Finite Group Databasebeta

← C41×#24142 #23800343

Subgroups — C41×#24142 #23800343

Order 10496.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3505C211yesmaximal, characteristic, complemented
2C41×#2626C211yesmaximal, characteristic, complemented
3C41×#2617C211yesmaximal, characteristic, complemented
4C41×#2321C211yesmaximal, characteristic, complemented
5C41×#2044C212yesmaximal, complemented
6C41×#2021C212yesmaximal, complemented
7C41×#1996C211yesmaximal, characteristic, complemented
8C41×#1964C211yesmaximal, characteristic, complemented
9C41×#1889C212yesmaximal, 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×C22⋊Q8×C41C2211yescharacteristic
24C2×#121×C41C2211yescharacteristic
25C2×#120×C41C2211yescharacteristic
26C2×#120×C41C2212yes—
27C41×#518C2212yes—
28C2×C4×D4×C41C2211yescharacteristic
29C22×C22⋊C4×C41C2211yescharacteristic
30C2×#99×C41C2212yes—
31C2×#99×C41C2212yes—
32C2×#99×C41C2212yes—
33C41×#399—21no—
34C41×#397—21no—
35C41×#396—22no—
36C41×#394—22no—
37C41×#393—21no—
38C41×#392—21no—
39C41×#390—21no—
40C41×#388—21no—
41C41×#388—21no—
42C41×#386—21no—
43C41×#386C2211yescharacteristic
44C41×#386C2212yes—
45C41×#385C2212yes—
46C41×#385C2211yescharacteristic
47C41×#380C2211yescharacteristic
48C41×#380C2211yescharacteristic
49C41×#379C2212yes—
50C41×#379C2211yescharacteristic
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—
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#120×C41—22no—
93#120×C41—22no—
94#120×C41—22no—
95#120×C41—22no—
96#120×C41—24no—
97#120×C41—42no—
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×C41—21no—
114C2×C4⋊C4×C41—21no—
115C2×C4⋊C4×C41—22no—
116C2×C4⋊C4×C41D411yescharacteristic, complemented
117C2×C4⋊C4×C41D411yescharacteristic, complemented
118C2×C4⋊C4×C41D412yescomplemented
119C2×C4⋊C4×C41D411yescharacteristic, complemented
120C2×C22⋊C4×C41—22no—
121C2×C22⋊C4×C41—21no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—21no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41—21no—
128C2×C22⋊C4×C41—22no—
129C2×C22⋊C4×C41—21no—
130C2×C22⋊C4×C41—22no—
131C2×C22⋊C4×C41—21no—
132C2×C22⋊C4×C41—21no—
133C2×C22⋊C4×C41—22no—
134C2×C22⋊C4×C41—22no—
135C2×C22⋊C4×C41D411yescharacteristic, complemented
136C2×C22⋊C4×C41D412yescomplemented
137C2×C22⋊C4×C41C2312yes—
138C2×C22⋊C4×C41C2311yescharacteristic
139C2×C22⋊C4×C41C2312yes—
140C2×C22⋊C4×C41C2311yescharacteristic
141C2×C22⋊C4×C41C2312yes—
142C2×C22⋊C4×C41C2311yescharacteristic
143C2×C42×C41—21no—
144C2×C42×C41D411yescharacteristic, complemented
145#99×C41—24no—
146#99×C41—42no—
147#99×C41—42no—
148#95×C41—21no—
149#95×C41—21no—
150#95×C41—21no—
151#95×C41—21no—
152#95×C41—22no—
153#95×C41—21no—
154#95×C41—22no—
155C24×C41—21no—
156C24×C41—21no—
157C24×C41—21no—
158C24×C41—21no—
159C24×C41—21no—
160C24×C41—21no—
161C24×C41—81no—
162C24×C41—81no—
163C24×C41C2×D412yes—
164C24×C41C2×D411yescharacteristic
165C24×C41#4112yescomplemented
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—21no—
177C2×D4×C41—21no—
178C2×D4×C41—22no—
179C2×D4×C41—21no—
180C2×D4×C41—22no—
181C2×D4×C41—21no—
182C2×D4×C41—22no—
183C2×D4×C41—22no—
184C2×D4×C41—22no—
185C2×D4×C41—24no—
186C2×D4×C41—21no—
187C2×D4×C41—21no—
188C2×D4×C41—44no—
189C2×D4×C41—81no—
190C2×D4×C41—81no—
191C2×D4×C41—81no—
192C2×D4×C41—82no—
193C2×D4×C41—82no—
194C22×C4×C41—21no—
195C22×C4×C41—22no—
196C22×C4×C41—22no—
197C22×C4×C41—21no—
198C22×C4×C41—21no—
199C22×C4×C41—21no—
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—22no—
203C22×C4×C41—22no—
204C22×C4×C41—21no—
205C22×C4×C41—81no—
206C22×C4×C41—81no—
207C22×C4×C41—81no—
208C22×C4×C41C2×D411yescharacteristic
209C22×C4×C41C2×D412yes—
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41C2×D412yes—
212C22×C4×C41C2×D411yescharacteristic
213C22×C4×C41C2×D412yes—
214C22×C4×C41C2×D411yescharacteristic
215C22×C4×C41C2×D411yescharacteristic
216C22×C4×C41C2×D411yescharacteristic
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2×D411yescharacteristic
219C22×C4×C41C2×D411yescharacteristic
220C4⋊C4×C41—22no—
221C4⋊C4×C41—22no—
222C4⋊C4×C41—22no—
223C4⋊C4×C41—22no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—22no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—22no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—81no—
233C4⋊C4×C41—81no—
234C4⋊C4×C41—81no—
235C4⋊C4×C41—82no—
236C22⋊C4×C41—22no—
237C22⋊C4×C41—22no—
238C22⋊C4×C41—24no—
239C22⋊C4×C41—22no—
240C22⋊C4×C41—22no—
241C22⋊C4×C41—22no—
242C22⋊C4×C41—22no—
243C22⋊C4×C41—21no—
244C22⋊C4×C41—22no—
245C22⋊C4×C41—21no—
246C22⋊C4×C41—22no—
247C22⋊C4×C41—21no—
248C22⋊C4×C41—22no—
249C22⋊C4×C41—21no—
250C22⋊C4×C41—21no—
251C22⋊C4×C41—22no—
252C22⋊C4×C41—22no—
253C22⋊C4×C41—22no—
254C22⋊C4×C41—21no—
255C22⋊C4×C41—22no—
256C22⋊C4×C41—22no—
257C22⋊C4×C41—21no—
258C22⋊C4×C41—44no—
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—81no—
266C22⋊C4×C41—82no—
267C22⋊C4×C41—81no—
268C22⋊C4×C41—82no—
269C22⋊C4×C41#4112yescomplemented
270C42×C41—22no—
271C42×C41—22no—
272C42×C41—21no—
273C42×C41—21no—
274C42×C41—81no—
275C23×C41—21no—
276C23×C41—22no—
277C23×C41—22no—
278C23×C41—21no—
279C23×C41—22no—
280C23×C41—22no—
281C23×C41—21no—
282C23×C41—22no—
283C23×C41—22no—
284C23×C41—41no—
285C23×C41—41no—
286C23×C41—41no—
287C23×C41—41no—
288C23×C41—42no—
289C23×C41—41no—
290C23×C41—42no—
291C23×C41—41no—
292C23×C41—41no—
293C23×C41—42no—
294C23×C41—41no—
295C23×C41—42no—
296C23×C41—42no—
297C23×C41—42no—
298C23×C41—41no—
299C23×C41—41no—
300C23×C41—41no—
301C23×C41—41no—
302C23×C41—82no—
303C23×C41—82no—
304C23×C41—82no—
305C23×C41—82no—
306C23×C41C22×D411yescharacteristic
307C23×C41C22×D411yescharacteristic
308C23×C41C22×D411yescharacteristic
309C23×C41C2×#4111yescharacteristic
310C23×C41C2×#4111yescharacteristic
311C23×C41H(5,𝔽2)11yescharacteristic
312C23×C412−1+411yescharacteristic
313Q8×C41—42no—
314Q8×C41—81no—
315D4×C41—42no—
316D4×C41—42no—
317D4×C41—42no—
318D4×C41—41no—
319D4×C41—41no—
320D4×C41—41no—
321D4×C41—42no—
322D4×C41—42no—
323D4×C41—41no—
324D4×C41—81no—
325D4×C41—82no—
326D4×C41—84no—
327D4×C41—82no—
328D4×C41—88no—
329C2×C4×C41—21no—
330C2×C4×C41—22no—
331C2×C4×C41—21no—
332C2×C4×C41—21no—
333C2×C4×C41—22no—
334C2×C4×C41—22no—
335C2×C4×C41—21no—
336C2×C4×C41—22no—
337C2×C4×C41—21no—
338C2×C4×C41—22no—
339C2×C4×C41—22no—
340C2×C4×C41—41no—
341C2×C4×C41—41no—
342C2×C4×C41—41no—
343C2×C4×C41—41no—
344C2×C4×C41—41no—
345C2×C4×C41—41no—
346C2×C4×C41—42no—
347C2×C4×C41—41no—
348C2×C4×C41—41no—
349C2×C4×C41—41no—
350C2×C4×C41—42no—
351C2×C4×C41—41no—
352C2×C4×C41—42no—
353C2×C4×C41—41no—
354C2×C4×C41—41no—
355C2×C4×C41—42no—
356C2×C4×C41—42no—
357C2×C4×C41—41no—
358C2×C4×C41—42no—
359C2×C4×C41—42no—
360C2×C4×C41—42no—
361C2×C4×C41—41no—
362C2×C4×C41—42no—
363C2×C4×C41—41no—
364C2×C4×C41—41no—
365C2×C4×C41—42no—
366C2×C4×C41—42no—
367C2×C4×C41—81no—
368C2×C4×C41—82no—
369C2×C4×C41—82no—
370C2×C4×C41#12011yescharacteristic
371C2×C4×C41#12011yescharacteristic
372C2×C4×C41#12011yescharacteristic
373C2×C4×C41#12011yescharacteristic
374#24142C4111yesmaximal, characteristic, direct product factor, Sylow
375C22×C41—21no—
376C22×C41—21no—
377C22×C41—21no—
378C22×C41—21no—
379C22×C41—21no—
380C22×C41—21no—
381C22×C41—41no—
382C22×C41—41no—
383C22×C41—41no—
384C22×C41—41no—
385C22×C41—42no—
386C22×C41—42no—
387C22×C41—44no—
388C22×C41—42no—
389C22×C41—44no—
390C22×C41—41no—
391C22×C41—42no—
392C22×C41—42no—
393C22×C41—41no—
394C22×C41—42no—
395C22×C41—42no—
396C22×C41—41no—
397C22×C41—82no—
398C22×C41—81no—
399C22×C41—82no—
400C22×C41—82no—
401C22×C41—81no—
402C22×C41—81no—
403C22×C41—82no—
404C22×C41—81no—
405C22×C41—81no—
406C22×C41C2×#12011yescharacteristic
407C22×C41#52511yescharacteristic
408C22×C41#53711yescharacteristic
409C22×C41#54611yescharacteristic
410C22×C41#54711yescharacteristic
411C22×C41#54811yescharacteristic
412C22×C41#55011yescharacteristic
413C4×C41—21no—
414C4×C41—21no—
415C4×C41—21no—
416C4×C41—21no—
417C4×C41—42no—
418C4×C41—41no—
419C4×C41—42no—
420C4×C41—41no—
421C4×C41—42no—
422C4×C41—41no—
423C4×C41—42no—
424C4×C41—82no—
425C4×C41—81no—
426C4×C41—82no—
427C4×C41—81no—
428#3505C2×C4111yescharacteristic, complemented
429#2626C2×C4111yescharacteristic, complemented
430#2617C2×C4111yescharacteristic, complemented
431#2321C2×C4111yescharacteristic, complemented
432#2044C2×C4112yescomplemented
433#2021C2×C4112yescomplemented
434#1996C2×C4111yescharacteristic, complemented
435#1964C2×C4111yescharacteristic, complemented
436#1889C2×C4112yescomplemented
437#1867C2×C4112yescomplemented
438#1799C2×C4111yescharacteristic, complemented
439C2×C41—21no—
440C2×C41—21no—
441C2×C41—21no—
442C2×C41—21no—
443C2×C41—21no—
444C2×C41—21no—
445C2×C41—82no—
446C2×C41—81no—
447C2×C41—82no—
448C2×C41#240711yescharacteristic
449C2×C41#302611yescharacteristic
450C2×C41#302711yescharacteristic
451#553—22no—
452#553—21no—
453#552—21no—
454#551—22no—
455#548—21no—
456#546—21no—
457#539—21no—
458#538—21no—
459#534C22×C4112yes—
460#529—21no—
461#525—21no—
462C2×C22⋊Q8C22×C4111yescharacteristic
463C2×#121C22×C4111yescharacteristic
464C2×#120C22×C4111yescharacteristic
465C2×#120C22×C4112yes—
466#518C22×C4112yes—
467C2×C4×D4C22×C4111yescharacteristic
468C22×C22⋊C4C22×C4111yescharacteristic
469C2×#99C22×C4112yes—
470C2×#99C22×C4112yes—
471C2×#99C22×C4112yes—
472#399—21no—
473#397—21no—
474#396—22no—
475#394—22no—
476#393—21no—
477#392—21no—
478#390—21no—
479#388—21no—
480#388—21no—
481#386—21no—
482#386C22×C4111yescharacteristic
483#386C22×C4112yes—
484#385C22×C4111yescharacteristic
485#385C22×C4112yes—
486#380C22×C4111yescharacteristic
487#380C22×C4111yescharacteristic
488#379C22×C4111yescharacteristic
489#379C22×C4112yes—
490C4×C22⋊C4C22×C4111yescharacteristic
491#342C22×C4112yes—
492#342C22×C4112yes—
493#342C22×C4112yes—
494C41#2414211yescharacteristic, direct product factor, Sylow
495C25C23×C4111yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C4111yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C4111yescharacteristic, complemented
501C22×D4C23×C4111yescharacteristic
502C22×D4C23×C4112yes—
503C23×C4D4×C4111yescharacteristic, complemented
504C23×C4C23×C4111yescharacteristic
505C23×C4C23×C4111yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C4111yescharacteristic, complemented
557C2×C4⋊C4D4×C4111yescharacteristic, complemented
558C2×C4⋊C4D4×C4112yescomplemented
559C2×C4⋊C4D4×C4111yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C4111yescharacteristic, complemented
576C2×C22⋊C4D4×C4112yescomplemented
577C2×C22⋊C4C23×C4112yes—
578C2×C22⋊C4C23×C4111yescharacteristic
579C2×C22⋊C4C23×C4112yes—
580C2×C22⋊C4C23×C4111yescharacteristic
581C2×C22⋊C4C23×C4112yes—
582C2×C22⋊C4C23×C4111yescharacteristic
583C2×C42—21no—
584C2×C42D4×C4111yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C4112yes—
604C24C2×D4×C4111yescharacteristic
605C24#41×C4112yescomplemented
606C24C24×C4111yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C4111yescharacteristic
649C22×C4C2×D4×C4112yes—
650C22×C4C2×D4×C4111yescharacteristic
651C22×C4C2×D4×C4112yes—
652C22×C4C2×D4×C4111yescharacteristic
653C22×C4C2×D4×C4112yes—
654C22×C4C2×D4×C4111yescharacteristic
655C22×C4C2×D4×C4111yescharacteristic
656C22×C4C2×D4×C4111yescharacteristic
657C22×C4C2×D4×C4111yescharacteristic
658C22×C4C2×D4×C4111yescharacteristic
659C22×C4C2×D4×C4111yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C4112yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C4111yescharacteristic
747C23C22×D4×C4111yescharacteristic
748C23C22×D4×C4111yescharacteristic
749C23C2×#41×C4111yescharacteristic
750C23C2×#41×C4111yescharacteristic
751C23H(5,𝔽2)×C4111yescharacteristic
752C232−1+4×C4111yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C4111yescharacteristic
811C2×C4#120×C4111yescharacteristic
812C2×C4#120×C4111yescharacteristic
813C2×C4#120×C4111yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C4111yescharacteristic
846C22C41×#52511yescharacteristic
847C22C41×#53711yescharacteristic
848C22C41×#54611yescharacteristic
849C22C41×#54711yescharacteristic
850C22C41×#54811yescharacteristic
851C22C41×#55011yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C41×#240711yescharacteristic
877C2C41×#302611yescharacteristic
878C2C41×#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×#2626C2semidirect
3. C41×#2617C2semidirect
4. C41×#2321C2semidirect
5. C41×#2044C2semidirect
6. C41×#2021C2semidirect
7. C41×#1996C2semidirect
8. C41×#1964C2semidirect
9. C41×#1889C2semidirect
10. C41×#1867C2semidirect
11. C41×#1799C2semidirect
57. C22×Q8×C41D4semidirect
60. C22×D4×C41D4semidirect
63. C23×C4×C41D4semidirect
116. C2×C4⋊C4×C41D4semidirect
117. C2×C4⋊C4×C41D4semidirect
118. C2×C4⋊C4×C41D4semidirect
119. C2×C4⋊C4×C41D4semidirect
135. C2×C22⋊C4×C41D4semidirect
136. C2×C22⋊C4×C41D4semidirect
144. C2×C42×C41D4semidirect
165. C24×C41#41semidirect
269. C22⋊C4×C41#41semidirect
374. #24142C41direct (N × H)
428. #3505C2×C41semidirect
429. #2626C2×C41semidirect
430. #2617C2×C41semidirect
431. #2321C2×C41semidirect
432. #2044C2×C41semidirect
433. #2021C2×C41semidirect
434. #1996C2×C41semidirect
435. #1964C2×C41semidirect
436. #1889C2×C41semidirect
437. #1867C2×C41semidirect
438. #1799C2×C41semidirect
494. C41#24142direct (N × H)
497. C22×Q8D4×C41semidirect
500. C22×D4D4×C41semidirect
503. C23×C4D4×C41semidirect
556. C2×C4⋊C4D4×C41semidirect
557. C2×C4⋊C4D4×C41semidirect
558. C2×C4⋊C4D4×C41semidirect
559. C2×C4⋊C4D4×C41semidirect
575. C2×C22⋊C4D4×C41semidirect
576. C2×C22⋊C4D4×C41semidirect
584. C2×C42D4×C41semidirect
605. C24#41×C41semidirect
709. 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×#26262
C41×#26172
C41×#23212
C41×#20442
C41×#20212
C41×#19962
C41×#19642
C41×#18892
C41×#18672
C41×#17992
#2414241