Finite Group Databasebeta

← C41×#25356 #23801557

Subgroups — C41×#25356 #23801557

Order 10496.

840 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#475C211yesmaximal, characteristic, complemented
2C2×C41×#435C211yesmaximal, characteristic
3C41×#2563C211yesmaximal, characteristic
4C41×#2536C211yesmaximal, characteristic
5C41×#2077C211yesmaximal, characteristic, complemented
6C41×#2077C211yesmaximal, characteristic, complemented
7C41×#2036C211yesmaximal, characteristic, complemented
8C41×#2035C211yesmaximal, characteristic, complemented
9C41×#1993C211yesmaximal, characteristic, complemented
10C41×#1949C211yesmaximal, characteristic, complemented
11C41×#1894C211yesmaximal, characteristic, complemented
12C41×#1892C211yesmaximal, characteristic, complemented
13C41×#1809C211yesmaximal, characteristic, complemented
14C41×#1807C211yesmaximal, characteristic, complemented
15C41×#1763C211yesmaximal, characteristic, complemented
16C22×M16×C41C2211yescharacteristic
17C23×C8×C41C2211yescharacteristic
18C2×C4⋊Q8×C41C2211yescharacteristic
19C2×C22⋊Q8×C41C2211yescharacteristic
20C2×C22⋊Q8×C41C2211yescharacteristic
21C2×C4×Q8×C41C2211yescharacteristic
22C2×C4×D4×C41C2211yescharacteristic
23C41×#475—24no—
24C41×#435—24no—
25C2×#107×C41C2211yescharacteristic
26C2×#106×C41C2211yescharacteristic
27C2×#106×C41C2211yescharacteristic
28C2×#106×C41C2211yescharacteristic
29C2×C4⋊C8×C41C2211yescharacteristic
30C2×#103×C41C2211yescharacteristic
31C2×#103×C41C2211yescharacteristic
32C2×#103×C41C2211yescharacteristic
33C2×#103×C41C2211yescharacteristic
34C2×C22⋊C8×C41C2211yescharacteristic
35C2×C22⋊C8×C41C2211yescharacteristic
36C2×#97×C41C2211yescharacteristic
37C41×#398—21no—
38C41×#394—21no—
39C41×#393—21no—
40C41×#393—21no—
41C41×#390—21no—
42C41×#388—21no—
43C41×#388—21no—
44C41×#382—21no—
45C41×#382C2211yescharacteristic
46C41×#380C2211yescharacteristic
47C41×#380C2211yescharacteristic
48C41×#380C2211yescharacteristic
49C41×#380C2211yescharacteristic
50C41×#380C2211yescharacteristic
51C41×#380C2211yescharacteristic
52C4×C4⋊C4×C41C2211yescharacteristic
53C41×#340C2211yescharacteristic
54C41×#340C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C22×Q8×C41—21no—
62C22×Q8×C41C2311yescharacteristic
63C22×D4×C41D411yescharacteristic
64C23×C4×C41C2311yescharacteristic
65C23×C4×C41C2311yescharacteristic
66C2×M16×C41—22no—
67C2×M16×C41—22no—
68C2×M16×C41—41no—
69C22×C8×C41—22no—
70C22×C8×C41—22no—
71C22×C8×C41—41no—
72C22×C8×C41C2311yescharacteristic
73C22×C8×C41C2311yescharacteristic
74C22×C8×C41C2311yescharacteristic
75C22×C8×C41C2311yescharacteristic
76C4⋊Q8×C41—22no—
77C4⋊Q8×C41—22no—
78C22⋊Q8×C41—22no—
79C22⋊Q8×C41—22no—
80C22⋊Q8×C41—41no—
81C22⋊Q8×C41—41no—
82C4×Q8×C41—22no—
83C4×Q8×C41—22no—
84C4×D4×C41—22no—
85C4×D4×C41—22no—
86C2×C4⋊C4×C41—21no—
87C2×C4⋊C4×C41—21no—
88C2×C4⋊C4×C41—21no—
89C2×C4⋊C4×C41—21no—
90C2×C4⋊C4×C41D411yescharacteristic
91C2×C4⋊C4×C41C2311yescharacteristic
92C2×C4⋊C4×C41C2311yescharacteristic
93C2×C4⋊C4×C41C2311yescharacteristic
94C2×C4⋊C4×C41C2311yescharacteristic
95C2×C4⋊C4×C41C2311yescharacteristic
96C2×C4⋊C4×C41C2311yescharacteristic
97C2×C4⋊C4×C41C2311yescharacteristic
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×C22⋊C4×C41—21no—
105C2×C22⋊C4×C41—21no—
106C2×C22⋊C4×C41D411yescharacteristic
107C2×C22⋊C4×C41D411yescharacteristic
108C2×C42×C41—21no—
109C2×C42×C41—21no—
110C2×C42×C41C2311yescharacteristic
111#107×C41—41no—
112#106×C41—22no—
113#106×C41—22no—
114#106×C41—41no—
115C4⋊C8×C41D414yes—
116#103×C41—22no—
117#103×C41—22no—
118#103×C41—22no—
119#103×C41—22no—
120C22⋊C8×C41—22no—
121C22⋊C8×C41—22no—
122#97×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—
132C24×C41C2×D411yescharacteristic
133C24×C41C2×D411yescharacteristic
134C2×Q8×C41—21no—
135C2×Q8×C41—21no—
136C2×Q8×C41—21no—
137C2×Q8×C41—21no—
138C2×Q8×C41—21no—
139C2×Q8×C41—42no—
140C2×Q8×C41—81no—
141C2×Q8×C41—81no—
142C2×Q8×C41#4112yes—
143C2×D4×C41—22no—
144C2×D4×C41—22no—
145C2×D4×C41—41no—
146C22×C4×C41—21no—
147C22×C4×C41—21no—
148C22×C4×C41—21no—
149C22×C4×C41—21no—
150C22×C4×C41—21no—
151C22×C4×C41—21no—
152C22×C4×C41—21no—
153C22×C4×C41—21no—
154C22×C4×C41—21no—
155C22×C4×C41—21no—
156C22×C4×C41—21no—
157C22×C4×C41—21no—
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—21no—
166C22×C4×C41C2×D411yescharacteristic
167C22×C4×C41C2×D411yescharacteristic
168C22×C4×C41C2×D411yescharacteristic
169C22×C4×C41C2×D411yescharacteristic
170C22×C4×C41C2411yescharacteristic
171M16×C41—44no—
172C2×C8×C41—21no—
173C2×C8×C41—21no—
174C2×C8×C41—21no—
175C2×C8×C41—21no—
176C2×C8×C41—21no—
177C2×C8×C41—21no—
178C2×C8×C41—21no—
179C2×C8×C41—21no—
180C2×C8×C41—21no—
181C2×C8×C41—44no—
182C2×C8×C41C2×D412yes—
183C2×C8×C41C2×D412yes—
184C2×C8×C41#4112yes—
185C4⋊C4×C41—22no—
186C4⋊C4×C41—21no—
187C4⋊C4×C41—21no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—21no—
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—42no—
201C4⋊C4×C41—42no—
202C4⋊C4×C41—42no—
203C4⋊C4×C41—42no—
204C22⋊C4×C41—22no—
205C22⋊C4×C41—22no—
206C22⋊C4×C41—42no—
207C22⋊C4×C41—42no—
208C22⋊C4×C41—42no—
209C22⋊C4×C41—42no—
210C22⋊C4×C41—81no—
211C22⋊C4×C41—81no—
212C22⋊C4×C41—81no—
213C22⋊C4×C41—81no—
214C42×C41—42no—
215C42×C41—42no—
216C42×C41C2×D412yes—
217C42×C41#4112yes—
218C23×C41—21no—
219C23×C41—21no—
220C23×C41—21no—
221C23×C41—21no—
222C23×C41—21no—
223C23×C41—21no—
224C23×C41—21no—
225C23×C41—21no—
226C23×C41—21no—
227C23×C41—21no—
228C23×C41—21no—
229C23×C41—21no—
230C23×C41—21no—
231C23×C41#13712yes—
232C23×C41C22×D411yescharacteristic
233Q8×C41—22no—
234Q8×C41—22no—
235Q8×C41—41no—
236Q8×C41—41no—
237Q8×C41—84no—
238D4×C41—44no—
239C2×C4×C41—21no—
240C2×C4×C41—21no—
241C2×C4×C41—21no—
242C2×C4×C41—21no—
243C2×C4×C41—21no—
244C2×C4×C41—21no—
245C2×C4×C41—22no—
246C2×C4×C41—21no—
247C2×C4×C41—21no—
248C2×C4×C41—21no—
249C2×C4×C41—21no—
250C2×C4×C41—41no—
251C2×C4×C41—41no—
252C2×C4×C41—41no—
253C2×C4×C41—41no—
254C2×C4×C41—41no—
255C2×C4×C41—41no—
256C2×C4×C41—41no—
257C2×C4×C41—41no—
258C2×C4×C41—41no—
259C2×C4×C41—41no—
260C2×C4×C41—41no—
261C2×C4×C41—41no—
262C2×C4×C41—41no—
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#12112yes—
282C2×C4×C41#12112yes—
283C2×C4×C41C22×D411yescharacteristic
284C2×C4×C41C2×#4111yescharacteristic
285C2×C4×C41C2×#4111yescharacteristic
286C2×C4×C41C2×#4111yescharacteristic
287C2×C4×C41H(5,𝔽2)11yescharacteristic
288C2×C4×C412−1+411yescharacteristic
289C8×C41—22no—
290C8×C41—22no—
291C8×C41—22no—
292C8×C41—41no—
293#25356C4111yesmaximal, characteristic, direct product factor, Sylow
294C22×C41—22no—
295C22×C41—22no—
296C22×C41—22no—
297C22×C41—41no—
298C22×C41—41no—
299C22×C41—41no—
300C22×C41—41no—
301C22×C41—41no—
302C22×C41—41no—
303C22×C41—41no—
304C22×C41—41no—
305C22×C41—41no—
306C22×C41—41no—
307C22×C41—41no—
308C22×C41C2×#12111yescharacteristic
309C22×C41#54611yescharacteristic
310C22×C41#54711yescharacteristic
311C22×C41C2×#13711yescharacteristic
312C22×C41#57511yescharacteristic
313C22×C41#57711yescharacteristic
314C22×C41#57711yescharacteristic
315C4×C41—22no—
316C4×C41—22no—
317C4×C41—41no—
318C4×C41—41no—
319C4×C41—42no—
320C4×C41—81no—
321C4×C41—81no—
322C4×C41—81no—
323C4×C41—81no—
324C4×C41—81no—
325C4×C41—81no—
326C4×C41—81no—
327C4×C41#52911yescharacteristic
328C4×C41#54211yescharacteristic
329C4×C41#54611yescharacteristic
330C4×C41#54811yescharacteristic
331C2×#475C2×C4111yescharacteristic, complemented
332C2×#435C2×C4111yescharacteristic
333#2563C2×C4111yescharacteristic
334#2536C2×C4111yescharacteristic
335#2077C2×C4111yescharacteristic, complemented
336#2077C2×C4111yescharacteristic, complemented
337#2036C2×C4111yescharacteristic, complemented
338#2035C2×C4111yescharacteristic, complemented
339#1993C2×C4111yescharacteristic, complemented
340#1949C2×C4111yescharacteristic, complemented
341#1894C2×C4111yescharacteristic, complemented
342#1892C2×C4111yescharacteristic, complemented
343#1809C2×C4111yescharacteristic, complemented
344#1807C2×C4111yescharacteristic, complemented
345#1763C2×C4111yescharacteristic, complemented
346C2×C41—42no—
347C2×C41—81no—
348C2×C41#242711yescharacteristic
349C2×C41#305611yescharacteristic
350C2×C41#305711yescharacteristic
351C2×C41#331611yescharacteristic
352C2×C41#332111yescharacteristic
353C2×C41#334411yescharacteristic
354C2×C41#334811yescharacteristic
355C22×M16C22×C4111yescharacteristic
356C23×C8C22×C4111yescharacteristic
357C2×C4⋊Q8C22×C4111yescharacteristic
358C2×C22⋊Q8C22×C4111yescharacteristic
359C2×C22⋊Q8C22×C4111yescharacteristic
360C2×C4×Q8C22×C4111yescharacteristic
361C2×C4×D4C22×C4111yescharacteristic
362#475—24no—
363#435—24no—
364C2×#107C22×C4111yescharacteristic
365C2×#106C22×C4111yescharacteristic
366C2×#106C22×C4111yescharacteristic
367C2×#106C22×C4111yescharacteristic
368C2×C4⋊C8C22×C4111yescharacteristic
369C2×#103C22×C4111yescharacteristic
370C2×#103C22×C4111yescharacteristic
371C2×#103C22×C4111yescharacteristic
372C2×#103C22×C4111yescharacteristic
373C2×C22⋊C8C22×C4111yescharacteristic
374C2×C22⋊C8C22×C4111yescharacteristic
375C2×#97C22×C4111yescharacteristic
376#398—21no—
377#394—21no—
378#393—21no—
379#393—21no—
380#390—21no—
381#388—21no—
382#388—21no—
383#382—21no—
384#382C22×C4111yescharacteristic
385#380C22×C4111yescharacteristic
386#380C22×C4111yescharacteristic
387#380C22×C4111yescharacteristic
388#380C22×C4111yescharacteristic
389#380C22×C4111yescharacteristic
390#380C22×C4111yescharacteristic
391C4×C4⋊C4C22×C4111yescharacteristic
392#340C22×C4111yescharacteristic
393#340C22×C4111yescharacteristic
394#340C22×C4111yescharacteristic
395#340C22×C4111yescharacteristic
396#340C22×C4111yescharacteristic
397#340C22×C4111yescharacteristic
398#340C22×C4111yescharacteristic
399#340C22×C4111yescharacteristic
400C41#2535611yescharacteristic, direct product factor, Sylow
401C22×Q8—21no—
402C22×Q8C23×C4111yescharacteristic
403C22×D4D4×C4111yescharacteristic
404C23×C4C23×C4111yescharacteristic
405C23×C4C23×C4111yescharacteristic
406C2×M16—22no—
407C2×M16—22no—
408C2×M16—41no—
409C22×C8—22no—
410C22×C8—22no—
411C22×C8—41no—
412C22×C8C23×C4111yescharacteristic
413C22×C8C23×C4111yescharacteristic
414C22×C8C23×C4111yescharacteristic
415C22×C8C23×C4111yescharacteristic
416C4⋊Q8—22no—
417C4⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—41no—
421C22⋊Q8—41no—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×D4—22no—
425C4×D4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4D4×C4111yescharacteristic
431C2×C4⋊C4C23×C4111yescharacteristic
432C2×C4⋊C4C23×C4111yescharacteristic
433C2×C4⋊C4C23×C4111yescharacteristic
434C2×C4⋊C4C23×C4111yescharacteristic
435C2×C4⋊C4C23×C4111yescharacteristic
436C2×C4⋊C4C23×C4111yescharacteristic
437C2×C4⋊C4C23×C4111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
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⋊C4D4×C4111yescharacteristic
447C2×C22⋊C4D4×C4111yescharacteristic
448C2×C42—21no—
449C2×C42—21no—
450C2×C42C23×C4111yescharacteristic
451#107—41no—
452#106—22no—
453#106—22no—
454#106—41no—
455C4⋊C8D4×C4114yes—
456#103—22no—
457#103—22no—
458#103—22no—
459#103—22no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462#97—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472C24C2×D4×C4111yescharacteristic
473C24C2×D4×C4111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—42no—
480C2×Q8—81no—
481C2×Q8—81no—
482C2×Q8#41×C4112yes—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—41no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4C2×D4×C4111yescharacteristic
507C22×C4C2×D4×C4111yescharacteristic
508C22×C4C2×D4×C4111yescharacteristic
509C22×C4C2×D4×C4111yescharacteristic
510C22×C4C24×C4111yescharacteristic
511M16—44no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—44no—
522C2×C8C2×D4×C4112yes—
523C2×C8C2×D4×C4112yes—
524C2×C8#41×C4112yes—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C42—42no—
555C42—42no—
556C42C2×D4×C4112yes—
557C42#41×C4112yes—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23#137×C4112yes—
572C23C22×D4×C4111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—84no—
578D4—44no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
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#121×C4112yes—
622C2×C4#121×C4112yes—
623C2×C4C22×D4×C4111yescharacteristic
624C2×C4C2×#41×C4111yescharacteristic
625C2×C4C2×#41×C4111yescharacteristic
626C2×C4C2×#41×C4111yescharacteristic
627C2×C4H(5,𝔽2)×C4111yescharacteristic
628C2×C42−1+4×C4111yescharacteristic
629C8—22no—
630C8—22no—
631C8—22no—
632C8—41no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×#121×C4111yescharacteristic
648C22C41×#54611yescharacteristic
649C22C41×#54711yescharacteristic
650C22C2×#137×C4111yescharacteristic
651C22C41×#57511yescharacteristic
652C22C41×#57711yescharacteristic
653C22C41×#57711yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4C41×#52911yescharacteristic
667C4C41×#54211yescharacteristic
668C4C41×#54611yescharacteristic
669C4C41×#54811yescharacteristic
670C2—42no—
671C2—81no—
672C2C41×#242711yescharacteristic
673C2C41×#305611yescharacteristic
674C2C41×#305711yescharacteristic
675C2C41×#331611yescharacteristic
676C2C41×#332111yescharacteristic
677C2C41×#334411yescharacteristic
678C2C41×#334811yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC22×D4×C41D4
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×#475C2semidirect
5. C41×#2077C2semidirect
6. C41×#2077C2semidirect
7. C41×#2036C2semidirect
8. C41×#2035C2semidirect
9. C41×#1993C2semidirect
10. C41×#1949C2semidirect
11. C41×#1894C2semidirect
12. C41×#1892C2semidirect
13. C41×#1809C2semidirect
14. C41×#1807C2semidirect
15. C41×#1763C2semidirect
293. #25356C41direct (N × H)
331. C2×#475C2×C41semidirect
335. #2077C2×C41semidirect
336. #2077C2×C41semidirect
337. #2036C2×C41semidirect
338. #2035C2×C41semidirect
339. #1993C2×C41semidirect
340. #1949C2×C41semidirect
341. #1894C2×C41semidirect
342. #1892C2×C41semidirect
343. #1809C2×C41semidirect
344. #1807C2×C41semidirect
345. #1763C2×C41semidirect
400. C41#25356direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4752
C2×C41×#4352
C41×#25632
C41×#25362
C41×#20772
C41×#20362
C41×#20352
C41×#19932
C41×#19492
C41×#18942
C41×#18922
C41×#18092
C41×#18072
C41×#17632
#2535641