Finite Group Databasebeta

← C41×#18252 #23794453

Subgroups — C41×#18252 #23794453

Order 10496.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3534C211yesmaximal, characteristic, complemented
2C41×#3006C211yesmaximal, characteristic, complemented
3C41×#3002C211yesmaximal, characteristic, complemented
4C41×#2430C211yesmaximal, characteristic, complemented
5C41×#1606C211yesmaximal, characteristic, complemented
6C41×#1604C211yesmaximal, characteristic, complemented
7C41×#1603C211yesmaximal, characteristic, complemented
8C41×#1601C211yesmaximal, characteristic, complemented
9C41×#1600C211yesmaximal, characteristic, complemented
10C41×#1598C211yesmaximal, characteristic, complemented
11C41×#1597C211yesmaximal, characteristic, complemented
12C41×#1595C211yesmaximal, characteristic, complemented
13C41×#1504C211yesmaximal, characteristic, complemented
14C2×C41×#327C211yesmaximal, characteristic, complemented
15C41×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C41—21no—
18C2×#135×C41—21no—
19C41×#562—21no—
20C41×#560—21no—
21C41×#553—21no—
22C41×#551—21no—
23C41×#546—21no—
24C41×#546—21no—
25C41×#546—21no—
26D42×C41—21no—
27C41×#540—21no—
28C41×#539—21no—
29C41×#539C2211yescharacteristic
30C41×#538—21no—
31C41×#538C2211yescharacteristic
32C41×#537C2211yescharacteristic
33C41×#534—21no—
34C41×#534C2211yescharacteristic
35C41×#525C2211yescharacteristic
36C2×#123×C41C2211yescharacteristic
37C2×#121×C41—21no—
38C2×#121×C41C2211yescharacteristic
39C41×#452—21no—
40C41×#451C2211yescharacteristic, complemented
41C41×#450C2211yescharacteristic, complemented
42C41×#449—21no—
43C41×#449—21no—
44C41×#449—21no—
45C41×#448C2211yescharacteristic
46C41×#448C2211yescharacteristic, complemented
47C41×#448C2211yescharacteristic, complemented
48C41×#447C2211yescharacteristic
49C41×#447C2211yescharacteristic, complemented
50C41×#447C2211yescharacteristic, complemented
51C41×#417—21no—
52C41×#416—21no—
53C41×#407C2211yescharacteristic, complemented
54C2×C22⋊C8×C41C2211yescharacteristic, complemented
55C41×#395C2211yescharacteristic, complemented
56C41×#394C2211yescharacteristic, complemented
57C41×#393C2211yescharacteristic, complemented
58C41×#392C2211yescharacteristic, complemented
59C41×#386—21no—
60C41×#386—21no—
61C41×#385—21no—
62C2×#95×C41C2211yescharacteristic, complemented
63C41×#328C2211yescharacteristic, complemented
64C41×#328C2211yescharacteristic, complemented
65C41×#327C2211yescharacteristic
66C41×#327C2211yescharacteristic
67C41×#327C2211yescharacteristic, complemented
68C41×#327C2211yescharacteristic, complemented
69C41×#327C2211yescharacteristic, complemented
70C41×#327C2211yescharacteristic, complemented
71C41×#324C2211yescharacteristic, complemented
72C41×#324C2211yescharacteristic, complemented
73C41×#323C2211yescharacteristic, complemented
74C41×#323C2211yescharacteristic, complemented
75C2×#41×C41—21no—
76C2×#41×C41—21no—
77C2×#41×C41—21no—
78C2×#41×C41—21no—
79C2×#41×C41—21no—
80C2×#41×C41—44no—
81C2×#41×C41D411yescharacteristic, complemented
82C22×Q8×C41C2311yescharacteristic
83C22×D4×C41—21no—
84C22×D4×C41—21no—
85C22×D4×C41—21no—
86C22×D4×C41—21no—
87C22×D4×C41—21no—
88C22×D4×C41D411yescharacteristic
89C22×D4×C41D411yescharacteristic, complemented
90C22×D4×C41C2311yescharacteristic
91C23×C4×C41—21no—
92C23×C4×C41—21no—
93C23×C4×C41C2311yescharacteristic
94AGL(1,ℤ/8)×C41—44no—
95#135×C41—44no—
96C2×Q16×C41—21no—
97C2×SD16×C41—21no—
98C2×SD16×C41—21no—
99C2×SD16×C41—21no—
100C2×SD16×C41—21no—
101C2×D8×C41—21no—
102C2×D8×C41—21no—
103C2×D8×C41—21no—
104C2×M16×C41—21no—
105C22×C8×C41—21no—
106#127×C41—21no—
107#126×C41—21no—
108#126×C41—21no—
109#126×C41—21no—
110#126×C41—21no—
111#125×C41—21no—
112#125×C41—21no—
113#124×C41—21no—
114#124×C41—21no—
115#124×C41—21no—
116#123×C41—21no—
117#123×C41—21no—
118#123×C41—21no—
119#123×C41—21no—
120#123×C41—21no—
121#123×C41—21no—
122#123×C41—21no—
123#123×C41—21no—
124#123×C41—21no—
125#123×C41—21no—
126#123×C41—21no—
127#123×C41—21no—
128#123×C41—21no—
129#123×C41—21no—
130C22⋊Q8×C41—21no—
131C22⋊Q8×C41—21no—
132C22⋊Q8×C41—21no—
133C22⋊Q8×C41—21no—
134C22⋊Q8×C41—21no—
135C22⋊Q8×C41D411yescharacteristic, complemented
136C22⋊Q8×C41C2311yescharacteristic
137#121×C41—21no—
138#121×C41—21no—
139#121×C41—21no—
140#121×C41—21no—
141#121×C41—21no—
142#121×C41—21no—
143#121×C41—21no—
144#121×C41—21no—
145#121×C41—21no—
146#121×C41—21no—
147#121×C41—21no—
148#121×C41—21no—
149#121×C41—21no—
150#121×C41—21no—
151#121×C41—21no—
152#121×C41—44no—
153#121×C41D411yescharacteristic, complemented
154#121×C41D411yescharacteristic, complemented
155#121×C41D411yescharacteristic, complemented
156#121×C41C2311yescharacteristic
157#121×C41C2311yescharacteristic
158#121×C41C2311yescharacteristic
159#120×C41—21no—
160#120×C41—21no—
161#120×C41—21no—
162#120×C41—21no—
163#120×C41—21no—
164#120×C41—21no—
165#120×C41—21no—
166#120×C41—21no—
167C4×D4×C41—21no—
168C4×D4×C41—21no—
169C4×D4×C41—21no—
170C4×D4×C41—21no—
171C4×D4×C41—21no—
172C4×D4×C41—21no—
173C4×D4×C41—21no—
174C4×D4×C41—21no—
175#117×C41—21no—
176#117×C41D411yescharacteristic, complemented
177C2×C4⋊C4×C41—21no—
178C2×C4⋊C4×C41D411yescharacteristic
179C2×C4⋊C4×C41D411yescharacteristic, complemented
180C2×C4⋊C4×C41C2311yescharacteristic
181C2×C22⋊C4×C41—21no—
182C2×C22⋊C4×C41—21no—
183C2×C22⋊C4×C41—21no—
184C2×C22⋊C4×C41—21no—
185C2×C22⋊C4×C41—21no—
186C2×C22⋊C4×C41—21no—
187C2×C22⋊C4×C41—21no—
188C2×C22⋊C4×C41D411yescharacteristic
189C2×C22⋊C4×C41D411yescharacteristic
190C2×C22⋊C4×C41C2311yescharacteristic
191#103×C41—21no—
192#103×C41—21no—
193#103×C41—21no—
194#103×C41—21no—
195#102×C41—21no—
196#102×C41—21no—
197#102×C41—21no—
198#102×C41—21no—
199C22⋊C8×C41—21no—
200C22⋊C8×C41—21no—
201C22⋊C8×C41C2311yescharacteristic
202C22⋊C8×C41C2311yescharacteristic
203C22⋊C8×C41C2311yescharacteristic
204C22⋊C8×C41C2311yescharacteristic
205#95×C41—21no—
206#95×C41—21no—
207#95×C41—21no—
208#95×C41C2311yescharacteristic
209#95×C41C2311yescharacteristic
210C24×C41—21no—
211C24×C41—21no—
212C24×C41—21no—
213C24×C41C2×D411yescharacteristic
214C24×C41C2×D411yescharacteristic
215#41×C41—24no—
216#41×C41—24no—
217#41×C41—42no—
218#41×C41—42no—
219#41×C41—42no—
220#41×C41—42no—
221#41×C41—42no—
222#41×C41—42no—
223#41×C41—42no—
224#41×C41—81no—
225#41×C41—81no—
226C2×Q8×C41—21no—
227C2×Q8×C41—21no—
228C2×Q8×C41—21no—
229C2×Q8×C41—42no—
230C2×Q8×C41C2×D411yescharacteristic
231C2×D4×C41—24no—
232C2×D4×C41—21no—
233C2×D4×C41—21no—
234C2×D4×C41—21no—
235C2×D4×C41—21no—
236C2×D4×C41—21no—
237C2×D4×C41—21no—
238C2×D4×C41—21no—
239C2×D4×C41—21no—
240C2×D4×C41—21no—
241C2×D4×C41—21no—
242C2×D4×C41—21no—
243C2×D4×C41—21no—
244C2×D4×C41—21no—
245C2×D4×C41—21no—
246C2×D4×C41—21no—
247C2×D4×C41—21no—
248C2×D4×C41—21no—
249C2×D4×C41—21no—
250C2×D4×C41—21no—
251C2×D4×C41—42no—
252C2×D4×C41—42no—
253C2×D4×C41—42no—
254C2×D4×C41—42no—
255C2×D4×C41—41no—
256C2×D4×C41—41no—
257C2×D4×C41—42no—
258C2×D4×C41—42no—
259C2×D4×C41—81no—
260C2×D4×C41—81no—
261C2×D4×C41—81no—
262C2×D4×C41—81no—
263C2×D4×C41—81no—
264C2×D4×C41—82no—
265C2×D4×C41C2×D411yescharacteristic
266C2×D4×C41C2×D411yescharacteristic
267C2×D4×C41C2×D411yescharacteristic
268C22×C4×C41—21no—
269C22×C4×C41—21no—
270C22×C4×C41—21no—
271C22×C4×C41—21no—
272C22×C4×C41—21no—
273C22×C4×C41—21no—
274C22×C4×C41—21no—
275C22×C4×C41—21no—
276C22×C4×C41—21no—
277C22×C4×C41—21no—
278C22×C4×C41—42no—
279C22×C4×C41—42no—
280C22×C4×C41—42no—
281C22×C4×C41—42no—
282C22×C4×C41—41no—
283C22×C4×C41—41no—
284C22×C4×C41—42no—
285C22×C4×C41—81no—
286C22×C4×C41C2×D411yescharacteristic
287C22×C4×C41C2×D411yescharacteristic
288C22×C4×C41C2×D411yescharacteristic
289C22×C4×C41C2×D411yescharacteristic
290C22×C4×C41C2×D411yescharacteristic
291C22×C4×C41C2×D411yescharacteristic
292C22×C4×C41C2×D411yescharacteristic
293C22×C4×C41C2×D411yescharacteristic
294C22×C4×C41C2411yescharacteristic
295Q16×C41—42no—
296SD16×C41—42no—
297SD16×C41—42no—
298SD16×C41—42no—
299SD16×C41—42no—
300D8×C41—42no—
301D8×C41—42no—
302D8×C41—42no—
303M16×C41—42no—
304C2×C8×C41—21no—
305C2×C8×C41—21no—
306C2×C8×C41—21no—
307C2×C8×C41—21no—
308C2×C8×C41—42no—
309C4⋊C4×C41—21no—
310C4⋊C4×C41—21no—
311C4⋊C4×C41—21no—
312C4⋊C4×C41—21no—
313C4⋊C4×C41—21no—
314C4⋊C4×C41—21no—
315C4⋊C4×C41—21no—
316C4⋊C4×C41—21no—
317C4⋊C4×C41—21no—
318C4⋊C4×C41—21no—
319C4⋊C4×C41—21no—
320C4⋊C4×C41—21no—
321C4⋊C4×C41—21no—
322C4⋊C4×C41—42no—
323C4⋊C4×C41C2×D411yescharacteristic
324C4⋊C4×C41C2×D411yescharacteristic
325C4⋊C4×C41C2×D411yescharacteristic
326C4⋊C4×C41C2×D411yescharacteristic
327C22⋊C4×C41—21no—
328C22⋊C4×C41—21no—
329C22⋊C4×C41—21no—
330C22⋊C4×C41—21no—
331C22⋊C4×C41—21no—
332C22⋊C4×C41—21no—
333C22⋊C4×C41—21no—
334C22⋊C4×C41—21no—
335C22⋊C4×C41—21no—
336C22⋊C4×C41—21no—
337C22⋊C4×C41—21no—
338C22⋊C4×C41—21no—
339C22⋊C4×C41—21no—
340C22⋊C4×C41—21no—
341C22⋊C4×C41—21no—
342C22⋊C4×C41—21no—
343C22⋊C4×C41—21no—
344C22⋊C4×C41—21no—
345C22⋊C4×C41—21no—
346C22⋊C4×C41—21no—
347C22⋊C4×C41—21no—
348C22⋊C4×C41—21no—
349C22⋊C4×C41—21no—
350C22⋊C4×C41—21no—
351C22⋊C4×C41—21no—
352C22⋊C4×C41—42no—
353C22⋊C4×C41—42no—
354C22⋊C4×C41—42no—
355C22⋊C4×C41—81no—
356C42×C41—21no—
357C42×C41—21no—
358C42×C41—21no—
359C23×C41—21no—
360C23×C41—21no—
361C23×C41—22no—
362C23×C41—22no—
363C23×C41—21no—
364C23×C41—21no—
365C23×C41—21no—
366C23×C41—21no—
367C23×C41—21no—
368C23×C41—21no—
369C23×C41—41no—
370C23×C41—41no—
371C23×C41—41no—
372C23×C41—41no—
373C23×C41—41no—
374C23×C41—41no—
375C23×C41—41no—
376C23×C41—41no—
377C23×C41—41no—
378C23×C41—42no—
379C23×C41—81no—
380C23×C41—81no—
381C23×C41—81no—
382C23×C41—81no—
383C23×C41—81no—
384C23×C41#12011yescharacteristic
385C23×C41#12011yescharacteristic
386C23×C41C22×D411yescharacteristic
387Q8×C41—22no—
388Q8×C41—22no—
389Q8×C41—41no—
390Q8×C41—41no—
391Q8×C41—41no—
392Q8×C41—81no—
393D4×C41—22no—
394D4×C41—22no—
395D4×C41—41no—
396D4×C41—41no—
397D4×C41—41no—
398D4×C41—41no—
399D4×C41—41no—
400D4×C41—44no—
401D4×C41—41no—
402D4×C41—41no—
403D4×C41—41no—
404D4×C41—41no—
405D4×C41—41no—
406D4×C41—41no—
407D4×C41—44no—
408D4×C41—42no—
409D4×C41—42no—
410D4×C41—81no—
411D4×C41—81no—
412D4×C41—81no—
413D4×C41—81no—
414D4×C41—81no—
415D4×C41—81no—
416D4×C41—81no—
417D4×C41—81no—
418D4×C41—81no—
419D4×C41—81no—
420D4×C41—81no—
421D4×C41—81no—
422D4×C41—84no—
423C2×C4×C41—22no—
424C2×C4×C41—22no—
425C2×C4×C41—22no—
426C2×C4×C41—22no—
427C2×C4×C41—21no—
428C2×C4×C41—21no—
429C2×C4×C41—21no—
430C2×C4×C41—21no—
431C2×C4×C41—21no—
432C2×C4×C41—21no—
433C2×C4×C41—21no—
434C2×C4×C41—21no—
435C2×C4×C41—21no—
436C2×C4×C41—21no—
437C2×C4×C41—41no—
438C2×C4×C41—41no—
439C2×C4×C41—41no—
440C2×C4×C41—41no—
441C2×C4×C41—44no—
442C2×C4×C41—44no—
443C2×C4×C41—41no—
444C2×C4×C41—41no—
445C2×C4×C41—41no—
446C2×C4×C41—41no—
447C2×C4×C41—41no—
448C2×C4×C41—41no—
449C2×C4×C41—41no—
450C2×C4×C41—41no—
451C2×C4×C41—41no—
452C2×C4×C41—81no—
453C2×C4×C41—81no—
454C2×C4×C41—81no—
455C2×C4×C41—81no—
456C2×C4×C41—81no—
457C2×C4×C41—81no—
458C2×C4×C41—81no—
459C2×C4×C41—84no—
460C2×C4×C41#12011yescharacteristic
461C2×C4×C41#12011yescharacteristic
462C2×C4×C41C22×D411yescharacteristic
463C2×C4×C41C22×D411yescharacteristic
464C8×C41—41no—
465C8×C41—41no—
466C8×C41—41no—
467C8×C41—41no—
468#18252C4111yesmaximal, characteristic, direct product factor, Sylow
469C22×C41—21no—
470C22×C41—21no—
471C22×C41—21no—
472C22×C41—21no—
473C22×C41—21no—
474C22×C41—21no—
475C22×C41—21no—
476C22×C41—42no—
477C22×C41—42no—
478C22×C41—42no—
479C22×C41—42no—
480C22×C41—41no—
481C22×C41—41no—
482C22×C41—41no—
483C22×C41—41no—
484C22×C41—41no—
485C22×C41—41no—
486C22×C41—41no—
487C22×C41—41no—
488C22×C41—42no—
489C22×C41—41no—
490C22×C41—41no—
491C22×C41—41no—
492C22×C41—41no—
493C22×C41—81no—
494C22×C41—81no—
495C22×C41—81no—
496C22×C41—81no—
497C22×C41—81no—
498C22×C41—81no—
499C22×C41—162no—
500C22×C41—162no—
501C22×C41B(4,𝔽2)12yes—
502C22×C41C2×#12011yescharacteristic
503C22×C41#57611yescharacteristic
504C22×C41#57711yescharacteristic
505C4×C41—21no—
506C4×C41—21no—
507C4×C41—21no—
508C4×C41—21no—
509C4×C41—42no—
510C4×C41—41no—
511C4×C41—41no—
512C4×C41—41no—
513C4×C41—41no—
514C4×C41—41no—
515C4×C41—41no—
516C4×C41—42no—
517C4×C41—41no—
518C4×C41—41no—
519C4×C41—81no—
520#3534C2×C4111yescharacteristic, complemented
521#3006C2×C4111yescharacteristic, complemented
522#3002C2×C4111yescharacteristic, complemented
523#2430C2×C4111yescharacteristic, complemented
524#1606C2×C4111yescharacteristic, complemented
525#1604C2×C4111yescharacteristic, complemented
526#1603C2×C4111yescharacteristic, complemented
527#1601C2×C4111yescharacteristic, complemented
528#1600C2×C4111yescharacteristic, complemented
529#1598C2×C4111yescharacteristic, complemented
530#1597C2×C4111yescharacteristic, complemented
531#1595C2×C4111yescharacteristic, complemented
532#1504C2×C4111yescharacteristic, complemented
533C2×#327C2×C4111yescharacteristic, complemented
534#1468C2×C4111yescharacteristic, complemented
535C2×C41—21no—
536C2×C41—21no—
537C2×C41—22no—
538C2×C41—41no—
539C2×C41—82no—
540C2×C41—81no—
541C2×C41—81no—
542C2×C41—81no—
543C2×C41—81no—
544C2×C41#301211yescharacteristic
545C2×C41#301811yescharacteristic
546C2×C41C2×B(4,𝔽2)11yescharacteristic
547C22×#41C22×C4111yescharacteristic, complemented
548C2×AGL(1,ℤ/8)—21no—
549C2×#135—21no—
550#562—21no—
551#560—21no—
552#553—21no—
553#551—21no—
554#546—21no—
555#546—21no—
556#546—21no—
557D42—21no—
558#540—21no—
559#539—21no—
560#539C22×C4111yescharacteristic
561#538—21no—
562#538C22×C4111yescharacteristic
563#537C22×C4111yescharacteristic
564#534—21no—
565#534C22×C4111yescharacteristic
566#525C22×C4111yescharacteristic
567C2×#123C22×C4111yescharacteristic
568C2×#121—21no—
569C2×#121C22×C4111yescharacteristic
570#452—21no—
571#451C22×C4111yescharacteristic, complemented
572#450C22×C4111yescharacteristic, complemented
573#449—21no—
574#449—21no—
575#449—21no—
576#448C22×C4111yescharacteristic
577#448C22×C4111yescharacteristic, complemented
578#448C22×C4111yescharacteristic, complemented
579#447C22×C4111yescharacteristic
580#447C22×C4111yescharacteristic, complemented
581#447C22×C4111yescharacteristic, complemented
582#417—21no—
583#416—21no—
584#407C22×C4111yescharacteristic, complemented
585C2×C22⋊C8C22×C4111yescharacteristic, complemented
586#395C22×C4111yescharacteristic, complemented
587#394C22×C4111yescharacteristic, complemented
588#393C22×C4111yescharacteristic, complemented
589#392C22×C4111yescharacteristic, complemented
590#386—21no—
591#386—21no—
592#385—21no—
593C2×#95C22×C4111yescharacteristic, complemented
594#328C22×C4111yescharacteristic, complemented
595#328C22×C4111yescharacteristic, complemented
596#327C22×C4111yescharacteristic
597#327C22×C4111yescharacteristic
598#327C22×C4111yescharacteristic, complemented
599#327C22×C4111yescharacteristic, complemented
600#327C22×C4111yescharacteristic, complemented
601#327C22×C4111yescharacteristic, complemented
602#324C22×C4111yescharacteristic, complemented
603#324C22×C4111yescharacteristic, complemented
604#323C22×C4111yescharacteristic, complemented
605#323C22×C4111yescharacteristic, complemented
606C41#1825211yescharacteristic, direct product factor, Sylow
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C4111yescharacteristic, complemented
614C22×Q8C23×C4111yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C4111yescharacteristic
621C22×D4D4×C4111yescharacteristic, complemented
622C22×D4C23×C4111yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C4111yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C4111yescharacteristic, complemented
668C22⋊Q8C23×C4111yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C4111yescharacteristic, complemented
686#121D4×C4111yescharacteristic, complemented
687#121D4×C4111yescharacteristic, complemented
688#121C23×C4111yescharacteristic
689#121C23×C4111yescharacteristic
690#121C23×C4111yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C4111yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C4111yescharacteristic
711C2×C4⋊C4D4×C4111yescharacteristic, complemented
712C2×C4⋊C4C23×C4111yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C4111yescharacteristic
721C2×C22⋊C4D4×C4111yescharacteristic
722C2×C22⋊C4C23×C4111yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C4111yescharacteristic
734C22⋊C8C23×C4111yescharacteristic
735C22⋊C8C23×C4111yescharacteristic
736C22⋊C8C23×C4111yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C4111yescharacteristic
741#95C23×C4111yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C4111yescharacteristic
746C24C2×D4×C4111yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C4111yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C4111yescharacteristic
798C2×D4C2×D4×C4111yescharacteristic
799C2×D4C2×D4×C4111yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C4111yescharacteristic
819C22×C4C2×D4×C4111yescharacteristic
820C22×C4C2×D4×C4111yescharacteristic
821C22×C4C2×D4×C4111yescharacteristic
822C22×C4C2×D4×C4111yescharacteristic
823C22×C4C2×D4×C4111yescharacteristic
824C22×C4C2×D4×C4111yescharacteristic
825C22×C4C2×D4×C4111yescharacteristic
826C22×C4C24×C4111yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C4111yescharacteristic
856C4⋊C4C2×D4×C4111yescharacteristic
857C4⋊C4C2×D4×C4111yescharacteristic
858C4⋊C4C2×D4×C4111yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C4111yescharacteristic
917C23#120×C4111yescharacteristic
918C23C22×D4×C4111yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—44no—
940D4—42no—
941D4—42no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C4111yescharacteristic
993C2×C4#120×C4111yescharacteristic
994C2×C4C22×D4×C4111yescharacteristic
995C2×C4C22×D4×C4111yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C41×B(4,𝔽2)12yes—
1033C22C2×#120×C4111yescharacteristic
1034C22C41×#57611yescharacteristic
1035C22C41×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C41×#301211yescharacteristic
1061C2C41×#301811yescharacteristic
1062C2C2×C41×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
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
1. C41×#3534C2semidirect
2. C41×#3006C2semidirect
3. C41×#3002C2semidirect
4. C41×#2430C2semidirect
5. C41×#1606C2semidirect
6. C41×#1604C2semidirect
7. C41×#1603C2semidirect
8. C41×#1601C2semidirect
9. C41×#1600C2semidirect
10. C41×#1598C2semidirect
11. C41×#1597C2semidirect
12. C41×#1595C2semidirect
13. C41×#1504C2semidirect
14. C2×C41×#327C2semidirect
15. C41×#1468C2semidirect
16. C22×#41×C41C22semidirect
40. C41×#451C22semidirect
41. C41×#450C22semidirect
46. C41×#448C22semidirect
47. C41×#448C22semidirect
49. C41×#447C22semidirect
50. C41×#447C22semidirect
53. C41×#407C22semidirect
54. C2×C22⋊C8×C41C22semidirect
55. C41×#395C22semidirect
56. C41×#394C22semidirect
57. C41×#393C22semidirect
58. C41×#392C22semidirect
62. C2×#95×C41C22semidirect
63. C41×#328C22semidirect
64. C41×#328C22semidirect
67. C41×#327C22semidirect
68. C41×#327C22semidirect
69. C41×#327C22semidirect
70. C41×#327C22semidirect
71. C41×#324C22semidirect
72. C41×#324C22semidirect
73. C41×#323C22semidirect
74. C41×#323C22semidirect
81. C2×#41×C41D4semidirect
89. C22×D4×C41D4semidirect
135. C22⋊Q8×C41D4semidirect
153. #121×C41D4semidirect
154. #121×C41D4semidirect
155. #121×C41D4semidirect
176. #117×C41D4semidirect
179. C2×C4⋊C4×C41D4semidirect
468. #18252C41direct (N × H)
520. #3534C2×C41semidirect
521. #3006C2×C41semidirect
522. #3002C2×C41semidirect
523. #2430C2×C41semidirect
524. #1606C2×C41semidirect
525. #1604C2×C41semidirect
526. #1603C2×C41semidirect
527. #1601C2×C41semidirect
528. #1600C2×C41semidirect
529. #1598C2×C41semidirect
530. #1597C2×C41semidirect
531. #1595C2×C41semidirect
532. #1504C2×C41semidirect
533. C2×#327C2×C41semidirect
534. #1468C2×C41semidirect
547. C22×#41C22×C41semidirect
571. #451C22×C41semidirect
572. #450C22×C41semidirect
577. #448C22×C41semidirect
578. #448C22×C41semidirect
580. #447C22×C41semidirect
581. #447C22×C41semidirect
584. #407C22×C41semidirect
585. C2×C22⋊C8C22×C41semidirect
586. #395C22×C41semidirect
587. #394C22×C41semidirect
588. #393C22×C41semidirect
589. #392C22×C41semidirect
593. C2×#95C22×C41semidirect
594. #328C22×C41semidirect
595. #328C22×C41semidirect
598. #327C22×C41semidirect
599. #327C22×C41semidirect
600. #327C22×C41semidirect
601. #327C22×C41semidirect
602. #324C22×C41semidirect
603. #324C22×C41semidirect
604. #323C22×C41semidirect
605. #323C22×C41semidirect
606. C41#18252direct (N × H)
613. C2×#41D4×C41semidirect
621. C22×D4D4×C41semidirect
667. C22⋊Q8D4×C41semidirect
685. #121D4×C41semidirect
686. #121D4×C41semidirect
687. #121D4×C41semidirect
708. #117D4×C41semidirect
711. C2×C4⋊C4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35342
C41×#30062
C41×#30022
C41×#24302
C41×#16062
C41×#16042
C41×#16032
C41×#16012
C41×#16002
C41×#15982
C41×#15972
C41×#15952
C41×#15042
C2×C41×#3272
C41×#14682
#1825241