Finite Group Databasebeta

← C151×#18539 #50323464

Subgroups — C151×#18539 #50323464

Order 38656.

1178 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C151C211yesmaximal, characteristic
2#3165×C151C211yesmaximal, characteristic, complemented
3#3110×C151C211yesmaximal, characteristic, complemented
4#3110×C151C211yesmaximal, characteristic, complemented
5#1654×C151C214yesmaximal, complemented
6#1647×C151C214yesmaximal, complemented
7#1556×C151C211yesmaximal, characteristic, complemented
8#1490×C151C211yesmaximal, characteristic, complemented
9#1490×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#501×C151—22no—
24#500×C151C2212yescomplemented
25#498×C151C2212yescomplemented
26#484×C151—21no—
27#484×C151—21no—
28#474×C151C2212yescomplemented
29#474×C151C2212yescomplemented
30#461×C151C2212yescomplemented
31#461×C151C2212yescomplemented
32#450×C151—21no—
33#450×C151—21no—
34#440×C151—22no—
35#440×C151—22no—
36#432×C151C2211yescharacteristic
37#432×C151C2211yescharacteristic
38#428×C151—22no—
39C4×M16×C151C2211yescharacteristic
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×SD16×C151—22no—
55C2×M16×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151D412yes—
59C4⋊Q8×C151C2311yescharacteristic
60C4⋊Q8×C151C2311yescharacteristic
61C4⋊Q8×C151C2312yes—
62#125×C151—21no—
63#123×C151—28no—
64#123×C151—28no—
65C22⋊Q8×C151—24no—
66C22⋊Q8×C151—24no—
67C22⋊Q8×C151—21no—
68C22⋊Q8×C151—21no—
69#121×C151—24no—
70#121×C151—24no—
71C4×Q8×C151—21no—
72C4×Q8×C151—21no—
73C4×D4×C151—21no—
74C4×D4×C151—21no—
75C4×D4×C151—21no—
76C4×D4×C151—21no—
77C4×D4×C151D412yes—
78C4×D4×C151D412yes—
79C4×D4×C151C2312yes—
80C4×D4×C151C2312yes—
81#117×C151—21no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—24no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—24no—
86C2×C4⋊C4×C151D412yes—
87C2×C4⋊C4×C151D411yescharacteristic
88C2×C4⋊C4×C151D411yescharacteristic
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C42×C151C2311yescharacteristic
93#107×C151—24no—
94#107×C151—22no—
95#107×C151—22no—
96#106×C151—24no—
97C4⋊C8×C151C2312yes—
98C4⋊C8×C151C2312yes—
99#103×C151—22no—
100#103×C151—22no—
101#102×C151—22no—
102#102×C151—22no—
103C22⋊C8×C151—21no—
104C22⋊C8×C151—21no—
105#97×C151—21no—
106#97×C151—21no—
107#97×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—42no—
124C2×D4×C151—48no—
125C2×D4×C151C2×D412yes—
126C2×D4×C151C2×D412yes—
127C22×C4×C151—28no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—44no—
136C22×C4×C151—44no—
137C22×C4×C151—48no—
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141SD16×C151—44no—
142SD16×C151—44no—
143M16×C151—24no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C4⋊C4×C151—28no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—41no—
158C4⋊C4×C151—41no—
159C4⋊C4×C151C2×D412yes—
160C4⋊C4×C151C2×D412yes—
161C4⋊C4×C151C2×D414yes—
162C22⋊C4×C151—28no—
163C22⋊C4×C151—22no—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—22no—
166C22⋊C4×C151—22no—
167C22⋊C4×C151—41no—
168C42×C151—41no—
169C42×C151C2×D411yescharacteristic
170C42×C151C2×D411yescharacteristic
171C42×C151C2×D411yescharacteristic
172C42×C151C2411yescharacteristic
173C23×C151—24no—
174C23×C151—22no—
175C23×C151—22no—
176C23×C151—42no—
177C23×C151—42no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151#12011yescharacteristic
182Q8×C151—44no—
183Q8×C151—44no—
184Q8×C151—42no—
185Q8×C151—42no—
186D4×C151—24no—
187D4×C151—22no—
188D4×C151—22no—
189D4×C151—22no—
190D4×C151—42no—
191D4×C151—416no—
192D4×C151AGL(1,ℤ/8)14yes—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—24no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—44no—
200C2×C4×C151—44no—
201C2×C4×C151—44no—
202C2×C4×C151—416no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—44no—
206C2×C4×C151—44no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151#12011yescharacteristic
210C2×C4×C151#12011yescharacteristic
211C2×C4×C151#12011yescharacteristic
212C2×C4×C151C22×D411yescharacteristic
213C2×C4×C151C22×D411yescharacteristic
214C2×C4×C151C22×D411yescharacteristic
215C8×C151—24no—
216C8×C151—42no—
217C8×C151—42no—
218C22×C151—21no—
219C22×C151—21no—
220C22×C151—24no—
221C22×C151—48no—
222C22×C151—42no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—42no—
226C22×C151—42no—
227C22×C151—84no—
228C22×C151#45612yes—
229C22×C151C2×#12011yescharacteristic
230C4×C151—21no—
231C4×C151—21no—
232C4×C151—21no—
233C4×C151—21no—
234C4×C151—42no—
235C4×C151—44no—
236C4×C151—42no—
237C4×C151—81no—
238C4×C151—81no—
239C4×C151C2×AGL(1,ℤ/8)12yes—
240C4×C151#57512yes—
241C2×C151—22no—
242C2×C151—44no—
243C2×C151—82no—
244C2×C151#300311yescharacteristic
245C2×C151#300511yescharacteristic
246C2×C151C2×#45611yescharacteristic
247#18539C15111yesmaximal, characteristic, direct product factor, Sylow
248C151#1853911yescharacteristic, direct product factor, Sylow
249C2×#547C2×C15111yescharacteristic
250#3165C2×C15111yescharacteristic, complemented
251#3110C2×C15111yescharacteristic, complemented
252#3110C2×C15111yescharacteristic, complemented
253#1654C2×C15114yescomplemented
254#1647C2×C15114yescomplemented
255#1556C2×C15111yescharacteristic, complemented
256#1490C2×C15111yescharacteristic, complemented
257#1490C2×C15111yescharacteristic, complemented
258C22×#41—21no—
259#547—22no—
260#547—22no—
261#547—22no—
262#547C22×C15114yes—
263#533C22×C15111yescharacteristic
264C2×C4⋊Q8C22×C15111yescharacteristic
265C2×#123—22no—
266C2×C22⋊Q8—21no—
267C2×#121—21no—
268C2×C4×D4C22×C15111yescharacteristic
269C2×C4×D4C22×C15111yescharacteristic
270C22×C4⋊C4—21no—
271#501—22no—
272#500C22×C15112yescomplemented
273#498C22×C15112yescomplemented
274#484—21no—
275#484—21no—
276#474C22×C15112yescomplemented
277#474C22×C15112yescomplemented
278#461C22×C15112yescomplemented
279#461C22×C15112yescomplemented
280#450—21no—
281#450—21no—
282#440—22no—
283#440—22no—
284#432C22×C15111yescharacteristic
285#432C22×C15111yescharacteristic
286#428—22no—
287C4×M16C22×C15111yescharacteristic
288#332C22×C15114yescomplemented
289D4⋊C8C22×C15114yescomplemented
290D4⋊C8C22×C15114yescomplemented
291C2×#41—24no—
292C2×#41—24no—
293C2×#41—48no—
294C22×Q8—21no—
295C22×D4—22no—
296C22×D4D4×C15111yescharacteristic
297C22×D4D4×C15111yescharacteristic
298C23×C4—22no—
299C23×C4—21no—
300C23×C4—21no—
301C2×SD16—22no—
302C2×SD16—22no—
303C2×M16—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8D4×C15112yes—
307C4⋊Q8C23×C15111yescharacteristic
308C4⋊Q8C23×C15111yescharacteristic
309C4⋊Q8C23×C15112yes—
310#125—21no—
311#123—28no—
312#123—28no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317#121—24no—
318#121—24no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4D4×C15112yes—
326C4×D4D4×C15112yes—
327C4×D4C23×C15112yes—
328C4×D4C23×C15112yes—
329#117—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4D4×C15111yescharacteristic
335C2×C4⋊C4D4×C15111yescharacteristic
336C2×C4⋊C4D4×C15112yes—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C42C23×C15111yescharacteristic
341#107—24no—
342#107—22no—
343#107—22no—
344#106—24no—
345C4⋊C8C23×C15112yes—
346C4⋊C8C23×C15112yes—
347#103—22no—
348#103—22no—
349#102—22no—
350#102—22no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353#97—21no—
354#97—21no—
355#97—21no—
356C4×C8C23×C15112yes—
357C24—21no—
358C24—21no—
359#41—416no—
360#41—48no—
361#41—48no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—44no—
367C2×D4—24no—
368C2×D4—28no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—42no—
372C2×D4—48no—
373C2×D4C2×D4×C15112yes—
374C2×D4C2×D4×C15112yes—
375C22×C4—28no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4—48no—
386C22×C4C2×D4×C15111yescharacteristic
387C22×C4C2×D4×C15111yescharacteristic
388C22×C4C2×D4×C15111yescharacteristic
389SD16—44no—
390SD16—44no—
391M16—24no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C4⋊C4—28no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4C2×D4×C15112yes—
408C4⋊C4C2×D4×C15112yes—
409C4⋊C4C2×D4×C15114yes—
410C22⋊C4—28no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—41no—
416C42—41no—
417C42C2×D4×C15111yescharacteristic
418C42C2×D4×C15111yescharacteristic
419C42C2×D4×C15111yescharacteristic
420C42C24×C15111yescharacteristic
421C23—24no—
422C23—22no—
423C23—22no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23#120×C15111yescharacteristic
430Q8—44no—
431Q8—44no—
432Q8—42no—
433Q8—42no—
434D4—24no—
435D4—22no—
436D4—22no—
437D4—22no—
438D4—42no—
439D4—416no—
440D4AGL(1,ℤ/8)×C15114yes—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—416no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4#120×C15111yescharacteristic
458C2×C4#120×C15111yescharacteristic
459C2×C4#120×C15111yescharacteristic
460C2×C4C22×D4×C15111yescharacteristic
461C2×C4C22×D4×C15111yescharacteristic
462C2×C4C22×D4×C15111yescharacteristic
463C8—24no—
464C8—42no—
465C8—42no—
466C22—21no—
467C22—21no—
468C22—24no—
469C22—48no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—84no—
476C22#456×C15112yes—
477C22C2×#120×C15111yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—44no—
484C4—42no—
485C4—81no—
486C4—81no—
487C4C2×AGL(1,ℤ/8)×C15112yes—
488C4#575×C15112yes—
489C2—22no—
490C2—44no—
491C2—82no—
492C2#3003×C15111yescharacteristic
493C2#3005×C15111yescharacteristic
494C2C2×#456×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. #3165×C151C2semidirect
3. #3110×C151C2semidirect
4. #3110×C151C2semidirect
5. #1654×C151C2semidirect
6. #1647×C151C2semidirect
7. #1556×C151C2semidirect
8. #1490×C151C2semidirect
9. #1490×C151C2semidirect
24. #500×C151C22semidirect
25. #498×C151C22semidirect
28. #474×C151C22semidirect
29. #474×C151C22semidirect
30. #461×C151C22semidirect
31. #461×C151C22semidirect
40. #332×C151C22semidirect
41. D4⋊C8×C151C22semidirect
42. D4⋊C8×C151C22semidirect
247. #18539C151direct (N × H)
248. C151#18539direct (N × H)
250. #3165C2×C151semidirect
251. #3110C2×C151semidirect
252. #3110C2×C151semidirect
253. #1654C2×C151semidirect
254. #1647C2×C151semidirect
255. #1556C2×C151semidirect
256. #1490C2×C151semidirect
257. #1490C2×C151semidirect
272. #500C22×C151semidirect
273. #498C22×C151semidirect
276. #474C22×C151semidirect
277. #474C22×C151semidirect
278. #461C22×C151semidirect
279. #461C22×C151semidirect
288. #332C22×C151semidirect
289. D4⋊C8C22×C151semidirect
290. 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
#3165×C1512
#3110×C1512
#1654×C1512
#1647×C1512
#1556×C1512
#1490×C1512
#18539151