Finite Group Databasebeta

← C151×#23065 #50327990

Subgroups — C151×#23065 #50327990

Order 38656.

774 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#478×C151C211yesmaximal, characteristic
2#2370×C151C211yesmaximal, characteristic, complemented
3#2357×C151C211yesmaximal, characteristic
4#1991×C151C211yesmaximal, characteristic, complemented
5#1949×C151C211yesmaximal, characteristic, complemented
6#1934×C151C211yesmaximal, characteristic
7#1934×C151C211yesmaximal, characteristic
8#1926×C151C211yesmaximal, characteristic
9#1925×C151C211yesmaximal, characteristic
10#1921×C151C211yesmaximal, characteristic, complemented
11#1919×C151C211yesmaximal, characteristic, complemented
12C4×#107×C151C211yesmaximal, characteristic, complemented
13C4×#106×C151C211yesmaximal, characteristic, complemented
14C8×C4⋊C4×C151C211yesmaximal, characteristic, complemented
15C4×#102×C151C211yesmaximal, characteristic
16C2×#125×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18#478×C151C418yescomplemented
19C2×#107×C151C2211yescharacteristic
20C2×#107×C151C2211yescharacteristic
21C2×#106×C151C2211yescharacteristic
22C2×#106×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×C4×C8×C151C2211yescharacteristic
29C2×C4×C8×C151C2211yescharacteristic
30C2×C4×C8×C151C2211yescharacteristic
31#390×C151C2211yescharacteristic
32#390×C151C2211yescharacteristic
33#389×C151—21no—
34#389×C151C2211yescharacteristic
35#389×C151C2211yescharacteristic
36#388×C151—21no—
37#388×C151—21no—
38#387×C151—21no—
39#387×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×D4×C151C2311yescharacteristic
61C23×C4×C151—21no—
62C22×C8×C151C2311yescharacteristic
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66#125×C151—22no—
67#125×C151C2×C414yes—
68C4×D4×C151—22no—
69C4×D4×C151C2×C414yes—
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×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#106×C151—22no—
99#106×C151C2×C414yes—
100C4⋊C8×C151C2×C414yes—
101#102×C151—22no—
102#102×C151—22no—
103#102×C151C2×C414yes—
104#102×C151C2×C414yes—
105C4×C8×C151—22no—
106C4×C8×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×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151C22×C412yes—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—24no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—81no—
135C22×C4×C151—81no—
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2411yescharacteristic
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×C151C22×C412yes—
153C2×C8×C151C22×C412yes—
154C2×C8×C151#4112yes—
155C4⋊C4×C151—24no—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
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×C151C22×C412yes—
172C4⋊C4×C151C22×C412yes—
173C4⋊C4×C151C22×C412yes—
174C4⋊C4×C151#4112yes—
175C22⋊C4×C151—24no—
176C22⋊C4×C151—42no—
177C22⋊C4×C151—42no—
178C22⋊C4×C151—81no—
179C22⋊C4×C151—81no—
180C42×C151—21no—
181C42×C151—21no—
182C42×C151—21no—
183C42×C151—21no—
184C42×C151—42no—
185C42×C151—81no—
186C42×C151—81no—
187C42×C151—81no—
188C42×C151—81no—
189C42×C151C22×C412yes—
190C42×C151#4112yes—
191C23×C151—22no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151—41no—
198C23×C151C22×D411yescharacteristic
199D4×C151—22no—
200D4×C151—22no—
201D4×C151—41no—
202D4×C151—41no—
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—21no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—22no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
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—41no—
238C2×C4×C151—84no—
239C2×C4×C151C4×D412yes—
240C2×C4×C151C4×D412yes—
241C2×C4×C151#13512yes—
242C2×C4×C151#13512yes—
243C2×C4×C151C23×C411yescharacteristic
244C2×C4×C151C2×#4111yescharacteristic
245C2×C4×C151C2×#4111yescharacteristic
246C2×C4×C151C2×#4111yescharacteristic
247C2×C4×C1512−1+411yescharacteristic
248C2×C4×C1512−1+411yescharacteristic
249C8×C151—22no—
250C8×C151—22no—
251C8×C151—22no—
252C8×C151—41no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—42no—
256C22×C151—81no—
257C22×C151—81no—
258C22×C151—81no—
259C22×C151—81no—
260C22×C151C2×C4×D411yescharacteristic
261C22×C151#54711yescharacteristic
262C22×C151#54811yescharacteristic
263C22×C151C2×#13511yescharacteristic
264C22×C151C2×#13511yescharacteristic
265C22×C151#57611yescharacteristic
266C22×C151#57711yescharacteristic
267C4×C151—22no—
268C4×C151—22no—
269C4×C151—22no—
270C4×C151—22no—
271C4×C151—41no—
272C4×C151—41no—
273C4×C151—42no—
274C4×C151—42no—
275C4×C151—42no—
276C4×C151—42no—
277C4×C151—81no—
278C4×C151—81no—
279C4×C151—81no—
280C4×C151C4×#4111yescharacteristic
281C4×C151#51911yescharacteristic
282C4×C151#55211yescharacteristic
283C4×C151#55611yescharacteristic
284C2×C151—82no—
285C2×C151#236211yescharacteristic
286C2×C151C4×#13511yescharacteristic
287C2×C151#294611yescharacteristic
288C2×C151#333711yescharacteristic
289C2×C151#333911yescharacteristic
290C2×C151#336111yescharacteristic
291C2×C151#336511yescharacteristic
292#23065C15111yesmaximal, characteristic, direct product factor, Sylow
293C151#2306511yescharacteristic, direct product factor, Sylow
294C2×#478C2×C15111yescharacteristic
295#2370C2×C15111yescharacteristic, complemented
296#2357C2×C15111yescharacteristic
297#1991C2×C15111yescharacteristic, complemented
298#1949C2×C15111yescharacteristic, complemented
299#1934C2×C15111yescharacteristic
300#1934C2×C15111yescharacteristic
301#1926C2×C15111yescharacteristic
302#1925C2×C15111yescharacteristic
303#1921C2×C15111yescharacteristic, complemented
304#1919C2×C15111yescharacteristic, complemented
305C4×#107C2×C15111yescharacteristic, complemented
306C4×#106C2×C15111yescharacteristic, complemented
307C8×C4⋊C4C2×C15111yescharacteristic, complemented
308C4×#102C2×C15111yescharacteristic
309C2×#125C22×C15111yescharacteristic
310C2×C4×D4C22×C15111yescharacteristic
311#478C4×C15118yescomplemented
312C2×#107C22×C15111yescharacteristic
313C2×#107C22×C15111yescharacteristic
314C2×#106C22×C15111yescharacteristic
315C2×#106C22×C15111yescharacteristic
316C2×C4⋊C8C22×C15111yescharacteristic
317C2×#102C22×C15111yescharacteristic
318C2×#102C22×C15111yescharacteristic
319C2×#102C22×C15111yescharacteristic
320C2×#102C22×C15111yescharacteristic
321C2×C4×C8C22×C15111yescharacteristic
322C2×C4×C8C22×C15111yescharacteristic
323C2×C4×C8C22×C15111yescharacteristic
324#390C22×C15111yescharacteristic
325#390C22×C15111yescharacteristic
326#389—21no—
327#389C22×C15111yescharacteristic
328#389C22×C15111yescharacteristic
329#388—21no—
330#388—21no—
331#387—21no—
332#387—21no—
333#382C22×C15111yescharacteristic
334#381—21no—
335C4×C4⋊C4—21no—
336C4×C4⋊C4C22×C15111yescharacteristic
337C4×C4⋊C4C22×C15111yescharacteristic
338C4×C4⋊C4C22×C15111yescharacteristic
339C4×C4⋊C4C22×C15111yescharacteristic
340C4×C4⋊C4C22×C15111yescharacteristic
341C4×C4⋊C4C22×C15111yescharacteristic
342C4×C22⋊C4—21no—
343#340C22×C15111yescharacteristic
344#340C22×C15111yescharacteristic
345#340C22×C15111yescharacteristic
346#340C22×C15111yescharacteristic
347#340C22×C15111yescharacteristic
348#340C22×C15111yescharacteristic
349#340C22×C15111yescharacteristic
350#340C22×C15111yescharacteristic
351#336C22×C15111yescharacteristic
352#336C22×C15111yescharacteristic
353C22×D4C23×C15111yescharacteristic
354C23×C4—21no—
355C22×C8C23×C15111yescharacteristic
356C22×C8C23×C15111yescharacteristic
357C22×C8C23×C15111yescharacteristic
358C22×C8C23×C15111yescharacteristic
359#125—22no—
360#125C2×C4×C15114yes—
361C4×D4—22no—
362C4×D4C2×C4×C15114yes—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C15111yescharacteristic
368C2×C4⋊C4D4×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×C4⋊C4C23×C15111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C23×C15111yescharacteristic
387C2×C42C23×C15111yescharacteristic
388C2×C42C23×C15111yescharacteristic
389#107—22no—
390#107C2×C4×C15114yes—
391#106—22no—
392#106C2×C4×C15114yes—
393C4⋊C8C2×C4×C15114yes—
394#102—22no—
395#102—22no—
396#102C2×C4×C15114yes—
397#102C2×C4×C15114yes—
398C4×C8—22no—
399C4×C8—22no—
400C4×C8—22no—
401#95—21no—
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#95D4×C15111yescharacteristic
411#95D4×C15111yescharacteristic
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C22×C4×C15112yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4C2×D4×C15111yescharacteristic
430C22×C4C2×D4×C15111yescharacteristic
431C22×C4C2×D4×C15111yescharacteristic
432C22×C4C2×D4×C15111yescharacteristic
433C22×C4C2×D4×C15111yescharacteristic
434C22×C4C2×D4×C15111yescharacteristic
435C22×C4C24×C15111yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8C22×C4×C15112yes—
446C2×C8C22×C4×C15112yes—
447C2×C8#41×C15112yes—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—22no—
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—21no—
461C4⋊C4—21no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4C22×C4×C15112yes—
465C4⋊C4C22×C4×C15112yes—
466C4⋊C4C22×C4×C15112yes—
467C4⋊C4#41×C15112yes—
468C22⋊C4—24no—
469C22⋊C4—42no—
470C22⋊C4—42no—
471C22⋊C4—81no—
472C22⋊C4—81no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—42no—
478C42—81no—
479C42—81no—
480C42—81no—
481C42—81no—
482C42C22×C4×C15112yes—
483C42#41×C15112yes—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C22×D4×C15111yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
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—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—84no—
532C2×C4C4×D4×C15112yes—
533C2×C4C4×D4×C15112yes—
534C2×C4#135×C15112yes—
535C2×C4#135×C15112yes—
536C2×C4C23×C4×C15111yescharacteristic
537C2×C4C2×#41×C15111yescharacteristic
538C2×C4C2×#41×C15111yescharacteristic
539C2×C4C2×#41×C15111yescharacteristic
540C2×C42−1+4×C15111yescharacteristic
541C2×C42−1+4×C15111yescharacteristic
542C8—22no—
543C8—22no—
544C8—22no—
545C8—41no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×C4×D4×C15111yescharacteristic
554C22#547×C15111yescharacteristic
555C22#548×C15111yescharacteristic
556C22C2×#135×C15111yescharacteristic
557C22C2×#135×C15111yescharacteristic
558C22#576×C15111yescharacteristic
559C22#577×C15111yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4C4×#41×C15111yescharacteristic
574C4#519×C15111yescharacteristic
575C4#552×C15111yescharacteristic
576C4#556×C15111yescharacteristic
577C2—82no—
578C2#2362×C15111yescharacteristic
579C2C4×#135×C15111yescharacteristic
580C2#2946×C15111yescharacteristic
581C2#3337×C15111yescharacteristic
582C2#3339×C15111yescharacteristic
583C2#3361×C15111yescharacteristic
584C2#3365×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. #2370×C151C2semidirect
4. #1991×C151C2semidirect
5. #1949×C151C2semidirect
10. #1921×C151C2semidirect
11. #1919×C151C2semidirect
12. C4×#107×C151C2semidirect
13. C4×#106×C151C2semidirect
14. C8×C4⋊C4×C151C2semidirect
18. #478×C151C4semidirect
292. #23065C151direct (N × H)
293. C151#23065direct (N × H)
295. #2370C2×C151semidirect
297. #1991C2×C151semidirect
298. #1949C2×C151semidirect
303. #1921C2×C151semidirect
304. #1919C2×C151semidirect
305. C4×#107C2×C151semidirect
306. C4×#106C2×C151semidirect
307. C8×C4⋊C4C2×C151semidirect
311. #478C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#478×C1512
#2370×C1512
#2357×C1512
#1991×C1512
#1949×C1512
#1934×C1512
#1926×C1512
#1925×C1512
#1921×C1512
#1919×C1512
C4×#107×C1512
C4×#106×C1512
C8×C4⋊C4×C1512
C4×#102×C1512
#23065151