Finite Group Databasebeta

← C151×#25944 #50330869

Subgroups — C151×#25944 #50330869

Order 38656.

1100 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C151C211yesmaximal, characteristic, complemented
2C2×#490×C151C211yesmaximal, characteristic
3C2×#460×C151C211yesmaximal, characteristic
4#2548×C151C211yesmaximal, characteristic
5#2025×C151C212yesmaximal, complemented
6#2023×C151C212yesmaximal, complemented
7#1989×C151C211yesmaximal, characteristic, complemented
8#1985×C151C211yesmaximal, characteristic, complemented
9#1880×C151C212yesmaximal, complemented
10#1880×C151C212yesmaximal, complemented
11#1763×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2212yes—
13#557×C151—24no—
14#557×C151—24no—
15C2×C4⋊Q8×C151—21no—
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#127×C151C2211yescharacteristic
18C2×#125×C151—21no—
19C2×#125×C151—21no—
20C2×#125×C151C2211yescharacteristic
21C2×#125×C151C2211yescharacteristic
22C2×#124×C151—21no—
23C2×C4×Q8×C151—21no—
24C2×C4×Q8×C151C2211yescharacteristic
25C2×C4×Q8×C151C2211yescharacteristic
26C2×C4×Q8×C151C2211yescharacteristic
27C2×C4×Q8×C151C2211yescharacteristic
28#490×C151—24no—
29#460×C151—24no—
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×#103×C151C2212yes—
32C2×#102×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×#97×C151C2211yescharacteristic
36#394×C151—21no—
37#394×C151—21no—
38#390×C151—21no—
39#390×C151C2212yes—
40#390×C151C2212yes—
41C4×C4⋊C4×C151C2211yescharacteristic
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45#336×C151C2212yes—
46#336×C151C2212yes—
47C22×Q8×C151—21no—
48C22×Q8×C151D411yescharacteristic
49C22×Q8×C151C2311yescharacteristic
50C22×D4×C151—21no—
51C22×D4×C151—21no—
52C22×D4×C151C2312yes—
53C2×SD16×C151—24no—
54C2×SD16×C151—24no—
55C2×SD16×C151—24no—
56C22×C8×C151C2312yes—
57C22×C8×C151C2312yes—
58C4⋊Q8×C151—28no—
59C4⋊Q8×C151—22no—
60C4⋊Q8×C151—22no—
61#127×C151—22no—
62#127×C151—22no—
63#125×C151—28no—
64#125×C151—28no—
65#125×C151—22no—
66#125×C151—22no—
67#125×C151—22no—
68#125×C151D414yes—
69#124×C151—44no—
70C4×Q8×C151—28no—
71C4×Q8×C151—22no—
72C4×Q8×C151—22no—
73C4×Q8×C151—22no—
74C4×Q8×C151—22no—
75C4×Q8×C151—22no—
76C4×Q8×C151—22no—
77C4×Q8×C151—22no—
78C4×Q8×C151D414yes—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151D411yescharacteristic
88C2×C4⋊C4×C151D411yescharacteristic
89C2×C4⋊C4×C151D411yescharacteristic
90C2×C4⋊C4×C151C2312yes—
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C4⋊C4×C151C2311yescharacteristic
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C22⋊C4×C151—22no—
95C2×C22⋊C4×C151—22no—
96C2×C22⋊C4×C151—22no—
97C2×C22⋊C4×C151—22no—
98C2×C42×C151—21no—
99C2×C42×C151—21no—
100C2×C42×C151—21no—
101C2×C42×C151—21no—
102C2×C42×C151C2311yescharacteristic
103C2×C42×C151C2311yescharacteristic
104C2×C42×C151C2311yescharacteristic
105C4⋊C8×C151—22no—
106#103×C151—24no—
107#102×C151—24no—
108#102×C151—24no—
109#102×C151—24no—
110#97×C151—22no—
111#95×C151—21no—
112C24×C151—22no—
113C2×Q8×C151—24no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—21no—
117C2×Q8×C151—22no—
118C2×Q8×C151—41no—
119C2×Q8×C151—42no—
120C2×Q8×C151—42no—
121C2×Q8×C151C2×D412yes—
122C2×Q8×C151#4114yes—
123C2×D4×C151—22no—
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—42no—
131C2×D4×C151—42no—
132C2×D4×C151—42no—
133C2×D4×C151—82no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—22no—
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2411yescharacteristic
146SD16×C151—48no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—24no—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—24no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151C2×D412yes—
170C4⋊C4×C151C2×D412yes—
171C4⋊C4×C151C2×D412yes—
172C22⋊C4×C151—44no—
173C22⋊C4×C151—44no—
174C22⋊C4×C151—82no—
175C22⋊C4×C151—82no—
176C42×C151—24no—
177C42×C151—24no—
178C42×C151—24no—
179C42×C151—21no—
180C42×C151—21no—
181C42×C151—21no—
182C42×C151—21no—
183C42×C151—42no—
184C42×C151C2×D412yes—
185C42×C151C2×D412yes—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151—42no—
189C23×C151—42no—
190C23×C151—42no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151C22×D411yescharacteristic
194Q8×C151—22no—
195Q8×C151—24no—
196Q8×C151—44no—
197Q8×C151—48no—
198Q8×C151#12414yescomplemented
199D4×C151—42no—
200D4×C151—42no—
201D4×C151—42no—
202D4×C151—42no—
203D4×C151—84no—
204D4×C151—84no—
205C2×C4×C151—21no—
206C2×C4×C151—22no—
207C2×C4×C151—24no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—22no—
212C2×C4×C151—21no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—22no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151#12012yes—
231C2×C4×C151#12012yes—
232C2×C4×C151AGL(1,ℤ/8)12yes—
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C22×D411yescharacteristic
235C2×C4×C151C2×#4112yes—
236C2×C4×C1512−1+412yes—
237C8×C151—42no—
238C8×C151—42no—
239C22×C151—82no—
240C22×C151—82no—
241C22×C151—82no—
242C22×C151—82no—
243C22×C151—82no—
244C22×C151—82no—
245C22×C151—82no—
246C22×C151C2×#12011yescharacteristic
247C22×C151#54812yes—
248C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
249C22×C151#57511yescharacteristic
250C22×C151#57712yes—
251C4×C151—24no—
252C4×C151—22no—
253C4×C151—22no—
254C4×C151—22no—
255C4×C151—41no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151—41no—
259C4×C151—41no—
260C4×C151—42no—
261C4×C151—82no—
262C4×C151C2×#12411yescharacteristic
263C4×C151#53611yescharacteristic
264C4×C151#54812yes—
265C2×C151—162no—
266C2×C151#243611yescharacteristic
267C2×C151#300611yescharacteristic
268C2×C151#301011yescharacteristic
269C2×C151#336812yes—
270C2×C151#337112yes—
271#25944C15111yesmaximal, characteristic, direct product factor, Sylow
272C151#2594411yescharacteristic, direct product factor, Sylow
273C2×#557C2×C15111yescharacteristic, complemented
274C2×#490C2×C15111yescharacteristic
275C2×#460C2×C15111yescharacteristic
276#2548C2×C15111yescharacteristic
277#2025C2×C15112yescomplemented
278#2023C2×C15112yescomplemented
279#1989C2×C15111yescharacteristic, complemented
280#1985C2×C15111yescharacteristic, complemented
281#1880C2×C15112yescomplemented
282#1880C2×C15112yescomplemented
283#1763C2×C15111yescharacteristic, complemented
284C22×SD16C22×C15112yes—
285#557—24no—
286#557—24no—
287C2×C4⋊Q8—21no—
288C2×C4⋊Q8C22×C15111yescharacteristic
289C2×#127C22×C15111yescharacteristic
290C2×#125—21no—
291C2×#125—21no—
292C2×#125C22×C15111yescharacteristic
293C2×#125C22×C15111yescharacteristic
294C2×#124—21no—
295C2×C4×Q8—21no—
296C2×C4×Q8C22×C15111yescharacteristic
297C2×C4×Q8C22×C15111yescharacteristic
298C2×C4×Q8C22×C15111yescharacteristic
299C2×C4×Q8C22×C15111yescharacteristic
300#490—24no—
301#460—24no—
302C2×C4⋊C8C22×C15111yescharacteristic
303C2×#103C22×C15112yes—
304C2×#102C22×C15112yes—
305C2×#102C22×C15112yes—
306C2×#102C22×C15112yes—
307C2×#97C22×C15111yescharacteristic
308#394—21no—
309#394—21no—
310#390—21no—
311#390C22×C15112yes—
312#390C22×C15112yes—
313C4×C4⋊C4C22×C15111yescharacteristic
314#340C22×C15112yes—
315#340C22×C15112yes—
316#340C22×C15112yes—
317#336C22×C15112yes—
318#336C22×C15112yes—
319C22×Q8—21no—
320C22×Q8D4×C15111yescharacteristic
321C22×Q8C23×C15111yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4C23×C15112yes—
325C2×SD16—24no—
326C2×SD16—24no—
327C2×SD16—24no—
328C22×C8C23×C15112yes—
329C22×C8C23×C15112yes—
330C4⋊Q8—28no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333#127—22no—
334#127—22no—
335#125—28no—
336#125—28no—
337#125—22no—
338#125—22no—
339#125—22no—
340#125D4×C15114yes—
341#124—44no—
342C4×Q8—28no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8D4×C15114yes—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4D4×C15111yescharacteristic
360C2×C4⋊C4D4×C15111yescharacteristic
361C2×C4⋊C4D4×C15111yescharacteristic
362C2×C4⋊C4C23×C15112yes—
363C2×C4⋊C4C23×C15111yescharacteristic
364C2×C4⋊C4C23×C15111yescharacteristic
365C2×C4⋊C4C23×C15111yescharacteristic
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42C23×C15111yescharacteristic
375C2×C42C23×C15111yescharacteristic
376C2×C42C23×C15111yescharacteristic
377C4⋊C8—22no—
378#103—24no—
379#102—24no—
380#102—24no—
381#102—24no—
382#97—22no—
383#95—21no—
384C24—22no—
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—41no—
391C2×Q8—42no—
392C2×Q8—42no—
393C2×Q8C2×D4×C15112yes—
394C2×Q8#41×C15114yes—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—82no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4C2×D4×C15111yescharacteristic
412C22×C4C2×D4×C15111yescharacteristic
413C22×C4C2×D4×C15111yescharacteristic
414C22×C4C2×D4×C15111yescharacteristic
415C22×C4C2×D4×C15111yescharacteristic
416C22×C4C2×D4×C15111yescharacteristic
417C22×C4C24×C15111yescharacteristic
418SD16—48no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4C2×D4×C15112yes—
442C4⋊C4C2×D4×C15112yes—
443C4⋊C4C2×D4×C15112yes—
444C22⋊C4—44no—
445C22⋊C4—44no—
446C22⋊C4—82no—
447C22⋊C4—82no—
448C42—24no—
449C42—24no—
450C42—24no—
451C42—21no—
452C42—21no—
453C42—21no—
454C42—21no—
455C42—42no—
456C42C2×D4×C15112yes—
457C42C2×D4×C15112yes—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23C22×D4×C15111yescharacteristic
466Q8—22no—
467Q8—24no—
468Q8—44no—
469Q8—48no—
470Q8#124×C15114yescomplemented
471D4—42no—
472D4—42no—
473D4—42no—
474D4—42no—
475D4—84no—
476D4—84no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—24no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4#120×C15112yes—
503C2×C4#120×C15112yes—
504C2×C4AGL(1,ℤ/8)×C15112yes—
505C2×C4C22×D4×C15111yescharacteristic
506C2×C4C22×D4×C15111yescharacteristic
507C2×C4C2×#41×C15112yes—
508C2×C42−1+4×C15112yes—
509C8—42no—
510C8—42no—
511C22—82no—
512C22—82no—
513C22—82no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22C2×#120×C15111yescharacteristic
519C22#548×C15112yes—
520C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
521C22#575×C15111yescharacteristic
522C22#577×C15112yes—
523C4—24no—
524C4—22no—
525C4—22no—
526C4—22no—
527C4—41no—
528C4—42no—
529C4—42no—
530C4—41no—
531C4—41no—
532C4—42no—
533C4—82no—
534C4C2×#124×C15111yescharacteristic
535C4#536×C15111yescharacteristic
536C4#548×C15112yes—
537C2—162no—
538C2#2436×C15111yescharacteristic
539C2#3006×C15111yescharacteristic
540C2#3010×C15111yescharacteristic
541C2#3368×C15112yes—
542C2#3371×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#127×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#557×C151C2semidirect
5. #2025×C151C2semidirect
6. #2023×C151C2semidirect
7. #1989×C151C2semidirect
8. #1985×C151C2semidirect
9. #1880×C151C2semidirect
10. #1880×C151C2semidirect
11. #1763×C151C2semidirect
198. Q8×C151#124semidirect
271. #25944C151direct (N × H)
272. C151#25944direct (N × H)
273. C2×#557C2×C151semidirect
277. #2025C2×C151semidirect
278. #2023C2×C151semidirect
279. #1989C2×C151semidirect
280. #1985C2×C151semidirect
281. #1880C2×C151semidirect
282. #1880C2×C151semidirect
283. #1763C2×C151semidirect
470. Q8#124×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1512
C2×#490×C1512
C2×#460×C1512
#2548×C1512
#2025×C1512
#2023×C1512
#1989×C1512
#1985×C1512
#1880×C1512
#1763×C1512
#25944151