Finite Group Databasebeta

← C41×#18262 #23794463

Subgroups — C41×#18262 #23794463

Order 10496.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3534C211yesmaximal, characteristic
2C41×#3094C211yesmaximal, characteristic, complemented
3C41×#3091C211yesmaximal, characteristic, complemented
4C41×#2498C211yesmaximal, characteristic, complemented
5C41×#1618C211yesmaximal, characteristic, complemented
6C41×#1616C211yesmaximal, characteristic, complemented
7C41×#1615C211yesmaximal, characteristic, complemented
8C41×#1613C211yesmaximal, characteristic, complemented
9C41×#1612C211yesmaximal, characteristic, complemented
10C41×#1610C211yesmaximal, characteristic, complemented
11C41×#1609C211yesmaximal, characteristic, complemented
12C41×#1607C211yesmaximal, characteristic, complemented
13C41×#1504C211yesmaximal, characteristic, complemented
14C2×C41×#327C211yesmaximal, characteristic, complemented
15C41×#1468C211yesmaximal, characteristic, complemented
16C41×#562—21no—
17C41×#560—21no—
18C41×#553—21no—
19C41×#551—21no—
20C41×#546—21no—
21C41×#546—21no—
22C41×#546—21no—
23D42×C41—21no—
24C41×#540—21no—
25C41×#539—21no—
26C41×#539C2211yescharacteristic
27C41×#538—21no—
28C41×#538C2211yescharacteristic
29C41×#537C2211yescharacteristic
30C41×#534—21no—
31C41×#534C2211yescharacteristic
32C41×#525C2211yescharacteristic
33C2×#123×C41C2211yescharacteristic
34C2×#121×C41C2211yescharacteristic
35C2×#117×C41C2211yescharacteristic, complemented
36C41×#485—21no—
37C41×#484C2211yescharacteristic, complemented
38C41×#483C2211yescharacteristic, complemented
39C41×#482—21no—
40C41×#482—21no—
41C41×#482—21no—
42C41×#481C2211yescharacteristic
43C41×#481C2211yescharacteristic, complemented
44C41×#481C2211yescharacteristic, complemented
45C41×#480C2211yescharacteristic
46C41×#480C2211yescharacteristic, complemented
47C41×#480C2211yescharacteristic, complemented
48C41×#428—21no—
49C41×#427—21no—
50C41×#418—21no—
51C41×#416—21no—
52C41×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic, complemented
54C41×#400C2211yescharacteristic, complemented
55C41×#399C2211yescharacteristic, complemented
56C41×#398C2211yescharacteristic, complemented
57C41×#397C2211yescharacteristic, complemented
58C41×#388—21no—
59C41×#387—21no—
60C41×#386—21no—
61C41×#380—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×C41D411yescharacteristic
77C22×D4×C41—21no—
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41D411yescharacteristic
81C22×D4×C41D411yescharacteristic
82C23×C4×C41—21no—
83C23×C4×C41C2311yescharacteristic
84C2×M16×C41—21no—
85C22×C8×C41—21no—
86#127×C41—21no—
87#126×C41—21no—
88#126×C41—21no—
89#126×C41—21no—
90#126×C41—21no—
91#125×C41—21no—
92#125×C41—21no—
93#124×C41—21no—
94#124×C41—21no—
95#124×C41—21no—
96#123×C41—21no—
97#123×C41—21no—
98#123×C41—21no—
99#123×C41—21no—
100#123×C41—21no—
101#123×C41—21no—
102#123×C41—21no—
103#123×C41—21no—
104#123×C41—21no—
105#123×C41—21no—
106#123×C41—21no—
107#123×C41—21no—
108#123×C41—21no—
109#123×C41—21no—
110C22⋊Q8×C41—21no—
111C22⋊Q8×C41—21no—
112C22⋊Q8×C41—21no—
113C22⋊Q8×C41—21no—
114C22⋊Q8×C41—21no—
115C22⋊Q8×C41D411yescharacteristic
116C22⋊Q8×C41C2311yescharacteristic
117#121×C41—21no—
118#121×C41—21no—
119#121×C41—21no—
120#121×C41—21no—
121#121×C41—21no—
122#121×C41—21no—
123#121×C41—21no—
124#121×C41—21no—
125#121×C41—21no—
126#121×C41—21no—
127#121×C41—21no—
128#121×C41—21no—
129#121×C41—21no—
130#121×C41—21no—
131#121×C41—21no—
132#121×C41D411yescharacteristic
133#121×C41D411yescharacteristic
134#121×C41D411yescharacteristic
135#121×C41C2311yescharacteristic
136#121×C41C2311yescharacteristic
137#121×C41C2311yescharacteristic
138#120×C41—21no—
139#120×C41—21no—
140#120×C41—21no—
141#120×C41—21no—
142#120×C41—21no—
143#120×C41—21no—
144#120×C41—21no—
145#120×C41—21no—
146C4×D4×C41—21no—
147C4×D4×C41—21no—
148C4×D4×C41—21no—
149C4×D4×C41—21no—
150C4×D4×C41—21no—
151C4×D4×C41—21no—
152C4×D4×C41—21no—
153C4×D4×C41—21no—
154#117×C41—21no—
155#117×C41—21no—
156#117×C41—21no—
157#117×C41—21no—
158#117×C41—21no—
159#117×C41D411yescharacteristic
160C2×C4⋊C4×C41—21no—
161C2×C4⋊C4×C41—21no—
162C2×C4⋊C4×C41D411yescharacteristic
163C2×C4⋊C4×C41D411yescharacteristic
164C2×C4⋊C4×C41C2311yescharacteristic
165C2×C4⋊C4×C41C2311yescharacteristic
166C2×C4⋊C4×C41C2311yescharacteristic
167C2×C22⋊C4×C41—21no—
168C2×C22⋊C4×C41—21no—
169C2×C22⋊C4×C41—21no—
170C2×C22⋊C4×C41—21no—
171C2×C22⋊C4×C41—21no—
172C2×C22⋊C4×C41—21no—
173C2×C22⋊C4×C41D411yescharacteristic
174C2×C22⋊C4×C41D411yescharacteristic
175C2×C22⋊C4×C41C2311yescharacteristic
176C2×C42×C41—21no—
177#107×C41—21no—
178#107×C41—21no—
179#107×C41—21no—
180#107×C41—21no—
181#106×C41—21no—
182#106×C41—21no—
183#106×C41—21no—
184#106×C41—21no—
185#103×C41—21no—
186#103×C41—21no—
187#102×C41—21no—
188#102×C41—21no—
189#102×C41—21no—
190#102×C41—21no—
191#102×C41—21no—
192#102×C41—21no—
193C22⋊C8×C41—21no—
194C22⋊C8×C41—21no—
195C22⋊C8×C41C2311yescharacteristic
196C22⋊C8×C41C2311yescharacteristic
197C22⋊C8×C41C2311yescharacteristic
198C22⋊C8×C41C2311yescharacteristic
199#95×C41—21no—
200#95×C41—21no—
201#95×C41—21no—
202#95×C41—21no—
203#95×C41—21no—
204#95×C41C2311yescharacteristic
205#95×C41C2311yescharacteristic
206C24×C41—21no—
207C24×C41—21no—
208C24×C41C2×D411yescharacteristic
209C24×C41C2×D411yescharacteristic
210#41×C41—42no—
211#41×C41—81no—
212#41×C41—81no—
213C2×Q8×C41—21no—
214C2×Q8×C41C2×D411yescharacteristic
215C2×D4×C41—21no—
216C2×D4×C41—21no—
217C2×D4×C41—21no—
218C2×D4×C41—21no—
219C2×D4×C41—21no—
220C2×D4×C41—21no—
221C2×D4×C41—21no—
222C2×D4×C41—21no—
223C2×D4×C41—21no—
224C2×D4×C41—21no—
225C2×D4×C41—21no—
226C2×D4×C41—21no—
227C2×D4×C41—21no—
228C2×D4×C41—21no—
229C2×D4×C41—21no—
230C2×D4×C41—21no—
231C2×D4×C41—21no—
232C2×D4×C41—42no—
233C2×D4×C41—42no—
234C2×D4×C41—81no—
235C2×D4×C41—81no—
236C2×D4×C41—81no—
237C2×D4×C41—81no—
238C2×D4×C41—82no—
239C2×D4×C41C2×D411yescharacteristic
240C2×D4×C41C2×D411yescharacteristic
241C2×D4×C41C2×D411yescharacteristic
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—21no—
246C22×C4×C41—21no—
247C22×C4×C41—21no—
248C22×C4×C41—21no—
249C22×C4×C41—21no—
250C22×C4×C41—21no—
251C22×C4×C41—21no—
252C22×C4×C41—21no—
253C22×C4×C41—42no—
254C22×C4×C41—42no—
255C22×C4×C41—42no—
256C22×C4×C41—81no—
257C22×C4×C41C2×D411yescharacteristic
258C22×C4×C41C2×D411yescharacteristic
259C22×C4×C41C2×D411yescharacteristic
260C22×C4×C41C2×D411yescharacteristic
261C22×C4×C41C2×D411yescharacteristic
262C22×C4×C41C2×D411yescharacteristic
263C22×C4×C41C2×D411yescharacteristic
264C22×C4×C41C2×D411yescharacteristic
265C22×C4×C41C2411yescharacteristic
266M16×C41—42no—
267C2×C8×C41—21no—
268C2×C8×C41—21no—
269C2×C8×C41—21no—
270C2×C8×C41—21no—
271C2×C8×C41—42no—
272C4⋊C4×C41—21no—
273C4⋊C4×C41—21no—
274C4⋊C4×C41—21no—
275C4⋊C4×C41—21no—
276C4⋊C4×C41—21no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—21no—
280C4⋊C4×C41—21no—
281C4⋊C4×C41—21no—
282C4⋊C4×C41—21no—
283C4⋊C4×C41—21no—
284C4⋊C4×C41—21no—
285C4⋊C4×C41—21no—
286C4⋊C4×C41—21no—
287C4⋊C4×C41—21no—
288C4⋊C4×C41—21no—
289C4⋊C4×C41—42no—
290C4⋊C4×C41—81no—
291C4⋊C4×C41C2×D411yescharacteristic
292C4⋊C4×C41C2×D411yescharacteristic
293C4⋊C4×C41C2×D411yescharacteristic
294C4⋊C4×C41C2×D411yescharacteristic
295C22⋊C4×C41—21no—
296C22⋊C4×C41—21no—
297C22⋊C4×C41—21no—
298C22⋊C4×C41—21no—
299C22⋊C4×C41—21no—
300C22⋊C4×C41—21no—
301C22⋊C4×C41—21no—
302C22⋊C4×C41—21no—
303C22⋊C4×C41—21no—
304C22⋊C4×C41—21no—
305C22⋊C4×C41—21no—
306C22⋊C4×C41—21no—
307C22⋊C4×C41—21no—
308C22⋊C4×C41—21no—
309C22⋊C4×C41—21no—
310C22⋊C4×C41—21no—
311C22⋊C4×C41—21no—
312C22⋊C4×C41—21no—
313C22⋊C4×C41—21no—
314C22⋊C4×C41—21no—
315C22⋊C4×C41—21no—
316C22⋊C4×C41—21no—
317C22⋊C4×C41—21no—
318C22⋊C4×C41—21no—
319C22⋊C4×C41—21no—
320C22⋊C4×C41—42no—
321C22⋊C4×C41—41no—
322C22⋊C4×C41—41no—
323C22⋊C4×C41—81no—
324C42×C41—21no—
325C42×C41—21no—
326C42×C41—21no—
327C42×C41—41no—
328C42×C41—41no—
329C23×C41—21no—
330C23×C41—21no—
331C23×C41—22no—
332C23×C41—21no—
333C23×C41—21no—
334C23×C41—21no—
335C23×C41—21no—
336C23×C41—21no—
337C23×C41—21no—
338C23×C41—41no—
339C23×C41—41no—
340C23×C41—41no—
341C23×C41—42no—
342C23×C41—81no—
343C23×C41—81no—
344C23×C41—81no—
345C23×C41—81no—
346C23×C41—81no—
347C23×C41#12011yescharacteristic
348C23×C41#12011yescharacteristic
349C23×C41C22×D411yescharacteristic
350Q8×C41—41no—
351Q8×C41—81no—
352D4×C41—41no—
353D4×C41—41no—
354D4×C41—41no—
355D4×C41—41no—
356D4×C41—41no—
357D4×C41—41no—
358D4×C41—41no—
359D4×C41—41no—
360D4×C41—41no—
361D4×C41—42no—
362D4×C41—42no—
363D4×C41—81no—
364D4×C41—81no—
365D4×C41—81no—
366D4×C41—81no—
367D4×C41—81no—
368D4×C41—81no—
369D4×C41—81no—
370D4×C41—81no—
371D4×C41—81no—
372D4×C41—81no—
373D4×C41—81no—
374D4×C41—81no—
375C2×C4×C41—22no—
376C2×C4×C41—22no—
377C2×C4×C41—22no—
378C2×C4×C41—21no—
379C2×C4×C41—21no—
380C2×C4×C41—21no—
381C2×C4×C41—21no—
382C2×C4×C41—21no—
383C2×C4×C41—21no—
384C2×C4×C41—21no—
385C2×C4×C41—21no—
386C2×C4×C41—21no—
387C2×C4×C41—21no—
388C2×C4×C41—41no—
389C2×C4×C41—41no—
390C2×C4×C41—41no—
391C2×C4×C41—41no—
392C2×C4×C41—41no—
393C2×C4×C41—41no—
394C2×C4×C41—41no—
395C2×C4×C41—41no—
396C2×C4×C41—41no—
397C2×C4×C41—41no—
398C2×C4×C41—41no—
399C2×C4×C41—41no—
400C2×C4×C41—41no—
401C2×C4×C41—41no—
402C2×C4×C41—41no—
403C2×C4×C41—41no—
404C2×C4×C41—41no—
405C2×C4×C41—81no—
406C2×C4×C41—81no—
407C2×C4×C41—81no—
408C2×C4×C41—81no—
409C2×C4×C41—81no—
410C2×C4×C41—81no—
411C2×C4×C41—81no—
412C2×C4×C41—84no—
413C2×C4×C41#12011yescharacteristic
414C2×C4×C41#12011yescharacteristic
415C2×C4×C41C22×D411yescharacteristic
416C2×C4×C41C22×D411yescharacteristic
417C8×C41—41no—
418C8×C41—41no—
419C8×C41—41no—
420C8×C41—41no—
421#18262C4111yesmaximal, characteristic, direct product factor, Sylow
422C22×C41—21no—
423C22×C41—21no—
424C22×C41—21no—
425C22×C41—21no—
426C22×C41—21no—
427C22×C41—21no—
428C22×C41—21no—
429C22×C41—42no—
430C22×C41—42no—
431C22×C41—41no—
432C22×C41—41no—
433C22×C41—41no—
434C22×C41—41no—
435C22×C41—41no—
436C22×C41—41no—
437C22×C41—41no—
438C22×C41—41no—
439C22×C41—41no—
440C22×C41—41no—
441C22×C41—41no—
442C22×C41—41no—
443C22×C41—81no—
444C22×C41—81no—
445C22×C41—162no—
446C22×C41—162no—
447C22×C41#45812yes—
448C22×C41C2×#12011yescharacteristic
449C22×C41#57611yescharacteristic
450C22×C41#57711yescharacteristic
451C4×C41—21no—
452C4×C41—21no—
453C4×C41—21no—
454C4×C41—21no—
455C4×C41—42no—
456C4×C41—41no—
457C4×C41—41no—
458C4×C41—41no—
459C4×C41—41no—
460C4×C41—41no—
461C4×C41—41no—
462C4×C41—41no—
463C4×C41—41no—
464C4×C41—81no—
465C4×C41—81no—
466C4×C41—81no—
467#3534C2×C4111yescharacteristic
468#3094C2×C4111yescharacteristic, complemented
469#3091C2×C4111yescharacteristic, complemented
470#2498C2×C4111yescharacteristic, complemented
471#1618C2×C4111yescharacteristic, complemented
472#1616C2×C4111yescharacteristic, complemented
473#1615C2×C4111yescharacteristic, complemented
474#1613C2×C4111yescharacteristic, complemented
475#1612C2×C4111yescharacteristic, complemented
476#1610C2×C4111yescharacteristic, complemented
477#1609C2×C4111yescharacteristic, complemented
478#1607C2×C4111yescharacteristic, complemented
479#1504C2×C4111yescharacteristic, complemented
480C2×#327C2×C4111yescharacteristic, complemented
481#1468C2×C4111yescharacteristic, complemented
482C2×C41—21no—
483C2×C41—21no—
484C2×C41—22no—
485C2×C41—41no—
486C2×C41—81no—
487C2×C41—81no—
488C2×C41—81no—
489C2×C41—81no—
490C2×C41#301211yescharacteristic
491C2×C41#301811yescharacteristic
492C2×C41C2×#45811yescharacteristic
493#562—21no—
494#560—21no—
495#553—21no—
496#551—21no—
497#546—21no—
498#546—21no—
499#546—21no—
500D42—21no—
501#540—21no—
502#539—21no—
503#539C22×C4111yescharacteristic
504#538—21no—
505#538C22×C4111yescharacteristic
506#537C22×C4111yescharacteristic
507#534—21no—
508#534C22×C4111yescharacteristic
509#525C22×C4111yescharacteristic
510C2×#123C22×C4111yescharacteristic
511C2×#121C22×C4111yescharacteristic
512C2×#117C22×C4111yescharacteristic, complemented
513#485—21no—
514#484C22×C4111yescharacteristic, complemented
515#483C22×C4111yescharacteristic, complemented
516#482—21no—
517#482—21no—
518#482—21no—
519#481C22×C4111yescharacteristic
520#481C22×C4111yescharacteristic, complemented
521#481C22×C4111yescharacteristic, complemented
522#480C22×C4111yescharacteristic
523#480C22×C4111yescharacteristic, complemented
524#480C22×C4111yescharacteristic, complemented
525#428—21no—
526#427—21no—
527#418—21no—
528#416—21no—
529#407C22×C4111yescharacteristic, complemented
530C2×C22⋊C8C22×C4111yescharacteristic, complemented
531#400C22×C4111yescharacteristic, complemented
532#399C22×C4111yescharacteristic, complemented
533#398C22×C4111yescharacteristic, complemented
534#397C22×C4111yescharacteristic, complemented
535#388—21no—
536#387—21no—
537#386—21no—
538#380—21no—
539C2×#95C22×C4111yescharacteristic, complemented
540#328C22×C4111yescharacteristic, complemented
541#328C22×C4111yescharacteristic, complemented
542#327C22×C4111yescharacteristic
543#327C22×C4111yescharacteristic
544#327C22×C4111yescharacteristic, complemented
545#327C22×C4111yescharacteristic, complemented
546#327C22×C4111yescharacteristic, complemented
547#327C22×C4111yescharacteristic, complemented
548#324C22×C4111yescharacteristic, complemented
549#324C22×C4111yescharacteristic, complemented
550#323C22×C4111yescharacteristic, complemented
551#323C22×C4111yescharacteristic, complemented
552C41#1826211yescharacteristic, direct product factor, Sylow
553C2×#41—21no—
554C2×#41D4×C4111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C4111yescharacteristic
559C22×D4D4×C4111yescharacteristic
560C23×C4—21no—
561C23×C4C23×C4111yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C4111yescharacteristic
594C22⋊Q8C23×C4111yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C4111yescharacteristic
611#121D4×C4111yescharacteristic
612#121D4×C4111yescharacteristic
613#121C23×C4111yescharacteristic
614#121C23×C4111yescharacteristic
615#121C23×C4111yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C4111yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C4111yescharacteristic
641C2×C4⋊C4D4×C4111yescharacteristic
642C2×C4⋊C4C23×C4111yescharacteristic
643C2×C4⋊C4C23×C4111yescharacteristic
644C2×C4⋊C4C23×C4111yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C4111yescharacteristic
652C2×C22⋊C4D4×C4111yescharacteristic
653C2×C22⋊C4C23×C4111yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C4111yescharacteristic
674C22⋊C8C23×C4111yescharacteristic
675C22⋊C8C23×C4111yescharacteristic
676C22⋊C8C23×C4111yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C4111yescharacteristic
683#95C23×C4111yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C4111yescharacteristic
687C24C2×D4×C4111yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C4111yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C4111yescharacteristic
718C2×D4C2×D4×C4111yescharacteristic
719C2×D4C2×D4×C4111yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C4111yescharacteristic
736C22×C4C2×D4×C4111yescharacteristic
737C22×C4C2×D4×C4111yescharacteristic
738C22×C4C2×D4×C4111yescharacteristic
739C22×C4C2×D4×C4111yescharacteristic
740C22×C4C2×D4×C4111yescharacteristic
741C22×C4C2×D4×C4111yescharacteristic
742C22×C4C2×D4×C4111yescharacteristic
743C22×C4C24×C4111yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C4111yescharacteristic
770C4⋊C4C2×D4×C4111yescharacteristic
771C4⋊C4C2×D4×C4111yescharacteristic
772C4⋊C4C2×D4×C4111yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C4111yescharacteristic
826C23#120×C4111yescharacteristic
827C23C22×D4×C4111yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C4111yescharacteristic
892C2×C4#120×C4111yescharacteristic
893C2×C4C22×D4×C4111yescharacteristic
894C2×C4C22×D4×C4111yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22C41×#45812yes—
925C22C2×#120×C4111yescharacteristic
926C22C41×#57611yescharacteristic
927C22C41×#57711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C41×#301211yescharacteristic
953C2C41×#301811yescharacteristic
954C2C2×C41×#45811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#3534C2
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×#3094C2semidirect
3. C41×#3091C2semidirect
4. C41×#2498C2semidirect
5. C41×#1618C2semidirect
6. C41×#1616C2semidirect
7. C41×#1615C2semidirect
8. C41×#1613C2semidirect
9. C41×#1612C2semidirect
10. C41×#1610C2semidirect
11. C41×#1609C2semidirect
12. C41×#1607C2semidirect
13. C41×#1504C2semidirect
14. C2×C41×#327C2semidirect
15. C41×#1468C2semidirect
35. C2×#117×C41C22semidirect
37. C41×#484C22semidirect
38. C41×#483C22semidirect
43. C41×#481C22semidirect
44. C41×#481C22semidirect
46. C41×#480C22semidirect
47. C41×#480C22semidirect
52. C41×#407C22semidirect
53. C2×C22⋊C8×C41C22semidirect
54. C41×#400C22semidirect
55. C41×#399C22semidirect
56. C41×#398C22semidirect
57. C41×#397C22semidirect
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
421. #18262C41direct (N × H)
468. #3094C2×C41semidirect
469. #3091C2×C41semidirect
470. #2498C2×C41semidirect
471. #1618C2×C41semidirect
472. #1616C2×C41semidirect
473. #1615C2×C41semidirect
474. #1613C2×C41semidirect
475. #1612C2×C41semidirect
476. #1610C2×C41semidirect
477. #1609C2×C41semidirect
478. #1607C2×C41semidirect
479. #1504C2×C41semidirect
480. C2×#327C2×C41semidirect
481. #1468C2×C41semidirect
512. C2×#117C22×C41semidirect
514. #484C22×C41semidirect
515. #483C22×C41semidirect
520. #481C22×C41semidirect
521. #481C22×C41semidirect
523. #480C22×C41semidirect
524. #480C22×C41semidirect
529. #407C22×C41semidirect
530. C2×C22⋊C8C22×C41semidirect
531. #400C22×C41semidirect
532. #399C22×C41semidirect
533. #398C22×C41semidirect
534. #397C22×C41semidirect
539. C2×#95C22×C41semidirect
540. #328C22×C41semidirect
541. #328C22×C41semidirect
544. #327C22×C41semidirect
545. #327C22×C41semidirect
546. #327C22×C41semidirect
547. #327C22×C41semidirect
548. #324C22×C41semidirect
549. #324C22×C41semidirect
550. #323C22×C41semidirect
551. #323C22×C41semidirect
552. C41#18262direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35342
C41×#30942
C41×#30912
C41×#24982
C41×#16182
C41×#16162
C41×#16152
C41×#16132
C41×#16122
C41×#16102
C41×#16092
C41×#16072
C41×#15042
C2×C41×#3272
C41×#14682
#1826241