Finite Group Databasebeta

← C151×#18612 #50323537

Subgroups — C151×#18612 #50323537

Order 38656.

876 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3502×C151C211yesmaximal, characteristic, complemented
2#3216×C151C211yesmaximal, characteristic
3#3182×C151C211yesmaximal, characteristic
4#3103×C151C211yesmaximal, characteristic
5#1648×C151C212yesmaximal, complemented
6#1645×C151C212yesmaximal, complemented
7#1626×C151C212yesmaximal, complemented
8#1623×C151C212yesmaximal, complemented
9#1554×C151C211yesmaximal, characteristic, complemented
10#1491×C151C211yesmaximal, characteristic, complemented
11#1485×C151C211yesmaximal, characteristic, complemented
12Q82×C151—21no—
13Q82×C151C2212yes—
14#557×C151—21no—
15#557×C151—22no—
16#557×C151—22no—
17#557×C151C2212yes—
18#544×C151—22no—
19#544×C151—21no—
20#533×C151—22no—
21#533×C151C2211yescharacteristic
22#533×C151C2211yescharacteristic
23#532×C151C2211yescharacteristic
24#519×C151—21no—
25C2×C4×Q8×C151C2211yescharacteristic
26#500×C151C2211yescharacteristic
27#497×C151—21no—
28#492×C151C2211yescharacteristic
29#489×C151—21no—
30#487×C151C2211yescharacteristic
31#486×C151C2211yescharacteristic
32#481×C151—21no—
33#475×C151C2212yes—
34#468×C151—22no—
35#462×C151C2212yes—
36#460×C151C2212yes—
37#460×C151C2212yes—
38#452×C151—22no—
39#448×C151—21no—
40#440×C151—22no—
41C4×SD16×C151—22no—
42#432×C151C2211yescharacteristic
43#431×C151C2211yescharacteristic
44C4×M16×C151C2211yescharacteristic
45#333×C151C2212yes—
46#332×C151C2212yes—
47Q8⋊C8×C151C2212yes—
48Q8⋊C8×C151C2212yes—
49Q8⋊C8×C151C2212yes—
50Q8⋊C8×C151C2212yes—
51C2×#41×C151—21no—
52C22×Q8×C151D411yescharacteristic
53C2×Q16×C151—22no—
54C2×SD16×C151—22no—
55C2×SD16×C151—22no—
56C2×SD16×C151—22no—
57C2×M16×C151—21no—
58C4⋊Q8×C151—22no—
59C4⋊Q8×C151—24no—
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151—22no—
63C4⋊Q8×C151—24no—
64C4⋊Q8×C151D411yescharacteristic
65C4⋊Q8×C151D411yescharacteristic
66C4⋊Q8×C151C2311yescharacteristic
67C4⋊Q8×C151C2311yescharacteristic
68C4⋊Q8×C151C2311yescharacteristic
69#127×C151C2311yescharacteristic
70#125×C151—24no—
71#125×C151—24no—
72#125×C151—22no—
73#125×C151—24no—
74#125×C151—22no—
75#125×C151—21no—
76#125×C151—21no—
77#124×C151—21no—
78C22⋊Q8×C151—24no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—21no—
81C22⋊Q8×C151D412yes—
82C22⋊Q8×C151D412yes—
83#121×C151—21no—
84#121×C151—21no—
85C4×Q8×C151—22no—
86C4×Q8×C151—22no—
87C4×Q8×C151—24no—
88C4×Q8×C151—22no—
89C4×Q8×C151—21no—
90C4×Q8×C151—21no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—22no—
94C4×Q8×C151—22no—
95C4×Q8×C151—22no—
96C4×Q8×C151D412yes—
97C4×Q8×C151D412yes—
98C4×Q8×C151C2312yes—
99C4×Q8×C151C2312yes—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102#117×C151—24no—
103#117×C151—21no—
104#117×C151—21no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151D411yescharacteristic
107C2×C42×C151—21no—
108C2×C42×C151C2311yescharacteristic
109#107×C151—22no—
110#106×C151—22no—
111C4⋊C8×C151C2312yes—
112C4⋊C8×C151C2312yes—
113#103×C151—22no—
114#103×C151—22no—
115#103×C151—22no—
116#102×C151—22no—
117#102×C151—22no—
118#102×C151—22no—
119C22⋊C8×C151—21no—
120C22⋊C8×C151—21no—
121#97×C151—21no—
122#97×C151—21no—
123C4×C8×C151—21no—
124C4×C8×C151C2311yescharacteristic
125C4×C8×C151C2311yescharacteristic
126#41×C151—82no—
127C2×Q8×C151—24no—
128C2×Q8×C151—24no—
129C2×Q8×C151—21no—
130C2×Q8×C151—21no—
131C2×Q8×C151—21no—
132C2×Q8×C151—21no—
133C2×Q8×C151C2×D412yes—
134C2×Q8×C151C2×D412yes—
135C2×Q8×C151C2×D412yes—
136C2×D4×C151—21no—
137C2×D4×C151—21no—
138C2×D4×C151—21no—
139C2×D4×C151—41no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—41no—
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146Q16×C151—82no—
147SD16×C151—44no—
148SD16×C151—44no—
149SD16×C151—82no—
150M16×C151—42no—
151C2×C8×C151—21no—
152C2×C8×C151—22no—
153C2×C8×C151—21no—
154C2×C8×C151—22no—
155C4⋊C4×C151—24no—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151C2×D412yes—
176C4⋊C4×C151C2×D412yes—
177C4⋊C4×C151C2×D412yes—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—22no—
180C22⋊C4×C151—41no—
181C22⋊C4×C151—41no—
182C42×C151—24no—
183C42×C151—24no—
184C42×C151—22no—
185C42×C151—22no—
186C42×C151—22no—
187C42×C151—22no—
188C42×C151C2×D411yescharacteristic
189C42×C151C2×D411yescharacteristic
190C42×C151C2×D411yescharacteristic
191C42×C151C2411yescharacteristic
192C23×C151—41no—
193C23×C151#12011yescharacteristic
194Q8×C151—24no—
195Q8×C151—22no—
196Q8×C151—22no—
197Q8×C151—22no—
198Q8×C151—42no—
199Q8×C151—42no—
200Q8×C151—42no—
201Q8×C151—81no—
202Q8×C151—84no—
203Q8×C151#13714yes—
204D4×C151—42no—
205D4×C151—42no—
206D4×C151—42no—
207D4×C151—82no—
208C2×C4×C151—24no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—82no—
220C2×C4×C151—81no—
221C2×C4×C151#12011yescharacteristic
222C2×C4×C151#12011yescharacteristic
223C2×C4×C151#12011yescharacteristic
224C2×C4×C151C22×D411yescharacteristic
225C2×C4×C151C22×D411yescharacteristic
226C2×C4×C151C22×D411yescharacteristic
227C8×C151—22no—
228C8×C151—41no—
229C8×C151—42no—
230C8×C151—42no—
231C22×C151—21no—
232C22×C151—21no—
233C22×C151—21no—
234C22×C151—81no—
235C22×C151—81no—
236C22×C151—81no—
237C22×C151C2×#12011yescharacteristic
238C4×C151—24no—
239C4×C151—21no—
240C4×C151—21no—
241C4×C151—21no—
242C4×C151—21no—
243C4×C151—42no—
244C4×C151—42no—
245C4×C151—42no—
246C4×C151—42no—
247C4×C151—42no—
248C4×C151—81no—
249C4×C151C2×#13712yes—
250C4×C151#57712yes—
251C2×C151—41no—
252C2×C151—161no—
253C2×C151#300411yescharacteristic
254C2×C151#301011yescharacteristic
255C2×C151#301811yescharacteristic
256#18612C15111yesmaximal, characteristic, direct product factor, Sylow
257C151#1861211yescharacteristic, direct product factor, Sylow
258#3502C2×C15111yescharacteristic, complemented
259#3216C2×C15111yescharacteristic
260#3182C2×C15111yescharacteristic
261#3103C2×C15111yescharacteristic
262#1648C2×C15112yescomplemented
263#1645C2×C15112yescomplemented
264#1626C2×C15112yescomplemented
265#1623C2×C15112yescomplemented
266#1554C2×C15111yescharacteristic, complemented
267#1491C2×C15111yescharacteristic, complemented
268#1485C2×C15111yescharacteristic, complemented
269Q82—21no—
270Q82C22×C15112yes—
271#557—21no—
272#557—22no—
273#557—22no—
274#557C22×C15112yes—
275#544—22no—
276#544—21no—
277#533—22no—
278#533C22×C15111yescharacteristic
279#533C22×C15111yescharacteristic
280#532C22×C15111yescharacteristic
281#519—21no—
282C2×C4×Q8C22×C15111yescharacteristic
283#500C22×C15111yescharacteristic
284#497—21no—
285#492C22×C15111yescharacteristic
286#489—21no—
287#487C22×C15111yescharacteristic
288#486C22×C15111yescharacteristic
289#481—21no—
290#475C22×C15112yes—
291#468—22no—
292#462C22×C15112yes—
293#460C22×C15112yes—
294#460C22×C15112yes—
295#452—22no—
296#448—21no—
297#440—22no—
298C4×SD16—22no—
299#432C22×C15111yescharacteristic
300#431C22×C15111yescharacteristic
301C4×M16C22×C15111yescharacteristic
302#333C22×C15112yes—
303#332C22×C15112yes—
304Q8⋊C8C22×C15112yes—
305Q8⋊C8C22×C15112yes—
306Q8⋊C8C22×C15112yes—
307Q8⋊C8C22×C15112yes—
308C2×#41—21no—
309C22×Q8D4×C15111yescharacteristic
310C2×Q16—22no—
311C2×SD16—22no—
312C2×SD16—22no—
313C2×SD16—22no—
314C2×M16—21no—
315C4⋊Q8—24no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—24no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8D4×C15111yescharacteristic
322C4⋊Q8D4×C15111yescharacteristic
323C4⋊Q8C23×C15111yescharacteristic
324C4⋊Q8C23×C15111yescharacteristic
325C4⋊Q8C23×C15111yescharacteristic
326#127C23×C15111yescharacteristic
327#125—24no—
328#125—24no—
329#125—22no—
330#125—24no—
331#125—22no—
332#125—21no—
333#125—21no—
334#124—21no—
335C22⋊Q8—24no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8D4×C15112yes—
339C22⋊Q8D4×C15112yes—
340#121—21no—
341#121—21no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—24no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8D4×C15112yes—
354C4×Q8D4×C15112yes—
355C4×Q8C23×C15112yes—
356C4×Q8C23×C15112yes—
357C4×D4—21no—
358C4×D4—21no—
359#117—24no—
360#117—21no—
361#117—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4D4×C15111yescharacteristic
364C2×C42—21no—
365C2×C42C23×C15111yescharacteristic
366#107—22no—
367#106—22no—
368C4⋊C8C23×C15112yes—
369C4⋊C8C23×C15112yes—
370#103—22no—
371#103—22no—
372#103—22no—
373#102—22no—
374#102—22no—
375#102—22no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378#97—21no—
379#97—21no—
380C4×C8—21no—
381C4×C8C23×C15111yescharacteristic
382C4×C8C23×C15111yescharacteristic
383#41—82no—
384C2×Q8—24no—
385C2×Q8—24no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8C2×D4×C15112yes—
391C2×Q8C2×D4×C15112yes—
392C2×Q8C2×D4×C15112yes—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—41no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4C2×D4×C15111yescharacteristic
401C22×C4C2×D4×C15111yescharacteristic
402C22×C4C2×D4×C15111yescharacteristic
403Q16—82no—
404SD16—44no—
405SD16—44no—
406SD16—82no—
407M16—42no—
408C2×C8—21no—
409C2×C8—22no—
410C2×C8—21no—
411C2×C8—22no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—24no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4C2×D4×C15112yes—
433C4⋊C4C2×D4×C15112yes—
434C4⋊C4C2×D4×C15112yes—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C42—24no—
440C42—24no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—22no—
445C42C2×D4×C15111yescharacteristic
446C42C2×D4×C15111yescharacteristic
447C42C2×D4×C15111yescharacteristic
448C42C24×C15111yescharacteristic
449C23—41no—
450C23#120×C15111yescharacteristic
451Q8—24no—
452Q8—22no—
453Q8—22no—
454Q8—22no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458Q8—81no—
459Q8—84no—
460Q8#137×C15114yes—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—82no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—82no—
477C2×C4—81no—
478C2×C4#120×C15111yescharacteristic
479C2×C4#120×C15111yescharacteristic
480C2×C4#120×C15111yescharacteristic
481C2×C4C22×D4×C15111yescharacteristic
482C2×C4C22×D4×C15111yescharacteristic
483C2×C4C22×D4×C15111yescharacteristic
484C8—22no—
485C8—41no—
486C8—42no—
487C8—42no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22C2×#120×C15111yescharacteristic
495C4—24no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—81no—
506C4C2×#137×C15112yes—
507C4#577×C15112yes—
508C2—41no—
509C2—161no—
510C2#3004×C15111yescharacteristic
511C2#3010×C15111yescharacteristic
512C2#3018×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
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
1. #3502×C151C2semidirect
5. #1648×C151C2semidirect
6. #1645×C151C2semidirect
7. #1626×C151C2semidirect
8. #1623×C151C2semidirect
9. #1554×C151C2semidirect
10. #1491×C151C2semidirect
11. #1485×C151C2semidirect
256. #18612C151direct (N × H)
257. C151#18612direct (N × H)
258. #3502C2×C151semidirect
262. #1648C2×C151semidirect
263. #1645C2×C151semidirect
264. #1626C2×C151semidirect
265. #1623C2×C151semidirect
266. #1554C2×C151semidirect
267. #1491C2×C151semidirect
268. #1485C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3502×C1512
#3216×C1512
#3182×C1512
#3103×C1512
#1648×C1512
#1645×C1512
#1626×C1512
#1623×C1512
#1554×C1512
#1491×C1512
#1485×C1512
#18612151