Finite Group Databasebeta

← C151×#19309 #50324234

Subgroups — C151×#19309 #50324234

Order 38656.

600 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3182×C151C211yesmaximal, characteristic
2#3112×C151C211yesmaximal, characteristic
3#3078×C151C211yesmaximal, characteristic, complemented
4Q8×M16×C151C211yesmaximal, characteristic, complemented
5#1704×C151C211yesmaximal, characteristic, complemented
6#1698×C151C211yesmaximal, characteristic, complemented
7#1696×C151C211yesmaximal, characteristic, complemented
8#1686×C151C211yesmaximal, characteristic, complemented
9#1684×C151C211yesmaximal, characteristic, complemented
10#1678×C151C211yesmaximal, characteristic, complemented
11#1676×C151C211yesmaximal, characteristic, complemented
12#1666×C151C211yesmaximal, characteristic, complemented
13#1569×C151C211yesmaximal, characteristic, complemented
14#1560×C151C211yesmaximal, characteristic
15#1559×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#532×C151C2211yescharacteristic
18C2×C4×Q8×C151C2211yescharacteristic
19#500×C151C2211yescharacteristic
20#492×C151C2211yescharacteristic
21#487×C151C2211yescharacteristic
22#486×C151C2211yescharacteristic
23#480×C151—21no—
24#479×C151—21no—
25#479×C151—21no—
26#477×C151C2211yescharacteristic
27#477×C151C2211yescharacteristic
28#477×C151C2211yescharacteristic
29#477×C151C2211yescharacteristic
30#475×C151C2211yescharacteristic
31#475×C151C2211yescharacteristic
32#468×C151—21no—
33#468×C151—21no—
34#460×C151C2211yescharacteristic
35#460×C151C2211yescharacteristic
36#448×C151—21no—
37#446×C151—21no—
38#446×C151—21no—
39#446×C151C2211yescharacteristic
40#446×C151C2211yescharacteristic
41C8×Q8×C151C2211yescharacteristic
42C8×Q8×C151C2211yescharacteristic
43#440×C151—21no—
44#440×C151—21no—
45#440×C151—21no—
46#440×C151—21no—
47#432×C151C2211yescharacteristic
48#428×C151—21no—
49#423×C151—21no—
50#423×C151C2211yescharacteristic
51#423×C151C2211yescharacteristic
52#419×C151—21no—
53C4×M16×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—
68C22×Q8×C151D411yescharacteristic
69C2×SD16×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×M16×C151—21no—
74C2×M16×C151—21no—
75C2×M16×C151D411yescharacteristic
76C2×M16×C151D411yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80#127×C151C2311yescharacteristic
81#125×C151—21no—
82#124×C151—21no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85#121×C151—21no—
86#121×C151—21no—
87C4×Q8×C151—21no—
88C4×Q8×C151—21no—
89C4×Q8×C151—21no—
90C4×Q8×C151—21no—
91C4×Q8×C151D411yescharacteristic
92C4×Q8×C151D411yescharacteristic
93C4×Q8×C151C2311yescharacteristic
94C4×Q8×C151C2311yescharacteristic
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97#117×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151D411yescharacteristic
100C2×C42×C151—21no—
101C2×C42×C151C2311yescharacteristic
102#107×C151—21no—
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—
110C4⋊C8×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151—21no—
115C4⋊C8×C151—21no—
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
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—21no—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134C22⋊C8×C151—21no—
135#97×C151—21no—
136#97×C151—21no—
137#97×C151—21no—
138#97×C151D411yescharacteristic
139#97×C151D411yescharacteristic
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—22no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—41no—
151C2×Q8×C151C2×D411yescharacteristic
152C2×Q8×C151C2×D411yescharacteristic
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—41no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—41no—
160C22×C4×C151C2×D411yescharacteristic
161C22×C4×C151C2×D411yescharacteristic
162C22×C4×C151#4111yescharacteristic
163SD16×C151—42no—
164SD16×C151—42no—
165SD16×C151—42no—
166SD16×C151—42no—
167M16×C151—22no—
168M16×C151—41no—
169M16×C151—42no—
170M16×C151—42no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151C2×D411yescharacteristic
178C2×C8×C151C2×D411yescharacteristic
179C2×C8×C151C2×D411yescharacteristic
180C2×C8×C151C2×D411yescharacteristic
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—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—41no—
193C4⋊C4×C151—41no—
194C4⋊C4×C151C2×D411yescharacteristic
195C4⋊C4×C151C2×D411yescharacteristic
196C22⋊C4×C151—41no—
197C22⋊C4×C151—41no—
198C22⋊C4×C151—41no—
199C42×C151—21no—
200C42×C151—21no—
201C42×C151—21no—
202C42×C151—21no—
203C42×C151—41no—
204C42×C151C2×D411yescharacteristic
205C42×C151C2×D411yescharacteristic
206C42×C151#4111yescharacteristic
207C42×C151C2411yescharacteristic
208C23×C151—41no—
209C23×C151#12111yescharacteristic
210Q8×C151—21no—
211Q8×C151—21no—
212Q8×C151—21no—
213Q8×C151—42no—
214Q8×C151—41no—
215Q8×C151—41no—
216Q8×C151—81no—
217Q8×C151—81no—
218Q8×C151#13712yes—
219D4×C151—41no—
220D4×C151—41no—
221D4×C151—41no—
222D4×C151—41no—
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—21no—
233C2×C4×C151—41no—
234C2×C4×C151—42no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—82no—
239C2×C4×C151—81no—
240C2×C4×C151#12111yescharacteristic
241C2×C4×C151#12111yescharacteristic
242C2×C4×C151#12111yescharacteristic
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C2×C4×C151C2×#4111yescharacteristic
246C8×C151—21no—
247C8×C151—21no—
248C8×C151—21no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151—41no—
252C8×C151—41no—
253C8×C151—41no—
254C8×C151—41no—
255C8×C151#13712yes—
256C22×C151—21no—
257C22×C151—21no—
258C22×C151—21no—
259C22×C151—81no—
260C22×C151—81no—
261C22×C151—81no—
262C22×C151C2×#12111yescharacteristic
263C4×C151—21no—
264C4×C151—21no—
265C4×C151—22no—
266C4×C151—21no—
267C4×C151—21no—
268C4×C151—41no—
269C4×C151—41no—
270C4×C151—41no—
271C4×C151—81no—
272C4×C151—81no—
273C4×C151—81no—
274C4×C151C2×#13711yescharacteristic
275C4×C151C2×#13711yescharacteristic
276C4×C151#57511yescharacteristic
277C4×C151#57511yescharacteristic
278C2×C151—41no—
279C2×C151—161no—
280C2×C151#303711yescharacteristic
281C2×C151#305611yescharacteristic
282C2×C151#306811yescharacteristic
283#19309C15111yesmaximal, characteristic, direct product factor, Sylow
284C151#1930911yescharacteristic, direct product factor, Sylow
285#3182C2×C15111yescharacteristic
286#3112C2×C15111yescharacteristic
287#3078C2×C15111yescharacteristic, complemented
288Q8×M16C2×C15111yescharacteristic, complemented
289#1704C2×C15111yescharacteristic, complemented
290#1698C2×C15111yescharacteristic, complemented
291#1696C2×C15111yescharacteristic, complemented
292#1686C2×C15111yescharacteristic, complemented
293#1684C2×C15111yescharacteristic, complemented
294#1678C2×C15111yescharacteristic, complemented
295#1676C2×C15111yescharacteristic, complemented
296#1666C2×C15111yescharacteristic, complemented
297#1569C2×C15111yescharacteristic, complemented
298#1560C2×C15111yescharacteristic
299#1559C2×C15111yescharacteristic, complemented
300#533C22×C15111yescharacteristic
301#532C22×C15111yescharacteristic
302C2×C4×Q8C22×C15111yescharacteristic
303#500C22×C15111yescharacteristic
304#492C22×C15111yescharacteristic
305#487C22×C15111yescharacteristic
306#486C22×C15111yescharacteristic
307#480—21no—
308#479—21no—
309#479—21no—
310#477C22×C15111yescharacteristic
311#477C22×C15111yescharacteristic
312#477C22×C15111yescharacteristic
313#477C22×C15111yescharacteristic
314#475C22×C15111yescharacteristic
315#475C22×C15111yescharacteristic
316#468—21no—
317#468—21no—
318#460C22×C15111yescharacteristic
319#460C22×C15111yescharacteristic
320#448—21no—
321#446—21no—
322#446—21no—
323#446C22×C15111yescharacteristic
324#446C22×C15111yescharacteristic
325C8×Q8C22×C15111yescharacteristic
326C8×Q8C22×C15111yescharacteristic
327#440—21no—
328#440—21no—
329#440—21no—
330#440—21no—
331#432C22×C15111yescharacteristic
332#428—21no—
333#423—21no—
334#423C22×C15111yescharacteristic
335#423C22×C15111yescharacteristic
336#419—21no—
337C4×M16—21no—
338C4×M16C22×C15111yescharacteristic
339#335C22×C15111yescharacteristic
340#335C22×C15111yescharacteristic
341#334C22×C15111yescharacteristic
342#334C22×C15111yescharacteristic
343#333C22×C15111yescharacteristic
344#333C22×C15111yescharacteristic
345#333C22×C15111yescharacteristic
346#333C22×C15111yescharacteristic
347#332C22×C15111yescharacteristic
348#332C22×C15111yescharacteristic
349#331C22×C15111yescharacteristic
350#331C22×C15111yescharacteristic
351C2×#41—21no—
352C22×Q8D4×C15111yescharacteristic
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16D4×C15111yescharacteristic
360C2×M16D4×C15111yescharacteristic
361C4⋊Q8C23×C15111yescharacteristic
362C4⋊Q8C23×C15111yescharacteristic
363C4⋊Q8C23×C15111yescharacteristic
364#127C23×C15111yescharacteristic
365#125—21no—
366#124—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8D4×C15111yescharacteristic
376C4×Q8D4×C15111yescharacteristic
377C4×Q8C23×C15111yescharacteristic
378C4×Q8C23×C15111yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381#117—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4D4×C15111yescharacteristic
384C2×C42—21no—
385C2×C42C23×C15111yescharacteristic
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#106—21no—
393#106—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—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#103—21no—
412#103—21no—
413#103—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418C22⋊C8—21no—
419#97—21no—
420#97—21no—
421#97—21no—
422#97D4×C15111yescharacteristic
423#97D4×C15111yescharacteristic
424C4×C8—21no—
425C4×C8—21no—
426C4×C8C23×C15111yescharacteristic
427C4×C8C23×C15111yescharacteristic
428#41—82no—
429C2×Q8—21no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—41no—
435C2×Q8C2×D4×C15111yescharacteristic
436C2×Q8C2×D4×C15111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—41no—
444C22×C4C2×D4×C15111yescharacteristic
445C22×C4C2×D4×C15111yescharacteristic
446C22×C4#41×C15111yescharacteristic
447SD16—42no—
448SD16—42no—
449SD16—42no—
450SD16—42no—
451M16—22no—
452M16—41no—
453M16—42no—
454M16—42no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
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—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4C2×D4×C15111yescharacteristic
479C4⋊C4C2×D4×C15111yescharacteristic
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—41no—
488C42C2×D4×C15111yescharacteristic
489C42C2×D4×C15111yescharacteristic
490C42#41×C15111yescharacteristic
491C42C24×C15111yescharacteristic
492C23—41no—
493C23#121×C15111yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—42no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502Q8#137×C15112yes—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—81no—
508D4—82no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4—81no—
524C2×C4#121×C15111yescharacteristic
525C2×C4#121×C15111yescharacteristic
526C2×C4#121×C15111yescharacteristic
527C2×C4C22×D4×C15111yescharacteristic
528C2×C4C22×D4×C15111yescharacteristic
529C2×C4C2×#41×C15111yescharacteristic
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8#137×C15112yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22C2×#121×C15111yescharacteristic
547C4—21no—
548C4—21no—
549C4—22no—
550C4—21no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C2×#137×C15111yescharacteristic
559C4C2×#137×C15111yescharacteristic
560C4#575×C15111yescharacteristic
561C4#575×C15111yescharacteristic
562C2—41no—
563C2—161no—
564C2#3037×C15111yescharacteristic
565C2#3056×C15111yescharacteristic
566C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
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
3. #3078×C151C2semidirect
4. Q8×M16×C151C2semidirect
5. #1704×C151C2semidirect
6. #1698×C151C2semidirect
7. #1696×C151C2semidirect
8. #1686×C151C2semidirect
9. #1684×C151C2semidirect
10. #1678×C151C2semidirect
11. #1676×C151C2semidirect
12. #1666×C151C2semidirect
13. #1569×C151C2semidirect
15. #1559×C151C2semidirect
283. #19309C151direct (N × H)
284. C151#19309direct (N × H)
287. #3078C2×C151semidirect
288. Q8×M16C2×C151semidirect
289. #1704C2×C151semidirect
290. #1698C2×C151semidirect
291. #1696C2×C151semidirect
292. #1686C2×C151semidirect
293. #1684C2×C151semidirect
294. #1678C2×C151semidirect
295. #1676C2×C151semidirect
296. #1666C2×C151semidirect
297. #1569C2×C151semidirect
299. #1559C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3182×C1512
#3112×C1512
#3078×C1512
Q8×M16×C1512
#1704×C1512
#1698×C1512
#1696×C1512
#1686×C1512
#1684×C1512
#1678×C1512
#1676×C1512
#1666×C1512
#1569×C1512
#1560×C1512
#1559×C1512
#19309151