Finite Group Databasebeta

← C151×#19007 #50323932

Subgroups — C151×#19007 #50323932

Order 38656.

862 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#563×C151C211yesmaximal, characteristic
2#3236×C151C211yesmaximal, characteristic, complemented
3#3215×C151C211yesmaximal, characteristic
4#3166×C151C211yesmaximal, characteristic, complemented
5#1664×C151C214yesmaximal, complemented
6#1660×C151C214yesmaximal, complemented
7#1534×C151C211yesmaximal, characteristic, complemented
8#1528×C151C211yesmaximal, characteristic, complemented
9#1527×C151C211yesmaximal, characteristic
10#563×C151—22no—
11#563×C151—22no—
12#563×C151—22no—
13#563×C151C2214yes—
14#533×C151C2211yescharacteristic
15C2×C4⋊Q8×C151—21no—
16C2×#126×C151—21no—
17C2×#126×C151—21no—
18C2×#125×C151C2211yescharacteristic
19C2×#125×C151C2211yescharacteristic
20C2×#124×C151C2211yescharacteristic
21C2×#123×C151—21no—
22C2×C22⋊Q8×C151—21no—
23C2×C22⋊Q8×C151—21no—
24#501×C151C2212yescomplemented
25#501×C151C2212yescomplemented
26#501×C151C2212yescomplemented
27#499×C151—22no—
28#497×C151C2212yes—
29#491×C151C2212yescomplemented
30#489×C151C2212yes—
31#484×C151—21no—
32#483×C151—21no—
33#479×C151—22no—
34#464×C151—22no—
35#451×C151—21no—
36#450×C151—21no—
37#432×C151C2211yescharacteristic
38#432×C151C2211yescharacteristic
39#428×C151—21no—
40#428×C151—21no—
41C4×M16×C151C2211yescharacteristic
42#330×C151C2214yescomplemented
43#330×C151C2214yescomplemented
44#329×C151C2214yes—
45C22×Q8×C151—21no—
46C22×Q8×C151D411yescharacteristic
47C22×D4×C151D411yescharacteristic
48C23×C4×C151—21no—
49C2×Q16×C151—22no—
50C2×SD16×C151—22no—
51C2×M16×C151—21no—
52C4⋊Q8×C151—24no—
53C4⋊Q8×C151—24no—
54C4⋊Q8×C151C2311yescharacteristic
55C4⋊Q8×C151C2311yescharacteristic
56#126×C151—24no—
57#126×C151—24no—
58#126×C151—24no—
59#126×C151—24no—
60#125×C151—21no—
61#125×C151—21no—
62#125×C151—21no—
63#125×C151—21no—
64#125×C151—21no—
65#125×C151D412yes—
66#125×C151D412yes—
67#125×C151C2312yes—
68#125×C151C2312yes—
69#124×C151—21no—
70#124×C151—21no—
71#124×C151D412yes—
72#124×C151C2312yes—
73#123×C151—24no—
74#123×C151—24no—
75C22⋊Q8×C151—24no—
76C22⋊Q8×C151—24no—
77C22⋊Q8×C151—24no—
78C22⋊Q8×C151—24no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—21no—
81C4×Q8×C151—21no—
82C4×Q8×C151—21no—
83#117×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151D411yescharacteristic
91C2×C4⋊C4×C151D411yescharacteristic
92C2×C4⋊C4×C151D411yescharacteristic
93C2×C4⋊C4×C151D411yescharacteristic
94C2×C22⋊C4×C151—21no—
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—21no—
97C2×C22⋊C4×C151—21no—
98C2×C22⋊C4×C151—21no—
99C2×C42×C151—21no—
100C2×C42×C151C2311yescharacteristic
101#107×C151—22no—
102#107×C151—22no—
103#107×C151—22no—
104#106×C151—22no—
105#106×C151—22no—
106#106×C151—22no—
107C4⋊C8×C151—21no—
108C4⋊C8×C151—21no—
109#103×C151—22no—
110#103×C151—22no—
111#103×C151—22no—
112#102×C151—22no—
113C22⋊C8×C151—21no—
114C22⋊C8×C151—21no—
115#97×C151C2312yes—
116#97×C151C2312yes—
117#97×C151C2312yes—
118C4×C8×C151—21no—
119C24×C151—21no—
120C2×Q8×C151—24no—
121C2×Q8×C151—21no—
122C2×Q8×C151—21no—
123C2×Q8×C151—21no—
124C2×Q8×C151—81no—
125C2×Q8×C151—82no—
126C2×Q8×C151C2×D412yes—
127C2×D4×C151—21no—
128C2×D4×C151—81no—
129C2×D4×C151C2×D412yes—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—24no—
136C22×C4×C151—82no—
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140Q16×C151—82no—
141SD16×C151—82no—
142M16×C151—24no—
143C2×C8×C151—22no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C4⋊C4×C151—24no—
147C4⋊C4×C151—24no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—41no—
165C4⋊C4×C151—41no—
166C4⋊C4×C151C2×D412yes—
167C4⋊C4×C151C2×D412yes—
168C4⋊C4×C151C2×D412yes—
169C4⋊C4×C151C2×D412yes—
170C22⋊C4×C151—24no—
171C22⋊C4×C151—24no—
172C22⋊C4×C151—24no—
173C22⋊C4×C151—22no—
174C22⋊C4×C151—22no—
175C22⋊C4×C151—22no—
176C22⋊C4×C151—22no—
177C22⋊C4×C151—41no—
178C42×C151—24no—
179C42×C151—41no—
180C42×C151C2×D411yescharacteristic
181C42×C151C2×D411yescharacteristic
182C42×C151C2×D411yescharacteristic
183C42×C151C2411yescharacteristic
184C23×C151—22no—
185C23×C151—42no—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151#12011yescharacteristic
189Q8×C151—42no—
190Q8×C151—42no—
191Q8×C151—42no—
192Q8×C151—81no—
193Q8×C151—84no—
194D4×C151—42no—
195D4×C151—81no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—41no—
210C2×C4×C151—41no—
211C2×C4×C151—84no—
212C2×C4×C151#12011yescharacteristic
213C2×C4×C151#12011yescharacteristic
214C2×C4×C151#12011yescharacteristic
215C2×C4×C151C22×D411yescharacteristic
216C2×C4×C151C22×D411yescharacteristic
217C2×C4×C151C22×D411yescharacteristic
218C8×C151—24no—
219C8×C151—42no—
220C8×C151—42no—
221C22×C151—21no—
222C22×C151—21no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—42no—
226C22×C151—84no—
227C22×C151#45612yes—
228C22×C151C2×#12011yescharacteristic
229C4×C151—21no—
230C4×C151—21no—
231C4×C151—21no—
232C4×C151—21no—
233C4×C151—21no—
234C4×C151—21no—
235C4×C151—42no—
236C4×C151—42no—
237C4×C151—42no—
238C4×C151—42no—
239C4×C151—42no—
240C4×C151—81no—
241C4×C151—81no—
242C2×C151—22no—
243C2×C151—82no—
244C2×C151C2×#45611yescharacteristic
245C2×C151#301911yescharacteristic
246C2×C151#302011yescharacteristic
247#19007C15111yesmaximal, characteristic, direct product factor, Sylow
248C151#1900711yescharacteristic, direct product factor, Sylow
249C2×#563C2×C15111yescharacteristic
250#3236C2×C15111yescharacteristic, complemented
251#3215C2×C15111yescharacteristic
252#3166C2×C15111yescharacteristic, complemented
253#1664C2×C15114yescomplemented
254#1660C2×C15114yescomplemented
255#1534C2×C15111yescharacteristic, complemented
256#1528C2×C15111yescharacteristic, complemented
257#1527C2×C15111yescharacteristic
258#563—22no—
259#563—22no—
260#563—22no—
261#563C22×C15114yes—
262#533C22×C15111yescharacteristic
263C2×C4⋊Q8—21no—
264C2×#126—21no—
265C2×#126—21no—
266C2×#125C22×C15111yescharacteristic
267C2×#125C22×C15111yescharacteristic
268C2×#124C22×C15111yescharacteristic
269C2×#123—21no—
270C2×C22⋊Q8—21no—
271C2×C22⋊Q8—21no—
272#501C22×C15112yescomplemented
273#501C22×C15112yescomplemented
274#501C22×C15112yescomplemented
275#499—22no—
276#497C22×C15112yes—
277#491C22×C15112yescomplemented
278#489C22×C15112yes—
279#484—21no—
280#483—21no—
281#479—22no—
282#464—22no—
283#451—21no—
284#450—21no—
285#432C22×C15111yescharacteristic
286#432C22×C15111yescharacteristic
287#428—21no—
288#428—21no—
289C4×M16C22×C15111yescharacteristic
290#330C22×C15114yescomplemented
291#330C22×C15114yescomplemented
292#329C22×C15114yes—
293C22×Q8—21no—
294C22×Q8D4×C15111yescharacteristic
295C22×D4D4×C15111yescharacteristic
296C23×C4—21no—
297C2×Q16—22no—
298C2×SD16—22no—
299C2×M16—21no—
300C4⋊Q8—24no—
301C4⋊Q8—24no—
302C4⋊Q8C23×C15111yescharacteristic
303C4⋊Q8C23×C15111yescharacteristic
304#126—24no—
305#126—24no—
306#126—24no—
307#126—24no—
308#125—21no—
309#125—21no—
310#125—21no—
311#125—21no—
312#125—21no—
313#125D4×C15112yes—
314#125D4×C15112yes—
315#125C23×C15112yes—
316#125C23×C15112yes—
317#124—21no—
318#124—21no—
319#124D4×C15112yes—
320#124C23×C15112yes—
321#123—24no—
322#123—24no—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C4×Q8—21no—
330C4×Q8—21no—
331#117—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4D4×C15111yescharacteristic
339C2×C4⋊C4D4×C15111yescharacteristic
340C2×C4⋊C4D4×C15111yescharacteristic
341C2×C4⋊C4D4×C15111yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C42—21no—
348C2×C42C23×C15111yescharacteristic
349#107—22no—
350#107—22no—
351#107—22no—
352#106—22no—
353#106—22no—
354#106—22no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357#103—22no—
358#103—22no—
359#103—22no—
360#102—22no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363#97C23×C15112yes—
364#97C23×C15112yes—
365#97C23×C15112yes—
366C4×C8—21no—
367C24—21no—
368C2×Q8—24no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—81no—
373C2×Q8—82no—
374C2×Q8C2×D4×C15112yes—
375C2×D4—21no—
376C2×D4—81no—
377C2×D4C2×D4×C15112yes—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—24no—
384C22×C4—82no—
385C22×C4C2×D4×C15111yescharacteristic
386C22×C4C2×D4×C15111yescharacteristic
387C22×C4C2×D4×C15111yescharacteristic
388Q16—82no—
389SD16—82no—
390M16—24no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4C2×D4×C15112yes—
415C4⋊C4C2×D4×C15112yes—
416C4⋊C4C2×D4×C15112yes—
417C4⋊C4C2×D4×C15112yes—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—41no—
426C42—24no—
427C42—41no—
428C42C2×D4×C15111yescharacteristic
429C42C2×D4×C15111yescharacteristic
430C42C2×D4×C15111yescharacteristic
431C42C24×C15111yescharacteristic
432C23—22no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23#120×C15111yescharacteristic
437Q8—42no—
438Q8—42no—
439Q8—42no—
440Q8—81no—
441Q8—84no—
442D4—42no—
443D4—81no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—84no—
460C2×C4#120×C15111yescharacteristic
461C2×C4#120×C15111yescharacteristic
462C2×C4#120×C15111yescharacteristic
463C2×C4C22×D4×C15111yescharacteristic
464C2×C4C22×D4×C15111yescharacteristic
465C2×C4C22×D4×C15111yescharacteristic
466C8—24no—
467C8—42no—
468C8—42no—
469C22—21no—
470C22—21no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—84no—
475C22#456×C15112yes—
476C22C2×#120×C15111yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—81no—
489C4—81no—
490C2—22no—
491C2—82no—
492C2C2×#456×C15111yescharacteristic
493C2#3019×C15111yescharacteristic
494C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC22×D4×C151D4
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. #3236×C151C2semidirect
4. #3166×C151C2semidirect
5. #1664×C151C2semidirect
6. #1660×C151C2semidirect
7. #1534×C151C2semidirect
8. #1528×C151C2semidirect
24. #501×C151C22semidirect
25. #501×C151C22semidirect
26. #501×C151C22semidirect
29. #491×C151C22semidirect
42. #330×C151C22semidirect
43. #330×C151C22semidirect
247. #19007C151direct (N × H)
248. C151#19007direct (N × H)
250. #3236C2×C151semidirect
252. #3166C2×C151semidirect
253. #1664C2×C151semidirect
254. #1660C2×C151semidirect
255. #1534C2×C151semidirect
256. #1528C2×C151semidirect
272. #501C22×C151semidirect
273. #501C22×C151semidirect
274. #501C22×C151semidirect
277. #491C22×C151semidirect
290. #330C22×C151semidirect
291. #330C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#563×C1512
#3236×C1512
#3215×C1512
#3166×C1512
#1664×C1512
#1660×C1512
#1534×C1512
#1528×C1512
#1527×C1512
#19007151