Finite Group Databasebeta

← C41×#18201 #23794402

Subgroups — C41×#18201 #23794402

Order 10496.

960 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3492C211yesmaximal, characteristic
2C41×#3091C212yesmaximal, complemented
3C41×#2484C211yesmaximal, characteristic, complemented
4C41×#1617C211yesmaximal, characteristic, complemented
5C41×#1616C211yesmaximal, characteristic, complemented
6C41×#1615C212yesmaximal, complemented
7C41×#1611C211yesmaximal, characteristic, complemented
8C41×#1610C211yesmaximal, characteristic, complemented
9C41×#1609C212yesmaximal, complemented
10C41×#1516C212yesmaximal, complemented
11C2×C41×#324C211yesmaximal, characteristic, complemented
12C41×#554—22no—
13C41×#553—22no—
14C41×#552—22no—
15C41×#547—22no—
16C41×#544C2211yescharacteristic
17C41×#539—21no—
18C41×#539C2212yes—
19C41×#537C2211yescharacteristic
20C41×#525—21no—
21C41×#525—21no—
22C41×#525C2212yes—
23C41×#520—21no—
24C2×#117×C41C2211yescharacteristic
25C22×C4⋊C4×C41C2211yescharacteristic
26C41×#485—22no—
27C41×#484C2212yes—
28C41×#483C2212yes—
29C41×#482—22no—
30C41×#481C2212yes—
31C41×#480C2212yes—
32C41×#427—22no—
33C41×#416—22no—
34C2×C22⋊C8×C41C2212yes—
35C41×#400C2211yescharacteristic
36C41×#400C2211yescharacteristic
37C41×#398C2211yescharacteristic
38C41×#398C2211yescharacteristic
39C41×#387—21no—
40C41×#387—21no—
41C41×#385—21no—
42C41×#381—21no—
43C41×#381C2211yescharacteristic
44C41×#328C2212yes—
45C41×#328C2212yes—
46C41×#327C2212yes—
47C41×#327C2212yes—
48C41×#324C2212yes—
49C41×#324C2211yescharacteristic
50C41×#324C2211yescharacteristic
51C2×#41×C41—21no—
52C2×#41×C41—21no—
53C2×#41×C41D412yes—
54C23×C4×C41D411yescharacteristic
55C23×C4×C41D411yescharacteristic
56C23×C4×C41C2311yescharacteristic
57C22×C8×C41—22no—
58C4⋊Q8×C41—22no—
59#126×C41—22no—
60#126×C41—22no—
61#125×C41—22no—
62#125×C41—22no—
63#125×C41—22no—
64#123×C41—22no—
65#123×C41—22no—
66#123×C41—22no—
67#123×C41—22no—
68#123×C41—22no—
69C22⋊Q8×C41—21no—
70C22⋊Q8×C41—21no—
71C22⋊Q8×C41—21no—
72C22⋊Q8×C41—22no—
73C22⋊Q8×C41—22no—
74C22⋊Q8×C41—21no—
75C22⋊Q8×C41—22no—
76C22⋊Q8×C41D412yes—
77C22⋊Q8×C41C2312yes—
78#121×C41—21no—
79#121×C41—21no—
80#121×C41—21no—
81#121×C41—22no—
82#121×C41—21no—
83#121×C41D412yes—
84#121×C41C2312yes—
85#120×C41—22no—
86C4×Q8×C41—22no—
87C4×D4×C41—22no—
88C4×D4×C41—22no—
89C4×D4×C41—22no—
90C4×D4×C41—22no—
91C4×D4×C41—22no—
92C4×D4×C41—22no—
93C4×D4×C41—22no—
94#117×C41—22no—
95#117×C41—21no—
96#117×C41—21no—
97#117×C41—22no—
98#117×C41—22no—
99#117×C41D412yes—
100C2×C4⋊C4×C41—22no—
101C2×C4⋊C4×C41—22no—
102C2×C4⋊C4×C41—22no—
103C2×C4⋊C4×C41—21no—
104C2×C4⋊C4×C41—21no—
105C2×C4⋊C4×C41D411yescharacteristic
106C2×C4⋊C4×C41D411yescharacteristic
107C2×C4⋊C4×C41C2311yescharacteristic
108C2×C4⋊C4×C41C2311yescharacteristic
109C2×C4⋊C4×C41C2311yescharacteristic
110C2×C4⋊C4×C41C2311yescharacteristic
111C2×C22⋊C4×C41—21no—
112C2×C22⋊C4×C41—21no—
113C2×C42×C41—21no—
114#107×C41—22no—
115#107×C41—22no—
116#106×C41—22no—
117#106×C41—22no—
118#103×C41—22no—
119#103×C41—22no—
120#102×C41—22no—
121#102×C41—22no—
122C22⋊C8×C41—22no—
123C22⋊C8×C41C2312yes—
124C22⋊C8×C41C2312yes—
125#95×C41—21no—
126#95×C41—21no—
127#95×C41—21no—
128#95×C41—21no—
129#95×C41—21no—
130#95×C41—21no—
131#95×C41—21no—
132#95×C41C2311yescharacteristic
133#95×C41C2311yescharacteristic
134C24×C41C2×D411yescharacteristic
135#41×C41—42no—
136#41×C41—44no—
137#41×C41—42no—
138#41×C41—82no—
139C2×Q8×C41—21no—
140C2×Q8×C41—21no—
141C2×Q8×C41C2×D412yes—
142C2×D4×C41—21no—
143C2×D4×C41—22no—
144C2×D4×C41—22no—
145C2×D4×C41—22no—
146C2×D4×C41—21no—
147C2×D4×C41C2×D412yes—
148C22×C4×C41—22no—
149C22×C4×C41—21no—
150C22×C4×C41—21no—
151C22×C4×C41—21no—
152C22×C4×C41—22no—
153C22×C4×C41—21no—
154C22×C4×C41—22no—
155C22×C4×C41—22no—
156C22×C4×C41—21no—
157C22×C4×C41—21no—
158C22×C4×C41—21no—
159C22×C4×C41—21no—
160C22×C4×C41—41no—
161C22×C4×C41—42no—
162C22×C4×C41—42no—
163C22×C4×C41C2×D411yescharacteristic
164C22×C4×C41C2×D412yes—
165C22×C4×C41C2×D411yescharacteristic
166C22×C4×C41C2×D411yescharacteristic
167C22×C4×C41C2×D411yescharacteristic
168C22×C4×C41C2×D411yescharacteristic
169C22×C4×C41C2×D412yes—
170C22×C4×C41C2411yescharacteristic
171C2×C8×C41—22no—
172C2×C8×C41—22no—
173C2×C8×C41—44no—
174C4⋊C4×C41—21no—
175C4⋊C4×C41—22no—
176C4⋊C4×C41—21no—
177C4⋊C4×C41—21no—
178C4⋊C4×C41—21no—
179C4⋊C4×C41—22no—
180C4⋊C4×C41—22no—
181C4⋊C4×C41—22no—
182C4⋊C4×C41—22no—
183C4⋊C4×C41—22no—
184C4⋊C4×C41—22no—
185C4⋊C4×C41—22no—
186C4⋊C4×C41—22no—
187C4⋊C4×C41—22no—
188C4⋊C4×C41—22no—
189C4⋊C4×C41—22no—
190C4⋊C4×C41—42no—
191C4⋊C4×C41—42no—
192C4⋊C4×C41C2×D412yes—
193C4⋊C4×C41C2×D412yes—
194C22⋊C4×C41—22no—
195C22⋊C4×C41—22no—
196C22⋊C4×C41—22no—
197C22⋊C4×C41—22no—
198C22⋊C4×C41—22no—
199C22⋊C4×C41—22no—
200C22⋊C4×C41—22no—
201C22⋊C4×C41—22no—
202C22⋊C4×C41—22no—
203C22⋊C4×C41—42no—
204C22⋊C4×C41—41no—
205C22⋊C4×C41—41no—
206C42×C41—22no—
207C42×C41—22no—
208C42×C41—22no—
209C42×C41—42no—
210C23×C41—21no—
211C23×C41—21no—
212C23×C41—22no—
213C23×C41—22no—
214C23×C41—41no—
215C23×C41#12011yescharacteristic
216C23×C41#12011yescharacteristic
217C23×C41C22×D411yescharacteristic
218Q8×C41—42no—
219Q8×C41—42no—
220Q8×C41—81no—
221D4×C41—42no—
222D4×C41—42no—
223D4×C41—44no—
224D4×C41—42no—
225D4×C41—42no—
226D4×C41—44no—
227D4×C41—81no—
228C2×C4×C41—21no—
229C2×C4×C41—21no—
230C2×C4×C41—24no—
231C2×C4×C41—22no—
232C2×C4×C41—22no—
233C2×C4×C41—21no—
234C2×C4×C41—22no—
235C2×C4×C41—21no—
236C2×C4×C41—21no—
237C2×C4×C41—21no—
238C2×C4×C41—21no—
239C2×C4×C41—42no—
240C2×C4×C41—41no—
241C2×C4×C41—41no—
242C2×C4×C41—42no—
243C2×C4×C41—42no—
244C2×C4×C41—44no—
245C2×C4×C41—42no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—41no—
249C2×C4×C41—41no—
250C2×C4×C41—41no—
251C2×C4×C41—41no—
252C2×C4×C41—42no—
253C2×C4×C41—41no—
254C2×C4×C41—41no—
255C2×C4×C41—41no—
256C2×C4×C41—41no—
257C2×C4×C41—41no—
258C2×C4×C41—41no—
259C2×C4×C41—82no—
260C2×C4×C41—81no—
261C2×C4×C41—82no—
262C2×C4×C41#12012yes—
263C2×C4×C41#13512yes—
264C2×C4×C41C22×D412yes—
265C8×C41—42no—
266C8×C41—42no—
267#18201C4111yesmaximal, characteristic, direct product factor, Sylow
268C22×C41—21no—
269C22×C41—21no—
270C22×C41—21no—
271C22×C41—21no—
272C22×C41—21no—
273C22×C41—21no—
274C22×C41—21no—
275C22×C41—42no—
276C22×C41—42no—
277C22×C41—42no—
278C22×C41—42no—
279C22×C41—42no—
280C22×C41#45812yes—
281C22×C41C2×#12011yescharacteristic
282C22×C41C2×#13511yescharacteristic
283C22×C41#57511yescharacteristic
284C4×C41—22no—
285C4×C41—22no—
286C4×C41—22no—
287C4×C41—41no—
288C4×C41—42no—
289C4×C41—42no—
290C4×C41—41no—
291C4×C41—41no—
292C4×C41—42no—
293C4×C41—81no—
294C4×C41—81no—
295C4×C41—81no—
296C4×C41—81no—
297#3492C2×C4111yescharacteristic
298#3091C2×C4112yescomplemented
299#2484C2×C4111yescharacteristic, complemented
300#1617C2×C4111yescharacteristic, complemented
301#1616C2×C4111yescharacteristic, complemented
302#1615C2×C4112yescomplemented
303#1611C2×C4111yescharacteristic, complemented
304#1610C2×C4111yescharacteristic, complemented
305#1609C2×C4112yescomplemented
306#1516C2×C4112yescomplemented
307C2×#324C2×C4111yescharacteristic, complemented
308C2×C41—21no—
309C2×C41—21no—
310C2×C41—22no—
311C2×C41—41no—
312C2×C41—82no—
313C2×C41#300211yescharacteristic
314C2×C41#302011yescharacteristic
315C2×C41C2×#45811yescharacteristic
316#554—22no—
317#553—22no—
318#552—22no—
319#547—22no—
320#544C22×C4111yescharacteristic
321#539—21no—
322#539C22×C4112yes—
323#537C22×C4111yescharacteristic
324#525—21no—
325#525—21no—
326#525C22×C4112yes—
327#520—21no—
328C2×#117C22×C4111yescharacteristic
329C22×C4⋊C4C22×C4111yescharacteristic
330#485—22no—
331#484C22×C4112yes—
332#483C22×C4112yes—
333#482—22no—
334#481C22×C4112yes—
335#480C22×C4112yes—
336#427—22no—
337#416—22no—
338C2×C22⋊C8C22×C4112yes—
339#400C22×C4111yescharacteristic
340#400C22×C4111yescharacteristic
341#398C22×C4111yescharacteristic
342#398C22×C4111yescharacteristic
343#387—21no—
344#387—21no—
345#385—21no—
346#381—21no—
347#381C22×C4111yescharacteristic
348#328C22×C4112yes—
349#328C22×C4112yes—
350#327C22×C4112yes—
351#327C22×C4112yes—
352#324C22×C4112yes—
353#324C22×C4111yescharacteristic
354#324C22×C4111yescharacteristic
355C41#1820111yescharacteristic, direct product factor, Sylow
356C2×#41—21no—
357C2×#41—21no—
358C2×#41D4×C4112yes—
359C23×C4D4×C4111yescharacteristic
360C23×C4D4×C4111yescharacteristic
361C23×C4C23×C4111yescharacteristic
362C22×C8—22no—
363C4⋊Q8—22no—
364#126—22no—
365#126—22no—
366#125—22no—
367#125—22no—
368#125—22no—
369#123—22no—
370#123—22no—
371#123—22no—
372#123—22no—
373#123—22no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—21no—
380C22⋊Q8—22no—
381C22⋊Q8D4×C4112yes—
382C22⋊Q8C23×C4112yes—
383#121—21no—
384#121—21no—
385#121—21no—
386#121—22no—
387#121—21no—
388#121D4×C4112yes—
389#121C23×C4112yes—
390#120—22no—
391C4×Q8—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399#117—22no—
400#117—21no—
401#117—21no—
402#117—22no—
403#117—22no—
404#117D4×C4112yes—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4D4×C4111yescharacteristic
411C2×C4⋊C4D4×C4111yescharacteristic
412C2×C4⋊C4C23×C4111yescharacteristic
413C2×C4⋊C4C23×C4111yescharacteristic
414C2×C4⋊C4C23×C4111yescharacteristic
415C2×C4⋊C4C23×C4111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C42—21no—
419#107—22no—
420#107—22no—
421#106—22no—
422#106—22no—
423#103—22no—
424#103—22no—
425#102—22no—
426#102—22no—
427C22⋊C8—22no—
428C22⋊C8C23×C4112yes—
429C22⋊C8C23×C4112yes—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95C23×C4111yescharacteristic
438#95C23×C4111yescharacteristic
439C24C2×D4×C4111yescharacteristic
440#41—42no—
441#41—44no—
442#41—42no—
443#41—82no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8C2×D4×C4112yes—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4C2×D4×C4112yes—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4C2×D4×C4111yescharacteristic
469C22×C4C2×D4×C4112yes—
470C22×C4C2×D4×C4111yescharacteristic
471C22×C4C2×D4×C4111yescharacteristic
472C22×C4C2×D4×C4111yescharacteristic
473C22×C4C2×D4×C4111yescharacteristic
474C22×C4C2×D4×C4112yes—
475C22×C4C24×C4111yescharacteristic
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—44no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4C2×D4×C4112yes—
498C4⋊C4C2×D4×C4112yes—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—42no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—22no—
512C42—22no—
513C42—22no—
514C42—42no—
515C23—21no—
516C23—21no—
517C23—22no—
518C23—22no—
519C23—41no—
520C23#120×C4111yescharacteristic
521C23#120×C4111yescharacteristic
522C23C22×D4×C4111yescharacteristic
523Q8—42no—
524Q8—42no—
525Q8—81no—
526D4—42no—
527D4—42no—
528D4—44no—
529D4—42no—
530D4—42no—
531D4—44no—
532D4—81no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—82no—
565C2×C4—81no—
566C2×C4—82no—
567C2×C4#120×C4112yes—
568C2×C4#135×C4112yes—
569C2×C4C22×D4×C4112yes—
570C8—42no—
571C8—42no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22C41×#45812yes—
585C22C2×#120×C4111yescharacteristic
586C22C2×#135×C4111yescharacteristic
587C22C41×#57511yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C2—21no—
602C2—21no—
603C2—22no—
604C2—41no—
605C2—82no—
606C2C41×#300211yescharacteristic
607C2C41×#302011yescharacteristic
608C2C2×C41×#45811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#3492C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#3091C2semidirect
3. C41×#2484C2semidirect
4. C41×#1617C2semidirect
5. C41×#1616C2semidirect
6. C41×#1615C2semidirect
7. C41×#1611C2semidirect
8. C41×#1610C2semidirect
9. C41×#1609C2semidirect
10. C41×#1516C2semidirect
11. C2×C41×#324C2semidirect
267. #18201C41direct (N × H)
298. #3091C2×C41semidirect
299. #2484C2×C41semidirect
300. #1617C2×C41semidirect
301. #1616C2×C41semidirect
302. #1615C2×C41semidirect
303. #1611C2×C41semidirect
304. #1610C2×C41semidirect
305. #1609C2×C41semidirect
306. #1516C2×C41semidirect
307. C2×#324C2×C41semidirect
355. C41#18201direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#34922
C41×#30912
C41×#24842
C41×#16172
C41×#16162
C41×#16152
C41×#16112
C41×#16102
C41×#16092
C41×#15162
C2×C41×#3242
#1820141