Finite Group Databasebeta

← C151×#19794 #50324719

Subgroups — C151×#19794 #50324719

Order 38656.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3372×C151C211yesmaximal, characteristic, complemented
2#3364×C151C211yesmaximal, characteristic, complemented
3#3335×C151C211yesmaximal, characteristic
4#3302×C151C211yesmaximal, characteristic
5#1718×C151C211yesmaximal, characteristic, complemented
6#1700×C151C211yesmaximal, characteristic, complemented
7#1683×C151C211yesmaximal, characteristic, complemented
8#1679×C151C211yesmaximal, characteristic, complemented
9#1672×C151C211yesmaximal, characteristic, complemented
10#1648×C151C211yesmaximal, characteristic, complemented
11#1647×C151C211yesmaximal, characteristic
12#1644×C151C211yesmaximal, characteristic, complemented
13#1638×C151C211yesmaximal, characteristic, complemented
14#1582×C151C211yesmaximal, characteristic, complemented
15SD16⋊C8×C151C211yesmaximal, characteristic, complemented
16#557×C151C2211yescharacteristic
17#556×C151C2211yescharacteristic
18#554×C151C2211yescharacteristic
19#547×C151C2211yescharacteristic
20#500×C151C2211yescharacteristic
21#498×C151C2211yescharacteristic
22#491×C151—21no—
23#488×C151—21no—
24#487×C151C2211yescharacteristic
25#487×C151C2211yescharacteristic
26#487×C151C2211yescharacteristic
27#487×C151C2211yescharacteristic
28#485×C151—21no—
29#483×C151—21no—
30#481×C151—21no—
31#479×C151—21no—
32#479×C151—21no—
33#477×C151C2211yescharacteristic
34#476×C151C2211yescharacteristic
35#475×C151C2211yescharacteristic
36#474×C151C2211yescharacteristic
37#474×C151C2211yescharacteristic
38#467×C151—21no—
39#465×C151—21no—
40#464×C151—21no—
41#462×C151C2211yescharacteristic
42#462×C151C2211yescharacteristic
43#461×C151—21no—
44#461×C151C2211yescharacteristic
45#452×C151—21no—
46#446×C151C2211yescharacteristic
47C8×Q8×C151C2211yescharacteristic
48#440×C151—21no—
49C4×Q16×C151—21no—
50C4×SD16×C151C2211yescharacteristic
51C4×SD16×C151C2211yescharacteristic
52C8×D4×C151C2211yescharacteristic
53C8×D4×C151C2211yescharacteristic
54C2×#106×C151—21no—
55#416×C151—21no—
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×Q16×C151—21no—
69C2×Q16×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151D411yescharacteristic
72C2×SD16×C151D411yescharacteristic
73C22×C8×C151—21no—
74C22×C8×C151—21no—
75C4⋊Q8×C151—21no—
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80#126×C151—41no—
81#125×C151—21no—
82#125×C151—21no—
83#125×C151—41no—
84#124×C151—21no—
85#123×C151—41no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—41no—
90#121×C151—21no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151C2311yescharacteristic
95C4×Q8×C151C2311yescharacteristic
96C4×D4×C151—21no—
97C4×D4×C151C2311yescharacteristic
98C4×D4×C151C2311yescharacteristic
99#117×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102#107×C151—21no—
103#107×C151—21no—
104#107×C151—21no—
105#107×C151—41no—
106#106×C151—21no—
107#106×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110#106×C151D411yescharacteristic
111#106×C151D411yescharacteristic
112C4⋊C8×C151—21no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118#103×C151—21no—
119#103×C151—21no—
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—21no—
128#103×C151—21no—
129#103×C151—41no—
130#103×C151D411yescharacteristic
131#103×C151D411yescharacteristic
132#102×C151—21no—
133#102×C151—21no—
134#102×C151—21no—
135#102×C151D411yescharacteristic
136#102×C151D411yescharacteristic
137C22⋊C8×C151—21no—
138C22⋊C8×C151—21no—
139#97×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151C2311yescharacteristic
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—42no—
145#41×C151—81no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151C2×D411yescharacteristic
151C2×Q8×C151C2×D411yescharacteristic
152C2×D4×C151—41no—
153C2×D4×C151C2×D411yescharacteristic
154C2×D4×C151C2×D411yescharacteristic
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—41no—
158C22×C4×C151—41no—
159Q16×C151—42no—
160Q16×C151—81no—
161SD16×C151—22no—
162SD16×C151—41no—
163SD16×C151—42no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—42no—
170C2×C8×C151—81no—
171C2×C8×C151C2×D411yescharacteristic
172C2×C8×C151C2×D411yescharacteristic
173C2×C8×C151C2×D411yescharacteristic
174C2×C8×C151C2×D411yescharacteristic
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
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—41no—
186C4⋊C4×C151—41no—
187C4⋊C4×C151—41no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151—41no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151C2×D411yescharacteristic
193C4⋊C4×C151C2×D411yescharacteristic
194C4⋊C4×C151C2×D411yescharacteristic
195C4⋊C4×C151C2×D411yescharacteristic
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—41no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C42×C151—21no—
203C42×C151—21no—
204C42×C151—41no—
205C42×C151—41no—
206C42×C151C2411yescharacteristic
207C23×C151—21no—
208C23×C151—21no—
209Q8×C151—21no—
210Q8×C151—21no—
211Q8×C151—21no—
212Q8×C151—21no—
213Q8×C151—41no—
214Q8×C151—41no—
215Q8×C151—41no—
216Q8×C151—41no—
217Q8×C151—41no—
218Q8×C151—41no—
219Q8×C151—81no—
220D4×C151—21no—
221D4×C151—21no—
222D4×C151—21no—
223D4×C151—82no—
224D4×C151#13512yes—
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—41no—
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—41no—
239C2×C4×C151—82no—
240C2×C4×C151—161no—
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151C22×D411yescharacteristic
243C2×C4×C151H(5,𝔽2)11yescharacteristic
244C8×C151—21no—
245C8×C151—21no—
246C8×C151—21no—
247C8×C151—21no—
248C8×C151—41no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151—41no—
252C8×C151—41no—
253C22×C151—22no—
254C22×C151—41no—
255C22×C151—41no—
256C22×C151—41no—
257C22×C151—41no—
258C22×C151—41no—
259C22×C151D4211yescharacteristic
260C4×C151—21no—
261C4×C151—41no—
262C4×C151—41no—
263C4×C151—41no—
264C4×C151—41no—
265C4×C151—41no—
266C4×C151—41no—
267C4×C151—81no—
268C4×C151—81no—
269C4×C151—81no—
270C4×C151—81no—
271C4×C151C2×#13511yescharacteristic
272C4×C151#57511yescharacteristic
273C4×C151#57711yescharacteristic
274C4×C151#57811yescharacteristic
275C2×C151—42no—
276C2×C151—81no—
277C2×C151#326911yescharacteristic
278C2×C151#328211yescharacteristic
279C2×C151#328911yescharacteristic
280#19794C15111yesmaximal, characteristic, direct product factor, Sylow
281C151#1979411yescharacteristic, direct product factor, Sylow
282#3372C2×C15111yescharacteristic, complemented
283#3364C2×C15111yescharacteristic, complemented
284#3335C2×C15111yescharacteristic
285#3302C2×C15111yescharacteristic
286#1718C2×C15111yescharacteristic, complemented
287#1700C2×C15111yescharacteristic, complemented
288#1683C2×C15111yescharacteristic, complemented
289#1679C2×C15111yescharacteristic, complemented
290#1672C2×C15111yescharacteristic, complemented
291#1648C2×C15111yescharacteristic, complemented
292#1647C2×C15111yescharacteristic
293#1644C2×C15111yescharacteristic, complemented
294#1638C2×C15111yescharacteristic, complemented
295#1582C2×C15111yescharacteristic, complemented
296SD16⋊C8C2×C15111yescharacteristic, complemented
297#557C22×C15111yescharacteristic
298#556C22×C15111yescharacteristic
299#554C22×C15111yescharacteristic
300#547C22×C15111yescharacteristic
301#500C22×C15111yescharacteristic
302#498C22×C15111yescharacteristic
303#491—21no—
304#488—21no—
305#487C22×C15111yescharacteristic
306#487C22×C15111yescharacteristic
307#487C22×C15111yescharacteristic
308#487C22×C15111yescharacteristic
309#485—21no—
310#483—21no—
311#481—21no—
312#479—21no—
313#479—21no—
314#477C22×C15111yescharacteristic
315#476C22×C15111yescharacteristic
316#475C22×C15111yescharacteristic
317#474C22×C15111yescharacteristic
318#474C22×C15111yescharacteristic
319#467—21no—
320#465—21no—
321#464—21no—
322#462C22×C15111yescharacteristic
323#462C22×C15111yescharacteristic
324#461—21no—
325#461C22×C15111yescharacteristic
326#452—21no—
327#446C22×C15111yescharacteristic
328C8×Q8C22×C15111yescharacteristic
329#440—21no—
330C4×Q16—21no—
331C4×SD16C22×C15111yescharacteristic
332C4×SD16C22×C15111yescharacteristic
333C8×D4C22×C15111yescharacteristic
334C8×D4C22×C15111yescharacteristic
335C2×#106—21no—
336#416—21no—
337#335C22×C15111yescharacteristic
338#334C22×C15111yescharacteristic
339#333C22×C15111yescharacteristic
340#332C22×C15111yescharacteristic
341#332C22×C15111yescharacteristic
342#332C22×C15111yescharacteristic
343Q8⋊C8C22×C15111yescharacteristic
344Q8⋊C8C22×C15111yescharacteristic
345D4⋊C8C22×C15111yescharacteristic
346D4⋊C8C22×C15111yescharacteristic
347#322C22×C15111yescharacteristic
348C2×#41—21no—
349C2×Q16—21no—
350C2×Q16—21no—
351C2×SD16—21no—
352C2×SD16D4×C15111yescharacteristic
353C2×SD16D4×C15111yescharacteristic
354C22×C8—21no—
355C22×C8—21no—
356C4⋊Q8—21no—
357C4⋊Q8C23×C15111yescharacteristic
358C4⋊Q8C23×C15111yescharacteristic
359C4⋊Q8C23×C15111yescharacteristic
360C4⋊Q8C23×C15111yescharacteristic
361#126—41no—
362#125—21no—
363#125—21no—
364#125—41no—
365#124—21no—
366#123—41no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371#121—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C15111yescharacteristic
376C4×Q8C23×C15111yescharacteristic
377C4×D4—21no—
378C4×D4C23×C15111yescharacteristic
379C4×D4C23×C15111yescharacteristic
380#117—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—41no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106D4×C15111yescharacteristic
392#106D4×C15111yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C15111yescharacteristic
396C4⋊C8C23×C15111yescharacteristic
397C4⋊C8C23×C15111yescharacteristic
398C4⋊C8C23×C15111yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—41no—
411#103D4×C15111yescharacteristic
412#103D4×C15111yescharacteristic
413#102—21no—
414#102—21no—
415#102—21no—
416#102D4×C15111yescharacteristic
417#102D4×C15111yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—21no—
420#97—21no—
421C4×C8—21no—
422C4×C8C23×C15111yescharacteristic
423C4×C8C23×C15111yescharacteristic
424C4×C8C23×C15111yescharacteristic
425#41—42no—
426#41—81no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C2×D4×C15111yescharacteristic
432C2×Q8C2×D4×C15111yescharacteristic
433C2×D4—41no—
434C2×D4C2×D4×C15111yescharacteristic
435C2×D4C2×D4×C15111yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—41no—
440Q16—42no—
441Q16—81no—
442SD16—22no—
443SD16—41no—
444SD16—42no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—81no—
452C2×C8C2×D4×C15111yescharacteristic
453C2×C8C2×D4×C15111yescharacteristic
454C2×C8C2×D4×C15111yescharacteristic
455C2×C8C2×D4×C15111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C15111yescharacteristic
474C4⋊C4C2×D4×C15111yescharacteristic
475C4⋊C4C2×D4×C15111yescharacteristic
476C4⋊C4C2×D4×C15111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—41no—
486C42—41no—
487C42C24×C15111yescharacteristic
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501D4—21no—
502D4—21no—
503D4—21no—
504D4—82no—
505D4#135×C15112yes—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—82no—
521C2×C4—161no—
522C2×C4C22×D4×C15111yescharacteristic
523C2×C4C22×D4×C15111yescharacteristic
524C2×C4H(5,𝔽2)×C15111yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22D42×C15111yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×#135×C15111yescharacteristic
553C4#575×C15111yescharacteristic
554C4#577×C15111yescharacteristic
555C4#578×C15111yescharacteristic
556C2—42no—
557C2—81no—
558C2#3269×C15111yescharacteristic
559C2#3282×C15111yescharacteristic
560C2#3289×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radical#547×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3372×C151C2semidirect
2. #3364×C151C2semidirect
5. #1718×C151C2semidirect
6. #1700×C151C2semidirect
7. #1683×C151C2semidirect
8. #1679×C151C2semidirect
9. #1672×C151C2semidirect
10. #1648×C151C2semidirect
12. #1644×C151C2semidirect
13. #1638×C151C2semidirect
14. #1582×C151C2semidirect
15. SD16⋊C8×C151C2semidirect
280. #19794C151direct (N × H)
281. C151#19794direct (N × H)
282. #3372C2×C151semidirect
283. #3364C2×C151semidirect
286. #1718C2×C151semidirect
287. #1700C2×C151semidirect
288. #1683C2×C151semidirect
289. #1679C2×C151semidirect
290. #1672C2×C151semidirect
291. #1648C2×C151semidirect
293. #1644C2×C151semidirect
294. #1638C2×C151semidirect
295. #1582C2×C151semidirect
296. SD16⋊C8C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3372×C1512
#3364×C1512
#3335×C1512
#3302×C1512
#1718×C1512
#1700×C1512
#1683×C1512
#1679×C1512
#1672×C1512
#1648×C1512
#1647×C1512
#1644×C1512
#1638×C1512
#1582×C1512
SD16⋊C8×C1512
#19794151