Finite Group Databasebeta

← C41×#24873 #23801074

Subgroups — C41×#24873 #23801074

Order 10496.

1180 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#482C211yesmaximal, characteristic, complemented
2C22×#102×C41C211yesmaximal, characteristic, complemented
3C41×#2408C211yesmaximal, characteristic
4C41×#2352C211yesmaximal, characteristic, complemented
5C41×#2092C211yesmaximal, characteristic, complemented
6C41×#2073C211yesmaximal, characteristic, complemented
7C41×#2034C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#1926C211yesmaximal, characteristic, complemented
10C41×#1925C211yesmaximal, characteristic, complemented
11C41×#1875C211yesmaximal, characteristic, complemented
12C41×#1869C211yesmaximal, characteristic, complemented
13C41×#1852C211yesmaximal, characteristic, complemented
14C41×#1807C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C41C2211yescharacteristic
17C23×C8×C41C2211yescharacteristic
18C2×#121×C41C2211yescharacteristic
19C2×#121×C41C2211yescharacteristic
20C2×#120×C41—21no—
21C2×C4×D4×C41C2211yescharacteristic
22C2×#117×C41C2211yescharacteristic, complemented
23C22×C4⋊C4×C41C2211yescharacteristic
24C41×#482—24no—
25C2×#107×C41C2211yescharacteristic, complemented
26C2×#107×C41C2211yescharacteristic, complemented
27C2×#106×C41C2211yescharacteristic, complemented
28C2×#106×C41C2211yescharacteristic, complemented
29C2×#102×C41—24no—
30C2×#102×C41C2211yescharacteristic
31C2×#102×C41C2211yescharacteristic
32C2×#102×C41C2211yescharacteristic
33C2×#102×C41C2211yescharacteristic
34C2×#102×C41C2211yescharacteristic
35C2×#102×C41C2211yescharacteristic
36C2×#102×C41C2211yescharacteristic
37C2×#102×C41C2211yescharacteristic
38C2×C22⋊C8×C41C2211yescharacteristic
39C2×C22⋊C8×C41C2211yescharacteristic, complemented
40C2×C22⋊C8×C41C2211yescharacteristic, complemented
41C41×#394—21no—
42C41×#392—21no—
43C41×#390C2211yescharacteristic
44C41×#390C2211yescharacteristic
45C41×#388—21no—
46C41×#387—21no—
47C41×#386—21no—
48C41×#382C2211yescharacteristic, complemented
49C41×#380C2211yescharacteristic
50C41×#380C2211yescharacteristic
51C41×#380C2211yescharacteristic, complemented
52C41×#379—21no—
53C4×C4⋊C4×C41C2211yescharacteristic, complemented
54C4×C22⋊C4×C41—21no—
55C41×#340C2211yescharacteristic, complemented
56C41×#340C2211yescharacteristic, complemented
57C41×#340C2211yescharacteristic, complemented
58C41×#340C2211yescharacteristic, complemented
59C41×#336C2211yescharacteristic, complemented
60C41×#336C2211yescharacteristic, complemented
61C25×C41—21no—
62C22×D4×C41—22no—
63C22×D4×C41—22no—
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41—22no—
68C22×D4×C41—22no—
69C22×D4×C41—41no—
70C22×D4×C41—41no—
71C22×D4×C41D411yescharacteristic
72C22×D4×C41C2311yescharacteristic
73C22×D4×C41C2311yescharacteristic
74C23×C4×C41—21no—
75C23×C4×C41C2311yescharacteristic
76C23×C4×C41C2311yescharacteristic
77C22×C8×C41—22no—
78C22×C8×C41—22no—
79C22×C8×C41—41no—
80C22×C8×C41C2311yescharacteristic
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84#121×C41—22no—
85#121×C41—22no—
86#121×C41—41no—
87#121×C41—41no—
88#120×C41—44no—
89C4×D4×C41—22no—
90C4×D4×C41—22no—
91#117×C41—22no—
92#117×C41—41no—
93C2×C4⋊C4×C41—22no—
94C2×C4⋊C4×C41—21no—
95C2×C4⋊C4×C41—41no—
96C2×C4⋊C4×C41D411yescharacteristic
97C2×C4⋊C4×C41C2311yescharacteristic
98C2×C4⋊C4×C41C2311yescharacteristic
99C2×C4⋊C4×C41C2311yescharacteristic
100C2×C4⋊C4×C41C2311yescharacteristic
101C2×C4⋊C4×C41C2311yescharacteristic
102C2×C4⋊C4×C41C2311yescharacteristic
103C2×C22⋊C4×C41—21no—
104C2×C22⋊C4×C41—21no—
105C2×C22⋊C4×C41—21no—
106C2×C22⋊C4×C41—21no—
107C2×C22⋊C4×C41—21no—
108C2×C22⋊C4×C41—21no—
109C2×C22⋊C4×C41—21no—
110C2×C22⋊C4×C41—21no—
111C2×C22⋊C4×C41—21no—
112C2×C22⋊C4×C41—21no—
113C2×C22⋊C4×C41D411yescharacteristic
114C2×C22⋊C4×C41D411yescharacteristic
115C2×C42×C41—21no—
116C2×C42×C41—21no—
117C2×C42×C41C2311yescharacteristic
118#107×C41—22no—
119#107×C41—41no—
120#106×C41—22no—
121#106×C41—41no—
122#102×C41—22no—
123#102×C41—22no—
124#102×C41—22no—
125#102×C41—22no—
126#102×C41—22no—
127#102×C41—41no—
128#102×C41—41no—
129#102×C41D414yescomplemented
130C22⋊C8×C41—22no—
131C22⋊C8×C41—22no—
132C22⋊C8×C41—41no—
133#95×C41—21no—
134#95×C41—21no—
135#95×C41—21no—
136#95×C41—21no—
137#95×C41—21no—
138#95×C41—21no—
139C24×C41—21no—
140C24×C41—21no—
141C24×C41—42no—
142C24×C41—42no—
143C24×C41—42no—
144C24×C41—42no—
145C24×C41—42no—
146C24×C41—81no—
147C24×C41—81no—
148C24×C41C2×D411yescharacteristic
149C24×C41C2×D411yescharacteristic
150C2×D4×C41—28no—
151C2×D4×C41—22no—
152C2×D4×C41—22no—
153C2×D4×C41—22no—
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—21no—
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—44no—
165C2×D4×C41—44no—
166C2×D4×C41—42no—
167C2×D4×C41—42no—
168C2×D4×C41—44no—
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×C41C2×D412yes—
177C2×D4×C41#4112yes—
178C22×C4×C41—21no—
179C22×C4×C41—21no—
180C22×C4×C41—21no—
181C22×C4×C41—21no—
182C22×C4×C41—21no—
183C22×C4×C41—21no—
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—42no—
195C22×C4×C41—42no—
196C22×C4×C41—81no—
197C22×C4×C41C2×D411yescharacteristic
198C22×C4×C41C2×D411yescharacteristic
199C22×C4×C41C2×D411yescharacteristic
200C22×C4×C41C2×D411yescharacteristic
201C22×C4×C41#4112yes—
202C22×C4×C41#4112yes—
203C22×C4×C41C2411yescharacteristic
204C2×C8×C41—21no—
205C2×C8×C41—21no—
206C2×C8×C41—21no—
207C2×C8×C41—21no—
208C2×C8×C41—21no—
209C2×C8×C41—21no—
210C2×C8×C41—21no—
211C2×C8×C41—21no—
212C2×C8×C41—21no—
213C2×C8×C41—21no—
214C2×C8×C41—21no—
215C2×C8×C41—44no—
216C2×C8×C41C2×D412yes—
217C4⋊C4×C41—22no—
218C4⋊C4×C41—21no—
219C4⋊C4×C41—21no—
220C4⋊C4×C41—21no—
221C4⋊C4×C41—21no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—21no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—42no—
230C4⋊C4×C41C2×D412yes—
231C22⋊C4×C41—22no—
232C22⋊C4×C41—22no—
233C22⋊C4×C41—42no—
234C22⋊C4×C41—42no—
235C22⋊C4×C41—42no—
236C22⋊C4×C41—42no—
237C22⋊C4×C41—42no—
238C22⋊C4×C41—42no—
239C22⋊C4×C41—42no—
240C22⋊C4×C41—81no—
241C22⋊C4×C41—81no—
242C22⋊C4×C41—81no—
243C42×C41—21no—
244C42×C41—21no—
245C42×C41—42no—
246C42×C41—81no—
247C23×C41—21no—
248C23×C41—21no—
249C23×C41—21no—
250C23×C41—21no—
251C23×C41—21no—
252C23×C41—21no—
253C23×C41—22no—
254C23×C41—22no—
255C23×C41—21no—
256C23×C41—21no—
257C23×C41—21no—
258C23×C41—21no—
259C23×C41—21no—
260C23×C41—48no—
261C23×C41—41no—
262C23×C41—41no—
263C23×C41—41no—
264C23×C41—41no—
265C23×C41—41no—
266C23×C41—41no—
267C23×C41—41no—
268C23×C41—41no—
269C23×C41—41no—
270C23×C41—41no—
271C23×C41—41no—
272C23×C41—41no—
273C23×C41—84no—
274C23×C41—84no—
275C23×C41—84no—
276C23×C41—84no—
277C23×C41—84no—
278C23×C41—84no—
279C23×C41#12312yes—
280C23×C41#13512yes—
281C23×C41AGL(1,ℤ/8)12yes—
282C23×C41C22×D411yescharacteristic
283D4×C41—22no—
284D4×C41—22no—
285D4×C41—22no—
286D4×C41—22no—
287D4×C41—48no—
288D4×C41—44no—
289D4×C41—41no—
290D4×C41—41no—
291D4×C41—41no—
292D4×C41—41no—
293D4×C41—84no—
294D4×C41—84no—
295C2×C4×C41—21no—
296C2×C4×C41—21no—
297C2×C4×C41—22no—
298C2×C4×C41—22no—
299C2×C4×C41—22no—
300C2×C4×C41—22no—
301C2×C4×C41—21no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—22no—
306C2×C4×C41—21no—
307C2×C4×C41—21no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—41no—
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—84no—
333C2×C4×C41#12312yes—
334C2×C4×C41C22×D411yescharacteristic
335C2×C4×C41C2×#4111yescharacteristic
336C2×C4×C41C2×#4111yescharacteristic
337C2×C4×C41C2×#4111yescharacteristic
338C2×C4×C41H(5,𝔽2)11yescharacteristic
339C2×C4×C41H(5,𝔽2)11yescharacteristic
340C8×C41—22no—
341C8×C41—41no—
342C8×C41—41no—
343C8×C41—41no—
344#24873C4111yesmaximal, characteristic, direct product factor, Sylow
345C22×C41—22no—
346C22×C41—22no—
347C22×C41—22no—
348C22×C41—22no—
349C22×C41—22no—
350C22×C41—22no—
351C22×C41—41no—
352C22×C41—41no—
353C22×C41—41no—
354C22×C41—42no—
355C22×C41—42no—
356C22×C41—41no—
357C22×C41—42no—
358C22×C41—41no—
359C22×C41—42no—
360C22×C41—41no—
361C22×C41—42no—
362C22×C41—41no—
363C22×C41—42no—
364C22×C41—816no—
365C22×C41—81no—
366C22×C41—81no—
367C22×C41—81no—
368C22×C41—81no—
369C22×C41—81no—
370C22×C41—81no—
371C22×C41—81no—
372C22×C41—81no—
373C22×C41#48214yescomplemented
374C22×C41C2×#12311yescharacteristic
375C22×C41D4211yescharacteristic
376C22×C41#54611yescharacteristic
377C22×C41C2×#13511yescharacteristic
378C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C41#57611yescharacteristic
380C22×C41#57711yescharacteristic
381C4×C41—22no—
382C4×C41—41no—
383C4×C41—41no—
384C4×C41—41no—
385C4×C41—42no—
386C4×C41—81no—
387C4×C41—81no—
388C4×C41—81no—
389C4×C41—81no—
390C4×C41—81no—
391C4×C41#52511yescharacteristic
392C4×C41#53811yescharacteristic
393C4×C41#54611yescharacteristic
394C4×C41#55111yescharacteristic
395C2×#482C2×C4111yescharacteristic, complemented
396C22×#102C2×C4111yescharacteristic, complemented
397#2408C2×C4111yescharacteristic
398#2352C2×C4111yescharacteristic, complemented
399#2092C2×C4111yescharacteristic, complemented
400#2073C2×C4111yescharacteristic, complemented
401#2034C2×C4111yescharacteristic, complemented
402#2033C2×C4111yescharacteristic, complemented
403#1926C2×C4111yescharacteristic, complemented
404#1925C2×C4111yescharacteristic, complemented
405#1875C2×C4111yescharacteristic, complemented
406#1869C2×C4111yescharacteristic, complemented
407#1852C2×C4111yescharacteristic, complemented
408#1807C2×C4111yescharacteristic, complemented
409#1786C2×C4111yescharacteristic, complemented
410C2×C41—24no—
411C2×C41—81no—
412C2×C41—82no—
413C2×C41—82no—
414C2×C41#241811yescharacteristic
415C2×C41C2×#48211yescharacteristic
416C2×C41#309611yescharacteristic
417C2×C41#326411yescharacteristic
418C2×C41#328211yescharacteristic
419C2×C41#329711yescharacteristic
420C2×C41#331011yescharacteristic
421C23×D4C22×C4111yescharacteristic
422C23×C8C22×C4111yescharacteristic
423C2×#121C22×C4111yescharacteristic
424C2×#121C22×C4111yescharacteristic
425C2×#120—21no—
426C2×C4×D4C22×C4111yescharacteristic
427C2×#117C22×C4111yescharacteristic, complemented
428C22×C4⋊C4C22×C4111yescharacteristic
429#482—24no—
430C2×#107C22×C4111yescharacteristic, complemented
431C2×#107C22×C4111yescharacteristic, complemented
432C2×#106C22×C4111yescharacteristic, complemented
433C2×#106C22×C4111yescharacteristic, complemented
434C2×#102—24no—
435C2×#102C22×C4111yescharacteristic
436C2×#102C22×C4111yescharacteristic
437C2×#102C22×C4111yescharacteristic
438C2×#102C22×C4111yescharacteristic
439C2×#102C22×C4111yescharacteristic
440C2×#102C22×C4111yescharacteristic
441C2×#102C22×C4111yescharacteristic
442C2×#102C22×C4111yescharacteristic
443C2×C22⋊C8C22×C4111yescharacteristic
444C2×C22⋊C8C22×C4111yescharacteristic, complemented
445C2×C22⋊C8C22×C4111yescharacteristic, complemented
446#394—21no—
447#392—21no—
448#390C22×C4111yescharacteristic
449#390C22×C4111yescharacteristic
450#388—21no—
451#387—21no—
452#386—21no—
453#382C22×C4111yescharacteristic, complemented
454#380C22×C4111yescharacteristic
455#380C22×C4111yescharacteristic
456#380C22×C4111yescharacteristic, complemented
457#379—21no—
458C4×C4⋊C4C22×C4111yescharacteristic, complemented
459C4×C22⋊C4—21no—
460#340C22×C4111yescharacteristic, complemented
461#340C22×C4111yescharacteristic, complemented
462#340C22×C4111yescharacteristic, complemented
463#340C22×C4111yescharacteristic, complemented
464#336C22×C4111yescharacteristic, complemented
465#336C22×C4111yescharacteristic, complemented
466C41#2487311yescharacteristic, direct product factor, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—41no—
476C22×D4—41no—
477C22×D4D4×C4111yescharacteristic
478C22×D4C23×C4111yescharacteristic
479C22×D4C23×C4111yescharacteristic
480C23×C4—21no—
481C23×C4C23×C4111yescharacteristic
482C23×C4C23×C4111yescharacteristic
483C22×C8—22no—
484C22×C8—22no—
485C22×C8—41no—
486C22×C8C23×C4111yescharacteristic
487C22×C8C23×C4111yescharacteristic
488C22×C8C23×C4111yescharacteristic
489C22×C8C23×C4111yescharacteristic
490#121—22no—
491#121—22no—
492#121—41no—
493#121—41no—
494#120—44no—
495C4×D4—22no—
496C4×D4—22no—
497#117—22no—
498#117—41no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4D4×C4111yescharacteristic
503C2×C4⋊C4C23×C4111yescharacteristic
504C2×C4⋊C4C23×C4111yescharacteristic
505C2×C4⋊C4C23×C4111yescharacteristic
506C2×C4⋊C4C23×C4111yescharacteristic
507C2×C4⋊C4C23×C4111yescharacteristic
508C2×C4⋊C4C23×C4111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C4111yescharacteristic
520C2×C22⋊C4D4×C4111yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42C23×C4111yescharacteristic
524#107—22no—
525#107—41no—
526#106—22no—
527#106—41no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535#102D4×C4114yescomplemented
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545C24—21no—
546C24—21no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24C2×D4×C4111yescharacteristic
555C24C2×D4×C4111yescharacteristic
556C2×D4—28no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4C2×D4×C4112yes—
583C2×D4#41×C4112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—81no—
603C22×C4C2×D4×C4111yescharacteristic
604C22×C4C2×D4×C4111yescharacteristic
605C22×C4C2×D4×C4111yescharacteristic
606C22×C4C2×D4×C4111yescharacteristic
607C22×C4#41×C4112yes—
608C22×C4#41×C4112yes—
609C22×C4C24×C4111yescharacteristic
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—44no—
622C2×C8C2×D4×C4112yes—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—42no—
636C4⋊C4C2×D4×C4112yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—42no—
652C42—81no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—48no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23#123×C4112yes—
686C23#135×C4112yes—
687C23AGL(1,ℤ/8)×C4112yes—
688C23C22×D4×C4111yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
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—84no—
739C2×C4#123×C4112yes—
740C2×C4C22×D4×C4111yescharacteristic
741C2×C4C2×#41×C4111yescharacteristic
742C2×C4C2×#41×C4111yescharacteristic
743C2×C4C2×#41×C4111yescharacteristic
744C2×C4H(5,𝔽2)×C4111yescharacteristic
745C2×C4H(5,𝔽2)×C4111yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—816no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22C41×#48214yescomplemented
779C22C2×#123×C4111yescharacteristic
780C22D42×C4111yescharacteristic
781C22C41×#54611yescharacteristic
782C22C2×#135×C4111yescharacteristic
783C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
784C22C41×#57611yescharacteristic
785C22C41×#57711yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C41×#52511yescharacteristic
797C4C41×#53811yescharacteristic
798C4C41×#54611yescharacteristic
799C4C41×#55111yescharacteristic
800C2—24no—
801C2—81no—
802C2—82no—
803C2—82no—
804C2C41×#241811yescharacteristic
805C2C2×C41×#48211yescharacteristic
806C2C41×#309611yescharacteristic
807C2C41×#326411yescharacteristic
808C2C41×#328211yescharacteristic
809C2C41×#329711yescharacteristic
810C2C41×#331011yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#2408C2
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×#482C2semidirect
2. C22×#102×C41C2semidirect
4. C41×#2352C2semidirect
5. C41×#2092C2semidirect
6. C41×#2073C2semidirect
7. C41×#2034C2semidirect
8. C41×#2033C2semidirect
9. C41×#1926C2semidirect
10. C41×#1925C2semidirect
11. C41×#1875C2semidirect
12. C41×#1869C2semidirect
13. C41×#1852C2semidirect
14. C41×#1807C2semidirect
15. C41×#1786C2semidirect
22. C2×#117×C41C22semidirect
25. C2×#107×C41C22semidirect
26. C2×#107×C41C22semidirect
27. C2×#106×C41C22semidirect
28. C2×#106×C41C22semidirect
39. C2×C22⋊C8×C41C22semidirect
40. C2×C22⋊C8×C41C22semidirect
48. C41×#382C22semidirect
51. C41×#380C22semidirect
53. C4×C4⋊C4×C41C22semidirect
55. C41×#340C22semidirect
56. C41×#340C22semidirect
57. C41×#340C22semidirect
58. C41×#340C22semidirect
59. C41×#336C22semidirect
60. C41×#336C22semidirect
129. #102×C41D4semidirect
344. #24873C41direct (N × H)
373. C22×C41#482semidirect
395. C2×#482C2×C41semidirect
396. C22×#102C2×C41semidirect
398. #2352C2×C41semidirect
399. #2092C2×C41semidirect
400. #2073C2×C41semidirect
401. #2034C2×C41semidirect
402. #2033C2×C41semidirect
403. #1926C2×C41semidirect
404. #1925C2×C41semidirect
405. #1875C2×C41semidirect
406. #1869C2×C41semidirect
407. #1852C2×C41semidirect
408. #1807C2×C41semidirect
409. #1786C2×C41semidirect
427. C2×#117C22×C41semidirect
430. C2×#107C22×C41semidirect
431. C2×#107C22×C41semidirect
432. C2×#106C22×C41semidirect
433. C2×#106C22×C41semidirect
444. C2×C22⋊C8C22×C41semidirect
445. C2×C22⋊C8C22×C41semidirect
453. #382C22×C41semidirect
456. #380C22×C41semidirect
458. C4×C4⋊C4C22×C41semidirect
460. #340C22×C41semidirect
461. #340C22×C41semidirect
462. #340C22×C41semidirect
463. #340C22×C41semidirect
464. #336C22×C41semidirect
465. #336C22×C41semidirect
466. C41#24873direct (N × H)
535. #102D4×C41semidirect
778. C22C41×#482semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4822
C22×#102×C412
C41×#24082
C41×#23522
C41×#20922
C41×#20732
C41×#20342
C41×#20332
C41×#19262
C41×#19252
C41×#18752
C41×#18692
C41×#18522
C41×#18072
C41×#17862
#2487341