Finite Group Databasebeta

← C151×#24624 #50329549

Subgroups — C151×#24624 #50329549

Order 38656.

670 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3095×C151C211yesmaximal, characteristic
2C2×#485×C151C211yesmaximal, characteristic
3#2924×C151C211yesmaximal, characteristic
4#2911×C151C211yesmaximal, characteristic
5#2090×C151C211yesmaximal, characteristic, complemented
6#2089×C151C211yesmaximal, characteristic, complemented
7#2064×C151C211yesmaximal, characteristic, complemented
8#2064×C151C211yesmaximal, characteristic, complemented
9#1952×C151C211yesmaximal, characteristic, complemented
10#1951×C151C211yesmaximal, characteristic, complemented
11#1930×C151C211yesmaximal, characteristic, complemented
12#1930×C151C211yesmaximal, characteristic, complemented
13#1901×C151C211yesmaximal, characteristic
14#1855×C151C211yesmaximal, characteristic
15#1822×C151C211yesmaximal, characteristic
16C22×M16×C151C2211yescharacteristic
17C2×C22⋊Q8×C151C2211yescharacteristic
18C2×#117×C151C2211yescharacteristic
19C2×#117×C151C2211yescharacteristic
20#485×C151—21no—
21#485×C151—21no—
22#485×C151—21no—
23#485×C151—21no—
24#485×C151—21no—
25#485×C151—21no—
26#484×C151—21no—
27#483×C151—21no—
28#433×C151—21no—
29#433×C151—21no—
30#432×C151—21no—
31#431×C151—21no—
32C2×#108×C151C2211yescharacteristic
33C2×#108×C151C2211yescharacteristic
34#428×C151—21no—
35#428×C151—21no—
36#428×C151C2211yescharacteristic
37#428×C151C2211yescharacteristic
38#428×C151C2211yescharacteristic
39#428×C151C2211yescharacteristic
40#428×C151C2211yescharacteristic
41#428×C151C2211yescharacteristic
42#427×C151—21no—
43#427×C151—21no—
44C2×#107×C151C2211yescharacteristic
45C2×#106×C151C2211yescharacteristic
46#424×C151C2211yescharacteristic
47#424×C151C2211yescharacteristic
48#419×C151C2211yescharacteristic
49#419×C151C2211yescharacteristic
50C2×#103×C151C2211yescharacteristic
51C2×#103×C151C2211yescharacteristic
52C2×#101×C151C2211yescharacteristic
53C2×#101×C151C2211yescharacteristic
54#407×C151C2211yescharacteristic
55#407×C151C2211yescharacteristic
56C2×C22⋊C8×C151C2211yescharacteristic
57#405×C151C2211yescharacteristic
58#405×C151C2211yescharacteristic
59#343×C151C2211yescharacteristic
60#343×C151C2211yescharacteristic
61#343×C151C2211yescharacteristic
62#343×C151C2211yescharacteristic
63#343×C151C2211yescharacteristic
64#343×C151C2211yescharacteristic
65#341×C151C2211yescharacteristic
66#341×C151C2211yescharacteristic
67C22×Q8×C151C2311yescharacteristic
68C23×C4×C151C2311yescharacteristic
69C2×M16×C151—21no—
70C2×M16×C151—22no—
71C2×M16×C151—22no—
72C2×M16×C151C2311yescharacteristic
73C2×M16×C151C2311yescharacteristic
74C2×M16×C151C2311yescharacteristic
75C2×M16×C151C2311yescharacteristic
76C2×M16×C151C2311yescharacteristic
77C2×M16×C151C2311yescharacteristic
78C22×C8×C151—21no—
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22⋊Q8×C151—21no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85#117×C151—21no—
86#117×C151—21no—
87#117×C151—21no—
88#117×C151—21no—
89#117×C151—21no—
90#117×C151—21no—
91#117×C151D411yescharacteristic
92#117×C151D411yescharacteristic
93#117×C151C2311yescharacteristic
94#117×C151C2311yescharacteristic
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151D411yescharacteristic
97C2×C4⋊C4×C151D411yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C42×C151—21no—
105C2×C42×C151—21no—
106#108×C151—22no—
107#108×C151—22no—
108#107×C151—21no—
109#107×C151—21no—
110#107×C151—21no—
111#107×C151—21no—
112#107×C151—21no—
113#107×C151—21no—
114#107×C151—21no—
115#107×C151—21no—
116#106×C151—21no—
117#106×C151—21no—
118#106×C151—21no—
119#106×C151—21no—
120#106×C151—21no—
121#106×C151—21no—
122#106×C151—21no—
123#106×C151—21no—
124C4⋊C8×C151—21no—
125C4⋊C8×C151—21no—
126C4⋊C8×C151—21no—
127C4⋊C8×C151—21no—
128#103×C151—21no—
129#103×C151—21no—
130#103×C151—21no—
131#103×C151—21no—
132#103×C151—21no—
133#103×C151—21no—
134#103×C151—21no—
135#103×C151—21no—
136#101×C151—22no—
137#101×C151—22no—
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140C22⋊C8×C151—21no—
141C22⋊C8×C151—21no—
142C22⋊C8×C151D411yescharacteristic
143C22⋊C8×C151D411yescharacteristic
144C22⋊C8×C151D411yescharacteristic
145C22⋊C8×C151D411yescharacteristic
146#97×C151—21no—
147#97×C151—21no—
148C4×C8×C151—21no—
149C4×C8×C151—21no—
150C24×C151#4111yescharacteristic
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151#4111yescharacteristic
172C22×C4×C151C2411yescharacteristic
173M16×C151—24no—
174M16×C151—21no—
175M16×C151—21no—
176M16×C151—21no—
177M16×C151—21no—
178M16×C151—21no—
179M16×C151—21no—
180M16×C151—21no—
181M16×C151—21no—
182M16×C151—21no—
183M16×C151—21no—
184M16×C151#4112yes—
185M16×C151#4112yes—
186C2×C8×C151—24no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151C2×D411yescharacteristic
198C2×C8×C151C2×D411yescharacteristic
199C2×C8×C151C2×D411yescharacteristic
200C2×C8×C151C2×D411yescharacteristic
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—41no—
210C4⋊C4×C151—41no—
211C4⋊C4×C151C2×D411yescharacteristic
212C4⋊C4×C151C2×D411yescharacteristic
213C4⋊C4×C151C2×D411yescharacteristic
214C4⋊C4×C151C2×D411yescharacteristic
215C22⋊C4×C151—21no—
216C22⋊C4×C151—21no—
217C22⋊C4×C151—21no—
218C22⋊C4×C151—21no—
219C22⋊C4×C151—41no—
220C22⋊C4×C151—41no—
221C22⋊C4×C151—41no—
222C22⋊C4×C151—41no—
223C42×C151—21no—
224C42×C151—21no—
225C42×C151—21no—
226C42×C151—21no—
227C42×C151—41no—
228C42×C151—41no—
229C23×C151—21no—
230C23×C151—21no—
231C23×C151—41no—
232C23×C151—41no—
233C23×C151#12111yescharacteristic
234C23×C151#12111yescharacteristic
235C23×C151C2×#4111yescharacteristic
236Q8×C151—41no—
237Q8×C151—41no—
238Q8×C151—41no—
239Q8×C151—41no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—42no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—81no—
262C2×C4×C151—81no—
263C2×C4×C151—81no—
264C2×C4×C151—81no—
265C2×C4×C151#12111yescharacteristic
266C2×C4×C151#12111yescharacteristic
267C2×C4×C151C22×D411yescharacteristic
268C2×C4×C151C22×D411yescharacteristic
269C2×C4×C151C2×#4111yescharacteristic
270C2×C4×C151C2×#4111yescharacteristic
271C2×C4×C1512−1+411yescharacteristic
272C2×C4×C1512−1+411yescharacteristic
273C8×C151—22no—
274C8×C151—22no—
275C8×C151—21no—
276C8×C151—21no—
277C8×C151—21no—
278C8×C151—21no—
279C8×C151—41no—
280C8×C151—41no—
281C8×C151—41no—
282C8×C151—41no—
283C22×C151—21no—
284C22×C151—21no—
285C22×C151—21no—
286C22×C151—21no—
287C22×C151—21no—
288C22×C151—21no—
289C22×C151—21no—
290C22×C151—21no—
291C22×C151—81no—
292C22×C151—81no—
293C22×C151C2×#12111yescharacteristic
294C22×C151#55211yescharacteristic
295C22×C151#55211yescharacteristic
296C4×C151—21no—
297C4×C151—21no—
298C4×C151—41no—
299C4×C151—41no—
300C4×C151—41no—
301C4×C151—41no—
302C4×C151—81no—
303C4×C151—81no—
304C4×C151—81no—
305C4×C151—81no—
306C4×C151#52511yescharacteristic
307C4×C151#53611yescharacteristic
308C4×C151#54711yescharacteristic
309C4×C151#54711yescharacteristic
310C2×C151—21no—
311C2×C151—21no—
312C2×C151—41no—
313C2×C151—41no—
314C2×C151#241311yescharacteristic
315C2×C151#306711yescharacteristic
316C2×C151#306911yescharacteristic
317#24624C15111yesmaximal, characteristic, direct product factor, Sylow
318C151#2462411yescharacteristic, direct product factor, Sylow
319#3095C2×C15111yescharacteristic
320C2×#485C2×C15111yescharacteristic
321#2924C2×C15111yescharacteristic
322#2911C2×C15111yescharacteristic
323#2090C2×C15111yescharacteristic, complemented
324#2089C2×C15111yescharacteristic, complemented
325#2064C2×C15111yescharacteristic, complemented
326#2064C2×C15111yescharacteristic, complemented
327#1952C2×C15111yescharacteristic, complemented
328#1951C2×C15111yescharacteristic, complemented
329#1930C2×C15111yescharacteristic, complemented
330#1930C2×C15111yescharacteristic, complemented
331#1901C2×C15111yescharacteristic
332#1855C2×C15111yescharacteristic
333#1822C2×C15111yescharacteristic
334C22×M16C22×C15111yescharacteristic
335C2×C22⋊Q8C22×C15111yescharacteristic
336C2×#117C22×C15111yescharacteristic
337C2×#117C22×C15111yescharacteristic
338#485—21no—
339#485—21no—
340#485—21no—
341#485—21no—
342#485—21no—
343#485—21no—
344#484—21no—
345#483—21no—
346#433—21no—
347#433—21no—
348#432—21no—
349#431—21no—
350C2×#108C22×C15111yescharacteristic
351C2×#108C22×C15111yescharacteristic
352#428—21no—
353#428—21no—
354#428C22×C15111yescharacteristic
355#428C22×C15111yescharacteristic
356#428C22×C15111yescharacteristic
357#428C22×C15111yescharacteristic
358#428C22×C15111yescharacteristic
359#428C22×C15111yescharacteristic
360#427—21no—
361#427—21no—
362C2×#107C22×C15111yescharacteristic
363C2×#106C22×C15111yescharacteristic
364#424C22×C15111yescharacteristic
365#424C22×C15111yescharacteristic
366#419C22×C15111yescharacteristic
367#419C22×C15111yescharacteristic
368C2×#103C22×C15111yescharacteristic
369C2×#103C22×C15111yescharacteristic
370C2×#101C22×C15111yescharacteristic
371C2×#101C22×C15111yescharacteristic
372#407C22×C15111yescharacteristic
373#407C22×C15111yescharacteristic
374C2×C22⋊C8C22×C15111yescharacteristic
375#405C22×C15111yescharacteristic
376#405C22×C15111yescharacteristic
377#343C22×C15111yescharacteristic
378#343C22×C15111yescharacteristic
379#343C22×C15111yescharacteristic
380#343C22×C15111yescharacteristic
381#343C22×C15111yescharacteristic
382#343C22×C15111yescharacteristic
383#341C22×C15111yescharacteristic
384#341C22×C15111yescharacteristic
385C22×Q8C23×C15111yescharacteristic
386C23×C4C23×C15111yescharacteristic
387C2×M16—21no—
388C2×M16—22no—
389C2×M16—22no—
390C2×M16C23×C15111yescharacteristic
391C2×M16C23×C15111yescharacteristic
392C2×M16C23×C15111yescharacteristic
393C2×M16C23×C15111yescharacteristic
394C2×M16C23×C15111yescharacteristic
395C2×M16C23×C15111yescharacteristic
396C22×C8—21no—
397C22×C8C23×C15111yescharacteristic
398C22×C8C23×C15111yescharacteristic
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403#117—21no—
404#117—21no—
405#117—21no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117D4×C15111yescharacteristic
410#117D4×C15111yescharacteristic
411#117C23×C15111yescharacteristic
412#117C23×C15111yescharacteristic
413C2×C4⋊C4—21no—
414C2×C4⋊C4D4×C15111yescharacteristic
415C2×C4⋊C4D4×C15111yescharacteristic
416C2×C4⋊C4C23×C15111yescharacteristic
417C2×C4⋊C4C23×C15111yescharacteristic
418C2×C4⋊C4C23×C15111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C42—21no—
423C2×C42—21no—
424#108—22no—
425#108—22no—
426#107—21no—
427#107—21no—
428#107—21no—
429#107—21no—
430#107—21no—
431#107—21no—
432#107—21no—
433#107—21no—
434#106—21no—
435#106—21no—
436#106—21no—
437#106—21no—
438#106—21no—
439#106—21no—
440#106—21no—
441#106—21no—
442C4⋊C8—21no—
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446#103—21no—
447#103—21no—
448#103—21no—
449#103—21no—
450#103—21no—
451#103—21no—
452#103—21no—
453#103—21no—
454#101—22no—
455#101—22no—
456C22⋊C8—21no—
457C22⋊C8—21no—
458C22⋊C8—21no—
459C22⋊C8—21no—
460C22⋊C8D4×C15111yescharacteristic
461C22⋊C8D4×C15111yescharacteristic
462C22⋊C8D4×C15111yescharacteristic
463C22⋊C8D4×C15111yescharacteristic
464#97—21no—
465#97—21no—
466C4×C8—21no—
467C4×C8—21no—
468C24#41×C15111yescharacteristic
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4C2×D4×C15111yescharacteristic
486C22×C4C2×D4×C15111yescharacteristic
487C22×C4C2×D4×C15111yescharacteristic
488C22×C4C2×D4×C15111yescharacteristic
489C22×C4#41×C15111yescharacteristic
490C22×C4C24×C15111yescharacteristic
491M16—24no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—21no—
496M16—21no—
497M16—21no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—21no—
502M16#41×C15112yes—
503M16#41×C15112yes—
504C2×C8—24no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8C2×D4×C15111yescharacteristic
516C2×C8C2×D4×C15111yescharacteristic
517C2×C8C2×D4×C15111yescharacteristic
518C2×C8C2×D4×C15111yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4C2×D4×C15111yescharacteristic
530C4⋊C4C2×D4×C15111yescharacteristic
531C4⋊C4C2×D4×C15111yescharacteristic
532C4⋊C4C2×D4×C15111yescharacteristic
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—41no—
546C42—41no—
547C23—21no—
548C23—21no—
549C23—41no—
550C23—41no—
551C23#121×C15111yescharacteristic
552C23#121×C15111yescharacteristic
553C23C2×#41×C15111yescharacteristic
554Q8—41no—
555Q8—41no—
556Q8—41no—
557Q8—41no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4#121×C15111yescharacteristic
584C2×C4#121×C15111yescharacteristic
585C2×C4C22×D4×C15111yescharacteristic
586C2×C4C22×D4×C15111yescharacteristic
587C2×C4C2×#41×C15111yescharacteristic
588C2×C4C2×#41×C15111yescharacteristic
589C2×C42−1+4×C15111yescharacteristic
590C2×C42−1+4×C15111yescharacteristic
591C8—22no—
592C8—22no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—41no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—81no—
610C22—81no—
611C22C2×#121×C15111yescharacteristic
612C22#552×C15111yescharacteristic
613C22#552×C15111yescharacteristic
614C4—21no—
615C4—21no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4#525×C15111yescharacteristic
625C4#536×C15111yescharacteristic
626C4#547×C15111yescharacteristic
627C4#547×C15111yescharacteristic
628C2—21no—
629C2—21no—
630C2—41no—
631C2—41no—
632C2#2413×C15111yescharacteristic
633C2#3067×C15111yescharacteristic
634C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
5. #2090×C151C2semidirect
6. #2089×C151C2semidirect
7. #2064×C151C2semidirect
8. #2064×C151C2semidirect
9. #1952×C151C2semidirect
10. #1951×C151C2semidirect
11. #1930×C151C2semidirect
12. #1930×C151C2semidirect
317. #24624C151direct (N × H)
318. C151#24624direct (N × H)
323. #2090C2×C151semidirect
324. #2089C2×C151semidirect
325. #2064C2×C151semidirect
326. #2064C2×C151semidirect
327. #1952C2×C151semidirect
328. #1951C2×C151semidirect
329. #1930C2×C151semidirect
330. #1930C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3095×C1512
C2×#485×C1512
#2924×C1512
#2911×C1512
#2090×C1512
#2089×C1512
#2064×C1512
#1952×C1512
#1951×C1512
#1930×C1512
#1901×C1512
#1855×C1512
#1822×C1512
#24624151