Finite Group Databasebeta

← C151×#23948 #50328873

Subgroups — C151×#23948 #50328873

Order 38656.

1474 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3492×C151C211yesmaximal, characteristic, complemented
2#3003×C151C212yesmaximal, complemented
3C2×#390×C151C211yesmaximal, characteristic, complemented
4#2027×C151C212yesmaximal, complemented
5#2006×C151C212yesmaximal, complemented
6#1896×C151C212yesmaximal, complemented
7#1883×C151C214yesmaximal, complemented
8#1821×C151C211yesmaximal, characteristic, complemented
9C23×D4×C151C2211yescharacteristic
10C2×AGL(1,ℤ/8)×C151C2214yes—
11#554×C151—22no—
12#553×C151—22no—
13#552×C151—22no—
14#547×C151—22no—
15#544×C151C2211yescharacteristic, complemented
16#539×C151—22no—
17#537×C151C2211yescharacteristic, complemented
18#525×C151—22no—
19#525×C151C2212yes—
20#520×C151C2212yescomplemented
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C22⋊C4×C151—22no—
23C22×C42×C151C2211yescharacteristic
24#450×C151—22no—
25#450×C151—22no—
26#447×C151—22no—
27#447×C151—22no—
28C2×#104×C151C2214yescomplemented
29#418×C151C2214yes—
30#407×C151C2212yes—
31#390×C151—22no—
32#390×C151C2212yes—
33#390×C151C2212yes—
34#343×C151C2212yescomplemented
35#343×C151C2212yescomplemented
36#339×C151C2214yescomplemented
37C25×C151—21no—
38C2×#41×C151—22no—
39C2×#41×C151C2312yes—
40C22×D4×C151—24no—
41C22×D4×C151—21no—
42C22×D4×C151—22no—
43C22×D4×C151—22no—
44C22×D4×C151—42no—
45C22×D4×C151C2312yes—
46C23×C4×C151—21no—
47C23×C4×C151D412yes—
48C23×C4×C151C2311yescharacteristic
49AGL(1,ℤ/8)×C151—28no—
50AGL(1,ℤ/8)×C151—44no—
51C2×SD16×C151—24no—
52C2×D8×C151—24no—
53C2×M16×C151C2314yes—
54C4⋊Q8×C151—22no—
55#126×C151—24no—
56#125×C151—24no—
57#125×C151—22no—
58#123×C151—24no—
59#123×C151—24no—
60#123×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151—24no—
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151D412yes—
66C22⋊Q8×C151D412yes—
67#121×C151—22no—
68#121×C151—22no—
69#121×C151—22no—
70#121×C151D412yes—
71#121×C151D412yes—
72#120×C151—22no—
73C4×Q8×C151—22no—
74C4×D4×C151—24no—
75C4×D4×C151—22no—
76C4×D4×C151—24no—
77C4×D4×C151—22no—
78C4×D4×C151—22no—
79#117×C151—22no—
80#117×C151—22no—
81#117×C151C2312yes—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151D412yes—
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C22⋊C4×C151—24no—
89C2×C22⋊C4×C151—24no—
90C2×C22⋊C4×C151—48no—
91C2×C42×C151—21no—
92C2×C42×C151—42no—
93C2×C42×C151C2312yes—
94#104×C151—44no—
95#102×C151—24no—
96#102×C151—24no—
97C22⋊C8×C151—22no—
98C22⋊C8×C151—22no—
99C24×C151—24no—
100C24×C151—22no—
101C24×C151—44no—
102C24×C151—42no—
103C24×C151—44no—
104C24×C151—41no—
105C24×C151—41no—
106C24×C151C2×D411yescharacteristic
107#41×C151—24no—
108#41×C151—24no—
109#41×C151—84no—
110C2×Q8×C151—22no—
111C2×Q8×C151C2×D412yes—
112C2×D4×C151—24no—
113C2×D4×C151—22no—
114C2×D4×C151—22no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151—24no—
118C2×D4×C151—22no—
119C2×D4×C151—24no—
120C2×D4×C151—48no—
121C2×D4×C151—48no—
122C2×D4×C151—42no—
123C2×D4×C151—42no—
124C2×D4×C151C2×D412yes—
125C2×D4×C151#4114yescomplemented
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—24no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—24no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—42no—
135C22×C4×C151—42no—
136C22×C4×C151—44no—
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D412yes—
139C22×C4×C151C2×D412yes—
140C22×C4×C151C2×D412yes—
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2411yescharacteristic
143SD16×C151—48no—
144D8×C151—48no—
145M16×C151—24no—
146M16×C151—24no—
147C2×C8×C151—24no—
148C4⋊C4×C151—24no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151C2×D412yes—
158C4⋊C4×C151C2×D412yes—
159C22⋊C4×C151—24no—
160C22⋊C4×C151—24no—
161C22⋊C4×C151—22no—
162C22⋊C4×C151—22no—
163C22⋊C4×C151—22no—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—22no—
166C22⋊C4×C151—48no—
167C22⋊C4×C151—48no—
168C42×C151—24no—
169C42×C151—22no—
170C42×C151—24no—
171C42×C151—42no—
172C23×C151—21no—
173C23×C151—21no—
174C23×C151—22no—
175C23×C151—22no—
176C23×C151—22no—
177C23×C151—24no—
178C23×C151—416no—
179C23×C151—44no—
180C23×C151—44no—
181C23×C151—44no—
182C23×C151—44no—
183C23×C151—42no—
184C23×C151—42no—
185C23×C151—88no—
186C23×C151—82no—
187C23×C151—82no—
188C23×C151—82no—
189C23×C151—82no—
190C23×C151#12011yescharacteristic
191C23×C151#12011yescharacteristic
192C23×C151C22×D411yescharacteristic
193Q8×C151—24no—
194Q8×C151—82no—
195D4×C151—24no—
196D4×C151—28no—
197D4×C151—48no—
198D4×C151—42no—
199D4×C151—42no—
200D4×C151—44no—
201D4×C151—44no—
202D4×C151—44no—
203D4×C151—82no—
204C2×C4×C151—21no—
205C2×C4×C151—21no—
206C2×C4×C151—24no—
207C2×C4×C151—24no—
208C2×C4×C151—24no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—48no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—44no—
218C2×C4×C151—44no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—82no—
222C2×C4×C151—84no—
223C2×C4×C151#12012yes—
224C2×C4×C151C22×D412yes—
225C2×C4×C151C2×#4112yes—
226C2×C4×C151H(5,𝔽2)12yes—
227C8×C151—44no—
228C22×C151—24no—
229C22×C151—24no—
230C22×C151—21no—
231C22×C151—21no—
232C22×C151—21no—
233C22×C151—21no—
234C22×C151—21no—
235C22×C151—21no—
236C22×C151—48no—
237C22×C151—42no—
238C22×C151—44no—
239C22×C151—42no—
240C22×C151—42no—
241C22×C151—84no—
242C22×C151—88no—
243C22×C151—88no—
244C22×C151—82no—
245C22×C151—82no—
246C22×C151#45312yes—
247C22×C151#45412yes—
248C22×C151C2×#12011yescharacteristic
249C22×C151#52511yescharacteristic
250C22×C151#53511yescharacteristic
251C4×C151—22no—
252C4×C151—44no—
253C4×C151—42no—
254C4×C151—42no—
255C4×C151—42no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151#54614yes—
259C2×C151—21no—
260C2×C151—21no—
261C2×C151—22no—
262C2×C151—22no—
263C2×C151—82no—
264C2×C151—84no—
265C2×C151#240411yescharacteristic
266C2×C151C2×#45311yescharacteristic
267C2×C151C2×#45411yescharacteristic
268#23948C15111yesmaximal, characteristic, direct product factor, Sylow
269C151#2394811yescharacteristic, direct product factor, Sylow
270#3492C2×C15111yescharacteristic, complemented
271#3003C2×C15112yescomplemented
272C2×#390C2×C15111yescharacteristic, complemented
273#2027C2×C15112yescomplemented
274#2006C2×C15112yescomplemented
275#1896C2×C15112yescomplemented
276#1883C2×C15114yescomplemented
277#1821C2×C15111yescharacteristic, complemented
278C23×D4C22×C15111yescharacteristic
279C2×AGL(1,ℤ/8)C22×C15114yes—
280#554—22no—
281#553—22no—
282#552—22no—
283#547—22no—
284#544C22×C15111yescharacteristic, complemented
285#539—22no—
286#537C22×C15111yescharacteristic, complemented
287#525—22no—
288#525C22×C15112yes—
289#520C22×C15112yescomplemented
290C22×C4⋊C4C22×C15111yescharacteristic
291C22×C22⋊C4—22no—
292C22×C42C22×C15111yescharacteristic
293#450—22no—
294#450—22no—
295#447—22no—
296#447—22no—
297C2×#104C22×C15114yescomplemented
298#418C22×C15114yes—
299#407C22×C15112yes—
300#390—22no—
301#390C22×C15112yes—
302#390C22×C15112yes—
303#343C22×C15112yescomplemented
304#343C22×C15112yescomplemented
305#339C22×C15114yescomplemented
306C25—21no—
307C2×#41—22no—
308C2×#41C23×C15112yes—
309C22×D4—24no—
310C22×D4—21no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—42no—
314C22×D4C23×C15112yes—
315C23×C4—21no—
316C23×C4D4×C15112yes—
317C23×C4C23×C15111yescharacteristic
318AGL(1,ℤ/8)—28no—
319AGL(1,ℤ/8)—44no—
320C2×SD16—24no—
321C2×D8—24no—
322C2×M16C23×C15114yes—
323C4⋊Q8—22no—
324#126—24no—
325#125—24no—
326#125—22no—
327#123—24no—
328#123—24no—
329#123—22no—
330C22⋊Q8—22no—
331C22⋊Q8—24no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8D4×C15112yes—
335C22⋊Q8D4×C15112yes—
336#121—22no—
337#121—22no—
338#121—22no—
339#121D4×C15112yes—
340#121D4×C15112yes—
341#120—22no—
342C4×Q8—22no—
343C4×D4—24no—
344C4×D4—22no—
345C4×D4—24no—
346C4×D4—22no—
347C4×D4—22no—
348#117—22no—
349#117—22no—
350#117C23×C15112yes—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4D4×C15112yes—
355C2×C4⋊C4C23×C15111yescharacteristic
356C2×C4⋊C4C23×C15111yescharacteristic
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—48no—
360C2×C42—21no—
361C2×C42—42no—
362C2×C42C23×C15112yes—
363#104—44no—
364#102—24no—
365#102—24no—
366C22⋊C8—22no—
367C22⋊C8—22no—
368C24—24no—
369C24—22no—
370C24—44no—
371C24—42no—
372C24—44no—
373C24—41no—
374C24—41no—
375C24C2×D4×C15111yescharacteristic
376#41—24no—
377#41—24no—
378#41—84no—
379C2×Q8—22no—
380C2×Q8C2×D4×C15112yes—
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—24no—
387C2×D4—22no—
388C2×D4—24no—
389C2×D4—48no—
390C2×D4—48no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4C2×D4×C15112yes—
394C2×D4#41×C15114yescomplemented
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—44no—
406C22×C4C2×D4×C15111yescharacteristic
407C22×C4C2×D4×C15112yes—
408C22×C4C2×D4×C15112yes—
409C22×C4C2×D4×C15112yes—
410C22×C4C2×D4×C15112yes—
411C22×C4C24×C15111yescharacteristic
412SD16—48no—
413D8—48no—
414M16—24no—
415M16—24no—
416C2×C8—24no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4C2×D4×C15112yes—
427C4⋊C4C2×D4×C15112yes—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—48no—
436C22⋊C4—48no—
437C42—24no—
438C42—22no—
439C42—24no—
440C42—42no—
441C23—22no—
442C23—22no—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—24no—
447C23—44no—
448C23—44no—
449C23—44no—
450C23—416no—
451C23—44no—
452C23—42no—
453C23—42no—
454C23—88no—
455C23—82no—
456C23—82no—
457C23—82no—
458C23—82no—
459C23#120×C15111yescharacteristic
460C23#120×C15111yescharacteristic
461C23C22×D4×C15111yescharacteristic
462Q8—24no—
463Q8—82no—
464D4—24no—
465D4—28no—
466D4—48no—
467D4—44no—
468D4—44no—
469D4—42no—
470D4—42no—
471D4—44no—
472D4—82no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—48no—
484C2×C4—42no—
485C2×C4—44no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—82no—
491C2×C4—84no—
492C2×C4#120×C15112yes—
493C2×C4C22×D4×C15112yes—
494C2×C4C2×#41×C15112yes—
495C2×C4H(5,𝔽2)×C15112yes—
496C8—44no—
497C22—24no—
498C22—24no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—48no—
506C22—42no—
507C22—44no—
508C22—42no—
509C22—42no—
510C22—84no—
511C22—88no—
512C22—88no—
513C22—82no—
514C22—82no—
515C22#453×C15112yes—
516C22#454×C15112yes—
517C22C2×#120×C15111yescharacteristic
518C22#525×C15111yescharacteristic
519C22#535×C15111yescharacteristic
520C4—22no—
521C4—44no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4#546×C15114yes—
528C2—21no—
529C2—21no—
530C2—22no—
531C2—22no—
532C2—84no—
533C2—82no—
534C2#2404×C15111yescharacteristic
535C2C2×#453×C15111yescharacteristic
536C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3492×C151C2semidirect
2. #3003×C151C2semidirect
3. C2×#390×C151C2semidirect
4. #2027×C151C2semidirect
5. #2006×C151C2semidirect
6. #1896×C151C2semidirect
7. #1883×C151C2semidirect
8. #1821×C151C2semidirect
15. #544×C151C22semidirect
17. #537×C151C22semidirect
20. #520×C151C22semidirect
28. C2×#104×C151C22semidirect
34. #343×C151C22semidirect
35. #343×C151C22semidirect
36. #339×C151C22semidirect
125. C2×D4×C151#41semidirect
268. #23948C151direct (N × H)
269. C151#23948direct (N × H)
270. #3492C2×C151semidirect
271. #3003C2×C151semidirect
272. C2×#390C2×C151semidirect
273. #2027C2×C151semidirect
274. #2006C2×C151semidirect
275. #1896C2×C151semidirect
276. #1883C2×C151semidirect
277. #1821C2×C151semidirect
284. #544C22×C151semidirect
286. #537C22×C151semidirect
289. #520C22×C151semidirect
297. C2×#104C22×C151semidirect
303. #343C22×C151semidirect
304. #343C22×C151semidirect
305. #339C22×C151semidirect
394. C2×D4#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3492×C1512
#3003×C1512
C2×#390×C1512
#2027×C1512
#2006×C1512
#1896×C1512
#1883×C1512
#1821×C1512
#23948151