Finite Group Databasebeta

← C151×#18783 #50323708

Subgroups — C151×#18783 #50323708

Order 38656.

1170 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C151C211yesmaximal, characteristic
2#3230×C151C211yesmaximal, characteristic, complemented
3#3101×C151C211yesmaximal, characteristic, complemented
4#3077×C151C211yesmaximal, characteristic, complemented
5#1647×C151C214yesmaximal, complemented
6#1635×C151C214yesmaximal, complemented
7#1549×C151C211yesmaximal, characteristic, complemented
8#1486×C151C211yesmaximal, characteristic, complemented
9#1478×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151—21no—
11#547×C151—22no—
12#547×C151—22no—
13#547×C151—22no—
14#547×C151C2214yes—
15#533×C151C2211yescharacteristic
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#123×C151—22no—
18C2×C22⋊Q8×C151—21no—
19C2×#121×C151—21no—
20C2×C4×D4×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C22×C4⋊C4×C151—21no—
23#500×C151C2212yescomplemented
24#487×C151C2212yescomplemented
25#484×C151—22no—
26#483×C151—21no—
27#478×C151—22no—
28#477×C151—22no—
29#476×C151C2212yescomplemented
30#476×C151C2212yescomplemented
31#474×C151C2212yescomplemented
32#461×C151C2212yescomplemented
33#450×C151—21no—
34C4×SD16×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#428×C151—21no—
38#423×C151C2211yescharacteristic
39#418×C151—21no—
40#332×C151C2214yescomplemented
41D4⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yescomplemented
43C2×#41×C151—24no—
44C2×#41×C151—24no—
45C2×#41×C151—48no—
46C22×Q8×C151—21no—
47C22×D4×C151—22no—
48C22×D4×C151D411yescharacteristic
49C22×D4×C151D411yescharacteristic
50C23×C4×C151—22no—
51C23×C4×C151—21no—
52C23×C4×C151—21no—
53C2×SD16×C151—22no—
54C2×M16×C151—21no—
55C4⋊Q8×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151D412yes—
58C4⋊Q8×C151C2311yescharacteristic
59C4⋊Q8×C151C2311yescharacteristic
60C4⋊Q8×C151C2312yes—
61#125×C151—21no—
62#123×C151—28no—
63#123×C151—28no—
64C22⋊Q8×C151—24no—
65C22⋊Q8×C151—24no—
66C22⋊Q8×C151—21no—
67C22⋊Q8×C151—21no—
68#121×C151—24no—
69#121×C151—24no—
70C4×Q8×C151—21no—
71C4×Q8×C151—21no—
72C4×D4×C151—21no—
73C4×D4×C151—21no—
74C4×D4×C151—21no—
75C4×D4×C151—21no—
76C4×D4×C151D412yes—
77C4×D4×C151D412yes—
78C4×D4×C151C2312yes—
79C4×D4×C151C2312yes—
80#117×C151—21no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—24no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—24no—
85C2×C4⋊C4×C151D411yescharacteristic
86C2×C4⋊C4×C151D411yescharacteristic
87C2×C4⋊C4×C151D412yes—
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151—21no—
91C2×C42×C151C2311yescharacteristic
92#107×C151—22no—
93#107×C151—24no—
94#106×C151—22no—
95#106×C151—22no—
96C4⋊C8×C151—21no—
97C4⋊C8×C151—21no—
98C4⋊C8×C151C2312yes—
99C4⋊C8×C151C2312yes—
100#103×C151—22no—
101#103×C151—24no—
102#102×C151—22no—
103#102×C151—22no—
104#102×C151—22no—
105C22⋊C8×C151—21no—
106C22⋊C8×C151—21no—
107C4×C8×C151—21no—
108C4×C8×C151C2312yes—
109C24×C151—21no—
110C24×C151—21no—
111#41×C151—416no—
112#41×C151—48no—
113#41×C151—48no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—21no—
117C2×Q8×C151—21no—
118C2×Q8×C151—44no—
119C2×D4×C151—24no—
120C2×D4×C151—28no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—22no—
124C2×D4×C151—22no—
125C2×D4×C151—48no—
126C2×D4×C151C2×D412yes—
127C2×D4×C151C2×D412yes—
128C22×C4×C151—28no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—44no—
137C22×C4×C151—48no—
138C22×C4×C151—42no—
139C22×C4×C151—42no—
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143SD16×C151—44no—
144M16×C151—42no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C4⋊C4×C151—28no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—41no—
159C4⋊C4×C151—41no—
160C4⋊C4×C151C2×D412yes—
161C4⋊C4×C151C2×D414yes—
162C4⋊C4×C151C2×D412yes—
163C22⋊C4×C151—28no—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—22no—
166C22⋊C4×C151—22no—
167C22⋊C4×C151—22no—
168C22⋊C4×C151—41no—
169C42×C151—41no—
170C42×C151C2×D411yescharacteristic
171C42×C151C2×D411yescharacteristic
172C42×C151C2×D411yescharacteristic
173C42×C151C2411yescharacteristic
174C23×C151—24no—
175C23×C151—22no—
176C23×C151—22no—
177C23×C151—42no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151#12011yescharacteristic
183Q8×C151—44no—
184Q8×C151—42no—
185Q8×C151—44no—
186Q8×C151—42no—
187D4×C151—24no—
188D4×C151—22no—
189D4×C151—22no—
190D4×C151—22no—
191D4×C151—416no—
192D4×C151—42no—
193D4×C151AGL(1,ℤ/8)14yes—
194C2×C4×C151—22no—
195C2×C4×C151—24no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—41no—
199C2×C4×C151—44no—
200C2×C4×C151—44no—
201C2×C4×C151—416no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—44no—
206C2×C4×C151—42no—
207C2×C4×C151—44no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151#12011yescharacteristic
211C2×C4×C151#12011yescharacteristic
212C2×C4×C151#12011yescharacteristic
213C2×C4×C151#13512yes—
214C2×C4×C151#13712yes—
215C2×C4×C151C22×D411yescharacteristic
216C2×C4×C151C22×D411yescharacteristic
217C2×C4×C151C22×D411yescharacteristic
218C8×C151—42no—
219C8×C151—42no—
220C8×C151—42no—
221C22×C151—21no—
222C22×C151—21no—
223C22×C151—24no—
224C22×C151—48no—
225C22×C151—42no—
226C22×C151—42no—
227C22×C151—42no—
228C22×C151—42no—
229C22×C151—42no—
230C22×C151—84no—
231C22×C151#45212yes—
232C22×C151C2×#12011yescharacteristic
233C4×C151—21no—
234C4×C151—21no—
235C4×C151—21no—
236C4×C151—42no—
237C4×C151—42no—
238C4×C151—44no—
239C4×C151—81no—
240C4×C151—81no—
241C4×C151#45212yes—
242C4×C151C2×#13511yescharacteristic
243C4×C151C2×AGL(1,ℤ/8)12yes—
244C4×C151C2×#13711yescharacteristic
245C2×C151—22no—
246C2×C151—44no—
247C2×C151—82no—
248C2×C151C2×#45211yescharacteristic
249C2×C151#300311yescharacteristic
250C2×C151#302011yescharacteristic
251#18783C15111yesmaximal, characteristic, direct product factor, Sylow
252C151#1878311yescharacteristic, direct product factor, Sylow
253C2×#547C2×C15111yescharacteristic
254#3230C2×C15111yescharacteristic, complemented
255#3101C2×C15111yescharacteristic, complemented
256#3077C2×C15111yescharacteristic, complemented
257#1647C2×C15114yescomplemented
258#1635C2×C15114yescomplemented
259#1549C2×C15111yescharacteristic, complemented
260#1486C2×C15111yescharacteristic, complemented
261#1478C2×C15111yescharacteristic, complemented
262C22×#41—21no—
263#547—22no—
264#547—22no—
265#547—22no—
266#547C22×C15114yes—
267#533C22×C15111yescharacteristic
268C2×C4⋊Q8C22×C15111yescharacteristic
269C2×#123—22no—
270C2×C22⋊Q8—21no—
271C2×#121—21no—
272C2×C4×D4C22×C15111yescharacteristic
273C2×C4×D4C22×C15111yescharacteristic
274C22×C4⋊C4—21no—
275#500C22×C15112yescomplemented
276#487C22×C15112yescomplemented
277#484—22no—
278#483—21no—
279#478—22no—
280#477—22no—
281#476C22×C15112yescomplemented
282#476C22×C15112yescomplemented
283#474C22×C15112yescomplemented
284#461C22×C15112yescomplemented
285#450—21no—
286C4×SD16—22no—
287#431C22×C15111yescharacteristic
288#431C22×C15111yescharacteristic
289#428—21no—
290#423C22×C15111yescharacteristic
291#418—21no—
292#332C22×C15114yescomplemented
293D4⋊C8C22×C15114yescomplemented
294D4⋊C8C22×C15114yescomplemented
295C2×#41—24no—
296C2×#41—24no—
297C2×#41—48no—
298C22×Q8—21no—
299C22×D4—22no—
300C22×D4D4×C15111yescharacteristic
301C22×D4D4×C15111yescharacteristic
302C23×C4—22no—
303C23×C4—21no—
304C23×C4—21no—
305C2×SD16—22no—
306C2×M16—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8D4×C15112yes—
310C4⋊Q8C23×C15111yescharacteristic
311C4⋊Q8C23×C15111yescharacteristic
312C4⋊Q8C23×C15112yes—
313#125—21no—
314#123—28no—
315#123—28no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320#121—24no—
321#121—24no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4D4×C15112yes—
329C4×D4D4×C15112yes—
330C4×D4C23×C15112yes—
331C4×D4C23×C15112yes—
332#117—21no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4D4×C15111yescharacteristic
338C2×C4⋊C4D4×C15111yescharacteristic
339C2×C4⋊C4D4×C15112yes—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C42C23×C15111yescharacteristic
344#107—22no—
345#107—24no—
346#106—22no—
347#106—22no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8C23×C15112yes—
351C4⋊C8C23×C15112yes—
352#103—22no—
353#103—24no—
354#102—22no—
355#102—22no—
356#102—22no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C4×C8—21no—
360C4×C8C23×C15112yes—
361C24—21no—
362C24—21no—
363#41—416no—
364#41—48no—
365#41—48no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—44no—
371C2×D4—24no—
372C2×D4—28no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—48no—
378C2×D4C2×D4×C15112yes—
379C2×D4C2×D4×C15112yes—
380C22×C4—28no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—44no—
389C22×C4—48no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4C2×D4×C15111yescharacteristic
393C22×C4C2×D4×C15111yescharacteristic
394C22×C4C2×D4×C15111yescharacteristic
395SD16—44no—
396M16—42no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C4⋊C4—28no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4C2×D4×C15112yes—
413C4⋊C4C2×D4×C15114yes—
414C4⋊C4C2×D4×C15112yes—
415C22⋊C4—28no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—41no—
421C42—41no—
422C42C2×D4×C15111yescharacteristic
423C42C2×D4×C15111yescharacteristic
424C42C2×D4×C15111yescharacteristic
425C42C24×C15111yescharacteristic
426C23—24no—
427C23—22no—
428C23—22no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23#120×C15111yescharacteristic
435Q8—44no—
436Q8—42no—
437Q8—44no—
438Q8—42no—
439D4—24no—
440D4—22no—
441D4—22no—
442D4—22no—
443D4—416no—
444D4—42no—
445D4AGL(1,ℤ/8)×C15114yes—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—41no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—416no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4#120×C15111yescharacteristic
463C2×C4#120×C15111yescharacteristic
464C2×C4#120×C15111yescharacteristic
465C2×C4#135×C15112yes—
466C2×C4#137×C15112yes—
467C2×C4C22×D4×C15111yescharacteristic
468C2×C4C22×D4×C15111yescharacteristic
469C2×C4C22×D4×C15111yescharacteristic
470C8—42no—
471C8—42no—
472C8—42no—
473C22—21no—
474C22—21no—
475C22—24no—
476C22—48no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—84no—
483C22#452×C15112yes—
484C22C2×#120×C15111yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—42no—
490C4—44no—
491C4—81no—
492C4—81no—
493C4#452×C15112yes—
494C4C2×#135×C15111yescharacteristic
495C4C2×AGL(1,ℤ/8)×C15112yes—
496C4C2×#137×C15111yescharacteristic
497C2—22no—
498C2—44no—
499C2—82no—
500C2C2×#452×C15111yescharacteristic
501C2#3003×C15111yescharacteristic
502C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#547×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
2. #3230×C151C2semidirect
3. #3101×C151C2semidirect
4. #3077×C151C2semidirect
5. #1647×C151C2semidirect
6. #1635×C151C2semidirect
7. #1549×C151C2semidirect
8. #1486×C151C2semidirect
9. #1478×C151C2semidirect
23. #500×C151C22semidirect
24. #487×C151C22semidirect
29. #476×C151C22semidirect
30. #476×C151C22semidirect
31. #474×C151C22semidirect
32. #461×C151C22semidirect
40. #332×C151C22semidirect
41. D4⋊C8×C151C22semidirect
42. D4⋊C8×C151C22semidirect
251. #18783C151direct (N × H)
252. C151#18783direct (N × H)
254. #3230C2×C151semidirect
255. #3101C2×C151semidirect
256. #3077C2×C151semidirect
257. #1647C2×C151semidirect
258. #1635C2×C151semidirect
259. #1549C2×C151semidirect
260. #1486C2×C151semidirect
261. #1478C2×C151semidirect
275. #500C22×C151semidirect
276. #487C22×C151semidirect
281. #476C22×C151semidirect
282. #476C22×C151semidirect
283. #474C22×C151semidirect
284. #461C22×C151semidirect
292. #332C22×C151semidirect
293. D4⋊C8C22×C151semidirect
294. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1512
#3230×C1512
#3101×C1512
#3077×C1512
#1647×C1512
#1635×C1512
#1549×C1512
#1486×C1512
#1478×C1512
#18783151