Finite Group Databasebeta

← C151×#29441 #50334366

Subgroups — C151×#29441 #50334366

Order 38656.

674 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2645×C151C211yesmaximal, characteristic, complemented
2#2319×C151C211yesmaximal, characteristic
3#2088×C151C211yesmaximal, characteristic, complemented
4#2068×C151C211yesmaximal, characteristic, complemented
5#2067×C151C211yesmaximal, characteristic
6#2055×C151C211yesmaximal, characteristic
7#1968×C151C211yesmaximal, characteristic
8#1942×C151C211yesmaximal, characteristic, complemented
9#1936×C151C211yesmaximal, characteristic
10#1935×C151C211yesmaximal, characteristic, complemented
11#1928×C151C211yesmaximal, characteristic, complemented
12#1920×C151C211yesmaximal, characteristic, complemented
13#1877×C151C211yesmaximal, characteristic
14#1862×C151C211yesmaximal, characteristic
15#1768×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18C2×#107×C151C2211yescharacteristic
19C2×#107×C151C2211yescharacteristic
20C2×#106×C151C2211yescharacteristic
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×#103×C151C2211yescharacteristic
24C2×#103×C151C2211yescharacteristic
25C2×#103×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2211yescharacteristic
29C2×#97×C151C2211yescharacteristic
30C2×C4×C8×C151C2211yescharacteristic
31#401×C151—21no—
32#400×C151—21no—
33#400×C151—21no—
34#400×C151—21no—
35#391×C151C2211yescharacteristic
36#391×C151C2211yescharacteristic
37#391×C151C2211yescharacteristic
38#390×C151C2211yescharacteristic
39#390×C151C2211yescharacteristic
40#389×C151C2211yescharacteristic
41#389×C151C2211yescharacteristic
42#389×C151C2211yescharacteristic
43#389×C151C2211yescharacteristic
44#389×C151C2211yescharacteristic
45#388×C151—21no—
46#388×C151—21no—
47#381×C151—21no—
48#380×C151—21no—
49C4×C4⋊C4×C151C2211yescharacteristic
50#376×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59C22×Q8×C151C2311yescharacteristic
60C22×D4×C151C2311yescharacteristic
61C23×C4×C151—21no—
62C2×SD16×C151—22no—
63C2×SD16×C151—22no—
64C2×SD16×C151—41no—
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2311yescharacteristic
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C4×D4×C151—22no—
70C4×D4×C151—22no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C4⋊C4×C151C2311yescharacteristic
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C4⋊C4×C151C2311yescharacteristic
82C2×C22⋊C4×C151—21no—
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—21no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—21no—
87C2×C42×C151—21no—
88C2×C42×C151C2311yescharacteristic
89C2×C42×C151C2311yescharacteristic
90C2×C42×C151C2311yescharacteristic
91#107×C151—22no—
92#107×C151—41no—
93#106×C151—22no—
94C4⋊C8×C151—22no—
95C4⋊C8×C151—22no—
96#103×C151—22no—
97#103×C151—22no—
98#103×C151—41no—
99#102×C151—22no—
100#102×C151—22no—
101#102×C151—41no—
102#97×C151—41no—
103C4×C8×C151—41no—
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—
114#95×C151—21no—
115#95×C151—21no—
116#95×C151D411yescharacteristic
117#95×C151D411yescharacteristic
118#95×C151D411yescharacteristic
119#95×C151D411yescharacteristic
120C24×C151—21no—
121C2×Q8×C151—21no—
122C2×Q8×C151—21no—
123C2×Q8×C151—21no—
124C2×Q8×C151—21no—
125C2×Q8×C151—21no—
126C2×Q8×C151—21no—
127C2×D4×C151—21no—
128C2×D4×C151—21no—
129C2×D4×C151—21no—
130C2×D4×C151—21no—
131C2×D4×C151—21no—
132C2×D4×C151#4112yes—
133C22×C4×C151—21no—
134C22×C4×C151—24no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—81no—
142C22×C4×C151—81no—
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2411yescharacteristic
150SD16×C151—44no—
151C2×C8×C151—21no—
152C2×C8×C151—21no—
153C2×C8×C151—21no—
154C2×C8×C151—21no—
155C2×C8×C151—21no—
156C2×C8×C151—21no—
157C2×C8×C151—21no—
158C2×C8×C151—21no—
159C2×C8×C151—21no—
160C2×C8×C151—21no—
161C2×C8×C151#4112yes—
162C2×C8×C151#4112yes—
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—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—81no—
175C4⋊C4×C151—81no—
176C4⋊C4×C151—81no—
177C4⋊C4×C151—81no—
178C4⋊C4×C151—81no—
179C4⋊C4×C151#4112yes—
180C22⋊C4×C151—24no—
181C22⋊C4×C151—81no—
182C22⋊C4×C151—81no—
183C22⋊C4×C151—81no—
184C22⋊C4×C151—81no—
185C42×C151—21no—
186C42×C151—21no—
187C42×C151—21no—
188C42×C151—21no—
189C42×C151—21no—
190C42×C151—21no—
191C42×C151—81no—
192C23×C151—22no—
193C23×C151—41no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151—41no—
198C23×C151—41no—
199C23×C151C22×D411yescharacteristic
200Q8×C151—41no—
201Q8×C151—41no—
202Q8×C151—41no—
203Q8×C151—41no—
204D4×C151—22no—
205D4×C151—22no—
206D4×C151—41no—
207D4×C151—41no—
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—21no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
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—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—84no—
248C2×C4×C151C2×#4111yescharacteristic
249C2×C4×C151C2×#4111yescharacteristic
250C2×C4×C151C2×#4111yescharacteristic
251C2×C4×C151C2×#4111yescharacteristic
252C2×C4×C151H(5,𝔽2)11yescharacteristic
253C2×C4×C1512−1+411yescharacteristic
254C8×C151—22no—
255C8×C151—22no—
256C8×C151—41no—
257C8×C151—41no—
258C22×C151—42no—
259C22×C151—42no—
260C22×C151—42no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151—81no—
264C22×C151—81no—
265C22×C151#52511yescharacteristic
266C22×C151#53211yescharacteristic
267C22×C151#53711yescharacteristic
268C22×C151#57611yescharacteristic
269C22×C151#57711yescharacteristic
270C22×C151#57711yescharacteristic
271C22×C151#57811yescharacteristic
272C4×C151—41no—
273C4×C151—42no—
274C4×C151—41no—
275C4×C151—41no—
276C4×C151—41no—
277C4×C151—41no—
278C4×C151—41no—
279C4×C151—81no—
280C4×C151—81no—
281C4×C151—81no—
282C4×C151—81no—
283C4×C151—81no—
284C4×C151—81no—
285C4×C151#55111yescharacteristic
286C4×C151#55211yescharacteristic
287C4×C151#55311yescharacteristic
288C4×C151#55611yescharacteristic
289C2×C151—82no—
290C2×C151#260111yescharacteristic
291C2×C151#311811yescharacteristic
292C2×C151#312011yescharacteristic
293C2×C151#317411yescharacteristic
294C2×C151#317511yescharacteristic
295C2×C151#325711yescharacteristic
296C2×C151#325811yescharacteristic
297#29441C15111yesmaximal, characteristic, direct product factor, Sylow
298C151#2944111yescharacteristic, direct product factor, Sylow
299#2645C2×C15111yescharacteristic, complemented
300#2319C2×C15111yescharacteristic
301#2088C2×C15111yescharacteristic, complemented
302#2068C2×C15111yescharacteristic, complemented
303#2067C2×C15111yescharacteristic
304#2055C2×C15111yescharacteristic
305#1968C2×C15111yescharacteristic
306#1942C2×C15111yescharacteristic, complemented
307#1936C2×C15111yescharacteristic
308#1935C2×C15111yescharacteristic, complemented
309#1928C2×C15111yescharacteristic, complemented
310#1920C2×C15111yescharacteristic, complemented
311#1877C2×C15111yescharacteristic
312#1862C2×C15111yescharacteristic
313#1768C2×C15111yescharacteristic, complemented
314C22×SD16C22×C15111yescharacteristic
315C2×C4×D4C22×C15111yescharacteristic
316C2×#107C22×C15111yescharacteristic
317C2×#107C22×C15111yescharacteristic
318C2×#106C22×C15111yescharacteristic
319C2×C4⋊C8C22×C15111yescharacteristic
320C2×C4⋊C8C22×C15111yescharacteristic
321C2×#103C22×C15111yescharacteristic
322C2×#103C22×C15111yescharacteristic
323C2×#103C22×C15111yescharacteristic
324C2×#102C22×C15111yescharacteristic
325C2×#102C22×C15111yescharacteristic
326C2×#102C22×C15111yescharacteristic
327C2×#97C22×C15111yescharacteristic
328C2×C4×C8C22×C15111yescharacteristic
329#401—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#391C22×C15111yescharacteristic
334#391C22×C15111yescharacteristic
335#391C22×C15111yescharacteristic
336#390C22×C15111yescharacteristic
337#390C22×C15111yescharacteristic
338#389C22×C15111yescharacteristic
339#389C22×C15111yescharacteristic
340#389C22×C15111yescharacteristic
341#389C22×C15111yescharacteristic
342#389C22×C15111yescharacteristic
343#388—21no—
344#388—21no—
345#381—21no—
346#380—21no—
347C4×C4⋊C4C22×C15111yescharacteristic
348#376C22×C15111yescharacteristic
349#340C22×C15111yescharacteristic
350#340C22×C15111yescharacteristic
351#340C22×C15111yescharacteristic
352#340C22×C15111yescharacteristic
353#340C22×C15111yescharacteristic
354#340C22×C15111yescharacteristic
355#336C22×C15111yescharacteristic
356#336C22×C15111yescharacteristic
357C22×Q8C23×C15111yescharacteristic
358C22×D4C23×C15111yescharacteristic
359C23×C4—21no—
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—41no—
363C22×C8C23×C15111yescharacteristic
364C22×C8C23×C15111yescharacteristic
365C22×C8C23×C15111yescharacteristic
366C22×C8C23×C15111yescharacteristic
367C4×D4—22no—
368C4×D4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C4⋊C4C23×C15111yescharacteristic
376C2×C4⋊C4C23×C15111yescharacteristic
377C2×C4⋊C4C23×C15111yescharacteristic
378C2×C4⋊C4C23×C15111yescharacteristic
379C2×C4⋊C4C23×C15111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C42—21no—
386C2×C42C23×C15111yescharacteristic
387C2×C42C23×C15111yescharacteristic
388C2×C42C23×C15111yescharacteristic
389#107—22no—
390#107—41no—
391#106—22no—
392C4⋊C8—22no—
393C4⋊C8—22no—
394#103—22no—
395#103—22no—
396#103—41no—
397#102—22no—
398#102—22no—
399#102—41no—
400#97—41no—
401C4×C8—41no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95D4×C15111yescharacteristic
415#95D4×C15111yescharacteristic
416#95D4×C15111yescharacteristic
417#95D4×C15111yescharacteristic
418C24—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4#41×C15112yes—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—81no—
440C22×C4—81no—
441C22×C4C2×D4×C15111yescharacteristic
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15111yescharacteristic
444C22×C4C2×D4×C15111yescharacteristic
445C22×C4C2×D4×C15111yescharacteristic
446C22×C4C2×D4×C15111yescharacteristic
447C22×C4C24×C15111yescharacteristic
448SD16—44no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8#41×C15112yes—
460C2×C8#41×C15112yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4#41×C15112yes—
478C22⋊C4—24no—
479C22⋊C4—81no—
480C22⋊C4—81no—
481C22⋊C4—81no—
482C22⋊C4—81no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—81no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C22×D4×C15111yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4C2×#41×C15111yescharacteristic
547C2×C4C2×#41×C15111yescharacteristic
548C2×C4C2×#41×C15111yescharacteristic
549C2×C4C2×#41×C15111yescharacteristic
550C2×C4H(5,𝔽2)×C15111yescharacteristic
551C2×C42−1+4×C15111yescharacteristic
552C8—22no—
553C8—22no—
554C8—41no—
555C8—41no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22#525×C15111yescharacteristic
564C22#532×C15111yescharacteristic
565C22#537×C15111yescharacteristic
566C22#576×C15111yescharacteristic
567C22#577×C15111yescharacteristic
568C22#577×C15111yescharacteristic
569C22#578×C15111yescharacteristic
570C4—41no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4#551×C15111yescharacteristic
584C4#552×C15111yescharacteristic
585C4#553×C15111yescharacteristic
586C4#556×C15111yescharacteristic
587C2—82no—
588C2#2601×C15111yescharacteristic
589C2#3118×C15111yescharacteristic
590C2#3120×C15111yescharacteristic
591C2#3174×C15111yescharacteristic
592C2#3175×C15111yescharacteristic
593C2#3257×C15111yescharacteristic
594C2#3258×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ #376×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2645×C151C2semidirect
3. #2088×C151C2semidirect
4. #2068×C151C2semidirect
8. #1942×C151C2semidirect
10. #1935×C151C2semidirect
11. #1928×C151C2semidirect
12. #1920×C151C2semidirect
15. #1768×C151C2semidirect
297. #29441C151direct (N × H)
298. C151#29441direct (N × H)
299. #2645C2×C151semidirect
301. #2088C2×C151semidirect
302. #2068C2×C151semidirect
306. #1942C2×C151semidirect
308. #1935C2×C151semidirect
309. #1928C2×C151semidirect
310. #1920C2×C151semidirect
313. #1768C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2645×C1512
#2319×C1512
#2088×C1512
#2068×C1512
#2067×C1512
#2055×C1512
#1968×C1512
#1942×C1512
#1936×C1512
#1935×C1512
#1928×C1512
#1920×C1512
#1877×C1512
#1862×C1512
#1768×C1512
#29441151