Finite Group Databasebeta

← C41×#33558 #23809759

Subgroups — C41×#33558 #23809759

Order 10496.

1158 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3545C211yesmaximal, characteristic, complemented
2C41×#3026C212yesmaximal, complemented
3C2×C41×#455C211yesmaximal, characteristic, complemented
4C41×#2201C212yesmaximal, complemented
5C41×#2199C212yesmaximal, complemented
6C41×#2197C214yesmaximal, complemented
7C2×C41×#354C211yesmaximal, characteristic, complemented
8C41×#2121C212yesmaximal, complemented
9C2×H(5,𝔽2)×C41C2211yescharacteristic
10C2×#137×C41—21no—
11C41×#563C2211yescharacteristic, complemented
12C41×#562—21no—
13C41×H(3,𝔽4)C2211yescharacteristic, complemented
14C41×#555—21no—
15C41×#551—22no—
16C41×#551C2212yescomplemented
17C41×#546—22no—
18C41×#542—22no—
19C41×#538—22no—
20C41×#536—21no—
21C41×#534—22no—
22C41×#534C2212yes—
23C41×#529—21no—
24C2×#124×C41C2211yescharacteristic
25C41×#458—22no—
26C41×#458C2214yes—
27C41×B(4,𝔽2)—22no—
28C41×B(4,𝔽2)C2214yes—
29C41×#455—21no—
30C41×#455—21no—
31C41×#455C2212yes—
32C41×#455C2212yes—
33C2×#104×C41—21no—
34C2×#100×C41C2211yescharacteristic
35C2×#99×C41—22no—
36C2×#99×C41C2212yes—
37C41×#354C2212yescomplemented
38C41×#354C2212yescomplemented
39C41×#352C2214yescomplemented
40C41×AΣL(1,𝔽16)C2214yescomplemented
41H(5,𝔽2)×C41—22no—
42H(5,𝔽2)×C41—21no—
43H(5,𝔽2)×C41—42no—
44H(5,𝔽2)×C41C2312yes—
45C2×#41×C41—21no—
46C2×#41×C41—21no—
47C2×#41×C41—41no—
48C22×Q8×C41D411yescharacteristic, complemented
49C22×D4×C41—22no—
50C22×D4×C41—41no—
51C22×D4×C41D412yescomplemented
52C22×D4×C41C2311yescharacteristic
53#137×C41—22no—
54#137×C41—22no—
55#137×C41—42no—
56C2×Q16×C41—41no—
57C2×SD16×C41—41no—
58C2×M16×C41—21no—
59C4⋊Q8×C41—21no—
60C4⋊Q8×C41—21no—
61#126×C41—22no—
62#126×C41—22no—
63#126×C41—22no—
64#125×C41—21no—
65#124×C41—21no—
66#124×C41—22no—
67#124×C41—21no—
68#124×C41—22no—
69#124×C41—22no—
70#124×C41—21no—
71#124×C41D411yescharacteristic, complemented
72#124×C41D411yescharacteristic, complemented
73#124×C41C2311yescharacteristic
74#124×C41C2311yescharacteristic
75#123×C41—22no—
76#123×C41—22no—
77#123×C41—22no—
78#123×C41—22no—
79#123×C41—22no—
80#123×C41—24no—
81#123×C41—42no—
82#123×C41D412yescomplemented
83#123×C41C2312yes—
84C22⋊Q8×C41—21no—
85C22⋊Q8×C41—22no—
86C22⋊Q8×C41—22no—
87C22⋊Q8×C41—22no—
88C22⋊Q8×C41—22no—
89#121×C41—21no—
90#121×C41—22no—
91#121×C41—22no—
92#121×C41—22no—
93#121×C41—22no—
94#121×C41—44no—
95#120×C41—22no—
96#120×C41—22no—
97#120×C41—24no—
98#120×C41—42no—
99#120×C41D412yescomplemented
100#120×C41C2312yes—
101C4×Q8×C41—21no—
102C4×D4×C41—21no—
103C4×D4×C41—22no—
104C4×D4×C41—22no—
105C4×D4×C41—22no—
106#117×C41—21no—
107#117×C41—22no—
108#117×C41—22no—
109C2×C22⋊C4×C41—22no—
110C2×C22⋊C4×C41—22no—
111C2×C22⋊C4×C41—22no—
112C2×C22⋊C4×C41D412yescomplemented
113C2×C42×C41D411yescharacteristic, complemented
114#104×C41—22no—
115#104×C41—22no—
116#100×C41—21no—
117#100×C41C2312yes—
118#99×C41—22no—
119#99×C41—24no—
120#99×C41—24no—
121#99×C41C2314yes—
122C24×C41—22no—
123C24×C41C2×D412yes—
124C24×C41C2×D412yes—
125#41×C41—22no—
126#41×C41—22no—
127#41×C41—42no—
128#41×C41—41no—
129#41×C41—44no—
130#41×C41—42no—
131#41×C41—41no—
132#41×C41—81no—
133#41×C41—81no—
134C2×Q8×C41—21no—
135C2×Q8×C41—21no—
136C2×Q8×C41—21no—
137C2×Q8×C41—21no—
138C2×Q8×C41—41no—
139C2×Q8×C41—41no—
140C2×Q8×C41C2×D411yescharacteristic
141C2×Q8×C41C2×D411yescharacteristic
142C2×D4×C41—21no—
143C2×D4×C41—24no—
144C2×D4×C41—22no—
145C2×D4×C41—24no—
146C2×D4×C41—21no—
147C2×D4×C41—21no—
148C2×D4×C41—22no—
149C2×D4×C41—22no—
150C2×D4×C41—22no—
151C2×D4×C41—41no—
152C2×D4×C41—41no—
153C2×D4×C41—42no—
154C2×D4×C41—42no—
155C2×D4×C41—42no—
156C2×D4×C41—42no—
157C2×D4×C41—44no—
158C2×D4×C41—42no—
159C2×D4×C41—41no—
160C2×D4×C41—42no—
161C2×D4×C41—42no—
162C2×D4×C41—44no—
163C2×D4×C41C2×D412yes—
164C2×D4×C41C2×D411yescharacteristic
165C2×D4×C41C2411yescharacteristic
166C22×C4×C41—22no—
167C22×C4×C41—21no—
168C22×C4×C41—22no—
169C22×C4×C41—22no—
170C22×C4×C41—22no—
171C22×C4×C41—21no—
172C22×C4×C41—41no—
173C22×C4×C41—42no—
174C22×C4×C41C2×D411yescharacteristic
175C22×C4×C41C2×D412yes—
176Q16×C41—42no—
177Q16×C41—42no—
178SD16×C41—42no—
179SD16×C41—42no—
180M16×C41—22no—
181M16×C41—41no—
182C2×C8×C41—41no—
183C4⋊C4×C41—22no—
184C4⋊C4×C41—22no—
185C4⋊C4×C41—22no—
186C4⋊C4×C41—22no—
187C4⋊C4×C41—22no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—21no—
190C4⋊C4×C41—22no—
191C4⋊C4×C41—22no—
192C4⋊C4×C41—44no—
193C22⋊C4×C41—22no—
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—22no—
204C22⋊C4×C41—22no—
205C22⋊C4×C41—22no—
206C22⋊C4×C41—24no—
207C22⋊C4×C41—44no—
208C22⋊C4×C41—42no—
209C22⋊C4×C41—44no—
210C22⋊C4×C41C2×D412yes—
211C22⋊C4×C41C2×D412yes—
212C42×C41—21no—
213C42×C41—22no—
214C42×C41—21no—
215C42×C41—21no—
216C42×C41C2×D411yescharacteristic
217C42×C41C2×D411yescharacteristic
218C23×C41—22no—
219C23×C41—22no—
220C23×C41—24no—
221C23×C41—22no—
222C23×C41—42no—
223C23×C41—42no—
224C23×C41—41no—
225C23×C41—82no—
226C23×C41—82no—
227C23×C41—162no—
228C23×C41#12012yes—
229C23×C41#12011yescharacteristic
230C23×C41C22×D412yes—
231Q8×C41—22no—
232Q8×C41—41no—
233Q8×C41—41no—
234Q8×C41—41no—
235Q8×C41—81no—
236Q8×C41—81no—
237Q8×C41—81no—
238D4×C41—22no—
239D4×C41—41no—
240D4×C41—42no—
241D4×C41—41no—
242D4×C41—41no—
243D4×C41—44no—
244D4×C41—44no—
245D4×C41—42no—
246D4×C41—42no—
247D4×C41—42no—
248D4×C41—42no—
249D4×C41—82no—
250D4×C41—82no—
251D4×C41—82no—
252D4×C41—81no—
253D4×C41—81no—
254D4×C41—164no—
255C2×C4×C41—21no—
256C2×C4×C41—21no—
257C2×C4×C41—24no—
258C2×C4×C41—21no—
259C2×C4×C41—21no—
260C2×C4×C41—22no—
261C2×C4×C41—21no—
262C2×C4×C41—22no—
263C2×C4×C41—22no—
264C2×C4×C41—21no—
265C2×C4×C41—42no—
266C2×C4×C41—42no—
267C2×C4×C41—42no—
268C2×C4×C41—41no—
269C2×C4×C41—41no—
270C2×C4×C41—41no—
271C2×C4×C41—42no—
272C2×C4×C41—44no—
273C2×C4×C41—82no—
274C2×C4×C41—81no—
275C2×C4×C41—82no—
276C2×C4×C41—82no—
277C2×C4×C41—162no—
278C2×C4×C41#12011yescharacteristic
279C2×C4×C41C22×D411yescharacteristic
280C8×C41—42no—
281#33558C4111yesmaximal, characteristic, direct product factor, Sylow
282C22×C41—22no—
283C22×C41—22no—
284C22×C41—41no—
285C22×C41—42no—
286C22×C41—42no—
287C22×C41—42no—
288C22×C41—42no—
289C22×C41—42no—
290C22×C41—42no—
291C22×C41—82no—
292C22×C41—82no—
293C22×C41—82no—
294C22×C41—84no—
295C22×C41—84no—
296C22×C41—162no—
297C22×C41B(4,𝔽2)11yescharacteristic
298C22×C41B(4,𝔽2)11yescharacteristic
299C22×C41C2×#12011yescharacteristic
300C4×C41—21no—
301C4×C41—21no—
302C4×C41—41no—
303C4×C41—42no—
304C4×C41—42no—
305C4×C41—41no—
306C4×C41—42no—
307C4×C41—41no—
308C4×C41—41no—
309C4×C41—42no—
310C4×C41—84no—
311#3545C2×C4111yescharacteristic, complemented
312#3026C2×C4112yescomplemented
313C2×#455C2×C4111yescharacteristic, complemented
314#2201C2×C4112yescomplemented
315#2199C2×C4112yescomplemented
316#2197C2×C4114yescomplemented
317C2×#354C2×C4111yescharacteristic, complemented
318#2121C2×C4112yescomplemented
319C2×C41—21no—
320C2×C41—21no—
321C2×C41—21no—
322C2×C41—42no—
323C2×C41—42no—
324C2×C41—82no—
325C2×C41—82no—
326C2×C41C2×B(4,𝔽2)11yescharacteristic
327C2×H(5,𝔽2)C22×C4111yescharacteristic
328C2×#137—21no—
329#563C22×C4111yescharacteristic, complemented
330#562—21no—
331H(3,𝔽4)C22×C4111yescharacteristic, complemented
332#555—21no—
333#551—22no—
334#551C22×C4112yescomplemented
335#546—22no—
336#542—22no—
337#538—22no—
338#536—21no—
339#534—22no—
340#534C22×C4112yes—
341#529—21no—
342C2×#124C22×C4111yescharacteristic
343#458—22no—
344#458C22×C4114yes—
345B(4,𝔽2)—22no—
346B(4,𝔽2)C22×C4114yes—
347#455—21no—
348#455—21no—
349#455C22×C4112yes—
350#455C22×C4112yes—
351C2×#104—21no—
352C2×#100C22×C4111yescharacteristic
353C2×#99—22no—
354C2×#99C22×C4112yes—
355#354C22×C4112yescomplemented
356#354C22×C4112yescomplemented
357#352C22×C4114yescomplemented
358AΣL(1,𝔽16)C22×C4114yescomplemented
359C41#3355811yescharacteristic, direct product factor, Sylow
360H(5,𝔽2)—22no—
361H(5,𝔽2)—21no—
362H(5,𝔽2)—42no—
363H(5,𝔽2)C23×C4112yes—
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—41no—
367C22×Q8D4×C4111yescharacteristic, complemented
368C22×D4—22no—
369C22×D4—41no—
370C22×D4D4×C4112yescomplemented
371C22×D4C23×C4111yescharacteristic
372#137—22no—
373#137—22no—
374#137—42no—
375C2×Q16—41no—
376C2×SD16—41no—
377C2×M16—21no—
378C4⋊Q8—21no—
379C4⋊Q8—21no—
380#126—22no—
381#126—22no—
382#126—22no—
383#125—21no—
384#124—21no—
385#124—22no—
386#124—21no—
387#124—22no—
388#124—22no—
389#124—21no—
390#124D4×C4111yescharacteristic, complemented
391#124D4×C4111yescharacteristic, complemented
392#124C23×C4111yescharacteristic
393#124C23×C4111yescharacteristic
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398#123—22no—
399#123—24no—
400#123—42no—
401#123D4×C4112yescomplemented
402#123C23×C4112yes—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408#121—21no—
409#121—22no—
410#121—22no—
411#121—22no—
412#121—22no—
413#121—44no—
414#120—22no—
415#120—22no—
416#120—24no—
417#120—42no—
418#120D4×C4112yescomplemented
419#120C23×C4112yes—
420C4×Q8—21no—
421C4×D4—21no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—22no—
425#117—21no—
426#117—22no—
427#117—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4D4×C4112yescomplemented
432C2×C42D4×C4111yescharacteristic, complemented
433#104—22no—
434#104—22no—
435#100—21no—
436#100C23×C4112yes—
437#99—22no—
438#99—24no—
439#99—24no—
440#99C23×C4114yes—
441C24—22no—
442C24C2×D4×C4112yes—
443C24C2×D4×C4112yes—
444#41—22no—
445#41—22no—
446#41—42no—
447#41—41no—
448#41—44no—
449#41—42no—
450#41—41no—
451#41—81no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8C2×D4×C4111yescharacteristic
460C2×Q8C2×D4×C4111yescharacteristic
461C2×D4—21no—
462C2×D4—24no—
463C2×D4—22no—
464C2×D4—24no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—44no—
477C2×D4—41no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4C2×D4×C4112yes—
483C2×D4C2×D4×C4111yescharacteristic
484C2×D4C24×C4111yescharacteristic
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—41no—
492C22×C4—42no—
493C22×C4C2×D4×C4111yescharacteristic
494C22×C4C2×D4×C4112yes—
495Q16—42no—
496Q16—42no—
497SD16—42no—
498SD16—42no—
499M16—22no—
500M16—41no—
501C2×C8—41no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—44no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—24no—
526C22⋊C4—44no—
527C22⋊C4—42no—
528C22⋊C4—44no—
529C22⋊C4C2×D4×C4112yes—
530C22⋊C4C2×D4×C4112yes—
531C42—21no—
532C42—22no—
533C42—21no—
534C42—21no—
535C42C2×D4×C4111yescharacteristic
536C42C2×D4×C4111yescharacteristic
537C23—22no—
538C23—22no—
539C23—24no—
540C23—22no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—82no—
545C23—82no—
546C23—162no—
547C23#120×C4112yes—
548C23#120×C4111yescharacteristic
549C23C22×D4×C4112yes—
550Q8—22no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—81no—
555Q8—81no—
556Q8—81no—
557D4—22no—
558D4—41no—
559D4—42no—
560D4—41no—
561D4—41no—
562D4—44no—
563D4—44no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—82no—
569D4—81no—
570D4—82no—
571D4—82no—
572D4—81no—
573D4—164no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—24no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—81no—
595C2×C4—82no—
596C2×C4—162no—
597C2×C4#120×C4111yescharacteristic
598C2×C4C22×D4×C4111yescharacteristic
599C8—42no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—84no—
613C22—84no—
614C22—162no—
615C22C41×B(4,𝔽2)11yescharacteristic
616C22C41×B(4,𝔽2)11yescharacteristic
617C22C2×#120×C4111yescharacteristic
618C4—21no—
619C4—21no—
620C4—41no—
621C4—42no—
622C4—42no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—84no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—42no—
633C2—42no—
634C2—82no—
635C2—82no—
636C2C2×C41×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C41C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C41
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C23×C41 ◁ C22×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3545C2semidirect
2. C41×#3026C2semidirect
3. C2×C41×#455C2semidirect
4. C41×#2201C2semidirect
5. C41×#2199C2semidirect
6. C41×#2197C2semidirect
7. C2×C41×#354C2semidirect
8. C41×#2121C2semidirect
11. C41×#563C22semidirect
13. C41×H(3,𝔽4)C22semidirect
16. C41×#551C22semidirect
37. C41×#354C22semidirect
38. C41×#354C22semidirect
39. C41×#352C22semidirect
40. C41×AΣL(1,𝔽16)C22semidirect
48. C22×Q8×C41D4semidirect
51. C22×D4×C41D4semidirect
71. #124×C41D4semidirect
72. #124×C41D4semidirect
82. #123×C41D4semidirect
99. #120×C41D4semidirect
112. C2×C22⋊C4×C41D4semidirect
113. C2×C42×C41D4semidirect
281. #33558C41direct (N × H)
311. #3545C2×C41semidirect
312. #3026C2×C41semidirect
313. C2×#455C2×C41semidirect
314. #2201C2×C41semidirect
315. #2199C2×C41semidirect
316. #2197C2×C41semidirect
317. C2×#354C2×C41semidirect
318. #2121C2×C41semidirect
329. #563C22×C41semidirect
331. H(3,𝔽4)C22×C41semidirect
334. #551C22×C41semidirect
355. #354C22×C41semidirect
356. #354C22×C41semidirect
357. #352C22×C41semidirect
358. AΣL(1,𝔽16)C22×C41semidirect
359. C41#33558direct (N × H)
367. C22×Q8D4×C41semidirect
370. C22×D4D4×C41semidirect
390. #124D4×C41semidirect
391. #124D4×C41semidirect
401. #123D4×C41semidirect
418. #120D4×C41semidirect
431. C2×C22⋊C4D4×C41semidirect
432. C2×C42D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35452
C41×#30262
C2×C41×#4552
C41×#22012
C41×#21992
C41×#21972
C2×C41×#3542
C41×#21212
#3355841