Finite Group Databasebeta

← C151×#18929 #50323854

Subgroups — C151×#18929 #50323854

Order 38656.

946 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3506×C151C211yesmaximal, characteristic
2#3230×C151C211yesmaximal, characteristic, complemented
3#3206×C151C211yesmaximal, characteristic, complemented
4C2×#474×C151C211yesmaximal, characteristic, complemented
5#1647×C151C214yesmaximal, complemented
6#1646×C151C214yesmaximal, complemented
7#1542×C151C211yesmaximal, characteristic, complemented
8#1480×C151C211yesmaximal, characteristic, complemented
9#1478×C151C211yesmaximal, characteristic, complemented
10#559×C151—22no—
11#556×C151—21no—
12#555×C151C2212yes—
13#553×C151—22no—
14#550×C151—21no—
15#547×C151C2212yes—
16#538×C151—22no—
17#535×C151—21no—
18#533×C151C2211yescharacteristic
19#532×C151C2211yescharacteristic
20C2×C4⋊Q8×C151C2211yescharacteristic
21#525×C151—22no—
22#520×C151—21no—
23C2×C4×D4×C151C2211yescharacteristic
24#500×C151C2212yescomplemented
25#492×C151—21no—
26#487×C151—21no—
27#487×C151C2212yescomplemented
28#484×C151—22no—
29#477×C151—22no—
30#474×C151—22no—
31#474×C151C2214yes—
32#461×C151C2214yescomplemented
33#448×C151—22no—
34#431×C151C2211yescharacteristic
35#431×C151C2211yescharacteristic
36C2×#107×C151—21no—
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#102×C151—21no—
39#333×C151C2212yescomplemented
40#332×C151C2212yescomplemented
41D4⋊C8×C151C2214yes—
42D4⋊C8×C151C2214yescomplemented
43C2×#41×C151—21no—
44C2×#41×C151—22no—
45C22×Q8×C151—21no—
46C22×D4×C151D411yescharacteristic
47C23×C4×C151—21no—
48C2×SD16×C151—24no—
49C22×C8×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151D411yescharacteristic
54C4⋊Q8×C151C2312yes—
55C4⋊Q8×C151C2311yescharacteristic
56C4⋊Q8×C151C2311yescharacteristic
57#127×C151—22no—
58#127×C151D411yescharacteristic
59#126×C151—24no—
60#125×C151—21no—
61#124×C151—22no—
62#124×C151—21no—
63#124×C151—24no—
64#123×C151—24no—
65#123×C151—24no—
66C22⋊Q8×C151—21no—
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151D412yes—
69#121×C151—24no—
70#121×C151—22no—
71#121×C151—22no—
72#121×C151—22no—
73#121×C151—21no—
74#121×C151D412yes—
75#120×C151—24no—
76C4×Q8×C151—22no—
77C4×Q8×C151—21no—
78C4×Q8×C151D412yes—
79C4×D4×C151—24no—
80C4×D4×C151—22no—
81C4×D4×C151—24no—
82C4×D4×C151—21no—
83C4×D4×C151—21no—
84C4×D4×C151—21no—
85C4×D4×C151D412yes—
86C4×D4×C151C2312yes—
87C4×D4×C151C2312yes—
88#117×C151—21no—
89#117×C151—22no—
90#117×C151—22no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151D411yescharacteristic
95C2×C22⋊C4×C151—21no—
96C2×C42×C151C2311yescharacteristic
97#107×C151—24no—
98#107×C151—24no—
99C4⋊C8×C151—21no—
100C4⋊C8×C151—21no—
101C4⋊C8×C151C2312yes—
102C4⋊C8×C151C2312yes—
103#103×C151—24no—
104#103×C151—24no—
105#102×C151—24no—
106C22⋊C8×C151—21no—
107C22⋊C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110C24×C151—21no—
111#41×C151—42no—
112#41×C151—42no—
113#41×C151—84no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—22no—
117C2×Q8×C151—41no—
118C2×Q8×C151—82no—
119C2×Q8×C151C2×D412yes—
120C2×D4×C151—22no—
121C2×D4×C151—24no—
122C2×D4×C151—24no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—22no—
127C2×D4×C151—22no—
128C2×D4×C151C2×D412yes—
129C2×D4×C151C2×D412yes—
130C22×C4×C151—24no—
131C22×C4×C151—21no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—41no—
136C22×C4×C151—82no—
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140SD16×C151—84no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C2×C8×C151—22no—
144C2×C8×C151—42no—
145C4⋊C4×C151—24no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—41no—
156C4⋊C4×C151—41no—
157C4⋊C4×C151C2×D412yes—
158C4⋊C4×C151C2×D412yes—
159C4⋊C4×C151C2×D412yes—
160C22⋊C4×C151—24no—
161C22⋊C4×C151—24no—
162C22⋊C4×C151—24no—
163C22⋊C4×C151—22no—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—22no—
166C22⋊C4×C151—22no—
167C22⋊C4×C151—22no—
168C42×C151—24no—
169C42×C151—22no—
170C42×C151C2×D411yescharacteristic
171C42×C151C2×D411yescharacteristic
172C42×C151C2×D411yescharacteristic
173C42×C151C2411yescharacteristic
174C23×C151—22no—
175C23×C151—22no—
176C23×C151—42no—
177C23×C151—81no—
178C23×C151—81no—
179C23×C151#12011yescharacteristic
180Q8×C151—42no—
181Q8×C151—42no—
182Q8×C151—42no—
183Q8×C151—44no—
184Q8×C151—82no—
185D4×C151—22no—
186D4×C151—22no—
187D4×C151—24no—
188D4×C151—44no—
189D4×C151—42no—
190D4×C151—42no—
191D4×C151—81no—
192D4×C151—84no—
193D4×C151—84no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—41no—
200C2×C4×C151—42no—
201C2×C4×C151—42no—
202C2×C4×C151—44no—
203C2×C4×C151—42no—
204C2×C4×C151—82no—
205C2×C4×C151—81no—
206C2×C4×C151—84no—
207C2×C4×C151—82no—
208C2×C4×C151#12011yescharacteristic
209C2×C4×C151#12011yescharacteristic
210C2×C4×C151#12011yescharacteristic
211C2×C4×C151#13512yes—
212C2×C4×C151#13712yes—
213C2×C4×C151C22×D411yescharacteristic
214C2×C4×C151C22×D411yescharacteristic
215C2×C4×C151C22×D411yescharacteristic
216C8×C151—42no—
217C8×C151—42no—
218C8×C151—42no—
219C22×C151—21no—
220C22×C151—21no—
221C22×C151—42no—
222C22×C151—42no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—42no—
226C22×C151—42no—
227C22×C151—84no—
228C22×C151#45212yes—
229C22×C151C2×#12011yescharacteristic
230C4×C151—21no—
231C4×C151—21no—
232C4×C151—21no—
233C4×C151—42no—
234C4×C151—42no—
235C4×C151—42no—
236C4×C151—42no—
237C4×C151—82no—
238C4×C151#45212yes—
239C4×C151C2×#13511yescharacteristic
240C4×C151C2×#13711yescharacteristic
241C4×C151#57612yes—
242C2×C151—22no—
243C2×C151—82no—
244C2×C151—82no—
245C2×C151C2×#45211yescharacteristic
246C2×C151#300811yescharacteristic
247C2×C151#302211yescharacteristic
248#18929C15111yesmaximal, characteristic, direct product factor, Sylow
249C151#1892911yescharacteristic, direct product factor, Sylow
250#3506C2×C15111yescharacteristic
251#3230C2×C15111yescharacteristic, complemented
252#3206C2×C15111yescharacteristic, complemented
253C2×#474C2×C15111yescharacteristic, complemented
254#1647C2×C15114yescomplemented
255#1646C2×C15114yescomplemented
256#1542C2×C15111yescharacteristic, complemented
257#1480C2×C15111yescharacteristic, complemented
258#1478C2×C15111yescharacteristic, complemented
259#559—22no—
260#556—21no—
261#555C22×C15112yes—
262#553—22no—
263#550—21no—
264#547C22×C15112yes—
265#538—22no—
266#535—21no—
267#533C22×C15111yescharacteristic
268#532C22×C15111yescharacteristic
269C2×C4⋊Q8C22×C15111yescharacteristic
270#525—22no—
271#520—21no—
272C2×C4×D4C22×C15111yescharacteristic
273#500C22×C15112yescomplemented
274#492—21no—
275#487—21no—
276#487C22×C15112yescomplemented
277#484—22no—
278#477—22no—
279#474—22no—
280#474C22×C15114yes—
281#461C22×C15114yescomplemented
282#448—22no—
283#431C22×C15111yescharacteristic
284#431C22×C15111yescharacteristic
285C2×#107—21no—
286C2×C4⋊C8C22×C15111yescharacteristic
287C2×#102—21no—
288#333C22×C15112yescomplemented
289#332C22×C15112yescomplemented
290D4⋊C8C22×C15114yes—
291D4⋊C8C22×C15114yescomplemented
292C2×#41—22no—
293C2×#41—21no—
294C22×Q8—21no—
295C22×D4D4×C15111yescharacteristic
296C23×C4—21no—
297C2×SD16—24no—
298C22×C8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8D4×C15111yescharacteristic
303C4⋊Q8C23×C15112yes—
304C4⋊Q8C23×C15111yescharacteristic
305C4⋊Q8C23×C15111yescharacteristic
306#127—22no—
307#127D4×C15111yescharacteristic
308#126—24no—
309#125—21no—
310#124—22no—
311#124—24no—
312#124—21no—
313#123—24no—
314#123—24no—
315C22⋊Q8—21no—
316C22⋊Q8—22no—
317C22⋊Q8D4×C15112yes—
318#121—24no—
319#121—22no—
320#121—22no—
321#121—22no—
322#121—21no—
323#121D4×C15112yes—
324#120—24no—
325C4×Q8—22no—
326C4×Q8—21no—
327C4×Q8D4×C15112yes—
328C4×D4—24no—
329C4×D4—22no—
330C4×D4—24no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4D4×C15112yes—
335C4×D4C23×C15112yes—
336C4×D4C23×C15112yes—
337#117—21no—
338#117—22no—
339#117—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4D4×C15111yescharacteristic
344C2×C22⋊C4—21no—
345C2×C42C23×C15111yescharacteristic
346#107—24no—
347#107—24no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8C23×C15112yes—
351C4⋊C8C23×C15112yes—
352#103—24no—
353#103—24no—
354#102—24no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C4×C8—21no—
358C4×C8C23×C15112yes—
359C24—21no—
360#41—42no—
361#41—42no—
362#41—84no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—41no—
367C2×Q8—82no—
368C2×Q8C2×D4×C15112yes—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4C2×D4×C15112yes—
378C2×D4C2×D4×C15112yes—
379C22×C4—24no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—41no—
385C22×C4—82no—
386C22×C4C2×D4×C15111yescharacteristic
387C22×C4C2×D4×C15111yescharacteristic
388C22×C4C2×D4×C15111yescharacteristic
389SD16—84no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—42no—
394C4⋊C4—24no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4C2×D4×C15112yes—
407C4⋊C4C2×D4×C15112yes—
408C4⋊C4C2×D4×C15112yes—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C42—24no—
418C42—22no—
419C42C2×D4×C15111yescharacteristic
420C42C2×D4×C15111yescharacteristic
421C42C2×D4×C15111yescharacteristic
422C42C24×C15111yescharacteristic
423C23—22no—
424C23—22no—
425C23—42no—
426C23—81no—
427C23—81no—
428C23#120×C15111yescharacteristic
429Q8—42no—
430Q8—42no—
431Q8—42no—
432Q8—44no—
433Q8—82no—
434D4—22no—
435D4—22no—
436D4—24no—
437D4—44no—
438D4—42no—
439D4—42no—
440D4—81no—
441D4—84no—
442D4—84no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—82no—
454C2×C4—81no—
455C2×C4—84no—
456C2×C4—82no—
457C2×C4#120×C15111yescharacteristic
458C2×C4#120×C15111yescharacteristic
459C2×C4#120×C15111yescharacteristic
460C2×C4#135×C15112yes—
461C2×C4#137×C15112yes—
462C2×C4C22×D4×C15111yescharacteristic
463C2×C4C22×D4×C15111yescharacteristic
464C2×C4C22×D4×C15111yescharacteristic
465C8—42no—
466C8—42no—
467C8—42no—
468C22—21no—
469C22—21no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—84no—
477C22#452×C15112yes—
478C22C2×#120×C15111yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—82no—
487C4#452×C15112yes—
488C4C2×#135×C15111yescharacteristic
489C4C2×#137×C15111yescharacteristic
490C4#576×C15112yes—
491C2—22no—
492C2—82no—
493C2—82no—
494C2C2×#452×C15111yescharacteristic
495C2#3008×C15111yescharacteristic
496C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3506×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. #3206×C151C2semidirect
4. C2×#474×C151C2semidirect
5. #1647×C151C2semidirect
6. #1646×C151C2semidirect
7. #1542×C151C2semidirect
8. #1480×C151C2semidirect
9. #1478×C151C2semidirect
24. #500×C151C22semidirect
27. #487×C151C22semidirect
32. #461×C151C22semidirect
39. #333×C151C22semidirect
40. #332×C151C22semidirect
42. D4⋊C8×C151C22semidirect
248. #18929C151direct (N × H)
249. C151#18929direct (N × H)
251. #3230C2×C151semidirect
252. #3206C2×C151semidirect
253. C2×#474C2×C151semidirect
254. #1647C2×C151semidirect
255. #1646C2×C151semidirect
256. #1542C2×C151semidirect
257. #1480C2×C151semidirect
258. #1478C2×C151semidirect
273. #500C22×C151semidirect
276. #487C22×C151semidirect
281. #461C22×C151semidirect
288. #333C22×C151semidirect
289. #332C22×C151semidirect
291. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3506×C1512
#3230×C1512
#3206×C1512
C2×#474×C1512
#1647×C1512
#1646×C1512
#1542×C1512
#1480×C1512
#1478×C1512
#18929151