Finite Group Databasebeta

← C41×#14231 #23790432

Subgroups — C41×#14231 #23790432

Order 10496.

1670 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#399C211yesmaximal, characteristic
2C2×C41×#388C212yesmaximal
3C2×C41×#388C211yesmaximal, characteristic
4C2×C41×#387C212yesmaximal, complemented
5C2×C4×C4⋊C4×C41C211yesmaximal, characteristic, complemented
6C41×#1445C211yesmaximal, characteristic, complemented
7C41×#1444C211yesmaximal, characteristic, complemented
8C41×#1439C211yesmaximal, characteristic
9C41×#1437C212yesmaximal
10C41×C4⋊#95C212yesmaximal, complemented
11C4×#95×C41C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C41C2211yescharacteristic
13C22×C4⋊C4×C41C2211yescharacteristic
14C22×C4⋊C4×C41C2212yes—
15C22×C4⋊C4×C41C2211yescharacteristic
16C22×C4⋊C4×C41C2212yes—
17C22×C22⋊C4×C41C2211yescharacteristic
18C22×C22⋊C4×C41C2211yescharacteristic
19C22×C22⋊C4×C41C2212yes—
20C22×C22⋊C4×C41C2212yes—
21C22×C22⋊C4×C41C2211yescharacteristic
22C22×C42×C41C2212yes—
23C22×C42×C41C2212yes—
24C22×C42×C41C2211yescharacteristic
25C41×#399C418yescomplemented
26C41×#388—24no—
27C41×#388—28no—
28C41×#387—28no—
29C4×C4⋊C4×C41—24no—
30C2×#95×C41C2212yes—
31C2×#95×C41C2212yes—
32C2×#95×C41C2212yes—
33C2×#95×C41C2212yes—
34C2×#95×C41C2211yescharacteristic
35C2×#95×C41C2212yes—
36C2×#95×C41C2211yescharacteristic
37C2×#95×C41C2211yescharacteristic
38C2×#95×C41C2211yescharacteristic
39C2×#95×C41C2212yes—
40C25×C41C2311yescharacteristic
41C23×C4×C41C2311yescharacteristic
42C23×C4×C41C2311yescharacteristic
43C23×C4×C41C2312yes—
44C23×C4×C41C2311yescharacteristic
45C23×C4×C41C2312yes—
46C23×C4×C41C2312yes—
47C23×C4×C41C2311yescharacteristic
48C23×C4×C41C2312yes—
49C23×C4×C41C2311yescharacteristic
50C23×C4×C41C2311yescharacteristic
51C2×C4⋊C4×C41—22no—
52C2×C4⋊C4×C41—22no—
53C2×C4⋊C4×C41—24no—
54C2×C4⋊C4×C41—24no—
55C2×C4⋊C4×C41—22no—
56C2×C4⋊C4×C41—24no—
57C2×C4⋊C4×C41—24no—
58C2×C4⋊C4×C41—24no—
59C2×C4⋊C4×C41—22no—
60C2×C4⋊C4×C41—24no—
61C2×C4⋊C4×C41—42no—
62C2×C4⋊C4×C41C2×C414yes—
63C2×C4⋊C4×C41C2×C418yes—
64C2×C22⋊C4×C41—24no—
65C2×C22⋊C4×C41—22no—
66C2×C22⋊C4×C41—22no—
67C2×C22⋊C4×C41—24no—
68C2×C22⋊C4×C41—24no—
69C2×C22⋊C4×C41—22no—
70C2×C22⋊C4×C41—22no—
71C2×C22⋊C4×C41—24no—
72C2×C22⋊C4×C41—24no—
73C2×C22⋊C4×C41—24no—
74C2×C22⋊C4×C41—42no—
75C2×C22⋊C4×C41C2×C418yes—
76C2×C22⋊C4×C41C2×C414yes—
77C2×C42×C41—24no—
78C2×C42×C41—24no—
79C2×C42×C41—24no—
80C2×C42×C41—24no—
81C2×C42×C41—24no—
82C2×C42×C41—24no—
83C2×C42×C41—42no—
84C2×C42×C41D414yes—
85#95×C41—24no—
86#95×C41—24no—
87#95×C41—24no—
88#95×C41—24no—
89#95×C41—24no—
90#95×C41—22no—
91#95×C41—22no—
92#95×C41—22no—
93#95×C41C2×C414yes—
94#95×C41D418yes—
95C24×C41—21no—
96C24×C41—22no—
97C24×C41—21no—
98C24×C41—22no—
99C24×C41—22no—
100C24×C41—22no—
101C24×C41—21no—
102C24×C41—21no—
103C24×C41—21no—
104C24×C41—21no—
105C24×C41C22×C412yes—
106C24×C41C2411yescharacteristic
107C22×C4×C41—22no—
108C22×C4×C41—22no—
109C22×C4×C41—22no—
110C22×C4×C41—22no—
111C22×C4×C41—22no—
112C22×C4×C41—22no—
113C22×C4×C41—21no—
114C22×C4×C41—22no—
115C22×C4×C41—22no—
116C22×C4×C41—21no—
117C22×C4×C41—21no—
118C22×C4×C41—21no—
119C22×C4×C41—22no—
120C22×C4×C41—22no—
121C22×C4×C41—22no—
122C22×C4×C41—22no—
123C22×C4×C41—22no—
124C22×C4×C41—21no—
125C22×C4×C41—22no—
126C22×C4×C41—22no—
127C22×C4×C41—22no—
128C22×C4×C41—22no—
129C22×C4×C41—22no—
130C22×C4×C41—21no—
131C22×C4×C41—22no—
132C22×C4×C41—22no—
133C22×C4×C41—22no—
134C22×C4×C41—22no—
135C22×C4×C41—22no—
136C22×C4×C41—22no—
137C22×C4×C41—22no—
138C22×C4×C41—22no—
139C22×C4×C41—22no—
140C22×C4×C41—22no—
141C22×C4×C41—21no—
142C22×C4×C41—22no—
143C22×C4×C41—21no—
144C22×C4×C41—22no—
145C22×C4×C41—22no—
146C22×C4×C41—22no—
147C22×C4×C41—21no—
148C22×C4×C41—21no—
149C22×C4×C41—21no—
150C22×C4×C41—21no—
151C22×C4×C41C22×C414yes—
152C22×C4×C41C22×C412yes—
153C22×C4×C41C22×C412yes—
154C22×C4×C41C22×C414yes—
155C22×C4×C41C2×D414yes—
156C22×C4×C41C2×D414yes—
157C22×C4×C41C2×D412yes—
158C22×C4×C41C2×D412yes—
159C22×C4×C41C2×D414yes—
160C22×C4×C41C2×D412yes—
161C22×C4×C41#4114yes—
162C22×C4×C41#4112yes—
163C22×C4×C41#4114yes—
164C22×C4×C41#4114yes—
165C4⋊C4×C41—28no—
166C4⋊C4×C41—28no—
167C4⋊C4×C41—216no—
168C4⋊C4×C41—48no—
169C4⋊C4×C41—44no—
170C22⋊C4×C41—28no—
171C22⋊C4×C41—216no—
172C22⋊C4×C41—48no—
173C22⋊C4×C41—44no—
174C22⋊C4×C41—44no—
175C42×C41—28no—
176C42×C41—48no—
177C42×C41—48no—
178C23×C41—22no—
179C23×C41—24no—
180C23×C41—24no—
181C23×C41—22no—
182C23×C41—22no—
183C23×C41—41no—
184C23×C41—41no—
185C23×C41—42no—
186C23×C41—41no—
187C23×C41—41no—
188C23×C41—42no—
189C23×C41—41no—
190C23×C41—41no—
191C23×C41—41no—
192C23×C41—41no—
193C23×C41—42no—
194C23×C41—42no—
195C23×C41—42no—
196C23×C41—42no—
197C23×C41—42no—
198C23×C41—42no—
199C23×C41—42no—
200C23×C41—42no—
201C23×C41C23×C411yescharacteristic
202C23×C41C22×D411yescharacteristic
203C23×C41C22×D412yes—
204C23×C41C2×#4111yescharacteristic
205C23×C41C2×#4112yes—
206C23×C41C2×#4112yes—
207C23×C41C2×#4112yes—
208C23×C41H(5,𝔽2)11yescharacteristic
209C23×C412−1+411yescharacteristic
210C23×C412−1+411yescharacteristic
211C23×C412−1+411yescharacteristic
212C2×C4×C41—24no—
213C2×C4×C41—24no—
214C2×C4×C41—24no—
215C2×C4×C41—22no—
216C2×C4×C41—22no—
217C2×C4×C41—22no—
218C2×C4×C41—24no—
219C2×C4×C41—22no—
220C2×C4×C41—22no—
221C2×C4×C41—22no—
222C2×C4×C41—24no—
223C2×C4×C41—24no—
224C2×C4×C41—24no—
225C2×C4×C41—24no—
226C2×C4×C41—24no—
227C2×C4×C41—24no—
228C2×C4×C41—24no—
229C2×C4×C41—24no—
230C2×C4×C41—22no—
231C2×C4×C41—24no—
232C2×C4×C41—24no—
233C2×C4×C41—24no—
234C2×C4×C41—24no—
235C2×C4×C41—24no—
236C2×C4×C41—24no—
237C2×C4×C41—24no—
238C2×C4×C41—24no—
239C2×C4×C41—24no—
240C2×C4×C41—24no—
241C2×C4×C41—42no—
242C2×C4×C41—42no—
243C2×C4×C41—42no—
244C2×C4×C41—41no—
245C2×C4×C41—42no—
246C2×C4×C41—41no—
247C2×C4×C41—42no—
248C2×C4×C41—42no—
249C2×C4×C41—42no—
250C2×C4×C41—42no—
251C2×C4×C41—42no—
252C2×C4×C41—42no—
253C2×C4×C41—42no—
254C2×C4×C41—42no—
255C2×C4×C41—42no—
256C2×C4×C41—41no—
257C2×C4×C41—41no—
258C2×C4×C41—41no—
259C2×C4×C41—41no—
260C2×C4×C41—41no—
261C2×C4×C41—41no—
262C2×C4×C41—42no—
263C2×C4×C41—42no—
264C2×C4×C41—42no—
265C2×C4×C41—42no—
266C2×C4×C41C4×D418yes—
267C2×C4×C41C4×D414yes—
268C2×C4×C41#12314yes—
269C2×C4×C41#12714yes—
270#14231C4111yesmaximal, characteristic, direct product factor, Sylow
271C22×C41—42no—
272C22×C41—42no—
273C22×C41—44no—
274C22×C41—44no—
275C22×C41—42no—
276C22×C41—81no—
277C22×C41—81no—
278C22×C41—81no—
279C22×C41—82no—
280C22×C41—82no—
281C22×C41—81no—
282C22×C41C2×C4×D411yescharacteristic
283C22×C41C2×C4×D412yes—
284C22×C41C4×#4112yes—
285C22×C41#51911yescharacteristic
286C22×C41#52011yescharacteristic
287C22×C41C2×#12311yescharacteristic
288C22×C41#52511yescharacteristic
289C22×C41#52912yes—
290C22×C41C2×#12711yescharacteristic
291C22×C41#53211yescharacteristic
292C22×C41#53212yes—
293C22×C41#53611yescharacteristic
294C22×C41#53711yescharacteristic
295C22×C41#54111yescharacteristic
296C22×C41#54211yescharacteristic
297C22×C41#54612yes—
298C22×C41#54712yes—
299C22×C41#54712yes—
300C22×C41#54812yes—
301C22×C41#55112yes—
302C22×C41#55212yes—
303C22×C41#55212yes—
304C22×C41#55612yes—
305C4×C41—28no—
306C4×C41—24no—
307C4×C41—24no—
308C4×C41—24no—
309C4×C41—44no—
310C4×C41—42no—
311C4×C41—44no—
312C4×C41—44no—
313C4×C41—81no—
314C4×C41—81no—
315C2×#399C2×C4111yescharacteristic
316C2×#388C2×C4111yescharacteristic
317C2×#388C2×C4112yes—
318C2×#387C2×C4112yescomplemented
319C2×C4×C4⋊C4C2×C4111yescharacteristic, complemented
320#1445C2×C4111yescharacteristic, complemented
321#1444C2×C4111yescharacteristic, complemented
322#1439C2×C4111yescharacteristic
323#1437C2×C4112yes—
324C4⋊#95C2×C4112yescomplemented
325C4×#95C2×C4111yescharacteristic, complemented
326C2×C41—82no—
327C2×C41C4×#12311yescharacteristic
328C2×C41C4×#12711yescharacteristic
329C2×C41#232311yescharacteristic
330C2×C41#235912yes—
331C2×C41#236212yes—
332C2×C41#249811yescharacteristic
333C2×C41#250111yescharacteristic
334C2×C41#251912yes—
335C2×C41#252112yes—
336C2×C41#254011yescharacteristic
337C2×C41#260411yescharacteristic
338C22×C4⋊C4C22×C4111yescharacteristic
339C22×C4⋊C4C22×C4111yescharacteristic
340C22×C4⋊C4C22×C4112yes—
341C22×C4⋊C4C22×C4112yes—
342C22×C4⋊C4C22×C4111yescharacteristic
343C22×C22⋊C4C22×C4111yescharacteristic
344C22×C22⋊C4C22×C4111yescharacteristic
345C22×C22⋊C4C22×C4112yes—
346C22×C22⋊C4C22×C4112yes—
347C22×C22⋊C4C22×C4111yescharacteristic
348C22×C42C22×C4112yes—
349C22×C42C22×C4112yes—
350C22×C42C22×C4111yescharacteristic
351#399C4×C4118yescomplemented
352#388—24no—
353#388—28no—
354#387—28no—
355C4×C4⋊C4—24no—
356C2×#95C22×C4111yescharacteristic
357C2×#95C22×C4111yescharacteristic
358C2×#95C22×C4112yes—
359C2×#95C22×C4112yes—
360C2×#95C22×C4112yes—
361C2×#95C22×C4112yes—
362C2×#95C22×C4112yes—
363C2×#95C22×C4111yescharacteristic
364C2×#95C22×C4111yescharacteristic
365C2×#95C22×C4112yes—
366C41#1423111yescharacteristic, direct product factor, Sylow
367C25C23×C4111yescharacteristic
368C23×C4C23×C4111yescharacteristic
369C23×C4C23×C4111yescharacteristic
370C23×C4C23×C4111yescharacteristic
371C23×C4C23×C4112yes—
372C23×C4C23×C4112yes—
373C23×C4C23×C4112yes—
374C23×C4C23×C4111yescharacteristic
375C23×C4C23×C4112yes—
376C23×C4C23×C4111yescharacteristic
377C23×C4C23×C4111yescharacteristic
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4C2×C4×C4118yes—
390C2×C4⋊C4C2×C4×C4114yes—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4C2×C4×C4118yes—
403C2×C22⋊C4C2×C4×C4114yes—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—42no—
411C2×C42D4×C4114yes—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95C2×C4×C4114yes—
421#95D4×C4118yes—
422C24—21no—
423C24—22no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24C22×C4×C4112yes—
433C24C24×C4111yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4C22×C4×C4112yes—
479C22×C4C22×C4×C4114yes—
480C22×C4C22×C4×C4112yes—
481C22×C4C22×C4×C4114yes—
482C22×C4C2×D4×C4114yes—
483C22×C4C2×D4×C4114yes—
484C22×C4C2×D4×C4112yes—
485C22×C4C2×D4×C4112yes—
486C22×C4C2×D4×C4114yes—
487C22×C4C2×D4×C4112yes—
488C22×C4#41×C4114yes—
489C22×C4#41×C4112yes—
490C22×C4#41×C4114yes—
491C22×C4#41×C4114yes—
492C4⋊C4—28no—
493C4⋊C4—28no—
494C4⋊C4—216no—
495C4⋊C4—48no—
496C4⋊C4—44no—
497C22⋊C4—28no—
498C22⋊C4—216no—
499C22⋊C4—48no—
500C22⋊C4—44no—
501C22⋊C4—44no—
502C42—28no—
503C42—48no—
504C42—48no—
505C23—22no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C23×C4×C4111yescharacteristic
529C23C22×D4×C4111yescharacteristic
530C23C22×D4×C4112yes—
531C23C2×#41×C4111yescharacteristic
532C23C2×#41×C4112yes—
533C23C2×#41×C4112yes—
534C23C2×#41×C4112yes—
535C23H(5,𝔽2)×C4111yescharacteristic
536C232−1+4×C4111yescharacteristic
537C232−1+4×C4111yescharacteristic
538C232−1+4×C4111yescharacteristic
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4C4×D4×C4114yes—
594C2×C4C4×D4×C4118yes—
595C2×C4#123×C4114yes—
596C2×C4#127×C4114yes—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—44no—
601C22—44no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—82no—
607C22—82no—
608C22C2×C4×D4×C4111yescharacteristic
609C22C2×C4×D4×C4112yes—
610C22C4×#41×C4112yes—
611C22C41×#51911yescharacteristic
612C22C41×#52011yescharacteristic
613C22C2×#123×C4111yescharacteristic
614C22C41×#52511yescharacteristic
615C22C41×#52912yes—
616C22C2×#127×C4111yescharacteristic
617C22C41×#53211yescharacteristic
618C22C41×#53212yes—
619C22C41×#53611yescharacteristic
620C22C41×#53711yescharacteristic
621C22C41×#54111yescharacteristic
622C22C41×#54211yescharacteristic
623C22C41×#54612yes—
624C22C41×#54712yes—
625C22C41×#54712yes—
626C22C41×#54812yes—
627C22C41×#55112yes—
628C22C41×#55212yes—
629C22C41×#55212yes—
630C22C41×#55612yes—
631C4—24no—
632C4—28no—
633C4—24no—
634C4—24no—
635C4—44no—
636C4—44no—
637C4—42no—
638C4—44no—
639C4—81no—
640C4—81no—
641C2—82no—
642C2C4×#123×C4111yescharacteristic
643C2C4×#127×C4111yescharacteristic
644C2C41×#232311yescharacteristic
645C2C41×#235912yes—
646C2C41×#236212yes—
647C2C41×#249811yescharacteristic
648C2C41×#250111yescharacteristic
649C2C41×#251912yes—
650C2C41×#252112yes—
651C2C41×#254011yescharacteristic
652C2C41×#260411yescharacteristic
subgroupG/H
center, socleC24×C41C24
commutatorC23C23×C4×C41
Frattini, cosocleC24C24×C41
prime radicalC25×C41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C41×#387C2semidirect
5. C2×C4×C4⋊C4×C41C2semidirect
6. C41×#1445C2semidirect
7. C41×#1444C2semidirect
10. C41×C4⋊#95C2semidirect
11. C4×#95×C41C2semidirect
25. C41×#399C4semidirect
270. #14231C41direct (N × H)
318. C2×#387C2×C41semidirect
319. C2×C4×C4⋊C4C2×C41semidirect
320. #1445C2×C41semidirect
321. #1444C2×C41semidirect
324. C4⋊#95C2×C41semidirect
325. C4×#95C2×C41semidirect
351. #399C4×C41semidirect
366. C41#14231direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#3992
C2×C41×#3882
C2×C41×#3872
C2×C4×C4⋊C4×C412
C41×#14452
C41×#14442
C41×#14392
C41×#14372
C41×C4⋊#952
C4×#95×C412
#1423141