Finite Group Databasebeta

← C41×#24861 #23801062

Subgroups — C41×#24861 #23801062

Order 10496.

1238 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×#480C211yesmaximal, characteristic, complemented
2C22×#102×C41C211yesmaximal, characteristic, complemented
3C41×#2408C211yesmaximal, characteristic
4D4×C4⋊C4×C41C211yesmaximal, characteristic, complemented
5C41×#2093C211yesmaximal, characteristic, complemented
6C41×#2071C211yesmaximal, characteristic, complemented
7C41×#2033C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#1925C211yesmaximal, characteristic, complemented
10C41×#1925C211yesmaximal, characteristic, complemented
11C41×#1874C211yesmaximal, characteristic, complemented
12C41×#1869C211yesmaximal, characteristic, complemented
13C41×#1852C211yesmaximal, characteristic, complemented
14C41×#1808C211yesmaximal, 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×C41—21no—
22C2×C4×D4×C41C2211yescharacteristic
23C22×C4⋊C4×C41C2211yescharacteristic
24C22×C4⋊C4×C41C2211yescharacteristic, complemented
25C41×#480—24no—
26C2×#107×C41C2211yescharacteristic, complemented
27C2×#107×C41C2211yescharacteristic, complemented
28C2×#107×C41C2211yescharacteristic, complemented
29C2×#107×C41C2211yescharacteristic, complemented
30C2×#102×C41—24no—
31C2×#102×C41C2211yescharacteristic
32C2×#102×C41C2211yescharacteristic
33C2×#102×C41C2211yescharacteristic
34C2×#102×C41C2211yescharacteristic
35C2×#102×C41C2211yescharacteristic
36C2×#102×C41C2211yescharacteristic
37C2×#102×C41C2211yescharacteristic
38C2×#102×C41C2211yescharacteristic
39C2×C22⋊C8×C41C2211yescharacteristic
40C2×C22⋊C8×C41C2211yescharacteristic, complemented
41C2×C22⋊C8×C41C2211yescharacteristic, complemented
42C41×#394—21no—
43C41×#392—21no—
44C41×#390C2211yescharacteristic
45C41×#390C2211yescharacteristic
46C41×#389—21no—
47C41×#385—21no—
48C41×#385—21no—
49C41×#384C2211yescharacteristic, complemented
50C41×#380C2211yescharacteristic
51C41×#380C2211yescharacteristic
52C41×#380C2211yescharacteristic, complemented
53C41×#379—21no—
54C4×C4⋊C4×C41C2211yescharacteristic, complemented
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×C41—21no—
76C23×C4×C41C2311yescharacteristic
77C23×C4×C41C2311yescharacteristic
78C22×C8×C41—22no—
79C22×C8×C41—22no—
80C22×C8×C41—41no—
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84C22×C8×C41C2311yescharacteristic
85#121×C41—22no—
86#121×C41—22no—
87#121×C41—41no—
88#121×C41—41no—
89#120×C41—44no—
90C4×D4×C41—22no—
91C4×D4×C41—22no—
92C4×D4×C41—44no—
93C2×C4⋊C4×C41—22no—
94C2×C4⋊C4×C41—22no—
95C2×C4⋊C4×C41—21no—
96C2×C4⋊C4×C41—21no—
97C2×C4⋊C4×C41—21no—
98C2×C4⋊C4×C41—21no—
99C2×C4⋊C4×C41—41no—
100C2×C4⋊C4×C41—41no—
101C2×C4⋊C4×C41D411yescharacteristic
102C2×C4⋊C4×C41C2311yescharacteristic
103C2×C4⋊C4×C41C2311yescharacteristic
104C2×C4⋊C4×C41C2311yescharacteristic
105C2×C4⋊C4×C41C2311yescharacteristic
106C2×C4⋊C4×C41C2311yescharacteristic
107C2×C4⋊C4×C41C2311yescharacteristic
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×C41—21no—
114C2×C22⋊C4×C41—21no—
115C2×C22⋊C4×C41—21no—
116C2×C22⋊C4×C41—21no—
117C2×C22⋊C4×C41D411yescharacteristic
118C2×C22⋊C4×C41D411yescharacteristic
119C2×C42×C41—21no—
120C2×C42×C41C2311yescharacteristic
121#107×C41—22no—
122#107×C41—22no—
123#107×C41—41no—
124#107×C41—41no—
125#102×C41—22no—
126#102×C41—22no—
127#102×C41—22no—
128#102×C41—22no—
129#102×C41—22no—
130#102×C41—41no—
131#102×C41—41no—
132#102×C41D414yescomplemented
133C22⋊C8×C41—22no—
134C22⋊C8×C41—22no—
135C22⋊C8×C41—41no—
136#95×C41—21no—
137#95×C41—21no—
138#95×C41—21no—
139#95×C41—21no—
140C24×C41—21no—
141C24×C41—21no—
142C24×C41—42no—
143C24×C41—42no—
144C24×C41—42no—
145C24×C41—42no—
146C24×C41—42no—
147C24×C41—81no—
148C24×C41—81no—
149C24×C41C2×D411yescharacteristic
150C24×C41C2×D411yescharacteristic
151C2×D4×C41—22no—
152C2×D4×C41—22no—
153C2×D4×C41—28no—
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×C41D814yes—
177C2×D4×C41C2×D412yes—
178C2×D4×C41#4112yes—
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—21no—
195C22×C4×C41—42no—
196C22×C4×C41—42no—
197C22×C4×C41—42no—
198C22×C4×C41—42no—
199C22×C4×C41—81no—
200C22×C4×C41—81no—
201C22×C4×C41C2×D411yescharacteristic
202C22×C4×C41C2×D411yescharacteristic
203C22×C4×C41C2×D411yescharacteristic
204C22×C4×C41C2×D411yescharacteristic
205C22×C4×C41#4112yes—
206C22×C4×C41#4112yes—
207C22×C4×C41C2411yescharacteristic
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—21no—
216C2×C8×C41—21no—
217C2×C8×C41—21no—
218C2×C8×C41—21no—
219C2×C8×C41—44no—
220C2×C8×C41C2×D412yes—
221C4⋊C4×C41—22no—
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—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—42no—
234C4⋊C4×C41—42no—
235C4⋊C4×C41—42no—
236C4⋊C4×C41—81no—
237C4⋊C4×C41C2×D412yes—
238C22⋊C4×C41—22no—
239C22⋊C4×C41—22no—
240C22⋊C4×C41—42no—
241C22⋊C4×C41—42no—
242C22⋊C4×C41—42no—
243C22⋊C4×C41—42no—
244C22⋊C4×C41—42no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—42no—
247C22⋊C4×C41—81no—
248C22⋊C4×C41—81no—
249C42×C41—21no—
250C42×C41—21no—
251C42×C41—42no—
252C23×C41—21no—
253C23×C41—21no—
254C23×C41—21no—
255C23×C41—21no—
256C23×C41—21no—
257C23×C41—21no—
258C23×C41—21no—
259C23×C41—21no—
260C23×C41—21no—
261C23×C41—21no—
262C23×C41—22no—
263C23×C41—22no—
264C23×C41—48no—
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—41no—
274C23×C41—41no—
275C23×C41—41no—
276C23×C41—41no—
277C23×C41—84no—
278C23×C41—84no—
279C23×C41—84no—
280C23×C41—84no—
281C23×C41—84no—
282C23×C41—84no—
283C23×C41#12312yes—
284C23×C41C2×D812yes—
285C23×C41C2×D812yes—
286C23×C41#13712yes—
287C23×C41C22×D411yescharacteristic
288D4×C41—28no—
289D4×C41—22no—
290D4×C41—22no—
291D4×C41—22no—
292D4×C41—22no—
293D4×C41—48no—
294D4×C41—41no—
295D4×C41—41no—
296D4×C41—41no—
297D4×C41—41no—
298D4×C41—84no—
299D4×C41—84no—
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—22no—
307C2×C4×C41—22no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—22no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
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—41no—
336C2×C4×C41—84no—
337C2×C4×C41—84no—
338C2×C4×C41#12312yes—
339C2×C4×C41C2×D812yes—
340C2×C4×C41C22×D411yescharacteristic
341C2×C4×C41C2×#4111yescharacteristic
342C2×C4×C41C2×#4111yescharacteristic
343C2×C4×C41C2×#4111yescharacteristic
344C2×C4×C41H(5,𝔽2)11yescharacteristic
345C2×C4×C41H(5,𝔽2)11yescharacteristic
346C8×C41—22no—
347C8×C41—41no—
348C8×C41—41no—
349C8×C41—41no—
350#24861C4111yesmaximal, characteristic, direct product factor, Sylow
351C22×C41—22no—
352C22×C41—22no—
353C22×C41—22no—
354C22×C41—22no—
355C22×C41—22no—
356C22×C41—22no—
357C22×C41—22no—
358C22×C41—22no—
359C22×C41—22no—
360C22×C41—41no—
361C22×C41—41no—
362C22×C41—41no—
363C22×C41—41no—
364C22×C41—42no—
365C22×C41—42no—
366C22×C41—42no—
367C22×C41—42no—
368C22×C41—42no—
369C22×C41—42no—
370C22×C41—816no—
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#48014yescomplemented
380C22×C41C2×#12311yescharacteristic
381C22×C41D4211yescharacteristic
382C22×C41#54611yescharacteristic
383C22×C41C22×D811yescharacteristic
384C22×C41C2×#13711yescharacteristic
385C22×C41#57611yescharacteristic
386C22×C41#57711yescharacteristic
387C4×C41—22no—
388C4×C41—22no—
389C4×C41—41no—
390C4×C41—41no—
391C4×C41—42no—
392C4×C41—81no—
393C4×C41—81no—
394C4×C41—81no—
395C4×C41—81no—
396C4×C41—81no—
397C4×C41#52511yescharacteristic
398C4×C41#53811yescharacteristic
399C4×C41#54611yescharacteristic
400C4×C41#55111yescharacteristic
401C2×#480C2×C4111yescharacteristic, complemented
402C22×#102C2×C4111yescharacteristic, complemented
403#2408C2×C4111yescharacteristic
404D4×C4⋊C4C2×C4111yescharacteristic, complemented
405#2093C2×C4111yescharacteristic, complemented
406#2071C2×C4111yescharacteristic, complemented
407#2033C2×C4111yescharacteristic, complemented
408#2033C2×C4111yescharacteristic, complemented
409#1925C2×C4111yescharacteristic, complemented
410#1925C2×C4111yescharacteristic, complemented
411#1874C2×C4111yescharacteristic, complemented
412#1869C2×C4111yescharacteristic, complemented
413#1852C2×C4111yescharacteristic, complemented
414#1808C2×C4111yescharacteristic, complemented
415#1786C2×C4111yescharacteristic, complemented
416C2×C41—24no—
417C2×C41—42no—
418C2×C41—82no—
419C2×C41—82no—
420C2×C41#241811yescharacteristic
421C2×C41C2×#48011yescharacteristic
422C2×C41#309611yescharacteristic
423C2×C41#326611yescharacteristic
424C2×C41D4×D811yescharacteristic
425C2×C41#329411yescharacteristic
426C2×C41#331411yescharacteristic
427C23×D4C22×C4111yescharacteristic
428C23×C8C22×C4111yescharacteristic
429C2×#121C22×C4111yescharacteristic
430C2×#121C22×C4111yescharacteristic
431C2×#120—21no—
432C2×C4×D4—21no—
433C2×C4×D4C22×C4111yescharacteristic
434C22×C4⋊C4C22×C4111yescharacteristic
435C22×C4⋊C4C22×C4111yescharacteristic, complemented
436#480—24no—
437C2×#107C22×C4111yescharacteristic, complemented
438C2×#107C22×C4111yescharacteristic, complemented
439C2×#107C22×C4111yescharacteristic, complemented
440C2×#107C22×C4111yescharacteristic, complemented
441C2×#102—24no—
442C2×#102C22×C4111yescharacteristic
443C2×#102C22×C4111yescharacteristic
444C2×#102C22×C4111yescharacteristic
445C2×#102C22×C4111yescharacteristic
446C2×#102C22×C4111yescharacteristic
447C2×#102C22×C4111yescharacteristic
448C2×#102C22×C4111yescharacteristic
449C2×#102C22×C4111yescharacteristic
450C2×C22⋊C8C22×C4111yescharacteristic
451C2×C22⋊C8C22×C4111yescharacteristic, complemented
452C2×C22⋊C8C22×C4111yescharacteristic, complemented
453#394—21no—
454#392—21no—
455#390C22×C4111yescharacteristic
456#390C22×C4111yescharacteristic
457#389—21no—
458#385—21no—
459#385—21no—
460#384C22×C4111yescharacteristic, complemented
461#380C22×C4111yescharacteristic
462#380C22×C4111yescharacteristic
463#380C22×C4111yescharacteristic, complemented
464#379—21no—
465C4×C4⋊C4C22×C4111yescharacteristic, complemented
466#340C22×C4111yescharacteristic, complemented
467#340C22×C4111yescharacteristic, complemented
468#340C22×C4111yescharacteristic, complemented
469#340C22×C4111yescharacteristic, complemented
470#336C22×C4111yescharacteristic, complemented
471#336C22×C4111yescharacteristic, complemented
472C41#2486111yescharacteristic, direct product factor, Sylow
473C25—21no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4D4×C4111yescharacteristic
484C22×D4C23×C4111yescharacteristic
485C22×D4C23×C4111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C23×C4111yescharacteristic
489C23×C4C23×C4111yescharacteristic
490C22×C8—22no—
491C22×C8—22no—
492C22×C8—41no—
493C22×C8C23×C4111yescharacteristic
494C22×C8C23×C4111yescharacteristic
495C22×C8C23×C4111yescharacteristic
496C22×C8C23×C4111yescharacteristic
497#121—22no—
498#121—22no—
499#121—41no—
500#121—41no—
501#120—44no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—44no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4D4×C4111yescharacteristic
514C2×C4⋊C4C23×C4111yescharacteristic
515C2×C4⋊C4C23×C4111yescharacteristic
516C2×C4⋊C4C23×C4111yescharacteristic
517C2×C4⋊C4C23×C4111yescharacteristic
518C2×C4⋊C4C23×C4111yescharacteristic
519C2×C4⋊C4C23×C4111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4D4×C4111yescharacteristic
530C2×C22⋊C4D4×C4111yescharacteristic
531C2×C42—21no—
532C2×C42C23×C4111yescharacteristic
533#107—22no—
534#107—22no—
535#107—41no—
536#107—41no—
537#102—22no—
538#102—22no—
539#102—22no—
540#102—22no—
541#102—22no—
542#102—41no—
543#102—41no—
544#102D4×C4114yescomplemented
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—41no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552C24—21no—
553C24—21no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—81no—
560C24—81no—
561C24C2×D4×C4111yescharacteristic
562C24C2×D4×C4111yescharacteristic
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—28no—
566C2×D4—21no—
567C2×D4—21no—
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—44no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4D8×C4114yes—
589C2×D4C2×D4×C4112yes—
590C2×D4#41×C4112yes—
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—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×D4×C4111yescharacteristic
614C22×C4C2×D4×C4111yescharacteristic
615C22×C4C2×D4×C4111yescharacteristic
616C22×C4C2×D4×C4111yescharacteristic
617C22×C4#41×C4112yes—
618C22×C4#41×C4112yes—
619C22×C4C24×C4111yescharacteristic
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—44no—
632C2×C8C2×D4×C4112yes—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—81no—
649C4⋊C4C2×D4×C4112yes—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—42no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—48no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23#123×C4112yes—
696C23C2×D8×C4112yes—
697C23C2×D8×C4112yes—
698C23#137×C4112yes—
699C23C22×D4×C4111yescharacteristic
700D4—28no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—48no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
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—41no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4#123×C4112yes—
751C2×C4C2×D8×C4112yes—
752C2×C4C22×D4×C4111yescharacteristic
753C2×C4C2×#41×C4111yescharacteristic
754C2×C4C2×#41×C4111yescharacteristic
755C2×C4C2×#41×C4111yescharacteristic
756C2×C4H(5,𝔽2)×C4111yescharacteristic
757C2×C4H(5,𝔽2)×C4111yescharacteristic
758C8—22no—
759C8—41no—
760C8—41no—
761C8—41no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—816no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22C41×#48014yescomplemented
791C22C2×#123×C4111yescharacteristic
792C22D42×C4111yescharacteristic
793C22C41×#54611yescharacteristic
794C22C22×D8×C4111yescharacteristic
795C22C2×#137×C4111yescharacteristic
796C22C41×#57611yescharacteristic
797C22C41×#57711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4C41×#52511yescharacteristic
809C4C41×#53811yescharacteristic
810C4C41×#54611yescharacteristic
811C4C41×#55111yescharacteristic
812C2—24no—
813C2—42no—
814C2—82no—
815C2—82no—
816C2C41×#241811yescharacteristic
817C2C2×C41×#48011yescharacteristic
818C2C41×#309611yescharacteristic
819C2C41×#326611yescharacteristic
820C2D4×D8×C4111yescharacteristic
821C2C41×#329411yescharacteristic
822C2C41×#331411yescharacteristic
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×#480C2semidirect
2. C22×#102×C41C2semidirect
4. D4×C4⋊C4×C41C2semidirect
5. C41×#2093C2semidirect
6. C41×#2071C2semidirect
7. C41×#2033C2semidirect
8. C41×#2033C2semidirect
9. C41×#1925C2semidirect
10. C41×#1925C2semidirect
11. C41×#1874C2semidirect
12. C41×#1869C2semidirect
13. C41×#1852C2semidirect
14. C41×#1808C2semidirect
15. C41×#1786C2semidirect
24. C22×C4⋊C4×C41C22semidirect
26. C2×#107×C41C22semidirect
27. C2×#107×C41C22semidirect
28. C2×#107×C41C22semidirect
29. C2×#107×C41C22semidirect
40. C2×C22⋊C8×C41C22semidirect
41. C2×C22⋊C8×C41C22semidirect
49. C41×#384C22semidirect
52. C41×#380C22semidirect
54. C4×C4⋊C4×C41C22semidirect
55. C41×#340C22semidirect
56. C41×#340C22semidirect
57. C41×#340C22semidirect
58. C41×#340C22semidirect
59. C41×#336C22semidirect
60. C41×#336C22semidirect
132. #102×C41D4semidirect
350. #24861C41direct (N × H)
379. C22×C41#480semidirect
401. C2×#480C2×C41semidirect
402. C22×#102C2×C41semidirect
404. D4×C4⋊C4C2×C41semidirect
405. #2093C2×C41semidirect
406. #2071C2×C41semidirect
407. #2033C2×C41semidirect
408. #2033C2×C41semidirect
409. #1925C2×C41semidirect
410. #1925C2×C41semidirect
411. #1874C2×C41semidirect
412. #1869C2×C41semidirect
413. #1852C2×C41semidirect
414. #1808C2×C41semidirect
415. #1786C2×C41semidirect
435. C22×C4⋊C4C22×C41semidirect
437. C2×#107C22×C41semidirect
438. C2×#107C22×C41semidirect
439. C2×#107C22×C41semidirect
440. C2×#107C22×C41semidirect
451. C2×C22⋊C8C22×C41semidirect
452. C2×C22⋊C8C22×C41semidirect
460. #384C22×C41semidirect
463. #380C22×C41semidirect
465. C4×C4⋊C4C22×C41semidirect
466. #340C22×C41semidirect
467. #340C22×C41semidirect
468. #340C22×C41semidirect
469. #340C22×C41semidirect
470. #336C22×C41semidirect
471. #336C22×C41semidirect
472. C41#24861direct (N × H)
544. #102D4×C41semidirect
790. C22C41×#480semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4802
C22×#102×C412
C41×#24082
D4×C4⋊C4×C412
C41×#20932
C41×#20712
C41×#20332
C41×#19252
C41×#18742
C41×#18692
C41×#18522
C41×#18082
C41×#17862
#2486141