Finite Group Databasebeta

← C151×#18757 #50323682

Subgroups — C151×#18757 #50323682

Order 38656.

1170 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C151C211yesmaximal, characteristic
2#3229×C151C211yesmaximal, characteristic, complemented
3#3101×C151C211yesmaximal, characteristic, complemented
4#3077×C151C211yesmaximal, characteristic, complemented
5#1654×C151C214yesmaximal, complemented
6#1635×C151C214yesmaximal, complemented
7#1546×C151C211yesmaximal, characteristic, complemented
8#1486×C151C211yesmaximal, characteristic, complemented
9#1478×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151—21no—
11#547×C151—22no—
12#547×C151—22no—
13#547×C151—22no—
14#547×C151C2214yes—
15#533×C151C2211yescharacteristic
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#123×C151—22no—
18C2×C22⋊Q8×C151—21no—
19C2×#121×C151—21no—
20C2×C4×D4×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C22×C4⋊C4×C151—21no—
23#498×C151C2212yescomplemented
24#487×C151C2212yescomplemented
25#483×C151—21no—
26#483×C151—22no—
27#478×C151—22no—
28#476×C151C2212yescomplemented
29#476×C151C2212yescomplemented
30#475×C151—22no—
31#474×C151C2212yescomplemented
32#461×C151C2212yescomplemented
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#332×C151C2214yescomplemented
41D4⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yescomplemented
43C2×#41×C151—24no—
44C2×#41×C151—24no—
45C2×#41×C151—44no—
46C2×#41×C151—44no—
47C22×Q8×C151—21no—
48C22×D4×C151—22no—
49C22×D4×C151D411yescharacteristic
50C22×D4×C151D411yescharacteristic
51C23×C4×C151—22no—
52C23×C4×C151—21no—
53C23×C4×C151—21no—
54C2×SD16×C151—22no—
55C2×M16×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151D412yes—
59C4⋊Q8×C151C2311yescharacteristic
60C4⋊Q8×C151C2311yescharacteristic
61C4⋊Q8×C151C2312yes—
62#125×C151—21no—
63#123×C151—28no—
64#123×C151—28no—
65C22⋊Q8×C151—24no—
66C22⋊Q8×C151—24no—
67C22⋊Q8×C151—21no—
68C22⋊Q8×C151—21no—
69#121×C151—24no—
70#121×C151—24no—
71C4×Q8×C151—21no—
72C4×Q8×C151—21no—
73C4×D4×C151—21no—
74C4×D4×C151—21no—
75C4×D4×C151—21no—
76C4×D4×C151—21no—
77C4×D4×C151D412yes—
78C4×D4×C151D412yes—
79C4×D4×C151C2312yes—
80C4×D4×C151C2312yes—
81#117×C151—21no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—24no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—24no—
86C2×C4⋊C4×C151D411yescharacteristic
87C2×C4⋊C4×C151D411yescharacteristic
88C2×C4⋊C4×C151D412yes—
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C42×C151C2311yescharacteristic
93#107×C151—22no—
94#106×C151—22no—
95#106×C151—22no—
96#106×C151—24no—
97C4⋊C8×C151—21no—
98C4⋊C8×C151—21no—
99C4⋊C8×C151C2312yes—
100C4⋊C8×C151C2312yes—
101#103×C151—22no—
102#103×C151—24no—
103#102×C151—22no—
104#102×C151—22no—
105#102×C151—22no—
106C22⋊C8×C151—21no—
107C22⋊C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110C24×C151—21no—
111C24×C151—21no—
112#41×C151—48no—
113#41×C151—416no—
114#41×C151—48no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—21no—
118C2×Q8×C151—21no—
119C2×Q8×C151—42no—
120C2×Q8×C151—42no—
121C2×D4×C151—28no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—22no—
125C2×D4×C151—42no—
126C2×D4×C151—48no—
127C2×D4×C151SD1614yescomplemented
128C2×D4×C151C2×D412yes—
129C2×D4×C151C2×D412yes—
130C22×C4×C151—28no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—44no—
139C22×C4×C151—48no—
140C22×C4×C151—42no—
141C22×C4×C151—42no—
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145SD16×C151—44no—
146M16×C151—42no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C4⋊C4×C151—28no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—41no—
161C4⋊C4×C151—41no—
162C4⋊C4×C151C2×D412yes—
163C4⋊C4×C151C2×D414yes—
164C4⋊C4×C151C2×D412yes—
165C22⋊C4×C151—28no—
166C22⋊C4×C151—22no—
167C22⋊C4×C151—22no—
168C22⋊C4×C151—22no—
169C22⋊C4×C151—22no—
170C22⋊C4×C151—41no—
171C42×C151—41no—
172C42×C151C2×D411yescharacteristic
173C42×C151C2×D411yescharacteristic
174C42×C151C2×D411yescharacteristic
175C42×C151C2411yescharacteristic
176C23×C151—22no—
177C23×C151—24no—
178C23×C151—22no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151#12011yescharacteristic
185Q8×C151—42no—
186Q8×C151—42no—
187Q8×C151—42no—
188Q8×C151—44no—
189Q8×C151—42no—
190D4×C151—22no—
191D4×C151—22no—
192D4×C151—22no—
193D4×C151—24no—
194D4×C151—42no—
195D4×C151—416no—
196D4×C151C2×SD1614yes—
197C2×C4×C151—22no—
198C2×C4×C151—24no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—41no—
202C2×C4×C151—44no—
203C2×C4×C151—416no—
204C2×C4×C151—42no—
205C2×C4×C151—44no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—44no—
210C2×C4×C151—44no—
211C2×C4×C151—41no—
212C2×C4×C151—41no—
213C2×C4×C151#12011yescharacteristic
214C2×C4×C151#12011yescharacteristic
215C2×C4×C151#12011yescharacteristic
216C2×C4×C151C2×SD1612yes—
217C2×C4×C151AGL(1,ℤ/8)12yes—
218C2×C4×C151C22×D411yescharacteristic
219C2×C4×C151C22×D411yescharacteristic
220C2×C4×C151C22×D411yescharacteristic
221C8×C151—42no—
222C8×C151—42no—
223C8×C151—42no—
224C22×C151—21no—
225C22×C151—21no—
226C22×C151—24no—
227C22×C151—48no—
228C22×C151—42no—
229C22×C151—42no—
230C22×C151—42no—
231C22×C151—42no—
232C22×C151—42no—
233C22×C151—84no—
234C22×C151#45012yes—
235C22×C151C2×#12011yescharacteristic
236C4×C151—21no—
237C4×C151—21no—
238C4×C151—21no—
239C4×C151—42no—
240C4×C151—44no—
241C4×C151—42no—
242C4×C151—81no—
243C4×C151—81no—
244C4×C151#45012yes—
245C4×C151C22×SD1611yescharacteristic
246C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C151#57512yes—
248C2×C151—22no—
249C2×C151—44no—
250C2×C151—82no—
251C2×C151C2×#45011yescharacteristic
252C2×C151#300511yescharacteristic
253C2×C151#302011yescharacteristic
254#18757C15111yesmaximal, characteristic, direct product factor, Sylow
255C151#1875711yescharacteristic, direct product factor, Sylow
256C2×#547C2×C15111yescharacteristic
257#3229C2×C15111yescharacteristic, complemented
258#3101C2×C15111yescharacteristic, complemented
259#3077C2×C15111yescharacteristic, complemented
260#1654C2×C15114yescomplemented
261#1635C2×C15114yescomplemented
262#1546C2×C15111yescharacteristic, complemented
263#1486C2×C15111yescharacteristic, complemented
264#1478C2×C15111yescharacteristic, complemented
265C22×#41—21no—
266#547—22no—
267#547—22no—
268#547—22no—
269#547C22×C15114yes—
270#533C22×C15111yescharacteristic
271C2×C4⋊Q8C22×C15111yescharacteristic
272C2×#123—22no—
273C2×C22⋊Q8—21no—
274C2×#121—21no—
275C2×C4×D4C22×C15111yescharacteristic
276C2×C4×D4C22×C15111yescharacteristic
277C22×C4⋊C4—21no—
278#498C22×C15112yescomplemented
279#487C22×C15112yescomplemented
280#483—21no—
281#483—22no—
282#478—22no—
283#476C22×C15112yescomplemented
284#476C22×C15112yescomplemented
285#475—22no—
286#474C22×C15112yescomplemented
287#461C22×C15112yescomplemented
288#450—21no—
289C4×SD16—22no—
290#431C22×C15111yescharacteristic
291#431C22×C15111yescharacteristic
292#428—21no—
293#423C22×C15111yescharacteristic
294#418—21no—
295#332C22×C15114yescomplemented
296D4⋊C8C22×C15114yescomplemented
297D4⋊C8C22×C15114yescomplemented
298C2×#41—24no—
299C2×#41—24no—
300C2×#41—44no—
301C2×#41—44no—
302C22×Q8—21no—
303C22×D4—22no—
304C22×D4D4×C15111yescharacteristic
305C22×D4D4×C15111yescharacteristic
306C23×C4—22no—
307C23×C4—21no—
308C23×C4—21no—
309C2×SD16—22no—
310C2×M16—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8D4×C15112yes—
314C4⋊Q8C23×C15111yescharacteristic
315C4⋊Q8C23×C15111yescharacteristic
316C4⋊Q8C23×C15112yes—
317#125—21no—
318#123—28no—
319#123—28no—
320C22⋊Q8—24no—
321C22⋊Q8—24no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324#121—24no—
325#121—24no—
326C4×Q8—21no—
327C4×Q8—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4D4×C15112yes—
333C4×D4D4×C15112yes—
334C4×D4C23×C15112yes—
335C4×D4C23×C15112yes—
336#117—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4D4×C15111yescharacteristic
342C2×C4⋊C4D4×C15111yescharacteristic
343C2×C4⋊C4D4×C15112yes—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C42C23×C15111yescharacteristic
348#107—22no—
349#106—22no—
350#106—22no—
351#106—24no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8C23×C15112yes—
355C4⋊C8C23×C15112yes—
356#103—22no—
357#103—24no—
358#102—22no—
359#102—22no—
360#102—22no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C4×C8—21no—
364C4×C8C23×C15112yes—
365C24—21no—
366C24—21no—
367#41—416no—
368#41—48no—
369#41—48no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—42no—
375C2×Q8—42no—
376C2×D4—28no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—42no—
381C2×D4—48no—
382C2×D4SD16×C15114yescomplemented
383C2×D4C2×D4×C15112yes—
384C2×D4C2×D4×C15112yes—
385C22×C4—28no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—44no—
394C22×C4—48no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4C2×D4×C15111yescharacteristic
398C22×C4C2×D4×C15111yescharacteristic
399C22×C4C2×D4×C15111yescharacteristic
400SD16—44no—
401M16—42no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C4⋊C4—28no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4C2×D4×C15112yes—
418C4⋊C4C2×D4×C15114yes—
419C4⋊C4C2×D4×C15112yes—
420C22⋊C4—28no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—41no—
426C42—41no—
427C42C2×D4×C15111yescharacteristic
428C42C2×D4×C15111yescharacteristic
429C42C2×D4×C15111yescharacteristic
430C42C24×C15111yescharacteristic
431C23—24no—
432C23—22no—
433C23—22no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23#120×C15111yescharacteristic
440Q8—42no—
441Q8—44no—
442Q8—42no—
443Q8—42no—
444Q8—42no—
445D4—24no—
446D4—22no—
447D4—22no—
448D4—22no—
449D4—42no—
450D4—416no—
451D4C2×SD16×C15114yes—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—41no—
457C2×C4—44no—
458C2×C4—416no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—44no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4#120×C15111yescharacteristic
469C2×C4#120×C15111yescharacteristic
470C2×C4#120×C15111yescharacteristic
471C2×C4C2×SD16×C15112yes—
472C2×C4AGL(1,ℤ/8)×C15112yes—
473C2×C4C22×D4×C15111yescharacteristic
474C2×C4C22×D4×C15111yescharacteristic
475C2×C4C22×D4×C15111yescharacteristic
476C8—42no—
477C8—42no—
478C8—42no—
479C22—21no—
480C22—21no—
481C22—24no—
482C22—48no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—84no—
489C22#450×C15112yes—
490C22C2×#120×C15111yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—44no—
496C4—42no—
497C4—81no—
498C4—81no—
499C4#450×C15112yes—
500C4C22×SD16×C15111yescharacteristic
501C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
502C4#575×C15112yes—
503C2—22no—
504C2—44no—
505C2—82no—
506C2C2×#450×C15111yescharacteristic
507C2#3005×C15111yescharacteristic
508C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#547×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. #3229×C151C2semidirect
3. #3101×C151C2semidirect
4. #3077×C151C2semidirect
5. #1654×C151C2semidirect
6. #1635×C151C2semidirect
7. #1546×C151C2semidirect
8. #1486×C151C2semidirect
9. #1478×C151C2semidirect
23. #498×C151C22semidirect
24. #487×C151C22semidirect
28. #476×C151C22semidirect
29. #476×C151C22semidirect
31. #474×C151C22semidirect
32. #461×C151C22semidirect
40. #332×C151C22semidirect
41. D4⋊C8×C151C22semidirect
42. D4⋊C8×C151C22semidirect
127. C2×D4×C151SD16semidirect
254. #18757C151direct (N × H)
255. C151#18757direct (N × H)
257. #3229C2×C151semidirect
258. #3101C2×C151semidirect
259. #3077C2×C151semidirect
260. #1654C2×C151semidirect
261. #1635C2×C151semidirect
262. #1546C2×C151semidirect
263. #1486C2×C151semidirect
264. #1478C2×C151semidirect
278. #498C22×C151semidirect
279. #487C22×C151semidirect
283. #476C22×C151semidirect
284. #476C22×C151semidirect
286. #474C22×C151semidirect
287. #461C22×C151semidirect
295. #332C22×C151semidirect
296. D4⋊C8C22×C151semidirect
297. D4⋊C8C22×C151semidirect
382. C2×D4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1512
#3229×C1512
#3101×C1512
#3077×C1512
#1654×C1512
#1635×C1512
#1546×C1512
#1486×C1512
#1478×C1512
#18757151