Finite Group Databasebeta

← C41×#33145 #23809346

Subgroups — C41×#33145 #23809346

Order 10496.

920 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#468C211yesmaximal, characteristic
2C2×C4×M16×C41C211yesmaximal, characteristic, complemented
3C41×#2855C211yesmaximal, characteristic, complemented
4C41×#2854C211yesmaximal, characteristic
5C41×#1973C211yesmaximal, characteristic, complemented
6C41×#1968C211yesmaximal, characteristic, complemented
7C41×#1944C211yesmaximal, characteristic, complemented
8C41×#1942C211yesmaximal, characteristic, complemented
9C41×#1936C211yesmaximal, characteristic, complemented
10C41×#1935C211yesmaximal, characteristic, complemented
11C41×#1934C211yesmaximal, characteristic, complemented
12C41×#1933C211yesmaximal, characteristic, complemented
13C41×#1895C211yesmaximal, characteristic
14C41×#1894C211yesmaximal, characteristic, complemented
15C41×#1809C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C22×M16×C41C2211yescharacteristic
18C22×M16×C41C2211yescharacteristic
19C2×#123×C41—21no—
20C2×C22⋊Q8×C41C2211yescharacteristic
21C2×#121×C41C2211yescharacteristic
22C22×C42×C41C2211yescharacteristic
23C41×#468—24no—
24C2×#107×C41C2211yescharacteristic
25C2×#107×C41C2211yescharacteristic
26C2×#106×C41C2211yescharacteristic
27C2×#103×C41C2211yescharacteristic
28C2×#103×C41C2211yescharacteristic
29C2×#103×C41C2211yescharacteristic
30C2×#102×C41C2211yescharacteristic
31C2×#102×C41C2211yescharacteristic
32C2×#102×C41C2211yescharacteristic
33C4×M16×C41—24no—
34C2×#97×C41C2211yescharacteristic
35C2×#97×C41C2211yescharacteristic
36C2×C4×C8×C41C2211yescharacteristic
37C2×C4×C8×C41C2211yescharacteristic
38C41×#391C2211yescharacteristic
39C41×#391C2211yescharacteristic
40C41×#390C2211yescharacteristic
41C41×#390C2211yescharacteristic
42C41×#389C2211yescharacteristic
43C41×#389C2211yescharacteristic
44C41×#389C2211yescharacteristic
45C41×#389C2211yescharacteristic
46C41×#388—21no—
47C41×#388—21no—
48C41×#387—21no—
49C41×#387—21no—
50C41×#386—21no—
51C41×#385—21no—
52C41×#381—21no—
53C41×#380C2211yescharacteristic
54C41×#380C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C22×Q8×C41C2311yescharacteristic
62C22×D4×C41—21no—
63C22×D4×C41C2311yescharacteristic
64C23×C4×C41D411yescharacteristic
65C23×C4×C41D411yescharacteristic
66C23×C4×C41C2311yescharacteristic
67C2×SD16×C41—22no—
68C2×SD16×C41—22no—
69C2×SD16×C41—22no—
70C2×M16×C41—22no—
71C2×M16×C41—22no—
72C2×M16×C41—22no—
73C2×M16×C41—22no—
74C2×M16×C41—22no—
75C2×M16×C41D414yes—
76C22×C8×C41C2311yescharacteristic
77C22×C8×C41C2311yescharacteristic
78C22×C8×C41C2311yescharacteristic
79C22×C8×C41C2311yescharacteristic
80#123×C41—44no—
81C22⋊Q8×C41—22no—
82C22⋊Q8×C41—22no—
83#121×C41—22no—
84#121×C41—22no—
85C2×C4⋊C4×C41—21no—
86C2×C4⋊C4×C41—21no—
87C2×C4⋊C4×C41—21no—
88C2×C4⋊C4×C41—21no—
89C2×C4⋊C4×C41—21no—
90C2×C4⋊C4×C41C2311yescharacteristic
91C2×C4⋊C4×C41C2311yescharacteristic
92C2×C4⋊C4×C41C2311yescharacteristic
93C2×C4⋊C4×C41C2311yescharacteristic
94C2×C4⋊C4×C41C2311yescharacteristic
95C2×C4⋊C4×C41C2311yescharacteristic
96C2×C22⋊C4×C41—21no—
97C2×C22⋊C4×C41—21no—
98C2×C22⋊C4×C41—21no—
99C2×C22⋊C4×C41—21no—
100C2×C22⋊C4×C41—21no—
101C2×C22⋊C4×C41—21no—
102C2×C22⋊C4×C41—21no—
103C2×C22⋊C4×C41—21no—
104C2×C42×C41—22no—
105C2×C42×C41—22no—
106C2×C42×C41D411yescharacteristic
107C2×C42×C41D411yescharacteristic
108C2×C42×C41C2311yescharacteristic
109C2×C42×C41C2311yescharacteristic
110#107×C41—22no—
111#107×C41—22no—
112#106×C41—22no—
113#103×C41—22no—
114#103×C41—22no—
115#103×C41—22no—
116#102×C41—22no—
117#102×C41—22no—
118#102×C41—22no—
119#97×C41—22no—
120#97×C41—22no—
121C4×C8×C41—22no—
122C4×C8×C41—22no—
123#95×C41—21no—
124#95×C41—21no—
125#95×C41—21no—
126#95×C41—21no—
127#95×C41—21no—
128#95×C41—21no—
129#95×C41—21no—
130#95×C41—21no—
131#95×C41—21no—
132#95×C41—21no—
133C24×C41—21no—
134C24×C41C2×D411yescharacteristic
135C2×Q8×C41—21no—
136C2×Q8×C41—21no—
137C2×Q8×C41—21no—
138C2×Q8×C41—21no—
139C2×Q8×C41—21no—
140C2×Q8×C41—21no—
141C2×D4×C41—21no—
142C2×D4×C41—21no—
143C2×D4×C41—21no—
144C2×D4×C41—21no—
145C2×D4×C41—21no—
146C2×D4×C41—21no—
147C2×D4×C41—42no—
148C2×D4×C41—42no—
149C2×D4×C41—42no—
150C22×C4×C41—21no—
151C22×C4×C41—21no—
152C22×C4×C41—21no—
153C22×C4×C41—21no—
154C22×C4×C41—22no—
155C22×C4×C41—22no—
156C22×C4×C41—22no—
157C22×C4×C41—22no—
158C22×C4×C41—21no—
159C22×C4×C41—21no—
160C22×C4×C41—21no—
161C22×C4×C41—21no—
162C22×C4×C41—21no—
163C22×C4×C41—21no—
164C22×C4×C41—21no—
165C22×C4×C41—41no—
166C22×C4×C41—41no—
167C22×C4×C41C2×D411yescharacteristic
168C22×C4×C41C2×D411yescharacteristic
169C22×C4×C41C2×D411yescharacteristic
170C22×C4×C41C2×D412yes—
171C22×C4×C41C2×D411yescharacteristic
172C22×C4×C41C2×D411yescharacteristic
173C22×C4×C41#4112yes—
174C22×C4×C41C2411yescharacteristic
175SD16×C41—44no—
176M16×C41—28no—
177M16×C41—28no—
178C2×C8×C41—21no—
179C2×C8×C41—21no—
180C2×C8×C41—21no—
181C2×C8×C41—21no—
182C2×C8×C41—21no—
183C2×C8×C41—21no—
184C2×C8×C41C2×D412yes—
185C2×C8×C41C2×D412yes—
186C2×C8×C41#4112yes—
187C2×C8×C41#4112yes—
188C2×C8×C41#4112yes—
189C2×C8×C41#4112yes—
190C4⋊C4×C41—21no—
191C4⋊C4×C41—21no—
192C4⋊C4×C41—21no—
193C4⋊C4×C41—21no—
194C4⋊C4×C41—21no—
195C4⋊C4×C41—21no—
196C4⋊C4×C41—21no—
197C4⋊C4×C41—21no—
198C4⋊C4×C41—21no—
199C4⋊C4×C41—21no—
200C4⋊C4×C41—21no—
201C4⋊C4×C41—21no—
202C4⋊C4×C41—42no—
203C4⋊C4×C41—42no—
204C4⋊C4×C41—42no—
205C4⋊C4×C41—42no—
206C4⋊C4×C41—42no—
207C22⋊C4×C41—42no—
208C22⋊C4×C41—42no—
209C22⋊C4×C41—42no—
210C22⋊C4×C41—42no—
211C22⋊C4×C41—42no—
212C22⋊C4×C41—42no—
213C22⋊C4×C41—42no—
214C22⋊C4×C41—42no—
215C42×C41—22no—
216C42×C41—22no—
217C42×C41—21no—
218C42×C41—21no—
219C42×C41—21no—
220C42×C41—21no—
221C23×C41—21no—
222C23×C41—21no—
223C23×C41—21no—
224C23×C41—21no—
225C23×C41—21no—
226C23×C41—21no—
227C23×C41—41no—
228C23×C41—41no—
229C23×C41—41no—
230C23×C41—41no—
231C23×C41—41no—
232C23×C41—41no—
233C23×C41—41no—
234C23×C41#12112yes—
235C23×C41C22×D411yescharacteristic
236Q8×C41—41no—
237Q8×C41—41no—
238Q8×C41—41no—
239Q8×C41—41no—
240D4×C41—41no—
241D4×C41—41no—
242D4×C41—41no—
243D4×C41—41no—
244D4×C41—84no—
245C2×C4×C41—21no—
246C2×C4×C41—21no—
247C2×C4×C41—21no—
248C2×C4×C41—21no—
249C2×C4×C41—21no—
250C2×C4×C41—21no—
251C2×C4×C41—22no—
252C2×C4×C41—22no—
253C2×C4×C41—22no—
254C2×C4×C41—22no—
255C2×C4×C41—21no—
256C2×C4×C41—21no—
257C2×C4×C41—21no—
258C2×C4×C41—21no—
259C2×C4×C41—21no—
260C2×C4×C41—21no—
261C2×C4×C41—44no—
262C2×C4×C41—44no—
263C2×C4×C41—41no—
264C2×C4×C41—41no—
265C2×C4×C41—41no—
266C2×C4×C41—41no—
267C2×C4×C41—41no—
268C2×C4×C41—41no—
269C2×C4×C41—41no—
270C2×C4×C41—41no—
271C2×C4×C41—41no—
272C2×C4×C41—41no—
273C2×C4×C41—41no—
274C2×C4×C41—41no—
275C2×C4×C41—41no—
276C2×C4×C41—41no—
277C2×C4×C41—41no—
278C2×C4×C41—41no—
279C2×C4×C41—41no—
280C2×C4×C41—41no—
281C2×C4×C41—41no—
282C2×C4×C41—41no—
283C2×C4×C41—41no—
284C2×C4×C41#12112yes—
285C2×C4×C41AGL(1,ℤ/8)12yes—
286C2×C4×C41#13712yes—
287C2×C4×C41C22×D411yescharacteristic
288C2×C4×C41C2×#4111yescharacteristic
289C2×C4×C41C2×#4111yescharacteristic
290C2×C4×C41C2×#4111yescharacteristic
291C2×C4×C41C2×#4111yescharacteristic
292C2×C4×C41C2×#4111yescharacteristic
293C8×C41—22no—
294C8×C41—22no—
295C8×C41—22no—
296C8×C41#12314yescomplemented
297#33145C4111yesmaximal, characteristic, direct product factor, Sylow
298C22×C41—22no—
299C22×C41—22no—
300C22×C41—22no—
301C22×C41—41no—
302C22×C41—41no—
303C22×C41—41no—
304C22×C41—41no—
305C22×C41—81no—
306C22×C41—81no—
307C22×C41—81no—
308C22×C41—81no—
309C22×C41—81no—
310C22×C41—81no—
311C22×C41—81no—
312C22×C41C2×#12111yescharacteristic
313C22×C41#53211yescharacteristic
314C22×C41#53211yescharacteristic
315C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C41C2×#13711yescharacteristic
317C22×C41#57511yescharacteristic
318C22×C41#57511yescharacteristic
319C4×C41—22no—
320C4×C41—22no—
321C4×C41—22no—
322C4×C41—41no—
323C4×C41—41no—
324C4×C41—81no—
325C4×C41—81no—
326C4×C41—81no—
327C4×C41—81no—
328C4×C41—81no—
329C4×C41—81no—
330C4×C41—81no—
331C4×C41C2×#12311yescharacteristic
332C4×C41#52511yescharacteristic
333C4×C41#52911yescharacteristic
334C4×C41#52911yescharacteristic
335C2×#468C2×C4111yescharacteristic
336C2×C4×M16C2×C4111yescharacteristic, complemented
337#2855C2×C4111yescharacteristic, complemented
338#2854C2×C4111yescharacteristic
339#1973C2×C4111yescharacteristic, complemented
340#1968C2×C4111yescharacteristic, complemented
341#1944C2×C4111yescharacteristic, complemented
342#1942C2×C4111yescharacteristic, complemented
343#1936C2×C4111yescharacteristic, complemented
344#1935C2×C4111yescharacteristic, complemented
345#1934C2×C4111yescharacteristic, complemented
346#1933C2×C4111yescharacteristic, complemented
347#1895C2×C4111yescharacteristic
348#1894C2×C4111yescharacteristic, complemented
349#1809C2×C4111yescharacteristic, complemented
350C2×C41—42no—
351C2×C41—161no—
352C2×C41#285411yescharacteristic
353C2×C41#305511yescharacteristic
354C2×C41#305611yescharacteristic
355C2×C41#317111yescharacteristic
356C2×C41#317211yescharacteristic
357C2×C41#318211yescharacteristic
358C2×C41#318311yescharacteristic
359C22×SD16C22×C4111yescharacteristic
360C22×M16C22×C4111yescharacteristic
361C22×M16C22×C4111yescharacteristic
362C2×#123—21no—
363C2×C22⋊Q8C22×C4111yescharacteristic
364C2×#121C22×C4111yescharacteristic
365C22×C42C22×C4111yescharacteristic
366#468—24no—
367C2×#107C22×C4111yescharacteristic
368C2×#107C22×C4111yescharacteristic
369C2×#106C22×C4111yescharacteristic
370C2×#103C22×C4111yescharacteristic
371C2×#103C22×C4111yescharacteristic
372C2×#103C22×C4111yescharacteristic
373C2×#102C22×C4111yescharacteristic
374C2×#102C22×C4111yescharacteristic
375C2×#102C22×C4111yescharacteristic
376C4×M16—24no—
377C2×#97C22×C4111yescharacteristic
378C2×#97C22×C4111yescharacteristic
379C2×C4×C8C22×C4111yescharacteristic
380C2×C4×C8C22×C4111yescharacteristic
381#391C22×C4111yescharacteristic
382#391C22×C4111yescharacteristic
383#390C22×C4111yescharacteristic
384#390C22×C4111yescharacteristic
385#389C22×C4111yescharacteristic
386#389C22×C4111yescharacteristic
387#389C22×C4111yescharacteristic
388#389C22×C4111yescharacteristic
389#388—21no—
390#388—21no—
391#387—21no—
392#387—21no—
393#386—21no—
394#385—21no—
395#381—21no—
396#380C22×C4111yescharacteristic
397#380C22×C4111yescharacteristic
398#340C22×C4111yescharacteristic
399#340C22×C4111yescharacteristic
400#340C22×C4111yescharacteristic
401#340C22×C4111yescharacteristic
402#340C22×C4111yescharacteristic
403#340C22×C4111yescharacteristic
404C41#3314511yescharacteristic, direct product factor, Sylow
405C22×Q8C23×C4111yescharacteristic
406C22×D4—21no—
407C22×D4C23×C4111yescharacteristic
408C23×C4D4×C4111yescharacteristic
409C23×C4D4×C4111yescharacteristic
410C23×C4C23×C4111yescharacteristic
411C2×SD16—22no—
412C2×SD16—22no—
413C2×SD16—22no—
414C2×M16—22no—
415C2×M16—22no—
416C2×M16—22no—
417C2×M16—22no—
418C2×M16—22no—
419C2×M16D4×C4114yes—
420C22×C8C23×C4111yescharacteristic
421C22×C8C23×C4111yescharacteristic
422C22×C8C23×C4111yescharacteristic
423C22×C8C23×C4111yescharacteristic
424#123—44no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427#121—22no—
428#121—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4C23×C4111yescharacteristic
435C2×C4⋊C4C23×C4111yescharacteristic
436C2×C4⋊C4C23×C4111yescharacteristic
437C2×C4⋊C4C23×C4111yescharacteristic
438C2×C4⋊C4C23×C4111yescharacteristic
439C2×C4⋊C4C23×C4111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42D4×C4111yescharacteristic
451C2×C42D4×C4111yescharacteristic
452C2×C42C23×C4111yescharacteristic
453C2×C42C23×C4111yescharacteristic
454#107—22no—
455#107—22no—
456#106—22no—
457#103—22no—
458#103—22no—
459#103—22no—
460#102—22no—
461#102—22no—
462#102—22no—
463#97—22no—
464#97—22no—
465C4×C8—22no—
466C4×C8—22no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477C24—21no—
478C24C2×D4×C4111yescharacteristic
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4C2×D4×C4111yescharacteristic
512C22×C4C2×D4×C4111yescharacteristic
513C22×C4C2×D4×C4111yescharacteristic
514C22×C4C2×D4×C4112yes—
515C22×C4C2×D4×C4111yescharacteristic
516C22×C4C2×D4×C4111yescharacteristic
517C22×C4#41×C4112yes—
518C22×C4C24×C4111yescharacteristic
519SD16—44no—
520M16—28no—
521M16—28no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8C2×D4×C4112yes—
529C2×C8C2×D4×C4112yes—
530C2×C8#41×C4112yes—
531C2×C8#41×C4112yes—
532C2×C8#41×C4112yes—
533C2×C8#41×C4112yes—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C42—22no—
560C42—22no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23#121×C4112yes—
579C23C22×D4×C4111yescharacteristic
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4#121×C4112yes—
629C2×C4AGL(1,ℤ/8)×C4112yes—
630C2×C4#137×C4112yes—
631C2×C4C22×D4×C4111yescharacteristic
632C2×C4C2×#41×C4111yescharacteristic
633C2×C4C2×#41×C4111yescharacteristic
634C2×C4C2×#41×C4111yescharacteristic
635C2×C4C2×#41×C4111yescharacteristic
636C2×C4C2×#41×C4111yescharacteristic
637C8—22no—
638C8—22no—
639C8—22no—
640C8#123×C4114yescomplemented
641C22—22no—
642C22—22no—
643C22—22no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C2×#121×C4111yescharacteristic
656C22C41×#53211yescharacteristic
657C22C41×#53211yescharacteristic
658C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
659C22C2×#137×C4111yescharacteristic
660C22C41×#57511yescharacteristic
661C22C41×#57511yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4C2×#123×C4111yescharacteristic
675C4C41×#52511yescharacteristic
676C4C41×#52911yescharacteristic
677C4C41×#52911yescharacteristic
678C2—42no—
679C2—161no—
680C2C41×#285411yescharacteristic
681C2C41×#305511yescharacteristic
682C2C41×#305611yescharacteristic
683C2C41×#317111yescharacteristic
684C2C41×#317211yescharacteristic
685C2C41×#318211yescharacteristic
686C2C41×#318311yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×#121×C41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C22×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×M16×C41C2semidirect
3. C41×#2855C2semidirect
5. C41×#1973C2semidirect
6. C41×#1968C2semidirect
7. C41×#1944C2semidirect
8. C41×#1942C2semidirect
9. C41×#1936C2semidirect
10. C41×#1935C2semidirect
11. C41×#1934C2semidirect
12. C41×#1933C2semidirect
14. C41×#1894C2semidirect
15. C41×#1809C2semidirect
296. C8×C41#123semidirect
297. #33145C41direct (N × H)
336. C2×C4×M16C2×C41semidirect
337. #2855C2×C41semidirect
339. #1973C2×C41semidirect
340. #1968C2×C41semidirect
341. #1944C2×C41semidirect
342. #1942C2×C41semidirect
343. #1936C2×C41semidirect
344. #1935C2×C41semidirect
345. #1934C2×C41semidirect
346. #1933C2×C41semidirect
348. #1894C2×C41semidirect
349. #1809C2×C41semidirect
404. C41#33145direct (N × H)
640. C8#123×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4682
C2×C4×M16×C412
C41×#28552
C41×#28542
C41×#19732
C41×#19682
C41×#19442
C41×#19422
C41×#19362
C41×#19352
C41×#19342
C41×#19332
C41×#18952
C41×#18942
C41×#18092
#3314541