Finite Group Databasebeta

← C151×#25945 #50330870

Subgroups — C151×#25945 #50330870

Order 38656.

1072 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic
2C2×#491×C151C211yesmaximal, characteristic, complemented
3C2×#461×C151C211yesmaximal, characteristic
4#2568×C151C211yesmaximal, characteristic, complemented
5#2026×C151C212yesmaximal, complemented
6#2024×C151C212yesmaximal, complemented
7#1989×C151C211yesmaximal, characteristic, complemented
8#1985×C151C211yesmaximal, characteristic, complemented
9#1877×C151C212yesmaximal
10#1877×C151C212yesmaximal
11#1762×C151C211yesmaximal, characteristic
12C22×SD16×C151C2212yes—
13#554×C151—24no—
14#554×C151—24no—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#125×C151C2211yescharacteristic
18C2×#125×C151C2211yescharacteristic
19C2×C22⋊Q8×C151—21no—
20C2×C22⋊Q8×C151—21no—
21C2×C22⋊Q8×C151—21no—
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×C4×D4×C151C2211yescharacteristic
25C2×C4×D4×C151C2211yescharacteristic
26C22×C4⋊C4×C151—21no—
27#491×C151—24no—
28#461×C151—24no—
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2212yes—
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#97×C151C2211yescharacteristic
35#400×C151—21no—
36#400×C151—21no—
37#391×C151—21no—
38#391×C151C2212yes—
39#391×C151C2212yes—
40#382×C151—21no—
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×C151C2312yes—
50C22×D4×C151C2311yescharacteristic
51C23×C4×C151—21no—
52C23×C4×C151—21no—
53C23×C4×C151—21no—
54C2×SD16×C151—24no—
55C2×SD16×C151—28no—
56C22×C8×C151C2312yes—
57C22×C8×C151C2312yes—
58C4⋊Q8×C151—22no—
59C4⋊Q8×C151—22no—
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151—22no—
62#125×C151—22no—
63#125×C151—22no—
64#125×C151—22no—
65#125×C151D414yes—
66C22⋊Q8×C151—28no—
67C22⋊Q8×C151—28no—
68C22⋊Q8×C151—28no—
69C4×Q8×C151—22no—
70C4×Q8×C151—22no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74C4×D4×C151—22no—
75C4×D4×C151—22no—
76C4×D4×C151D414yes—
77C2×C4⋊C4×C151—28no—
78C2×C4⋊C4×C151—21no—
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×C151D411yescharacteristic
86C2×C4⋊C4×C151D411yescharacteristic
87C2×C4⋊C4×C151D411yescharacteristic
88C2×C4⋊C4×C151C2312yes—
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C4⋊C4×C151C2311yescharacteristic
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151—21no—
95C2×C42×C151—21no—
96C2×C42×C151C2311yescharacteristic
97C2×C42×C151C2311yescharacteristic
98C2×C42×C151C2311yescharacteristic
99C4⋊C8×C151—22no—
100#103×C151—24no—
101#103×C151—24no—
102#103×C151—24no—
103#102×C151—24no—
104#97×C151—22no—
105#95×C151—21no—
106#95×C151—22no—
107#95×C151—22no—
108#95×C151—22no—
109#95×C151—22no—
110C24×C151—21no—
111C2×Q8×C151—24no—
112C2×Q8×C151—22no—
113C2×Q8×C151—22no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—24no—
117C2×Q8×C151—24no—
118C2×Q8×C151—41no—
119C2×Q8×C151—82no—
120C2×D4×C151—21no—
121C2×D4×C151—22no—
122C2×D4×C151C2×D412yes—
123C2×D4×C151#4114yes—
124C22×C4×C151—24no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—24no—
129C22×C4×C151—24no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—42no—
133C22×C4×C151—42no—
134C22×C4×C151—82no—
135C22×C4×C151—82no—
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2411yescharacteristic
143SD16×C151—48no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—24no—
148C2×C8×C151—22no—
149C4⋊C4×C151—24no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—42no—
163C4⋊C4×C151—42no—
164C4⋊C4×C151C2×D412yes—
165C4⋊C4×C151C2×D412yes—
166C4⋊C4×C151C2×D412yes—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—24no—
169C22⋊C4×C151—24no—
170C42×C151—21no—
171C42×C151—21no—
172C42×C151—21no—
173C42×C151—21no—
174C42×C151—42no—
175C42×C151C2×D412yes—
176C42×C151C2×D412yes—
177C23×C151—22no—
178C23×C151—24no—
179C23×C151—41no—
180C23×C151—41no—
181C23×C151—42no—
182C23×C151C22×D411yescharacteristic
183Q8×C151—44no—
184Q8×C151—42no—
185Q8×C151—42no—
186Q8×C151—44no—
187Q8×C151—84no—
188D4×C151—22no—
189D4×C151—24no—
190D4×C151#12414yes—
191C2×C4×C151—21no—
192C2×C4×C151—21no—
193C2×C4×C151—21no—
194C2×C4×C151—21no—
195C2×C4×C151—22no—
196C2×C4×C151—21no—
197C2×C4×C151—21no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—21no—
201C2×C4×C151—22no—
202C2×C4×C151—21no—
203C2×C4×C151—21no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—48no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—44no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—84no—
217C2×C4×C151—84no—
218C2×C4×C151#12012yes—
219C2×C4×C151#12012yes—
220C2×C4×C151#13712yes—
221C2×C4×C151C22×D411yescharacteristic
222C2×C4×C151C22×D411yescharacteristic
223C2×C4×C151C2×#4112yes—
224C2×C4×C1512−1+412yes—
225C8×C151—42no—
226C8×C151—42no—
227C22×C151—24no—
228C22×C151—44no—
229C22×C151—44no—
230C22×C151—42no—
231C22×C151—42no—
232C22×C151C2×#12011yescharacteristic
233C22×C151#54812yes—
234C22×C151C2×#13711yescharacteristic
235C22×C151#57511yescharacteristic
236C22×C151#57712yes—
237C4×C151—22no—
238C4×C151—22no—
239C4×C151—22no—
240C4×C151—41no—
241C4×C151—42no—
242C4×C151—41no—
243C4×C151—41no—
244C4×C151—42no—
245C4×C151—42no—
246C4×C151—82no—
247C4×C151—82no—
248C4×C151C2×#12411yescharacteristic
249C4×C151#53611yescharacteristic
250C4×C151#54812yes—
251C2×C151—44no—
252C2×C151#243611yescharacteristic
253C2×C151#300711yescharacteristic
254C2×C151#300911yescharacteristic
255C2×C151#337212yes—
256C2×C151#337612yes—
257#25945C15111yesmaximal, characteristic, direct product factor, Sylow
258C151#2594511yescharacteristic, direct product factor, Sylow
259C2×#554C2×C15111yescharacteristic
260C2×#491C2×C15111yescharacteristic, complemented
261C2×#461C2×C15111yescharacteristic
262#2568C2×C15111yescharacteristic, complemented
263#2026C2×C15112yescomplemented
264#2024C2×C15112yescomplemented
265#1989C2×C15111yescharacteristic, complemented
266#1985C2×C15111yescharacteristic, complemented
267#1877C2×C15112yes—
268#1877C2×C15112yes—
269#1762C2×C15111yescharacteristic
270C22×SD16C22×C15112yes—
271#554—24no—
272#554—24no—
273C2×C4⋊Q8C22×C15111yescharacteristic
274C2×C4⋊Q8C22×C15111yescharacteristic
275C2×#125C22×C15111yescharacteristic
276C2×#125C22×C15111yescharacteristic
277C2×C22⋊Q8—21no—
278C2×C22⋊Q8—21no—
279C2×C22⋊Q8—21no—
280C2×C4×Q8C22×C15111yescharacteristic
281C2×C4×D4C22×C15111yescharacteristic
282C2×C4×D4C22×C15111yescharacteristic
283C2×C4×D4C22×C15111yescharacteristic
284C22×C4⋊C4—21no—
285#491—24no—
286#461—24no—
287C2×C4⋊C8C22×C15111yescharacteristic
288C2×#103C22×C15112yes—
289C2×#103C22×C15112yes—
290C2×#103C22×C15112yes—
291C2×#102C22×C15112yes—
292C2×#97C22×C15111yescharacteristic
293#400—21no—
294#400—21no—
295#391—21no—
296#391C22×C15112yes—
297#391C22×C15112yes—
298#382—21no—
299C4×C4⋊C4C22×C15111yescharacteristic
300#340C22×C15112yes—
301#340C22×C15112yes—
302#340C22×C15112yes—
303#336C22×C15112yes—
304#336C22×C15112yes—
305C22×Q8—21no—
306C22×Q8D4×C15111yescharacteristic
307C22×Q8C23×C15112yes—
308C22×D4C23×C15111yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—21no—
312C2×SD16—28no—
313C2×SD16—24no—
314C22×C8C23×C15112yes—
315C22×C8C23×C15112yes—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320#125—22no—
321#125—22no—
322#125—22no—
323#125D4×C15114yes—
324C22⋊Q8—28no—
325C22⋊Q8—28no—
326C22⋊Q8—28no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4D4×C15114yes—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4D4×C15111yescharacteristic
344C2×C4⋊C4D4×C15111yescharacteristic
345C2×C4⋊C4D4×C15111yescharacteristic
346C2×C4⋊C4C23×C15112yes—
347C2×C4⋊C4C23×C15111yescharacteristic
348C2×C4⋊C4C23×C15111yescharacteristic
349C2×C4⋊C4C23×C15111yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C42—21no—
354C2×C42C23×C15111yescharacteristic
355C2×C42C23×C15111yescharacteristic
356C2×C42C23×C15111yescharacteristic
357C4⋊C8—22no—
358#103—24no—
359#103—24no—
360#103—24no—
361#102—24no—
362#97—22no—
363#95—21no—
364#95—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368C24—21no—
369C2×Q8—24no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—24no—
375C2×Q8—24no—
376C2×Q8—41no—
377C2×Q8—82no—
378C2×D4—21no—
379C2×D4—22no—
380C2×D4C2×D4×C15112yes—
381C2×D4#41×C15114yes—
382C22×C4—24no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—82no—
393C22×C4—82no—
394C22×C4C2×D4×C15111yescharacteristic
395C22×C4C2×D4×C15111yescharacteristic
396C22×C4C2×D4×C15111yescharacteristic
397C22×C4C2×D4×C15111yescharacteristic
398C22×C4C2×D4×C15111yescharacteristic
399C22×C4C2×D4×C15111yescharacteristic
400C22×C4C24×C15111yescharacteristic
401SD16—48no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—24no—
406C2×C8—22no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—22no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—42no—
421C4⋊C4—42no—
422C4⋊C4C2×D4×C15112yes—
423C4⋊C4C2×D4×C15112yes—
424C4⋊C4C2×D4×C15112yes—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—21no—
432C42—42no—
433C42C2×D4×C15112yes—
434C42C2×D4×C15112yes—
435C23—22no—
436C23—24no—
437C23—41no—
438C23—41no—
439C23—42no—
440C23C22×D4×C15111yescharacteristic
441Q8—44no—
442Q8—42no—
443Q8—42no—
444Q8—44no—
445Q8—84no—
446D4—22no—
447D4—24no—
448D4#124×C15114yes—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—48no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—84no—
475C2×C4—84no—
476C2×C4#120×C15112yes—
477C2×C4#120×C15112yes—
478C2×C4#137×C15112yes—
479C2×C4C22×D4×C15111yescharacteristic
480C2×C4C22×D4×C15111yescharacteristic
481C2×C4C2×#41×C15112yes—
482C2×C42−1+4×C15112yes—
483C8—42no—
484C8—42no—
485C22—24no—
486C22—44no—
487C22—44no—
488C22—42no—
489C22—42no—
490C22C2×#120×C15111yescharacteristic
491C22#548×C15112yes—
492C22C2×#137×C15111yescharacteristic
493C22#575×C15111yescharacteristic
494C22#577×C15112yes—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—42no—
500C4—41no—
501C4—41no—
502C4—42no—
503C4—42no—
504C4—82no—
505C4—82no—
506C4C2×#124×C15111yescharacteristic
507C4#536×C15111yescharacteristic
508C4#548×C15112yes—
509C2—44no—
510C2#2436×C15111yescharacteristic
511C2#3007×C15111yescharacteristic
512C2#3009×C15111yescharacteristic
513C2#3372×C15112yes—
514C2#3376×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
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
2. C2×#491×C151C2semidirect
4. #2568×C151C2semidirect
5. #2026×C151C2semidirect
6. #2024×C151C2semidirect
7. #1989×C151C2semidirect
8. #1985×C151C2semidirect
257. #25945C151direct (N × H)
258. C151#25945direct (N × H)
260. C2×#491C2×C151semidirect
262. #2568C2×C151semidirect
263. #2026C2×C151semidirect
264. #2024C2×C151semidirect
265. #1989C2×C151semidirect
266. #1985C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#491×C1512
C2×#461×C1512
#2568×C1512
#2026×C1512
#2024×C1512
#1989×C1512
#1985×C1512
#1877×C1512
#1762×C1512
#25945151