Finite Group Databasebeta

← C151×#25000 #50329925

Subgroups — C151×#25000 #50329925

Order 38656.

630 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2581×C151C211yesmaximal, characteristic
2#2355×C151C211yesmaximal, characteristic
3#2101×C151C211yesmaximal, characteristic
4#2099×C151C211yesmaximal, characteristic
5#2074×C151C211yesmaximal, characteristic
6#2072×C151C211yesmaximal, characteristic
7#1984×C151C211yesmaximal, characteristic
8#1949×C151C211yesmaximal, characteristic
9#1928×C151C211yesmaximal, characteristic
10#1927×C151C211yesmaximal, characteristic
11#1921×C151C211yesmaximal, characteristic
12#1919×C151C211yesmaximal, characteristic
13#1835×C151C211yesmaximal, characteristic
14#1805×C151C211yesmaximal, characteristic
15C4×#103×C151C211yesmaximal, characteristic
16C2×C4×Q8×C151C2211yescharacteristic
17C2×C4×Q8×C151C2211yescharacteristic
18C2×#107×C151C2211yescharacteristic
19C2×#106×C151C2211yescharacteristic
20C2×C4⋊C8×C151C2211yescharacteristic
21C2×#103×C151C2211yescharacteristic
22C2×#103×C151C2211yescharacteristic
23C2×#103×C151C2211yescharacteristic
24C2×#103×C151C2211yescharacteristic
25C2×C4×C8×C151C2211yescharacteristic
26#400×C151—21no—
27#395×C151—21no—
28#391×C151—21no—
29#391×C151C2211yescharacteristic
30#391×C151C2211yescharacteristic
31#389×C151C2211yescharacteristic
32#389×C151C2211yescharacteristic
33#387×C151—21no—
34#387×C151—21no—
35#387×C151—21no—
36#387×C151—21no—
37#384×C151C2211yescharacteristic
38#382×C151C2211yescharacteristic
39#382×C151C2211yescharacteristic
40#382×C151C2211yescharacteristic
41C4×C4⋊C4×C151—21no—
42C4×C4⋊C4×C151C2211yescharacteristic
43C4×C4⋊C4×C151C2211yescharacteristic
44C4×C4⋊C4×C151C2211yescharacteristic
45#340×C151C2211yescharacteristic
46#340×C151C2211yescharacteristic
47#340×C151C2211yescharacteristic
48#340×C151C2211yescharacteristic
49#340×C151C2211yescharacteristic
50#340×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#336×C151C2211yescharacteristic
56#336×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59C22×Q8×C151D411yescharacteristic
60C22×Q8×C151C2311yescharacteristic
61C22×C8×C151C2311yescharacteristic
62C22×C8×C151C2311yescharacteristic
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65C4×Q8×C151—22no—
66C4×Q8×C151—22no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C2×C4⋊C4×C151—21no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151D411yescharacteristic
75C2×C4⋊C4×C151D411yescharacteristic
76C2×C4⋊C4×C151D411yescharacteristic
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C4⋊C4×C151C2311yescharacteristic
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C4⋊C4×C151C2311yescharacteristic
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C42×C151—21no—
85C2×C42×C151—21no—
86C2×C42×C151—21no—
87C2×C42×C151—21no—
88C2×C42×C151C2311yescharacteristic
89C2×C42×C151C2311yescharacteristic
90C2×C42×C151C2311yescharacteristic
91#107×C151—22no—
92#106×C151—22no—
93C4⋊C8×C151—22no—
94#103×C151—22no—
95#103×C151—22no—
96#103×C151—22no—
97#103×C151—22no—
98C4×C8×C151—22no—
99#95×C151—21no—
100#95×C151—21no—
101#95×C151—21no—
102#95×C151—21no—
103#95×C151—21no—
104#95×C151—21no—
105#95×C151—21no—
106#95×C151—21no—
107#95×C151—21no—
108#95×C151—21no—
109#95×C151—21no—
110#95×C151—21no—
111#95×C151—21no—
112#95×C151—21no—
113#95×C151—21no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—21no—
117C2×Q8×C151—21no—
118C2×Q8×C151—21no—
119C2×Q8×C151—21no—
120C2×Q8×C151—21no—
121C2×Q8×C151—41no—
122C2×Q8×C151#4112yes—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
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×C151C2×D411yescharacteristic
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2411yescharacteristic
138C2×C8×C151—21no—
139C2×C8×C151—21no—
140C2×C8×C151—21no—
141C2×C8×C151—21no—
142C2×C8×C151—21no—
143C2×C8×C151—21no—
144C2×C8×C151—21no—
145C2×C8×C151—21no—
146C2×C8×C151—21no—
147C2×C8×C151—21no—
148C2×C8×C151—21no—
149C2×C8×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—42no—
167C4⋊C4×C151—42no—
168C4⋊C4×C151—42no—
169C4⋊C4×C151—42no—
170C4⋊C4×C151—81no—
171C4⋊C4×C151#4112yes—
172C42×C151—21no—
173C42×C151—21no—
174C42×C151—21no—
175C42×C151—21no—
176C42×C151—42no—
177C42×C151—42no—
178C42×C151—81no—
179C42×C151—81no—
180C42×C151#4112yes—
181C42×C151#4112yes—
182C23×C151C22×D411yescharacteristic
183Q8×C151—22no—
184Q8×C151—22no—
185Q8×C151—44no—
186Q8×C151—41no—
187Q8×C151—41no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—21no—
193C2×C4×C151—21no—
194C2×C4×C151—21no—
195C2×C4×C151—21no—
196C2×C4×C151—21no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—21no—
200C2×C4×C151—21no—
201C2×C4×C151—21no—
202C2×C4×C151—21no—
203C2×C4×C151—21no—
204C2×C4×C151—21no—
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—41no—
213C2×C4×C151—41no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—41no—
220C2×C4×C151—41no—
221C2×C4×C151—41no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151#12312yes—
228C2×C4×C151#12312yes—
229C2×C4×C151#13512yes—
230C2×C4×C151C2×#4111yescharacteristic
231C2×C4×C151C2×#4111yescharacteristic
232C2×C4×C151C2×#4111yescharacteristic
233C2×C4×C151C2×#4111yescharacteristic
234C2×C4×C1512−1+411yescharacteristic
235C2×C4×C1512−1+411yescharacteristic
236C8×C151—41no—
237C8×C151—41no—
238C8×C151—41no—
239C8×C151—41no—
240C22×C151C2×#12311yescharacteristic
241C22×C151#54811yescharacteristic
242C22×C151#54811yescharacteristic
243C22×C151C2×#13511yescharacteristic
244C22×C151#57511yescharacteristic
245C22×C151#57711yescharacteristic
246C22×C151#57811yescharacteristic
247C4×C151—22no—
248C4×C151—22no—
249C4×C151—22no—
250C4×C151—41no—
251C4×C151—41no—
252C4×C151—41no—
253C4×C151—42no—
254C4×C151—42no—
255C4×C151—81no—
256C4×C151—81no—
257C4×C151—81no—
258C4×C151—81no—
259C4×C151—81no—
260C4×C151—81no—
261C4×C151#52911yescharacteristic
262C4×C151#54111yescharacteristic
263C4×C151#55211yescharacteristic
264C4×C151#55611yescharacteristic
265C2×C151#242111yescharacteristic
266C2×C151#309111yescharacteristic
267C2×C151#309711yescharacteristic
268C2×C151#336411yescharacteristic
269C2×C151#336511yescharacteristic
270C2×C151#337611yescharacteristic
271C2×C151#337711yescharacteristic
272#25000C15111yesmaximal, characteristic, direct product factor, Sylow
273C151#2500011yescharacteristic, direct product factor, Sylow
274#2581C2×C15111yescharacteristic
275#2355C2×C15111yescharacteristic
276#2101C2×C15111yescharacteristic
277#2099C2×C15111yescharacteristic
278#2074C2×C15111yescharacteristic
279#2072C2×C15111yescharacteristic
280#1984C2×C15111yescharacteristic
281#1949C2×C15111yescharacteristic
282#1928C2×C15111yescharacteristic
283#1927C2×C15111yescharacteristic
284#1921C2×C15111yescharacteristic
285#1919C2×C15111yescharacteristic
286#1835C2×C15111yescharacteristic
287#1805C2×C15111yescharacteristic
288C4×#103C2×C15111yescharacteristic
289C2×C4×Q8C22×C15111yescharacteristic
290C2×C4×Q8C22×C15111yescharacteristic
291C2×#107C22×C15111yescharacteristic
292C2×#106C22×C15111yescharacteristic
293C2×C4⋊C8C22×C15111yescharacteristic
294C2×#103C22×C15111yescharacteristic
295C2×#103C22×C15111yescharacteristic
296C2×#103C22×C15111yescharacteristic
297C2×#103C22×C15111yescharacteristic
298C2×C4×C8C22×C15111yescharacteristic
299#400—21no—
300#395—21no—
301#391—21no—
302#391C22×C15111yescharacteristic
303#391C22×C15111yescharacteristic
304#389C22×C15111yescharacteristic
305#389C22×C15111yescharacteristic
306#387—21no—
307#387—21no—
308#387—21no—
309#387—21no—
310#384C22×C15111yescharacteristic
311#382C22×C15111yescharacteristic
312#382C22×C15111yescharacteristic
313#382C22×C15111yescharacteristic
314C4×C4⋊C4—21no—
315C4×C4⋊C4C22×C15111yescharacteristic
316C4×C4⋊C4C22×C15111yescharacteristic
317C4×C4⋊C4C22×C15111yescharacteristic
318#340C22×C15111yescharacteristic
319#340C22×C15111yescharacteristic
320#340C22×C15111yescharacteristic
321#340C22×C15111yescharacteristic
322#340C22×C15111yescharacteristic
323#340C22×C15111yescharacteristic
324#340C22×C15111yescharacteristic
325#340C22×C15111yescharacteristic
326#340C22×C15111yescharacteristic
327#340C22×C15111yescharacteristic
328#336C22×C15111yescharacteristic
329#336C22×C15111yescharacteristic
330#336C22×C15111yescharacteristic
331#336C22×C15111yescharacteristic
332C22×Q8D4×C15111yescharacteristic
333C22×Q8C23×C15111yescharacteristic
334C22×C8C23×C15111yescharacteristic
335C22×C8C23×C15111yescharacteristic
336C22×C8C23×C15111yescharacteristic
337C22×C8C23×C15111yescharacteristic
338C4×Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4D4×C15111yescharacteristic
348C2×C4⋊C4D4×C15111yescharacteristic
349C2×C4⋊C4D4×C15111yescharacteristic
350C2×C4⋊C4C23×C15111yescharacteristic
351C2×C4⋊C4C23×C15111yescharacteristic
352C2×C4⋊C4C23×C15111yescharacteristic
353C2×C4⋊C4C23×C15111yescharacteristic
354C2×C4⋊C4C23×C15111yescharacteristic
355C2×C4⋊C4C23×C15111yescharacteristic
356C2×C4⋊C4C23×C15111yescharacteristic
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42C23×C15111yescharacteristic
362C2×C42C23×C15111yescharacteristic
363C2×C42C23×C15111yescharacteristic
364#107—22no—
365#106—22no—
366C4⋊C8—22no—
367#103—22no—
368#103—22no—
369#103—22no—
370#103—22no—
371C4×C8—22no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—41no—
395C2×Q8#41×C15112yes—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4C2×D4×C15111yescharacteristic
405C22×C4C2×D4×C15111yescharacteristic
406C22×C4C2×D4×C15111yescharacteristic
407C22×C4C2×D4×C15111yescharacteristic
408C22×C4C2×D4×C15111yescharacteristic
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C24×C15111yescharacteristic
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—42no—
440C4⋊C4—42no—
441C4⋊C4—42no—
442C4⋊C4—42no—
443C4⋊C4—81no—
444C4⋊C4#41×C15112yes—
445C42—21no—
446C42—21no—
447C42—21no—
448C42—21no—
449C42—42no—
450C42—42no—
451C42—81no—
452C42—81no—
453C42#41×C15112yes—
454C42#41×C15112yes—
455C23C22×D4×C15111yescharacteristic
456Q8—22no—
457Q8—22no—
458Q8—44no—
459Q8—41no—
460Q8—41no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4#123×C15112yes—
501C2×C4#123×C15112yes—
502C2×C4#135×C15112yes—
503C2×C4C2×#41×C15111yescharacteristic
504C2×C4C2×#41×C15111yescharacteristic
505C2×C4C2×#41×C15111yescharacteristic
506C2×C4C2×#41×C15111yescharacteristic
507C2×C42−1+4×C15111yescharacteristic
508C2×C42−1+4×C15111yescharacteristic
509C8—41no—
510C8—41no—
511C8—41no—
512C8—41no—
513C22C2×#123×C15111yescharacteristic
514C22#548×C15111yescharacteristic
515C22#548×C15111yescharacteristic
516C22C2×#135×C15111yescharacteristic
517C22#575×C15111yescharacteristic
518C22#577×C15111yescharacteristic
519C22#578×C15111yescharacteristic
520C4—22no—
521C4—22no—
522C4—22no—
523C4—42no—
524C4—42no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4#529×C15111yescharacteristic
535C4#541×C15111yescharacteristic
536C4#552×C15111yescharacteristic
537C4#556×C15111yescharacteristic
538C2#2421×C15111yescharacteristic
539C2#3091×C15111yescharacteristic
540C2#3097×C15111yescharacteristic
541C2#3364×C15111yescharacteristic
542C2#3365×C15111yescharacteristic
543C2#3376×C15111yescharacteristic
544C2#3377×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
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
272. #25000C151direct (N × H)
273. C151#25000direct (N × H)

Maximal subgroups

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

subgroupindex
#2581×C1512
#2355×C1512
#2101×C1512
#2099×C1512
#2074×C1512
#2072×C1512
#1984×C1512
#1949×C1512
#1928×C1512
#1927×C1512
#1921×C1512
#1919×C1512
#1835×C1512
#1805×C1512
C4×#103×C1512
#25000151