Finite Group Databasebeta

← C151×#18577 #50323502

Subgroups — C151×#18577 #50323502

Order 38656.

916 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C151C211yesmaximal, characteristic
2#3254×C151C211yesmaximal, characteristic, complemented
3#3139×C151C211yesmaximal, characteristic, complemented
4#3107×C151C211yesmaximal, characteristic, complemented
5#1646×C151C212yesmaximal, complemented
6#1646×C151C212yesmaximal, complemented
7#1644×C151C212yesmaximal, complemented
8#1643×C151C212yesmaximal, complemented
9#1548×C151C211yesmaximal, characteristic, complemented
10#1489×C151C211yesmaximal, characteristic, complemented
11#1484×C151C211yesmaximal, characteristic, complemented
12#556×C151—21no—
13#555×C151C2212yes—
14#554×C151C2212yes—
15#553×C151—22no—
16#548×C151—22no—
17#547×C151—21no—
18#542×C151—22no—
19#537×C151—21no—
20#533×C151—21no—
21#533×C151C2211yescharacteristic
22#532×C151—21no—
23#532×C151C2211yescharacteristic
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#477×C151—21no—
32#475×C151C2211yescharacteristic
33#474×C151C2211yescharacteristic
34#474×C151C2212yes—
35#468×C151—22no—
36#462×C151C2211yescharacteristic
37#461×C151C2211yescharacteristic
38#461×C151C2212yes—
39#460×C151—21no—
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—
50D4⋊C8×C151C2212yes—
51D4⋊C8×C151C2212yes—
52D4⋊C8×C151C2212yes—
53C2×#41×C151—21no—
54C2×#41×C151—22no—
55C2×#41×C151D411yescharacteristic
56C22×Q8×C151D412yes—
57C2×Q16×C151—21no—
58C2×SD16×C151—21no—
59C2×SD16×C151—22no—
60C2×M16×C151—21no—
61C2×M16×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151D411yescharacteristic
65C4⋊Q8×C151D412yes—
66C4⋊Q8×C151C2311yescharacteristic
67C4⋊Q8×C151C2311yescharacteristic
68C4⋊Q8×C151C2312yes—
69#127×C151D411yescharacteristic
70#126×C151—24no—
71#125×C151—22no—
72#125×C151—21no—
73#124×C151—22no—
74#124×C151—21no—
75#124×C151—24no—
76#123×C151—24no—
77C22⋊Q8×C151—22no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—21no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—24no—
83#121×C151—22no—
84#121×C151—24no—
85#121×C151—22no—
86#121×C151—22no—
87#121×C151—21no—
88#121×C151D412yes—
89C4×Q8×C151—22no—
90C4×Q8×C151—22no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151D411yescharacteristic
94C4×Q8×C151C2311yescharacteristic
95C4×D4×C151—22no—
96C4×D4×C151—24no—
97C4×D4×C151—22no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151D411yescharacteristic
102C4×D4×C151C2311yescharacteristic
103C4×D4×C151C2312yes—
104#117×C151—22no—
105#117×C151—22no—
106#117×C151—21no—
107#117×C151—21no—
108#117×C151D411yescharacteristic
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#107×C151—22no—
116#106×C151—21no—
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#102×C151—21no—
128#102×C151—22no—
129C22⋊C8×C151—21no—
130#97×C151—21no—
131C4×C8×C151—21no—
132C4×C8×C151C2312yes—
133#41×C151—41no—
134#41×C151—41no—
135#41×C151—42no—
136#41×C151—42no—
137#41×C151—84no—
138C2×Q8×C151—21no—
139C2×Q8×C151—22no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—44no—
143C2×Q8×C151C2×D411yescharacteristic
144C2×Q8×C151C2×D414yes—
145C2×D4×C151—21no—
146C2×D4×C151—22no—
147C2×D4×C151—24no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151C2×D412yes—
151C2×D4×C151C2×D411yescharacteristic
152C22×C4×C151—24no—
153C22×C4×C151—22no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—22no—
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151C2×D411yescharacteristic
160C22×C4×C151C2×D411yescharacteristic
161Q16×C151—42no—
162SD16×C151—42no—
163SD16×C151—82no—
164M16×C151—42no—
165M16×C151—81no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C4⋊C4×C151—24no—
171C4⋊C4×C151—24no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—22no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—22no—
178C4⋊C4×C151—21no—
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×D411yescharacteristic
186C4⋊C4×C151C2×D411yescharacteristic
187C4⋊C4×C151C2×D412yes—
188C22⋊C4×C151—24no—
189C22⋊C4×C151—24no—
190C22⋊C4×C151—24no—
191C22⋊C4×C151—21no—
192C22⋊C4×C151—21no—
193C22⋊C4×C151—22no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—22no—
196C22⋊C4×C151—41no—
197C42×C151—24no—
198C42×C151—21no—
199C42×C151—21no—
200C42×C151—21no—
201C42×C151—41no—
202C42×C151C2×D411yescharacteristic
203C42×C151C2×D411yescharacteristic
204C42×C151C2×D411yescharacteristic
205C42×C151C2411yescharacteristic
206C23×C151—21no—
207C23×C151—22no—
208C23×C151#12011yescharacteristic
209Q8×C151—21no—
210Q8×C151—21no—
211Q8×C151—44no—
212Q8×C151—42no—
213Q8×C151—44no—
214Q8×C151—41no—
215Q8×C151—41no—
216Q8×C151—41no—
217Q8×C151—41no—
218D4×C151—21no—
219D4×C151—21no—
220D4×C151—22no—
221D4×C151—22no—
222D4×C151—42no—
223D4×C151—42no—
224D4×C151—44no—
225D4×C151—42no—
226D4×C151—84no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—22no—
232C2×C4×C151—24no—
233C2×C4×C151—22no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—42no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—42no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—82no—
246C2×C4×C151—84no—
247C2×C4×C151#12011yescharacteristic
248C2×C4×C151#12011yescharacteristic
249C2×C4×C151#12011yescharacteristic
250C2×C4×C151C22×D411yescharacteristic
251C2×C4×C151C22×D411yescharacteristic
252C2×C4×C151C22×D411yescharacteristic
253C8×C151—42no—
254C8×C151—41no—
255C8×C151—41no—
256C8×C151—42no—
257C22×C151—21no—
258C22×C151—21no—
259C22×C151—21no—
260C22×C151—41no—
261C22×C151—42no—
262C22×C151—41no—
263C22×C151—42no—
264C22×C151—41no—
265C22×C151—42no—
266C22×C151C2×#12011yescharacteristic
267C4×C151—21no—
268C4×C151—21no—
269C4×C151—21no—
270C4×C151—41no—
271C4×C151—42no—
272C4×C151—41no—
273C4×C151—41no—
274C4×C151—44no—
275C4×C151—81no—
276C4×C151—81no—
277C4×C151#45512yes—
278C4×C151#57511yescharacteristic
279C4×C151#57511yescharacteristic
280C4×C151#57711yescharacteristic
281C4×C151#57811yescharacteristic
282C2×C151—41no—
283C2×C151—81no—
284C2×C151—82no—
285C2×C151#300511yescharacteristic
286C2×C151#301311yescharacteristic
287C2×C151C2×#45511yescharacteristic
288#18577C15111yesmaximal, characteristic, direct product factor, Sylow
289C151#1857711yescharacteristic, direct product factor, Sylow
290#3511C2×C15111yescharacteristic
291#3254C2×C15111yescharacteristic, complemented
292#3139C2×C15111yescharacteristic, complemented
293#3107C2×C15111yescharacteristic, complemented
294#1646C2×C15112yescomplemented
295#1646C2×C15112yescomplemented
296#1644C2×C15112yescomplemented
297#1643C2×C15112yescomplemented
298#1548C2×C15111yescharacteristic, complemented
299#1489C2×C15111yescharacteristic, complemented
300#1484C2×C15111yescharacteristic, complemented
301#556—21no—
302#555C22×C15112yes—
303#554C22×C15112yes—
304#553—22no—
305#548—22no—
306#547—21no—
307#542—22no—
308#537—21no—
309#533—21no—
310#533C22×C15111yescharacteristic
311#532—21no—
312#532C22×C15111yescharacteristic
313C2×C4⋊Q8C22×C15111yescharacteristic
314#520—21no—
315C4×#41C22×C15111yescharacteristic
316#491—22no—
317#487C22×C15112yes—
318#487C22×C15112yes—
319#485—21no—
320#477—21no—
321#475C22×C15111yescharacteristic
322#474C22×C15111yescharacteristic
323#474C22×C15112yes—
324#468—22no—
325#462C22×C15111yescharacteristic
326#461C22×C15111yescharacteristic
327#461C22×C15112yes—
328#460—21no—
329#452—21no—
330C4×Q16—21no—
331C4×SD16—21no—
332#431C22×C15111yescharacteristic
333#423C22×C15111yescharacteristic
334#419—22no—
335C4×M16C22×C15111yescharacteristic
336#333C22×C15112yes—
337#333C22×C15112yes—
338Q8⋊C8C22×C15112yes—
339D4⋊C8C22×C15112yes—
340D4⋊C8C22×C15112yes—
341D4⋊C8C22×C15112yes—
342C2×#41—22no—
343C2×#41—21no—
344C2×#41D4×C15111yescharacteristic
345C22×Q8D4×C15112yes—
346C2×Q16—21no—
347C2×SD16—21no—
348C2×SD16—22no—
349C2×M16—21no—
350C2×M16—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8D4×C15112yes—
354C4⋊Q8D4×C15111yescharacteristic
355C4⋊Q8C23×C15111yescharacteristic
356C4⋊Q8C23×C15111yescharacteristic
357C4⋊Q8C23×C15112yes—
358#127D4×C15111yescharacteristic
359#126—24no—
360#125—22no—
361#125—21no—
362#124—22no—
363#124—24no—
364#124—21no—
365#123—24no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—24no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372#121—22no—
373#121—24no—
374#121—22no—
375#121—22no—
376#121—21no—
377#121D4×C15112yes—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8D4×C15111yescharacteristic
383C4×Q8C23×C15111yescharacteristic
384C4×D4—22no—
385C4×D4—24no—
386C4×D4—22no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4D4×C15111yescharacteristic
391C4×D4C23×C15111yescharacteristic
392C4×D4C23×C15112yes—
393#117—22no—
394#117—22no—
395#117—21no—
396#117—21no—
397#117D4×C15111yescharacteristic
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C42—21no—
402C2×C42C23×C15111yescharacteristic
403#107—21no—
404#107—22no—
405#106—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C15111yescharacteristic
408C4⋊C8C23×C15111yescharacteristic
409C4⋊C8C23×C15112yes—
410#103—24no—
411#103—24no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—22no—
416#102—21no—
417#102—22no—
418C22⋊C8—21no—
419#97—21no—
420C4×C8—21no—
421C4×C8C23×C15112yes—
422#41—41no—
423#41—41no—
424#41—42no—
425#41—42no—
426#41—84no—
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—44no—
432C2×Q8C2×D4×C15111yescharacteristic
433C2×Q8C2×D4×C15114yes—
434C2×D4—21no—
435C2×D4—22no—
436C2×D4—24no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4C2×D4×C15112yes—
440C2×D4C2×D4×C15111yescharacteristic
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4C2×D4×C15111yescharacteristic
448C22×C4C2×D4×C15111yescharacteristic
449C22×C4C2×D4×C15111yescharacteristic
450Q16—42no—
451SD16—42no—
452SD16—82no—
453M16—42no—
454M16—81no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—22no—
458C2×C8—22no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4C2×D4×C15111yescharacteristic
475C4⋊C4C2×D4×C15111yescharacteristic
476C4⋊C4C2×D4×C15112yes—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—22no—
485C22⋊C4—41no—
486C42—24no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—41no—
491C42C2×D4×C15111yescharacteristic
492C42C2×D4×C15111yescharacteristic
493C42C2×D4×C15111yescharacteristic
494C42C24×C15111yescharacteristic
495C23—21no—
496C23—22no—
497C23#120×C15111yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—44no—
501Q8—42no—
502Q8—44no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507D4—21no—
508D4—21no—
509D4—22no—
510D4—22no—
511D4—42no—
512D4—42no—
513D4—44no—
514D4—42no—
515D4—84no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—84no—
536C2×C4#120×C15111yescharacteristic
537C2×C4#120×C15111yescharacteristic
538C2×C4#120×C15111yescharacteristic
539C2×C4C22×D4×C15111yescharacteristic
540C2×C4C22×D4×C15111yescharacteristic
541C2×C4C22×D4×C15111yescharacteristic
542C8—42no—
543C8—41no—
544C8—41no—
545C8—42no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—42no—
551C22—41no—
552C22—42no—
553C22—41no—
554C22—42no—
555C22C2×#120×C15111yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—42no—
561C4—41no—
562C4—41no—
563C4—44no—
564C4—81no—
565C4—81no—
566C4#455×C15112yes—
567C4#575×C15111yescharacteristic
568C4#575×C15111yescharacteristic
569C4#577×C15111yescharacteristic
570C4#578×C15111yescharacteristic
571C2—41no—
572C2—81no—
573C2—82no—
574C2#3005×C15111yescharacteristic
575C2#3013×C15111yescharacteristic
576C2C2×#455×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3511×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. #3254×C151C2semidirect
3. #3139×C151C2semidirect
4. #3107×C151C2semidirect
5. #1646×C151C2semidirect
6. #1646×C151C2semidirect
7. #1644×C151C2semidirect
8. #1643×C151C2semidirect
9. #1548×C151C2semidirect
10. #1489×C151C2semidirect
11. #1484×C151C2semidirect
288. #18577C151direct (N × H)
289. C151#18577direct (N × H)
291. #3254C2×C151semidirect
292. #3139C2×C151semidirect
293. #3107C2×C151semidirect
294. #1646C2×C151semidirect
295. #1646C2×C151semidirect
296. #1644C2×C151semidirect
297. #1643C2×C151semidirect
298. #1548C2×C151semidirect
299. #1489C2×C151semidirect
300. #1484C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3511×C1512
#3254×C1512
#3139×C1512
#3107×C1512
#1646×C1512
#1644×C1512
#1643×C1512
#1548×C1512
#1489×C1512
#1484×C1512
#18577151