Finite Group Databasebeta

← C151×#18927 #50323852

Subgroups — C151×#18927 #50323852

Order 38656.

946 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3506×C151C211yesmaximal, characteristic
2#3227×C151C211yesmaximal, characteristic, complemented
3#3209×C151C211yesmaximal, characteristic, complemented
4C2×#474×C151C211yesmaximal, characteristic, complemented
5#1652×C151C214yesmaximal, complemented
6#1641×C151C214yesmaximal, complemented
7#1540×C151C211yesmaximal, characteristic, complemented
8#1481×C151C211yesmaximal, characteristic, complemented
9#1478×C151C211yesmaximal, characteristic, complemented
10#559×C151—22no—
11#556×C151C2212yes—
12#555×C151—21no—
13#553×C151—22no—
14#550×C151C2212yes—
15#547×C151—21no—
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#498×C151C2212yescomplemented
25#494×C151—21no—
26#487×C151—21no—
27#486×C151C2212yescomplemented
28#481×C151—22no—
29#476×C151—22no—
30#474×C151—22no—
31#474×C151C2214yes—
32#462×C151C2214yescomplemented
33#451×C151—22no—
34#431×C151C2211yescharacteristic
35#431×C151C2211yescharacteristic
36C2×#107×C151—21no—
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#102×C151—21no—
39#332×C151C2212yescomplemented
40#331×C151C2212yescomplemented
41Q8⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yes—
43C2×#41×C151—21no—
44C2×#41×C151—22no—
45C22×Q8×C151—21no—
46C22×D4×C151D411yescharacteristic
47C23×C4×C151—21no—
48C2×Q16×C151—24no—
49C22×C8×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151D411yescharacteristic
54C4⋊Q8×C151D411yescharacteristic
55C4⋊Q8×C151C2312yes—
56C4⋊Q8×C151C2311yescharacteristic
57#127×C151—22no—
58#127×C151C2311yescharacteristic
59#126×C151—24no—
60#125×C151—21no—
61#124×C151—24no—
62#124×C151—22no—
63#124×C151—21no—
64#123×C151—24no—
65#123×C151—24no—
66C22⋊Q8×C151—21no—
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151D412yes—
69#121×C151—22no—
70#121×C151—22no—
71#121×C151—24no—
72#121×C151—21no—
73#121×C151—22no—
74#121×C151D412yes—
75#120×C151—24no—
76C4×Q8×C151—22no—
77C4×Q8×C151—21no—
78C4×Q8×C151C2312yes—
79C4×D4×C151—24no—
80C4×D4×C151—24no—
81C4×D4×C151—22no—
82C4×D4×C151—21no—
83C4×D4×C151—21no—
84C4×D4×C151—21no—
85C4×D4×C151D412yes—
86C4×D4×C151D412yes—
87C4×D4×C151C2312yes—
88#117×C151—22no—
89#117×C151—21no—
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#106×C151—24no—
99C4⋊C8×C151—21no—
100C4⋊C8×C151—21no—
101C4⋊C8×C151C2312yes—
102C4⋊C8×C151C2312yes—
103#103×C151—24no—
104#102×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—22no—
125C2×D4×C151—22no—
126C2×D4×C151—21no—
127C2×D4×C151—21no—
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
140Q16×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—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—22no—
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—24no—
181Q8×C151—41no—
182Q8×C151—41no—
183Q8×C151—44no—
184Q8×C151—81no—
185Q8×C151—82no—
186D4×C151—22no—
187D4×C151—22no—
188D4×C151—42no—
189D4×C151—44no—
190D4×C151—41no—
191D4×C151—41no—
192D4×C151—42no—
193D4×C151—42no—
194D4×C151—84no—
195D4×C151—84no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—41no—
202C2×C4×C151—44no—
203C2×C4×C151—44no—
204C2×C4×C151—42no—
205C2×C4×C151—82no—
206C2×C4×C151—81no—
207C2×C4×C151—84no—
208C2×C4×C151—82no—
209C2×C4×C151#12011yescharacteristic
210C2×C4×C151#12011yescharacteristic
211C2×C4×C151#12011yescharacteristic
212C2×C4×C151#13512yes—
213C2×C4×C151#13712yes—
214C2×C4×C151C22×D411yescharacteristic
215C2×C4×C151C22×D411yescharacteristic
216C2×C4×C151C22×D411yescharacteristic
217C8×C151—42no—
218C8×C151—42no—
219C8×C151—42no—
220C22×C151—21no—
221C22×C151—21no—
222C22×C151—42no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—42no—
226C22×C151—42no—
227C22×C151—42no—
228C22×C151—84no—
229C22×C151#45212yes—
230C22×C151C2×#12011yescharacteristic
231C4×C151—21no—
232C4×C151—21no—
233C4×C151—21no—
234C4×C151—42no—
235C4×C151—42no—
236C4×C151—42no—
237C4×C151—42no—
238C4×C151—82no—
239C4×C151#45212yes—
240C4×C151C2×#13511yescharacteristic
241C4×C151C2×#13711yescharacteristic
242C4×C151#57612yes—
243C2×C151—22no—
244C2×C151—82no—
245C2×C151—82no—
246C2×C151C2×#45211yescharacteristic
247C2×C151#300811yescharacteristic
248C2×C151#302211yescharacteristic
249#18927C15111yesmaximal, characteristic, direct product factor, Sylow
250C151#1892711yescharacteristic, direct product factor, Sylow
251#3506C2×C15111yescharacteristic
252#3227C2×C15111yescharacteristic, complemented
253#3209C2×C15111yescharacteristic, complemented
254C2×#474C2×C15111yescharacteristic, complemented
255#1652C2×C15114yescomplemented
256#1641C2×C15114yescomplemented
257#1540C2×C15111yescharacteristic, complemented
258#1481C2×C15111yescharacteristic, complemented
259#1478C2×C15111yescharacteristic, complemented
260#559—22no—
261#556C22×C15112yes—
262#555—21no—
263#553—22no—
264#550C22×C15112yes—
265#547—21no—
266#538—22no—
267#535—21no—
268#533C22×C15111yescharacteristic
269#532C22×C15111yescharacteristic
270C2×C4⋊Q8C22×C15111yescharacteristic
271#525—22no—
272#520—21no—
273C2×C4×D4C22×C15111yescharacteristic
274#498C22×C15112yescomplemented
275#494—21no—
276#487—21no—
277#486C22×C15112yescomplemented
278#481—22no—
279#476—22no—
280#474—22no—
281#474C22×C15114yes—
282#462C22×C15114yescomplemented
283#451—22no—
284#431C22×C15111yescharacteristic
285#431C22×C15111yescharacteristic
286C2×#107—21no—
287C2×C4⋊C8C22×C15111yescharacteristic
288C2×#102—21no—
289#332C22×C15112yescomplemented
290#331C22×C15112yescomplemented
291Q8⋊C8C22×C15114yescomplemented
292D4⋊C8C22×C15114yes—
293C2×#41—22no—
294C2×#41—21no—
295C22×Q8—21no—
296C22×D4D4×C15111yescharacteristic
297C23×C4—21no—
298C2×Q16—24no—
299C22×C8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8D4×C15111yescharacteristic
304C4⋊Q8D4×C15111yescharacteristic
305C4⋊Q8C23×C15112yes—
306C4⋊Q8C23×C15111yescharacteristic
307#127—22no—
308#127C23×C15111yescharacteristic
309#126—24no—
310#125—21no—
311#124—24no—
312#124—22no—
313#124—21no—
314#123—24no—
315#123—24no—
316C22⋊Q8—22no—
317C22⋊Q8—21no—
318C22⋊Q8D4×C15112yes—
319#121—22no—
320#121—22no—
321#121—24no—
322#121—21no—
323#121—22no—
324#121D4×C15112yes—
325#120—24no—
326C4×Q8—22no—
327C4×Q8—21no—
328C4×Q8C23×C15112yes—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—22no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4D4×C15112yes—
336C4×D4D4×C15112yes—
337C4×D4C23×C15112yes—
338#117—22no—
339#117—21no—
340#117—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4D4×C15111yescharacteristic
345C2×C22⋊C4—21no—
346C2×C42C23×C15111yescharacteristic
347#107—24no—
348#106—24no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8C23×C15112yes—
352C4⋊C8C23×C15112yes—
353#103—24no—
354#102—24no—
355#102—24no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C4×C8—21no—
359C4×C8C23×C15112yes—
360C24—21no—
361#41—42no—
362#41—42no—
363#41—84no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—41no—
368C2×Q8—82no—
369C2×Q8C2×D4×C15112yes—
370C2×D4—22no—
371C2×D4—24no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4C2×D4×C15112yes—
379C2×D4C2×D4×C15112yes—
380C22×C4—24no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—41no—
386C22×C4—82no—
387C22×C4C2×D4×C15111yescharacteristic
388C22×C4C2×D4×C15111yescharacteristic
389C22×C4C2×D4×C15111yescharacteristic
390Q16—84no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—42no—
395C4⋊C4—24no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4C2×D4×C15112yes—
408C4⋊C4C2×D4×C15112yes—
409C4⋊C4C2×D4×C15112yes—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C42—24no—
419C42—22no—
420C42C2×D4×C15111yescharacteristic
421C42C2×D4×C15111yescharacteristic
422C42C2×D4×C15111yescharacteristic
423C42C24×C15111yescharacteristic
424C23—22no—
425C23—22no—
426C23—42no—
427C23—81no—
428C23—81no—
429C23#120×C15111yescharacteristic
430Q8—24no—
431Q8—41no—
432Q8—41no—
433Q8—44no—
434Q8—81no—
435Q8—82no—
436D4—22no—
437D4—22no—
438D4—42no—
439D4—44no—
440D4—42no—
441D4—41no—
442D4—41no—
443D4—42no—
444D4—84no—
445D4—84no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—82no—
456C2×C4—81no—
457C2×C4—84no—
458C2×C4—82no—
459C2×C4#120×C15111yescharacteristic
460C2×C4#120×C15111yescharacteristic
461C2×C4#120×C15111yescharacteristic
462C2×C4#135×C15112yes—
463C2×C4#137×C15112yes—
464C2×C4C22×D4×C15111yescharacteristic
465C2×C4C22×D4×C15111yescharacteristic
466C2×C4C22×D4×C15111yescharacteristic
467C8—42no—
468C8—42no—
469C8—42no—
470C22—21no—
471C22—21no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—84no—
479C22#452×C15112yes—
480C22C2×#120×C15111yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—82no—
489C4#452×C15112yes—
490C4C2×#135×C15111yescharacteristic
491C4C2×#137×C15111yescharacteristic
492C4#576×C15112yes—
493C2—22no—
494C2—82no—
495C2—82no—
496C2C2×#452×C15111yescharacteristic
497C2#3008×C15111yescharacteristic
498C2#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. #3227×C151C2semidirect
3. #3209×C151C2semidirect
4. C2×#474×C151C2semidirect
5. #1652×C151C2semidirect
6. #1641×C151C2semidirect
7. #1540×C151C2semidirect
8. #1481×C151C2semidirect
9. #1478×C151C2semidirect
24. #498×C151C22semidirect
27. #486×C151C22semidirect
32. #462×C151C22semidirect
39. #332×C151C22semidirect
40. #331×C151C22semidirect
41. Q8⋊C8×C151C22semidirect
249. #18927C151direct (N × H)
250. C151#18927direct (N × H)
252. #3227C2×C151semidirect
253. #3209C2×C151semidirect
254. C2×#474C2×C151semidirect
255. #1652C2×C151semidirect
256. #1641C2×C151semidirect
257. #1540C2×C151semidirect
258. #1481C2×C151semidirect
259. #1478C2×C151semidirect
274. #498C22×C151semidirect
277. #486C22×C151semidirect
282. #462C22×C151semidirect
289. #332C22×C151semidirect
290. #331C22×C151semidirect
291. Q8⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3506×C1512
#3227×C1512
#3209×C1512
C2×#474×C1512
#1652×C1512
#1641×C1512
#1540×C1512
#1481×C1512
#1478×C1512
#18927151