Finite Group Databasebeta

← C151×#24065 #50328990

Subgroups — C151×#24065 #50328990

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×#533×C151C211yesmaximal, characteristic
2C2×#485×C151C212yesmaximal
3#2296×C151C211yesmaximal, characteristic
4#2058×C151C211yesmaximal, characteristic, complemented
5#2057×C151C211yesmaximal, characteristic, complemented
6#2043×C151C211yesmaximal, characteristic, complemented
7#2043×C151C211yesmaximal, characteristic, complemented
8#1873×C151C212yesmaximal
9#1865×C151C212yesmaximal, complemented
10#1863×C151C212yesmaximal, complemented
11#1817×C151C211yesmaximal, characteristic
12#533×C151—28no—
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×#125×C151—21no—
16C2×C22⋊Q8×C151—21no—
17C2×C22⋊Q8×C151C2212yes—
18C2×C4×Q8×C151—21no—
19C2×C4×Q8×C151C2212yes—
20C2×#117×C151—21no—
21C2×#117×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23C22×C42×C151C2211yescharacteristic
24#485×C151—28no—
25C2×#107×C151C2212yes—
26C2×#106×C151C2212yes—
27C2×#103×C151C2212yes—
28C2×#103×C151C2212yes—
29C2×#103×C151C2212yes—
30C2×#103×C151C2212yes—
31C2×C22⋊C8×C151C2212yes—
32#389×C151C2211yescharacteristic
33#389×C151C2211yescharacteristic
34#389×C151C2211yescharacteristic
35#389×C151C2211yescharacteristic
36#385×C151—21no—
37#385×C151—21no—
38C4×C4⋊C4×C151—21no—
39C4×C4⋊C4×C151—21no—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43#336×C151C2211yescharacteristic
44#336×C151C2211yescharacteristic
45C22×Q8×C151—21no—
46C22×Q8×C151C2312yes—
47C23×C4×C151D411yescharacteristic
48C23×C4×C151D411yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C22×C8×C151C2312yes—
51C22×C8×C151C2312yes—
52C4⋊Q8×C151—24no—
53C4⋊Q8×C151—24no—
54#125×C151—28no—
55C22⋊Q8×C151—28no—
56C22⋊Q8×C151—24no—
57C22⋊Q8×C151D418yes—
58C4×Q8×C151—28no—
59C4×Q8×C151—24no—
60C4×Q8×C151—24no—
61#117×C151—28no—
62#117×C151—22no—
63#117×C151—22no—
64#117×C151—24no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151—22no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151C2311yescharacteristic
75C2×C4⋊C4×C151C2311yescharacteristic
76C2×C4⋊C4×C151C2312yes—
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C4⋊C4×C151C2311yescharacteristic
79C2×C22⋊C4×C151—21no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—21no—
82C2×C42×C151—21no—
83C2×C42×C151—24no—
84C2×C42×C151—22no—
85C2×C42×C151—21no—
86C2×C42×C151D411yescharacteristic
87C2×C42×C151D411yescharacteristic
88C2×C42×C151C2311yescharacteristic
89C2×C42×C151C2311yescharacteristic
90#107×C151—24no—
91#106×C151—24no—
92#103×C151—24no—
93#103×C151—24no—
94#103×C151—24no—
95#103×C151—24no—
96C22⋊C8×C151—24no—
97#95×C151—21no—
98#95×C151—21no—
99#95×C151—21no—
100#95×C151—21no—
101C24×C151C2×D411yescharacteristic
102C2×Q8×C151—24no—
103C2×Q8×C151—22no—
104C2×Q8×C151—22no—
105C2×Q8×C151—22no—
106C2×Q8×C151—22no—
107C2×Q8×C151—22no—
108C2×Q8×C151—42no—
109C2×Q8×C151—42no—
110C2×Q8×C151C2×D414yes—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—21no—
115C22×C4×C151—21no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—21no—
119C22×C4×C151—21no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—41no—
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D414yes—
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151C2411yescharacteristic
133C2×C8×C151—22no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C4⋊C4×C151—24no—
140C4⋊C4×C151—24no—
141C4⋊C4×C151—28no—
142C4⋊C4×C151—24no—
143C4⋊C4×C151—28no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—42no—
150C4⋊C4×C151—42no—
151C4⋊C4×C151—42no—
152C4⋊C4×C151—42no—
153C4⋊C4×C151C2×D414yes—
154C4⋊C4×C151#4112yes—
155C4⋊C4×C151#4112yes—
156C22⋊C4×C151—24no—
157C22⋊C4×C151—28no—
158C22⋊C4×C151—42no—
159C42×C151—24no—
160C42×C151—28no—
161C42×C151—22no—
162C42×C151—22no—
163C42×C151—22no—
164C42×C151—22no—
165C42×C151—42no—
166C23×C151—21no—
167C23×C151—21no—
168C23×C151—21no—
169C23×C151—21no—
170C23×C151—21no—
171C23×C151—21no—
172C23×C151#12012yes—
173C23×C151C22×D411yescharacteristic
174Q8×C151—24no—
175Q8×C151—24no—
176Q8×C151—48no—
177Q8×C151—42no—
178Q8×C151—42no—
179C2×C4×C151—28no—
180C2×C4×C151—21no—
181C2×C4×C151—21no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—21no—
185C2×C4×C151—21no—
186C2×C4×C151—21no—
187C2×C4×C151—21no—
188C2×C4×C151—24no—
189C2×C4×C151—24no—
190C2×C4×C151—24no—
191C2×C4×C151—24no—
192C2×C4×C151—21no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—21no—
196C2×C4×C151—21no—
197C2×C4×C151—44no—
198C2×C4×C151—42no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—42no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—41no—
211C2×C4×C151—41no—
212C2×C4×C151#12012yes—
213C2×C4×C151#13512yes—
214C2×C4×C151#13712yes—
215C2×C4×C151#13712yes—
216C2×C4×C151C22×D412yes—
217C2×C4×C151C2×#4111yescharacteristic
218C2×C4×C151C2×#4111yescharacteristic
219C2×C4×C1512−1+412yes—
220C8×C151—42no—
221C8×C151—42no—
222C22×C151—22no—
223C22×C151—22no—
224C22×C151—22no—
225C22×C151—41no—
226C22×C151—41no—
227C22×C151—41no—
228C22×C151—41no—
229C22×C151C2×#12011yescharacteristic
230C22×C151#52511yescharacteristic
231C22×C151#53611yescharacteristic
232C22×C151C2×#13511yescharacteristic
233C22×C151C2×#13711yescharacteristic
234C22×C151C2×#13711yescharacteristic
235C22×C151#57511yescharacteristic
236C4×C151—22no—
237C4×C151—22no—
238C4×C151—22no—
239C4×C151—22no—
240C4×C151—42no—
241C4×C151—42no—
242C4×C151—44no—
243C4×C151—41no—
244C4×C151—44no—
245C4×C151—81no—
246C4×C151—81no—
247C4×C151#54712yes—
248C4×C151#54712yes—
249C2×C151—42no—
250C2×C151#240611yescharacteristic
251C2×C151#300211yescharacteristic
252C2×C151#300411yescharacteristic
253C2×C151#310711yescharacteristic
254C2×C151#311611yescharacteristic
255C2×C151#323111yescharacteristic
256C2×C151#323711yescharacteristic
257#24065C15111yesmaximal, characteristic, direct product factor, Sylow
258C151#2406511yescharacteristic, direct product factor, Sylow
259C2×#533C2×C15111yescharacteristic
260C2×#485C2×C15112yes—
261#2296C2×C15111yescharacteristic
262#2058C2×C15111yescharacteristic, complemented
263#2057C2×C15111yescharacteristic, complemented
264#2043C2×C15111yescharacteristic, complemented
265#2043C2×C15111yescharacteristic, complemented
266#1873C2×C15112yes—
267#1865C2×C15112yescomplemented
268#1863C2×C15112yescomplemented
269#1817C2×C15111yescharacteristic
270#533—28no—
271C2×C4⋊Q8C22×C15111yescharacteristic
272C2×C4⋊Q8C22×C15111yescharacteristic
273C2×#125—21no—
274C2×C22⋊Q8—21no—
275C2×C22⋊Q8C22×C15112yes—
276C2×C4×Q8—21no—
277C2×C4×Q8C22×C15112yes—
278C2×#117—21no—
279C2×#117C22×C15111yescharacteristic
280C2×#117C22×C15111yescharacteristic
281C22×C42C22×C15111yescharacteristic
282#485—28no—
283C2×#107C22×C15112yes—
284C2×#106C22×C15112yes—
285C2×#103C22×C15112yes—
286C2×#103C22×C15112yes—
287C2×#103C22×C15112yes—
288C2×#103C22×C15112yes—
289C2×C22⋊C8C22×C15112yes—
290#389C22×C15111yescharacteristic
291#389C22×C15111yescharacteristic
292#389C22×C15111yescharacteristic
293#389C22×C15111yescharacteristic
294#385—21no—
295#385—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298#340C22×C15112yes—
299#340C22×C15112yes—
300#336C22×C15111yescharacteristic
301#336C22×C15111yescharacteristic
302#336C22×C15112yes—
303C22×Q8—21no—
304C22×Q8C23×C15112yes—
305C23×C4D4×C15111yescharacteristic
306C23×C4D4×C15111yescharacteristic
307C23×C4C23×C15111yescharacteristic
308C22×C8C23×C15112yes—
309C22×C8C23×C15112yes—
310C4⋊Q8—24no—
311C4⋊Q8—24no—
312#125—28no—
313C22⋊Q8—28no—
314C22⋊Q8—24no—
315C22⋊Q8D4×C15118yes—
316C4×Q8—28no—
317C4×Q8—24no—
318C4×Q8—24no—
319#117—28no—
320#117—22no—
321#117—22no—
322#117—24no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4C23×C15111yescharacteristic
333C2×C4⋊C4C23×C15111yescharacteristic
334C2×C4⋊C4C23×C15111yescharacteristic
335C2×C4⋊C4C23×C15111yescharacteristic
336C2×C4⋊C4C23×C15112yes—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C42—22no—
341C2×C42—21no—
342C2×C42—24no—
343C2×C42—21no—
344C2×C42D4×C15111yescharacteristic
345C2×C42D4×C15111yescharacteristic
346C2×C42C23×C15111yescharacteristic
347C2×C42C23×C15111yescharacteristic
348#107—24no—
349#106—24no—
350#103—24no—
351#103—24no—
352#103—24no—
353#103—24no—
354C22⋊C8—24no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359C24C2×D4×C15111yescharacteristic
360C2×Q8—24no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8C2×D4×C15114yes—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—41no—
384C22×C4C2×D4×C15111yescharacteristic
385C22×C4C2×D4×C15111yescharacteristic
386C22×C4C2×D4×C15114yes—
387C22×C4C2×D4×C15111yescharacteristic
388C22×C4C2×D4×C15111yescharacteristic
389C22×C4C2×D4×C15111yescharacteristic
390C22×C4C24×C15111yescharacteristic
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—28no—
400C4⋊C4—24no—
401C4⋊C4—28no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4C2×D4×C15114yes—
412C4⋊C4#41×C15112yes—
413C4⋊C4#41×C15112yes—
414C22⋊C4—24no—
415C22⋊C4—28no—
416C22⋊C4—42no—
417C42—28no—
418C42—24no—
419C42—22no—
420C42—22no—
421C42—22no—
422C42—22no—
423C42—42no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23#120×C15112yes—
431C23C22×D4×C15111yescharacteristic
432Q8—24no—
433Q8—24no—
434Q8—48no—
435Q8—42no—
436Q8—42no—
437C2×C4—28no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—44no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4#120×C15112yes—
471C2×C4#135×C15112yes—
472C2×C4#137×C15112yes—
473C2×C4#137×C15112yes—
474C2×C4C22×D4×C15112yes—
475C2×C4C2×#41×C15111yescharacteristic
476C2×C4C2×#41×C15111yescharacteristic
477C2×C42−1+4×C15112yes—
478C8—42no—
479C8—42no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22C2×#120×C15111yescharacteristic
488C22#525×C15111yescharacteristic
489C22#536×C15111yescharacteristic
490C22C2×#135×C15111yescharacteristic
491C22C2×#137×C15111yescharacteristic
492C22C2×#137×C15111yescharacteristic
493C22#575×C15111yescharacteristic
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—42no—
499C4—42no—
500C4—44no—
501C4—41no—
502C4—44no—
503C4—81no—
504C4—81no—
505C4#547×C15112yes—
506C4#547×C15112yes—
507C2—42no—
508C2#2406×C15111yescharacteristic
509C2#3002×C15111yescharacteristic
510C2#3004×C15111yescharacteristic
511C2#3107×C15111yescharacteristic
512C2#3116×C15111yescharacteristic
513C2#3231×C15111yescharacteristic
514C2#3237×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #2058×C151C2semidirect
5. #2057×C151C2semidirect
6. #2043×C151C2semidirect
7. #2043×C151C2semidirect
9. #1865×C151C2semidirect
10. #1863×C151C2semidirect
257. #24065C151direct (N × H)
258. C151#24065direct (N × H)
262. #2058C2×C151semidirect
263. #2057C2×C151semidirect
264. #2043C2×C151semidirect
265. #2043C2×C151semidirect
267. #1865C2×C151semidirect
268. #1863C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#533×C1512
C2×#485×C1512
#2296×C1512
#2058×C1512
#2057×C1512
#2043×C1512
#1873×C1512
#1865×C1512
#1863×C1512
#1817×C1512
#24065151