Finite Group Databasebeta

← C151×#18776 #50323701

Subgroups — C151×#18776 #50323701

Order 38656.

1192 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C151C211yesmaximal, characteristic, complemented
2#3226×C151C211yesmaximal, characteristic, complemented
3#3100×C151C211yesmaximal, characteristic
4#3037×C151C211yesmaximal, characteristic, complemented
5#1649×C151C214yesmaximal, complemented
6#1627×C151C214yesmaximal, complemented
7#1546×C151C211yesmaximal, characteristic, complemented
8#1486×C151C211yesmaximal, characteristic, complemented
9#1479×C151C211yesmaximal, characteristic, complemented
10C23×Q8×C151—21no—
11C2×#137×C151—21no—
12D4×Q8×C151—22no—
13D4×Q8×C151—22no—
14D4×Q8×C151—22no—
15D4×Q8×C151C2214yes—
16#532×C151C2211yescharacteristic
17C2×C4⋊Q8×C151—21no—
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×C22⋊Q8×C151—21no—
20C2×C22⋊Q8×C151—22no—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151—21no—
23C2×C4×D4×C151C2211yescharacteristic
24#500×C151C2212yescomplemented
25#486×C151C2212yescomplemented
26#480×C151—21no—
27#480×C151—22no—
28#474×C151—22no—
29#474×C151C2212yes—
30#464×C151—22no—
31#462×C151C2212yescomplemented
32#460×C151C2212yescomplemented
33#459×C151C2212yes—
34#447×C151—21no—
35C4×D8×C151—22no—
36#431×C151C2211yescharacteristic
37#431×C151C2211yescharacteristic
38#423×C151C2211yescharacteristic
39#417×C151—21no—
40#332×C151C2214yescomplemented
41Q8⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yes—
43C2×#41×C151—21no—
44C22×Q8×C151—22no—
45C22×Q8×C151—24no—
46C22×Q8×C151—21no—
47C22×Q8×C151—24no—
48C22×Q8×C151—44no—
49C22×Q8×C151—44no—
50C22×Q8×C151D411yescharacteristic
51C22×D4×C151D411yescharacteristic
52C23×C4×C151—22no—
53C23×C4×C151—21no—
54#137×C151—44no—
55C2×Q16×C151—22no—
56C2×SD16×C151—22no—
57C2×D8×C151—22no—
58C2×M16×C151—21no—
59C4⋊Q8×C151—24no—
60C4⋊Q8×C151—24no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151D412yes—
64C4⋊Q8×C151C2311yescharacteristic
65C4⋊Q8×C151C2312yes—
66#127×C151C2311yescharacteristic
67#124×C151—21no—
68C22⋊Q8×C151—28no—
69C22⋊Q8×C151—24no—
70C22⋊Q8×C151—28no—
71C22⋊Q8×C151—24no—
72#121×C151—21no—
73#121×C151—21no—
74C4×Q8×C151—21no—
75C4×Q8×C151—21no—
76C4×Q8×C151D412yes—
77C4×Q8×C151C2312yes—
78C4×D4×C151—24no—
79C4×D4×C151—24no—
80C4×D4×C151—21no—
81C4×D4×C151—21no—
82C4×D4×C151—21no—
83C4×D4×C151—21no—
84C4×D4×C151D412yes—
85C4×D4×C151C2312yes—
86C2×C4⋊C4×C151—22no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151D411yescharacteristic
90C2×C4⋊C4×C151D411yescharacteristic
91C2×C4⋊C4×C151D412yes—
92C2×C22⋊C4×C151—22no—
93C2×C22⋊C4×C151—21no—
94C2×C42×C151—21no—
95C2×C42×C151C2311yescharacteristic
96#107×C151—22no—
97#107×C151—24no—
98C4⋊C8×C151—21no—
99C4⋊C8×C151—21no—
100C4⋊C8×C151C2312yes—
101C4⋊C8×C151C2312yes—
102#103×C151—22no—
103#102×C151—22no—
104#102×C151—22no—
105#102×C151—22no—
106#102×C151—24no—
107C22⋊C8×C151—21no—
108C22⋊C8×C151—21no—
109C4×C8×C151—21no—
110C4×C8×C151C2312yes—
111C24×C151—21no—
112#41×C151—42no—
113#41×C151—42no—
114C2×Q8×C151—28no—
115C2×Q8×C151—21no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151—22no—
119C2×Q8×C151—21no—
120C2×Q8×C151—48no—
121C2×Q8×C151—48no—
122C2×Q8×C151—416no—
123C2×Q8×C151—48no—
124C2×Q8×C151—42no—
125C2×Q8×C151—42no—
126C2×Q8×C151D814yescomplemented
127C2×Q8×C151C2×D412yes—
128C2×D4×C151—24no—
129C2×D4×C151—21no—
130C2×D4×C151—21no—
131C2×D4×C151—21no—
132C2×D4×C151—21no—
133C2×D4×C151—41no—
134C2×D4×C151C2×D412yes—
135C22×C4×C151—21no—
136C22×C4×C151—28no—
137C22×C4×C151—21no—
138C22×C4×C151—22no—
139C22×C4×C151—21no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—48no—
143C22×C4×C151—42no—
144C22×C4×C151—42no—
145C22×C4×C151—41no—
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149Q16×C151—44no—
150SD16×C151—44no—
151D8×C151—44no—
152M16×C151—42no—
153C2×C8×C151—22no—
154C2×C8×C151—22no—
155C2×C8×C151—22no—
156C4⋊C4×C151—28no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151C2×D412yes—
167C4⋊C4×C151C2×D412yes—
168C4⋊C4×C151C2×D414yes—
169C22⋊C4×C151—28no—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—22no—
172C22⋊C4×C151—41no—
173C22⋊C4×C151—41no—
174C42×C151—22no—
175C42×C151—22no—
176C42×C151C2×D411yescharacteristic
177C42×C151C2×D411yescharacteristic
178C42×C151C2×D411yescharacteristic
179C42×C151C2411yescharacteristic
180C23×C151—24no—
181C23×C151—22no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151—41no—
185C23×C151#12011yescharacteristic
186Q8×C151—22no—
187Q8×C151—24no—
188Q8×C151—416no—
189Q8×C151—42no—
190Q8×C151—42no—
191Q8×C151—44no—
192Q8×C151—41no—
193Q8×C151—41no—
194Q8×C151C2×D814yes—
195D4×C151—24no—
196D4×C151—22no—
197D4×C151—42no—
198D4×C151—41no—
199D4×C151—41no—
200D4×C151—42no—
201D4×C151—82no—
202D4×C151#13714yescomplemented
203C2×C4×C151—22no—
204C2×C4×C151—24no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—24no—
208C2×C4×C151—22no—
209C2×C4×C151—41no—
210C2×C4×C151—416no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—44no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—44no—
217C2×C4×C151—41no—
218C2×C4×C151—82no—
219C2×C4×C151#12011yescharacteristic
220C2×C4×C151#12011yescharacteristic
221C2×C4×C151#12011yescharacteristic
222C2×C4×C151C2×D812yes—
223C2×C4×C151AGL(1,ℤ/8)12yes—
224C2×C4×C151C22×D411yescharacteristic
225C2×C4×C151C22×D411yescharacteristic
226C2×C4×C151C22×D411yescharacteristic
227C8×C151—42no—
228C8×C151—42no—
229C8×C151—42no—
230C22×C151—21no—
231C22×C151—21no—
232C22×C151—24no—
233C22×C151—48no—
234C22×C151—42no—
235C22×C151—42no—
236C22×C151—81no—
237C22×C151—81no—
238C22×C151—81no—
239C22×C151#44712yes—
240C22×C151C2×#12011yescharacteristic
241C4×C151—24no—
242C4×C151—21no—
243C4×C151—21no—
244C4×C151—21no—
245C4×C151—44no—
246C4×C151—42no—
247C4×C151—42no—
248C4×C151—81no—
249C4×C151#44712yes—
250C4×C151C22×D811yescharacteristic
251C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
252C4×C151C2×#13712yes—
253C2×C151—22no—
254C2×C151—44no—
255C2×C151—161no—
256C2×C151C2×#44711yescharacteristic
257C2×C151#300411yescharacteristic
258C2×C151#302011yescharacteristic
259#18776C15111yesmaximal, characteristic, direct product factor, Sylow
260C151#1877611yescharacteristic, direct product factor, Sylow
261C2×D4×Q8C2×C15111yescharacteristic, complemented
262#3226C2×C15111yescharacteristic, complemented
263#3100C2×C15111yescharacteristic
264#3037C2×C15111yescharacteristic, complemented
265#1649C2×C15114yescomplemented
266#1627C2×C15114yescomplemented
267#1546C2×C15111yescharacteristic, complemented
268#1486C2×C15111yescharacteristic, complemented
269#1479C2×C15111yescharacteristic, complemented
270C23×Q8—21no—
271C2×#137—21no—
272D4×Q8—22no—
273D4×Q8—22no—
274D4×Q8—22no—
275D4×Q8C22×C15114yes—
276#532C22×C15111yescharacteristic
277C2×C4⋊Q8—21no—
278C2×C4⋊Q8C22×C15111yescharacteristic
279C2×C22⋊Q8—21no—
280C2×C22⋊Q8—22no—
281C2×C4×Q8C22×C15111yescharacteristic
282C2×C4×D4—21no—
283C2×C4×D4C22×C15111yescharacteristic
284#500C22×C15112yescomplemented
285#486C22×C15112yescomplemented
286#480—21no—
287#480—22no—
288#474—22no—
289#474C22×C15112yes—
290#464—22no—
291#462C22×C15112yescomplemented
292#460C22×C15112yescomplemented
293#459C22×C15112yes—
294#447—21no—
295C4×D8—22no—
296#431C22×C15111yescharacteristic
297#431C22×C15111yescharacteristic
298#423C22×C15111yescharacteristic
299#417—21no—
300#332C22×C15114yescomplemented
301Q8⋊C8C22×C15114yescomplemented
302D4⋊C8C22×C15114yes—
303C2×#41—21no—
304C22×Q8—22no—
305C22×Q8—24no—
306C22×Q8—24no—
307C22×Q8—21no—
308C22×Q8—44no—
309C22×Q8—44no—
310C22×Q8D4×C15111yescharacteristic
311C22×D4D4×C15111yescharacteristic
312C23×C4—22no—
313C23×C4—21no—
314#137—44no—
315C2×Q16—22no—
316C2×SD16—22no—
317C2×D8—22no—
318C2×M16—21no—
319C4⋊Q8—24no—
320C4⋊Q8—24no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8D4×C15112yes—
324C4⋊Q8C23×C15111yescharacteristic
325C4⋊Q8C23×C15112yes—
326#127C23×C15111yescharacteristic
327#124—21no—
328C22⋊Q8—24no—
329C22⋊Q8—28no—
330C22⋊Q8—24no—
331C22⋊Q8—28no—
332#121—21no—
333#121—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8D4×C15112yes—
337C4×Q8C23×C15112yes—
338C4×D4—24no—
339C4×D4—24no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4D4×C15112yes—
345C4×D4C23×C15112yes—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4D4×C15111yescharacteristic
350C2×C4⋊C4D4×C15111yescharacteristic
351C2×C4⋊C4D4×C15112yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—21no—
354C2×C42—21no—
355C2×C42C23×C15111yescharacteristic
356#107—22no—
357#107—24no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8C23×C15112yes—
361C4⋊C8C23×C15112yes—
362#103—22no—
363#102—22no—
364#102—22no—
365#102—22no—
366#102—24no—
367C22⋊C8—21no—
368C22⋊C8—21no—
369C4×C8—21no—
370C4×C8C23×C15112yes—
371C24—21no—
372#41—42no—
373#41—42no—
374C2×Q8—28no—
375C2×Q8—21no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—21no—
380C2×Q8—48no—
381C2×Q8—416no—
382C2×Q8—48no—
383C2×Q8—48no—
384C2×Q8—42no—
385C2×Q8—42no—
386C2×Q8D8×C15114yescomplemented
387C2×Q8C2×D4×C15112yes—
388C2×D4—24no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—41no—
394C2×D4C2×D4×C15112yes—
395C22×C4—21no—
396C22×C4—28no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—48no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—41no—
406C22×C4C2×D4×C15111yescharacteristic
407C22×C4C2×D4×C15111yescharacteristic
408C22×C4C2×D4×C15111yescharacteristic
409Q16—44no—
410SD16—44no—
411D8—44no—
412M16—42no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C4⋊C4—28no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4C2×D4×C15112yes—
427C4⋊C4C2×D4×C15112yes—
428C4⋊C4C2×D4×C15114yes—
429C22⋊C4—28no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C42—22no—
435C42—22no—
436C42C2×D4×C15111yescharacteristic
437C42C2×D4×C15111yescharacteristic
438C42C2×D4×C15111yescharacteristic
439C42C24×C15111yescharacteristic
440C23—24no—
441C23—22no—
442C23—42no—
443C23—42no—
444C23—41no—
445C23#120×C15111yescharacteristic
446Q8—24no—
447Q8—22no—
448Q8—416no—
449Q8—44no—
450Q8—42no—
451Q8—42no—
452Q8—41no—
453Q8—41no—
454Q8C2×D8×C15114yes—
455D4—24no—
456D4—22no—
457D4—42no—
458D4—41no—
459D4—41no—
460D4—42no—
461D4—82no—
462D4#137×C15114yescomplemented
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—416no—
471C2×C4—42no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—82no—
479C2×C4#120×C15111yescharacteristic
480C2×C4#120×C15111yescharacteristic
481C2×C4#120×C15111yescharacteristic
482C2×C4C2×D8×C15112yes—
483C2×C4AGL(1,ℤ/8)×C15112yes—
484C2×C4C22×D4×C15111yescharacteristic
485C2×C4C22×D4×C15111yescharacteristic
486C2×C4C22×D4×C15111yescharacteristic
487C8—42no—
488C8—42no—
489C8—42no—
490C22—21no—
491C22—21no—
492C22—24no—
493C22—48no—
494C22—42no—
495C22—42no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22#447×C15112yes—
500C22C2×#120×C15111yescharacteristic
501C4—24no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—44no—
506C4—42no—
507C4—42no—
508C4—81no—
509C4#447×C15112yes—
510C4C22×D8×C15111yescharacteristic
511C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
512C4C2×#137×C15112yes—
513C2—22no—
514C2—44no—
515C2—161no—
516C2C2×#447×C15111yescharacteristic
517C2#3004×C15111yescharacteristic
518C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3100×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. C2×D4×Q8×C151C2semidirect
2. #3226×C151C2semidirect
4. #3037×C151C2semidirect
5. #1649×C151C2semidirect
6. #1627×C151C2semidirect
7. #1546×C151C2semidirect
8. #1486×C151C2semidirect
9. #1479×C151C2semidirect
24. #500×C151C22semidirect
25. #486×C151C22semidirect
31. #462×C151C22semidirect
32. #460×C151C22semidirect
40. #332×C151C22semidirect
41. Q8⋊C8×C151C22semidirect
126. C2×Q8×C151D8semidirect
202. D4×C151#137semidirect
259. #18776C151direct (N × H)
260. C151#18776direct (N × H)
261. C2×D4×Q8C2×C151semidirect
262. #3226C2×C151semidirect
264. #3037C2×C151semidirect
265. #1649C2×C151semidirect
266. #1627C2×C151semidirect
267. #1546C2×C151semidirect
268. #1486C2×C151semidirect
269. #1479C2×C151semidirect
284. #500C22×C151semidirect
285. #486C22×C151semidirect
291. #462C22×C151semidirect
292. #460C22×C151semidirect
300. #332C22×C151semidirect
301. Q8⋊C8C22×C151semidirect
386. C2×Q8D8×C151semidirect
462. D4#137×C151semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1512
#3226×C1512
#3100×C1512
#3037×C1512
#1649×C1512
#1627×C1512
#1546×C1512
#1486×C1512
#1479×C1512
#18776151