yes—
159C22⋊C4×C151—24no—
160C22⋊C4×C151—24no—
161C22⋊C4×C151—24no—
162C22⋊C4×C151—22no—
163C22⋊C4×C151—22no—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—22no—
166C42×C151—24no—
167C42×C151—22no—
168C42×C151—22no—
169C42×C151C2×D411yescharacteristic
170C42×C151C2×D411yescharacteristic
171C42×C151C2×D411yescharacteristic
172C42×C151C2411yescharacteristic
173C23×C151—22no—
174C23×C151—42no—
175C23×C151—82no—
176C23×C151—82no—
177C23×C151—82no—
178C23×C151#12011yescharacteristic
179Q8×C151—24no—
180Q8×C151—42no—
181Q8×C151—42no—
182Q8×C151—42no—
183Q8×C151—81no—
184Q8×C151—84no—
185D4×C151—24no—
186D4×C151—44no—
187D4×C151—44no—
188D4×C151—44no—
189D4×C151—42no—
190D4×C151—81no—
191D4×C151—82no—
192D4×C151—82no—
193D4×C151—82no—
194D4×C151—82no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—44no—
204C2×C4×C151—84no—
205C2×C4×C151#12011yescharacteristic
206C2×C4×C151#12011yescharacteristic
207C2×C4×C151#12011yescharacteristic
208C2×C4×C151C22×D411yescharacteristic
209C2×C4×C151C22×D411yescharacteristic
210C2×C4×C151C22×D411yescharacteristic
211C8×C151—42no—
212C8×C151—42no—
213C8×C151—42no—
214C22×C151—21no—
215C22×C151—21no—
216C22×C151—21no—
217C22×C151—42no—
218C22×C151—42no—
219C22×C151—42no—
220C22×C151—82no—
221C22×C151—82no—
222C22×C151—82no—
223C22×C151—164no—
224C22×C151C2×#12011yescharacteristic
225C4×C151—21no—
226C4×C151—21no—
227C4×C151—21no—
228C4×C151—42no—
229C4×C151—42no—
230C4×C151—42no—
231C4×C151—42no—
232C4×C151—42no—
233C4×C151#45412yes—
234C4×C151#57612yes—
235C4×C151#57712yes—
236C2×C151—41no—
237C2×C151—82no—
238C2×C151—162no—
239C2×C151#300811yescharacteristic
240C2×C151#301011yescharacteristic
241C2×C151C2×#45411yescharacteristic
242#18729C15111yesmaximal, characteristic, direct product factor, Sylow
243C151#1872911yescharacteristic, direct product factor, Sylow
244#3550C2×C15111yescharacteristic, complemented
245#3208C2×C15111yescharacteristic, complemented
246#3205C2×C15111yescharacteristic
247#3138C2×C15111yescharacteristic, complemented
248#1628C2×C15114yescomplemented
249#1627C2×C15114yescomplemented
250#1544C2×C15111yescharacteristic, complemented
251#1485C2×C15111yescharacteristic, complemented
252#1484C2×C15111yescharacteristic, complemented
253#563—22no—
254#559—21no—
255Q82—21no—
256#556—21no—
257#556C22×C15112yescomplemented
258D4×Q8—21no—
259D4×Q8C22×C15112yescomplemented
260#542—22no—
261#542—22no—
262#536—22no—
263#533C22×C15111yescharacteristic
264#533C22×C15111yescharacteristic
265#532C22×C15111yescharacteristic
266C2×#127C22×C15111yescharacteristic
267#493—21no—
268#492—21no—
269#490—22no—
270#486—21no—
271#486—21no—
272#486C22×C15112yes—
273#486C22×C15112yes—
274#460C22×C15114yes—
275#459C22×C15114yes—
276#450—22no—
277#447—22no—
278#431C22×C15111yescharacteristic
279#431C22×C15111yescharacteristic
280#418—22no—
281C4×M16C22×C15111yescharacteristic
282#332C22×C15112yescomplemented
283#332C22×C15112yescomplemented
284Q8⋊C8C22×C15114yescomplemented
285D4⋊C8C22×C15114yescomplemented
286C2×#41—21no—
287C22×Q8—22no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C2×SD16—24no—
292C2×D8—24no—
293C2×M16—21no—
294C4⋊Q8—24no—
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297C4⋊Q8D4×C15111yescharacteristic
298C4⋊Q8D4×C15111yescharacteristic
299C4⋊Q8D4×C15111yescharacteristic
300C4⋊Q8C23×C15111yescharacteristic
301C4⋊Q8C23×C15111yescharacteristic
302#127—21no—
303#127—21no—
304#127—21no—
305#127D4×C15111yescharacteristic
306#127C23×C15112yes—
307#126—24no—
308#126—24no—
309#125—21no—
310#125D4×C15112yes—
311#124—24no—
312#124—22no—
313#124—22no—
314#124—21no—
315#123—24no—
316#123—24no—
317C22⋊Q8—24no—
318C22⋊Q8—22no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—22no—
323C22⋊Q8—24no—
324C22⋊Q8D4×C15112yes—
325#121—21no—
326#121D4×C15112yes—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8C23×C15112yes—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—21no—
336C4×D4C23×C15112yes—
337#117—21no—
338#117—22no—
339#117D4×C15112yes—
340C2×C42C23×C15111yescharacteristic
341C4⋊C8C23×C15112yes—
342C4⋊C8C23×C15112yes—
343#102—24no—
344#102—24no—
345#102—24no—
346#102—24no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349#97—21no—
350C4×C8—21no—
351C4×C8—21no—
352C4×C8C23×C15112yes—
353C24—41no—
354#41—82no—
355C2×Q8—24no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—84no—
361C2×Q8C2×D4×C15112yes—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—44no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—82no—
373C2×D4—82no—
374C2×D4C2×D4×C15112yes—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4C2×D4×C15111yescharacteristic
378C22×C4C2×D4×C15111yescharacteristic
379C22×C4C2×D4×C15111yescharacteristic
380SD16—84no—
381D8—84no—
382M16—42no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4C2×D4×C15112yes—
399C4⋊C4C2×D4×C15112yes—
400C4⋊C4C2×D4×C15112yes—
401C4⋊C4C2×D4×C15112yes—
402C22⋊C4—24no—
403C22⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C42—24no—
410C42—22no—
411C42—22no—
412C42C2×D4×C15111yescharacteristic
413C42C2×D4×C15111yescharacteristic
414C42C2×D4×C15111yescharacteristic
415C42C24×C15111yescharacteristic
416C23—22no—
417C23—42no—
418C23—82no—
419C23—82no—
420C23—82no—
421C23#120×C15111yescharacteristic
422Q8—24no—
423Q8—42no—
424Q8—42no—
425Q8—42no—
426Q8—81no—
427Q8—84no—
428D4—24no—
429D4—44no—
430D4—42no—
431D4—44no—
432D4—44no—
433D4—81no—
434D4—82no—
435D4—82no—
436D4—82no—
437D4—82no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—44no—
447C2×C4—84no—
448C2×C4#120×C15111yescharacteristic
449C2×C4#120×C15111yescharacteristic
450C2×C4#120×C15111yescharacteristic
451C2×C4C22×D4×C15111yescharacteristic
452C2×C4C22×D4×C15111yescharacteristic
453C2×C4C22×D4×C15111yescharacteristic
454C8—42no—
455C8—42no—
456C8—42no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—82no—
464C22—82no—
465C22—82no—
466C22—164no—
467C22C2×#120×C15111yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—42no—
476C4#454×C15112yes—
477C4#576×C15112yes—
478C4#577×C15112yes—
479C2—41no—
480C2—82no—
481C2—162no—
482C2#3008×C15111yescharacteristic
483C2#3010×C15111yescharacteristic
484C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3205×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3550×C151C2semidirect
2. #3208×C151C2semidirect
4. #3138×C151C2semidirect
5. #1628×C151C2semidirect
6. #1627×C151C2semidirect
7. #1544×C151C2semidirect
8. #1485×C151C2semidirect
9. #1484×C151C2semidirect
14. #556×C151C22semidirect
16. D4×Q8×C151C22semidirect
39. #332×C151C22semidirect
40. #332×C151C22semidirect
41. Q8⋊C8×C151C22semidirect
42. D4⋊C8×C151C22semidirect
242. #18729C151direct (N × H)
243. C151#18729direct (N × H)
244. #3550C2×C151semidirect
245. #3208C2×C151semidirect
247. #3138C2×C151semidirect
248. #1628C2×C151semidirect
249. #1627C2×C151semidirect
250. #1544C2×C151semidirect
251. #1485C2×C151semidirect
252. #1484C2×C151semidirect
257. #556C22×C151semidirect
259. D4×Q8C22×C151semidirect
282. #332C22×C151semidirect
283. #332C22×C151semidirect
284. Q8⋊C8C22×C151semidirect
285. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3550×C1512
#3208×C1512
#3205×C1512
#3138×C1512
#1628×C1512
#1627×C1512
#1544×C1512
#1485×C1512
#1484×C1512
#18729151