Finite Group Databasebeta

← C151×#24998 #50329923

Subgroups — C151×#24998 #50329923

Order 38656.

678 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2580×C151C211yesmaximal, characteristic
2#2355×C151C211yesmaximal, characteristic, complemented
3#2101×C151C211yesmaximal, characteristic, complemented
4#2099×C151C211yesmaximal, characteristic, complemented
5#2073×C151C211yesmaximal, characteristic
6#2071×C151C211yesmaximal, characteristic
7#1984×C151C211yesmaximal, characteristic, complemented
8#1949×C151C211yesmaximal, characteristic, complemented
9#1926×C151C211yesmaximal, characteristic
10#1925×C151C211yesmaximal, characteristic
11#1921×C151C211yesmaximal, characteristic, complemented
12#1919×C151C211yesmaximal, characteristic, complemented
13#1835×C151C211yesmaximal, characteristic, complemented
14#1804×C151C211yesmaximal, characteristic
15C4×#102×C151C211yesmaximal, characteristic
16C2×C4×Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18C2×#107×C151C2211yescharacteristic
19C2×#106×C151C2211yescharacteristic
20C2×C4⋊C8×C151C2211yescharacteristic
21C2×#102×C151C2211yescharacteristic
22C2×#102×C151C2211yescharacteristic
23C2×#102×C151C2211yescharacteristic
24C2×#102×C151C2211yescharacteristic
25C2×C4×C8×C151C2211yescharacteristic
26#399×C151—21no—
27#393×C151—21no—
28#391×C151—21no—
29#390×C151C2211yescharacteristic
30#390×C151C2211yescharacteristic
31#389×C151C2211yescharacteristic
32#389×C151C2211yescharacteristic
33#387×C151—21no—
34#387×C151—21no—
35#385×C151—21no—
36#385×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×D4×C151C2311yescharacteristic
61C23×C4×C151—21no—
62C22×C8×C151C2311yescharacteristic
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66C4×Q8×C151—22no—
67C4×Q8×C151—22no—
68C4×D4×C151—22no—
69C4×D4×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×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×C22⋊C4×C151—21no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151—21no—
89C2×C42×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151—21no—
92C2×C42×C151C2311yescharacteristic
93C2×C42×C151C2311yescharacteristic
94C2×C42×C151C2311yescharacteristic
95#107×C151—22no—
96#106×C151—22no—
97C4⋊C8×C151—22no—
98#102×C151—22no—
99#102×C151—22no—
100#102×C151—22no—
101#102×C151—22no—
102C4×C8×C151—22no—
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—
114C24×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—41no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151#4112yes—
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×C151—42no—
132C22×C4×C151—81no—
133C22×C4×C151—81no—
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2411yescharacteristic
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—
150C2×C8×C151—21no—
151C2×C8×C151—21no—
152C2×C8×C151—21no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
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—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—42no—
170C4⋊C4×C151—81no—
171C4⋊C4×C151—81no—
172C4⋊C4×C151—81no—
173C4⋊C4×C151#4112yes—
174C22⋊C4×C151—42no—
175C22⋊C4×C151—42no—
176C22⋊C4×C151—42no—
177C22⋊C4×C151—81no—
178C22⋊C4×C151—81no—
179C42×C151—21no—
180C42×C151—21no—
181C42×C151—21no—
182C42×C151—21no—
183C42×C151—42no—
184C42×C151—81no—
185C42×C151—81no—
186C42×C151#4112yes—
187C42×C151#4112yes—
188C23×C151—22no—
189C23×C151—41no—
190C23×C151—41no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151—41no—
195C23×C151C22×D411yescharacteristic
196Q8×C151—44no—
197D4×C151—22no—
198D4×C151—22no—
199D4×C151—41no—
200D4×C151—41no—
201C2×C4×C151—21no—
202C2×C4×C151—21no—
203C2×C4×C151—21no—
204C2×C4×C151—21no—
205C2×C4×C151—21no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—22no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
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—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—84no—
238C2×C4×C151#12312yes—
239C2×C4×C151#12312yes—
240C2×C4×C151#13512yes—
241C2×C4×C151C2×#4111yescharacteristic
242C2×C4×C151C2×#4111yescharacteristic
243C2×C4×C151C2×#4111yescharacteristic
244C2×C4×C151C2×#4111yescharacteristic
245C2×C4×C1512−1+411yescharacteristic
246C2×C4×C1512−1+411yescharacteristic
247C8×C151—41no—
248C8×C151—41no—
249C8×C151—41no—
250C8×C151—41no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—81no—
255C22×C151—81no—
256C22×C151—81no—
257C22×C151—81no—
258C22×C151C2×#12311yescharacteristic
259C22×C151#54811yescharacteristic
260C22×C151#54811yescharacteristic
261C22×C151C2×#13511yescharacteristic
262C22×C151#57511yescharacteristic
263C22×C151#57611yescharacteristic
264C22×C151#57711yescharacteristic
265C4×C151—22no—
266C4×C151—22no—
267C4×C151—22no—
268C4×C151—41no—
269C4×C151—41no—
270C4×C151—41no—
271C4×C151—42no—
272C4×C151—81no—
273C4×C151—81no—
274C4×C151—81no—
275C4×C151—81no—
276C4×C151—81no—
277C4×C151—81no—
278C4×C151#52911yescharacteristic
279C4×C151#54111yescharacteristic
280C4×C151#55211yescharacteristic
281C4×C151#55611yescharacteristic
282C2×C151—82no—
283C2×C151#242111yescharacteristic
284C2×C151#309111yescharacteristic
285C2×C151#309611yescharacteristic
286C2×C151#336111yescharacteristic
287C2×C151#336511yescharacteristic
288C2×C151#337011yescharacteristic
289C2×C151#337611yescharacteristic
290#24998C15111yesmaximal, characteristic, direct product factor, Sylow
291C151#2499811yescharacteristic, direct product factor, Sylow
292#2580C2×C15111yescharacteristic
293#2355C2×C15111yescharacteristic, complemented
294#2101C2×C15111yescharacteristic, complemented
295#2099C2×C15111yescharacteristic, complemented
296#2073C2×C15111yescharacteristic
297#2071C2×C15111yescharacteristic
298#1984C2×C15111yescharacteristic, complemented
299#1949C2×C15111yescharacteristic, complemented
300#1926C2×C15111yescharacteristic
301#1925C2×C15111yescharacteristic
302#1921C2×C15111yescharacteristic, complemented
303#1919C2×C15111yescharacteristic, complemented
304#1835C2×C15111yescharacteristic, complemented
305#1804C2×C15111yescharacteristic
306C4×#102C2×C15111yescharacteristic
307C2×C4×Q8C22×C15111yescharacteristic
308C2×C4×D4C22×C15111yescharacteristic
309C2×#107C22×C15111yescharacteristic
310C2×#106C22×C15111yescharacteristic
311C2×C4⋊C8C22×C15111yescharacteristic
312C2×#102C22×C15111yescharacteristic
313C2×#102C22×C15111yescharacteristic
314C2×#102C22×C15111yescharacteristic
315C2×#102C22×C15111yescharacteristic
316C2×C4×C8C22×C15111yescharacteristic
317#399—21no—
318#393—21no—
319#391—21no—
320#390C22×C15111yescharacteristic
321#390C22×C15111yescharacteristic
322#389C22×C15111yescharacteristic
323#389C22×C15111yescharacteristic
324#387—21no—
325#387—21no—
326#385—21no—
327#385—21no—
328#384C22×C15111yescharacteristic
329#382C22×C15111yescharacteristic
330#382C22×C15111yescharacteristic
331#382C22×C15111yescharacteristic
332C4×C4⋊C4—21no—
333C4×C4⋊C4C22×C15111yescharacteristic
334C4×C4⋊C4C22×C15111yescharacteristic
335C4×C4⋊C4C22×C15111yescharacteristic
336#340C22×C15111yescharacteristic
337#340C22×C15111yescharacteristic
338#340C22×C15111yescharacteristic
339#340C22×C15111yescharacteristic
340#340C22×C15111yescharacteristic
341#340C22×C15111yescharacteristic
342#340C22×C15111yescharacteristic
343#340C22×C15111yescharacteristic
344#340C22×C15111yescharacteristic
345#340C22×C15111yescharacteristic
346#336C22×C15111yescharacteristic
347#336C22×C15111yescharacteristic
348#336C22×C15111yescharacteristic
349#336C22×C15111yescharacteristic
350C22×Q8D4×C15111yescharacteristic
351C22×D4C23×C15111yescharacteristic
352C23×C4—21no—
353C22×C8C23×C15111yescharacteristic
354C22×C8C23×C15111yescharacteristic
355C22×C8C23×C15111yescharacteristic
356C22×C8C23×C15111yescharacteristic
357C4×Q8—22no—
358C4×Q8—22no—
359C4×D4—22no—
360C4×D4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4D4×C15111yescharacteristic
366C2×C4⋊C4D4×C15111yescharacteristic
367C2×C4⋊C4D4×C15111yescharacteristic
368C2×C4⋊C4C23×C15111yescharacteristic
369C2×C4⋊C4C23×C15111yescharacteristic
370C2×C4⋊C4C23×C15111yescharacteristic
371C2×C4⋊C4C23×C15111yescharacteristic
372C2×C4⋊C4C23×C15111yescharacteristic
373C2×C4⋊C4C23×C15111yescharacteristic
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42C23×C15111yescharacteristic
384C2×C42C23×C15111yescharacteristic
385C2×C42C23×C15111yescharacteristic
386#107—22no—
387#106—22no—
388C4⋊C8—22no—
389#102—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393C4×C8—22no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405C24—21no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—41no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4#41×C15112yes—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—42no—
423C22×C4—81no—
424C22×C4—81no—
425C22×C4C2×D4×C15111yescharacteristic
426C22×C4C2×D4×C15111yescharacteristic
427C22×C4C2×D4×C15111yescharacteristic
428C22×C4C2×D4×C15111yescharacteristic
429C22×C4C2×D4×C15111yescharacteristic
430C22×C4C2×D4×C15111yescharacteristic
431C22×C4C24×C15111yescharacteristic
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4#41×C15112yes—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—42no—
468C22⋊C4—81no—
469C22⋊C4—81no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—42no—
475C42—81no—
476C42—81no—
477C42#41×C15112yes—
478C42#41×C15112yes—
479C23—22no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23C22×D4×C15111yescharacteristic
487Q8—44no—
488D4—22no—
489D4—22no—
490D4—41no—
491D4—41no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—84no—
529C2×C4#123×C15112yes—
530C2×C4#123×C15112yes—
531C2×C4#135×C15112yes—
532C2×C4C2×#41×C15111yescharacteristic
533C2×C4C2×#41×C15111yescharacteristic
534C2×C4C2×#41×C15111yescharacteristic
535C2×C4C2×#41×C15111yescharacteristic
536C2×C42−1+4×C15111yescharacteristic
537C2×C42−1+4×C15111yescharacteristic
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22C2×#123×C15111yescharacteristic
550C22#548×C15111yescharacteristic
551C22#548×C15111yescharacteristic
552C22C2×#135×C15111yescharacteristic
553C22#575×C15111yescharacteristic
554C22#576×C15111yescharacteristic
555C22#577×C15111yescharacteristic
556C4—22no—
557C4—22no—
558C4—22no—
559C4—42no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4#529×C15111yescharacteristic
570C4#541×C15111yescharacteristic
571C4#552×C15111yescharacteristic
572C4#556×C15111yescharacteristic
573C2—82no—
574C2#2421×C15111yescharacteristic
575C2#3091×C15111yescharacteristic
576C2#3096×C15111yescharacteristic
577C2#3361×C15111yescharacteristic
578C2#3365×C15111yescharacteristic
579C2#3370×C15111yescharacteristic
580C2#3376×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
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
2. #2355×C151C2semidirect
3. #2101×C151C2semidirect
4. #2099×C151C2semidirect
7. #1984×C151C2semidirect
8. #1949×C151C2semidirect
11. #1921×C151C2semidirect
12. #1919×C151C2semidirect
13. #1835×C151C2semidirect
290. #24998C151direct (N × H)
291. C151#24998direct (N × H)
293. #2355C2×C151semidirect
294. #2101C2×C151semidirect
295. #2099C2×C151semidirect
298. #1984C2×C151semidirect
299. #1949C2×C151semidirect
302. #1921C2×C151semidirect
303. #1919C2×C151semidirect
304. #1835C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2580×C1512
#2355×C1512
#2101×C1512
#2099×C1512
#2073×C1512
#2071×C1512
#1984×C1512
#1949×C1512
#1926×C1512
#1925×C1512
#1921×C1512
#1919×C1512
#1835×C1512
#1804×C1512
C4×#102×C1512
#24998151