Finite Group Databasebeta

← C151×#18773 #50323698

Subgroups — C151×#18773 #50323698

Order 38656.

986 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C151C211yesmaximal, characteristic
2#3209×C151C211yesmaximal, characteristic, complemented
3#3101×C151C211yesmaximal, characteristic, complemented
4#3077×C151C211yesmaximal, characteristic, complemented
5#1646×C151C214yesmaximal, complemented
6#1634×C151C214yesmaximal, complemented
7#1548×C151C211yesmaximal, characteristic, complemented
8#1486×C151C211yesmaximal, characteristic, complemented
9#1478×C151C211yesmaximal, characteristic, complemented
10#555×C151—22no—
11#555×C151—22no—
12#555×C151—22no—
13#555×C151C2214yes—
14#533×C151C2211yescharacteristic
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#124×C151—22no—
17C2×#121×C151—21no—
18C2×#121×C151—21no—
19C2×C4×D4×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×#117×C151—21no—
22C2×#117×C151—21no—
23#494×C151C2212yescomplemented
24#487×C151C2212yescomplemented
25#483×C151—21no—
26#478×C151—22no—
27#476×C151C2212yescomplemented
28#476×C151C2212yescomplemented
29#474×C151C2212yescomplemented
30#462×C151—22no—
31#461×C151C2212yescomplemented
32#451×C151—22no—
33#450×C151—21no—
34C4×SD16×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#428×C151—21no—
38#423×C151C2211yescharacteristic
39#418×C151—21no—
40#333×C151C2214yescomplemented
41D4⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yescomplemented
43C22×Q8×C151D412yes—
44C22×D4×C151—22no—
45C22×D4×C151D411yescharacteristic
46C22×D4×C151D411yescharacteristic
47C23×C4×C151—21no—
48C23×C4×C151—21no—
49C2×Q16×C151—24no—
50C2×SD16×C151—22no—
51C2×M16×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151—21no—
54C4⋊Q8×C151D412yes—
55C4⋊Q8×C151C2311yescharacteristic
56C4⋊Q8×C151C2311yescharacteristic
57C4⋊Q8×C151C2312yes—
58#125×C151—21no—
59#124×C151—28no—
60#124×C151—28no—
61C22⋊Q8×C151—21no—
62C22⋊Q8×C151—21no—
63#121×C151—24no—
64#121×C151—24no—
65#121×C151—24no—
66#121×C151—24no—
67C4×Q8×C151—21no—
68C4×Q8×C151—21no—
69C4×D4×C151—21no—
70C4×D4×C151—21no—
71C4×D4×C151—21no—
72C4×D4×C151—21no—
73C4×D4×C151D412yes—
74C4×D4×C151D412yes—
75C4×D4×C151C2312yes—
76C4×D4×C151C2312yes—
77#117×C151—24no—
78#117×C151—24no—
79#117×C151—24no—
80#117×C151—24no—
81#117×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151D411yescharacteristic
86C2×C22⋊C4×C151—22no—
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—21no—
89C2×C22⋊C4×C151—21no—
90C2×C42×C151—22no—
91C2×C42×C151C2311yescharacteristic
92#107×C151—22no—
93#106×C151—22no—
94#106×C151—22no—
95C4⋊C8×C151—21no—
96C4⋊C8×C151—21no—
97C4⋊C8×C151C2312yes—
98C4⋊C8×C151C2312yes—
99#103×C151—22no—
100#103×C151—24no—
101#102×C151—22no—
102#102×C151—22no—
103#102×C151—22no—
104C22⋊C8×C151—21no—
105C22⋊C8×C151—21no—
106C4×C8×C151—21no—
107C4×C8×C151C2312yes—
108C24×C151—21no—
109C24×C151—21no—
110C2×Q8×C151—22no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—82no—
114C2×Q8×C151C2×D414yes—
115C2×D4×C151—28no—
116C2×D4×C151—21no—
117C2×D4×C151—21no—
118C2×D4×C151—22no—
119C2×D4×C151—22no—
120C2×D4×C151—42no—
121C2×D4×C151—84no—
122C2×D4×C151C2×D412yes—
123C2×D4×C151C2×D412yes—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—44no—
132C22×C4×C151—42no—
133C22×C4×C151—42no—
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137Q16×C151—84no—
138SD16×C151—44no—
139M16×C151—42no—
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—41no—
154C4⋊C4×C151—41no—
155C4⋊C4×C151C2×D412yes—
156C4⋊C4×C151C2×D412yes—
157C22⋊C4×C151—28no—
158C22⋊C4×C151—28no—
159C22⋊C4×C151—22no—
160C22⋊C4×C151—22no—
161C22⋊C4×C151—22no—
162C22⋊C4×C151—22no—
163C22⋊C4×C151—41no—
164C42×C151—28no—
165C42×C151—41no—
166C42×C151C2×D411yescharacteristic
167C42×C151C2×D411yescharacteristic
168C42×C151C2×D411yescharacteristic
169C42×C151C2411yescharacteristic
170C23×C151—22no—
171C23×C151—22no—
172C23×C151—42no—
173C23×C151—42no—
174C23×C151—42no—
175C23×C151—42no—
176C23×C151—42no—
177C23×C151—42no—
178C23×C151#12011yescharacteristic
179Q8×C151—44no—
180Q8×C151—42no—
181Q8×C151—42no—
182Q8×C151—82no—
183D4×C151—22no—
184D4×C151—22no—
185D4×C151—22no—
186D4×C151—22no—
187D4×C151—42no—
188D4×C151—42no—
189D4×C151—88no—
190C2×C4×C151—22no—
191C2×C4×C151—24no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—41no—
195C2×C4×C151—44no—
196C2×C4×C151—44no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—44no—
202C2×C4×C151—44no—
203C2×C4×C151—41no—
204C2×C4×C151—41no—
205C2×C4×C151#12011yescharacteristic
206C2×C4×C151#12011yescharacteristic
207C2×C4×C151#12011yescharacteristic
208C2×C4×C151#13512yes—
209C2×C4×C151#13712yes—
210C2×C4×C151C22×D411yescharacteristic
211C2×C4×C151C22×D411yescharacteristic
212C2×C4×C151C22×D411yescharacteristic
213C8×C151—42no—
214C8×C151—42no—
215C8×C151—42no—
216C22×C151—21no—
217C22×C151—21no—
218C22×C151—42no—
219C22×C151—42no—
220C22×C151—42no—
221C22×C151—42no—
222C22×C151—42no—
223C22×C151—42no—
224C22×C151—84no—
225C22×C151—84no—
226C22×C151#45212yes—
227C22×C151C2×#12011yescharacteristic
228C4×C151—21no—
229C4×C151—21no—
230C4×C151—21no—
231C4×C151—42no—
232C4×C151—42no—
233C4×C151—44no—
234C4×C151—81no—
235C4×C151—81no—
236C4×C151#45212yes—
237C4×C151C2×#13511yescharacteristic
238C4×C151C2×#13711yescharacteristic
239C4×C151#57512yes—
240C2×C151—22no—
241C2×C151—82no—
242C2×C151—82no—
243C2×C151C2×#45211yescharacteristic
244C2×C151#300511yescharacteristic
245C2×C151#301911yescharacteristic
246#18773C15111yesmaximal, characteristic, direct product factor, Sylow
247C151#1877311yescharacteristic, direct product factor, Sylow
248C2×#555C2×C15111yescharacteristic
249#3209C2×C15111yescharacteristic, complemented
250#3101C2×C15111yescharacteristic, complemented
251#3077C2×C15111yescharacteristic, complemented
252#1646C2×C15114yescomplemented
253#1634C2×C15114yescomplemented
254#1548C2×C15111yescharacteristic, complemented
255#1486C2×C15111yescharacteristic, complemented
256#1478C2×C15111yescharacteristic, complemented
257#555—22no—
258#555—22no—
259#555—22no—
260#555C22×C15114yes—
261#533C22×C15111yescharacteristic
262C2×C4⋊Q8C22×C15111yescharacteristic
263C2×#124—22no—
264C2×#121—21no—
265C2×#121—21no—
266C2×C4×D4C22×C15111yescharacteristic
267C2×C4×D4C22×C15111yescharacteristic
268C2×#117—21no—
269C2×#117—21no—
270#494C22×C15112yescomplemented
271#487C22×C15112yescomplemented
272#483—21no—
273#478—22no—
274#476C22×C15112yescomplemented
275#476C22×C15112yescomplemented
276#474C22×C15112yescomplemented
277#462—22no—
278#461C22×C15112yescomplemented
279#451—22no—
280#450—21no—
281C4×SD16—22no—
282#431C22×C15111yescharacteristic
283#431C22×C15111yescharacteristic
284#428—21no—
285#423C22×C15111yescharacteristic
286#418—21no—
287#333C22×C15114yescomplemented
288D4⋊C8C22×C15114yescomplemented
289D4⋊C8C22×C15114yescomplemented
290C22×Q8D4×C15112yes—
291C22×D4—22no—
292C22×D4D4×C15111yescharacteristic
293C22×D4D4×C15111yescharacteristic
294C23×C4—21no—
295C23×C4—21no—
296C2×Q16—24no—
297C2×SD16—22no—
298C2×M16—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8D4×C15112yes—
302C4⋊Q8C23×C15111yescharacteristic
303C4⋊Q8C23×C15111yescharacteristic
304C4⋊Q8C23×C15112yes—
305#125—21no—
306#124—28no—
307#124—28no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310#121—24no—
311#121—24no—
312#121—24no—
313#121—24no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4D4×C15112yes—
321C4×D4D4×C15112yes—
322C4×D4C23×C15112yes—
323C4×D4C23×C15112yes—
324#117—24no—
325#117—24no—
326#117—24no—
327#117—24no—
328#117—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4D4×C15111yescharacteristic
332C2×C4⋊C4D4×C15111yescharacteristic
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C42—22no—
338C2×C42C23×C15111yescharacteristic
339#107—22no—
340#106—22no—
341#106—22no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8C23×C15112yes—
345C4⋊C8C23×C15112yes—
346#103—24no—
347#103—22no—
348#102—22no—
349#102—22no—
350#102—22no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C4×C8—21no—
354C4×C8C23×C15112yes—
355C24—21no—
356C24—21no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—82no—
361C2×Q8C2×D4×C15114yes—
362C2×D4—28no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—42no—
368C2×D4—84no—
369C2×D4C2×D4×C15112yes—
370C2×D4C2×D4×C15112yes—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—44no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4C2×D4×C15111yescharacteristic
382C22×C4C2×D4×C15111yescharacteristic
383C22×C4C2×D4×C15111yescharacteristic
384Q16—84no—
385SD16—44no—
386M16—42no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4C2×D4×C15112yes—
403C4⋊C4C2×D4×C15112yes—
404C22⋊C4—28no—
405C22⋊C4—28no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C42—28no—
412C42—41no—
413C42C2×D4×C15111yescharacteristic
414C42C2×D4×C15111yescharacteristic
415C42C2×D4×C15111yescharacteristic
416C42C24×C15111yescharacteristic
417C23—22no—
418C23—22no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23#120×C15111yescharacteristic
426Q8—44no—
427Q8—42no—
428Q8—42no—
429Q8—82no—
430D4—22no—
431D4—22no—
432D4—22no—
433D4—22no—
434D4—42no—
435D4—42no—
436D4—88no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—41no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4#120×C15111yescharacteristic
453C2×C4#120×C15111yescharacteristic
454C2×C4#120×C15111yescharacteristic
455C2×C4#135×C15112yes—
456C2×C4#137×C15112yes—
457C2×C4C22×D4×C15111yescharacteristic
458C2×C4C22×D4×C15111yescharacteristic
459C2×C4C22×D4×C15111yescharacteristic
460C8—42no—
461C8—42no—
462C8—42no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—84no—
472C22—84no—
473C22#452×C15112yes—
474C22C2×#120×C15111yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—42no—
480C4—44no—
481C4—81no—
482C4—81no—
483C4#452×C15112yes—
484C4C2×#135×C15111yescharacteristic
485C4C2×#137×C15111yescharacteristic
486C4#575×C15112yes—
487C2—22no—
488C2—82no—
489C2—82no—
490C2C2×#452×C15111yescharacteristic
491C2#3005×C15111yescharacteristic
492C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#555×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
2. #3209×C151C2semidirect
3. #3101×C151C2semidirect
4. #3077×C151C2semidirect
5. #1646×C151C2semidirect
6. #1634×C151C2semidirect
7. #1548×C151C2semidirect
8. #1486×C151C2semidirect
9. #1478×C151C2semidirect
23. #494×C151C22semidirect
24. #487×C151C22semidirect
27. #476×C151C22semidirect
28. #476×C151C22semidirect
29. #474×C151C22semidirect
31. #461×C151C22semidirect
40. #333×C151C22semidirect
41. D4⋊C8×C151C22semidirect
42. D4⋊C8×C151C22semidirect
246. #18773C151direct (N × H)
247. C151#18773direct (N × H)
249. #3209C2×C151semidirect
250. #3101C2×C151semidirect
251. #3077C2×C151semidirect
252. #1646C2×C151semidirect
253. #1634C2×C151semidirect
254. #1548C2×C151semidirect
255. #1486C2×C151semidirect
256. #1478C2×C151semidirect
270. #494C22×C151semidirect
271. #487C22×C151semidirect
274. #476C22×C151semidirect
275. #476C22×C151semidirect
276. #474C22×C151semidirect
278. #461C22×C151semidirect
287. #333C22×C151semidirect
288. D4⋊C8C22×C151semidirect
289. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C1512
#3209×C1512
#3101×C1512
#3077×C1512
#1646×C1512
#1634×C1512
#1548×C1512
#1486×C1512
#1478×C1512
#18773151