Finite Group Databasebeta

← C41×#25587 #23801788

Subgroups — C41×#25587 #23801788

Order 10496.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3505C211yesmaximal, characteristic, complemented
2C41×#2561C211yesmaximal, characteristic, complemented
3C41×#2539C211yesmaximal, characteristic, complemented
4C41×#2534C211yesmaximal, characteristic, complemented
5C41×#2022C212yesmaximal, complemented
6C41×#2021C212yesmaximal, complemented
7C41×#1996C211yesmaximal, characteristic, complemented
8C41×#1964C211yesmaximal, characteristic, complemented
9C41×#1890C212yesmaximal, complemented
10C41×#1889C212yesmaximal, complemented
11C4×#99×C41C211yesmaximal, 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×C41C2212yes—
24C2×#123×C41C2211yescharacteristic
25C2×C22⋊Q8×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×#120×C41C2212yes—
28C2×#120×C41C2211yescharacteristic
29C41×#518C2212yes—
30C2×C4×D4×C41C2211yescharacteristic
31C22×C22⋊C4×C41C2211yescharacteristic
32C2×#99×C41C2212yes—
33C2×#99×C41C2212yes—
34C2×#99×C41C2212yes—
35C41×#399—21no—
36C41×#397—21no—
37C41×#396—21no—
38C41×#394—21no—
39C41×#393—21no—
40C41×#392—21no—
41C41×#390—22no—
42C41×#388—22no—
43C41×#388—21no—
44C41×#386—21no—
45C41×#381C2212yes—
46C41×#381C2211yescharacteristic
47C41×#380C2211yescharacteristic
48C41×#379C2212yes—
49C41×#379C2211yescharacteristic
50C4×C22⋊C4×C41C2211yescharacteristic
51C4×C22⋊C4×C41C2211yescharacteristic
52C41×#342C2212yes—
53C41×#342C2212yes—
54C41×#342C2212yes—
55C25×C41C2311yescharacteristic
56C2×#41×C41—21no—
57C22×Q8×C41D411yescharacteristic, complemented
58C22×D4×C41—21no—
59C22×D4×C41—22no—
60C22×D4×C41D411yescharacteristic, complemented
61C22×D4×C41C2311yescharacteristic
62C22×D4×C41C2312yes—
63C23×C4×C41D411yescharacteristic, complemented
64C23×C4×C41C2311yescharacteristic
65C23×C4×C41C2311yescharacteristic
66#126×C41—22no—
67#126×C41—22no—
68#126×C41—22no—
69#125×C41—21no—
70#125×C41—22no—
71#124×C41—21no—
72#124×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—
80#123×C41—42no—
81C22⋊Q8×C41—21no—
82C22⋊Q8×C41—22no—
83C22⋊Q8×C41—21no—
84C22⋊Q8×C41—21no—
85C22⋊Q8×C41—21no—
86C22⋊Q8×C41—21no—
87#121×C41—21no—
88#121×C41—22no—
89#121×C41—21no—
90#121×C41—21no—
91#121×C41—21no—
92#121×C41—21no—
93#121×C41—22no—
94#121×C41—22no—
95#120×C41—22no—
96#120×C41—22no—
97#120×C41—24no—
98#120×C41—42no—
99#120×C41—42no—
100C4×Q8×C41—21no—
101C4×D4×C41—22no—
102C4×D4×C41—21no—
103C4×D4×C41—21no—
104C4×D4×C41—21no—
105C4×D4×C41—21no—
106C4×D4×C41—21no—
107C4×D4×C41—22no—
108C4×D4×C41—22no—
109C4×D4×C41—22no—
110C4×D4×C41—22no—
111#117×C41—21no—
112#117×C41—22no—
113#117×C41—22no—
114C2×C4⋊C4×C41—21no—
115C2×C4⋊C4×C41—22no—
116C2×C4⋊C4×C41—21no—
117C2×C4⋊C4×C41D411yescharacteristic, complemented
118C2×C4⋊C4×C41D411yescharacteristic, complemented
119C2×C4⋊C4×C41D412yescomplemented
120C2×C4⋊C4×C41D411yescharacteristic, complemented
121C2×C22⋊C4×C41—22no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—22no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41—21no—
128C2×C22⋊C4×C41—21no—
129C2×C22⋊C4×C41—21no—
130C2×C22⋊C4×C41—21no—
131C2×C22⋊C4×C41—22no—
132C2×C22⋊C4×C41—21no—
133C2×C22⋊C4×C41—22no—
134C2×C22⋊C4×C41—21no—
135C2×C22⋊C4×C41—22no—
136C2×C22⋊C4×C41D411yescharacteristic, complemented
137C2×C22⋊C4×C41D412yescomplemented
138C2×C22⋊C4×C41C2311yescharacteristic
139C2×C22⋊C4×C41C2311yescharacteristic
140C2×C22⋊C4×C41C2312yes—
141C2×C22⋊C4×C41C2311yescharacteristic
142C2×C22⋊C4×C41C2312yes—
143C2×C22⋊C4×C41C2312yes—
144C2×C42×C41—21no—
145C2×C42×C41—21no—
146C2×C42×C41D411yescharacteristic, complemented
147#99×C41—24no—
148#99×C41—42no—
149#99×C41—42no—
150#95×C41—21no—
151#95×C41—21no—
152#95×C41—21no—
153#95×C41—21no—
154#95×C41—22no—
155#95×C41—21no—
156#95×C41—22no—
157C24×C41—21no—
158C24×C41—21no—
159C24×C41—21no—
160C24×C41—22no—
161C24×C41—22no—
162C24×C41—42no—
163C24×C41—81no—
164C24×C41C2×D412yes—
165C24×C41C2×D411yescharacteristic
166C24×C41C2411yescharacteristic
167#41×C41—82no—
168C2×Q8×C41—21no—
169C2×Q8×C41—21no—
170C2×Q8×C41—81no—
171C2×D4×C41—21no—
172C2×D4×C41—22no—
173C2×D4×C41—21no—
174C2×D4×C41—22no—
175C2×D4×C41—22no—
176C2×D4×C41—22no—
177C2×D4×C41—22no—
178C2×D4×C41—22no—
179C2×D4×C41—22no—
180C2×D4×C41—22no—
181C2×D4×C41—22no—
182C2×D4×C41—22no—
183C2×D4×C41—21no—
184C2×D4×C41—21no—
185C2×D4×C41—44no—
186C2×D4×C41—42no—
187C2×D4×C41—44no—
188C2×D4×C41—42no—
189C2×D4×C41—81no—
190C2×D4×C41—82no—
191C2×D4×C41—81no—
192C22×C4×C41—22no—
193C22×C4×C41—22no—
194C22×C4×C41—22no—
195C22×C4×C41—21no—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—22no—
199C22×C4×C41—21no—
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—22no—
204C22×C4×C41—22no—
205C22×C4×C41—81no—
206C22×C4×C41—81no—
207C22×C4×C41C2×D411yescharacteristic
208C22×C4×C41C2×D412yes—
209C22×C4×C41C2×D411yescharacteristic
210C22×C4×C41C2×D412yes—
211C22×C4×C41C2×D411yescharacteristic
212C22×C4×C41C2×D412yes—
213C22×C4×C41C2×D411yescharacteristic
214C22×C4×C41C2×D411yescharacteristic
215C22×C4×C41C2×D411yescharacteristic
216C22×C4×C41C2×D411yescharacteristic
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2×D411yescharacteristic
219C4⋊C4×C41—22no—
220C4⋊C4×C41—22no—
221C4⋊C4×C41—22no—
222C4⋊C4×C41—22no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—22no—
225C4⋊C4×C41—21no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—22no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—44no—
232C4⋊C4×C41—42no—
233C4⋊C4×C41—81no—
234C22⋊C4×C41—22no—
235C22⋊C4×C41—22no—
236C22⋊C4×C41—22no—
237C22⋊C4×C41—22no—
238C22⋊C4×C41—22no—
239C22⋊C4×C41—22no—
240C22⋊C4×C41—21no—
241C22⋊C4×C41—22no—
242C22⋊C4×C41—21no—
243C22⋊C4×C41—22no—
244C22⋊C4×C41—22no—
245C22⋊C4×C41—22no—
246C22⋊C4×C41—21no—
247C22⋊C4×C41—21no—
248C22⋊C4×C41—22no—
249C22⋊C4×C41—22no—
250C22⋊C4×C41—22no—
251C22⋊C4×C41—22no—
252C22⋊C4×C41—22no—
253C22⋊C4×C41—44no—
254C22⋊C4×C41—44no—
255C22⋊C4×C41—42no—
256C22⋊C4×C41—44no—
257C22⋊C4×C41—42no—
258C22⋊C4×C41—42no—
259C22⋊C4×C41—41no—
260C22⋊C4×C41—41no—
261C22⋊C4×C41—41no—
262C22⋊C4×C41—41no—
263C22⋊C4×C41—81no—
264C22⋊C4×C41—82no—
265C22⋊C4×C41#4114yescomplemented
266C42×C41—22no—
267C42×C41—22no—
268C42×C41—21no—
269C42×C41—21no—
270C42×C41—81no—
271C42×C41—81no—
272C23×C41—22no—
273C23×C41—22no—
274C23×C41—22no—
275C23×C41—22no—
276C23×C41—21no—
277C23×C41—21no—
278C23×C41—21no—
279C23×C41—22no—
280C23×C41—22no—
281C23×C41—41no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—41no—
285C23×C41—42no—
286C23×C41—41no—
287C23×C41—41no—
288C23×C41—42no—
289C23×C41—41no—
290C23×C41—41no—
291C23×C41—41no—
292C23×C41—42no—
293C23×C41—42no—
294C23×C41—41no—
295C23×C41—41no—
296C23×C41—41no—
297C23×C41—42no—
298C23×C41—42no—
299C23×C41—84no—
300C23×C41—84no—
301C23×C41C22×D411yescharacteristic
302C23×C41C22×D411yescharacteristic
303C23×C41C22×D411yescharacteristic
304C23×C41C2×#4112yes—
305C23×C41H(5,𝔽2)12yes—
306Q8×C41—42no—
307Q8×C41—81no—
308D4×C41—42no—
309D4×C41—42no—
310D4×C41—42no—
311D4×C41—42no—
312D4×C41—42no—
313D4×C41—42no—
314D4×C41—42no—
315D4×C41—81no—
316D4×C41—82no—
317D4×C41—82no—
318D4×C41—88no—
319D4×C41—84no—
320C2×C4×C41—21no—
321C2×C4×C41—22no—
322C2×C4×C41—21no—
323C2×C4×C41—21no—
324C2×C4×C41—22no—
325C2×C4×C41—22no—
326C2×C4×C41—21no—
327C2×C4×C41—21no—
328C2×C4×C41—24no—
329C2×C4×C41—22no—
330C2×C4×C41—22no—
331C2×C4×C41—41no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41—41no—
335C2×C4×C41—41no—
336C2×C4×C41—41no—
337C2×C4×C41—42no—
338C2×C4×C41—42no—
339C2×C4×C41—42no—
340C2×C4×C41—41no—
341C2×C4×C41—42no—
342C2×C4×C41—41no—
343C2×C4×C41—42no—
344C2×C4×C41—42no—
345C2×C4×C41—42no—
346C2×C4×C41—41no—
347C2×C4×C41—41no—
348C2×C4×C41—41no—
349C2×C4×C41—41no—
350C2×C4×C41—41no—
351C2×C4×C41—41no—
352C2×C4×C41—41no—
353C2×C4×C41—41no—
354C2×C4×C41—41no—
355C2×C4×C41—42no—
356C2×C4×C41—42no—
357C2×C4×C41—42no—
358C2×C4×C41—81no—
359C2×C4×C41—82no—
360C2×C4×C41—82no—
361C2×C4×C41#12011yescharacteristic
362C2×C4×C41#12011yescharacteristic
363C2×C4×C41#12011yescharacteristic
364C2×C4×C41#12011yescharacteristic
365#25587C4111yesmaximal, characteristic, direct product factor, Sylow
366C22×C41—21no—
367C22×C41—21no—
368C22×C41—21no—
369C22×C41—21no—
370C22×C41—21no—
371C22×C41—21no—
372C22×C41—42no—
373C22×C41—42no—
374C22×C41—42no—
375C22×C41—44no—
376C22×C41—42no—
377C22×C41—44no—
378C22×C41—42no—
379C22×C41—41no—
380C22×C41—42no—
381C22×C41—42no—
382C22×C41—41no—
383C22×C41—42no—
384C22×C41—41no—
385C22×C41—42no—
386C22×C41—82no—
387C22×C41—82no—
388C22×C41—81no—
389C22×C41—82no—
390C22×C41—81no—
391C22×C41—82no—
392C22×C41—81no—
393C22×C41—81no—
394C22×C41—81no—
395C22×C41C2×#12011yescharacteristic
396C22×C41#53211yescharacteristic
397C22×C41#53511yescharacteristic
398C22×C41#54612yes—
399C22×C41#55012yes—
400C4×C41—21no—
401C4×C41—21no—
402C4×C41—21no—
403C4×C41—21no—
404C4×C41—44no—
405C4×C41—41no—
406C4×C41—42no—
407C4×C41—41no—
408C4×C41—42no—
409C4×C41—41no—
410C4×C41—42no—
411C4×C41—81no—
412C4×C41—82no—
413C4×C41—81no—
414C4×C41—81no—
415#3505C2×C4111yescharacteristic, complemented
416#2561C2×C4111yescharacteristic, complemented
417#2539C2×C4111yescharacteristic, complemented
418#2534C2×C4111yescharacteristic, complemented
419#2022C2×C4112yescomplemented
420#2021C2×C4112yescomplemented
421#1996C2×C4111yescharacteristic, complemented
422#1964C2×C4111yescharacteristic, complemented
423#1890C2×C4112yescomplemented
424#1889C2×C4112yescomplemented
425C4×#99C2×C4111yescharacteristic, complemented
426C2×C41—22no—
427C2×C41—21no—
428C2×C41—22no—
429C2×C41—21no—
430C2×C41—82no—
431C2×C41—81no—
432C2×C41—82no—
433C2×C41#243111yescharacteristic
434C2×C41#302511yescharacteristic
435C2×C41#302611yescharacteristic
436#553—22no—
437#553—21no—
438#552—21no—
439#551—22no—
440#548—21no—
441#546—21no—
442#539—21no—
443#538—21no—
444#534C22×C4112yes—
445#529—21no—
446#525—21no—
447C2×#123C22×C4112yes—
448C2×#123C22×C4111yescharacteristic
449C2×C22⋊Q8C22×C4111yescharacteristic
450C2×#121C22×C4111yescharacteristic
451C2×#120C22×C4112yes—
452C2×#120C22×C4111yescharacteristic
453#518C22×C4112yes—
454C2×C4×D4C22×C4111yescharacteristic
455C22×C22⋊C4C22×C4111yescharacteristic
456C2×#99C22×C4112yes—
457C2×#99C22×C4112yes—
458C2×#99C22×C4112yes—
459#399—21no—
460#397—21no—
461#396—21no—
462#394—21no—
463#393—21no—
464#392—21no—
465#390—22no—
466#388—22no—
467#388—21no—
468#386—21no—
469#381C22×C4112yes—
470#381C22×C4111yescharacteristic
471#380C22×C4111yescharacteristic
472#379C22×C4112yes—
473#379C22×C4111yescharacteristic
474C4×C22⋊C4C22×C4111yescharacteristic
475C4×C22⋊C4C22×C4111yescharacteristic
476#342C22×C4112yes—
477#342C22×C4112yes—
478#342C22×C4112yes—
479C41#2558711yescharacteristic, direct product factor, Sylow
480C25C23×C4111yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C4111yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C4111yescharacteristic, complemented
486C22×D4C23×C4111yescharacteristic
487C22×D4C23×C4112yes—
488C23×C4D4×C4111yescharacteristic, complemented
489C23×C4C23×C4111yescharacteristic
490C23×C4C23×C4111yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C4111yescharacteristic, complemented
543C2×C4⋊C4D4×C4111yescharacteristic, complemented
544C2×C4⋊C4D4×C4112yescomplemented
545C2×C4⋊C4D4×C4111yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C4111yescharacteristic, complemented
562C2×C22⋊C4D4×C4112yescomplemented
563C2×C22⋊C4C23×C4111yescharacteristic
564C2×C22⋊C4C23×C4111yescharacteristic
565C2×C22⋊C4C23×C4112yes—
566C2×C22⋊C4C23×C4111yescharacteristic
567C2×C22⋊C4C23×C4112yes—
568C2×C22⋊C4C23×C4112yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C4111yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C4112yes—
590C24C2×D4×C4111yescharacteristic
591C24C24×C4111yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C4111yescharacteristic
633C22×C4C2×D4×C4112yes—
634C22×C4C2×D4×C4111yescharacteristic
635C22×C4C2×D4×C4112yes—
636C22×C4C2×D4×C4111yescharacteristic
637C22×C4C2×D4×C4112yes—
638C22×C4C2×D4×C4111yescharacteristic
639C22×C4C2×D4×C4111yescharacteristic
640C22×C4C2×D4×C4111yescharacteristic
641C22×C4C2×D4×C4111yescharacteristic
642C22×C4C2×D4×C4111yescharacteristic
643C22×C4C2×D4×C4111yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C4114yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C4111yescharacteristic
727C23C22×D4×C4111yescharacteristic
728C23C22×D4×C4111yescharacteristic
729C23C2×#41×C4112yes—
730C23H(5,𝔽2)×C4112yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C4111yescharacteristic
787C2×C4#120×C4111yescharacteristic
788C2×C4#120×C4111yescharacteristic
789C2×C4#120×C4111yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C4111yescharacteristic
820C22C41×#53211yescharacteristic
821C22C41×#53511yescharacteristic
822C22C41×#54612yes—
823C22C41×#55012yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C41×#243111yescharacteristic
847C2C41×#302511yescharacteristic
848C2C41×#302611yescharacteristic
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×#2561C2semidirect
3. C41×#2539C2semidirect
4. C41×#2534C2semidirect
5. C41×#2022C2semidirect
6. C41×#2021C2semidirect
7. C41×#1996C2semidirect
8. C41×#1964C2semidirect
9. C41×#1890C2semidirect
10. C41×#1889C2semidirect
11. C4×#99×C41C2semidirect
57. C22×Q8×C41D4semidirect
60. C22×D4×C41D4semidirect
63. C23×C4×C41D4semidirect
117. C2×C4⋊C4×C41D4semidirect
118. C2×C4⋊C4×C41D4semidirect
119. C2×C4⋊C4×C41D4semidirect
120. C2×C4⋊C4×C41D4semidirect
136. C2×C22⋊C4×C41D4semidirect
137. C2×C22⋊C4×C41D4semidirect
146. C2×C42×C41D4semidirect
265. C22⋊C4×C41#41semidirect
365. #25587C41direct (N × H)
415. #3505C2×C41semidirect
416. #2561C2×C41semidirect
417. #2539C2×C41semidirect
418. #2534C2×C41semidirect
419. #2022C2×C41semidirect
420. #2021C2×C41semidirect
421. #1996C2×C41semidirect
422. #1964C2×C41semidirect
423. #1890C2×C41semidirect
424. #1889C2×C41semidirect
425. C4×#99C2×C41semidirect
479. C41#25587direct (N × H)
482. C22×Q8D4×C41semidirect
485. C22×D4D4×C41semidirect
488. C23×C4D4×C41semidirect
542. C2×C4⋊C4D4×C41semidirect
543. C2×C4⋊C4D4×C41semidirect
544. C2×C4⋊C4D4×C41semidirect
545. C2×C4⋊C4D4×C41semidirect
561. C2×C22⋊C4D4×C41semidirect
562. C2×C22⋊C4D4×C41semidirect
571. C2×C42D4×C41semidirect
690. 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×#25612
C41×#25392
C41×#25342
C41×#20222
C41×#20212
C41×#19962
C41×#19642
C41×#18902
C41×#18892
C4×#99×C412
#2558741