Finite Group Databasebeta

← C151×#18611 #50323536

Subgroups — C151×#18611 #50323536

Order 38656.

1106 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3497×C151C211yesmaximal, characteristic
2#3235×C151C211yesmaximal, characteristic, complemented
3#3182×C151C211yesmaximal, characteristic, complemented
4#3104×C151C211yesmaximal, characteristic, complemented
5#1649×C151C212yesmaximal, complemented
6#1641×C151C212yesmaximal, complemented
7#1637×C151C212yesmaximal, complemented
8#1631×C151C212yesmaximal, complemented
9#1553×C151C211yesmaximal, characteristic, complemented
10#1491×C151C211yesmaximal, characteristic, complemented
11#1484×C151C211yesmaximal, characteristic, complemented
12C2×2−1+4×C151—21no—
13#550×C151—21no—
14#550×C151C2212yes—
15D4×Q8×C151—21no—
16D4×Q8×C151C2212yes—
17#548×C151—22no—
18#548×C151—22no—
19#537×C151—22no—
20#537×C151—21no—
21#533×C151C2211yescharacteristic
22#532×C151—22no—
23#532×C151C2211yescharacteristic
24#532×C151C2211yescharacteristic
25C2×C4×Q8×C151C2211yescharacteristic
26#501×C151—21no—
27#500×C151C2211yescharacteristic
28#492×C151C2211yescharacteristic
29#490×C151—21no—
30#487×C151C2211yescharacteristic
31#486×C151C2211yescharacteristic
32#484×C151—21no—
33#482×C151—22no—
34#477×C151C2212yes—
35#476×C151C2212yes—
36#474×C151C2212yes—
37#468×C151—22no—
38#462×C151C2212yes—
39#451×C151—21no—
40#440×C151—22no—
41C4×Q16×C151—22no—
42#432×C151C2211yescharacteristic
43#431×C151C2211yescharacteristic
44C4×M16×C151C2211yescharacteristic
45#332×C151C2212yes—
46#331×C151C2212yes—
47Q8⋊C8×C151C2212yes—
48Q8⋊C8×C151C2212yes—
49D4⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
512−1+4×C151—48no—
52C2×#41×C151—24no—
53C2×#41×C151—22no—
54C2×#41×C151—21no—
55C2×#41×C151—21no—
56C2×#41×C151—22no—
57C22×Q8×C151—22no—
58C22×Q8×C151—22no—
59C22×Q8×C151D411yescharacteristic
60C2×Q16×C151—22no—
61C2×SD16×C151—22no—
62C2×M16×C151—21no—
63C4⋊Q8×C151—22no—
64C4⋊Q8×C151D411yescharacteristic
65C4⋊Q8×C151C2311yescharacteristic
66C4⋊Q8×C151C2311yescharacteristic
67C4⋊Q8×C151C2311yescharacteristic
68#127×C151—22no—
69#127×C151D411yescharacteristic
70#127×C151C2311yescharacteristic
71#125×C151—21no—
72#124×C151—24no—
73#124×C151—21no—
74#124×C151—21no—
75C22⋊Q8×C151—24no—
76C22⋊Q8×C151—22no—
77C22⋊Q8×C151—24no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—21no—
81#121×C151—24no—
82#121×C151—22no—
83#121×C151—24no—
84#121×C151—24no—
85#121×C151—21no—
86#121×C151—21no—
87#121×C151—22no—
88#121×C151D412yes—
89#121×C151D412yes—
90C4×Q8×C151—21no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151D412yes—
95C4×Q8×C151C2312yes—
96C4×D4×C151—24no—
97C4×D4×C151—22no—
98C4×D4×C151—22no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151D412yes—
102C4×D4×C151C2312yes—
103#117×C151—21no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151D411yescharacteristic
106C2×C42×C151—21no—
107C2×C42×C151C2311yescharacteristic
108#107×C151—22no—
109#107×C151—22no—
110#107×C151—22no—
111#106×C151—22no—
112C4⋊C8×C151C2312yes—
113C4⋊C8×C151C2312yes—
114#103×C151—22no—
115#103×C151—22no—
116#103×C151—22no—
117#102×C151—22no—
118#102×C151—22no—
119#102×C151—22no—
120C22⋊C8×C151—21no—
121C22⋊C8×C151—21no—
122#97×C151—21no—
123#97×C151—21no—
124C4×C8×C151—21no—
125C4×C8×C151C2311yescharacteristic
126C4×C8×C151C2311yescharacteristic
127#41×C151—416no—
128#41×C151—44no—
129#41×C151—44no—
130#41×C151—48no—
131#41×C151—44no—
132#41×C151—44no—
133C2×Q8×C151—24no—
134C2×Q8×C151—24no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—21no—
138C2×Q8×C151—21no—
139C2×Q8×C151—21no—
140C2×Q8×C151—48no—
141C2×Q8×C151—44no—
142C2×Q8×C151—44no—
143C2×Q8×C151C2×D412yes—
144C2×D4×C151—24no—
145C2×D4×C151—22no—
146C2×D4×C151—22no—
147C2×D4×C151—24no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151C2×D412yes—
153C2×D4×C151C2×D412yes—
154C22×C4×C151—21no—
155C22×C4×C151—24no—
156C22×C4×C151—24no—
157C22×C4×C151—21no—
158C22×C4×C151—22no—
159C22×C4×C151—22no—
160C22×C4×C151C2×D411yescharacteristic
161C22×C4×C151C2×D411yescharacteristic
162C22×C4×C151C2×D411yescharacteristic
163Q16×C151—44no—
164SD16×C151—44no—
165M16×C151—42no—
166C2×C8×C151—21no—
167C2×C8×C151—22no—
168C2×C8×C151—21no—
169C2×C8×C151—22no—
170C4⋊C4×C151—24no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—41no—
181C4⋊C4×C151—41no—
182C4⋊C4×C151C2×D412yes—
183C4⋊C4×C151C2×D412yes—
184C4⋊C4×C151C2×D412yes—
185C22⋊C4×C151—24no—
186C22⋊C4×C151—24no—
187C22⋊C4×C151—22no—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—41no—
192C42×C151—22no—
193C42×C151—22no—
194C42×C151—41no—
195C42×C151C2×D411yescharacteristic
196C42×C151C2×D411yescharacteristic
197C42×C151C2×D411yescharacteristic
198C42×C151C2411yescharacteristic
199C23×C151—22no—
200C23×C151—22no—
201C23×C151#12011yescharacteristic
202Q8×C151—24no—
203Q8×C151—22no—
204Q8×C151—48no—
205Q8×C151—42no—
206Q8×C151—42no—
207Q8×C151—42no—
208Q8×C151—42no—
209Q8×C151AGL(1,ℤ/8)14yes—
210D4×C151—24no—
211D4×C151—42no—
212D4×C151—48no—
213D4×C151—42no—
214D4×C151—44no—
215D4×C151—44no—
216D4×C151—42no—
217D4×C151—42no—
218D4×C151—81no—
219D4×C151—84no—
220C2×C4×C151—24no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—22no—
226C2×C4×C151—22no—
227C2×C4×C151—41no—
228C2×C4×C151—48no—
229C2×C4×C151—48no—
230C2×C4×C151—44no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—81no—
236C2×C4×C151#12011yescharacteristic
237C2×C4×C151#12011yescharacteristic
238C2×C4×C151#12011yescharacteristic
239C2×C4×C151C22×D411yescharacteristic
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C22×D411yescharacteristic
242C8×C151—22no—
243C8×C151—41no—
244C8×C151—42no—
245C8×C151—42no—
246C22×C151—21no—
247C22×C151—21no—
248C22×C151—21no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151C2×#12011yescharacteristic
256C4×C151—24no—
257C4×C151—21no—
258C4×C151—21no—
259C4×C151—21no—
260C4×C151—21no—
261C4×C151—42no—
262C4×C151—42no—
263C4×C151—42no—
264C4×C151—81no—
265C4×C151—81no—
266C4×C151C2×AGL(1,ℤ/8)12yes—
267C4×C151#57812yes—
268C2×C151—41no—
269C2×C151—82no—
270C2×C151—82no—
271C2×C151#300311yescharacteristic
272C2×C151#301111yescharacteristic
273C2×C151#301811yescharacteristic
274#18611C15111yesmaximal, characteristic, direct product factor, Sylow
275C151#1861111yescharacteristic, direct product factor, Sylow
276#3497C2×C15111yescharacteristic
277#3235C2×C15111yescharacteristic, complemented
278#3182C2×C15111yescharacteristic, complemented
279#3104C2×C15111yescharacteristic, complemented
280#1649C2×C15112yescomplemented
281#1641C2×C15112yescomplemented
282#1637C2×C15112yescomplemented
283#1631C2×C15112yescomplemented
284#1553C2×C15111yescharacteristic, complemented
285#1491C2×C15111yescharacteristic, complemented
286#1484C2×C15111yescharacteristic, complemented
287C2×2−1+4—21no—
288#550—21no—
289#550C22×C15112yes—
290D4×Q8—21no—
291D4×Q8C22×C15112yes—
292#548—22no—
293#548—22no—
294#537—22no—
295#537—21no—
296#533C22×C15111yescharacteristic
297#532—22no—
298#532C22×C15111yescharacteristic
299#532C22×C15111yescharacteristic
300C2×C4×Q8C22×C15111yescharacteristic
301#501—21no—
302#500C22×C15111yescharacteristic
303#492C22×C15111yescharacteristic
304#490—21no—
305#487C22×C15111yescharacteristic
306#486C22×C15111yescharacteristic
307#484—21no—
308#482—22no—
309#477C22×C15112yes—
310#476C22×C15112yes—
311#474C22×C15112yes—
312#468—22no—
313#462C22×C15112yes—
314#451—21no—
315#440—22no—
316C4×Q16—22no—
317#432C22×C15111yescharacteristic
318#431C22×C15111yescharacteristic
319C4×M16C22×C15111yescharacteristic
320#332C22×C15112yes—
321#331C22×C15112yes—
322Q8⋊C8C22×C15112yes—
323Q8⋊C8C22×C15112yes—
324D4⋊C8C22×C15112yes—
325D4⋊C8C22×C15112yes—
3262−1+4—48no—
327C2×#41—24no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—21no—
331C2×#41—21no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8D4×C15111yescharacteristic
335C2×Q16—22no—
336C2×SD16—22no—
337C2×M16—21no—
338C4⋊Q8—22no—
339C4⋊Q8D4×C15111yescharacteristic
340C4⋊Q8C23×C15111yescharacteristic
341C4⋊Q8C23×C15111yescharacteristic
342C4⋊Q8C23×C15111yescharacteristic
343#127—22no—
344#127D4×C15111yescharacteristic
345#127C23×C15111yescharacteristic
346#125—21no—
347#124—24no—
348#124—21no—
349#124—21no—
350C22⋊Q8—22no—
351C22⋊Q8—24no—
352C22⋊Q8—22no—
353C22⋊Q8—24no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356#121—24no—
357#121—22no—
358#121—24no—
359#121—24no—
360#121—21no—
361#121—21no—
362#121—22no—
363#121D4×C15112yes—
364#121D4×C15112yes—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8D4×C15112yes—
370C4×Q8C23×C15112yes—
371C4×D4—24no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4D4×C15112yes—
377C4×D4C23×C15112yes—
378#117—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4D4×C15111yescharacteristic
381C2×C42—21no—
382C2×C42C23×C15111yescharacteristic
383#107—22no—
384#107—22no—
385#107—22no—
386#106—22no—
387C4⋊C8C23×C15112yes—
388C4⋊C8C23×C15112yes—
389#103—22no—
390#103—22no—
391#103—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397#97—21no—
398#97—21no—
399C4×C8—21no—
400C4×C8C23×C15111yescharacteristic
401C4×C8C23×C15111yescharacteristic
402#41—416no—
403#41—44no—
404#41—44no—
405#41—48no—
406#41—44no—
407#41—44no—
408C2×Q8—24no—
409C2×Q8—24no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—48no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8C2×D4×C15112yes—
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—24no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4C2×D4×C15112yes—
428C2×D4C2×D4×C15112yes—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4C2×D4×C15111yescharacteristic
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C2×D4×C15111yescharacteristic
438Q16—44no—
439SD16—44no—
440M16—42no—
441C2×C8—21no—
442C2×C8—22no—
443C2×C8—21no—
444C2×C8—22no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4C2×D4×C15112yes—
458C4⋊C4C2×D4×C15112yes—
459C4⋊C4C2×D4×C15112yes—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—41no—
467C42—22no—
468C42—22no—
469C42—41no—
470C42C2×D4×C15111yescharacteristic
471C42C2×D4×C15111yescharacteristic
472C42C2×D4×C15111yescharacteristic
473C42C24×C15111yescharacteristic
474C23—22no—
475C23—22no—
476C23#120×C15111yescharacteristic
477Q8—24no—
478Q8—22no—
479Q8—48no—
480Q8—42no—
481Q8—42no—
482Q8—42no—
483Q8—42no—
484Q8AGL(1,ℤ/8)×C15114yes—
485D4—24no—
486D4—42no—
487D4—48no—
488D4—42no—
489D4—44no—
490D4—44no—
491D4—42no—
492D4—42no—
493D4—81no—
494D4—84no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—41no—
503C2×C4—48no—
504C2×C4—48no—
505C2×C4—44no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—81no—
511C2×C4#120×C15111yescharacteristic
512C2×C4#120×C15111yescharacteristic
513C2×C4#120×C15111yescharacteristic
514C2×C4C22×D4×C15111yescharacteristic
515C2×C4C22×D4×C15111yescharacteristic
516C2×C4C22×D4×C15111yescharacteristic
517C8—22no—
518C8—41no—
519C8—42no—
520C8—42no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22C2×#120×C15111yescharacteristic
531C4—24no—
532C4—21no—
533C4—21no—
534C4—21no—
535C4—21no—
536C4—42no—
537C4—42no—
538C4—42no—
539C4—81no—
540C4—81no—
541C4C2×AGL(1,ℤ/8)×C15112yes—
542C4#578×C15112yes—
543C2—41no—
544C2—82no—
545C2—82no—
546C2#3003×C15111yescharacteristic
547C2#3011×C15111yescharacteristic
548C2#3018×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3497×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. #3235×C151C2semidirect
3. #3182×C151C2semidirect
4. #3104×C151C2semidirect
5. #1649×C151C2semidirect
6. #1641×C151C2semidirect
7. #1637×C151C2semidirect
8. #1631×C151C2semidirect
9. #1553×C151C2semidirect
10. #1491×C151C2semidirect
11. #1484×C151C2semidirect
274. #18611C151direct (N × H)
275. C151#18611direct (N × H)
277. #3235C2×C151semidirect
278. #3182C2×C151semidirect
279. #3104C2×C151semidirect
280. #1649C2×C151semidirect
281. #1641C2×C151semidirect
282. #1637C2×C151semidirect
283. #1631C2×C151semidirect
284. #1553C2×C151semidirect
285. #1491C2×C151semidirect
286. #1484C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3497×C1512
#3235×C1512
#3182×C1512
#3104×C1512
#1649×C1512
#1641×C1512
#1637×C1512
#1631×C1512
#1553×C1512
#1491×C1512
#1484×C1512
#18611151