Finite Group Databasebeta

← C151×#18767 #50323692

Subgroups — C151×#18767 #50323692

Order 38656.

1234 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C151C211yesmaximal, characteristic
2#3208×C151C211yesmaximal, characteristic, complemented
3#3101×C151C211yesmaximal, characteristic, complemented
4#3078×C151C211yesmaximal, characteristic, complemented
5#1642×C151C214yesmaximal, complemented
6#1631×C151C214yesmaximal, complemented
7#1545×C151C211yesmaximal, characteristic, complemented
8#1486×C151C211yesmaximal, characteristic, complemented
9#1479×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151—21no—
11#550×C151—22no—
12#550×C151—22no—
13#550×C151—22no—
14#550×C151C2214yes—
15#533×C151C2211yescharacteristic
16C2×#127×C151—21no—
17C2×#127×C151C2211yescharacteristic
18C2×#121×C151—22no—
19C2×#121×C151—21no—
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151—21no—
22C2×C4×D4×C151C2211yescharacteristic
23#492×C151C2212yescomplemented
24#486×C151C2212yescomplemented
25#483×C151—21no—
26#479×C151—22no—
27#477×C151C2212yescomplemented
28#476×C151C2212yescomplemented
29#475×C151C2212yescomplemented
30#461×C151C2212yescomplemented
31#460×C151—22no—
32#450×C151—21no—
33#450×C151—22no—
34C4×SD16×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#428×C151—21no—
38#423×C151C2211yescharacteristic
39#419×C151—21no—
40#331×C151C2214yescomplemented
41Q8⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yescomplemented
43C2×#41×C151—24no—
44C2×#41×C151—24no—
45C2×#41×C151—44no—
46C2×#41×C151—44no—
47C22×Q8×C151D411yescharacteristic
48C22×D4×C151—22no—
49C22×D4×C151—22no—
50C22×D4×C151—21no—
51C22×D4×C151—21no—
52C22×D4×C151D411yescharacteristic
53C22×D4×C151D412yes—
54C23×C4×C151—22no—
55C23×C4×C151—21no—
56C2×SD16×C151—22no—
57C2×SD16×C151—24no—
58C2×M16×C151—21no—
59C4⋊Q8×C151C2311yescharacteristic
60C4⋊Q8×C151C2311yescharacteristic
61#127×C151—24no—
62#127×C151—24no—
63#127×C151—21no—
64#127×C151—21no—
65#127×C151D412yes—
66#127×C151C2312yes—
67#125×C151—21no—
68C22⋊Q8×C151—21no—
69C22⋊Q8×C151—21no—
70#121×C151—24no—
71#121×C151—28no—
72#121×C151—28no—
73#121×C151—24no—
74C4×Q8×C151—21no—
75C4×Q8×C151—21no—
76C4×Q8×C151—21no—
77C4×Q8×C151—21no—
78C4×Q8×C151D412yes—
79C4×Q8×C151C2312yes—
80C4×D4×C151—24no—
81C4×D4×C151—24no—
82C4×D4×C151—21no—
83C4×D4×C151—21no—
84C4×D4×C151D412yes—
85C4×D4×C151C2312yes—
86#117×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151D411yescharacteristic
89C2×C4⋊C4×C151D411yescharacteristic
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151—21no—
92C2×C42×C151—21no—
93C2×C42×C151C2311yescharacteristic
94#107×C151—22no—
95#106×C151—22no—
96#106×C151—22no—
97C4⋊C8×C151—21no—
98C4⋊C8×C151—21no—
99C4⋊C8×C151C2312yes—
100C4⋊C8×C151C2312yes—
101#103×C151—22no—
102#103×C151—22no—
103#103×C151—22no—
104#102×C151—22no—
105#102×C151—24no—
106C22⋊C8×C151—21no—
107C22⋊C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110C24×C151—22no—
111C24×C151—21no—
112#41×C151—48no—
113#41×C151—416no—
114#41×C151—48no—
115C2×Q8×C151—21no—
116C2×Q8×C151—22no—
117C2×Q8×C151—21no—
118C2×Q8×C151—21no—
119C2×Q8×C151SD1614yescomplemented
120C2×Q8×C151C2×D412yes—
121C2×D4×C151—28no—
122C2×D4×C151—28no—
123C2×D4×C151—21no—
124C2×D4×C151—22no—
125C2×D4×C151—22no—
126C2×D4×C151—22no—
127C2×D4×C151—22no—
128C2×D4×C151—22no—
129C2×D4×C151—42no—
130C2×D4×C151—44no—
131C2×D4×C151—48no—
132C2×D4×C151—42no—
133C2×D4×C151—42no—
134C2×D4×C151—82no—
135C2×D4×C151—84no—
136C2×D4×C151C2×D412yes—
137C2×D4×C151C2×D414yes—
138C22×C4×C151—21no—
139C22×C4×C151—28no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—48no—
145C22×C4×C151—42no—
146C22×C4×C151—42no—
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150SD16×C151—44no—
151SD16×C151—84no—
152M16×C151—42no—
153C2×C8×C151—22no—
154C2×C8×C151—22no—
155C2×C8×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
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—
168C22⋊C4×C151—28no—
169C22⋊C4×C151—22no—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—41no—
172C42×C151—22no—
173C42×C151—22no—
174C42×C151—41no—
175C42×C151C2×D411yescharacteristic
176C42×C151C2×D411yescharacteristic
177C42×C151C2×D411yescharacteristic
178C42×C151C2411yescharacteristic
179C23×C151—22no—
180C23×C151—24no—
181C23×C151—42no—
182C23×C151—44no—
183C23×C151—44no—
184C23×C151—42no—
185C23×C151—44no—
186C23×C151—42no—
187C23×C151#12011yescharacteristic
188Q8×C151—22no—
189Q8×C151—24no—
190Q8×C151—42no—
191Q8×C151—42no—
192Q8×C151C2×SD1614yes—
193D4×C151—22no—
194D4×C151—22no—
195D4×C151—44no—
196D4×C151—416no—
197D4×C151—42no—
198D4×C151—44no—
199D4×C151—42no—
200D4×C151—42no—
201D4×C151—44no—
202D4×C151—44no—
203D4×C151—82no—
204D4×C151—88no—
205C2×C4×C151—22no—
206C2×C4×C151—24no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—22no—
210C2×C4×C151—41no—
211C2×C4×C151—416no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—44no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151#12011yescharacteristic
220C2×C4×C151#12011yescharacteristic
221C2×C4×C151#12011yescharacteristic
222C2×C4×C151C2×SD1612yes—
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—44no—
233C22×C151—42no—
234C22×C151—42no—
235C22×C151—44no—
236C22×C151—44no—
237C22×C151—42no—
238C22×C151—84no—
239C22×C151—88no—
240C22×C151#45012yes—
241C22×C151C2×#12011yescharacteristic
242C4×C151—24no—
243C4×C151—21no—
244C4×C151—21no—
245C4×C151—21no—
246C4×C151—42no—
247C4×C151—42no—
248C4×C151—81no—
249C4×C151—81no—
250C4×C151#45012yes—
251C4×C151C22×SD1611yescharacteristic
252C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
253C4×C151#57512yes—
254C2×C151—22no—
255C2×C151—82no—
256C2×C151—84no—
257C2×C151C2×#45011yescharacteristic
258C2×C151#300511yescharacteristic
259C2×C151#301911yescharacteristic
260#18767C15111yesmaximal, characteristic, direct product factor, Sylow
261C151#1876711yescharacteristic, direct product factor, Sylow
262C2×#550C2×C15111yescharacteristic
263#3208C2×C15111yescharacteristic, complemented
264#3101C2×C15111yescharacteristic, complemented
265#3078C2×C15111yescharacteristic, complemented
266#1642C2×C15114yescomplemented
267#1631C2×C15114yescomplemented
268#1545C2×C15111yescharacteristic, complemented
269#1486C2×C15111yescharacteristic, complemented
270#1479C2×C15111yescharacteristic, complemented
271C22×#41—21no—
272#550—22no—
273#550—22no—
274#550—22no—
275#550C22×C15114yes—
276#533C22×C15111yescharacteristic
277C2×#127—21no—
278C2×#127C22×C15111yescharacteristic
279C2×#121—22no—
280C2×#121—21no—
281C2×C4×Q8C22×C15111yescharacteristic
282C2×C4×D4—21no—
283C2×C4×D4C22×C15111yescharacteristic
284#492C22×C15112yescomplemented
285#486C22×C15112yescomplemented
286#483—21no—
287#479—22no—
288#477C22×C15112yescomplemented
289#476C22×C15112yescomplemented
290#475C22×C15112yescomplemented
291#461C22×C15112yescomplemented
292#460—22no—
293#450—21no—
294#450—22no—
295C4×SD16—22no—
296#431C22×C15111yescharacteristic
297#431C22×C15111yescharacteristic
298#428—21no—
299#423C22×C15111yescharacteristic
300#419—21no—
301#331C22×C15114yescomplemented
302Q8⋊C8C22×C15114yescomplemented
303D4⋊C8C22×C15114yescomplemented
304C2×#41—24no—
305C2×#41—24no—
306C2×#41—44no—
307C2×#41—44no—
308C22×Q8D4×C15111yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4D4×C15111yescharacteristic
314C22×D4D4×C15112yes—
315C23×C4—22no—
316C23×C4—21no—
317C2×SD16—22no—
318C2×SD16—24no—
319C2×M16—21no—
320C4⋊Q8C23×C15111yescharacteristic
321C4⋊Q8C23×C15111yescharacteristic
322#127—24no—
323#127—24no—
324#127—21no—
325#127—21no—
326#127D4×C15112yes—
327#127C23×C15112yes—
328#125—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331#121—24no—
332#121—28no—
333#121—28no—
334#121—24no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8D4×C15112yes—
340C4×Q8C23×C15112yes—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4D4×C15112yes—
346C4×D4C23×C15112yes—
347#117—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4D4×C15111yescharacteristic
350C2×C4⋊C4D4×C15111yescharacteristic
351C2×C22⋊C4—22no—
352C2×C22⋊C4—21no—
353C2×C42—21no—
354C2×C42C23×C15111yescharacteristic
355#107—22no—
356#106—22no—
357#106—22no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8C23×C15112yes—
361C4⋊C8C23×C15112yes—
362#103—22no—
363#103—22no—
364#103—22no—
365#102—22no—
366#102—24no—
367C22⋊C8—21no—
368C22⋊C8—21no—
369C4×C8—21no—
370C4×C8C23×C15112yes—
371C24—22no—
372C24—21no—
373#41—416no—
374#41—48no—
375#41—48no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8SD16×C15114yescomplemented
381C2×Q8C2×D4×C15112yes—
382C2×D4—28no—
383C2×D4—28no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—42no—
391C2×D4—48no—
392C2×D4—44no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—82no—
396C2×D4—84no—
397C2×D4C2×D4×C15112yes—
398C2×D4C2×D4×C15114yes—
399C22×C4—21no—
400C22×C4—28no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—48no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4C2×D4×C15111yescharacteristic
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C2×D4×C15111yescharacteristic
411SD16—44no—
412SD16—84no—
413M16—42no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4C2×D4×C15112yes—
428C4⋊C4C2×D4×C15112yes—
429C22⋊C4—28no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—41no—
433C42—22no—
434C42—22no—
435C42—41no—
436C42C2×D4×C15111yescharacteristic
437C42C2×D4×C15111yescharacteristic
438C42C2×D4×C15111yescharacteristic
439C42C24×C15111yescharacteristic
440C23—22no—
441C23—24no—
442C23—42no—
443C23—44no—
444C23—44no—
445C23—42no—
446C23—44no—
447C23—42no—
448C23#120×C15111yescharacteristic
449Q8—24no—
450Q8—22no—
451Q8—42no—
452Q8—42no—
453Q8C2×SD16×C15114yes—
454D4—22no—
455D4—22no—
456D4—44no—
457D4—416no—
458D4—42no—
459D4—44no—
460D4—44no—
461D4—42no—
462D4—42no—
463D4—44no—
464D4—82no—
465D4—88no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—416no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4#120×C15111yescharacteristic
481C2×C4#120×C15111yescharacteristic
482C2×C4#120×C15111yescharacteristic
483C2×C4C2×SD16×C15112yes—
484C2×C4AGL(1,ℤ/8)×C15112yes—
485C2×C4C22×D4×C15111yescharacteristic
486C2×C4C22×D4×C15111yescharacteristic
487C2×C4C22×D4×C15111yescharacteristic
488C8—42no—
489C8—42no—
490C8—42no—
491C22—21no—
492C22—21no—
493C22—44no—
494C22—42no—
495C22—42no—
496C22—44no—
497C22—44no—
498C22—42no—
499C22—84no—
500C22—88no—
501C22#450×C15112yes—
502C22C2×#120×C15111yescharacteristic
503C4—24no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—42no—
509C4—81no—
510C4—81no—
511C4#450×C15112yes—
512C4C22×SD16×C15111yescharacteristic
513C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
514C4#575×C15112yes—
515C2—22no—
516C2—82no—
517C2—84no—
518C2C2×#450×C15111yescharacteristic
519C2#3005×C15111yescharacteristic
520C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#550×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. #3208×C151C2semidirect
3. #3101×C151C2semidirect
4. #3078×C151C2semidirect
5. #1642×C151C2semidirect
6. #1631×C151C2semidirect
7. #1545×C151C2semidirect
8. #1486×C151C2semidirect
9. #1479×C151C2semidirect
23. #492×C151C22semidirect
24. #486×C151C22semidirect
27. #477×C151C22semidirect
28. #476×C151C22semidirect
29. #475×C151C22semidirect
30. #461×C151C22semidirect
40. #331×C151C22semidirect
41. Q8⋊C8×C151C22semidirect
42. D4⋊C8×C151C22semidirect
119. C2×Q8×C151SD16semidirect
260. #18767C151direct (N × H)
261. C151#18767direct (N × H)
263. #3208C2×C151semidirect
264. #3101C2×C151semidirect
265. #3078C2×C151semidirect
266. #1642C2×C151semidirect
267. #1631C2×C151semidirect
268. #1545C2×C151semidirect
269. #1486C2×C151semidirect
270. #1479C2×C151semidirect
284. #492C22×C151semidirect
285. #486C22×C151semidirect
288. #477C22×C151semidirect
289. #476C22×C151semidirect
290. #475C22×C151semidirect
291. #461C22×C151semidirect
301. #331C22×C151semidirect
302. Q8⋊C8C22×C151semidirect
303. D4⋊C8C22×C151semidirect
380. C2×Q8SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1512
#3208×C1512
#3101×C1512
#3078×C1512
#1642×C1512
#1631×C1512
#1545×C1512
#1486×C1512
#1479×C1512
#18767151