Finite Group Databasebeta

← C41×#18415 #23794616

Subgroups — C41×#18415 #23794616

Order 10496.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3534C211yesmaximal, characteristic
2C41×#3196C211yesmaximal, characteristic, complemented
3C41×#3187C211yesmaximal, characteristic, complemented
4C41×#2663C211yesmaximal, characteristic, complemented
5C41×#1618C211yesmaximal, characteristic, complemented
6C41×#1616C211yesmaximal, characteristic, complemented
7C41×#1615C211yesmaximal, characteristic, complemented
8C41×#1613C211yesmaximal, characteristic, complemented
9C41×#1606C211yesmaximal, characteristic, complemented
10C41×#1604C211yesmaximal, characteristic, complemented
11C41×#1603C211yesmaximal, characteristic, complemented
12C41×#1601C211yesmaximal, characteristic, complemented
13C41×#1507C211yesmaximal, characteristic, complemented
14C41×#1501C211yesmaximal, 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×C22⋊Q8×C41C2211yescharacteristic, complemented
35C2×#121×C41C2211yescharacteristic
36C41×#485—21no—
37C41×#484C2211yescharacteristic, complemented
38C41×#483—21no—
39C41×#481C2211yescharacteristic
40C41×#481C2211yescharacteristic, complemented
41C41×#481C2211yescharacteristic, complemented
42C41×#470—21no—
43C41×#468—21no—
44C41×#465—21no—
45C41×#465—21no—
46C41×#452—21no—
47C41×#451C2211yescharacteristic, complemented
48C41×#450—21no—
49C41×#448C2211yescharacteristic
50C41×#448C2211yescharacteristic, complemented
51C41×#448C2211yescharacteristic, complemented
52C41×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic, complemented
54C41×#400C2211yescharacteristic, complemented
55C41×#399C2211yescharacteristic, complemented
56C41×#397—21no—
57C41×#395C2211yescharacteristic, complemented
58C41×#394—21no—
59C41×#393C2211yescharacteristic, complemented
60C41×#389—21no—
61C41×#388—21no—
62C4×C22⋊C4×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×Q8×C41C2311yescharacteristic
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41—21no—
81C22×D4×C41D411yescharacteristic
82C22×D4×C41D411yescharacteristic
83C23×C4×C41C2311yescharacteristic
84C2×Q16×C41—21no—
85C2×SD16×C41—21no—
86C2×SD16×C41—21no—
87C2×SD16×C41—21no—
88C2×M16×C41—21no—
89C22×C8×C41—21no—
90#127×C41—21no—
91#126×C41—21no—
92#126×C41—21no—
93#126×C41—21no—
94#126×C41—21no—
95#125×C41—21no—
96#125×C41—21no—
97#124×C41—21no—
98#124×C41—21no—
99#124×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—
110#123×C41—21no—
111#123×C41—21no—
112#123×C41—21no—
113#123×C41—21no—
114C22⋊Q8×C41—21no—
115C22⋊Q8×C41—21no—
116C22⋊Q8×C41—21no—
117C22⋊Q8×C41—21no—
118C22⋊Q8×C41—21no—
119C22⋊Q8×C41—21no—
120C22⋊Q8×C41—21no—
121C22⋊Q8×C41—21no—
122C22⋊Q8×C41—21no—
123C22⋊Q8×C41D411yescharacteristic
124C22⋊Q8×C41C2311yescharacteristic
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×C41—21no—
133#121×C41—21no—
134#121×C41—21no—
135#121×C41—21no—
136#121×C41—21no—
137#121×C41—21no—
138#121×C41—21no—
139#121×C41—21no—
140#121×C41D411yescharacteristic
141#121×C41D411yescharacteristic
142#121×C41D411yescharacteristic
143#121×C41C2311yescharacteristic
144#121×C41C2311yescharacteristic
145#121×C41C2311yescharacteristic
146#120×C41—21no—
147#120×C41—21no—
148#120×C41—21no—
149#120×C41—21no—
150#120×C41—21no—
151#120×C41—21no—
152#120×C41—21no—
153#120×C41—21no—
154C4×D4×C41—21no—
155C4×D4×C41—21no—
156C4×D4×C41—21no—
157C4×D4×C41—21no—
158C4×D4×C41—21no—
159C4×D4×C41—21no—
160C4×D4×C41—21no—
161C4×D4×C41—21no—
162#117×C41—21no—
163#117×C41D411yescharacteristic
164C2×C4⋊C4×C41—21no—
165C2×C4⋊C4×C41—21no—
166C2×C4⋊C4×C41—21no—
167C2×C4⋊C4×C41D411yescharacteristic
168C2×C4⋊C4×C41D411yescharacteristic
169C2×C4⋊C4×C41C2311yescharacteristic
170C2×C4⋊C4×C41C2311yescharacteristic
171C2×C22⋊C4×C41—21no—
172C2×C22⋊C4×C41—21no—
173C2×C22⋊C4×C41—21no—
174C2×C22⋊C4×C41—21no—
175C2×C22⋊C4×C41—21no—
176C2×C22⋊C4×C41—21no—
177C2×C22⋊C4×C41—21no—
178C2×C22⋊C4×C41D411yescharacteristic
179C2×C22⋊C4×C41D411yescharacteristic
180C2×C22⋊C4×C41C2311yescharacteristic
181C2×C42×C41—21no—
182#107×C41—21no—
183#106×C41—21no—
184#106×C41—21no—
185#106×C41—21no—
186#103×C41—21no—
187#103×C41—21no—
188#103×C41—21no—
189#103×C41—21no—
190#103×C41—21no—
191#102×C41—21no—
192#102×C41—21no—
193#102×C41—21no—
194C22⋊C8×C41—21no—
195C22⋊C8×C41—21no—
196C22⋊C8×C41C2311yescharacteristic
197C22⋊C8×C41C2311yescharacteristic
198C22⋊C8×C41C2311yescharacteristic
199C22⋊C8×C41C2311yescharacteristic
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—81no—
211#41×C41—81no—
212#41×C41—81no—
213C2×Q8×C41—21no—
214C2×Q8×C41—21no—
215C2×Q8×C41—21no—
216C2×Q8×C41—81no—
217C2×Q8×C41C2×D411yescharacteristic
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—21no—
233C2×D4×C41—21no—
234C2×D4×C41—21no—
235C2×D4×C41—81no—
236C2×D4×C41—81no—
237C2×D4×C41—81no—
238C2×D4×C41—81no—
239C2×D4×C41—81no—
240C2×D4×C41—81no—
241C2×D4×C41—82no—
242C2×D4×C41C2×D411yescharacteristic
243C2×D4×C41C2×D411yescharacteristic
244C2×D4×C41C2×D411yescharacteristic
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—21no—
254C22×C4×C41—21no—
255C22×C4×C41—21no—
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
266Q16×C41—81no—
267SD16×C41—81no—
268SD16×C41—81no—
269SD16×C41—81no—
270M16×C41—81no—
271C2×C8×C41—21no—
272C2×C8×C41—21no—
273C2×C8×C41—21no—
274C2×C8×C41—21no—
275C2×C8×C41—81no—
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—21no—
290C4⋊C4×C41—21no—
291C4⋊C4×C41—42no—
292C4⋊C4×C41—41no—
293C4⋊C4×C41—41no—
294C4⋊C4×C41—81no—
295C4⋊C4×C41C2×D411yescharacteristic
296C4⋊C4×C41C2×D411yescharacteristic
297C4⋊C4×C41C2×D411yescharacteristic
298C4⋊C4×C41C2×D411yescharacteristic
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—21no—
321C22⋊C4×C41—21no—
322C22⋊C4×C41—21no—
323C22⋊C4×C41—21no—
324C22⋊C4×C41—42no—
325C22⋊C4×C41—42no—
326C22⋊C4×C41—41no—
327C22⋊C4×C41—41no—
328C22⋊C4×C41—81no—
329C42×C41—21no—
330C42×C41—21no—
331C42×C41—21no—
332C42×C41—81no—
333C23×C41—21no—
334C23×C41—21no—
335C23×C41—21no—
336C23×C41—21no—
337C23×C41—21no—
338C23×C41—21no—
339C23×C41—21no—
340C23×C41—21no—
341C23×C41—41no—
342C23×C41—41no—
343C23×C41—42no—
344C23×C41—41no—
345C23×C41—41no—
346C23×C41—81no—
347C23×C41—81no—
348C23×C41—81no—
349C23×C41—81no—
350C23×C41—81no—
351C23×C41#12011yescharacteristic
352C23×C41#12011yescharacteristic
353C23×C41C22×D411yescharacteristic
354Q8×C41—41no—
355Q8×C41—41no—
356Q8×C41—41no—
357Q8×C41—41no—
358Q8×C41—41no—
359Q8×C41—81no—
360D4×C41—41no—
361D4×C41—41no—
362D4×C41—41no—
363D4×C41—42no—
364D4×C41—42no—
365D4×C41—41no—
366D4×C41—41no—
367D4×C41—41no—
368D4×C41—41no—
369D4×C41—41no—
370D4×C41—41no—
371D4×C41—81no—
372D4×C41—81no—
373D4×C41—81no—
374D4×C41—81no—
375D4×C41—81no—
376D4×C41—81no—
377D4×C41—81no—
378D4×C41—81no—
379D4×C41—81no—
380D4×C41—81no—
381D4×C41—81no—
382D4×C41—81no—
383C2×C4×C41—22no—
384C2×C4×C41—21no—
385C2×C4×C41—21no—
386C2×C4×C41—21no—
387C2×C4×C41—21no—
388C2×C4×C41—21no—
389C2×C4×C41—21no—
390C2×C4×C41—21no—
391C2×C4×C41—21no—
392C2×C4×C41—21no—
393C2×C4×C41—21no—
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—41no—
406C2×C4×C41—41no—
407C2×C4×C41—41no—
408C2×C4×C41—41no—
409C2×C4×C41—41no—
410C2×C4×C41—41no—
411C2×C4×C41—41no—
412C2×C4×C41—41no—
413C2×C4×C41—81no—
414C2×C4×C41—81no—
415C2×C4×C41—81no—
416C2×C4×C41—81no—
417C2×C4×C41—81no—
418C2×C4×C41—81no—
419C2×C4×C41—81no—
420C2×C4×C41#12011yescharacteristic
421C2×C4×C41#12011yescharacteristic
422C2×C4×C41C22×D411yescharacteristic
423C2×C4×C41C22×D411yescharacteristic
424C8×C41—41no—
425C8×C41—41no—
426C8×C41—41no—
427C8×C41—41no—
428#18415C4111yesmaximal, characteristic, direct product factor, Sylow
429C22×C41—21no—
430C22×C41—21no—
431C22×C41—21no—
432C22×C41—21no—
433C22×C41—21no—
434C22×C41—21no—
435C22×C41—21no—
436C22×C41—21no—
437C22×C41—41no—
438C22×C41—41no—
439C22×C41—41no—
440C22×C41—41no—
441C22×C41—41no—
442C22×C41—41no—
443C22×C41—41no—
444C22×C41—41no—
445C22×C41—41no—
446C22×C41—41no—
447C22×C41—41no—
448C22×C41—41no—
449C22×C41—81no—
450C22×C41—81no—
451C22×C41—81no—
452C22×C41—81no—
453C22×C41—162no—
454C22×C41—162no—
455C22×C41C2×#12011yescharacteristic
456C22×C41#57711yescharacteristic
457C22×C41#57711yescharacteristic
458C4×C41—21no—
459C4×C41—21no—
460C4×C41—21no—
461C4×C41—21no—
462C4×C41—42no—
463C4×C41—41no—
464C4×C41—41no—
465C4×C41—41no—
466C4×C41—41no—
467C4×C41—41no—
468C4×C41—41no—
469C4×C41—41no—
470C4×C41—41no—
471C4×C41—81no—
472C4×C41—81no—
473C4×C41—81no—
474#3534C2×C4111yescharacteristic
475#3196C2×C4111yescharacteristic, complemented
476#3187C2×C4111yescharacteristic, complemented
477#2663C2×C4111yescharacteristic, complemented
478#1618C2×C4111yescharacteristic, complemented
479#1616C2×C4111yescharacteristic, complemented
480#1615C2×C4111yescharacteristic, complemented
481#1613C2×C4111yescharacteristic, complemented
482#1606C2×C4111yescharacteristic, complemented
483#1604C2×C4111yescharacteristic, complemented
484#1603C2×C4111yescharacteristic, complemented
485#1601C2×C4111yescharacteristic, complemented
486#1507C2×C4111yescharacteristic, complemented
487#1501C2×C4111yescharacteristic, complemented
488#1468C2×C4111yescharacteristic, complemented
489C2×C41—21no—
490C2×C41—21no—
491C2×C41—41no—
492C2×C41—41no—
493C2×C41—81no—
494C2×C41—81no—
495C2×C41—81no—
496C2×C41—81no—
497C2×C41#300911yescharacteristic
498C2×C41#301811yescharacteristic
499C2×C41#302611yescharacteristic
500#562—21no—
501#560—21no—
502#553—21no—
503#551—21no—
504#546—21no—
505#546—21no—
506#546—21no—
507D42—21no—
508#540—21no—
509#539—21no—
510#539C22×C4111yescharacteristic
511#538—21no—
512#538C22×C4111yescharacteristic
513#537C22×C4111yescharacteristic
514#534—21no—
515#534C22×C4111yescharacteristic
516#525C22×C4111yescharacteristic
517C2×#123C22×C4111yescharacteristic
518C2×C22⋊Q8C22×C4111yescharacteristic, complemented
519C2×#121C22×C4111yescharacteristic
520#485—21no—
521#484C22×C4111yescharacteristic, complemented
522#483—21no—
523#481C22×C4111yescharacteristic
524#481C22×C4111yescharacteristic, complemented
525#481C22×C4111yescharacteristic, complemented
526#470—21no—
527#468—21no—
528#465—21no—
529#465—21no—
530#452—21no—
531#451C22×C4111yescharacteristic, complemented
532#450—21no—
533#448C22×C4111yescharacteristic
534#448C22×C4111yescharacteristic, complemented
535#448C22×C4111yescharacteristic, complemented
536#407C22×C4111yescharacteristic, complemented
537C2×C22⋊C8C22×C4111yescharacteristic, complemented
538#400C22×C4111yescharacteristic, complemented
539#399C22×C4111yescharacteristic, complemented
540#397—21no—
541#395C22×C4111yescharacteristic, complemented
542#394—21no—
543#393C22×C4111yescharacteristic, complemented
544#389—21no—
545#388—21no—
546C4×C22⋊C4C22×C4111yescharacteristic, complemented
547#328C22×C4111yescharacteristic, complemented
548#328C22×C4111yescharacteristic, complemented
549#327C22×C4111yescharacteristic
550#327C22×C4111yescharacteristic
551#327C22×C4111yescharacteristic, complemented
552#327C22×C4111yescharacteristic, complemented
553#327C22×C4111yescharacteristic, complemented
554#327C22×C4111yescharacteristic, complemented
555#324C22×C4111yescharacteristic, complemented
556#324C22×C4111yescharacteristic, complemented
557#323C22×C4111yescharacteristic, complemented
558#323C22×C4111yescharacteristic, complemented
559C41#1841511yescharacteristic, direct product factor, Sylow
560C2×#41—21no—
561C2×#41D4×C4111yescharacteristic
562C22×Q8C23×C4111yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C4111yescharacteristic
567C22×D4D4×C4111yescharacteristic
568C23×C4C23×C4111yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C4111yescharacteristic
609C22⋊Q8C23×C4111yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C4111yescharacteristic
626#121D4×C4111yescharacteristic
627#121D4×C4111yescharacteristic
628#121C23×C4111yescharacteristic
629#121C23×C4111yescharacteristic
630#121C23×C4111yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C4111yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C4111yescharacteristic
653C2×C4⋊C4D4×C4111yescharacteristic
654C2×C4⋊C4C23×C4111yescharacteristic
655C2×C4⋊C4C23×C4111yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C4111yescharacteristic
664C2×C22⋊C4D4×C4111yescharacteristic
665C2×C22⋊C4C23×C4111yescharacteristic
666C2×C42—21no—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C4111yescharacteristic
682C22⋊C8C23×C4111yescharacteristic
683C22⋊C8C23×C4111yescharacteristic
684C22⋊C8C23×C4111yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C4111yescharacteristic
690#95C23×C4111yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C4111yescharacteristic
694C24C2×D4×C4111yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C4111yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C4111yescharacteristic
728C2×D4C2×D4×C4111yescharacteristic
729C2×D4C2×D4×C4111yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C4111yescharacteristic
743C22×C4C2×D4×C4111yescharacteristic
744C22×C4C2×D4×C4111yescharacteristic
745C22×C4C2×D4×C4111yescharacteristic
746C22×C4C2×D4×C4111yescharacteristic
747C22×C4C2×D4×C4111yescharacteristic
748C22×C4C2×D4×C4111yescharacteristic
749C22×C4C2×D4×C4111yescharacteristic
750C22×C4C24×C4111yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C4111yescharacteristic
781C4⋊C4C2×D4×C4111yescharacteristic
782C4⋊C4C2×D4×C4111yescharacteristic
783C4⋊C4C2×D4×C4111yescharacteristic
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—21no—
799C22⋊C4—21no—
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—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C4111yescharacteristic
837C23#120×C4111yescharacteristic
838C23C22×D4×C4111yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C4111yescharacteristic
906C2×C4#120×C4111yescharacteristic
907C2×C4C22×D4×C4111yescharacteristic
908C2×C4C22×D4×C4111yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C4111yescharacteristic
940C22C41×#57711yescharacteristic
941C22C41×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C41×#300911yescharacteristic
967C2C41×#301811yescharacteristic
968C2C41×#302611yescharacteristic
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×#3196C2semidirect
3. C41×#3187C2semidirect
4. C41×#2663C2semidirect
5. C41×#1618C2semidirect
6. C41×#1616C2semidirect
7. C41×#1615C2semidirect
8. C41×#1613C2semidirect
9. C41×#1606C2semidirect
10. C41×#1604C2semidirect
11. C41×#1603C2semidirect
12. C41×#1601C2semidirect
13. C41×#1507C2semidirect
14. C41×#1501C2semidirect
15. C41×#1468C2semidirect
34. C2×C22⋊Q8×C41C22semidirect
37. C41×#484C22semidirect
40. C41×#481C22semidirect
41. C41×#481C22semidirect
47. C41×#451C22semidirect
50. C41×#448C22semidirect
51. C41×#448C22semidirect
52. C41×#407C22semidirect
53. C2×C22⋊C8×C41C22semidirect
54. C41×#400C22semidirect
55. C41×#399C22semidirect
57. C41×#395C22semidirect
59. C41×#393C22semidirect
62. C4×C22⋊C4×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
428. #18415C41direct (N × H)
475. #3196C2×C41semidirect
476. #3187C2×C41semidirect
477. #2663C2×C41semidirect
478. #1618C2×C41semidirect
479. #1616C2×C41semidirect
480. #1615C2×C41semidirect
481. #1613C2×C41semidirect
482. #1606C2×C41semidirect
483. #1604C2×C41semidirect
484. #1603C2×C41semidirect
485. #1601C2×C41semidirect
486. #1507C2×C41semidirect
487. #1501C2×C41semidirect
488. #1468C2×C41semidirect
518. C2×C22⋊Q8C22×C41semidirect
521. #484C22×C41semidirect
524. #481C22×C41semidirect
525. #481C22×C41semidirect
531. #451C22×C41semidirect
534. #448C22×C41semidirect
535. #448C22×C41semidirect
536. #407C22×C41semidirect
537. C2×C22⋊C8C22×C41semidirect
538. #400C22×C41semidirect
539. #399C22×C41semidirect
541. #395C22×C41semidirect
543. #393C22×C41semidirect
546. C4×C22⋊C4C22×C41semidirect
547. #328C22×C41semidirect
548. #328C22×C41semidirect
551. #327C22×C41semidirect
552. #327C22×C41semidirect
553. #327C22×C41semidirect
554. #327C22×C41semidirect
555. #324C22×C41semidirect
556. #324C22×C41semidirect
557. #323C22×C41semidirect
558. #323C22×C41semidirect
559. C41#18415direct (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×#31962
C41×#31872
C41×#26632
C41×#16182
C41×#16162
C41×#16152
C41×#16132
C41×#16062
C41×#16042
C41×#16032
C41×#16012
C41×#15072
C41×#15012
C41×#14682
#1841541