Finite Group Databasebeta

← C41×#26844 #23803045

Subgroups — C41×#26844 #23803045

Order 10496.

868 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#489C211yesmaximal, characteristic, complemented
2C2×C41×#440C211yesmaximal, characteristic, complemented
3C41×#2452C211yesmaximal, characteristic, complemented
4C41×#2448C211yesmaximal, characteristic, complemented
5C41×#2067C211yesmaximal, characteristic, complemented
6C41×#2057C211yesmaximal, characteristic, complemented
7C41×#2055C211yesmaximal, characteristic, complemented
8C41×#2012C211yesmaximal, characteristic
9C41×#1970C211yesmaximal, characteristic
10C41×#1936C211yesmaximal, characteristic, complemented
11C41×#1936C211yesmaximal, characteristic, complemented
12C41×#1933C211yesmaximal, characteristic, complemented
13C41×#1879C211yesmaximal, characteristic
14C41×#1863C211yesmaximal, characteristic, complemented
15C41×#1770C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C22×D8×C41C2211yescharacteristic
18C2×C4⋊Q8×C41C2211yescharacteristic
19C2×#124×C41C2211yescharacteristic
20C2×C22⋊Q8×C41—21no—
21C2×C4×Q8×C41C2211yescharacteristic
22C2×C4×D4×C41C2211yescharacteristic
23C41×#489—24no—
24C41×#440—24no—
25C2×#107×C41C2211yescharacteristic
26C2×#107×C41C2211yescharacteristic
27C2×C4⋊C8×C41C2211yescharacteristic
28C2×#103×C41C2211yescharacteristic
29C2×#103×C41C2211yescharacteristic
30C2×#103×C41C2211yescharacteristic
31C2×#102×C41C2211yescharacteristic
32C2×#102×C41C2211yescharacteristic
33C2×#102×C41C2211yescharacteristic
34C2×#102×C41C2211yescharacteristic
35C2×#102×C41C2211yescharacteristic
36C2×#97×C41C2211yescharacteristic
37C2×#97×C41C2211yescharacteristic
38C2×C4×C8×C41C2211yescharacteristic
39C41×#399—21no—
40C41×#397—21no—
41C41×#396—21no—
42C41×#393—21no—
43C41×#391C2211yescharacteristic
44C41×#390C2211yescharacteristic
45C41×#390C2211yescharacteristic
46C41×#390C2211yescharacteristic
47C41×#390C2211yescharacteristic
48C41×#389C2211yescharacteristic
49C41×#389C2211yescharacteristic
50C41×#389C2211yescharacteristic
51C41×#388—21no—
52C41×#388—21no—
53C41×#385—21no—
54C4×C4⋊C4×C41C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#336C2211yescharacteristic
60C41×#336C2211yescharacteristic
61C22×Q8×C41—21no—
62C22×Q8×C41C2311yescharacteristic
63C22×D4×C41C2311yescharacteristic
64C22×D4×C41C2311yescharacteristic
65C23×C4×C41—21no—
66C2×SD16×C41—22no—
67C2×SD16×C41—22no—
68C2×SD16×C41—22no—
69C2×D8×C41—22no—
70C2×D8×C41—22no—
71C2×D8×C41—41no—
72C22×C8×C41C2311yescharacteristic
73C22×C8×C41C2311yescharacteristic
74C22×C8×C41C2311yescharacteristic
75C22×C8×C41C2311yescharacteristic
76C4⋊Q8×C41—22no—
77C4⋊Q8×C41—41no—
78#124×C41—22no—
79#124×C41—41no—
80C22⋊Q8×C41—44no—
81C4×Q8×C41—22no—
82C4×Q8×C41—41no—
83C4×D4×C41—22no—
84C4×D4×C41—41no—
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×C41D411yescharacteristic
91C2×C4⋊C4×C41D411yescharacteristic
92C2×C4⋊C4×C41C2311yescharacteristic
93C2×C4⋊C4×C41C2311yescharacteristic
94C2×C4⋊C4×C41C2311yescharacteristic
95C2×C4⋊C4×C41C2311yescharacteristic
96C2×C4⋊C4×C41C2311yescharacteristic
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×C22⋊C4×C41—21no—
105C2×C22⋊C4×C41—21no—
106C2×C22⋊C4×C41—21no—
107C2×C22⋊C4×C41—21no—
108C2×C42×C41—21no—
109C2×C42×C41C2311yescharacteristic
110C2×C42×C41C2311yescharacteristic
111C2×C42×C41C2311yescharacteristic
112#107×C41—22no—
113#107×C41—41no—
114C4⋊C8×C41—22no—
115#103×C41—22no—
116#103×C41—22no—
117#103×C41D414yes—
118#102×C41—22no—
119#102×C41—22no—
120#102×C41—22no—
121#102×C41—22no—
122#102×C41—22no—
123#97×C41—22no—
124#97×C41—22no—
125C4×C8×C41—22no—
126#95×C41—21no—
127#95×C41—21no—
128#95×C41—21no—
129#95×C41—21no—
130#95×C41—21no—
131#95×C41D411yescharacteristic
132#95×C41D411yescharacteristic
133C24×C41—21no—
134C24×C41—21no—
135C2×Q8×C41—21no—
136C2×Q8×C41—21no—
137C2×Q8×C41—21no—
138C2×Q8×C41—21no—
139C2×Q8×C41—21no—
140C2×Q8×C41—42no—
141C2×Q8×C41—42no—
142C2×Q8×C41—81no—
143C2×Q8×C41C2×D412yes—
144C2×D4×C41—21no—
145C2×D4×C41—21no—
146C2×D4×C41—21no—
147C2×D4×C41—21no—
148C2×D4×C41—21no—
149C2×D4×C41—21no—
150C2×D4×C41—21no—
151C2×D4×C41—21no—
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41#4112yes—
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—42no—
163C22×C4×C41—42no—
164C22×C4×C41—81no—
165C22×C4×C41C2×D411yescharacteristic
166C22×C4×C41C2×D411yescharacteristic
167C22×C4×C41C2×D411yescharacteristic
168C22×C4×C41C2×D411yescharacteristic
169C22×C4×C41C2×D411yescharacteristic
170C22×C4×C41C2×D411yescharacteristic
171C22×C4×C41C2411yescharacteristic
172SD16×C41—28no—
173D8×C41—44no—
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—21no—
182C2×C8×C41—21no—
183C2×C8×C41C2×D412yes—
184C2×C8×C41#4112yes—
185C2×C8×C41#4112yes—
186C4⋊C4×C41—22no—
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—41no—
197C4⋊C4×C41—42no—
198C4⋊C4×C41—42no—
199C4⋊C4×C41—42no—
200C4⋊C4×C41—42no—
201C4⋊C4×C41—81no—
202C4⋊C4×C41C2×D412yes—
203C22⋊C4×C41—42no—
204C22⋊C4×C41—42no—
205C22⋊C4×C41—42no—
206C22⋊C4×C41—42no—
207C22⋊C4×C41—42no—
208C22⋊C4×C41—42no—
209C22⋊C4×C41—42no—
210C22⋊C4×C41—42no—
211C22⋊C4×C41—81no—
212C22⋊C4×C41—81no—
213C22⋊C4×C41—81no—
214C42×C41—21no—
215C42×C41—21no—
216C42×C41—21no—
217C42×C41—21no—
218C42×C41—21no—
219C42×C41—21no—
220C42×C41—42no—
221C23×C41—22no—
222C23×C41—41no—
223C23×C41—41no—
224C23×C41—41no—
225C23×C41—41no—
226C23×C41—41no—
227C23×C41—41no—
228C23×C41—41no—
229C23×C41—41no—
230C23×C41—41no—
231C23×C41—41no—
232C23×C41—41no—
233C23×C41—41no—
234C23×C41—41no—
235C23×C41C22×D411yescharacteristic
236Q8×C41—22no—
237Q8×C41—22no—
238Q8×C41—41no—
239Q8×C41—41no—
240Q8×C41—84no—
241D4×C41—22no—
242D4×C41—22no—
243D4×C41—41no—
244D4×C41—41no—
245D4×C41—41no—
246D4×C41—41no—
247D4×C41—41no—
248D4×C41—41no—
249C2×C4×C41—21no—
250C2×C4×C41—21no—
251C2×C4×C41—21no—
252C2×C4×C41—21no—
253C2×C4×C41—21no—
254C2×C4×C41—21no—
255C2×C4×C41—21no—
256C2×C4×C41—22no—
257C2×C4×C41—22no—
258C2×C4×C41—21no—
259C2×C4×C41—21no—
260C2×C4×C41—21no—
261C2×C4×C41—21no—
262C2×C4×C41—21no—
263C2×C4×C41—21no—
264C2×C4×C41—21no—
265C2×C4×C41—21no—
266C2×C4×C41—21no—
267C2×C4×C41—21no—
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—84no—
285C2×C4×C41AGL(1,ℤ/8)12yes—
286C2×C4×C41C22×D411yescharacteristic
287C2×C4×C41C2×#4111yescharacteristic
288C2×C4×C41C2×#4111yescharacteristic
289C2×C4×C41C2×#4111yescharacteristic
290C2×C4×C41H(5,𝔽2)11yescharacteristic
291C2×C4×C412−1+411yescharacteristic
292C8×C41—22no—
293C8×C41—22no—
294C8×C41—22no—
295C8×C41—41no—
296#26844C4111yesmaximal, characteristic, direct product factor, Sylow
297C22×C41—42no—
298C22×C41—42no—
299C22×C41—42no—
300C22×C41—81no—
301C22×C41—81no—
302C22×C41—81no—
303C22×C41—81no—
304C22×C41—81no—
305C22×C41—81no—
306C22×C41—81no—
307C22×C41—81no—
308C22×C41—81no—
309C22×C41—81no—
310C22×C41—81no—
311C22×C41#53211yescharacteristic
312C22×C41D4211yescharacteristic
313C22×C41#54811yescharacteristic
314C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C41#57511yescharacteristic
316C22×C41#57611yescharacteristic
317C22×C41#57811yescharacteristic
318C4×C41—22no—
319C4×C41—41no—
320C4×C41—42no—
321C4×C41—41no—
322C4×C41—41no—
323C4×C41—42no—
324C4×C41—41no—
325C4×C41—41no—
326C4×C41—81no—
327C4×C41—81no—
328C4×C41—81no—
329C4×C41—81no—
330C4×C41#52511yescharacteristic
331C4×C41#54211yescharacteristic
332C4×C41#54711yescharacteristic
333C4×C41#55111yescharacteristic
334C2×#489C2×C4111yescharacteristic, complemented
335C2×#440C2×C4111yescharacteristic, complemented
336#2452C2×C4111yescharacteristic, complemented
337#2448C2×C4111yescharacteristic, complemented
338#2067C2×C4111yescharacteristic, complemented
339#2057C2×C4111yescharacteristic, complemented
340#2055C2×C4111yescharacteristic, complemented
341#2012C2×C4111yescharacteristic
342#1970C2×C4111yescharacteristic
343#1936C2×C4111yescharacteristic, complemented
344#1936C2×C4111yescharacteristic, complemented
345#1933C2×C4111yescharacteristic, complemented
346#1879C2×C4111yescharacteristic
347#1863C2×C4111yescharacteristic, complemented
348#1770C2×C4111yescharacteristic, complemented
349C2×C41—82no—
350C2×C41—161no—
351C2×C41#246111yescharacteristic
352C2×C41#317511yescharacteristic
353C2×C41#318011yescharacteristic
354C2×C41#327411yescharacteristic
355C2×C41#327711yescharacteristic
356C2×C41#336711yescharacteristic
357C2×C41#337011yescharacteristic
358C22×SD16C22×C4111yescharacteristic
359C22×D8C22×C4111yescharacteristic
360C2×C4⋊Q8C22×C4111yescharacteristic
361C2×#124C22×C4111yescharacteristic
362C2×C22⋊Q8—21no—
363C2×C4×Q8C22×C4111yescharacteristic
364C2×C4×D4C22×C4111yescharacteristic
365#489—24no—
366#440—24no—
367C2×#107C22×C4111yescharacteristic
368C2×#107C22×C4111yescharacteristic
369C2×C4⋊C8C22×C4111yescharacteristic
370C2×#103C22×C4111yescharacteristic
371C2×#103C22×C4111yescharacteristic
372C2×#103C22×C4111yescharacteristic
373C2×#102C22×C4111yescharacteristic
374C2×#102C22×C4111yescharacteristic
375C2×#102C22×C4111yescharacteristic
376C2×#102C22×C4111yescharacteristic
377C2×#102C22×C4111yescharacteristic
378C2×#97C22×C4111yescharacteristic
379C2×#97C22×C4111yescharacteristic
380C2×C4×C8C22×C4111yescharacteristic
381#399—21no—
382#397—21no—
383#396—21no—
384#393—21no—
385#391C22×C4111yescharacteristic
386#390C22×C4111yescharacteristic
387#390C22×C4111yescharacteristic
388#390C22×C4111yescharacteristic
389#390C22×C4111yescharacteristic
390#389C22×C4111yescharacteristic
391#389C22×C4111yescharacteristic
392#389C22×C4111yescharacteristic
393#388—21no—
394#388—21no—
395#385—21no—
396C4×C4⋊C4C22×C4111yescharacteristic
397#340C22×C4111yescharacteristic
398#340C22×C4111yescharacteristic
399#340C22×C4111yescharacteristic
400#340C22×C4111yescharacteristic
401#336C22×C4111yescharacteristic
402#336C22×C4111yescharacteristic
403C41#2684411yescharacteristic, direct product factor, Sylow
404C22×Q8—21no—
405C22×Q8C23×C4111yescharacteristic
406C22×D4C23×C4111yescharacteristic
407C22×D4C23×C4111yescharacteristic
408C23×C4—21no—
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16—22no—
412C2×D8—22no—
413C2×D8—22no—
414C2×D8—41no—
415C22×C8C23×C4111yescharacteristic
416C22×C8C23×C4111yescharacteristic
417C22×C8C23×C4111yescharacteristic
418C22×C8C23×C4111yescharacteristic
419C4⋊Q8—22no—
420C4⋊Q8—41no—
421#124—22no—
422#124—41no—
423C22⋊Q8—44no—
424C4×Q8—22no—
425C4×Q8—41no—
426C4×D4—22no—
427C4×D4—41no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C4111yescharacteristic
434C2×C4⋊C4D4×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×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C42—21no—
452C2×C42C23×C4111yescharacteristic
453C2×C42C23×C4111yescharacteristic
454C2×C42C23×C4111yescharacteristic
455#107—22no—
456#107—41no—
457C4⋊C8—22no—
458#103—22no—
459#103—22no—
460#103D4×C4114yes—
461#102—22no—
462#102—22no—
463#102—22no—
464#102—22no—
465#102—22no—
466#97—22no—
467#97—22no—
468C4×C8—22no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95D4×C4111yescharacteristic
475#95D4×C4111yescharacteristic
476C24—21no—
477C24—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—81no—
486C2×Q8C2×D4×C4112yes—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4#41×C4112yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—81no—
508C22×C4C2×D4×C4111yescharacteristic
509C22×C4C2×D4×C4111yescharacteristic
510C22×C4C2×D4×C4111yescharacteristic
511C22×C4C2×D4×C4111yescharacteristic
512C22×C4C2×D4×C4111yescharacteristic
513C22×C4C2×D4×C4111yescharacteristic
514C22×C4C24×C4111yescharacteristic
515SD16—28no—
516D8—44no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8C2×D4×C4112yes—
527C2×C8#41×C4112yes—
528C2×C8#41×C4112yes—
529C4⋊C4—22no—
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—41no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—81no—
545C4⋊C4C2×D4×C4112yes—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—81no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—42no—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C22×D4×C4111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—84no—
584D4—22no—
585D4—22no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
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—84no—
628C2×C4AGL(1,ℤ/8)×C4112yes—
629C2×C4C22×D4×C4111yescharacteristic
630C2×C4C2×#41×C4111yescharacteristic
631C2×C4C2×#41×C4111yescharacteristic
632C2×C4C2×#41×C4111yescharacteristic
633C2×C4H(5,𝔽2)×C4111yescharacteristic
634C2×C42−1+4×C4111yescharacteristic
635C8—22no—
636C8—22no—
637C8—22no—
638C8—41no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C41×#53211yescharacteristic
654C22D42×C4111yescharacteristic
655C22C41×#54811yescharacteristic
656C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
657C22C41×#57511yescharacteristic
658C22C41×#57611yescharacteristic
659C22C41×#57811yescharacteristic
660C4—22no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—41no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4C41×#52511yescharacteristic
673C4C41×#54211yescharacteristic
674C4C41×#54711yescharacteristic
675C4C41×#55111yescharacteristic
676C2—82no—
677C2—161no—
678C2C41×#246111yescharacteristic
679C2C41×#317511yescharacteristic
680C2C41×#318011yescharacteristic
681C2C41×#327411yescharacteristic
682C2C41×#327711yescharacteristic
683C2C41×#336711yescharacteristic
684C2C41×#337011yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC22×D8×C41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C4×C4⋊C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#489C2semidirect
2. C2×C41×#440C2semidirect
3. C41×#2452C2semidirect
4. C41×#2448C2semidirect
5. C41×#2067C2semidirect
6. C41×#2057C2semidirect
7. C41×#2055C2semidirect
10. C41×#1936C2semidirect
11. C41×#1936C2semidirect
12. C41×#1933C2semidirect
14. C41×#1863C2semidirect
15. C41×#1770C2semidirect
296. #26844C41direct (N × H)
334. C2×#489C2×C41semidirect
335. C2×#440C2×C41semidirect
336. #2452C2×C41semidirect
337. #2448C2×C41semidirect
338. #2067C2×C41semidirect
339. #2057C2×C41semidirect
340. #2055C2×C41semidirect
343. #1936C2×C41semidirect
344. #1936C2×C41semidirect
345. #1933C2×C41semidirect
347. #1863C2×C41semidirect
348. #1770C2×C41semidirect
403. C41#26844direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4892
C2×C41×#4402
C41×#24522
C41×#24482
C41×#20672
C41×#20572
C41×#20552
C41×#20122
C41×#19702
C41×#19362
C41×#19332
C41×#18792
C41×#18632
C41×#17702
#2684441