Finite Group Databasebeta

← C151×#18622 #50323547

Subgroups — C151×#18622 #50323547

Order 38656.

1066 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C151C211yesmaximal, characteristic, complemented
2#3208×C151C211yesmaximal, characteristic, complemented
3C2×#492×C151C211yesmaximal, characteristic, complemented
4#3038×C151C211yesmaximal, characteristic
5#1623×C151C214yesmaximal, complemented
6#1622×C151C214yesmaximal, complemented
7#1548×C151C211yesmaximal, characteristic, complemented
8#1493×C151C211yesmaximal, characteristic, complemented
9#1476×C151C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C151—21no—
11C22×SD16×C151—22no—
12Q82×C151C2212yescomplemented
13#557×C151—21no—
14#554×C151—22no—
15#554×C151C2212yescomplemented
16D4×Q8×C151—22no—
17D4×Q8×C151—21no—
18#544×C151—22no—
19#544×C151—21no—
20#533×C151—21no—
21#533×C151C2211yescharacteristic
22C2×C4⋊Q8×C151—21no—
23C2×C4⋊Q8×C151C2211yescharacteristic
24C2×#127×C151C2211yescharacteristic
25#520×C151—21no—
26C4×#41×C151C2211yescharacteristic
27#492×C151—22no—
28#492×C151—21no—
29#492×C151C2214yes—
30#486×C151—21no—
31#460×C151—21no—
32#460×C151C2214yes—
33#460×C151C2212yes—
34#459×C151—21no—
35#459×C151C2212yes—
36#450×C151—22no—
37#431×C151C2211yescharacteristic
38#423×C151C2211yescharacteristic
39#418×C151—21no—
40C2×C4×C8×C151C2211yescharacteristic
41#333×C151C2214yescomplemented
42Q8⋊C8×C151C2214yescomplemented
43Q8⋊C8×C151C2212yescomplemented
44D4⋊C8×C151C2212yescomplemented
45C2×#41×C151D411yescharacteristic
46C22×Q8×C151—22no—
47C22×Q8×C151D412yes—
48C22×D4×C151—21no—
49C22×D4×C151—21no—
50C22×D4×C151—21no—
51AGL(1,ℤ/8)×C151—44no—
52C2×SD16×C151—22no—
53C2×SD16×C151—28no—
54C2×SD16×C151—24no—
55C2×SD16×C151—48no—
56C2×D8×C151—22no—
57C2×M16×C151—21no—
58C22×C8×C151—21no—
59C4⋊Q8×C151—22no—
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151—22no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151—24no—
66C4⋊Q8×C151D411yescharacteristic
67C4⋊Q8×C151D412yes—
68C4⋊Q8×C151D411yescharacteristic
69C4⋊Q8×C151C2312yes—
70#127×C151—21no—
71#127×C151—21no—
72#127×C151—21no—
73#127×C151C2312yes—
74#125×C151—22no—
75#125×C151—24no—
76#125×C151—22no—
77#125×C151—21no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151—24no—
80C22⋊Q8×C151—24no—
81C22⋊Q8×C151—21no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—24no—
84C22⋊Q8×C151D412yes—
85C4×Q8×C151—22no—
86C4×Q8×C151—21no—
87C4×Q8×C151—22no—
88C4×Q8×C151—22no—
89C4×Q8×C151D411yescharacteristic
90C4×Q8×C151C2311yescharacteristic
91C4×Q8×C151C2312yes—
92C4×D4×C151—24no—
93C4×D4×C151—22no—
94C4×D4×C151—21no—
95C4×D4×C151—21no—
96C4×D4×C151D411yescharacteristic
97C4×D4×C151C2311yescharacteristic
98#117×C151—22no—
99#117×C151—21no—
100#117×C151—21no—
101#117×C151D411yescharacteristic
102C2×C4⋊C4×C151—22no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—22no—
106C2×C42×C151—21no—
107C2×C42×C151C2311yescharacteristic
108C4⋊C8×C151—21no—
109C4⋊C8×C151C2312yes—
110C4⋊C8×C151C2312yes—
111#102×C151—22no—
112#102×C151—22no—
113#102×C151—24no—
114C22⋊C8×C151—21no—
115C4×C8×C151—21no—
116C4×C8×C151—21no—
117C4×C8×C151C2312yes—
118C24×C151—41no—
119#41×C151—22no—
120#41×C151SD1614yescomplemented
121C2×Q8×C151—24no—
122C2×Q8×C151—22no—
123C2×Q8×C151—21no—
124C2×Q8×C151—44no—
125C2×Q8×C151—84no—
126C2×Q8×C151C2×D412yes—
127C2×Q8×C151C2×D411yescharacteristic
128C2×Q8×C151C2×D414yes—
129C2×D4×C151—21no—
130C2×D4×C151—22no—
131C2×D4×C151—22no—
132C2×D4×C151—22no—
133C2×D4×C151—44no—
134C2×D4×C151—41no—
135C2×D4×C151—41no—
136C2×D4×C151—41no—
137C2×D4×C151—42no—
138C2×D4×C151—42no—
139C2×D4×C151—82no—
140C2×D4×C151C2×D411yescharacteristic
141C22×C4×C151—21no—
142C22×C4×C151—24no—
143C22×C4×C151—22no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149SD16×C151—416no—
150SD16×C151—44no—
151SD16×C151—84no—
152D8×C151—44no—
153M16×C151—42no—
154C2×C8×C151—24no—
155C2×C8×C151—22no—
156C2×C8×C151—22no—
157C2×C8×C151—22no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—24no—
161C4⋊C4×C151—24no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151C2×D412yes—
174C4⋊C4×C151C2×D411yescharacteristic
175C4⋊C4×C151C2×D411yescharacteristic
176C22⋊C4×C151—24no—
177C22⋊C4×C151—22no—
178C22⋊C4×C151—21no—
179C22⋊C4×C151—21no—
180C22⋊C4×C151—21no—
181C42×C151—24no—
182C42×C151—21no—
183C42×C151—21no—
184C42×C151—21no—
185C42×C151—22no—
186C42×C151C2×D411yescharacteristic
187C42×C151C2×D411yescharacteristic
188C42×C151C2×D411yescharacteristic
189C42×C151C2411yescharacteristic
190C23×C151—21no—
191C23×C151—42no—
192C23×C151—82no—
193C23×C151—82no—
194C23×C151—82no—
195C23×C151#12011yescharacteristic
196Q8×C151—21no—
197Q8×C151—24no—
198Q8×C151—44no—
199Q8×C151—44no—
200Q8×C151—42no—
201Q8×C151—84no—
202Q8×C151C2×SD1612yescomplemented
203D4×C151—24no—
204D4×C151—21no—
205D4×C151—44no—
206D4×C151—42no—
207D4×C151—42no—
208D4×C151—44no—
209D4×C151—82no—
210D4×C151—82no—
211D4×C151—82no—
212D4×C151C2×SD1612yescomplemented
213C2×C4×C151—21no—
214C2×C4×C151—22no—
215C2×C4×C151—24no—
216C2×C4×C151—22no—
217C2×C4×C151—21no—
218C2×C4×C151—22no—
219C2×C4×C151—24no—
220C2×C4×C151—22no—
221C2×C4×C151—21no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—82no—
225C2×C4×C151—84no—
226C2×C4×C151#12011yescharacteristic
227C2×C4×C151#12011yescharacteristic
228C2×C4×C151#12011yescharacteristic
229C2×C4×C151C2×SD1612yes—
230C2×C4×C151#13712yes—
231C2×C4×C151C22×D411yescharacteristic
232C2×C4×C151C22×D411yescharacteristic
233C2×C4×C151C22×D411yescharacteristic
234C8×C151—24no—
235C8×C151—42no—
236C8×C151—42no—
237C22×C151—21no—
238C22×C151—21no—
239C22×C151—22no—
240C22×C151—41no—
241C22×C151—41no—
242C22×C151—82no—
243C22×C151—82no—
244C22×C151—82no—
245C22×C151—164no—
246C22×C151#44812yes—
247C22×C151C2×#12011yescharacteristic
248C4×C151—22no—
249C4×C151—21no—
250C4×C151—21no—
251C4×C151—41no—
252C4×C151—42no—
253C4×C151—41no—
254C4×C151—44no—
255C4×C151—42no—
256C4×C151#44812yes—
257C4×C151#45312yes—
258C4×C151C22×SD1611yescharacteristic
259C4×C151C2×#13711yescharacteristic
260C4×C151#57712yes—
261C2×C151—22no—
262C2×C151—42no—
263C2×C151—162no—
264C2×C151C2×#44811yescharacteristic
265C2×C151#301011yescharacteristic
266C2×C151C2×#45311yescharacteristic
267#18622C15111yesmaximal, characteristic, direct product factor, Sylow
268C151#1862211yescharacteristic, direct product factor, Sylow
269#3503C2×C15111yescharacteristic, complemented
270#3208C2×C15111yescharacteristic, complemented
271C2×#492C2×C15111yescharacteristic, complemented
272#3038C2×C15111yescharacteristic
273#1623C2×C15114yescomplemented
274#1622C2×C15114yescomplemented
275#1548C2×C15111yescharacteristic, complemented
276#1493C2×C15111yescharacteristic, complemented
277#1476C2×C15111yescharacteristic, complemented
278C2×AGL(1,ℤ/8)—21no—
279C22×SD16—22no—
280Q82C22×C15112yescomplemented
281#557—21no—
282#554—22no—
283#554C22×C15112yescomplemented
284D4×Q8—22no—
285D4×Q8—21no—
286#544—22no—
287#544—21no—
288#533—21no—
289#533C22×C15111yescharacteristic
290C2×C4⋊Q8—21no—
291C2×C4⋊Q8C22×C15111yescharacteristic
292C2×#127C22×C15111yescharacteristic
293#520—21no—
294C4×#41C22×C15111yescharacteristic
295#492—22no—
296#492—21no—
297#492C22×C15114yes—
298#486—21no—
299#460—21no—
300#460C22×C15114yes—
301#460C22×C15112yes—
302#459—21no—
303#459C22×C15112yes—
304#450—22no—
305#431C22×C15111yescharacteristic
306#423C22×C15111yescharacteristic
307#418—21no—
308C2×C4×C8C22×C15111yescharacteristic
309#333C22×C15114yescomplemented
310Q8⋊C8C22×C15114yescomplemented
311Q8⋊C8C22×C15112yescomplemented
312D4⋊C8C22×C15112yescomplemented
313C2×#41D4×C15111yescharacteristic
314C22×Q8—22no—
315C22×Q8D4×C15112yes—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4—21no—
319AGL(1,ℤ/8)—44no—
320C2×SD16—28no—
321C2×SD16—22no—
322C2×SD16—24no—
323C2×SD16—48no—
324C2×D8—22no—
325C2×M16—21no—
326C22×C8—21no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—24no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8D4×C15112yes—
335C4⋊Q8D4×C15111yescharacteristic
336C4⋊Q8D4×C15111yescharacteristic
337C4⋊Q8C23×C15112yes—
338#127—21no—
339#127—21no—
340#127—21no—
341#127C23×C15112yes—
342#125—22no—
343#125—24no—
344#125—22no—
345#125—21no—
346C22⋊Q8—22no—
347C22⋊Q8—24no—
348C22⋊Q8—24no—
349C22⋊Q8—22no—
350C22⋊Q8—24no—
351C22⋊Q8—21no—
352C22⋊Q8D4×C15112yes—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×Q8—21no—
357C4×Q8D4×C15111yescharacteristic
358C4×Q8C23×C15111yescharacteristic
359C4×Q8C23×C15112yes—
360C4×D4—24no—
361C4×D4—22no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4D4×C15111yescharacteristic
365C4×D4C23×C15111yescharacteristic
366#117—22no—
367#117—21no—
368#117—21no—
369#117D4×C15111yescharacteristic
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C42—21no—
375C2×C42C23×C15111yescharacteristic
376C4⋊C8—21no—
377C4⋊C8C23×C15112yes—
378C4⋊C8C23×C15112yes—
379#102—22no—
380#102—22no—
381#102—24no—
382C22⋊C8—21no—
383C4×C8—21no—
384C4×C8—21no—
385C4×C8C23×C15112yes—
386C24—41no—
387#41—22no—
388#41SD16×C15114yescomplemented
389C2×Q8—24no—
390C2×Q8—22no—
391C2×Q8—21no—
392C2×Q8—44no—
393C2×Q8—84no—
394C2×Q8C2×D4×C15112yes—
395C2×Q8C2×D4×C15111yescharacteristic
396C2×Q8C2×D4×C15114yes—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—44no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—82no—
408C2×D4C2×D4×C15111yescharacteristic
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4C2×D4×C15111yescharacteristic
415C22×C4C2×D4×C15111yescharacteristic
416C22×C4C2×D4×C15111yescharacteristic
417SD16—416no—
418SD16—44no—
419SD16—84no—
420D8—44no—
421M16—42no—
422C2×C8—24no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4C2×D4×C15112yes—
442C4⋊C4C2×D4×C15111yescharacteristic
443C4⋊C4C2×D4×C15111yescharacteristic
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C42—24no—
450C42—21no—
451C42—21no—
452C42—21no—
453C42—22no—
454C42C2×D4×C15111yescharacteristic
455C42C2×D4×C15111yescharacteristic
456C42C2×D4×C15111yescharacteristic
457C42C24×C15111yescharacteristic
458C23—21no—
459C23—42no—
460C23—82no—
461C23—82no—
462C23—82no—
463C23#120×C15111yescharacteristic
464Q8—21no—
465Q8—24no—
466Q8—44no—
467Q8—44no—
468Q8—42no—
469Q8—84no—
470Q8C2×SD16×C15112yescomplemented
471D4—24no—
472D4—21no—
473D4—44no—
474D4—42no—
475D4—42no—
476D4—44no—
477D4—82no—
478D4—82no—
479D4—82no—
480D4C2×SD16×C15112yescomplemented
481C2×C4—21no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—82no—
493C2×C4—84no—
494C2×C4#120×C15111yescharacteristic
495C2×C4#120×C15111yescharacteristic
496C2×C4#120×C15111yescharacteristic
497C2×C4C2×SD16×C15112yes—
498C2×C4#137×C15112yes—
499C2×C4C22×D4×C15111yescharacteristic
500C2×C4C22×D4×C15111yescharacteristic
501C2×C4C22×D4×C15111yescharacteristic
502C8—24no—
503C8—42no—
504C8—42no—
505C22—21no—
506C22—21no—
507C22—22no—
508C22—41no—
509C22—41no—
510C22—82no—
511C22—82no—
512C22—82no—
513C22—164no—
514C22#448×C15112yes—
515C22C2×#120×C15111yescharacteristic
516C4—22no—
517C4—21no—
518C4—21no—
519C4—41no—
520C4—42no—
521C4—41no—
522C4—44no—
523C4—42no—
524C4#448×C15112yes—
525C4#453×C15112yes—
526C4C22×SD16×C15111yescharacteristic
527C4C2×#137×C15111yescharacteristic
528C4#577×C15112yes—
529C2—22no—
530C2—42no—
531C2—162no—
532C2C2×#448×C15111yescharacteristic
533C2#3010×C15111yescharacteristic
534C2C2×#453×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3038×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
1. #3503×C151C2semidirect
2. #3208×C151C2semidirect
3. C2×#492×C151C2semidirect
5. #1623×C151C2semidirect
6. #1622×C151C2semidirect
7. #1548×C151C2semidirect
8. #1493×C151C2semidirect
9. #1476×C151C2semidirect
12. Q82×C151C22semidirect
15. #554×C151C22semidirect
41. #333×C151C22semidirect
42. Q8⋊C8×C151C22semidirect
43. Q8⋊C8×C151C22semidirect
44. D4⋊C8×C151C22semidirect
120. #41×C151SD16semidirect
202. Q8×C151C2×SD16semidirect
212. D4×C151C2×SD16semidirect
267. #18622C151direct (N × H)
268. C151#18622direct (N × H)
269. #3503C2×C151semidirect
270. #3208C2×C151semidirect
271. C2×#492C2×C151semidirect
273. #1623C2×C151semidirect
274. #1622C2×C151semidirect
275. #1548C2×C151semidirect
276. #1493C2×C151semidirect
277. #1476C2×C151semidirect
280. Q82C22×C151semidirect
283. #554C22×C151semidirect
309. #333C22×C151semidirect
310. Q8⋊C8C22×C151semidirect
311. Q8⋊C8C22×C151semidirect
312. D4⋊C8C22×C151semidirect
388. #41SD16×C151semidirect
470. Q8C2×SD16×C151semidirect
480. D4C2×SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3503×C1512
#3208×C1512
C2×#492×C1512
#3038×C1512
#1623×C1512
#1622×C1512
#1548×C1512
#1493×C1512
#1476×C1512
#18622151