Finite Group Databasebeta

← C41×#24141 #23800342

Subgroups — C41×#24141 #23800342

Order 10496.

1200 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3505C211yesmaximal, characteristic
2C41×#2855C211yesmaximal, characteristic, complemented
3C41×#2854C211yesmaximal, characteristic, complemented
4C4×#123×C41C211yesmaximal, characteristic, complemented
5C41×#2044C212yesmaximal, complemented
6C41×#2022C212yesmaximal, complemented
7C41×#1996C211yesmaximal, characteristic, complemented
8C41×#1964C211yesmaximal, characteristic, complemented
9C41×#1890C212yesmaximal, complemented
10C41×#1867C212yesmaximal, complemented
11C41×#1799C211yesmaximal, characteristic, complemented
12C41×#553—22no—
13C41×#553—21no—
14C41×#552—21no—
15C41×#551—22no—
16C41×#548—21no—
17C41×#546—21no—
18C41×#539—21no—
19C41×#538—21no—
20C41×#534C2212yes—
21C41×#529—21no—
22C41×#525—21no—
23C2×#123×C41C2211yescharacteristic
24C2×#123×C41C2212yes—
25C2×C22⋊Q8×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C41×#518C2212yes—
28C2×C4×D4×C41C2211yescharacteristic
29C22×C42×C41C2211yescharacteristic
30C2×#99×C41C2212yes—
31C2×#99×C41C2212yes—
32C2×#99×C41C2212yes—
33C41×#391—21no—
34C41×#390—21no—
35C41×#389—21no—
36C41×#389—21no—
37C41×#388—21no—
38C41×#388—22no—
39C41×#387—21no—
40C41×#387—22no—
41C41×#386C2211yescharacteristic
42C41×#386C2212yes—
43C41×#385C2212yes—
44C41×#385C2211yescharacteristic
45C41×#381C2212yes—
46C41×#381C2211yescharacteristic
47C41×#380C2211yescharacteristic
48C41×#380C2211yescharacteristic
49C4×C4⋊C4×C41—21no—
50C4×C22⋊C4×C41—21no—
51C4×C22⋊C4×C41C2211yescharacteristic
52C41×#342C2212yes—
53C41×#342C2212yes—
54C41×#342C2212yes—
55C2×#41×C41—21no—
56C22×Q8×C41D411yescharacteristic
57C22×D4×C41D411yescharacteristic
58C22×D4×C41C2311yescharacteristic
59C22×D4×C41C2312yes—
60C23×C4×C41D411yescharacteristic
61C23×C4×C41C2311yescharacteristic
62C23×C4×C41C2311yescharacteristic
63C23×C4×C41C2311yescharacteristic
64#126×C41—22no—
65#126×C41—22no—
66#126×C41—22no—
67#125×C41—21no—
68#125×C41—22no—
69#124×C41—21no—
70#124×C41—22no—
71#123×C41—22no—
72#123×C41—22no—
73#123×C41—22no—
74#123×C41—22no—
75#123×C41—22no—
76#123×C41—22no—
77#123×C41—22no—
78#123×C41—24no—
79#123×C41—42no—
80C22⋊Q8×C41—21no—
81C22⋊Q8×C41—22no—
82C22⋊Q8×C41—21no—
83C22⋊Q8×C41—21no—
84C22⋊Q8×C41—21no—
85C22⋊Q8×C41—21no—
86#121×C41—21no—
87#121×C41—22no—
88#121×C41—21no—
89#121×C41—21no—
90#121×C41—21no—
91#121×C41—21no—
92#121×C41—22no—
93#121×C41—22no—
94#120×C41—22no—
95#120×C41—22no—
96C4×Q8×C41—21no—
97C4×D4×C41—22no—
98C4×D4×C41—21no—
99C4×D4×C41—21no—
100C4×D4×C41—21no—
101C4×D4×C41—21no—
102C4×D4×C41—21no—
103C4×D4×C41—22no—
104C4×D4×C41—22no—
105C4×D4×C41—22no—
106C4×D4×C41—22no—
107#117×C41—21no—
108#117×C41—22no—
109#117×C41—22no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—22no—
112C2×C4⋊C4×C41—21no—
113C2×C4⋊C4×C41—21no—
114C2×C4⋊C4×C41—21no—
115C2×C4⋊C4×C41—22no—
116C2×C4⋊C4×C41D411yescharacteristic
117C2×C4⋊C4×C41D411yescharacteristic
118C2×C4⋊C4×C41D412yes—
119C2×C4⋊C4×C41D411yescharacteristic
120C2×C22⋊C4×C41—22no—
121C2×C22⋊C4×C41—21no—
122C2×C22⋊C4×C41—22no—
123C2×C22⋊C4×C41—21no—
124C2×C22⋊C4×C41—22no—
125C2×C22⋊C4×C41D411yescharacteristic
126C2×C22⋊C4×C41D412yes—
127C2×C22⋊C4×C41C2312yes—
128C2×C22⋊C4×C41C2311yescharacteristic
129C2×C22⋊C4×C41C2312yes—
130C2×C22⋊C4×C41C2311yescharacteristic
131C2×C22⋊C4×C41C2312yes—
132C2×C22⋊C4×C41C2311yescharacteristic
133C2×C42×C41—21no—
134C2×C42×C41—21no—
135C2×C42×C41—21no—
136C2×C42×C41—21no—
137C2×C42×C41—21no—
138C2×C42×C41—21no—
139C2×C42×C41—21no—
140C2×C42×C41D411yescharacteristic
141#99×C41—24no—
142#99×C41—42no—
143#99×C41—42no—
144#95×C41—21no—
145#95×C41—21no—
146#95×C41—21no—
147#95×C41—21no—
148#95×C41—21no—
149#95×C41—21no—
150#95×C41—21no—
151#95×C41—22no—
152#95×C41—22no—
153#95×C41—22no—
154#95×C41—22no—
155C24×C41C2×D412yes—
156C24×C41C2×D411yescharacteristic
157C24×C41C2411yescharacteristic
158#41×C41—82no—
159C2×Q8×C41—21no—
160C2×Q8×C41—21no—
161C2×Q8×C41—42no—
162C2×D4×C41—21no—
163C2×D4×C41—22no—
164C2×D4×C41—21no—
165C2×D4×C41—22no—
166C2×D4×C41—22no—
167C2×D4×C41—21no—
168C2×D4×C41—21no—
169C2×D4×C41—22no—
170C2×D4×C41—21no—
171C2×D4×C41—22no—
172C2×D4×C41—21no—
173C2×D4×C41—22no—
174C2×D4×C41—22no—
175C2×D4×C41—22no—
176C2×D4×C41—21no—
177C2×D4×C41—21no—
178C2×D4×C41—42no—
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—22no—
190C22×C4×C41—22no—
191C22×C4×C41—21no—
192C22×C4×C41—21no—
193C22×C4×C41—21no—
194C22×C4×C41—22no—
195C22×C4×C41—22no—
196C22×C4×C41—42no—
197C22×C4×C41—42no—
198C22×C4×C41—42no—
199C22×C4×C41C2×D411yescharacteristic
200C22×C4×C41C2×D412yes—
201C22×C4×C41C2×D411yescharacteristic
202C22×C4×C41C2×D411yescharacteristic
203C22×C4×C41C2×D411yescharacteristic
204C22×C4×C41C2×D411yescharacteristic
205C22×C4×C41C2×D412yes—
206C22×C4×C41C2×D411yescharacteristic
207C22×C4×C41C2×D412yes—
208C22×C4×C41C2×D411yescharacteristic
209C22×C4×C41C2×D411yescharacteristic
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41#4112yescomplemented
212C4⋊C4×C41—24no—
213C4⋊C4×C41—22no—
214C4⋊C4×C41—22no—
215C4⋊C4×C41—22no—
216C4⋊C4×C41—22no—
217C4⋊C4×C41—21no—
218C4⋊C4×C41—22no—
219C4⋊C4×C41—21no—
220C4⋊C4×C41—21no—
221C4⋊C4×C41—21no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—22no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—44no—
226C4⋊C4×C41—42no—
227C4⋊C4×C41—42no—
228C4⋊C4×C41—42no—
229C4⋊C4×C41—44no—
230C22⋊C4×C41—22no—
231C22⋊C4×C41—22no—
232C22⋊C4×C41—24no—
233C22⋊C4×C41—22no—
234C22⋊C4×C41—22no—
235C22⋊C4×C41—22no—
236C22⋊C4×C41—22no—
237C22⋊C4×C41—21no—
238C22⋊C4×C41—22no—
239C22⋊C4×C41—21no—
240C22⋊C4×C41—22no—
241C22⋊C4×C41—21no—
242C22⋊C4×C41—22no—
243C22⋊C4×C41—21no—
244C22⋊C4×C41—21no—
245C22⋊C4×C41—22no—
246C22⋊C4×C41—22no—
247C22⋊C4×C41—22no—
248C22⋊C4×C41—21no—
249C22⋊C4×C41—22no—
250C22⋊C4×C41—22no—
251C22⋊C4×C41—21no—
252C22⋊C4×C41—44no—
253C22⋊C4×C41—44no—
254C22⋊C4×C41—42no—
255C22⋊C4×C41#4112yescomplemented
256C42×C41—22no—
257C42×C41—22no—
258C42×C41—21no—
259C42×C41—21no—
260C42×C41—42no—
261C42×C41—41no—
262C42×C41—41no—
263C42×C41—41no—
264C42×C41—41no—
265C23×C41—21no—
266C23×C41—22no—
267C23×C41—21no—
268C23×C41—21no—
269C23×C41—22no—
270C23×C41—22no—
271C23×C41—41no—
272C23×C41—41no—
273C23×C41—41no—
274C23×C41—41no—
275C23×C41—42no—
276C23×C41—42no—
277C23×C41C22×D411yescharacteristic
278C23×C41C22×D411yescharacteristic
279C23×C41C22×D411yescharacteristic
280C23×C41C2×#4111yescharacteristic
281C23×C41C2×#4111yescharacteristic
282C23×C41H(5,𝔽2)11yescharacteristic
283C23×C412−1+411yescharacteristic
284Q8×C41—42no—
285Q8×C41—81no—
286D4×C41—42no—
287D4×C41—42no—
288D4×C41—41no—
289D4×C41—41no—
290D4×C41—41no—
291D4×C41—42no—
292D4×C41—42no—
293D4×C41—41no—
294D4×C41—42no—
295D4×C41—81no—
296D4×C41—82no—
297D4×C41—82no—
298C2×C4×C41—22no—
299C2×C4×C41—22no—
300C2×C4×C41—22no—
301C2×C4×C41—22no—
302C2×C4×C41—22no—
303C2×C4×C41—22no—
304C2×C4×C41—21no—
305C2×C4×C41—22no—
306C2×C4×C41—21no—
307C2×C4×C41—21no—
308C2×C4×C41—22no—
309C2×C4×C41—22no—
310C2×C4×C41—22no—
311C2×C4×C41—22no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—22no—
315C2×C4×C41—22no—
316C2×C4×C41—22no—
317C2×C4×C41—22no—
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—42no—
332C2×C4×C41—41no—
333C2×C4×C41—42no—
334C2×C4×C41—41no—
335C2×C4×C41—42no—
336C2×C4×C41—41no—
337C2×C4×C41—41no—
338C2×C4×C41—42no—
339C2×C4×C41—42no—
340C2×C4×C41—42no—
341C2×C4×C41—42no—
342C2×C4×C41—41no—
343C2×C4×C41—42no—
344C2×C4×C41—42no—
345C2×C4×C41—81no—
346C2×C4×C41—82no—
347C2×C4×C41—82no—
348C2×C4×C41#12011yescharacteristic
349C2×C4×C41#12011yescharacteristic
350C2×C4×C41#12011yescharacteristic
351C2×C4×C41#12011yescharacteristic
352#24141C4111yesmaximal, characteristic, direct product factor, Sylow
353C22×C41—21no—
354C22×C41—21no—
355C22×C41—21no—
356C22×C41—21no—
357C22×C41—21no—
358C22×C41—21no—
359C22×C41—41no—
360C22×C41—41no—
361C22×C41—41no—
362C22×C41—41no—
363C22×C41—42no—
364C22×C41—41no—
365C22×C41—42no—
366C22×C41—41no—
367C22×C41—42no—
368C22×C41—42no—
369C22×C41—41no—
370C22×C41—82no—
371C22×C41—81no—
372C22×C41—82no—
373C22×C41C2×#12011yescharacteristic
374C22×C41#52511yescharacteristic
375C22×C41#53711yescharacteristic
376C22×C41#54611yescharacteristic
377C22×C41#54711yescharacteristic
378C22×C41#54811yescharacteristic
379C22×C41#55011yescharacteristic
380C4×C41—21no—
381C4×C41—21no—
382C4×C41—21no—
383C4×C41—42no—
384C4×C41—42no—
385C4×C41—41no—
386C4×C41—42no—
387C4×C41—41no—
388C4×C41—42no—
389C4×C41—42no—
390C4×C41—41no—
391C4×C41—42no—
392C4×C41—82no—
393C4×C41—82no—
394C4×C41—81no—
395C4×C41#45812yes—
396#3505C2×C4111yescharacteristic
397#2855C2×C4111yescharacteristic, complemented
398#2854C2×C4111yescharacteristic, complemented
399C4×#123C2×C4111yescharacteristic, complemented
400#2044C2×C4112yescomplemented
401#2022C2×C4112yescomplemented
402#1996C2×C4111yescharacteristic, complemented
403#1964C2×C4111yescharacteristic, complemented
404#1890C2×C4112yescomplemented
405#1867C2×C4112yescomplemented
406#1799C2×C4111yescharacteristic, complemented
407C2×C41—21no—
408C2×C41—21no—
409C2×C41—21no—
410C2×C41—21no—
411C2×C41—21no—
412C2×C41—21no—
413C2×C41—81no—
414C2×C41—82no—
415C2×C41#240711yescharacteristic
416C2×C41C2×#45811yescharacteristic
417C2×C41#302511yescharacteristic
418#553—22no—
419#553—21no—
420#552—21no—
421#551—22no—
422#548—21no—
423#546—21no—
424#539—21no—
425#538—21no—
426#534C22×C4112yes—
427#529—21no—
428#525—21no—
429C2×#123C22×C4111yescharacteristic
430C2×#123C22×C4112yes—
431C2×C22⋊Q8C22×C4111yescharacteristic
432C2×#121C22×C4111yescharacteristic
433#518C22×C4112yes—
434C2×C4×D4C22×C4111yescharacteristic
435C22×C42C22×C4111yescharacteristic
436C2×#99C22×C4112yes—
437C2×#99C22×C4112yes—
438C2×#99C22×C4112yes—
439#391—21no—
440#390—21no—
441#389—21no—
442#389—21no—
443#388—22no—
444#388—21no—
445#387—22no—
446#387—21no—
447#386C22×C4112yes—
448#386C22×C4111yescharacteristic
449#385C22×C4112yes—
450#385C22×C4111yescharacteristic
451#381C22×C4112yes—
452#381C22×C4111yescharacteristic
453#380C22×C4111yescharacteristic
454#380C22×C4111yescharacteristic
455C4×C4⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4C22×C4111yescharacteristic
458#342C22×C4112yes—
459#342C22×C4112yes—
460#342C22×C4112yes—
461C41#2414111yescharacteristic, direct product factor, Sylow
462C2×#41—21no—
463C22×Q8D4×C4111yescharacteristic
464C22×D4D4×C4111yescharacteristic
465C22×D4C23×C4111yescharacteristic
466C22×D4C23×C4112yes—
467C23×C4D4×C4111yescharacteristic
468C23×C4C23×C4111yescharacteristic
469C23×C4C23×C4111yescharacteristic
470C23×C4C23×C4111yescharacteristic
471#126—22no—
472#126—22no—
473#126—22no—
474#125—21no—
475#125—22no—
476#124—21no—
477#124—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—22no—
484#123—22no—
485#123—24no—
486#123—42no—
487C22⋊Q8—21no—
488C22⋊Q8—22no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493#121—21no—
494#121—22no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—22no—
500#121—22no—
501#120—22no—
502#120—22no—
503C4×Q8—21no—
504C4×D4—22no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514#117—21no—
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4D4×C4111yescharacteristic
524C2×C4⋊C4D4×C4111yescharacteristic
525C2×C4⋊C4D4×C4112yes—
526C2×C4⋊C4D4×C4111yescharacteristic
527C2×C22⋊C4—22no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4D4×C4111yescharacteristic
533C2×C22⋊C4D4×C4112yes—
534C2×C22⋊C4C23×C4112yes—
535C2×C22⋊C4C23×C4111yescharacteristic
536C2×C22⋊C4C23×C4112yes—
537C2×C22⋊C4C23×C4111yescharacteristic
538C2×C22⋊C4C23×C4112yes—
539C2×C22⋊C4C23×C4111yescharacteristic
540C2×C42—21no—
541C2×C42—21no—
542C2×C42—21no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—21no—
546C2×C42—21no—
547C2×C42D4×C4111yescharacteristic
548#99—24no—
549#99—42no—
550#99—42no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562C24C2×D4×C4112yes—
563C24C2×D4×C4111yescharacteristic
564C24C24×C4111yescharacteristic
565#41—82no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—42no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—42no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C2×D4×C4111yescharacteristic
607C22×C4C2×D4×C4112yes—
608C22×C4C2×D4×C4111yescharacteristic
609C22×C4C2×D4×C4111yescharacteristic
610C22×C4C2×D4×C4111yescharacteristic
611C22×C4C2×D4×C4111yescharacteristic
612C22×C4C2×D4×C4112yes—
613C22×C4C2×D4×C4111yescharacteristic
614C22×C4C2×D4×C4112yes—
615C22×C4C2×D4×C4111yescharacteristic
616C22×C4C2×D4×C4111yescharacteristic
617C22×C4C2×D4×C4111yescharacteristic
618C22×C4#41×C4112yescomplemented
619C4⋊C4—24no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—22no—
631C4⋊C4—21no—
632C4⋊C4—44no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—44no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—24no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—21no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—21no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—21no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—42no—
662C22⋊C4#41×C4112yescomplemented
663C42—22no—
664C42—22no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23C22×D4×C4111yescharacteristic
685C23C22×D4×C4111yescharacteristic
686C23C22×D4×C4111yescharacteristic
687C23C2×#41×C4111yescharacteristic
688C23C2×#41×C4111yescharacteristic
689C23H(5,𝔽2)×C4111yescharacteristic
690C232−1+4×C4111yescharacteristic
691Q8—42no—
692Q8—81no—
693D4—42no—
694D4—42no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—42no—
699D4—42no—
700D4—41no—
701D4—42no—
702D4—81no—
703D4—82no—
704D4—82no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—41no—
726C2×C4—41no—
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—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—81no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4#120×C4111yescharacteristic
756C2×C4#120×C4111yescharacteristic
757C2×C4#120×C4111yescharacteristic
758C2×C4#120×C4111yescharacteristic
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—82no—
777C22—81no—
778C22—82no—
779C22C2×#120×C4111yescharacteristic
780C22C41×#52511yescharacteristic
781C22C41×#53711yescharacteristic
782C22C41×#54611yescharacteristic
783C22C41×#54711yescharacteristic
784C22C41×#54811yescharacteristic
785C22C41×#55011yescharacteristic
786C4—21no—
787C4—21no—
788C4—21no—
789C4—42no—
790C4—42no—
791C4—41no—
792C4—42no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—41no—
797C4—42no—
798C4—82no—
799C4—82no—
800C4—81no—
801C4C41×#45812yes—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—81no—
809C2—82no—
810C2C41×#240711yescharacteristic
811C2C2×C41×#45811yescharacteristic
812C2C41×#302511yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
prime radicalC41×#3505C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2855C2semidirect
3. C41×#2854C2semidirect
4. C4×#123×C41C2semidirect
5. C41×#2044C2semidirect
6. C41×#2022C2semidirect
7. C41×#1996C2semidirect
8. C41×#1964C2semidirect
9. C41×#1890C2semidirect
10. C41×#1867C2semidirect
11. C41×#1799C2semidirect
211. C22×C4×C41#41semidirect
255. C22⋊C4×C41#41semidirect
352. #24141C41direct (N × H)
397. #2855C2×C41semidirect
398. #2854C2×C41semidirect
399. C4×#123C2×C41semidirect
400. #2044C2×C41semidirect
401. #2022C2×C41semidirect
402. #1996C2×C41semidirect
403. #1964C2×C41semidirect
404. #1890C2×C41semidirect
405. #1867C2×C41semidirect
406. #1799C2×C41semidirect
461. C41#24141direct (N × H)
618. C22×C4#41×C41semidirect
662. C22⋊C4#41×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35052
C41×#28552
C41×#28542
C4×#123×C412
C41×#20442
C41×#20222
C41×#19962
C41×#19642
C41×#18902
C41×#18672
C41×#17992
#2414141