Finite Group Databasebeta

← C151×#18575 #50323500

Subgroups — C151×#18575 #50323500

Order 38656.

894 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C151C211yesmaximal, characteristic
2#3255×C151C211yesmaximal, characteristic, complemented
3#3139×C151C211yesmaximal, characteristic, complemented
4#3107×C151C211yesmaximal, characteristic
5#1645×C151C212yesmaximal, complemented
6#1645×C151C212yesmaximal, complemented
7#1644×C151C212yesmaximal, complemented
8#1643×C151C212yesmaximal, complemented
9#1548×C151C211yesmaximal, characteristic, complemented
10#1489×C151C211yesmaximal, characteristic
11#1485×C151C211yesmaximal, characteristic, complemented
12Q82×C151C2212yes—
13#557×C151—21no—
14#554×C151—22no—
15#554×C151C2212yes—
16D4×Q8×C151—22no—
17D4×Q8×C151—21no—
18#544×C151—22no—
19#544×C151—21no—
20#533×C151—21no—
21#533×C151C2211yescharacteristic
22#533×C151C2211yescharacteristic
23C2×C4⋊Q8×C151—21no—
24C2×C4⋊Q8×C151C2211yescharacteristic
25#520×C151—21no—
26C4×#41×C151C2211yescharacteristic
27#491×C151—22no—
28#487×C151C2212yes—
29#487×C151C2212yes—
30#485×C151—21no—
31#475×C151—21no—
32#475×C151C2211yescharacteristic
33#475×C151C2212yes—
34#474×C151C2211yescharacteristic
35#470×C151—22no—
36#462×C151—21no—
37#462×C151C2211yescharacteristic
38#462×C151C2212yes—
39#461×C151C2211yescharacteristic
40#452×C151—21no—
41C4×Q16×C151—21no—
42C4×SD16×C151—21no—
43#431×C151C2211yescharacteristic
44#423×C151C2211yescharacteristic
45#419×C151—22no—
46C4×M16×C151C2211yescharacteristic
47#333×C151C2212yes—
48#333×C151C2212yes—
49Q8⋊C8×C151C2212yes—
50Q8⋊C8×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52D4⋊C8×C151C2212yes—
53C2×#41×C151D411yescharacteristic
54C22×Q8×C151—22no—
55C22×Q8×C151D412yes—
56C2×Q16×C151—21no—
57C2×Q16×C151—22no—
58C2×SD16×C151—21no—
59C2×M16×C151—21no—
60C2×M16×C151—21no—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151—22no—
63C4⋊Q8×C151—22no—
64C4⋊Q8×C151—22no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151—24no—
68C4⋊Q8×C151D411yescharacteristic
69C4⋊Q8×C151D411yescharacteristic
70C4⋊Q8×C151D412yes—
71C4⋊Q8×C151C2311yescharacteristic
72C4⋊Q8×C151C2311yescharacteristic
73C4⋊Q8×C151C2312yes—
74#125×C151—22no—
75#125×C151—24no—
76#125×C151—22no—
77#125×C151—21no—
78#125×C151—21no—
79C22⋊Q8×C151—22no—
80C22⋊Q8×C151—24no—
81C22⋊Q8×C151—24no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—24no—
87C22⋊Q8×C151D412yes—
88C4×Q8×C151—22no—
89C4×Q8×C151—21no—
90C4×Q8×C151—21no—
91C4×Q8×C151—21no—
92C4×Q8×C151—22no—
93C4×Q8×C151—22no—
94C4×Q8×C151D411yescharacteristic
95C4×Q8×C151C2311yescharacteristic
96C4×Q8×C151C2312yes—
97C4×D4×C151—24no—
98C4×D4×C151—22no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151D411yescharacteristic
102C4×D4×C151C2311yescharacteristic
103#117×C151—22no—
104#117×C151—21no—
105#117×C151—21no—
106#117×C151—21no—
107#117×C151D411yescharacteristic
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—22no—
112C2×C42×C151—21no—
113C2×C42×C151C2311yescharacteristic
114#107×C151—21no—
115#106×C151—21no—
116#106×C151—22no—
117C4⋊C8×C151—21no—
118C4⋊C8×C151C2312yes—
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—22no—
124#103×C151—24no—
125#103×C151—24no—
126#103×C151—21no—
127#103×C151—22no—
128#102×C151—21no—
129C22⋊C8×C151—21no—
130#97×C151—21no—
131C4×C8×C151—21no—
132C4×C8×C151C2312yes—
133#41×C151—22no—
134#41×C151—22no—
135C2×Q8×C151—24no—
136C2×Q8×C151—22no—
137C2×Q8×C151—21no—
138C2×Q8×C151—21no—
139C2×Q8×C151—21no—
140C2×Q8×C151—44no—
141C2×Q8×C151—84no—
142C2×Q8×C151C2×D412yes—
143C2×Q8×C151C2×D411yescharacteristic
144C2×Q8×C151C2×D414yes—
145C2×D4×C151—21no—
146C2×D4×C151C2×D411yescharacteristic
147C22×C4×C151—21no—
148C22×C4×C151—24no—
149C22×C4×C151—22no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155Q16×C151—42no—
156Q16×C151—82no—
157SD16×C151—42no—
158M16×C151—42no—
159M16×C151—81no—
160C2×C8×C151—21no—
161C2×C8×C151—21no—
162C2×C8×C151—22no—
163C2×C8×C151—22no—
164C4⋊C4×C151—24no—
165C4⋊C4×C151—24no—
166C4⋊C4×C151—24no—
167C4⋊C4×C151—24no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—41no—
184C4⋊C4×C151—41no—
185C4⋊C4×C151C2×D412yes—
186C4⋊C4×C151C2×D411yescharacteristic
187C4⋊C4×C151C2×D411yescharacteristic
188C22⋊C4×C151—24no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—21no—
191C22⋊C4×C151—21no—
192C22⋊C4×C151—21no—
193C22⋊C4×C151—41no—
194C42×C151—24no—
195C42×C151—21no—
196C42×C151—21no—
197C42×C151—21no—
198C42×C151—22no—
199C42×C151—41no—
200C42×C151C2×D411yescharacteristic
201C42×C151C2×D411yescharacteristic
202C42×C151C2×D411yescharacteristic
203C42×C151C2411yescharacteristic
204C23×C151—21no—
205C23×C151#12011yescharacteristic
206Q8×C151—21no—
207Q8×C151—22no—
208Q8×C151—22no—
209Q8×C151—44no—
210Q8×C151—44no—
211Q8×C151—42no—
212Q8×C151—41no—
213Q8×C151—41no—
214Q8×C151—41no—
215Q8×C151—41no—
216Q8×C151—84no—
217Q8×C151#13712yes—
218D4×C151—24no—
219D4×C151—21no—
220D4×C151#13712yes—
221C2×C4×C151—24no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—22no—
228C2×C4×C151—21no—
229C2×C4×C151—22no—
230C2×C4×C151—24no—
231C2×C4×C151—22no—
232C2×C4×C151—21no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—42no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—82no—
239C2×C4×C151—84no—
240C2×C4×C151#12011yescharacteristic
241C2×C4×C151#12011yescharacteristic
242C2×C4×C151#12011yescharacteristic
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C2×C4×C151C22×D411yescharacteristic
246C8×C151—42no—
247C8×C151—41no—
248C8×C151—41no—
249C8×C151—42no—
250C22×C151—21no—
251C22×C151—22no—
252C22×C151—21no—
253C22×C151—21no—
254C22×C151—41no—
255C22×C151—41no—
256C22×C151C2×#12011yescharacteristic
257C4×C151—21no—
258C4×C151—22no—
259C4×C151—21no—
260C4×C151—21no—
261C4×C151—41no—
262C4×C151—42no—
263C4×C151—41no—
264C4×C151—44no—
265C4×C151—42no—
266C4×C151—81no—
267C4×C151—81no—
268C4×C151#45512yes—
269C4×C151C2×#13711yescharacteristic
270C4×C151C2×#13711yescharacteristic
271C4×C151#57711yescharacteristic
272C4×C151#57811yescharacteristic
273C2×C151—41no—
274C2×C151—42no—
275C2×C151#300411yescharacteristic
276C2×C151#301311yescharacteristic
277C2×C151C2×#45511yescharacteristic
278#18575C15111yesmaximal, characteristic, direct product factor, Sylow
279C151#1857511yescharacteristic, direct product factor, Sylow
280#3503C2×C15111yescharacteristic
281#3255C2×C15111yescharacteristic, complemented
282#3139C2×C15111yescharacteristic, complemented
283#3107C2×C15111yescharacteristic
284#1645C2×C15112yescomplemented
285#1645C2×C15112yescomplemented
286#1644C2×C15112yescomplemented
287#1643C2×C15112yescomplemented
288#1548C2×C15111yescharacteristic, complemented
289#1489C2×C15111yescharacteristic
290#1485C2×C15111yescharacteristic, complemented
291Q82C22×C15112yes—
292#557—21no—
293#554—22no—
294#554C22×C15112yes—
295D4×Q8—22no—
296D4×Q8—21no—
297#544—22no—
298#544—21no—
299#533—21no—
300#533C22×C15111yescharacteristic
301#533C22×C15111yescharacteristic
302C2×C4⋊Q8—21no—
303C2×C4⋊Q8C22×C15111yescharacteristic
304#520—21no—
305C4×#41C22×C15111yescharacteristic
306#491—22no—
307#487C22×C15112yes—
308#487C22×C15112yes—
309#485—21no—
310#475—21no—
311#475C22×C15111yescharacteristic
312#475C22×C15112yes—
313#474C22×C15111yescharacteristic
314#470—22no—
315#462—21no—
316#462C22×C15111yescharacteristic
317#462C22×C15112yes—
318#461C22×C15111yescharacteristic
319#452—21no—
320C4×Q16—21no—
321C4×SD16—21no—
322#431C22×C15111yescharacteristic
323#423C22×C15111yescharacteristic
324#419—22no—
325C4×M16C22×C15111yescharacteristic
326#333C22×C15112yes—
327#333C22×C15112yes—
328Q8⋊C8C22×C15112yes—
329Q8⋊C8C22×C15112yes—
330Q8⋊C8C22×C15112yes—
331D4⋊C8C22×C15112yes—
332C2×#41D4×C15111yescharacteristic
333C22×Q8—22no—
334C22×Q8D4×C15112yes—
335C2×Q16—21no—
336C2×Q16—22no—
337C2×SD16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—24no—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8D4×C15112yes—
348C4⋊Q8D4×C15111yescharacteristic
349C4⋊Q8D4×C15111yescharacteristic
350C4⋊Q8C23×C15111yescharacteristic
351C4⋊Q8C23×C15111yescharacteristic
352C4⋊Q8C23×C15112yes—
353#125—22no—
354#125—24no—
355#125—22no—
356#125—21no—
357#125—21no—
358C22⋊Q8—22no—
359C22⋊Q8—24no—
360C22⋊Q8—24no—
361C22⋊Q8—22no—
362C22⋊Q8—24no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8D4×C15112yes—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8D4×C15111yescharacteristic
374C4×Q8C23×C15111yescharacteristic
375C4×Q8C23×C15112yes—
376C4×D4—24no—
377C4×D4—22no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4D4×C15111yescharacteristic
381C4×D4C23×C15111yescharacteristic
382#117—22no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117D4×C15111yescharacteristic
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C42—21no—
392C2×C42C23×C15111yescharacteristic
393#107—21no—
394#106—21no—
395#106—22no—
396C4⋊C8—21no—
397C4⋊C8C23×C15112yes—
398C4⋊C8C23×C15111yescharacteristic
399C4⋊C8C23×C15111yescharacteristic
400#103—24no—
401#103—24no—
402#103—21no—
403#103—22no—
404#103—21no—
405#103—21no—
406#103—22no—
407#102—21no—
408C22⋊C8—21no—
409#97—21no—
410C4×C8—21no—
411C4×C8C23×C15112yes—
412#41—22no—
413#41—22no—
414C2×Q8—24no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—44no—
420C2×Q8—84no—
421C2×Q8C2×D4×C15112yes—
422C2×Q8C2×D4×C15111yescharacteristic
423C2×Q8C2×D4×C15114yes—
424C2×D4—21no—
425C2×D4C2×D4×C15111yescharacteristic
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4C2×D4×C15111yescharacteristic
432C22×C4C2×D4×C15111yescharacteristic
433C22×C4C2×D4×C15111yescharacteristic
434Q16—42no—
435Q16—82no—
436SD16—42no—
437M16—42no—
438M16—81no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—22no—
442C2×C8—22no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C15112yes—
465C4⋊C4C2×D4×C15111yescharacteristic
466C4⋊C4C2×D4×C15111yescharacteristic
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—41no—
473C42—24no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—22no—
478C42—41no—
479C42C2×D4×C15111yescharacteristic
480C42C2×D4×C15111yescharacteristic
481C42C2×D4×C15111yescharacteristic
482C42C24×C15111yescharacteristic
483C23—21no—
484C23#120×C15111yescharacteristic
485Q8—21no—
486Q8—22no—
487Q8—22no—
488Q8—44no—
489Q8—44no—
490Q8—42no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—84no—
496Q8#137×C15112yes—
497D4—24no—
498D4—21no—
499D4#137×C15112yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4—84no—
519C2×C4#120×C15111yescharacteristic
520C2×C4#120×C15111yescharacteristic
521C2×C4#120×C15111yescharacteristic
522C2×C4C22×D4×C15111yescharacteristic
523C2×C4C22×D4×C15111yescharacteristic
524C2×C4C22×D4×C15111yescharacteristic
525C8—42no—
526C8—41no—
527C8—41no—
528C8—42no—
529C22—21no—
530C22—22no—
531C22—21no—
532C22—21no—
533C22—41no—
534C22—41no—
535C22C2×#120×C15111yescharacteristic
536C4—21no—
537C4—22no—
538C4—21no—
539C4—21no—
540C4—41no—
541C4—42no—
542C4—41no—
543C4—44no—
544C4—42no—
545C4—81no—
546C4—81no—
547C4#455×C15112yes—
548C4C2×#137×C15111yescharacteristic
549C4C2×#137×C15111yescharacteristic
550C4#577×C15111yescharacteristic
551C4#578×C15111yescharacteristic
552C2—41no—
553C2—42no—
554C2#3004×C15111yescharacteristic
555C2#3013×C15111yescharacteristic
556C2C2×#455×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#41×C151D4
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. #3255×C151C2semidirect
3. #3139×C151C2semidirect
5. #1645×C151C2semidirect
6. #1645×C151C2semidirect
7. #1644×C151C2semidirect
8. #1643×C151C2semidirect
9. #1548×C151C2semidirect
11. #1485×C151C2semidirect
278. #18575C151direct (N × H)
279. C151#18575direct (N × H)
281. #3255C2×C151semidirect
282. #3139C2×C151semidirect
284. #1645C2×C151semidirect
285. #1645C2×C151semidirect
286. #1644C2×C151semidirect
287. #1643C2×C151semidirect
288. #1548C2×C151semidirect
290. #1485C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3503×C1512
#3255×C1512
#3139×C1512
#3107×C1512
#1645×C1512
#1644×C1512
#1643×C1512
#1548×C1512
#1489×C1512
#1485×C1512
#18575151