Finite Group Databasebeta

← C41×#18522 #23794723

Subgroups — C41×#18522 #23794723

Order 10496.

1000 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3475C211yesmaximal, characteristic, complemented
2C41×#3167C211yesmaximal, characteristic, complemented
3C41×#3100C211yesmaximal, characteristic, complemented
4C41×#3035C211yesmaximal, characteristic, complemented
5C41×#1654C211yesmaximal, characteristic, complemented
6C41×#1652C211yesmaximal, characteristic, complemented
7C41×#1646C211yesmaximal, characteristic, complemented
8C41×#1644C211yesmaximal, characteristic, complemented
9C41×#1628C211yesmaximal, characteristic, complemented
10C41×#1625C211yesmaximal, characteristic, complemented
11C41×#1624C211yesmaximal, characteristic, complemented
12C41×#1622C211yesmaximal, characteristic, complemented
13C41×#1542C211yesmaximal, characteristic, complemented
14C41×#1476C211yesmaximal, characteristic, complemented
15C2×C41×D4⋊C8C211yesmaximal, characteristic, complemented
16C2×#135×C41—21no—
17C41×#556C2211yescharacteristic
18C41×#555C2211yescharacteristic
19C41×#554C2211yescharacteristic
20C41×#553—21no—
21C41×#552—21no—
22C41×#552—21no—
23C41×#551—22no—
24C41×#547C2211yescharacteristic
25C41×#546—21no—
26C41×#533C2211yescharacteristic
27C41×#532C2211yescharacteristic
28C41×#529—22no—
29C41×#529—21no—
30C41×#525—21no—
31C4×#41×C41—21no—
32C4×#41×C41C2211yescharacteristic
33C2×C4×D4×C41C2211yescharacteristic
34C2×#117×C41—21no—
35C41×#498C2211yescharacteristic, complemented
36C41×#492C2211yescharacteristic, complemented
37C41×#487C2211yescharacteristic, complemented
38C41×#486C2211yescharacteristic, complemented
39C41×#480—21no—
40C41×#474C2211yescharacteristic
41C41×#474C2211yescharacteristic
42C41×#465—22no—
43C41×#464—21no—
44C41×#463—21no—
45C41×#462C2211yescharacteristic, complemented
46C41×#461C2211yescharacteristic, complemented
47C41×#460C2211yescharacteristic, complemented
48C41×#459C2211yescharacteristic
49C41×#459C2211yescharacteristic
50C41×#459C2211yescharacteristic, complemented
51C41×#447—21no—
52C4×SD16×C41—22no—
53C4×D8×C41—21no—
54C4×D8×C41—21no—
55C41×#431C2211yescharacteristic
56C2×C4⋊C8×C41C2211yescharacteristic
57C41×#416—21no—
58C2×C4×C8×C41C2211yescharacteristic
59C41×#333C2211yescharacteristic, complemented
60C41×#333C2211yescharacteristic, complemented
61C41×#332C2211yescharacteristic, complemented
62C41×#332C2211yescharacteristic, complemented
63C41×Q8⋊C8C2211yescharacteristic, complemented
64C41×Q8⋊C8C2211yescharacteristic, complemented
65C41×D4⋊C8C2211yescharacteristic
66C41×D4⋊C8C2211yescharacteristic
67C41×D4⋊C8C2211yescharacteristic
68C41×D4⋊C8C2211yescharacteristic
69C41×D4⋊C8C2211yescharacteristic, complemented
70C41×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C41—21no—
72C2×#41×C41—21no—
73C2×#41×C41D411yescharacteristic
74C22×D4×C41D411yescharacteristic
75C23×C4×C41—21no—
76#135×C41—44no—
77C2×Q16×C41—21no—
78C2×SD16×C41—21no—
79C2×SD16×C41—22no—
80C2×SD16×C41—21no—
81C2×D8×C41—21no—
82C2×D8×C41—21no—
83C2×D8×C41—21no—
84C22×C8×C41—21no—
85C22×C8×C41—21no—
86C4⋊Q8×C41C2311yescharacteristic
87C4⋊Q8×C41C2311yescharacteristic
88C4⋊Q8×C41C2311yescharacteristic
89#127×C41C2311yescharacteristic
90#126×C41—22no—
91#126×C41—22no—
92#126×C41—22no—
93#125×C41—22no—
94#125×C41—21no—
95#125×C41—21no—
96#124×C41—22no—
97#124×C41—21no—
98#124×C41—21no—
99#123×C41—22no—
100#123×C41—22no—
101#123×C41—22no—
102#123×C41—22no—
103C22⋊Q8×C41—21no—
104C22⋊Q8×C41—21no—
105C22⋊Q8×C41—22no—
106C22⋊Q8×C41—21no—
107C22⋊Q8×C41—21no—
108C22⋊Q8×C41D412yes—
109#121×C41—22no—
110#121×C41—21no—
111#121×C41—21no—
112#121×C41—21no—
113#121×C41—21no—
114#121×C41—21no—
115#120×C41—22no—
116C4×Q8×C41—21no—
117C4×Q8×C41—21no—
118C4×Q8×C41D411yescharacteristic
119C4×Q8×C41D412yes—
120C4×Q8×C41C2311yescharacteristic
121C4×D4×C41—22no—
122C4×D4×C41—22no—
123C4×D4×C41—22no—
124C4×D4×C41—21no—
125C4×D4×C41—21no—
126C4×D4×C41—21no—
127C4×D4×C41—21no—
128C4×D4×C41—21no—
129C4×D4×C41—21no—
130C4×D4×C41—21no—
131C4×D4×C41D411yescharacteristic
132C4×D4×C41D411yescharacteristic
133C4×D4×C41D411yescharacteristic
134C4×D4×C41C2311yescharacteristic
135C4×D4×C41C2311yescharacteristic
136C4×D4×C41C2311yescharacteristic
137#117×C41—22no—
138#117×C41—22no—
139#117×C41—22no—
140#117×C41—21no—
141#117×C41—21no—
142#117×C41—21no—
143#117×C41—21no—
144#117×C41—21no—
145#117×C41D411yescharacteristic
146C2×C4⋊C4×C41—21no—
147C2×C4⋊C4×C41—21no—
148C2×C4⋊C4×C41D411yescharacteristic
149C2×C22⋊C4×C41—22no—
150C2×C22⋊C4×C41—21no—
151C2×C42×C41—22no—
152C2×C42×C41—21no—
153C2×C42×C41C2311yescharacteristic
154#107×C41—21no—
155#107×C41—21no—
156#106×C41—22no—
157C4⋊C8×C41—21no—
158C4⋊C8×C41C2311yescharacteristic
159C4⋊C8×C41C2311yescharacteristic
160C4⋊C8×C41C2311yescharacteristic
161C4⋊C8×C41C2311yescharacteristic
162#103×C41—22no—
163#103×C41—21no—
164#103×C41—21no—
165#102×C41—21no—
166#102×C41—21no—
167#102×C41—21no—
168#102×C41—21no—
169#102×C41—21no—
170#102×C41—21no—
171#102×C41—22no—
172C22⋊C8×C41—21no—
173C4×C8×C41—21no—
174C4×C8×C41—21no—
175C4×C8×C41C2311yescharacteristic
176C4×C8×C41C2311yescharacteristic
177C24×C41—21no—
178#41×C41—22no—
179#41×C41—22no—
180#41×C41—42no—
181#41×C41—42no—
182#41×C41—42no—
183#41×C41—42no—
184C2×Q8×C41—21no—
185C2×Q8×C41—21no—
186C2×Q8×C41C2×D411yescharacteristic
187C2×Q8×C41C2×D412yes—
188C2×D4×C41—22no—
189C2×D4×C41—22no—
190C2×D4×C41—21no—
191C2×D4×C41—22no—
192C2×D4×C41—21no—
193C2×D4×C41—21no—
194C2×D4×C41—21no—
195C2×D4×C41—21no—
196C2×D4×C41—41no—
197C2×D4×C41—41no—
198C2×D4×C41C2×D411yescharacteristic
199C2×D4×C41C2×D411yescharacteristic
200C2×D4×C41C2×D411yescharacteristic
201C22×C4×C41—22no—
202C22×C4×C41—21no—
203C22×C4×C41—22no—
204C22×C4×C41—21no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—42no—
212C22×C4×C41—42no—
213C22×C4×C41—41no—
214C22×C4×C41C2×D411yescharacteristic
215C22×C4×C41C2×D411yescharacteristic
216C22×C4×C41C2×D411yescharacteristic
217Q16×C41—42no—
218SD16×C41—44no—
219SD16×C41—42no—
220SD16×C41—42no—
221D8×C41—42no—
222D8×C41—42no—
223D8×C41—42no—
224C2×C8×C41—21no—
225C2×C8×C41—21no—
226C2×C8×C41—21no—
227C2×C8×C41—21no—
228C2×C8×C41—21no—
229C2×C8×C41—21no—
230C2×C8×C41—42no—
231C2×C8×C41—42no—
232C4⋊C4×C41—22no—
233C4⋊C4×C41—22no—
234C4⋊C4×C41—22no—
235C4⋊C4×C41—22no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—22no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—22no—
240C4⋊C4×C41—21no—
241C4⋊C4×C41—21no—
242C4⋊C4×C41—21no—
243C4⋊C4×C41—21no—
244C4⋊C4×C41—21no—
245C4⋊C4×C41—21no—
246C4⋊C4×C41C2×D411yescharacteristic
247C4⋊C4×C41C2×D411yescharacteristic
248C4⋊C4×C41C2×D412yes—
249C4⋊C4×C41C2×D411yescharacteristic
250C4⋊C4×C41C2×D411yescharacteristic
251C22⋊C4×C41—22no—
252C22⋊C4×C41—22no—
253C22⋊C4×C41—22no—
254C22⋊C4×C41—22no—
255C22⋊C4×C41—22no—
256C22⋊C4×C41—22no—
257C22⋊C4×C41—21no—
258C22⋊C4×C41—22no—
259C22⋊C4×C41—21no—
260C22⋊C4×C41—21no—
261C22⋊C4×C41—21no—
262C22⋊C4×C41—21no—
263C22⋊C4×C41—21no—
264C22⋊C4×C41—21no—
265C22⋊C4×C41—41no—
266C22⋊C4×C41—41no—
267C42×C41—22no—
268C42×C41—22no—
269C42×C41—21no—
270C42×C41—21no—
271C42×C41—22no—
272C42×C41—21no—
273C42×C41C2×D411yescharacteristic
274C42×C41C2×D411yescharacteristic
275C42×C41C2×D411yescharacteristic
276C42×C41C2411yescharacteristic
277C23×C41—21no—
278C23×C41—21no—
279C23×C41—21no—
280C23×C41—42no—
281C23×C41—42no—
282C23×C41—41no—
283C23×C41—81no—
284C23×C41#12011yescharacteristic
285Q8×C41—21no—
286Q8×C41—21no—
287Q8×C41—42no—
288Q8×C41—41no—
289Q8×C41—41no—
290Q8×C41—41no—
291Q8×C41—41no—
292D4×C41—21no—
293D4×C41—21no—
294D4×C41—21no—
295D4×C41—21no—
296D4×C41—21no—
297D4×C41—42no—
298D4×C41—42no—
299D4×C41—44no—
300D4×C41—42no—
301D4×C41—41no—
302D4×C41—41no—
303D4×C41—41no—
304D4×C41—41no—
305D4×C41—82no—
306D4×C41—82no—
307D4×C41#13512yescomplemented
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—22no—
315C2×C4×C41—22no—
316C2×C4×C41—21no—
317C2×C4×C41—41no—
318C2×C4×C41—44no—
319C2×C4×C41—42no—
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—42no—
327C2×C4×C41—42no—
328C2×C4×C41—42no—
329C2×C4×C41—41no—
330C2×C4×C41—81no—
331C2×C4×C41—82no—
332C2×C4×C41—82no—
333C2×C4×C41#12011yescharacteristic
334C2×C4×C41#12011yescharacteristic
335C2×C4×C41#12011yescharacteristic
336C2×C4×C41#13512yes—
337C2×C4×C41AGL(1,ℤ/8)12yes—
338C2×C4×C41C22×D411yescharacteristic
339C2×C4×C41C22×D411yescharacteristic
340C2×C4×C41C22×D411yescharacteristic
341C8×C41—22no—
342C8×C41—41no—
343C8×C41—41no—
344C8×C41—41no—
345C8×C41—41no—
346C8×C41—41no—
347#18522C4111yesmaximal, characteristic, direct product factor, Sylow
348C22×C41—21no—
349C22×C41—21no—
350C22×C41—22no—
351C22×C41—41no—
352C22×C41—41no—
353C22×C41—41no—
354C22×C41—41no—
355C22×C41—41no—
356C22×C41—41no—
357C22×C41—41no—
358C22×C41—41no—
359C22×C41—84no—
360C22×C41—81no—
361C22×C41—81no—
362C22×C41—81no—
363C22×C41#44912yes—
364C22×C41C2×#12011yescharacteristic
365C4×C41—21no—
366C4×C41—21no—
367C4×C41—21no—
368C4×C41—41no—
369C4×C41—41no—
370C4×C41—41no—
371C4×C41—41no—
372C4×C41—42no—
373C4×C41—41no—
374C4×C41—42no—
375C4×C41—81no—
376C4×C41#44912yes—
377C4×C41C2×#13511yescharacteristic
378C4×C41C2×#13511yescharacteristic
379C4×C41C2×AGL(1,ℤ/8)11yescharacteristic
380C4×C41#57511yescharacteristic
381#3475C2×C4111yescharacteristic, complemented
382#3167C2×C4111yescharacteristic, complemented
383#3100C2×C4111yescharacteristic, complemented
384#3035C2×C4111yescharacteristic, complemented
385#1654C2×C4111yescharacteristic, complemented
386#1652C2×C4111yescharacteristic, complemented
387#1646C2×C4111yescharacteristic, complemented
388#1644C2×C4111yescharacteristic, complemented
389#1628C2×C4111yescharacteristic, complemented
390#1625C2×C4111yescharacteristic, complemented
391#1624C2×C4111yescharacteristic, complemented
392#1622C2×C4111yescharacteristic, complemented
393#1542C2×C4111yescharacteristic, complemented
394#1476C2×C4111yescharacteristic, complemented
395C2×D4⋊C8C2×C4111yescharacteristic, complemented
396C2×C41—22no—
397C2×C41—42no—
398C2×C41—81no—
399C2×C41—81no—
400C2×C41—161no—
401C2×C41C2×#44911yescharacteristic
402C2×C41#300211yescharacteristic
403C2×C41#301811yescharacteristic
404C2×#135—21no—
405#556C22×C4111yescharacteristic
406#555C22×C4111yescharacteristic
407#554C22×C4111yescharacteristic
408#553—21no—
409#552—21no—
410#552—21no—
411#551—22no—
412#547C22×C4111yescharacteristic
413#546—21no—
414#533C22×C4111yescharacteristic
415#532C22×C4111yescharacteristic
416#529—22no—
417#529—21no—
418#525—21no—
419C4×#41—21no—
420C4×#41C22×C4111yescharacteristic
421C2×C4×D4C22×C4111yescharacteristic
422C2×#117—21no—
423#498C22×C4111yescharacteristic, complemented
424#492C22×C4111yescharacteristic, complemented
425#487C22×C4111yescharacteristic, complemented
426#486C22×C4111yescharacteristic, complemented
427#480—21no—
428#474C22×C4111yescharacteristic
429#474C22×C4111yescharacteristic
430#465—22no—
431#464—21no—
432#463—21no—
433#462C22×C4111yescharacteristic, complemented
434#461C22×C4111yescharacteristic, complemented
435#460C22×C4111yescharacteristic, complemented
436#459C22×C4111yescharacteristic
437#459C22×C4111yescharacteristic
438#459C22×C4111yescharacteristic, complemented
439#447—21no—
440C4×SD16—22no—
441C4×D8—21no—
442C4×D8—21no—
443#431C22×C4111yescharacteristic
444C2×C4⋊C8C22×C4111yescharacteristic
445#416—21no—
446C2×C4×C8C22×C4111yescharacteristic
447#333C22×C4111yescharacteristic, complemented
448#333C22×C4111yescharacteristic, complemented
449#332C22×C4111yescharacteristic, complemented
450#332C22×C4111yescharacteristic, complemented
451Q8⋊C8C22×C4111yescharacteristic, complemented
452Q8⋊C8C22×C4111yescharacteristic, complemented
453D4⋊C8C22×C4111yescharacteristic
454D4⋊C8C22×C4111yescharacteristic
455D4⋊C8C22×C4111yescharacteristic
456D4⋊C8C22×C4111yescharacteristic
457D4⋊C8C22×C4111yescharacteristic, complemented
458D4⋊C8C22×C4111yescharacteristic, complemented
459C41#1852211yescharacteristic, direct product factor, Sylow
460C2×#41—21no—
461C2×#41—21no—
462C2×#41D4×C4111yescharacteristic
463C22×D4D4×C4111yescharacteristic
464C23×C4—21no—
465#135—44no—
466C2×Q16—21no—
467C2×SD16—21no—
468C2×SD16—22no—
469C2×SD16—21no—
470C2×D8—21no—
471C2×D8—21no—
472C2×D8—21no—
473C22×C8—21no—
474C22×C8—21no—
475C4⋊Q8C23×C4111yescharacteristic
476C4⋊Q8C23×C4111yescharacteristic
477C4⋊Q8C23×C4111yescharacteristic
478#127C23×C4111yescharacteristic
479#126—22no—
480#126—22no—
481#126—22no—
482#125—22no—
483#125—21no—
484#125—21no—
485#124—22no—
486#124—21no—
487#124—21no—
488#123—22no—
489#123—22no—
490#123—22no—
491#123—22no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C4112yes—
498#121—22no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#120—22no—
505C4×Q8—21no—
506C4×Q8—21no—
507C4×Q8D4×C4111yescharacteristic
508C4×Q8D4×C4112yes—
509C4×Q8C23×C4111yescharacteristic
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4D4×C4111yescharacteristic
521C4×D4D4×C4111yescharacteristic
522C4×D4D4×C4111yescharacteristic
523C4×D4C23×C4111yescharacteristic
524C4×D4C23×C4111yescharacteristic
525C4×D4C23×C4111yescharacteristic
526#117—22no—
527#117—22no—
528#117—22no—
529#117—21no—
530#117—21no—
531#117—21no—
532#117—21no—
533#117—21no—
534#117D4×C4111yescharacteristic
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4D4×C4111yescharacteristic
538C2×C22⋊C4—22no—
539C2×C22⋊C4—21no—
540C2×C42—22no—
541C2×C42—21no—
542C2×C42C23×C4111yescharacteristic
543#107—21no—
544#107—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8C23×C4111yescharacteristic
548C4⋊C8C23×C4111yescharacteristic
549C4⋊C8C23×C4111yescharacteristic
550C4⋊C8C23×C4111yescharacteristic
551#103—22no—
552#103—21no—
553#103—21no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102—21no—
560#102—22no—
561C22⋊C8—21no—
562C4×C8—21no—
563C4×C8—21no—
564C4×C8C23×C4111yescharacteristic
565C4×C8C23×C4111yescharacteristic
566C24—21no—
567#41—22no—
568#41—22no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8C2×D4×C4111yescharacteristic
576C2×Q8C2×D4×C4112yes—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4C2×D4×C4111yescharacteristic
588C2×D4C2×D4×C4111yescharacteristic
589C2×D4C2×D4×C4111yescharacteristic
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
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—41no—
603C22×C4C2×D4×C4111yescharacteristic
604C22×C4C2×D4×C4111yescharacteristic
605C22×C4C2×D4×C4111yescharacteristic
606Q16—42no—
607SD16—44no—
608SD16—42no—
609SD16—42no—
610D8—42no—
611D8—42no—
612D8—42no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—42no—
620C2×C8—42no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—22no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4C2×D4×C4111yescharacteristic
636C4⋊C4C2×D4×C4111yescharacteristic
637C4⋊C4C2×D4×C4112yes—
638C4⋊C4C2×D4×C4111yescharacteristic
639C4⋊C4C2×D4×C4111yescharacteristic
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C22⋊C4—41no—
656C42—22no—
657C42—22no—
658C42—21no—
659C42—22no—
660C42—21no—
661C42—21no—
662C42C2×D4×C4111yescharacteristic
663C42C2×D4×C4111yescharacteristic
664C42C2×D4×C4111yescharacteristic
665C42C24×C4111yescharacteristic
666C23—21no—
667C23—21no—
668C23—21no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—81no—
673C23#120×C4111yescharacteristic
674Q8—21no—
675Q8—21no—
676Q8—42no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—42no—
687D4—42no—
688D4—44no—
689D4—42no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—82no—
695D4—82no—
696D4#135×C4112yescomplemented
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C4111yescharacteristic
723C2×C4#120×C4111yescharacteristic
724C2×C4#120×C4111yescharacteristic
725C2×C4#135×C4112yes—
726C2×C4AGL(1,ℤ/8)×C4112yes—
727C2×C4C22×D4×C4111yescharacteristic
728C2×C4C22×D4×C4111yescharacteristic
729C2×C4C22×D4×C4111yescharacteristic
730C8—22no—
731C8—41no—
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—84no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C41×#44912yes—
752C22C2×#120×C4111yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—81no—
764C4C41×#44912yes—
765C4C2×#135×C4111yescharacteristic
766C4C2×#135×C4111yescharacteristic
767C4C2×AGL(1,ℤ/8)×C4111yescharacteristic
768C4C41×#57511yescharacteristic
769C2—22no—
770C2—42no—
771C2—81no—
772C2—81no—
773C2—161no—
774C2C2×C41×#44911yescharacteristic
775C2C41×#300211yescharacteristic
776C2C41×#301811yescharacteristic
subgroupG/H
centerC2×C4×C41#120
commutator, Frattini, cosocleC42C24×C41
socleC22×C41C2×#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3475C2semidirect
2. C41×#3167C2semidirect
3. C41×#3100C2semidirect
4. C41×#3035C2semidirect
5. C41×#1654C2semidirect
6. C41×#1652C2semidirect
7. C41×#1646C2semidirect
8. C41×#1644C2semidirect
9. C41×#1628C2semidirect
10. C41×#1625C2semidirect
11. C41×#1624C2semidirect
12. C41×#1622C2semidirect
13. C41×#1542C2semidirect
14. C41×#1476C2semidirect
15. C2×C41×D4⋊C8C2semidirect
35. C41×#498C22semidirect
36. C41×#492C22semidirect
37. C41×#487C22semidirect
38. C41×#486C22semidirect
45. C41×#462C22semidirect
46. C41×#461C22semidirect
47. C41×#460C22semidirect
50. C41×#459C22semidirect
59. C41×#333C22semidirect
60. C41×#333C22semidirect
61. C41×#332C22semidirect
62. C41×#332C22semidirect
63. C41×Q8⋊C8C22semidirect
64. C41×Q8⋊C8C22semidirect
69. C41×D4⋊C8C22semidirect
70. C41×D4⋊C8C22semidirect
307. D4×C41#135semidirect
347. #18522C41direct (N × H)
381. #3475C2×C41semidirect
382. #3167C2×C41semidirect
383. #3100C2×C41semidirect
384. #3035C2×C41semidirect
385. #1654C2×C41semidirect
386. #1652C2×C41semidirect
387. #1646C2×C41semidirect
388. #1644C2×C41semidirect
389. #1628C2×C41semidirect
390. #1625C2×C41semidirect
391. #1624C2×C41semidirect
392. #1622C2×C41semidirect
393. #1542C2×C41semidirect
394. #1476C2×C41semidirect
395. C2×D4⋊C8C2×C41semidirect
423. #498C22×C41semidirect
424. #492C22×C41semidirect
425. #487C22×C41semidirect
426. #486C22×C41semidirect
433. #462C22×C41semidirect
434. #461C22×C41semidirect
435. #460C22×C41semidirect
438. #459C22×C41semidirect
447. #333C22×C41semidirect
448. #333C22×C41semidirect
449. #332C22×C41semidirect
450. #332C22×C41semidirect
451. Q8⋊C8C22×C41semidirect
452. Q8⋊C8C22×C41semidirect
457. D4⋊C8C22×C41semidirect
458. D4⋊C8C22×C41semidirect
459. C41#18522direct (N × H)
696. D4#135×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34752
C41×#31672
C41×#31002
C41×#30352
C41×#16542
C41×#16522
C41×#16462
C41×#16442
C41×#16282
C41×#16252
C41×#16242
C41×#16222
C41×#15422
C41×#14762
C2×C41×D4⋊C82
#1852241