Finite Group Databasebeta

← C41×#25585 #23801786

Subgroups — C41×#25585 #23801786

Order 10496.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3505C211yesmaximal, characteristic, complemented
2C41×#2435C211yesmaximal, characteristic, complemented
3C41×#2433C211yesmaximal, characteristic, complemented
4C41×#2408C211yesmaximal, characteristic, complemented
5C41×#2021C214yesmaximal, complemented
6C41×#1996C211yesmaximal, characteristic, complemented
7C41×#1964C211yesmaximal, characteristic, complemented
8C41×#1889C214yesmaximal, complemented
9C4×#99×C41C211yesmaximal, characteristic, complemented
10C23×D4×C41C2211yescharacteristic
11C41×#553—21no—
12C41×#553—22no—
13C41×#552—21no—
14C41×#551—22no—
15C41×#548—21no—
16C41×#546—21no—
17C41×#539—21no—
18C41×#538—21no—
19C41×#534C2212yes—
20C2×#127×C41—21no—
21C41×#529—21no—
22C2×#124×C41—21no—
23C41×#525—21no—
24C2×C22⋊Q8×C41C2211yescharacteristic
25C2×#121×C41—21no—
26C2×#121×C41C2211yescharacteristic
27C2×#120×C41C2214yes—
28C2×#120×C41C2212yes—
29C41×#518C2212yes—
30C2×C4×D4×C41C2211yescharacteristic
31C2×#99×C41C2212yes—
32C2×#99×C41C2214yes—
33C41×#394—21no—
34C41×#394—22no—
35C41×#392—21no—
36C41×#392—22no—
37C41×#390—21no—
38C41×#390—21no—
39C41×#390—21no—
40C41×#380C2211yescharacteristic
41C41×#379C2214yes—
42C41×#379C2212yes—
43C4×C22⋊C4×C41C2211yescharacteristic
44C4×C22⋊C4×C41C2211yescharacteristic
45C41×#342C2214yes—
46C41×#342C2212yes—
47C25×C41C2312yes—
48C2×#41×C41—21no—
49C22×Q8×C41D411yescharacteristic, complemented
50C22×D4×C41—22no—
51C22×D4×C41—24no—
52C22×D4×C41—21no—
53C22×D4×C41—21no—
54C22×D4×C41—21no—
55C22×D4×C41—21no—
56C22×D4×C41—21no—
57C22×D4×C41—21no—
58C22×D4×C41—44no—
59C22×D4×C41D411yescharacteristic, complemented
60C22×D4×C41C2311yescharacteristic
61C22×D4×C41C2312yes—
62C23×C4×C41D411yescharacteristic, complemented
63C23×C4×C41C2311yescharacteristic
64#127×C41—44no—
65#126×C41—22no—
66#126×C41—22no—
67#126×C41—22no—
68#125×C41—21no—
69#125×C41—22no—
70#124×C41—21no—
71#124×C41—22no—
72#124×C41—44no—
73#123×C41—22no—
74#123×C41—22no—
75#123×C41—22no—
76#123×C41—22no—
77#123×C41—22no—
78C22⋊Q8×C41—21no—
79C22⋊Q8×C41—22no—
80C22⋊Q8×C41—21no—
81C22⋊Q8×C41—21no—
82C22⋊Q8×C41—21no—
83C22⋊Q8×C41—21no—
84#121×C41—21no—
85#121×C41—22no—
86#121×C41—21no—
87#121×C41—21no—
88#121×C41—21no—
89#121×C41—21no—
90#121×C41—22no—
91#121×C41—22no—
92#121×C41—44no—
93#120×C41—22no—
94#120×C41—22no—
95#120×C41—28no—
96#120×C41—44no—
97#120×C41—44no—
98C4×Q8×C41—21no—
99C4×D4×C41—22no—
100C4×D4×C41—21no—
101C4×D4×C41—21no—
102C4×D4×C41—21no—
103C4×D4×C41—21no—
104C4×D4×C41—21no—
105C4×D4×C41—22no—
106C4×D4×C41—22no—
107C4×D4×C41—22no—
108C4×D4×C41—22no—
109#117×C41—21no—
110#117×C41—22no—
111#117×C41—22no—
112C2×C4⋊C4×C41—21no—
113C2×C4⋊C4×C41D411yescharacteristic, complemented
114C2×C4⋊C4×C41D411yescharacteristic, complemented
115C2×C4⋊C4×C41D411yescharacteristic, complemented
116C2×C4⋊C4×C41D412yescomplemented
117C2×C22⋊C4×C41—22no—
118C2×C22⋊C4×C41—24no—
119C2×C22⋊C4×C41—22no—
120C2×C22⋊C4×C41—22no—
121C2×C22⋊C4×C41—24no—
122C2×C22⋊C4×C41—22no—
123C2×C22⋊C4×C41—24no—
124C2×C22⋊C4×C41D411yescharacteristic, complemented
125C2×C22⋊C4×C41D412yescomplemented
126C2×C22⋊C4×C41C2312yes—
127C2×C22⋊C4×C41C2312yes—
128C2×C22⋊C4×C41C2311yescharacteristic
129C2×C22⋊C4×C41C2312yes—
130C2×C22⋊C4×C41C2312yes—
131C2×C42×C41—21no—
132C2×C42×C41—21no—
133C2×C42×C41D411yescharacteristic, complemented
134#99×C41—24no—
135#99×C41—44no—
136#95×C41—21no—
137#95×C41—21no—
138#95×C41—21no—
139C24×C41—22no—
140C24×C41—22no—
141C24×C41—22no—
142C24×C41—24no—
143C24×C41—24no—
144C24×C41—44no—
145C24×C41—82no—
146C24×C41C2×D412yes—
147C24×C41C2×D411yescharacteristic
148C24×C41C2411yescharacteristic
149#41×C41—82no—
150C2×Q8×C41—21no—
151C2×Q8×C41—21no—
152C2×Q8×C41—42no—
153C2×D4×C41—24no—
154C2×D4×C41—24no—
155C2×D4×C41—24no—
156C2×D4×C41—21no—
157C2×D4×C41—22no—
158C2×D4×C41—21no—
159C2×D4×C41—22no—
160C2×D4×C41—22no—
161C2×D4×C41—24no—
162C2×D4×C41—24no—
163C2×D4×C41—22no—
164C2×D4×C41—22no—
165C2×D4×C41—22no—
166C2×D4×C41—21no—
167C2×D4×C41—21no—
168C2×D4×C41—42no—
169C2×D4×C41—42no—
170C2×D4×C41—42no—
171C2×D4×C41—42no—
172C2×D4×C41—48no—
173C2×D4×C41—44no—
174C2×D4×C41—44no—
175C2×D4×C41—44no—
176C2×D4×C41—44no—
177C2×D4×C41—44no—
178C2×D4×C41—48no—
179C2×D4×C41—41no—
180C2×D4×C41—41no—
181C2×D4×C41—41no—
182C2×D4×C41—41no—
183C2×D4×C41—84no—
184C2×D4×C41—82no—
185C22×C4×C41—22no—
186C22×C4×C41—22no—
187C22×C4×C41—22no—
188C22×C4×C41—21no—
189C22×C4×C41—21no—
190C22×C4×C41—22no—
191C22×C4×C41—22no—
192C22×C4×C41—42no—
193C22×C4×C41—42no—
194C22×C4×C41C2×D411yescharacteristic
195C22×C4×C41C2×D412yes—
196C22×C4×C41C2×D411yescharacteristic
197C22×C4×C41C2×D411yescharacteristic
198C22×C4×C41C2×D411yescharacteristic
199C22×C4×C41C2×D411yescharacteristic
200C22×C4×C41C2×D412yes—
201C22×C4×C41C2×D411yescharacteristic
202C22×C4×C41C2×D412yes—
203C22×C4×C41C2×D411yescharacteristic
204C22×C4×C41C2×D411yescharacteristic
205C22×C4×C41C2×D411yescharacteristic
206C4⋊C4×C41—22no—
207C4⋊C4×C41—22no—
208C4⋊C4×C41—22no—
209C4⋊C4×C41—22no—
210C4⋊C4×C41—21no—
211C4⋊C4×C41—22no—
212C4⋊C4×C41—21no—
213C4⋊C4×C41—21no—
214C4⋊C4×C41—21no—
215C4⋊C4×C41—21no—
216C4⋊C4×C41—22no—
217C4⋊C4×C41—21no—
218C4⋊C4×C41—42no—
219C22⋊C4×C41—22no—
220C22⋊C4×C41—22no—
221C22⋊C4×C41—22no—
222C22⋊C4×C41—22no—
223C22⋊C4×C41—22no—
224C22⋊C4×C41—22no—
225C22⋊C4×C41—21no—
226C22⋊C4×C41—22no—
227C22⋊C4×C41—21no—
228C22⋊C4×C41—22no—
229C22⋊C4×C41—22no—
230C22⋊C4×C41—22no—
231C22⋊C4×C41—21no—
232C22⋊C4×C41—21no—
233C22⋊C4×C41—22no—
234C22⋊C4×C41—22no—
235C22⋊C4×C41—22no—
236C22⋊C4×C41—24no—
237C22⋊C4×C41—48no—
238C22⋊C4×C41—44no—
239C22⋊C4×C41—44no—
240C22⋊C4×C41—48no—
241C22⋊C4×C41—84no—
242C22⋊C4×C41—82no—
243C22⋊C4×C41#4114yescomplemented
244C42×C41—22no—
245C42×C41—22no—
246C42×C41—21no—
247C42×C41—21no—
248C42×C41—42no—
249C42×C41—42no—
250C23×C41—24no—
251C23×C41—24no—
252C23×C41—24no—
253C23×C41—21no—
254C23×C41—22no—
255C23×C41—21no—
256C23×C41—21no—
257C23×C41—24no—
258C23×C41—41no—
259C23×C41—41no—
260C23×C41—41no—
261C23×C41—41no—
262C23×C41—44no—
263C23×C41—42no—
264C23×C41—42no—
265C23×C41—42no—
266C23×C41—42no—
267C23×C41—42no—
268C23×C41—44no—
269C23×C41—42no—
270C23×C41—42no—
271C23×C41—42no—
272C23×C41—42no—
273C23×C41—42no—
274C23×C41—44no—
275C23×C41—44no—
276C23×C41—88no—
277C23×C41—88no—
278C23×C41C22×D411yescharacteristic
279C23×C41C22×D411yescharacteristic
280C23×C41C22×D411yescharacteristic
281C23×C41C2×#4112yes—
282C23×C41H(5,𝔽2)12yes—
283Q8×C41—42no—
284Q8×C41—81no—
285D4×C41—44no—
286D4×C41—44no—
287D4×C41—44no—
288D4×C41—42no—
289D4×C41—42no—
290D4×C41—42no—
291D4×C41—42no—
292D4×C41—44no—
293D4×C41—44no—
294D4×C41—42no—
295D4×C41—81no—
296D4×C41—82no—
297D4×C41—82no—
298D4×C41—816no—
299D4×C41—88no—
300C2×C4×C41—22no—
301C2×C4×C41—22no—
302C2×C4×C41—22no—
303C2×C4×C41—21no—
304C2×C4×C41—22no—
305C2×C4×C41—21no—
306C2×C4×C41—21no—
307C2×C4×C41—22no—
308C2×C4×C41—22no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—24no—
312C2×C4×C41—24no—
313C2×C4×C41—41no—
314C2×C4×C41—41no—
315C2×C4×C41—41no—
316C2×C4×C41—42no—
317C2×C4×C41—42no—
318C2×C4×C41—42no—
319C2×C4×C41—41no—
320C2×C4×C41—42no—
321C2×C4×C41—41no—
322C2×C4×C41—42no—
323C2×C4×C41—42no—
324C2×C4×C41—42no—
325C2×C4×C41—42no—
326C2×C4×C41—42no—
327C2×C4×C41—42no—
328C2×C4×C41—42no—
329C2×C4×C41—81no—
330C2×C4×C41—82no—
331C2×C4×C41—82no—
332C2×C4×C41#12011yescharacteristic
333C2×C4×C41#12011yescharacteristic
334C2×C4×C41#12011yescharacteristic
335C2×C4×C41#12011yescharacteristic
336#25585C4111yesmaximal, characteristic, direct product factor, Sylow
337C22×C41—21no—
338C22×C41—21no—
339C22×C41—21no—
340C22×C41—21no—
341C22×C41—21no—
342C22×C41—21no—
343C22×C41—42no—
344C22×C41—42no—
345C22×C41—42no—
346C22×C41—48no—
347C22×C41—44no—
348C22×C41—48no—
349C22×C41—44no—
350C22×C41—41no—
351C22×C41—42no—
352C22×C41—41no—
353C22×C41—42no—
354C22×C41—44no—
355C22×C41—42no—
356C22×C41—41no—
357C22×C41—84no—
358C22×C41—81no—
359C22×C41—84no—
360C22×C41—82no—
361C22×C41—84no—
362C22×C41—82no—
363C22×C41—82no—
364C22×C41—82no—
365C22×C41C2×#12011yescharacteristic
366C22×C41#53211yescharacteristic
367C22×C41#53511yescharacteristic
368C22×C41#54612yes—
369C22×C41#55012yes—
370C4×C41—21no—
371C4×C41—21no—
372C4×C41—21no—
373C4×C41—44no—
374C4×C41—41no—
375C4×C41—42no—
376C4×C41—41no—
377C4×C41—42no—
378C4×C41—41no—
379C4×C41—42no—
380C4×C41—82no—
381C4×C41—82no—
382C4×C41B(4,𝔽2)12yes—
383#3505C2×C4111yescharacteristic, complemented
384#2435C2×C4111yescharacteristic, complemented
385#2433C2×C4111yescharacteristic, complemented
386#2408C2×C4111yescharacteristic, complemented
387#2021C2×C4114yescomplemented
388#1996C2×C4111yescharacteristic, complemented
389#1964C2×C4111yescharacteristic, complemented
390#1889C2×C4114yescomplemented
391C4×#99C2×C4111yescharacteristic, complemented
392C2×C41—22no—
393C2×C41—21no—
394C2×C41—22no—
395C2×C41—21no—
396C2×C41—84no—
397C2×C41—81no—
398C2×C41—82no—
399C2×C41#243111yescharacteristic
400C2×C41C2×B(4,𝔽2)11yescharacteristic
401C2×C41#302711yescharacteristic
402C23×D4C22×C4111yescharacteristic
403#553—21no—
404#553—22no—
405#552—21no—
406#551—22no—
407#548—21no—
408#546—21no—
409#539—21no—
410#538—21no—
411#534C22×C4112yes—
412C2×#127—21no—
413#529—21no—
414C2×#124—21no—
415#525—21no—
416C2×C22⋊Q8C22×C4111yescharacteristic
417C2×#121—21no—
418C2×#121C22×C4111yescharacteristic
419C2×#120C22×C4114yes—
420C2×#120C22×C4112yes—
421#518C22×C4112yes—
422C2×C4×D4C22×C4111yescharacteristic
423C2×#99C22×C4112yes—
424C2×#99C22×C4114yes—
425#394—21no—
426#394—22no—
427#392—21no—
428#392—22no—
429#390—21no—
430#390—21no—
431#390—21no—
432#380C22×C4111yescharacteristic
433#379C22×C4112yes—
434#379C22×C4114yes—
435C4×C22⋊C4C22×C4111yescharacteristic
436C4×C22⋊C4C22×C4111yescharacteristic
437#342C22×C4112yes—
438#342C22×C4114yes—
439C41#2558511yescharacteristic, direct product factor, Sylow
440C25C23×C4112yes—
441C2×#41—21no—
442C22×Q8D4×C4111yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C4111yescharacteristic, complemented
453C22×D4C23×C4111yescharacteristic
454C22×D4C23×C4112yes—
455C23×C4D4×C4111yescharacteristic, complemented
456C23×C4C23×C4111yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C4111yescharacteristic, complemented
507C2×C4⋊C4D4×C4111yescharacteristic, complemented
508C2×C4⋊C4D4×C4111yescharacteristic, complemented
509C2×C4⋊C4D4×C4112yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C4111yescharacteristic, complemented
518C2×C22⋊C4D4×C4112yescomplemented
519C2×C22⋊C4C23×C4112yes—
520C2×C22⋊C4C23×C4112yes—
521C2×C22⋊C4C23×C4111yescharacteristic
522C2×C22⋊C4C23×C4112yes—
523C2×C22⋊C4C23×C4112yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C4111yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C4112yes—
540C24C2×D4×C4111yescharacteristic
541C24C24×C4111yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C4111yescharacteristic
588C22×C4C2×D4×C4112yes—
589C22×C4C2×D4×C4111yescharacteristic
590C22×C4C2×D4×C4111yescharacteristic
591C22×C4C2×D4×C4111yescharacteristic
592C22×C4C2×D4×C4111yescharacteristic
593C22×C4C2×D4×C4112yes—
594C22×C4C2×D4×C4111yescharacteristic
595C22×C4C2×D4×C4112yes—
596C22×C4C2×D4×C4111yescharacteristic
597C22×C4C2×D4×C4111yescharacteristic
598C22×C4C2×D4×C4111yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C4114yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C4111yescharacteristic
672C23C22×D4×C4111yescharacteristic
673C23C22×D4×C4111yescharacteristic
674C23C2×#41×C4112yes—
675C23H(5,𝔽2)×C4112yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C4111yescharacteristic
726C2×C4#120×C4111yescharacteristic
727C2×C4#120×C4111yescharacteristic
728C2×C4#120×C4111yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—41no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C4111yescharacteristic
758C22C41×#53211yescharacteristic
759C22C41×#53511yescharacteristic
760C22C41×#54612yes—
761C22C41×#55012yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4C41×B(4,𝔽2)12yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C41×#243111yescharacteristic
783C2C2×C41×B(4,𝔽2)11yescharacteristic
784C2C41×#302711yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
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
1. C41×#3505C2semidirect
2. C41×#2435C2semidirect
3. C41×#2433C2semidirect
4. C41×#2408C2semidirect
5. C41×#2021C2semidirect
6. C41×#1996C2semidirect
7. C41×#1964C2semidirect
8. C41×#1889C2semidirect
9. C4×#99×C41C2semidirect
49. C22×Q8×C41D4semidirect
59. C22×D4×C41D4semidirect
62. C23×C4×C41D4semidirect
113. C2×C4⋊C4×C41D4semidirect
114. C2×C4⋊C4×C41D4semidirect
115. C2×C4⋊C4×C41D4semidirect
116. C2×C4⋊C4×C41D4semidirect
124. C2×C22⋊C4×C41D4semidirect
125. C2×C22⋊C4×C41D4semidirect
133. C2×C42×C41D4semidirect
243. C22⋊C4×C41#41semidirect
336. #25585C41direct (N × H)
383. #3505C2×C41semidirect
384. #2435C2×C41semidirect
385. #2433C2×C41semidirect
386. #2408C2×C41semidirect
387. #2021C2×C41semidirect
388. #1996C2×C41semidirect
389. #1964C2×C41semidirect
390. #1889C2×C41semidirect
391. C4×#99C2×C41semidirect
439. C41#25585direct (N × H)
442. C22×Q8D4×C41semidirect
452. C22×D4D4×C41semidirect
455. C23×C4D4×C41semidirect
506. C2×C4⋊C4D4×C41semidirect
507. C2×C4⋊C4D4×C41semidirect
508. C2×C4⋊C4D4×C41semidirect
509. C2×C4⋊C4D4×C41semidirect
517. C2×C22⋊C4D4×C41semidirect
518. C2×C22⋊C4D4×C41semidirect
526. C2×C42D4×C41semidirect
636. 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×#24352
C41×#24332
C41×#24082
C41×#20212
C41×#19962
C41×#19642
C41×#18892
C4×#99×C412
#2558541