Finite Group Databasebeta

← C151×#24108 #50329033

Subgroups — C151×#24108 #50329033

Order 38656.

1062 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C151C211yesmaximal, characteristic
2C2×#483×C151C211yesmaximal, characteristic, complemented
3C2×#428×C151C211yesmaximal, characteristic, complemented
4#2487×C151C211yesmaximal, characteristic
5#2058×C151C212yesmaximal, complemented
6#2035×C151C212yesmaximal, complemented
7#1894×C151C211yesmaximal, characteristic, complemented
8#1870×C151C211yesmaximal, characteristic
9#1863×C151C212yesmaximal, complemented
10#1854×C151C212yesmaximal, complemented
11#1825×C151C211yesmaximal, characteristic, complemented
12C22×M16×C151C2211yescharacteristic
13#556×C151—24no—
14#556×C151—24no—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#126×C151—21no—
17C2×#126×C151—21no—
18C2×#124×C151—21no—
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×C4×Q8×C151—21no—
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×#117×C151C2211yescharacteristic
25C2×#117×C151C2211yescharacteristic
26C22×C4⋊C4×C151C2211yescharacteristic
27#483×C151—24no—
28#428×C151—24no—
29C2×#107×C151C2212yes—
30C2×#106×C151C2212yes—
31C2×#106×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#103×C151C2212yes—
34C2×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2212yes—
36#400×C151—21no—
37#399×C151—21no—
38#389×C151C2212yes—
39#386×C151—21no—
40#385×C151—21no—
41#380×C151C2211yescharacteristic
42#380×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45#340×C151C2212yes—
46#336×C151C2212yes—
47C22×Q8×C151—21no—
48C22×Q8×C151C2311yescharacteristic
49C22×D4×C151D411yescharacteristic
50C23×C4×C151—21no—
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2311yescharacteristic
53C2×M16×C151—22no—
54C2×M16×C151—24no—
55C22×C8×C151C2312yes—
56C22×C8×C151C2312yes—
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151—22no—
59#126×C151—28no—
60#126×C151—28no—
61#124×C151—28no—
62C22⋊Q8×C151—22no—
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151D414yes—
66C4×Q8×C151—28no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×D4×C151—22no—
70C4×D4×C151—22no—
71#117×C151—22no—
72#117×C151—22no—
73#117×C151—22no—
74#117×C151D414yes—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151D411yescharacteristic
84C2×C4⋊C4×C151C2312yes—
85C2×C4⋊C4×C151C2312yes—
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C4⋊C4×C151C2311yescharacteristic
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—22no—
95C2×C22⋊C4×C151D411yescharacteristic
96C2×C22⋊C4×C151D411yescharacteristic
97C2×C42×C151—21no—
98C2×C42×C151—21no—
99C2×C42×C151—21no—
100C2×C42×C151C2311yescharacteristic
101#107×C151—24no—
102#106×C151—24no—
103#106×C151—24no—
104#103×C151—24no—
105#103×C151—24no—
106C22⋊C8×C151—22no—
107C22⋊C8×C151—24no—
108#95×C151—22no—
109#95×C151—21no—
110#95×C151—22no—
111C24×C151C2×D411yescharacteristic
112C24×C151C2×D411yescharacteristic
113C2×Q8×C151—24no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—42no—
118C2×Q8×C151—42no—
119C2×Q8×C151C2×D412yes—
120C2×D4×C151—22no—
121C2×D4×C151—22no—
122C2×D4×C151—41no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—42no—
136C22×C4×C151—82no—
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D412yes—
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2411yescharacteristic
144M16×C151—28no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C2×C8×C151#4114yes—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—42no—
164C4⋊C4×C151—82no—
165C4⋊C4×C151C2×D412yes—
166C4⋊C4×C151C2×D412yes—
167C4⋊C4×C151C2×D412yes—
168C22⋊C4×C151—24no—
169C22⋊C4×C151—24no—
170C22⋊C4×C151—24no—
171C22⋊C4×C151—24no—
172C22⋊C4×C151—22no—
173C22⋊C4×C151—22no—
174C22⋊C4×C151—42no—
175C22⋊C4×C151—82no—
176C42×C151—24no—
177C42×C151—24no—
178C42×C151—24no—
179C42×C151—21no—
180C42×C151—21no—
181C23×C151—22no—
182C23×C151—21no—
183C23×C151—21no—
184C23×C151—22no—
185C23×C151—21no—
186C23×C151—22no—
187C23×C151—21no—
188C23×C151—21no—
189C23×C151—22no—
190C23×C151#12012yes—
191C23×C151C22×D411yescharacteristic
192Q8×C151—24no—
193Q8×C151—48no—
194Q8×C151—41no—
195Q8×C151—41no—
196D4×C151—44no—
197C2×C4×C151—21no—
198C2×C4×C151—22no—
199C2×C4×C151—21no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—24no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—42no—
212C2×C4×C151—41no—
213C2×C4×C151—41no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—42no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—84no—
227C2×C4×C151#12012yes—
228C2×C4×C151#13712yes—
229C2×C4×C151C22×D411yescharacteristic
230C2×C4×C151C22×D411yescharacteristic
231C2×C4×C151C2×#4112yes—
232C2×C4×C1512−1+412yes—
233C8×C151—24no—
234C8×C151—42no—
235C22×C151—22no—
236C22×C151—22no—
237C22×C151—22no—
238C22×C151—42no—
239C22×C151—42no—
240C22×C151—42no—
241C22×C151—42no—
242C22×C151—41no—
243C22×C151—41no—
244C22×C151—41no—
245C22×C151C2×#12011yescharacteristic
246C22×C151#54712yes—
247C22×C151C2×#13711yescharacteristic
248C22×C151#57511yescharacteristic
249C22×C151#57712yes—
250C4×C151—22no—
251C4×C151—22no—
252C4×C151—41no—
253C4×C151—42no—
254C4×C151—42no—
255C4×C151—42no—
256C4×C151—41no—
257C4×C151—42no—
258C4×C151—82no—
259C4×C151—82no—
260C4×C151#52511yescharacteristic
261C4×C151#53611yescharacteristic
262C4×C151#54712yes—
263C2×C151—42no—
264C2×C151—81no—
265C2×C151#240611yescharacteristic
266C2×C151#300711yescharacteristic
267C2×C151#301011yescharacteristic
268C2×C151#335012yes—
269C2×C151#335612yes—
270#24108C15111yesmaximal, characteristic, direct product factor, Sylow
271C151#2410811yescharacteristic, direct product factor, Sylow
272C2×#556C2×C15111yescharacteristic
273C2×#483C2×C15111yescharacteristic, complemented
274C2×#428C2×C15111yescharacteristic, complemented
275#2487C2×C15111yescharacteristic
276#2058C2×C15112yescomplemented
277#2035C2×C15112yescomplemented
278#1894C2×C15111yescharacteristic, complemented
279#1870C2×C15111yescharacteristic
280#1863C2×C15112yescomplemented
281#1854C2×C15112yescomplemented
282#1825C2×C15111yescharacteristic, complemented
283C22×M16C22×C15111yescharacteristic
284#556—24no—
285#556—24no—
286C2×C4⋊Q8C22×C15111yescharacteristic
287C2×#126—21no—
288C2×#126—21no—
289C2×#124—21no—
290C2×C22⋊Q8C22×C15111yescharacteristic
291C2×C22⋊Q8C22×C15111yescharacteristic
292C2×C4×Q8—21no—
293C2×C4×Q8C22×C15111yescharacteristic
294C2×C4×D4C22×C15111yescharacteristic
295C2×#117C22×C15111yescharacteristic
296C2×#117C22×C15111yescharacteristic
297C22×C4⋊C4C22×C15111yescharacteristic
298#483—24no—
299#428—24no—
300C2×#107C22×C15112yes—
301C2×#106C22×C15112yes—
302C2×#106C22×C15112yes—
303C2×#103C22×C15112yes—
304C2×#103C22×C15112yes—
305C2×C22⋊C8C22×C15111yescharacteristic
306C2×C22⋊C8C22×C15112yes—
307#400—21no—
308#399—21no—
309#389C22×C15112yes—
310#386—21no—
311#385—21no—
312#380C22×C15111yescharacteristic
313#380C22×C15112yes—
314#340C22×C15112yes—
315#340C22×C15112yes—
316#340C22×C15112yes—
317#336C22×C15112yes—
318C22×Q8—21no—
319C22×Q8C23×C15111yescharacteristic
320C22×D4D4×C15111yescharacteristic
321C23×C4—21no—
322C23×C4C23×C15111yescharacteristic
323C23×C4C23×C15111yescharacteristic
324C2×M16—22no—
325C2×M16—24no—
326C22×C8C23×C15112yes—
327C22×C8C23×C15112yes—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330#126—28no—
331#126—28no—
332#124—28no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8D4×C15114yes—
337C4×Q8—28no—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×D4—22no—
341C4×D4—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117D4×C15114yes—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4D4×C15111yescharacteristic
355C2×C4⋊C4C23×C15112yes—
356C2×C4⋊C4C23×C15112yes—
357C2×C4⋊C4C23×C15111yescharacteristic
358C2×C4⋊C4C23×C15111yescharacteristic
359C2×C4⋊C4C23×C15111yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4D4×C15111yescharacteristic
367C2×C22⋊C4D4×C15111yescharacteristic
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42C23×C15111yescharacteristic
372#107—24no—
373#106—24no—
374#106—24no—
375#103—24no—
376#103—24no—
377C22⋊C8—22no—
378C22⋊C8—24no—
379#95—22no—
380#95—21no—
381#95—22no—
382C24C2×D4×C15111yescharacteristic
383C24C2×D4×C15111yescharacteristic
384C2×Q8—24no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—42no—
389C2×Q8—42no—
390C2×Q8C2×D4×C15112yes—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—41no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—42no—
407C22×C4—82no—
408C22×C4C2×D4×C15111yescharacteristic
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C2×D4×C15111yescharacteristic
411C22×C4C2×D4×C15112yes—
412C22×C4C2×D4×C15112yes—
413C22×C4C2×D4×C15111yescharacteristic
414C22×C4C24×C15111yescharacteristic
415M16—28no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8#41×C15114yes—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—42no—
435C4⋊C4—82no—
436C4⋊C4C2×D4×C15112yes—
437C4⋊C4C2×D4×C15112yes—
438C4⋊C4C2×D4×C15112yes—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—42no—
446C22⋊C4—82no—
447C42—24no—
448C42—24no—
449C42—24no—
450C42—21no—
451C42—21no—
452C23—22no—
453C23—21no—
454C23—21no—
455C23—22no—
456C23—21no—
457C23—22no—
458C23—21no—
459C23—21no—
460C23—22no—
461C23#120×C15112yes—
462C23C22×D4×C15111yescharacteristic
463Q8—24no—
464Q8—48no—
465Q8—41no—
466Q8—41no—
467D4—44no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—84no—
498C2×C4#120×C15112yes—
499C2×C4#137×C15112yes—
500C2×C4C22×D4×C15111yescharacteristic
501C2×C4C22×D4×C15111yescharacteristic
502C2×C4C2×#41×C15112yes—
503C2×C42−1+4×C15112yes—
504C8—24no—
505C8—42no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—42no—
516C22C2×#120×C15111yescharacteristic
517C22#547×C15112yes—
518C22C2×#137×C15111yescharacteristic
519C22#575×C15111yescharacteristic
520C22#577×C15112yes—
521C4—22no—
522C4—22no—
523C4—41no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—41no—
528C4—42no—
529C4—82no—
530C4—82no—
531C4#525×C15111yescharacteristic
532C4#536×C15111yescharacteristic
533C4#547×C15112yes—
534C2—42no—
535C2—81no—
536C2#2406×C15111yescharacteristic
537C2#3007×C15111yescharacteristic
538C2#3010×C15111yescharacteristic
539C2#3350×C15112yes—
540C2#3356×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#483×C151C2semidirect
3. C2×#428×C151C2semidirect
5. #2058×C151C2semidirect
6. #2035×C151C2semidirect
7. #1894×C151C2semidirect
9. #1863×C151C2semidirect
10. #1854×C151C2semidirect
11. #1825×C151C2semidirect
270. #24108C151direct (N × H)
271. C151#24108direct (N × H)
273. C2×#483C2×C151semidirect
274. C2×#428C2×C151semidirect
276. #2058C2×C151semidirect
277. #2035C2×C151semidirect
278. #1894C2×C151semidirect
280. #1863C2×C151semidirect
281. #1854C2×C151semidirect
282. #1825C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#556×C1512
C2×#483×C1512
C2×#428×C1512
#2487×C1512
#2058×C1512
#2035×C1512
#1894×C1512
#1870×C1512
#1863×C1512
#1854×C1512
#1825×C1512
#24108151