Finite Group Databasebeta

← C151×#19253 #50324178

Subgroups — C151×#19253 #50324178

Order 38656.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3247×C151C211yesmaximal, characteristic
2#3233×C151C211yesmaximal, characteristic, complemented
3#3182×C151C211yesmaximal, characteristic, complemented
4#2969×C151C211yesmaximal, characteristic, complemented
5#1704×C151C211yesmaximal, characteristic, complemented
6#1698×C151C211yesmaximal, characteristic, complemented
7#1695×C151C211yesmaximal, characteristic, complemented
8#1685×C151C211yesmaximal, characteristic, complemented
9#1683×C151C211yesmaximal, characteristic, complemented
10#1677×C151C211yesmaximal, characteristic, complemented
11#1676×C151C211yesmaximal, characteristic, complemented
12#1666×C151C211yesmaximal, characteristic, complemented
13#1565×C151C211yesmaximal, characteristic, complemented
14#1543×C151C211yesmaximal, characteristic, complemented
15#1542×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#532×C151C2211yescharacteristic
18#529×C151C2211yescharacteristic
19#500×C151C2211yescharacteristic
20#499×C151—21no—
21#492×C151C2211yescharacteristic
22#488×C151—21no—
23#487×C151C2211yescharacteristic
24#486×C151C2211yescharacteristic
25#485×C151—21no—
26#482×C151—21no—
27#478×C151—21no—
28#477×C151C2211yescharacteristic
29#477×C151C2211yescharacteristic
30#476×C151C2211yescharacteristic
31#476×C151C2211yescharacteristic
32#475×C151C2211yescharacteristic
33#474×C151C2211yescharacteristic
34#468×C151—21no—
35#468×C151—21no—
36#466×C151—21no—
37#465×C151—21no—
38#463×C151—21no—
39#460×C151C2211yescharacteristic
40#459×C151C2211yescharacteristic
41#446×C151C2211yescharacteristic
42C8×Q8×C151C2211yescharacteristic
43#440×C151—21no—
44#440×C151—21no—
45#436×C151—21no—
46#436×C151C2211yescharacteristic
47#435×C151—21no—
48C8×D4×C151C2211yescharacteristic
49#433×C151—21no—
50#431×C151C2211yescharacteristic
51#431×C151C2211yescharacteristic
52C2×C4⋊C8×C151C2211yescharacteristic
53#405×C151—21no—
54C4×M16×C151C2211yescharacteristic
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#333×C151C2211yescharacteristic
62#333×C151C2211yescharacteristic
63#332×C151C2211yescharacteristic
64#332×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×SD16×C151—21no—
69C2×SD16×C151—21no—
70C2×SD16×C151—21no—
71C2×D8×C151—21no—
72C2×M16×C151—21no—
73C2×M16×C151D411yescharacteristic
74C2×M16×C151D411yescharacteristic
75C22×C8×C151—21no—
76C22×C8×C151—21no—
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80#127×C151C2311yescharacteristic
81#126×C151—21no—
82#125×C151—21no—
83#125×C151D411yescharacteristic
84#124×C151—21no—
85#124×C151D411yescharacteristic
86#123×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151D411yescharacteristic
90#121×C151—21no—
91#121×C151—21no—
92#121×C151D411yescharacteristic
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151C2311yescharacteristic
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151C2311yescharacteristic
100#117×C151—21no—
101#117×C151—21no—
102C2×C42×C151C2311yescharacteristic
103#107×C151—21no—
104#107×C151—21no—
105#107×C151—21no—
106#107×C151—21no—
107#107×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110#106×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
124#103×C151—21no—
125#102×C151—21no—
126#102×C151—21no—
127#102×C151—21no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132C22⋊C8×C151—21no—
133C22⋊C8×C151—21no—
134C22⋊C8×C151—21no—
135C22⋊C8×C151—21no—
136#97×C151—21no—
137#97×C151D411yescharacteristic
138#97×C151D411yescharacteristic
139C4×C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—82no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151C2×D411yescharacteristic
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—41no—
154C2×D4×C151C2×D411yescharacteristic
155C22×C4×C151—21no—
156C22×C4×C151—41no—
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151#4111yescharacteristic
160SD16×C151—42no—
161SD16×C151—42no—
162SD16×C151—81no—
163D8×C151—81no—
164M16×C151—22no—
165M16×C151—41no—
166M16×C151—42no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—42no—
174C2×C8×C151—81no—
175C2×C8×C151C2×D411yescharacteristic
176C2×C8×C151C2×D411yescharacteristic
177C2×C8×C151C2×D411yescharacteristic
178C2×C8×C151C2×D411yescharacteristic
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—41no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151C2×D411yescharacteristic
192C4⋊C4×C151C2×D411yescharacteristic
193C22⋊C4×C151—21no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—41no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C42×C151—21no—
202C42×C151—41no—
203C42×C151C2×D411yescharacteristic
204C42×C151C2×D411yescharacteristic
205C42×C151#4111yescharacteristic
206C42×C151C2411yescharacteristic
207C23×C151—21no—
208C23×C151—41no—
209C23×C151#12111yescharacteristic
210Q8×C151—21no—
211Q8×C151—21no—
212Q8×C151—41no—
213Q8×C151—41no—
214Q8×C151—81no—
215Q8×C151—81no—
216D4×C151—21no—
217D4×C151—21no—
218D4×C151—41no—
219D4×C151—41no—
220D4×C151—41no—
221D4×C151—41no—
222D4×C151—81no—
223D4×C151—81no—
224D4×C151—82no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—82no—
239C2×C4×C151#12111yescharacteristic
240C2×C4×C151#12111yescharacteristic
241C2×C4×C151#12111yescharacteristic
242C2×C4×C151C22×D411yescharacteristic
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C2×#4111yescharacteristic
245C8×C151—21no—
246C8×C151—21no—
247C8×C151—21no—
248C8×C151—41no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151—41no—
252C8×C151—41no—
253C8×C151—41no—
254C8×C151#13512yes—
255C22×C151—21no—
256C22×C151—21no—
257C22×C151—21no—
258C22×C151—41no—
259C22×C151—41no—
260C22×C151—41no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151—81no—
264C22×C151C2×#12111yescharacteristic
265C4×C151—21no—
266C4×C151—21no—
267C4×C151—21no—
268C4×C151—21no—
269C4×C151—41no—
270C4×C151—41no—
271C4×C151—41no—
272C4×C151—81no—
273C4×C151—81no—
274C4×C151—81no—
275C4×C151C2×#13511yescharacteristic
276C4×C151#57511yescharacteristic
277C4×C151#57711yescharacteristic
278C4×C151#57811yescharacteristic
279C2×C151—41no—
280C2×C151—81no—
281C2×C151—161no—
282C2×C151#303511yescharacteristic
283C2×C151#306311yescharacteristic
284C2×C151#306811yescharacteristic
285#19253C15111yesmaximal, characteristic, direct product factor, Sylow
286C151#1925311yescharacteristic, direct product factor, Sylow
287#3247C2×C15111yescharacteristic
288#3233C2×C15111yescharacteristic, complemented
289#3182C2×C15111yescharacteristic, complemented
290#2969C2×C15111yescharacteristic, complemented
291#1704C2×C15111yescharacteristic, complemented
292#1698C2×C15111yescharacteristic, complemented
293#1695C2×C15111yescharacteristic, complemented
294#1685C2×C15111yescharacteristic, complemented
295#1683C2×C15111yescharacteristic, complemented
296#1677C2×C15111yescharacteristic, complemented
297#1676C2×C15111yescharacteristic, complemented
298#1666C2×C15111yescharacteristic, complemented
299#1565C2×C15111yescharacteristic, complemented
300#1543C2×C15111yescharacteristic, complemented
301#1542C2×C15111yescharacteristic, complemented
302#533C22×C15111yescharacteristic
303#532C22×C15111yescharacteristic
304#529C22×C15111yescharacteristic
305#500C22×C15111yescharacteristic
306#499—21no—
307#492C22×C15111yescharacteristic
308#488—21no—
309#487C22×C15111yescharacteristic
310#486C22×C15111yescharacteristic
311#485—21no—
312#482—21no—
313#478—21no—
314#477C22×C15111yescharacteristic
315#477C22×C15111yescharacteristic
316#476C22×C15111yescharacteristic
317#476C22×C15111yescharacteristic
318#475C22×C15111yescharacteristic
319#474C22×C15111yescharacteristic
320#468—21no—
321#468—21no—
322#466—21no—
323#465—21no—
324#463—21no—
325#460C22×C15111yescharacteristic
326#459C22×C15111yescharacteristic
327#446C22×C15111yescharacteristic
328C8×Q8C22×C15111yescharacteristic
329#440—21no—
330#440—21no—
331#436—21no—
332#436C22×C15111yescharacteristic
333#435—21no—
334C8×D4C22×C15111yescharacteristic
335#433—21no—
336#431C22×C15111yescharacteristic
337#431C22×C15111yescharacteristic
338C2×C4⋊C8C22×C15111yescharacteristic
339#405—21no—
340C4×M16C22×C15111yescharacteristic
341#335C22×C15111yescharacteristic
342#335C22×C15111yescharacteristic
343#334C22×C15111yescharacteristic
344#334C22×C15111yescharacteristic
345#333C22×C15111yescharacteristic
346#333C22×C15111yescharacteristic
347#333C22×C15111yescharacteristic
348#333C22×C15111yescharacteristic
349#332C22×C15111yescharacteristic
350#332C22×C15111yescharacteristic
351#331C22×C15111yescharacteristic
352#331C22×C15111yescharacteristic
353C2×#41—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×D8—21no—
358C2×M16—21no—
359C2×M16D4×C15111yescharacteristic
360C2×M16D4×C15111yescharacteristic
361C22×C8—21no—
362C22×C8—21no—
363C4⋊Q8C23×C15111yescharacteristic
364C4⋊Q8C23×C15111yescharacteristic
365C4⋊Q8C23×C15111yescharacteristic
366#127C23×C15111yescharacteristic
367#126—21no—
368#125—21no—
369#125D4×C15111yescharacteristic
370#124—21no—
371#124D4×C15111yescharacteristic
372#123—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8D4×C15111yescharacteristic
376#121—21no—
377#121—21no—
378#121D4×C15111yescharacteristic
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C23×C15111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C23×C15111yescharacteristic
386#117—21no—
387#117—21no—
388C2×C42C23×C15111yescharacteristic
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#107—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C23×C15111yescharacteristic
401C4⋊C8C23×C15111yescharacteristic
402C4⋊C8C23×C15111yescharacteristic
403C4⋊C8C23×C15111yescharacteristic
404C4⋊C8C23×C15111yescharacteristic
405C4⋊C8C23×C15111yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422#97—21no—
423#97D4×C15111yescharacteristic
424#97D4×C15111yescharacteristic
425C4×C8—21no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8C23×C15111yescharacteristic
429C4×C8C23×C15111yescharacteristic
430#41—82no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C2×D4×C15111yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4C2×D4×C15111yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4C2×D4×C15111yescharacteristic
444C22×C4C2×D4×C15111yescharacteristic
445C22×C4#41×C15111yescharacteristic
446SD16—42no—
447SD16—42no—
448SD16—81no—
449D8—81no—
450M16—22no—
451M16—41no—
452M16—42no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—42no—
460C2×C8—81no—
461C2×C8C2×D4×C15111yescharacteristic
462C2×C8C2×D4×C15111yescharacteristic
463C2×C8C2×D4×C15111yescharacteristic
464C2×C8C2×D4×C15111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4C2×D4×C15111yescharacteristic
478C4⋊C4C2×D4×C15111yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—41no—
489C42C2×D4×C15111yescharacteristic
490C42C2×D4×C15111yescharacteristic
491C42#41×C15111yescharacteristic
492C42C24×C15111yescharacteristic
493C23—21no—
494C23—41no—
495C23#121×C15111yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502D4—21no—
503D4—21no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—81no—
509D4—81no—
510D4—82no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4#121×C15111yescharacteristic
526C2×C4#121×C15111yescharacteristic
527C2×C4#121×C15111yescharacteristic
528C2×C4C22×D4×C15111yescharacteristic
529C2×C4C22×D4×C15111yescharacteristic
530C2×C4C2×#41×C15111yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8#135×C15112yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22C2×#121×C15111yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4C2×#135×C15111yescharacteristic
562C4#575×C15111yescharacteristic
563C4#577×C15111yescharacteristic
564C4#578×C15111yescharacteristic
565C2—41no—
566C2—81no—
567C2—161no—
568C2#3035×C15111yescharacteristic
569C2#3063×C15111yescharacteristic
570C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3247×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. #3233×C151C2semidirect
3. #3182×C151C2semidirect
4. #2969×C151C2semidirect
5. #1704×C151C2semidirect
6. #1698×C151C2semidirect
7. #1695×C151C2semidirect
8. #1685×C151C2semidirect
9. #1683×C151C2semidirect
10. #1677×C151C2semidirect
11. #1676×C151C2semidirect
12. #1666×C151C2semidirect
13. #1565×C151C2semidirect
14. #1543×C151C2semidirect
15. #1542×C151C2semidirect
285. #19253C151direct (N × H)
286. C151#19253direct (N × H)
288. #3233C2×C151semidirect
289. #3182C2×C151semidirect
290. #2969C2×C151semidirect
291. #1704C2×C151semidirect
292. #1698C2×C151semidirect
293. #1695C2×C151semidirect
294. #1685C2×C151semidirect
295. #1683C2×C151semidirect
296. #1677C2×C151semidirect
297. #1676C2×C151semidirect
298. #1666C2×C151semidirect
299. #1565C2×C151semidirect
300. #1543C2×C151semidirect
301. #1542C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3247×C1512
#3233×C1512
#3182×C1512
#2969×C1512
#1704×C1512
#1698×C1512
#1695×C1512
#1685×C1512
#1683×C1512
#1677×C1512
#1676×C1512
#1666×C1512
#1565×C1512
#1543×C1512
#1542×C1512
#19253151