Finite Group Databasebeta

← C41×#25554 #23801755

Subgroups — C41×#25554 #23801755

Order 10496.

1236 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#555C211yesmaximal, characteristic, complemented
2C2×C41×#482C211yesmaximal, characteristic, complemented
3C2×C41×#469C211yesmaximal, characteristic, complemented
4C41×#2416C211yesmaximal, characteristic, complemented
5C41×#2058C211yesmaximal, characteristic, complemented
6C41×#2034C211yesmaximal, characteristic, complemented
7C41×#2023C211yesmaximal, characteristic, complemented
8C41×#1999C211yesmaximal, characteristic, complemented
9C41×#1879C211yesmaximal, characteristic, complemented
10C41×#1875C211yesmaximal, characteristic, complemented
11C41×#1874C211yesmaximal, characteristic, complemented
12C41×#1870C211yesmaximal, characteristic, complemented
13C41×#1862C211yesmaximal, characteristic, complemented
14C41×#1854C211yesmaximal, characteristic, complemented
15C41×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C41C2211yescharacteristic
17C22×M16×C41C2211yescharacteristic
18C41×#555—24no—
19C41×#555—24no—
20C2×C4⋊Q8×C41C2211yescharacteristic
21C2×#124×C41—21no—
22C2×#124×C41—21no—
23C2×#121×C41—21no—
24C2×#121×C41—21no—
25C2×#121×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×#121×C41C2211yescharacteristic
29C2×C4×D4×C41C2211yescharacteristic
30C2×C4×D4×C41C2211yescharacteristic
31C2×#117×C41—21no—
32C2×#117×C41C2211yescharacteristic
33C2×#117×C41C2211yescharacteristic
34C22×C4⋊C4×C41C2211yescharacteristic
35C41×#482—24no—
36C41×#469—24no—
37C2×#107×C41C2211yescharacteristic
38C2×#106×C41C2211yescharacteristic
39C2×#106×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×#102×C41C2211yescharacteristic
46C2×C22⋊C8×C41C2211yescharacteristic
47C2×C22⋊C8×C41C2211yescharacteristic
48C2×C22⋊C8×C41C2211yescharacteristic
49C41×#396—21no—
50C41×#394—21no—
51C41×#390C2211yescharacteristic
52C41×#389C2211yescharacteristic
53C41×#386—21no—
54C41×#380C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#336C2211yescharacteristic
62C41×#336C2211yescharacteristic
63C22×Q8×C41—21no—
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41—21no—
68C22×D4×C41D411yescharacteristic
69C22×D4×C41C2311yescharacteristic
70C22×D4×C41C2311yescharacteristic
71C23×C4×C41—21no—
72C23×C4×C41—21no—
73C23×C4×C41C2311yescharacteristic
74C23×C4×C41C2311yescharacteristic
75C2×D8×C41—22no—
76C2×D8×C41—22no—
77C2×D8×C41—41no—
78C2×M16×C41—22no—
79C2×M16×C41—22no—
80C2×M16×C41—41no—
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84C22×C8×C41C2311yescharacteristic
85C4⋊Q8×C41—22no—
86C4⋊Q8×C41—22no—
87#124×C41—28no—
88#124×C41—28no—
89#121×C41—28no—
90#121×C41—22no—
91#121×C41—22no—
92#121×C41—22no—
93#121×C41—22no—
94#121×C41—22no—
95#121×C41—22no—
96#121×C41—41no—
97#121×C41—44no—
98#121×C41D414yescomplemented
99C4×D4×C41—22no—
100C4×D4×C41—22no—
101C4×D4×C41—22no—
102C4×D4×C41—22no—
103#117×C41—28no—
104#117×C41—22no—
105#117×C41—22no—
106#117×C41—22no—
107#117×C41D414yescomplemented
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—22no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41—41no—
113C2×C4⋊C4×C41D411yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C4⋊C4×C41C2311yescharacteristic
116C2×C4⋊C4×C41C2311yescharacteristic
117C2×C4⋊C4×C41C2311yescharacteristic
118C2×C4⋊C4×C41C2311yescharacteristic
119C2×C4⋊C4×C41C2311yescharacteristic
120C2×C22⋊C4×C41—21no—
121C2×C22⋊C4×C41—21no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—21no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41—21no—
128C2×C22⋊C4×C41—21no—
129C2×C22⋊C4×C41—21no—
130C2×C22⋊C4×C41D411yescharacteristic
131C2×C22⋊C4×C41D411yescharacteristic
132C2×C42×C41—21no—
133C2×C42×C41—21no—
134C2×C42×C41C2311yescharacteristic
135#107×C41—22no—
136#106×C41—22no—
137#106×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—22no—
142#102×C41—22no—
143#102×C41—41no—
144C22⋊C8×C41—22no—
145C22⋊C8×C41—22no—
146C22⋊C8×C41—41no—
147#95×C41—21no—
148#95×C41—21no—
149C24×C41—21no—
150C24×C41—21no—
151C24×C41C2×D411yescharacteristic
152C24×C41C2×D411yescharacteristic
153C2×Q8×C41—24no—
154C2×Q8×C41—81no—
155C2×Q8×C41—81no—
156C2×D4×C41—22no—
157C2×D4×C41—24no—
158C2×D4×C41—24no—
159C2×D4×C41—22no—
160C2×D4×C41—21no—
161C2×D4×C41—21no—
162C2×D4×C41—21no—
163C2×D4×C41—21no—
164C2×D4×C41—21no—
165C2×D4×C41—21no—
166C2×D4×C41—21no—
167C2×D4×C41—21no—
168C2×D4×C41—21no—
169C2×D4×C41—21no—
170C2×D4×C41—21no—
171C2×D4×C41—41no—
172C2×D4×C41—42no—
173C2×D4×C41—42no—
174C2×D4×C41—42no—
175C2×D4×C41—42no—
176C2×D4×C41—42no—
177C2×D4×C41—81no—
178C2×D4×C41—81no—
179C2×D4×C41—81no—
180C2×D4×C41—81no—
181C2×D4×C41—81no—
182C2×D4×C41C2×D412yes—
183C22×C4×C41—21no—
184C22×C4×C41—21no—
185C22×C4×C41—21no—
186C22×C4×C41—21no—
187C22×C4×C41—24no—
188C22×C4×C41—21no—
189C22×C4×C41—21no—
190C22×C4×C41—21no—
191C22×C4×C41—21no—
192C22×C4×C41—21no—
193C22×C4×C41—21no—
194C22×C4×C41—21no—
195C22×C4×C41—21no—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—21no—
199C22×C4×C41—21no—
200C22×C4×C41—42no—
201C22×C4×C41—42no—
202C22×C4×C41—42no—
203C22×C4×C41—42no—
204C22×C4×C41—81no—
205C22×C4×C41C2×D411yescharacteristic
206C22×C4×C41C2×D411yescharacteristic
207C22×C4×C41C2×D411yescharacteristic
208C22×C4×C41C2×D412yes—
209C22×C4×C41C2×D412yes—
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41C2411yescharacteristic
212D8×C41—44no—
213M16×C41—44no—
214C2×C8×C41—21no—
215C2×C8×C41—21no—
216C2×C8×C41—21no—
217C2×C8×C41—21no—
218C2×C8×C41—21no—
219C2×C8×C41—21no—
220C2×C8×C41—21no—
221C2×C8×C41—21no—
222C2×C8×C41—21no—
223C2×C8×C41—21no—
224C2×C8×C41—21no—
225C2×C8×C41#4112yes—
226C4⋊C4×C41—24no—
227C4⋊C4×C41—22no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—42no—
237C4⋊C4×C41—42no—
238C4⋊C4×C41C2×D412yes—
239C4⋊C4×C41C2×D412yes—
240C4⋊C4×C41C2×D412yes—
241C4⋊C4×C41#4112yes—
242C22⋊C4×C41—24no—
243C22⋊C4×C41—24no—
244C22⋊C4×C41—24no—
245C22⋊C4×C41—24no—
246C22⋊C4×C41—22no—
247C22⋊C4×C41—24no—
248C22⋊C4×C41—22no—
249C22⋊C4×C41—42no—
250C22⋊C4×C41—42no—
251C22⋊C4×C41—42no—
252C22⋊C4×C41—42no—
253C22⋊C4×C41—81no—
254C42×C41—24no—
255C42×C41—24no—
256C42×C41—21no—
257C42×C41—21no—
258C23×C41—21no—
259C23×C41—21no—
260C23×C41—21no—
261C23×C41—21no—
262C23×C41—21no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—22no—
266C23×C41—21no—
267C23×C41—21no—
268C23×C41—21no—
269C23×C41—21no—
270C23×C41—21no—
271C23×C41—21no—
272C23×C41—41no—
273C23×C41—41no—
274C23×C41—41no—
275C23×C41—41no—
276C23×C41—41no—
277C23×C41—41no—
278C23×C41—41no—
279C23×C41—41no—
280C23×C41—41no—
281C23×C41—41no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—41no—
285C23×C41#12012yes—
286C23×C41C22×D411yescharacteristic
287Q8×C41—84no—
288D4×C41—22no—
289D4×C41—22no—
290D4×C41—44no—
291D4×C41—41no—
292D4×C41—41no—
293D4×C41—41no—
294D4×C41—41no—
295D4×C41—41no—
296D4×C41—41no—
297D4×C41—84no—
298D4×C41—84no—
299D4×C41—84no—
300D4×C41—84no—
301C2×C4×C41—21no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—22no—
306C2×C4×C41—22no—
307C2×C4×C41—22no—
308C2×C4×C41—22no—
309C2×C4×C41—21no—
310C2×C4×C41—22no—
311C2×C4×C41—21no—
312C2×C4×C41—22no—
313C2×C4×C41—22no—
314C2×C4×C41—21no—
315C2×C4×C41—22no—
316C2×C4×C41—21no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—48no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—41no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41—41no—
335C2×C4×C41—41no—
336C2×C4×C41—41no—
337C2×C4×C41—41no—
338C2×C4×C41—84no—
339C2×C4×C41#12012yes—
340C2×C4×C41AGL(1,ℤ/8)12yes—
341C2×C4×C41C22×D411yescharacteristic
342C2×C4×C41C22×D411yescharacteristic
343C2×C4×C41C2×#4111yescharacteristic
344C2×C4×C41C2×#4111yescharacteristic
345C2×C4×C41H(5,𝔽2)11yescharacteristic
346C2×C4×C412−1+411yescharacteristic
347C8×C41—22no—
348C8×C41—41no—
349C8×C41—41no—
350C8×C41—41no—
351#25554C4111yesmaximal, characteristic, direct product factor, Sylow
352C22×C41—22no—
353C22×C41—22no—
354C22×C41—22no—
355C22×C41—41no—
356C22×C41—41no—
357C22×C41—41no—
358C22×C41—41no—
359C22×C41—41no—
360C22×C41—41no—
361C22×C41—41no—
362C22×C41—42no—
363C22×C41—42no—
364C22×C41—41no—
365C22×C41—41no—
366C22×C41—42no—
367C22×C41—41no—
368C22×C41—41no—
369C22×C41—81no—
370C22×C41—81no—
371C22×C41—81no—
372C22×C41—81no—
373C22×C41—81no—
374C22×C41—81no—
375C22×C41—81no—
376C22×C41—81no—
377C22×C41—81no—
378C22×C41—81no—
379C22×C41—81no—
380C22×C41C2×#12011yescharacteristic
381C22×C41#54611yescharacteristic
382C22×C41#54711yescharacteristic
383C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C41#57511yescharacteristic
385C22×C41#57611yescharacteristic
386C22×C41#57711yescharacteristic
387C4×C41—22no—
388C4×C41—22no—
389C4×C41—41no—
390C4×C41—42no—
391C4×C41—41no—
392C4×C41—42no—
393C4×C41—42no—
394C4×C41—42no—
395C4×C41—81no—
396C4×C41—81no—
397C4×C41#53211yescharacteristic
398C4×C41#53711yescharacteristic
399C4×C41#54611yescharacteristic
400C4×C41#54711yescharacteristic
401C2×#555C2×C4111yescharacteristic, complemented
402C2×#482C2×C4111yescharacteristic, complemented
403C2×#469C2×C4111yescharacteristic, complemented
404#2416C2×C4111yescharacteristic, complemented
405#2058C2×C4111yescharacteristic, complemented
406#2034C2×C4111yescharacteristic, complemented
407#2023C2×C4111yescharacteristic, complemented
408#1999C2×C4111yescharacteristic, complemented
409#1879C2×C4111yescharacteristic, complemented
410#1875C2×C4111yescharacteristic, complemented
411#1874C2×C4111yescharacteristic, complemented
412#1870C2×C4111yescharacteristic, complemented
413#1862C2×C4111yescharacteristic, complemented
414#1854C2×C4111yescharacteristic, complemented
415#1736C2×C4111yescharacteristic, complemented
416C2×C41—42no—
417C2×C41—81no—
418C2×C41—82no—
419C2×C41—161no—
420C2×C41#243011yescharacteristic
421C2×C41#300611yescharacteristic
422C2×C41#301211yescharacteristic
423C2×C41#332111yescharacteristic
424C2×C41#332511yescharacteristic
425C2×C41#334711yescharacteristic
426C2×C41#335411yescharacteristic
427C22×D8C22×C4111yescharacteristic
428C22×M16C22×C4111yescharacteristic
429#555—24no—
430#555—24no—
431C2×C4⋊Q8C22×C4111yescharacteristic
432C2×#124—21no—
433C2×#124—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C4111yescharacteristic
437C2×#121C22×C4111yescharacteristic
438C2×#121C22×C4111yescharacteristic
439C2×#121C22×C4111yescharacteristic
440C2×C4×D4C22×C4111yescharacteristic
441C2×C4×D4C22×C4111yescharacteristic
442C2×#117—21no—
443C2×#117C22×C4111yescharacteristic
444C2×#117C22×C4111yescharacteristic
445C22×C4⋊C4C22×C4111yescharacteristic
446#482—24no—
447#469—24no—
448C2×#107C22×C4111yescharacteristic
449C2×#106C22×C4111yescharacteristic
450C2×#106C22×C4111yescharacteristic
451C2×#102C22×C4111yescharacteristic
452C2×#102C22×C4111yescharacteristic
453C2×#102C22×C4111yescharacteristic
454C2×#102C22×C4111yescharacteristic
455C2×#102C22×C4111yescharacteristic
456C2×#102C22×C4111yescharacteristic
457C2×C22⋊C8C22×C4111yescharacteristic
458C2×C22⋊C8C22×C4111yescharacteristic
459C2×C22⋊C8C22×C4111yescharacteristic
460#396—21no—
461#394—21no—
462#390C22×C4111yescharacteristic
463#389C22×C4111yescharacteristic
464#386—21no—
465#380C22×C4111yescharacteristic
466#340C22×C4111yescharacteristic
467#340C22×C4111yescharacteristic
468#340C22×C4111yescharacteristic
469#340C22×C4111yescharacteristic
470#340C22×C4111yescharacteristic
471#340C22×C4111yescharacteristic
472#336C22×C4111yescharacteristic
473#336C22×C4111yescharacteristic
474C41#2555411yescharacteristic, direct product factor, Sylow
475C22×Q8—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4D4×C4111yescharacteristic
481C22×D4C23×C4111yescharacteristic
482C22×D4C23×C4111yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C4111yescharacteristic
486C23×C4C23×C4111yescharacteristic
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—41no—
493C22×C8C23×C4111yescharacteristic
494C22×C8C23×C4111yescharacteristic
495C22×C8C23×C4111yescharacteristic
496C22×C8C23×C4111yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—22no—
499#124—28no—
500#124—28no—
501#121—28no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—41no—
509#121—44no—
510#121D4×C4114yescomplemented
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515#117—28no—
516#117—22no—
517#117—22no—
518#117—22no—
519#117D4×C4114yescomplemented
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4D4×C4111yescharacteristic
526C2×C4⋊C4C23×C4111yescharacteristic
527C2×C4⋊C4C23×C4111yescharacteristic
528C2×C4⋊C4C23×C4111yescharacteristic
529C2×C4⋊C4C23×C4111yescharacteristic
530C2×C4⋊C4C23×C4111yescharacteristic
531C2×C4⋊C4C23×C4111yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4D4×C4111yescharacteristic
543C2×C22⋊C4D4×C4111yescharacteristic
544C2×C42—21no—
545C2×C42—21no—
546C2×C42C23×C4111yescharacteristic
547#107—22no—
548#106—22no—
549#106—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—22no—
555#102—41no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—41no—
559#95—21no—
560#95—21no—
561C24—21no—
562C24—21no—
563C24C2×D4×C4111yescharacteristic
564C24C2×D4×C4111yescharacteristic
565C2×Q8—24no—
566C2×Q8—81no—
567C2×Q8—81no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4C2×D4×C4112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4C2×D4×C4111yescharacteristic
618C22×C4C2×D4×C4111yescharacteristic
619C22×C4C2×D4×C4111yescharacteristic
620C22×C4C2×D4×C4112yes—
621C22×C4C2×D4×C4112yes—
622C22×C4C2×D4×C4111yescharacteristic
623C22×C4C24×C4111yescharacteristic
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8#41×C4112yes—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4C2×D4×C4112yes—
651C4⋊C4C2×D4×C4112yes—
652C4⋊C4C2×D4×C4112yes—
653C4⋊C4#41×C4112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—22no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C42—24no—
667C42—24no—
668C42—21no—
669C42—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23#120×C4112yes—
698C23C22×D4×C4111yescharacteristic
699Q8—84no—
700D4—22no—
701D4—22no—
702D4—44no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4#120×C4112yes—
752C2×C4AGL(1,ℤ/8)×C4112yes—
753C2×C4C22×D4×C4111yescharacteristic
754C2×C4C22×D4×C4111yescharacteristic
755C2×C4C2×#41×C4111yescharacteristic
756C2×C4C2×#41×C4111yescharacteristic
757C2×C4H(5,𝔽2)×C4111yescharacteristic
758C2×C42−1+4×C4111yescharacteristic
759C8—22no—
760C8—41no—
761C8—41no—
762C8—41no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#120×C4111yescharacteristic
792C22C41×#54611yescharacteristic
793C22C41×#54711yescharacteristic
794C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
795C22C41×#57511yescharacteristic
796C22C41×#57611yescharacteristic
797C22C41×#57711yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4C41×#53211yescharacteristic
809C4C41×#53711yescharacteristic
810C4C41×#54611yescharacteristic
811C4C41×#54711yescharacteristic
812C2—42no—
813C2—81no—
814C2—82no—
815C2—161no—
816C2C41×#243011yescharacteristic
817C2C41×#300611yescharacteristic
818C2C41×#301211yescharacteristic
819C2C41×#332111yescharacteristic
820C2C41×#332511yescharacteristic
821C2C41×#334711yescharacteristic
822C2C41×#335411yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C4×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#555C2semidirect
2. C2×C41×#482C2semidirect
3. C2×C41×#469C2semidirect
4. C41×#2416C2semidirect
5. C41×#2058C2semidirect
6. C41×#2034C2semidirect
7. C41×#2023C2semidirect
8. C41×#1999C2semidirect
9. C41×#1879C2semidirect
10. C41×#1875C2semidirect
11. C41×#1874C2semidirect
12. C41×#1870C2semidirect
13. C41×#1862C2semidirect
14. C41×#1854C2semidirect
15. C41×#1736C2semidirect
98. #121×C41D4semidirect
107. #117×C41D4semidirect
351. #25554C41direct (N × H)
401. C2×#555C2×C41semidirect
402. C2×#482C2×C41semidirect
403. C2×#469C2×C41semidirect
404. #2416C2×C41semidirect
405. #2058C2×C41semidirect
406. #2034C2×C41semidirect
407. #2023C2×C41semidirect
408. #1999C2×C41semidirect
409. #1879C2×C41semidirect
410. #1875C2×C41semidirect
411. #1874C2×C41semidirect
412. #1870C2×C41semidirect
413. #1862C2×C41semidirect
414. #1854C2×C41semidirect
415. #1736C2×C41semidirect
474. C41#25554direct (N × H)
510. #121D4×C41semidirect
519. #117D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5552
C2×C41×#4822
C2×C41×#4692
C41×#24162
C41×#20582
C41×#20342
C41×#20232
C41×#19992
C41×#18792
C41×#18752
C41×#18742
C41×#18702
C41×#18622
C41×#18542
C41×#17362
#2555441