Finite Group Databasebeta

← C151×#24353 #50329278

Subgroups — C151×#24353 #50329278

Order 38656.

1078 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C151C211yesmaximal, characteristic
2#2627×C151C212yesmaximal, complemented
3#2322×C151C211yesmaximal, characteristic
4#2062×C151C212yesmaximal, complemented
5#2030×C151C212yesmaximal, complemented
6#1996×C151C212yesmaximal, complemented
7#1890×C151C212yesmaximal
8#1867×C151C212yesmaximal
9#1799×C151C211yesmaximal, characteristic
10#554×C151—24no—
11#554×C151—22no—
12D4×Q8×C151—22no—
13#544×C151—21no—
14#543×C151—21no—
15#543×C151C2212yes—
16#533×C151—21no—
17C2×#123×C151C2211yescharacteristic
18C2×C22⋊Q8×C151—21no—
19C2×C22⋊Q8×C151C2212yes—
20#518×C151C2212yes—
21C2×C4×D4×C151C2211yescharacteristic
22C22×C4⋊C4×C151C2211yescharacteristic
23C2×#99×C151C2212yes—
24#400×C151—22no—
25#398×C151—24no—
26#395×C151—22no—
27#389×C151—21no—
28#388×C151—21no—
29#387×C151—21no—
30#386×C151C2211yescharacteristic
31#385×C151—21no—
32#385×C151C2214yes—
33#385×C151C2211yescharacteristic
34#381×C151C2214yes—
35#381×C151C2211yescharacteristic
36#380×C151C2212yes—
37C4×C22⋊C4×C151C2211yescharacteristic
38#342×C151C2214yes—
39#342×C151C2214yes—
40#342×C151C2212yes—
41C22×Q8×C151—21no—
42C22×Q8×C151D412yes—
43C22×D4×C151C2311yescharacteristic
44C23×C4×C151D411yescharacteristic
45C23×C4×C151C2311yescharacteristic
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2311yescharacteristic
48C4⋊Q8×C151—21no—
49C4⋊Q8×C151—21no—
50C4⋊Q8×C151—24no—
51#125×C151—22no—
52#125×C151—24no—
53#123×C151—22no—
54#123×C151Q814yescomplemented
55C22⋊Q8×C151—22no—
56C22⋊Q8×C151—22no—
57C22⋊Q8×C151—24no—
58C22⋊Q8×C151—24no—
59C22⋊Q8×C151—22no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151—22no—
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151—24no—
66C22⋊Q8×C151—24no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×D4×C151—22no—
70C4×D4×C151—22no—
71C4×D4×C151—24no—
72C4×D4×C151—24no—
73#117×C151—22no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—22no—
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—22no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—24no—
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151D414yes—
86C2×C4⋊C4×C151D412yes—
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151D411yescharacteristic
91C2×C22⋊C4×C151C2311yescharacteristic
92C2×C22⋊C4×C151C2314yes—
93C2×C22⋊C4×C151C2311yescharacteristic
94C2×C22⋊C4×C151C2314yes—
95C2×C22⋊C4×C151C2311yescharacteristic
96C2×C42×C151—21no—
97C2×C42×C151D411yescharacteristic
98#99×C151—24no—
99#95×C151—21no—
100#95×C151—22no—
101#95×C151—21no—
102#95×C151—21no—
103#95×C151—24no—
104#95×C151—24no—
105#95×C151—21no—
106#95×C151—24no—
107#95×C151—21no—
108C24×C151C2×D411yescharacteristic
109C24×C151C2411yescharacteristic
110C2×Q8×C151—22no—
111C2×Q8×C151—22no—
112C2×Q8×C151—22no—
113C2×Q8×C151—22no—
114C2×Q8×C151—82no—
115C2×Q8×C151—82no—
116C2×D4×C151—22no—
117C2×D4×C151—22no—
118C2×D4×C151C2×Q812yes—
119C2×D4×C151#4112yes—
120C22×C4×C151—22no—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—24no—
131C22×C4×C151—21no—
132C22×C4×C151—22no—
133C22×C4×C151—81no—
134C22×C4×C151—81no—
135C22×C4×C151—81no—
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D414yes—
139C22×C4×C151C2×D414yes—
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D412yes—
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D412yes—
145C22×C4×C151C2×Q812yescomplemented
146C4⋊C4×C151—22no—
147C4⋊C4×C151—24no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—41no—
159C4⋊C4×C151—42no—
160C4⋊C4×C151—41no—
161C4⋊C4×C151—82no—
162C4⋊C4×C151—81no—
163C4⋊C4×C151—84no—
164C22⋊C4×C151—24no—
165C22⋊C4×C151—24no—
166C22⋊C4×C151—24no—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—22no—
169C22⋊C4×C151—21no—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—24no—
172C22⋊C4×C151—22no—
173C22⋊C4×C151—24no—
174C22⋊C4×C151—81no—
175C22⋊C4×C151C2×Q812yescomplemented
176C42×C151—24no—
177C42×C151—21no—
178C42×C151—21no—
179C42×C151—81no—
180C23×C151—21no—
181C23×C151—21no—
182C23×C151—41no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151C22⋊Q812yes—
187C23×C151C22×D411yescharacteristic
188C23×C151C22×D412yes—
189C23×C151C22×Q811yescharacteristic
190C23×C151C2×#4111yescharacteristic
191C23×C1512−1+412yes—
192Q8×C151—44no—
193Q8×C151—82no—
194Q8×C151—82no—
195Q8×C151—82no—
196D4×C151—24no—
197D4×C151—24no—
198C2×C4×C151—21no—
199C2×C4×C151—21no—
200C2×C4×C151—24no—
201C2×C4×C151—21no—
202C2×C4×C151—21no—
203C2×C4×C151—24no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—24no—
207C2×C4×C151—42no—
208C2×C4×C151—41no—
209C2×C4×C151—42no—
210C2×C4×C151—41no—
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—44no—
218C2×C4×C151—41no—
219C2×C4×C151—44no—
220C2×C4×C151—41no—
221C2×C4×C151—41no—
222C2×C4×C151—41no—
223C2×C4×C151—44no—
224C2×C4×C151—44no—
225C2×C4×C151—41no—
226C2×C4×C151—44no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—44no—
231C2×C4×C151—81no—
232C2×C4×C151—82no—
233C2×C4×C151—82no—
234C2×C4×C151#12011yescharacteristic
235C2×C4×C151#12012yes—
236C2×C4×C151#12011yescharacteristic
237C2×C4×C151C22⋊Q812yes—
238C22×C151—22no—
239C22×C151—21no—
240C22×C151—22no—
241C22×C151—21no—
242C22×C151—22no—
243C22×C151—41no—
244C22×C151—41no—
245C22×C151—42no—
246C22×C151—42no—
247C22×C151—41no—
248C22×C151—41no—
249C22×C151—81no—
250C22×C151C2×#12011yescharacteristic
251C22×C151C2×C22⋊Q811yescharacteristic
252C22×C151#53611yescharacteristic
253C22×C151#54812yes—
254C22×C151D4×Q812yes—
255C4×C151—22no—
256C4×C151—21no—
257C4×C151—21no—
258C4×C151—22no—
259C4×C151—42no—
260C4×C151—42no—
261C4×C151—41no—
262C4×C151—44no—
263C4×C151—44no—
264C4×C151—41no—
265C4×C151—84no—
266C4×C151—81no—
267C4×C151—81no—
268C2×C151—21no—
269C2×C151—22no—
270C2×C151—21no—
271C2×C151—22no—
272C2×C151—42no—
273C2×C151#240911yescharacteristic
274C2×C151#302611yescharacteristic
275C2×C151#302811yescharacteristic
276#24353C15111yesmaximal, characteristic, direct product factor, Sylow
277C151#2435311yescharacteristic, direct product factor, Sylow
278#3501C2×C15111yescharacteristic
279#2627C2×C15112yescomplemented
280#2322C2×C15111yescharacteristic
281#2062C2×C15112yescomplemented
282#2030C2×C15112yescomplemented
283#1996C2×C15112yescomplemented
284#1890C2×C15112yes—
285#1867C2×C15112yes—
286#1799C2×C15111yescharacteristic
287#554—24no—
288#554—22no—
289D4×Q8—22no—
290#544—21no—
291#543—21no—
292#543C22×C15112yes—
293#533—21no—
294C2×#123C22×C15111yescharacteristic
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8C22×C15112yes—
297#518C22×C15112yes—
298C2×C4×D4C22×C15111yescharacteristic
299C22×C4⋊C4C22×C15111yescharacteristic
300C2×#99C22×C15112yes—
301#400—22no—
302#398—24no—
303#395—22no—
304#389—21no—
305#388—21no—
306#387—21no—
307#386C22×C15111yescharacteristic
308#385—21no—
309#385C22×C15111yescharacteristic
310#385C22×C15114yes—
311#381C22×C15111yescharacteristic
312#381C22×C15114yes—
313#380C22×C15112yes—
314C4×C22⋊C4C22×C15111yescharacteristic
315#342C22×C15112yes—
316#342C22×C15114yes—
317#342C22×C15114yes—
318C22×Q8—21no—
319C22×Q8D4×C15112yes—
320C22×D4C23×C15111yescharacteristic
321C23×C4D4×C15111yescharacteristic
322C23×C4C23×C15111yescharacteristic
323C23×C4C23×C15111yescharacteristic
324C23×C4C23×C15111yescharacteristic
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8—24no—
328#125—22no—
329#125—24no—
330#123—22no—
331#123Q8×C15114yescomplemented
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—24no—
349C4×D4—24no—
350#117—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4D4×C15111yescharacteristic
362C2×C4⋊C4D4×C15114yes—
363C2×C4⋊C4D4×C15112yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4D4×C15111yescharacteristic
368C2×C22⋊C4C23×C15111yescharacteristic
369C2×C22⋊C4C23×C15114yes—
370C2×C22⋊C4C23×C15111yescharacteristic
371C2×C22⋊C4C23×C15114yes—
372C2×C22⋊C4C23×C15111yescharacteristic
373C2×C42—21no—
374C2×C42D4×C15111yescharacteristic
375#99—24no—
376#95—21no—
377#95—22no—
378#95—21no—
379#95—21no—
380#95—24no—
381#95—24no—
382#95—21no—
383#95—24no—
384#95—21no—
385C24C2×D4×C15111yescharacteristic
386C24C24×C15111yescharacteristic
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—82no—
392C2×Q8—82no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4C2×Q8×C15112yes—
396C2×D4#41×C15112yes—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—81no—
411C22×C4—81no—
412C22×C4—81no—
413C22×C4C2×D4×C15111yescharacteristic
414C22×C4C2×D4×C15111yescharacteristic
415C22×C4C2×D4×C15114yes—
416C22×C4C2×D4×C15114yes—
417C22×C4C2×D4×C15111yescharacteristic
418C22×C4C2×D4×C15111yescharacteristic
419C22×C4C2×D4×C15112yes—
420C22×C4C2×D4×C15111yescharacteristic
421C22×C4C2×D4×C15112yes—
422C22×C4C2×Q8×C15112yescomplemented
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—24no—
434C4⋊C4—24no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—42no—
438C4⋊C4—82no—
439C4⋊C4—81no—
440C4⋊C4—84no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—22no—
445C22⋊C4—24no—
446C22⋊C4—21no—
447C22⋊C4—22no—
448C22⋊C4—24no—
449C22⋊C4—22no—
450C22⋊C4—24no—
451C22⋊C4—81no—
452C22⋊C4C2×Q8×C15112yescomplemented
453C42—24no—
454C42—21no—
455C42—21no—
456C42—81no—
457C23—21no—
458C23—21no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23C22⋊Q8×C15112yes—
464C23C22×D4×C15111yescharacteristic
465C23C22×D4×C15112yes—
466C23C22×Q8×C15111yescharacteristic
467C23C2×#41×C15111yescharacteristic
468C232−1+4×C15112yes—
469Q8—44no—
470Q8—82no—
471Q8—82no—
472Q8—82no—
473D4—24no—
474D4—24no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—41no—
503C2×C4—44no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—44no—
508C2×C4—81no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4#120×C15111yescharacteristic
512C2×C4#120×C15111yescharacteristic
513C2×C4#120×C15112yes—
514C2×C4C22⋊Q8×C15112yes—
515C22—22no—
516C22—21no—
517C22—22no—
518C22—21no—
519C22—22no—
520C22—41no—
521C22—41no—
522C22—42no—
523C22—42no—
524C22—41no—
525C22—41no—
526C22—81no—
527C22C2×#120×C15111yescharacteristic
528C22C2×C22⋊Q8×C15111yescharacteristic
529C22#536×C15111yescharacteristic
530C22#548×C15112yes—
531C22D4×Q8×C15112yes—
532C4—22no—
533C4—21no—
534C4—21no—
535C4—22no—
536C4—42no—
537C4—42no—
538C4—41no—
539C4—44no—
540C4—44no—
541C4—41no—
542C4—84no—
543C4—81no—
544C4—81no—
545C2—21no—
546C2—22no—
547C2—21no—
548C2—22no—
549C2—42no—
550C2#2409×C15111yescharacteristic
551C2#3026×C15111yescharacteristic
552C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2627×C151C2semidirect
4. #2062×C151C2semidirect
5. #2030×C151C2semidirect
6. #1996×C151C2semidirect
54. #123×C151Q8semidirect
145. C22×C4×C151C2×Q8semidirect
175. C22⋊C4×C151C2×Q8semidirect
276. #24353C151direct (N × H)
277. C151#24353direct (N × H)
279. #2627C2×C151semidirect
281. #2062C2×C151semidirect
282. #2030C2×C151semidirect
283. #1996C2×C151semidirect
331. #123Q8×C151semidirect
422. C22×C4C2×Q8×C151semidirect
452. C22⋊C4C2×Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
#2627×C1512
#2322×C1512
#2062×C1512
#2030×C1512
#1996×C1512
#1890×C1512
#1867×C1512
#1799×C1512
#24353151