Finite Group Databasebeta

← C41×#24136 #23800337

Subgroups — C41×#24136 #23800337

Order 10496.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#553C211yesmaximal, characteristic, complemented
2C2×C41×#478C211yesmaximal, characteristic, complemented
3C2×C41×#442C211yesmaximal, characteristic, complemented
4C41×#2537C211yesmaximal, characteristic, complemented
5C41×#2034C211yesmaximal, characteristic, complemented
6C41×#2033C211yesmaximal, characteristic, complemented
7C41×#1999C211yesmaximal, characteristic, complemented
8C41×#1999C211yesmaximal, characteristic, complemented
9C41×#1992C211yesmaximal, characteristic, complemented
10C41×#1955C211yesmaximal, characteristic, complemented
11C41×#1875C211yesmaximal, characteristic, complemented
12C41×#1874C211yesmaximal, characteristic, complemented
13C41×#1854C211yesmaximal, characteristic, complemented
14C41×#1853C211yesmaximal, characteristic, complemented
15C41×#1802C211yesmaximal, characteristic, complemented
16C22×D8×C41C2211yescharacteristic
17C41×#553—24no—
18C41×#553—24no—
19C2×#126×C41—21no—
20C2×#125×C41C2211yescharacteristic
21C2×#123×C41—21no—
22C2×#121×C41—21no—
23C2×#121×C41—21no—
24C2×#121×C41C2211yescharacteristic
25C2×#121×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×C4×D4×C41—21no—
29C2×C4×D4×C41C2211yescharacteristic
30C2×C4×D4×C41C2211yescharacteristic
31C2×C4×D4×C41C2211yescharacteristic
32C2×#117×C41C2211yescharacteristic
33C22×C4⋊C4×C41C2211yescharacteristic
34C41×#478—24no—
35C41×#442—24no—
36C2×#107×C41C2211yescharacteristic
37C2×#106×C41C2211yescharacteristic
38C2×#106×C41C2211yescharacteristic
39C2×C4⋊C8×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
49C2×C22⋊C8×C41C2211yescharacteristic
50C2×#97×C41C2211yescharacteristic
51C41×#394—21no—
52C41×#394—21no—
53C41×#384C2211yescharacteristic
54C41×#380—21no—
55C41×#380C2211yescharacteristic
56C41×#380C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#340C2211yescharacteristic
62C41×#340C2211yescharacteristic
63C22×D4×C41—21no—
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41D411yescharacteristic
68C22×D4×C41C2311yescharacteristic
69C22×D4×C41C2311yescharacteristic
70C23×C4×C41—21no—
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—22no—
78C22×C8×C41C2311yescharacteristic
79C22×C8×C41C2311yescharacteristic
80C22×C8×C41C2311yescharacteristic
81C22×C8×C41C2311yescharacteristic
82#126×C41—28no—
83#125×C41—22no—
84#125×C41D414yescomplemented
85#123×C41—28no—
86#121×C41—28no—
87#121×C41—22no—
88#121×C41—22no—
89#121×C41—22no—
90#121×C41—22no—
91#121×C41—22no—
92#121×C41—22no—
93#121×C41—41no—
94#121×C41—41no—
95#121×C41—44no—
96C4×D4×C41—28no—
97C4×D4×C41—22no—
98C4×D4×C41—22no—
99C4×D4×C41—22no—
100C4×D4×C41—22no—
101C4×D4×C41—22no—
102C4×D4×C41D414yescomplemented
103#117×C41—22no—
104#117×C41—22no—
105C2×C4⋊C4×C41—21no—
106C2×C4⋊C4×C41—21no—
107C2×C4⋊C4×C41—21no—
108C2×C4⋊C4×C41—22no—
109C2×C4⋊C4×C41—22no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41D411yescharacteristic
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C4⋊C4×C41C2311yescharacteristic
116C2×C4⋊C4×C41C2311yescharacteristic
117C2×C4⋊C4×C41C2311yescharacteristic
118C2×C4⋊C4×C41C2311yescharacteristic
119C2×C22⋊C4×C41—21no—
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×C41D411yescharacteristic
129C2×C22⋊C4×C41D411yescharacteristic
130C2×C42×C41—21no—
131C2×C42×C41C2311yescharacteristic
132#107×C41—22no—
133#106×C41—22no—
134#106×C41—22no—
135C4⋊C8×C41—22no—
136#102×C41—22no—
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—41no—
141#102×C41—41no—
142C22⋊C8×C41—22no—
143C22⋊C8×C41—22no—
144C22⋊C8×C41—41no—
145C22⋊C8×C41—41no—
146#97×C41—22no—
147#95×C41—21no—
148#95×C41—21no—
149C24×C41—21no—
150C24×C41—21no—
151C24×C41C2×D411yescharacteristic
152C24×C41C2×D411yescharacteristic
153C2×D4×C41—24no—
154C2×D4×C41—22no—
155C2×D4×C41—24no—
156C2×D4×C41—22no—
157C2×D4×C41—21no—
158C2×D4×C41—21no—
159C2×D4×C41—21no—
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—41no—
168C2×D4×C41—42no—
169C2×D4×C41—42no—
170C2×D4×C41—42no—
171C2×D4×C41—42no—
172C2×D4×C41—42no—
173C2×D4×C41—42no—
174C2×D4×C41—81no—
175C2×D4×C41—81no—
176C2×D4×C41—81no—
177C2×D4×C41—81no—
178C2×D4×C41C2×D412yes—
179C2×D4×C41#4112yes—
180C22×C4×C41—21no—
181C22×C4×C41—21no—
182C22×C4×C41—21no—
183C22×C4×C41—24no—
184C22×C4×C41—21no—
185C22×C4×C41—21no—
186C22×C4×C41—21no—
187C22×C4×C41—21no—
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—24no—
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—81no—
204C22×C4×C41—81no—
205C22×C4×C41—81no—
206C22×C4×C41—81no—
207C22×C4×C41C2×D411yescharacteristic
208C22×C4×C41C2×D411yescharacteristic
209C22×C4×C41C2×D411yescharacteristic
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41C2411yescharacteristic
212D8×C41—28no—
213C2×C8×C41—21no—
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#4112yes—
225C4⋊C4×C41—24no—
226C4⋊C4×C41—24no—
227C4⋊C4×C41—24no—
228C4⋊C4×C41—22no—
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—21no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—42no—
239C4⋊C4×C41—81no—
240C4⋊C4×C41C2×D412yes—
241C4⋊C4×C41C2×D412yes—
242C4⋊C4×C41C2×D412yes—
243C22⋊C4×C41—24no—
244C22⋊C4×C41—24no—
245C22⋊C4×C41—24no—
246C22⋊C4×C41—24no—
247C22⋊C4×C41—22no—
248C22⋊C4×C41—22no—
249C22⋊C4×C41—42no—
250C22⋊C4×C41—42no—
251C22⋊C4×C41—42no—
252C22⋊C4×C41—42no—
253C22⋊C4×C41—42no—
254C42×C41—24no—
255C42×C41C2×D412yes—
256C42×C41C2×D412yes—
257C23×C41—21no—
258C23×C41—21no—
259C23×C41—21no—
260C23×C41—21no—
261C23×C41—21no—
262C23×C41—21no—
263C23×C41—21no—
264C23×C41—22no—
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×C41AGL(1,ℤ/8)12yes—
285C23×C41C22×D411yescharacteristic
286D4×C41—22no—
287D4×C41—22no—
288D4×C41—22no—
289D4×C41—22no—
290D4×C41—44no—
291D4×C41—48no—
292D4×C41—41no—
293D4×C41—41no—
294D4×C41—41no—
295D4×C41—41no—
296D4×C41—84no—
297D4×C41—84no—
298D4×C41—84no—
299C2×C4×C41—21no—
300C2×C4×C41—21no—
301C2×C4×C41—21no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—22no—
305C2×C4×C41—22no—
306C2×C4×C41—21no—
307C2×C4×C41—22no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—41no—
313C2×C4×C41—41no—
314C2×C4×C41—41no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
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—84no—
336C2×C4×C41—84no—
337C2×C4×C41—84no—
338C2×C4×C41#12012yes—
339C2×C4×C41#12012yes—
340C2×C4×C41C22×D411yescharacteristic
341C2×C4×C41C22×D411yescharacteristic
342C2×C4×C41C2×#4111yescharacteristic
343C2×C4×C41C2×#4111yescharacteristic
344C2×C4×C41H(5,𝔽2)11yescharacteristic
345C2×C4×C412−1+411yescharacteristic
346C8×C41—22no—
347C8×C41—41no—
348C8×C41—41no—
349C8×C41—41no—
350#24136C4111yesmaximal, characteristic, direct product factor, Sylow
351C22×C41—22no—
352C22×C41—22no—
353C22×C41—22no—
354C22×C41—41no—
355C22×C41—41no—
356C22×C41—41no—
357C22×C41—41no—
358C22×C41—41no—
359C22×C41—41no—
360C22×C41—41no—
361C22×C41—42no—
362C22×C41—42no—
363C22×C41—41no—
364C22×C41—42no—
365C22×C41—42no—
366C22×C41—41no—
367C22×C41—41no—
368C22×C41—42no—
369C22×C41—41no—
370C22×C41—42no—
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×C41C2×#12011yescharacteristic
380C22×C41#54611yescharacteristic
381C22×C41#54711yescharacteristic
382C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C41#57511yescharacteristic
384C22×C41#57611yescharacteristic
385C22×C41#57711yescharacteristic
386C4×C41—22no—
387C4×C41—22no—
388C4×C41—41no—
389C4×C41—41no—
390C4×C41—42no—
391C4×C41—42no—
392C4×C41—42no—
393C4×C41—81no—
394C4×C41—81no—
395C4×C41—81no—
396C4×C41#52511yescharacteristic
397C4×C41#53711yescharacteristic
398C4×C41#54811yescharacteristic
399C4×C41#55011yescharacteristic
400C2×#553C2×C4111yescharacteristic, complemented
401C2×#478C2×C4111yescharacteristic, complemented
402C2×#442C2×C4111yescharacteristic, complemented
403#2537C2×C4111yescharacteristic, complemented
404#2034C2×C4111yescharacteristic, complemented
405#2033C2×C4111yescharacteristic, complemented
406#1999C2×C4111yescharacteristic, complemented
407#1999C2×C4111yescharacteristic, complemented
408#1992C2×C4111yescharacteristic, complemented
409#1955C2×C4111yescharacteristic, complemented
410#1875C2×C4111yescharacteristic, complemented
411#1874C2×C4111yescharacteristic, complemented
412#1854C2×C4111yescharacteristic, complemented
413#1853C2×C4111yescharacteristic, complemented
414#1802C2×C4111yescharacteristic, complemented
415C2×C41—42no—
416C2×C41—81no—
417C2×C41—82no—
418C2×C41—82no—
419C2×C41#240711yescharacteristic
420C2×C41#300611yescharacteristic
421C2×C41#301211yescharacteristic
422C2×C41#330711yescharacteristic
423C2×C41#331811yescharacteristic
424C2×C41#334511yescharacteristic
425C2×C41#334711yescharacteristic
426C22×D8C22×C4111yescharacteristic
427#553—24no—
428#553—24no—
429C2×#126—21no—
430C2×#125C22×C4111yescharacteristic
431C2×#123—21no—
432C2×#121—21no—
433C2×#121—21no—
434C2×#121C22×C4111yescharacteristic
435C2×#121C22×C4111yescharacteristic
436C2×#121C22×C4111yescharacteristic
437C2×#121C22×C4111yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4C22×C4111yescharacteristic
440C2×C4×D4C22×C4111yescharacteristic
441C2×C4×D4C22×C4111yescharacteristic
442C2×#117C22×C4111yescharacteristic
443C22×C4⋊C4C22×C4111yescharacteristic
444#478—24no—
445#442—24no—
446C2×#107C22×C4111yescharacteristic
447C2×#106C22×C4111yescharacteristic
448C2×#106C22×C4111yescharacteristic
449C2×C4⋊C8C22×C4111yescharacteristic
450C2×#102C22×C4111yescharacteristic
451C2×#102C22×C4111yescharacteristic
452C2×#102C22×C4111yescharacteristic
453C2×#102C22×C4111yescharacteristic
454C2×#102C22×C4111yescharacteristic
455C2×#102C22×C4111yescharacteristic
456C2×C22⋊C8C22×C4111yescharacteristic
457C2×C22⋊C8C22×C4111yescharacteristic
458C2×C22⋊C8C22×C4111yescharacteristic
459C2×C22⋊C8C22×C4111yescharacteristic
460C2×#97C22×C4111yescharacteristic
461#394—21no—
462#394—21no—
463#384C22×C4111yescharacteristic
464#380—21no—
465#380C22×C4111yescharacteristic
466#380C22×C4111yescharacteristic
467#340C22×C4111yescharacteristic
468#340C22×C4111yescharacteristic
469#340C22×C4111yescharacteristic
470#340C22×C4111yescharacteristic
471#340C22×C4111yescharacteristic
472#340C22×C4111yescharacteristic
473C41#2413611yescharacteristic, direct product factor, Sylow
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C4111yescharacteristic
479C22×D4C23×C4111yescharacteristic
480C22×D4C23×C4111yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C4111yescharacteristic
485C23×C4C23×C4111yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C22×C8C23×C4111yescharacteristic
490C22×C8C23×C4111yescharacteristic
491C22×C8C23×C4111yescharacteristic
492C22×C8C23×C4111yescharacteristic
493#126—28no—
494#125—22no—
495#125D4×C4114yescomplemented
496#123—28no—
497#121—28no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—41no—
505#121—41no—
506#121—44no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C4114yescomplemented
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C4111yescharacteristic
524C2×C4⋊C4C23×C4111yescharacteristic
525C2×C4⋊C4C23×C4111yescharacteristic
526C2×C4⋊C4C23×C4111yescharacteristic
527C2×C4⋊C4C23×C4111yescharacteristic
528C2×C4⋊C4C23×C4111yescharacteristic
529C2×C4⋊C4C23×C4111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
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⋊C4D4×C4111yescharacteristic
540C2×C22⋊C4D4×C4111yescharacteristic
541C2×C42—21no—
542C2×C42C23×C4111yescharacteristic
543#107—22no—
544#106—22no—
545#106—22no—
546C4⋊C8—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557#97—22no—
558#95—21no—
559#95—21no—
560C24—21no—
561C24—21no—
562C24C2×D4×C4111yescharacteristic
563C24C2×D4×C4111yescharacteristic
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4C2×D4×C4112yes—
590C2×D4#41×C4112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C2×D4×C4111yescharacteristic
619C22×C4C2×D4×C4111yescharacteristic
620C22×C4C2×D4×C4111yescharacteristic
621C22×C4C2×D4×C4111yescharacteristic
622C22×C4C24×C4111yescharacteristic
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
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#41×C4112yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
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—21no—
649C4⋊C4—42no—
650C4⋊C4—81no—
651C4⋊C4C2×D4×C4112yes—
652C4⋊C4C2×D4×C4112yes—
653C4⋊C4C2×D4×C4112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—24no—
666C42C2×D4×C4112yes—
667C42C2×D4×C4112yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23AGL(1,ℤ/8)×C4112yes—
696C23C22×D4×C4111yescharacteristic
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
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—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4#120×C4112yes—
750C2×C4#120×C4112yes—
751C2×C4C22×D4×C4111yescharacteristic
752C2×C4C22×D4×C4111yescharacteristic
753C2×C4C2×#41×C4111yescharacteristic
754C2×C4C2×#41×C4111yescharacteristic
755C2×C4H(5,𝔽2)×C4111yescharacteristic
756C2×C42−1+4×C4111yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×#120×C4111yescharacteristic
790C22C41×#54611yescharacteristic
791C22C41×#54711yescharacteristic
792C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
793C22C41×#57511yescharacteristic
794C22C41×#57611yescharacteristic
795C22C41×#57711yescharacteristic
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4C41×#52511yescharacteristic
807C4C41×#53711yescharacteristic
808C4C41×#54811yescharacteristic
809C4C41×#55011yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2C41×#240711yescharacteristic
815C2C41×#300611yescharacteristic
816C2C41×#301211yescharacteristic
817C2C41×#330711yescharacteristic
818C2C41×#331811yescharacteristic
819C2C41×#334511yescharacteristic
820C2C41×#334711yescharacteristic
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×#553C2semidirect
2. C2×C41×#478C2semidirect
3. C2×C41×#442C2semidirect
4. C41×#2537C2semidirect
5. C41×#2034C2semidirect
6. C41×#2033C2semidirect
7. C41×#1999C2semidirect
8. C41×#1999C2semidirect
9. C41×#1992C2semidirect
10. C41×#1955C2semidirect
11. C41×#1875C2semidirect
12. C41×#1874C2semidirect
13. C41×#1854C2semidirect
14. C41×#1853C2semidirect
15. C41×#1802C2semidirect
84. #125×C41D4semidirect
102. C4×D4×C41D4semidirect
350. #24136C41direct (N × H)
400. C2×#553C2×C41semidirect
401. C2×#478C2×C41semidirect
402. C2×#442C2×C41semidirect
403. #2537C2×C41semidirect
404. #2034C2×C41semidirect
405. #2033C2×C41semidirect
406. #1999C2×C41semidirect
407. #1999C2×C41semidirect
408. #1992C2×C41semidirect
409. #1955C2×C41semidirect
410. #1875C2×C41semidirect
411. #1874C2×C41semidirect
412. #1854C2×C41semidirect
413. #1853C2×C41semidirect
414. #1802C2×C41semidirect
473. C41#24136direct (N × H)
495. #125D4×C41semidirect
513. C4×D4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5532
C2×C41×#4782
C2×C41×#4422
C41×#25372
C41×#20342
C41×#20332
C41×#19992
C41×#19922
C41×#19552
C41×#18752
C41×#18742
C41×#18542
C41×#18532
C41×#18022
#2413641