Finite Group Databasebeta

← C151×#24074 #50328999

Subgroups — C151×#24074 #50328999

Order 38656.

1066 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#542×C151C211yesmaximal, characteristic
2C2×#481×C151C211yesmaximal, characteristic
3C2×#483×C151C211yesmaximal, characteristic, complemented
4#2317×C151C211yesmaximal, characteristic, complemented
5#2058×C151C212yesmaximal, complemented
6#2042×C151C212yesmaximal, complemented
7#1875×C151C211yesmaximal, characteristic
8#1873×C151C211yesmaximal, characteristic, complemented
9#1865×C151C212yesmaximal, complemented
10#1864×C151C212yesmaximal, complemented
11#1818×C151C211yesmaximal, characteristic, complemented
12#542×C151—24no—
13#542×C151—24no—
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×#126×C151—21no—
16C2×#124×C151—21no—
17C2×#124×C151C2211yescharacteristic
18C2×#123×C151—21no—
19C2×C22⋊Q8×C151—21no—
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×#121×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×#117×C151C2211yescharacteristic
25C2×#117×C151C2211yescharacteristic
26C22×C4⋊C4×C151C2211yescharacteristic
27#483×C151—24no—
28#481×C151—24no—
29C2×#106×C151C2212yes—
30C2×#106×C151C2212yes—
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37#389×C151C2212yes—
38#389×C151C2212yes—
39#385×C151—21no—
40#385×C151—21no—
41#384×C151—21no—
42#382×C151—21no—
43#340×C151C2212yes—
44#340×C151C2212yes—
45#336×C151C2212yes—
46#336×C151C2212yes—
47C22×Q8×C151—21no—
48C22×Q8×C151C2311yescharacteristic
49C22×D4×C151—21no—
50C22×D4×C151C2311yescharacteristic
51C23×C4×C151—21no—
52C23×C4×C151—21no—
53C23×C4×C151C2311yescharacteristic
54C22×C8×C151C2312yes—
55C22×C8×C151C2312yes—
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151—22no—
58#126×C151—28no—
59#124×C151—28no—
60#124×C151—22no—
61#124×C151—22no—
62#123×C151—28no—
63C22⋊Q8×C151—28no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151D414yes—
66#121×C151—22no—
67#121×C151D414yes—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×D4×C151—22no—
71C4×D4×C151—22no—
72#117×C151—22no—
73#117×C151—22no—
74#117×C151—24no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151D411yescharacteristic
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151C2312yes—
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C4⋊C4×C151C2312yes—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151—21no—
95C2×C22⋊C4×C151D411yescharacteristic
96C2×C22⋊C4×C151D411yescharacteristic
97C2×C42×C151—21no—
98C2×C42×C151—21no—
99C2×C42×C151C2311yescharacteristic
100C2×C42×C151C2311yescharacteristic
101#106×C151—24no—
102#106×C151—24no—
103#103×C151—24no—
104#103×C151—24no—
105#102×C151—24no—
106#102×C151—24no—
107C22⋊C8×C151—22no—
108C22⋊C8×C151—22no—
109#95×C151—22no—
110#95×C151—22no—
111C24×C151—21no—
112C24×C151C2×D411yescharacteristic
113C2×Q8×C151—24no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—82no—
118C2×Q8×C151C2×D412yes—
119C2×D4×C151—24no—
120C2×D4×C151—21no—
121C2×D4×C151—22no—
122C2×D4×C151—22no—
123C2×D4×C151—82no—
124C2×D4×C151C2×D412yes—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—24no—
132C22×C4×C151—22no—
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×D412yes—
142C22×C4×C151C2×D412yes—
143C22×C4×C151C2411yescharacteristic
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—42no—
161C4⋊C4×C151—82no—
162C4⋊C4×C151—82no—
163C4⋊C4×C151C2×D412yes—
164C4⋊C4×C151C2×D412yes—
165C4⋊C4×C151#4114yes—
166C22⋊C4×C151—24no—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—24no—
169C22⋊C4×C151—24no—
170C22⋊C4×C151—24no—
171C22⋊C4×C151—22no—
172C22⋊C4×C151—22no—
173C22⋊C4×C151—24no—
174C42×C151—24no—
175C42×C151—24no—
176C42×C151—21no—
177C42×C151—21no—
178C42×C151—21no—
179C42×C151—21no—
180C23×C151—21no—
181C23×C151—21no—
182C23×C151—22no—
183C23×C151—22no—
184C23×C151—22no—
185C23×C151—41no—
186C23×C151—41no—
187C23×C151—42no—
188C23×C151—42no—
189C23×C151#12012yes—
190C23×C151C22×D411yescharacteristic
191Q8×C151—24no—
192Q8×C151—42no—
193Q8×C151—84no—
194D4×C151—24no—
195D4×C151—42no—
196D4×C151—84no—
197C2×C4×C151—21no—
198C2×C4×C151—21no—
199C2×C4×C151—24no—
200C2×C4×C151—24no—
201C2×C4×C151—21no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—21no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—24no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—41no—
214C2×C4×C151—41no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—84no—
223C2×C4×C151—84no—
224C2×C4×C151#12012yes—
225C2×C4×C151C22×D411yescharacteristic
226C2×C4×C151C22×D411yescharacteristic
227C2×C4×C151C2×#4112yes—
228C2×C4×C1512−1+412yes—
229C8×C151—42no—
230C8×C151—42no—
231C22×C151—22no—
232C22×C151—22no—
233C22×C151—22no—
234C22×C151—42no—
235C22×C151—42no—
236C22×C151—42no—
237C22×C151—42no—
238C22×C151—42no—
239C22×C151—82no—
240C22×C151—82no—
241C22×C151C2×#12011yescharacteristic
242C22×C151#52511yescharacteristic
243C22×C151#53611yescharacteristic
244C22×C151#57712yes—
245C22×C151#57712yes—
246C4×C151—22no—
247C4×C151—44no—
248C4×C151—42no—
249C4×C151—41no—
250C4×C151—41no—
251C4×C151—42no—
252C4×C151—42no—
253C4×C151—41no—
254C4×C151—41no—
255C4×C151—82no—
256C4×C151#54712yes—
257C4×C151#54712yes—
258C2×C151—42no—
259C2×C151—82no—
260C2×C151#240611yescharacteristic
261C2×C151#300911yescharacteristic
262C2×C151#301011yescharacteristic
263C2×C151#312512yes—
264C2×C151#324412yes—
265#24074C15111yesmaximal, characteristic, direct product factor, Sylow
266C151#2407411yescharacteristic, direct product factor, Sylow
267C2×#542C2×C15111yescharacteristic
268C2×#481C2×C15111yescharacteristic
269C2×#483C2×C15111yescharacteristic, complemented
270#2317C2×C15111yescharacteristic, complemented
271#2058C2×C15112yescomplemented
272#2042C2×C15112yescomplemented
273#1875C2×C15111yescharacteristic
274#1873C2×C15111yescharacteristic, complemented
275#1865C2×C15112yescomplemented
276#1864C2×C15112yescomplemented
277#1818C2×C15111yescharacteristic, complemented
278#542—24no—
279#542—24no—
280C2×C4⋊Q8C22×C15111yescharacteristic
281C2×#126—21no—
282C2×#124—21no—
283C2×#124C22×C15111yescharacteristic
284C2×#123—21no—
285C2×C22⋊Q8—21no—
286C2×C22⋊Q8C22×C15111yescharacteristic
287C2×#121C22×C15111yescharacteristic
288C2×C4×Q8C22×C15111yescharacteristic
289C2×C4×D4C22×C15111yescharacteristic
290C2×#117C22×C15111yescharacteristic
291C2×#117C22×C15111yescharacteristic
292C22×C4⋊C4C22×C15111yescharacteristic
293#483—24no—
294#481—24no—
295C2×#106C22×C15112yes—
296C2×#106C22×C15112yes—
297C2×#103C22×C15112yes—
298C2×#103C22×C15112yes—
299C2×#102C22×C15112yes—
300C2×#102C22×C15112yes—
301C2×C22⋊C8C22×C15111yescharacteristic
302C2×C22⋊C8C22×C15111yescharacteristic
303#389C22×C15112yes—
304#389C22×C15112yes—
305#385—21no—
306#385—21no—
307#384—21no—
308#382—21no—
309#340C22×C15112yes—
310#340C22×C15112yes—
311#336C22×C15112yes—
312#336C22×C15112yes—
313C22×Q8—21no—
314C22×Q8C23×C15111yescharacteristic
315C22×D4—21no—
316C22×D4C23×C15111yescharacteristic
317C23×C4—21no—
318C23×C4—21no—
319C23×C4C23×C15111yescharacteristic
320C22×C8C23×C15112yes—
321C22×C8C23×C15112yes—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324#126—28no—
325#124—28no—
326#124—22no—
327#124—22no—
328#123—28no—
329C22⋊Q8—28no—
330C22⋊Q8—22no—
331C22⋊Q8D4×C15114yes—
332#121—22no—
333#121D4×C15114yes—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×D4—22no—
337C4×D4—22no—
338#117—22no—
339#117—22no—
340#117—24no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4D4×C15111yescharacteristic
350C2×C4⋊C4D4×C15111yescharacteristic
351C2×C4⋊C4C23×C15112yes—
352C2×C4⋊C4C23×C15112yes—
353C2×C4⋊C4C23×C15111yescharacteristic
354C2×C4⋊C4C23×C15111yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4D4×C15111yescharacteristic
362C2×C22⋊C4D4×C15111yescharacteristic
363C2×C42—21no—
364C2×C42—21no—
365C2×C42C23×C15111yescharacteristic
366C2×C42C23×C15111yescharacteristic
367#106—24no—
368#106—24no—
369#103—24no—
370#103—24no—
371#102—24no—
372#102—24no—
373C22⋊C8—22no—
374C22⋊C8—22no—
375#95—22no—
376#95—22no—
377C24—21no—
378C24C2×D4×C15111yescharacteristic
379C2×Q8—24no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—82no—
384C2×Q8C2×D4×C15112yes—
385C2×D4—24no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—82no—
390C2×D4C2×D4×C15112yes—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—42no—
400C22×C4—82no—
401C22×C4—82no—
402C22×C4C2×D4×C15111yescharacteristic
403C22×C4C2×D4×C15111yescharacteristic
404C22×C4C2×D4×C15111yescharacteristic
405C22×C4C2×D4×C15111yescharacteristic
406C22×C4C2×D4×C15111yescharacteristic
407C22×C4C2×D4×C15112yes—
408C22×C4C2×D4×C15112yes—
409C22×C4C24×C15111yescharacteristic
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—42no—
427C4⋊C4—82no—
428C4⋊C4—82no—
429C4⋊C4C2×D4×C15112yes—
430C4⋊C4C2×D4×C15112yes—
431C4⋊C4#41×C15114yes—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—24no—
440C42—24no—
441C42—24no—
442C42—21no—
443C42—21no—
444C42—21no—
445C42—21no—
446C23—21no—
447C23—21no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23#120×C15112yes—
456C23C22×D4×C15111yescharacteristic
457Q8—24no—
458Q8—42no—
459Q8—84no—
460D4—24no—
461D4—42no—
462D4—84no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4—84no—
490C2×C4#120×C15112yes—
491C2×C4C22×D4×C15111yescharacteristic
492C2×C4C22×D4×C15111yescharacteristic
493C2×C4C2×#41×C15112yes—
494C2×C42−1+4×C15112yes—
495C8—42no—
496C8—42no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—82no—
506C22—82no—
507C22C2×#120×C15111yescharacteristic
508C22#525×C15111yescharacteristic
509C22#536×C15111yescharacteristic
510C22#577×C15112yes—
511C22#577×C15112yes—
512C4—22no—
513C4—44no—
514C4—42no—
515C4—41no—
516C4—41no—
517C4—42no—
518C4—42no—
519C4—41no—
520C4—41no—
521C4—82no—
522C4#547×C15112yes—
523C4#547×C15112yes—
524C2—42no—
525C2—82no—
526C2#2406×C15111yescharacteristic
527C2#3009×C15111yescharacteristic
528C2#3010×C15111yescharacteristic
529C2#3125×C15112yes—
530C2#3244×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#483×C151C2semidirect
4. #2317×C151C2semidirect
5. #2058×C151C2semidirect
6. #2042×C151C2semidirect
8. #1873×C151C2semidirect
9. #1865×C151C2semidirect
10. #1864×C151C2semidirect
11. #1818×C151C2semidirect
265. #24074C151direct (N × H)
266. C151#24074direct (N × H)
269. C2×#483C2×C151semidirect
270. #2317C2×C151semidirect
271. #2058C2×C151semidirect
272. #2042C2×C151semidirect
274. #1873C2×C151semidirect
275. #1865C2×C151semidirect
276. #1864C2×C151semidirect
277. #1818C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#542×C1512
C2×#481×C1512
C2×#483×C1512
#2317×C1512
#2058×C1512
#2042×C1512
#1875×C1512
#1873×C1512
#1865×C1512
#1864×C1512
#1818×C1512
#24074151