Finite Group Databasebeta

← C151×#23079 #50328004

Subgroups — C151×#23079 #50328004

Order 38656.

778 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C151C211yesmaximal, characteristic
2#2369×C151C211yesmaximal, characteristic, complemented
3#2357×C151C211yesmaximal, characteristic
4#1993×C151C211yesmaximal, characteristic, complemented
5#1949×C151C211yesmaximal, characteristic, complemented
6#1936×C151C211yesmaximal, characteristic
7#1934×C151C211yesmaximal, characteristic
8#1926×C151C211yesmaximal, characteristic
9#1925×C151C211yesmaximal, characteristic
10#1921×C151C211yesmaximal, characteristic, complemented
11#1918×C151C211yesmaximal, characteristic, complemented
12#1776×C151C211yesmaximal, characteristic, complemented
13C4×#107×C151C211yesmaximal, characteristic, complemented
14#1771×C151C211yesmaximal, characteristic, complemented
15#1762×C151C211yesmaximal, characteristic
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18#474×C151C418yescomplemented
19C2×#107×C151C2211yescharacteristic
20C2×#107×C151C2211yescharacteristic
21C2×#107×C151C2211yescharacteristic
22C2×#106×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×#97×C151C2211yescharacteristic
29C2×#97×C151C2211yescharacteristic
30C2×C4×C8×C151C2211yescharacteristic
31#391×C151—21no—
32#391×C151—21no—
33#390×C151C2211yescharacteristic
34#390×C151C2211yescharacteristic
35#389×C151—21no—
36#389×C151C2211yescharacteristic
37#389×C151C2211yescharacteristic
38#388×C151—21no—
39#388×C151—21no—
40#382×C151C2211yescharacteristic
41#381×C151—21no—
42C4×C4⋊C4×C151—21no—
43C4×C4⋊C4×C151C2211yescharacteristic
44C4×C4⋊C4×C151C2211yescharacteristic
45C4×C4⋊C4×C151C2211yescharacteristic
46C4×C4⋊C4×C151C2211yescharacteristic
47C4×C4⋊C4×C151C2211yescharacteristic
48C4×C4⋊C4×C151C2211yescharacteristic
49C4×C22⋊C4×C151—21no—
50#340×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60C22×Q8×C151—21no—
61C22×D4×C151C2311yescharacteristic
62C23×C4×C151—21no—
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2311yescharacteristic
67C4⋊Q8×C151—22no—
68C4⋊Q8×C151C2×C414yes—
69C4×D4×C151—22no—
70C4×D4×C151C2×C414yes—
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×C151C2311yescharacteristic
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×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—21no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—21no—
88C2×C42×C151—21no—
89C2×C42×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151—21no—
92C2×C42×C151—21no—
93C2×C42×C151C2311yescharacteristic
94C2×C42×C151C2311yescharacteristic
95C2×C42×C151C2311yescharacteristic
96#107×C151—22no—
97#107×C151C2×C414yes—
98#107×C151C2×C414yes—
99#106×C151—22no—
100C4⋊C8×C151C2×C414yes—
101#102×C151—22no—
102#102×C151—22no—
103#102×C151C2×C414yes—
104#102×C151C2×C414yes—
105#97×C151—22no—
106#97×C151—22no—
107C4×C8×C151—22no—
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×C151—21no—
117#95×C151D411yescharacteristic
118#95×C151D411yescharacteristic
119C24×C151—21no—
120C2×Q8×C151—24no—
121C2×Q8×C151—81no—
122C2×Q8×C151—81no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—21no—
127C2×D4×C151—21no—
128C2×D4×C151C22×C412yes—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—24no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—81no—
138C22×C4×C151—81no—
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2411yescharacteristic
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—
153C2×C8×C151—21no—
154C2×C8×C151—21no—
155C2×C8×C151C22×C412yes—
156C2×C8×C151C22×C412yes—
157C2×C8×C151#4112yes—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—22no—
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—21no—
170C4⋊C4×C151—41no—
171C4⋊C4×C151—81no—
172C4⋊C4×C151—81no—
173C4⋊C4×C151C22×C412yes—
174C4⋊C4×C151C22×C412yes—
175C4⋊C4×C151C22×C412yes—
176C4⋊C4×C151#4112yes—
177C22⋊C4×C151—24no—
178C22⋊C4×C151—42no—
179C22⋊C4×C151—42no—
180C22⋊C4×C151—81no—
181C22⋊C4×C151—81no—
182C42×C151—21no—
183C42×C151—21no—
184C42×C151—21no—
185C42×C151—21no—
186C42×C151—42no—
187C42×C151—81no—
188C42×C151—81no—
189C42×C151—81no—
190C42×C151—81no—
191C42×C151C22×C412yes—
192C42×C151#4112yes—
193C23×C151—22no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151—41no—
198C23×C151—41no—
199C23×C151—41no—
200C23×C151C22×D411yescharacteristic
201Q8×C151—84no—
202D4×C151—22no—
203D4×C151—22no—
204D4×C151—41no—
205D4×C151—41no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—22no—
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—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—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—84no—
243C2×C4×C151C4×D412yes—
244C2×C4×C151C4×D412yes—
245C2×C4×C151#13712yes—
246C2×C4×C151C23×C411yescharacteristic
247C2×C4×C151C2×#4111yescharacteristic
248C2×C4×C151C2×#4111yescharacteristic
249C2×C4×C151C2×#4111yescharacteristic
250C2×C4×C1512−1+411yescharacteristic
251C2×C4×C1512−1+411yescharacteristic
252C8×C151—22no—
253C8×C151—22no—
254C8×C151—22no—
255C8×C151—41no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—42no—
259C22×C151—81no—
260C22×C151—81no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151C2×C4×D411yescharacteristic
264C22×C151#54711yescharacteristic
265C22×C151#54811yescharacteristic
266C22×C151C2×#13711yescharacteristic
267C22×C151#57511yescharacteristic
268C22×C151#57611yescharacteristic
269C22×C151#57611yescharacteristic
270C4×C151—22no—
271C4×C151—22no—
272C4×C151—22no—
273C4×C151—41no—
274C4×C151—41no—
275C4×C151—41no—
276C4×C151—42no—
277C4×C151—42no—
278C4×C151—42no—
279C4×C151—42no—
280C4×C151—81no—
281C4×C151—81no—
282C4×C151—81no—
283C4×C151C4×#4111yescharacteristic
284C4×C151#51911yescharacteristic
285C4×C151#55211yescharacteristic
286C4×C151#55611yescharacteristic
287C2×C151—82no—
288C2×C151#236211yescharacteristic
289C2×C151C4×#13711yescharacteristic
290C2×C151#294811yescharacteristic
291C2×C151#334611yescharacteristic
292C2×C151#334711yescharacteristic
293C2×C151#337011yescharacteristic
294C2×C151#337511yescharacteristic
295#23079C15111yesmaximal, characteristic, direct product factor, Sylow
296C151#2307911yescharacteristic, direct product factor, Sylow
297C2×#474C2×C15111yescharacteristic
298#2369C2×C15111yescharacteristic, complemented
299#2357C2×C15111yescharacteristic
300#1993C2×C15111yescharacteristic, complemented
301#1949C2×C15111yescharacteristic, complemented
302#1936C2×C15111yescharacteristic
303#1934C2×C15111yescharacteristic
304#1926C2×C15111yescharacteristic
305#1925C2×C15111yescharacteristic
306#1921C2×C15111yescharacteristic, complemented
307#1918C2×C15111yescharacteristic, complemented
308#1776C2×C15111yescharacteristic, complemented
309C4×#107C2×C15111yescharacteristic, complemented
310#1771C2×C15111yescharacteristic, complemented
311#1762C2×C15111yescharacteristic
312C2×C4⋊Q8C22×C15111yescharacteristic
313C2×C4×D4C22×C15111yescharacteristic
314#474C4×C15118yescomplemented
315C2×#107C22×C15111yescharacteristic
316C2×#107C22×C15111yescharacteristic
317C2×#107C22×C15111yescharacteristic
318C2×#106C22×C15111yescharacteristic
319C2×C4⋊C8C22×C15111yescharacteristic
320C2×#102C22×C15111yescharacteristic
321C2×#102C22×C15111yescharacteristic
322C2×#102C22×C15111yescharacteristic
323C2×#102C22×C15111yescharacteristic
324C2×#97C22×C15111yescharacteristic
325C2×#97C22×C15111yescharacteristic
326C2×C4×C8C22×C15111yescharacteristic
327#391—21no—
328#391—21no—
329#390C22×C15111yescharacteristic
330#390C22×C15111yescharacteristic
331#389—21no—
332#389C22×C15111yescharacteristic
333#389C22×C15111yescharacteristic
334#388—21no—
335#388—21no—
336#382C22×C15111yescharacteristic
337#381—21no—
338C4×C4⋊C4—21no—
339C4×C4⋊C4C22×C15111yescharacteristic
340C4×C4⋊C4C22×C15111yescharacteristic
341C4×C4⋊C4C22×C15111yescharacteristic
342C4×C4⋊C4C22×C15111yescharacteristic
343C4×C4⋊C4C22×C15111yescharacteristic
344C4×C4⋊C4C22×C15111yescharacteristic
345C4×C22⋊C4—21no—
346#340C22×C15111yescharacteristic
347#340C22×C15111yescharacteristic
348#340C22×C15111yescharacteristic
349#340C22×C15111yescharacteristic
350#340C22×C15111yescharacteristic
351#340C22×C15111yescharacteristic
352#340C22×C15111yescharacteristic
353#340C22×C15111yescharacteristic
354#336C22×C15111yescharacteristic
355#336C22×C15111yescharacteristic
356C22×Q8—21no—
357C22×D4C23×C15111yescharacteristic
358C23×C4—21no—
359C22×C8C23×C15111yescharacteristic
360C22×C8C23×C15111yescharacteristic
361C22×C8C23×C15111yescharacteristic
362C22×C8C23×C15111yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8C2×C4×C15114yes—
365C4×D4—22no—
366C4×D4C2×C4×C15114yes—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4D4×C15111yescharacteristic
371C2×C4⋊C4D4×C15111yescharacteristic
372C2×C4⋊C4C23×C15111yescharacteristic
373C2×C4⋊C4C23×C15111yescharacteristic
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C4⋊C4C23×C15111yescharacteristic
376C2×C4⋊C4C23×C15111yescharacteristic
377C2×C4⋊C4C23×C15111yescharacteristic
378C2×C4⋊C4C23×C15111yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C15111yescharacteristic
390C2×C42C23×C15111yescharacteristic
391C2×C42C23×C15111yescharacteristic
392#107—22no—
393#107C2×C4×C15114yes—
394#107C2×C4×C15114yes—
395#106—22no—
396C4⋊C8C2×C4×C15114yes—
397#102—22no—
398#102—22no—
399#102C2×C4×C15114yes—
400#102C2×C4×C15114yes—
401#97—22no—
402#97—22no—
403C4×C8—22no—
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#95D4×C15111yescharacteristic
414#95D4×C15111yescharacteristic
415C24—21no—
416C2×Q8—24no—
417C2×Q8—81no—
418C2×Q8—81no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C22×C4×C15112yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4C2×D4×C15111yescharacteristic
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C2×D4×C15111yescharacteristic
438C22×C4C2×D4×C15111yescharacteristic
439C22×C4C2×D4×C15111yescharacteristic
440C22×C4C2×D4×C15111yescharacteristic
441C22×C4C24×C15111yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8C22×C4×C15112yes—
452C2×C8C22×C4×C15112yes—
453C2×C8#41×C15112yes—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4C22×C4×C15112yes—
470C4⋊C4C22×C4×C15112yes—
471C4⋊C4C22×C4×C15112yes—
472C4⋊C4#41×C15112yes—
473C22⋊C4—24no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—42no—
483C42—81no—
484C42—81no—
485C42—81no—
486C42—81no—
487C42C22×C4×C15112yes—
488C42#41×C15112yes—
489C23—22no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23C22×D4×C15111yescharacteristic
497Q8—84no—
498D4—22no—
499D4—22no—
500D4—41no—
501D4—41no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
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—84no—
539C2×C4C4×D4×C15112yes—
540C2×C4C4×D4×C15112yes—
541C2×C4#137×C15112yes—
542C2×C4C23×C4×C15111yescharacteristic
543C2×C4C2×#41×C15111yescharacteristic
544C2×C4C2×#41×C15111yescharacteristic
545C2×C4C2×#41×C15111yescharacteristic
546C2×C42−1+4×C15111yescharacteristic
547C2×C42−1+4×C15111yescharacteristic
548C8—22no—
549C8—22no—
550C8—22no—
551C8—41no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22C2×C4×D4×C15111yescharacteristic
560C22#547×C15111yescharacteristic
561C22#548×C15111yescharacteristic
562C22C2×#137×C15111yescharacteristic
563C22#575×C15111yescharacteristic
564C22#576×C15111yescharacteristic
565C22#576×C15111yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—42no—
570C4—42no—
571C4—42no—
572C4—42no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C4×#41×C15111yescharacteristic
580C4#519×C15111yescharacteristic
581C4#552×C15111yescharacteristic
582C4#556×C15111yescharacteristic
583C2—82no—
584C2#2362×C15111yescharacteristic
585C2C4×#137×C15111yescharacteristic
586C2#2948×C15111yescharacteristic
587C2#3346×C15111yescharacteristic
588C2#3347×C15111yescharacteristic
589C2#3370×C15111yescharacteristic
590C2#3375×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2369×C151C2semidirect
4. #1993×C151C2semidirect
5. #1949×C151C2semidirect
10. #1921×C151C2semidirect
11. #1918×C151C2semidirect
12. #1776×C151C2semidirect
13. C4×#107×C151C2semidirect
14. #1771×C151C2semidirect
18. #474×C151C4semidirect
295. #23079C151direct (N × H)
296. C151#23079direct (N × H)
298. #2369C2×C151semidirect
300. #1993C2×C151semidirect
301. #1949C2×C151semidirect
306. #1921C2×C151semidirect
307. #1918C2×C151semidirect
308. #1776C2×C151semidirect
309. C4×#107C2×C151semidirect
310. #1771C2×C151semidirect
314. #474C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1512
#2369×C1512
#2357×C1512
#1993×C1512
#1949×C1512
#1936×C1512
#1934×C1512
#1926×C1512
#1925×C1512
#1921×C1512
#1918×C1512
#1776×C1512
C4×#107×C1512
#1771×C1512
#1762×C1512
#23079151