Finite Group Databasebeta

← C151×#18203 #50323128

Subgroups — C151×#18203 #50323128

Order 38656.

1262 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3496×C151C211yesmaximal, characteristic
2C2×#481×C151C212yesmaximal, complemented
3#2487×C151C211yesmaximal, characteristic, complemented
4#1616×C151C214yesmaximal, complemented
5#1613×C151C214yesmaximal, complemented
6#1519×C151C212yesmaximal, complemented
7#1459×C151C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C151—21no—
9#547×C151—22no—
10#546×C151—24no—
11D42×C151—22no—
12#537×C151C2212yes—
13#534×C151—21no—
14#534×C151C2212yes—
15#532×C151—21no—
16C2×#121×C151—21no—
17C2×#121×C151C2212yes—
18C2×C4×D4×C151C2211yescharacteristic
19C22×C4⋊C4×C151C2211yescharacteristic, complemented
20#481×C151—24no—
21#481×C151C2218yescomplemented
22C2×#106×C151—22no—
23C2×#102×C151—22no—
24C2×C22⋊C8×C151C2212yescomplemented
25#400×C151C2212yescomplemented
26#399×C151C2212yescomplemented
27#389×C151—21no—
28#386×C151—21no—
29#385×C151—21no—
30#380×C151—21no—
31#380×C151C2211yescharacteristic, complemented
32#327×C151C2218yescomplemented
33#324×C151C2212yescomplemented
34#323×C151C2212yescomplemented
35H(5,𝔽2)×C151—44no—
36H(5,𝔽2)×C151—44no—
37C2×#41×C151—24no—
38C2×#41×C151—22no—
39C22×D4×C151—24no—
40C22×D4×C151—21no—
41C22×D4×C151—22no—
42C22×D4×C151—22no—
43C22×D4×C151D412yes—
44C22×D4×C151D411yescharacteristic
45C23×C4×C151—21no—
46C23×C4×C151D411yescharacteristic
47C23×C4×C151C2311yescharacteristic
48C22×C8×C151—22no—
49C4⋊Q8×C151—21no—
50#127×C151—21no—
51#124×C151—22no—
52#123×C151—24no—
53#123×C151—24no—
54C22⋊Q8×C151—24no—
55#121×C151—22no—
56#121×C151—22no—
57#121×C151—24no—
58#121×C151—22no—
59#121×C151—22no—
60#121×C151—22no—
61#121×C151—22no—
62#121×C151D414yes—
63#121×C151C2314yes—
64#120×C151—24no—
65#120×C151—24no—
66C4×D4×C151—22no—
67C4×D4×C151—22no—
68C4×D4×C151—22no—
69C4×D4×C151—22no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—22no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151D412yes—
77C2×C4⋊C4×C151C2312yes—
78C2×C4⋊C4×C151C2311yescharacteristic
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—21no—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151D411yescharacteristic
84C2×C22⋊C4×C151C2311yescharacteristic
85C2×C42×C151D411yescharacteristic
86#106×C151—28no—
87#102×C151—28no—
88C22⋊C8×C151—22no—
89C22⋊C8×C151C2314yes—
90#95×C151—22no—
91#95×C151—22no—
92#95×C151C2312yes—
93C24×C151—22no—
94C24×C151—22no—
95C24×C151C2×D411yescharacteristic
96C24×C151C2×D411yescharacteristic
97#41×C151—44no—
98#41×C151—416no—
99#41×C151—44no—
100C2×Q8×C151—22no—
101C2×D4×C151—22no—
102C2×D4×C151—22no—
103C2×D4×C151—24no—
104C2×D4×C151—22no—
105C2×D4×C151—24no—
106C2×D4×C151—24no—
107C2×D4×C151—22no—
108C2×D4×C151—22no—
109C2×D4×C151—22no—
110C2×D4×C151—44no—
111C2×D4×C151—416no—
112C2×D4×C151—44no—
113C2×D4×C151—44no—
114C2×D4×C151—44no—
115C2×D4×C151—44no—
116C2×D4×C151—82no—
117C2×D4×C151SD1614yes—
118C2×D4×C151C2×D414yes—
119C22×C4×C151—22no—
120C22×C4×C151—24no—
121C22×C4×C151—22no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—42no—
127C22×C4×C151—42no—
128C22×C4×C151—42no—
129C22×C4×C151—82no—
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D412yes—
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D412yes—
136C22×C4×C151C2411yescharacteristic
137C2×C8×C151—24no—
138C2×C8×C151—44no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—24no—
144C4⋊C4×C151—42no—
145C4⋊C4×C151—41no—
146C4⋊C4×C151—41no—
147C4⋊C4×C151—82no—
148C4⋊C4×C151C2×D414yes—
149C22⋊C4×C151—24no—
150C22⋊C4×C151—24no—
151C22⋊C4×C151—22no—
152C22⋊C4×C151—24no—
153C22⋊C4×C151—24no—
154C22⋊C4×C151—22no—
155C22⋊C4×C151—42no—
156C22⋊C4×C151—82no—
157C42×C151—21no—
158C42×C151—21no—
159C23×C151—21no—
160C23×C151—21no—
161C23×C151—24no—
162C23×C151—41no—
163C23×C151—41no—
164C23×C151—41no—
165C23×C151—41no—
166C23×C151—44no—
167C23×C151—44no—
168C23×C151—82no—
169C23×C151—82no—
170C23×C151—82no—
171C23×C151—82no—
172C23×C151#12012yes—
173C23×C151C2×SD1612yes—
174C23×C151C2×SD1612yes—
175C23×C151AGL(1,ℤ/8)12yes—
176C23×C151C22×D411yescharacteristic
177Q8×C151—44no—
178D4×C151—28no—
179D4×C151—44no—
180D4×C151—44no—
181D4×C151—48no—
182D4×C151—44no—
183D4×C151—44no—
184D4×C151—48no—
185D4×C151—44no—
186D4×C151—82no—
187D4×C151—82no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—22no—
191C2×C4×C151—24no—
192C2×C4×C151—24no—
193C2×C4×C151—21no—
194C2×C4×C151—21no—
195C2×C4×C151—42no—
196C2×C4×C151—41no—
197C2×C4×C151—48no—
198C2×C4×C151—44no—
199C2×C4×C151—44no—
200C2×C4×C151—42no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—81no—
210C2×C4×C151—84no—
211C2×C4×C151#12011yescharacteristic
212C2×C4×C151#12011yescharacteristic
213C2×C4×C151C2×SD1612yes—
214C2×C4×C151C22×D412yes—
215C8×C151—44no—
216C22×C151—21no—
217C22×C151—22no—
218C22×C151—21no—
219C22×C151—22no—
220C22×C151—22no—
221C22×C151—42no—
222C22×C151—42no—
223C22×C151—42no—
224C22×C151—41no—
225C22×C151—41no—
226C22×C151—44no—
227C22×C151—44no—
228C22×C151—44no—
229C22×C151—81no—
230C22×C151—164no—
231C22×C151—164no—
232C22×C151#45014yes—
233C22×C151C2×#12011yescharacteristic
234C22×C151C22×SD1611yescharacteristic
235C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
236C4×C151—22no—
237C4×C151—22no—
238C4×C151—21no—
239C4×C151—44no—
240C4×C151—41no—
241C4×C151—41no—
242C4×C151—82no—
243C4×C151—82no—
244C4×C151#45812yes—
245C2×C151—21no—
246C2×C151—21no—
247C2×C151—24no—
248C2×C151—42no—
249C2×C151—84no—
250C2×C151C2×#45011yescharacteristic
251C2×C151#302111yescharacteristic
252C2×C151C2×#45811yescharacteristic
253#18203C15111yesmaximal, characteristic, direct product factor, Sylow
254C151#1820311yescharacteristic, direct product factor, Sylow
255#3496C2×C15111yescharacteristic
256C2×#481C2×C15112yescomplemented
257#2487C2×C15111yescharacteristic, complemented
258#1616C2×C15114yescomplemented
259#1613C2×C15114yescomplemented
260#1519C2×C15112yescomplemented
261#1459C2×C15111yescharacteristic, complemented
262C2×H(5,𝔽2)—21no—
263#547—22no—
264#546—24no—
265D42—22no—
266#537C22×C15112yes—
267#534—21no—
268#534C22×C15112yes—
269#532—21no—
270C2×#121—21no—
271C2×#121C22×C15112yes—
272C2×C4×D4C22×C15111yescharacteristic
273C22×C4⋊C4C22×C15111yescharacteristic, complemented
274#481—24no—
275#481C22×C15118yescomplemented
276C2×#106—22no—
277C2×#102—22no—
278C2×C22⋊C8C22×C15112yescomplemented
279#400C22×C15112yescomplemented
280#399C22×C15112yescomplemented
281#389—21no—
282#386—21no—
283#385—21no—
284#380—21no—
285#380C22×C15111yescharacteristic, complemented
286#327C22×C15118yescomplemented
287#324C22×C15112yescomplemented
288#323C22×C15112yescomplemented
289H(5,𝔽2)—44no—
290H(5,𝔽2)—44no—
291C2×#41—24no—
292C2×#41—22no—
293C22×D4—24no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—21no—
297C22×D4D4×C15111yescharacteristic
298C22×D4D4×C15112yes—
299C23×C4—21no—
300C23×C4D4×C15111yescharacteristic
301C23×C4C23×C15111yescharacteristic
302C22×C8—22no—
303C4⋊Q8—21no—
304#127—21no—
305#124—22no—
306#123—24no—
307#123—24no—
308C22⋊Q8—24no—
309#121—22no—
310#121—22no—
311#121—24no—
312#121—22no—
313#121—22no—
314#121—22no—
315#121—22no—
316#121D4×C15114yes—
317#121C23×C15114yes—
318#120—24no—
319#120—24no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4D4×C15112yes—
331C2×C4⋊C4C23×C15112yes—
332C2×C4⋊C4C23×C15111yescharacteristic
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4D4×C15111yescharacteristic
338C2×C22⋊C4C23×C15111yescharacteristic
339C2×C42D4×C15111yescharacteristic
340#106—28no—
341#102—28no—
342C22⋊C8—22no—
343C22⋊C8C23×C15114yes—
344#95—22no—
345#95—22no—
346#95C23×C15112yes—
347C24—22no—
348C24—22no—
349C24C2×D4×C15111yescharacteristic
350C24C2×D4×C15111yescharacteristic
351#41—44no—
352#41—416no—
353#41—44no—
354C2×Q8—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—24no—
358C2×D4—22no—
359C2×D4—24no—
360C2×D4—24no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—44no—
365C2×D4—416no—
366C2×D4—44no—
367C2×D4—44no—
368C2×D4—44no—
369C2×D4—44no—
370C2×D4—82no—
371C2×D4SD16×C15114yes—
372C2×D4C2×D4×C15114yes—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—82no—
384C22×C4C2×D4×C15111yescharacteristic
385C22×C4C2×D4×C15112yes—
386C22×C4C2×D4×C15111yescharacteristic
387C22×C4C2×D4×C15111yescharacteristic
388C22×C4C2×D4×C15111yescharacteristic
389C22×C4C2×D4×C15112yes—
390C22×C4C24×C15111yescharacteristic
391C2×C8—24no—
392C2×C8—44no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—24no—
398C4⋊C4—42no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—82no—
402C4⋊C4C2×D4×C15114yes—
403C22⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—22no—
406C22⋊C4—24no—
407C22⋊C4—24no—
408C22⋊C4—22no—
409C22⋊C4—42no—
410C22⋊C4—82no—
411C42—21no—
412C42—21no—
413C23—21no—
414C23—21no—
415C23—24no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—44no—
421C23—44no—
422C23—82no—
423C23—82no—
424C23—82no—
425C23—82no—
426C23#120×C15112yes—
427C23C2×SD16×C15112yes—
428C23C2×SD16×C15112yes—
429C23AGL(1,ℤ/8)×C15112yes—
430C23C22×D4×C15111yescharacteristic
431Q8—44no—
432D4—28no—
433D4—44no—
434D4—44no—
435D4—48no—
436D4—48no—
437D4—44no—
438D4—44no—
439D4—44no—
440D4—82no—
441D4—82no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—24no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—48no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—81no—
464C2×C4—84no—
465C2×C4#120×C15111yescharacteristic
466C2×C4#120×C15111yescharacteristic
467C2×C4C2×SD16×C15112yes—
468C2×C4C22×D4×C15112yes—
469C8—44no—
470C22—21no—
471C22—22no—
472C22—21no—
473C22—22no—
474C22—22no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—41no—
479C22—41no—
480C22—44no—
481C22—44no—
482C22—44no—
483C22—81no—
484C22—164no—
485C22—164no—
486C22#450×C15114yes—
487C22C2×#120×C15111yescharacteristic
488C22C22×SD16×C15111yescharacteristic
489C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
490C4—22no—
491C4—22no—
492C4—21no—
493C4—44no—
494C4—41no—
495C4—41no—
496C4—82no—
497C4—82no—
498C4#458×C15112yes—
499C2—21no—
500C2—21no—
501C2—24no—
502C2—42no—
503C2—84no—
504C2C2×#450×C15111yescharacteristic
505C2#3021×C15111yescharacteristic
506C2C2×#458×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3496×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#481×C151C2semidirect
3. #2487×C151C2semidirect
4. #1616×C151C2semidirect
5. #1613×C151C2semidirect
6. #1519×C151C2semidirect
7. #1459×C151C2semidirect
19. C22×C4⋊C4×C151C22semidirect
21. #481×C151C22semidirect
24. C2×C22⋊C8×C151C22semidirect
25. #400×C151C22semidirect
26. #399×C151C22semidirect
31. #380×C151C22semidirect
32. #327×C151C22semidirect
33. #324×C151C22semidirect
34. #323×C151C22semidirect
253. #18203C151direct (N × H)
254. C151#18203direct (N × H)
256. C2×#481C2×C151semidirect
257. #2487C2×C151semidirect
258. #1616C2×C151semidirect
259. #1613C2×C151semidirect
260. #1519C2×C151semidirect
261. #1459C2×C151semidirect
273. C22×C4⋊C4C22×C151semidirect
275. #481C22×C151semidirect
278. C2×C22⋊C8C22×C151semidirect
279. #400C22×C151semidirect
280. #399C22×C151semidirect
285. #380C22×C151semidirect
286. #327C22×C151semidirect
287. #324C22×C151semidirect
288. #323C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3496×C1512
C2×#481×C1512
#2487×C1512
#1616×C1512
#1613×C1512
#1519×C1512
#1459×C1512
#18203151