Finite Group Databasebeta

← C41×#24389 #23800590

Subgroups — C41×#24389 #23800590

Order 10496.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#525C211yesmaximal, characteristic
2C2×C41×#470C211yesmaximal, characteristic, complemented
3C2×C41×#468C211yesmaximal, characteristic, complemented
4C2×C41×#452C211yesmaximal, characteristic, complemented
5C2×C41×#407C211yesmaximal, characteristic, complemented
6C41×#2848C211yesmaximal, characteristic, complemented
7C41×#2036C211yesmaximal, characteristic, complemented
8C41×#2034C211yesmaximal, characteristic, complemented
9C41×#2001C211yesmaximal, characteristic, complemented
10C41×#2000C211yesmaximal, characteristic, complemented
11C41×#1895C211yesmaximal, characteristic, complemented
12C41×#1894C211yesmaximal, characteristic, complemented
13C41×#1873C211yesmaximal, characteristic, complemented
14C41×#1854C211yesmaximal, characteristic, complemented
15C41×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C24×C4×C41C2211yescharacteristic
18C22×Q16×C41C2211yescharacteristic, complemented
19C22×SD16×C41C2211yescharacteristic, complemented
20C22×M16×C41C2211yescharacteristic
21C22×M16×C41C2211yescharacteristic
22C41×#525—24no—
23C41×#525—24no—
24C2×#123×C41—21no—
25C2×C22⋊Q8×C41C2211yescharacteristic
26C2×C22⋊Q8×C41C2211yescharacteristic
27C2×C22⋊Q8×C41C2211yescharacteristic
28C2×C22⋊Q8×C41C2211yescharacteristic
29C2×C22⋊Q8×C41C2211yescharacteristic
30C2×#121×C41C2211yescharacteristic
31C2×#121×C41C2211yescharacteristic
32C2×#120×C41—21no—
33C2×C4×D4×C41—21no—
34C2×C4×D4×C41—21no—
35C2×#117×C41C2211yescharacteristic
36C41×#470—24no—
37C41×#468—24no—
38C41×#452—24no—
39C2×#107×C41C2211yescharacteristic, complemented
40C2×#106×C41C2211yescharacteristic, complemented
41C2×#103×C41C2211yescharacteristic, complemented
42C2×#103×C41C2211yescharacteristic, complemented
43C2×#103×C41C2211yescharacteristic, complemented
44C2×#103×C41C2211yescharacteristic, complemented
45C2×#103×C41C2211yescharacteristic, complemented
46C2×#102×C41C2211yescharacteristic, complemented
47C2×#102×C41C2211yescharacteristic, complemented
48C2×#102×C41C2211yescharacteristic, complemented
49C41×#407—24no—
50C2×C22⋊C8×C41C2211yescharacteristic
51C2×C22⋊C8×C41C2211yescharacteristic
52C2×C22⋊C8×C41C2211yescharacteristic
53C2×C22⋊C8×C41C2211yescharacteristic
54C41×#385—21no—
55C41×#385—21no—
56C41×#385—21no—
57C41×#380C2211yescharacteristic
58C41×#380C2211yescharacteristic
59C41×#380C2211yescharacteristic
60C41×#379—21no—
61C41×#340C2211yescharacteristic, complemented
62C41×#340C2211yescharacteristic, complemented
63C41×#340C2211yescharacteristic, complemented
64C41×#340C2211yescharacteristic, complemented
65C25×C41D411yescharacteristic
66C2×#41×C41—22no—
67C2×#41×C41—22no—
68C2×#41×C41—22no—
69C2×#41×C41—22no—
70C2×#41×C41—41no—
71C2×#41×C41—41no—
72C22×Q8×C41C2311yescharacteristic
73C22×Q8×C41C2311yescharacteristic
74C22×D4×C41—21no—
75C22×D4×C41—21no—
76C22×D4×C41—21no—
77C22×D4×C41C2311yescharacteristic
78C23×C4×C41—21no—
79C23×C4×C41—22no—
80C23×C4×C41—22no—
81C23×C4×C41—22no—
82C23×C4×C41—22no—
83C23×C4×C41—41no—
84C23×C4×C41—41no—
85C23×C4×C41D411yescharacteristic
86C23×C4×C41D411yescharacteristic
87C23×C4×C41D411yescharacteristic
88C23×C4×C41C2311yescharacteristic
89C23×C4×C41C2311yescharacteristic
90C23×C4×C41C2311yescharacteristic
91C2×Q16×C41—22no—
92C2×Q16×C41—22no—
93C2×Q16×C41—41no—
94C2×SD16×C41—22no—
95C2×SD16×C41—22no—
96C2×SD16×C41—41no—
97C2×M16×C41—22no—
98C2×M16×C41—22no—
99C2×M16×C41—22no—
100C2×M16×C41—22no—
101C2×M16×C41—41no—
102C2×M16×C41—41no—
103C22×C8×C41C2311yescharacteristic
104C22×C8×C41C2311yescharacteristic
105C22×C8×C41C2311yescharacteristic
106C22×C8×C41C2311yescharacteristic
107#123×C41—28no—
108C22⋊Q8×C41—22no—
109C22⋊Q8×C41—22no—
110C22⋊Q8×C41—22no—
111C22⋊Q8×C41—22no—
112C22⋊Q8×C41—22no—
113C22⋊Q8×C41—22no—
114C22⋊Q8×C41—22no—
115C22⋊Q8×C41—41no—
116C22⋊Q8×C41—41no—
117C22⋊Q8×C41D414yes—
118#121×C41—22no—
119#121×C41—22no—
120#121×C41—22no—
121#121×C41D414yes—
122#120×C41—28no—
123C4×D4×C41—28no—
124C4×D4×C41—28no—
125#117×C41—22no—
126#117×C41—22no—
127C2×C4⋊C4×C41—21no—
128C2×C4⋊C4×C41—21no—
129C2×C4⋊C4×C41—21no—
130C2×C4⋊C4×C41—21no—
131C2×C4⋊C4×C41—21no—
132C2×C4⋊C4×C41C2311yescharacteristic
133C2×C4⋊C4×C41C2311yescharacteristic
134C2×C4⋊C4×C41C2311yescharacteristic
135C2×C4⋊C4×C41C2311yescharacteristic
136C2×C4⋊C4×C41C2311yescharacteristic
137C2×C22⋊C4×C41—21no—
138C2×C22⋊C4×C41—21no—
139C2×C22⋊C4×C41—21no—
140C2×C22⋊C4×C41—21no—
141C2×C22⋊C4×C41—21no—
142C2×C22⋊C4×C41—21no—
143C2×C22⋊C4×C41—21no—
144C2×C22⋊C4×C41—21no—
145C2×C22⋊C4×C41—21no—
146C2×C22⋊C4×C41—21no—
147C2×C22⋊C4×C41—21no—
148C2×C42×C41—21no—
149#107×C41—22no—
150#106×C41—22no—
151#103×C41—22no—
152#103×C41—22no—
153#103×C41—22no—
154#103×C41—22no—
155#103×C41—41no—
156#102×C41—22no—
157#102×C41—22no—
158#102×C41—41no—
159C22⋊C8×C41—22no—
160C22⋊C8×C41—22no—
161C22⋊C8×C41—22no—
162C22⋊C8×C41D414yescomplemented
163#95×C41—21no—
164#95×C41—21no—
165#95×C41—21no—
166C24×C41—22no—
167C24×C41—22no—
168C24×C41—22no—
169C24×C41—21no—
170C24×C41—41no—
171C24×C41—41no—
172C24×C41—41no—
173C24×C41—41no—
174C24×C41C2×D411yescharacteristic
175C24×C41C2×D411yescharacteristic
176C24×C41C2×D411yescharacteristic
177#41×C41—44no—
178#41×C41—44no—
179#41×C41—44no—
180#41×C41—44no—
181C2×Q8×C41—21no—
182C2×Q8×C41—21no—
183C2×Q8×C41—21no—
184C2×Q8×C41—21no—
185C2×Q8×C41—21no—
186C2×Q8×C41—21no—
187C2×Q8×C41—21no—
188C2×Q8×C41—21no—
189C2×Q8×C41—21no—
190C2×Q8×C41—21no—
191C2×Q8×C41—21no—
192C2×Q8×C41C2×D412yes—
193C2×D4×C41—24no—
194C2×D4×C41—24no—
195C2×D4×C41—24no—
196C2×D4×C41—21no—
197C2×D4×C41—21no—
198C2×D4×C41—21no—
199C2×D4×C41—21no—
200C2×D4×C41—21no—
201C2×D4×C41—42no—
202C2×D4×C41—42no—
203C2×D4×C41—42no—
204C2×D4×C41—42no—
205C2×D4×C41—42no—
206C2×D4×C41—42no—
207C2×D4×C41C2×D412yes—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—21no—
212C22×C4×C41—21no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—21no—
216C22×C4×C41—24no—
217C22×C4×C41—22no—
218C22×C4×C41—22no—
219C22×C4×C41—21no—
220C22×C4×C41—21no—
221C22×C4×C41—21no—
222C22×C4×C41—22no—
223C22×C4×C41—22no—
224C22×C4×C41—22no—
225C22×C4×C41—22no—
226C22×C4×C41—21no—
227C22×C4×C41—21no—
228C22×C4×C41—21no—
229C22×C4×C41—21no—
230C22×C4×C41—21no—
231C22×C4×C41—21no—
232C22×C4×C41—21no—
233C22×C4×C41—21no—
234C22×C4×C41—21no—
235C22×C4×C41—21no—
236C22×C4×C41—41no—
237C22×C4×C41—41no—
238C22×C4×C41—41no—
239C22×C4×C41—44no—
240C22×C4×C41—44no—
241C22×C4×C41—44no—
242C22×C4×C41—44no—
243C22×C4×C41—42no—
244C22×C4×C41—42no—
245C22×C4×C41C2×D411yescharacteristic
246C22×C4×C41C2×D411yescharacteristic
247C22×C4×C41C2×D412yes—
248C22×C4×C41C2×D412yes—
249C22×C4×C41C2×D411yescharacteristic
250C22×C4×C41C2×D412yes—
251C22×C4×C41#4112yes—
252C22×C4×C41C2411yescharacteristic
253Q16×C41—44no—
254SD16×C41—44no—
255M16×C41—44no—
256M16×C41—44no—
257C2×C8×C41—21no—
258C2×C8×C41—21no—
259C2×C8×C41—21no—
260C2×C8×C41—21no—
261C2×C8×C41—21no—
262C2×C8×C41—21no—
263C2×C8×C41—21no—
264C2×C8×C41—21no—
265C2×C8×C41—21no—
266C2×C8×C41—21no—
267C2×C8×C41C2×D412yes—
268C2×C8×C41C2×D412yes—
269C4⋊C4×C41—24no—
270C4⋊C4×C41—24no—
271C4⋊C4×C41—21no—
272C4⋊C4×C41—21no—
273C4⋊C4×C41—21no—
274C4⋊C4×C41—21no—
275C4⋊C4×C41—21no—
276C4⋊C4×C41—21no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—42no—
280C4⋊C4×C41—42no—
281C4⋊C4×C41—42no—
282C4⋊C4×C41C2×D412yes—
283C4⋊C4×C41C2×D412yes—
284C22⋊C4×C41—24no—
285C22⋊C4×C41—24no—
286C22⋊C4×C41—24no—
287C22⋊C4×C41—24no—
288C22⋊C4×C41—24no—
289C22⋊C4×C41—42no—
290C22⋊C4×C41—42no—
291C22⋊C4×C41—42no—
292C22⋊C4×C41—42no—
293C22⋊C4×C41—42no—
294C22⋊C4×C41—42no—
295C42×C41—24no—
296C23×C41—21no—
297C23×C41—21no—
298C23×C41—21no—
299C23×C41—21no—
300C23×C41—21no—
301C23×C41—21no—
302C23×C41—21no—
303C23×C41—21no—
304C23×C41—21no—
305C23×C41—21no—
306C23×C41—21no—
307C23×C41—21no—
308C23×C41—21no—
309C23×C41—21no—
310C23×C41—21no—
311C23×C41—21no—
312C23×C41—21no—
313C23×C41—21no—
314C23×C41—22no—
315C23×C41—44no—
316C23×C41—44no—
317C23×C41—44no—
318C23×C41—44no—
319C23×C41—44no—
320C23×C41—44no—
321C23×C41—44no—
322C23×C41—41no—
323C23×C41—41no—
324C23×C41—41no—
325C23×C41—41no—
326C23×C41—41no—
327C23×C41—41no—
328C23×C41#12012yes—
329C23×C41#12112yes—
330C23×C41#13712yes—
331C23×C41C22×D411yescharacteristic
332Q8×C41—22no—
333Q8×C41—22no—
334Q8×C41—41no—
335Q8×C41—41no—
336Q8×C41—41no—
337Q8×C41—41no—
338Q8×C41—41no—
339Q8×C41—41no—
340D4×C41—22no—
341D4×C41—22no—
342D4×C41—48no—
343D4×C41—48no—
344D4×C41—48no—
345D4×C41—41no—
346D4×C41—41no—
347C2×C4×C41—21no—
348C2×C4×C41—21no—
349C2×C4×C41—21no—
350C2×C4×C41—21no—
351C2×C4×C41—22no—
352C2×C4×C41—22no—
353C2×C4×C41—22no—
354C2×C4×C41—22no—
355C2×C4×C41—22no—
356C2×C4×C41—22no—
357C2×C4×C41—22no—
358C2×C4×C41—22no—
359C2×C4×C41—22no—
360C2×C4×C41—22no—
361C2×C4×C41—21no—
362C2×C4×C41—22no—
363C2×C4×C41—21no—
364C2×C4×C41—21no—
365C2×C4×C41—44no—
366C2×C4×C41—44no—
367C2×C4×C41—44no—
368C2×C4×C41—48no—
369C2×C4×C41—41no—
370C2×C4×C41—41no—
371C2×C4×C41—41no—
372C2×C4×C41—41no—
373C2×C4×C41—41no—
374C2×C4×C41—41no—
375C2×C4×C41—41no—
376C2×C4×C41—41no—
377C2×C4×C41—41no—
378C2×C4×C41—41no—
379C2×C4×C41—41no—
380C2×C4×C41—41no—
381C2×C4×C41—41no—
382C2×C4×C41—41no—
383C2×C4×C41—41no—
384C2×C4×C41—41no—
385C2×C4×C41—41no—
386C2×C4×C41—41no—
387C2×C4×C41—41no—
388C2×C4×C41—41no—
389C2×C4×C41—41no—
390C2×C4×C41—41no—
391C2×C4×C41#12012yes—
392C2×C4×C41#12112yes—
393C2×C4×C41C22×D411yescharacteristic
394C2×C4×C41C22×D411yescharacteristic
395C2×C4×C41C22×D411yescharacteristic
396C2×C4×C41C2×#4111yescharacteristic
397C2×C4×C41H(5,𝔽2)11yescharacteristic
398C2×C4×C41H(5,𝔽2)11yescharacteristic
399C8×C41—22no—
400C8×C41—22no—
401C8×C41—41no—
402C8×C41—41no—
403#24389C4111yesmaximal, characteristic, direct product factor, Sylow
404C22×C41—22no—
405C22×C41—22no—
406C22×C41—22no—
407C22×C41—22no—
408C22×C41—22no—
409C22×C41—22no—
410C22×C41—22no—
411C22×C41—22no—
412C22×C41—22no—
413C22×C41—416no—
414C22×C41—41no—
415C22×C41—41no—
416C22×C41—41no—
417C22×C41—41no—
418C22×C41—41no—
419C22×C41—41no—
420C22×C41—41no—
421C22×C41—41no—
422C22×C41—41no—
423C22×C41—41no—
424C22×C41—41no—
425C22×C41—41no—
426C22×C41—42no—
427C22×C41—42no—
428C22×C41—42no—
429C22×C41—81no—
430C22×C41—81no—
431C22×C41—81no—
432C22×C41—81no—
433C22×C41C2×#12011yescharacteristic
434C22×C41C2×#12111yescharacteristic
435C22×C41#53411yescharacteristic
436C22×C41C2×#13711yescharacteristic
437C22×C41#57511yescharacteristic
438C22×C41#57511yescharacteristic
439C22×C41#57511yescharacteristic
440C4×C41—22no—
441C4×C41—22no—
442C4×C41—41no—
443C4×C41—42no—
444C4×C41—42no—
445C4×C41—42no—
446C4×C41—81no—
447C4×C41—81no—
448C4×C41—81no—
449C4×C41—81no—
450C4×C41D4211yescharacteristic
451C4×C41D4211yescharacteristic
452C4×C41#54611yescharacteristic
453C4×C41#54611yescharacteristic
454C2×#525C2×C4111yescharacteristic
455C2×#470C2×C4111yescharacteristic, complemented
456C2×#468C2×C4111yescharacteristic, complemented
457C2×#452C2×C4111yescharacteristic, complemented
458C2×#407C2×C4111yescharacteristic, complemented
459#2848C2×C4111yescharacteristic, complemented
460#2036C2×C4111yescharacteristic, complemented
461#2034C2×C4111yescharacteristic, complemented
462#2001C2×C4111yescharacteristic, complemented
463#2000C2×C4111yescharacteristic, complemented
464#1895C2×C4111yescharacteristic, complemented
465#1894C2×C4111yescharacteristic, complemented
466#1873C2×C4111yescharacteristic, complemented
467#1854C2×C4111yescharacteristic, complemented
468#1788C2×C4111yescharacteristic, complemented
469C2×C41—42no—
470C2×C41—42no—
471C2×C41—42no—
472C2×C41—82no—
473C2×C41#241011yescharacteristic
474C2×C41#300511yescharacteristic
475C2×C41#300711yescharacteristic
476C2×C41#305411yescharacteristic
477C2×C41#305611yescharacteristic
478C2×C41#319611yescharacteristic
479C2×C41#319711yescharacteristic
480C22×#41C22×C4111yescharacteristic
481C24×C4C22×C4111yescharacteristic
482C22×Q16C22×C4111yescharacteristic, complemented
483C22×SD16C22×C4111yescharacteristic, complemented
484C22×M16C22×C4111yescharacteristic
485C22×M16C22×C4111yescharacteristic
486#525—24no—
487#525—24no—
488C2×#123—21no—
489C2×C22⋊Q8C22×C4111yescharacteristic
490C2×C22⋊Q8C22×C4111yescharacteristic
491C2×C22⋊Q8C22×C4111yescharacteristic
492C2×C22⋊Q8C22×C4111yescharacteristic
493C2×C22⋊Q8C22×C4111yescharacteristic
494C2×#121C22×C4111yescharacteristic
495C2×#121C22×C4111yescharacteristic
496C2×#120—21no—
497C2×C4×D4—21no—
498C2×C4×D4—21no—
499C2×#117C22×C4111yescharacteristic
500#470—24no—
501#468—24no—
502#452—24no—
503C2×#107C22×C4111yescharacteristic, complemented
504C2×#106C22×C4111yescharacteristic, complemented
505C2×#103C22×C4111yescharacteristic, complemented
506C2×#103C22×C4111yescharacteristic, complemented
507C2×#103C22×C4111yescharacteristic, complemented
508C2×#103C22×C4111yescharacteristic, complemented
509C2×#103C22×C4111yescharacteristic, complemented
510C2×#102C22×C4111yescharacteristic, complemented
511C2×#102C22×C4111yescharacteristic, complemented
512C2×#102C22×C4111yescharacteristic, complemented
513#407—24no—
514C2×C22⋊C8C22×C4111yescharacteristic
515C2×C22⋊C8C22×C4111yescharacteristic
516C2×C22⋊C8C22×C4111yescharacteristic
517C2×C22⋊C8C22×C4111yescharacteristic
518#385—21no—
519#385—21no—
520#385—21no—
521#380C22×C4111yescharacteristic
522#380C22×C4111yescharacteristic
523#380C22×C4111yescharacteristic
524#379—21no—
525#340C22×C4111yescharacteristic, complemented
526#340C22×C4111yescharacteristic, complemented
527#340C22×C4111yescharacteristic, complemented
528#340C22×C4111yescharacteristic, complemented
529C41#2438911yescharacteristic, direct product factor, Sylow
530C25D4×C4111yescharacteristic
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—41no—
536C2×#41—41no—
537C22×Q8C23×C4111yescharacteristic
538C22×Q8C23×C4111yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4C23×C4111yescharacteristic
543C23×C4—21no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—41no—
549C23×C4—41no—
550C23×C4D4×C4111yescharacteristic
551C23×C4D4×C4111yescharacteristic
552C23×C4D4×C4111yescharacteristic
553C23×C4C23×C4111yescharacteristic
554C23×C4C23×C4111yescharacteristic
555C23×C4C23×C4111yescharacteristic
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8C23×C4111yescharacteristic
569C22×C8C23×C4111yescharacteristic
570C22×C8C23×C4111yescharacteristic
571C22×C8C23×C4111yescharacteristic
572#123—28no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8D4×C4114yes—
583#121—22no—
584#121—22no—
585#121—22no—
586#121D4×C4114yes—
587#120—28no—
588C4×D4—28no—
589C4×D4—28no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4C23×C4111yescharacteristic
598C2×C4⋊C4C23×C4111yescharacteristic
599C2×C4⋊C4C23×C4111yescharacteristic
600C2×C4⋊C4C23×C4111yescharacteristic
601C2×C4⋊C4C23×C4111yescharacteristic
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C42—21no—
614#107—22no—
615#106—22no—
616#103—22no—
617#103—22no—
618#103—22no—
619#103—22no—
620#103—41no—
621#102—22no—
622#102—22no—
623#102—41no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8—22no—
627C22⋊C8D4×C4114yescomplemented
628#95—21no—
629#95—21no—
630#95—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—41no—
636C24—41no—
637C24—41no—
638C24—41no—
639C24C2×D4×C4111yescharacteristic
640C24C2×D4×C4111yescharacteristic
641C24C2×D4×C4111yescharacteristic
642#41—44no—
643#41—44no—
644#41—44no—
645#41—44no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C4112yes—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C4112yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4C2×D4×C4111yescharacteristic
711C22×C4C2×D4×C4111yescharacteristic
712C22×C4C2×D4×C4112yes—
713C22×C4C2×D4×C4112yes—
714C22×C4C2×D4×C4111yescharacteristic
715C22×C4C2×D4×C4112yes—
716C22×C4#41×C4112yes—
717C22×C4C24×C4111yescharacteristic
718Q16—44no—
719SD16—44no—
720M16—44no—
721M16—44no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C4112yes—
733C2×C8C2×D4×C4112yes—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4C2×D4×C4112yes—
748C4⋊C4C2×D4×C4112yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—24no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23#120×C4112yes—
794C23#121×C4112yes—
795C23#137×C4112yes—
796C23C22×D4×C4111yescharacteristic
797Q8—22no—
798Q8—22no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—48no—
810D4—41no—
811D4—41no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4#120×C4112yes—
857C2×C4#121×C4112yes—
858C2×C4C22×D4×C4111yescharacteristic
859C2×C4C22×D4×C4111yescharacteristic
860C2×C4C22×D4×C4111yescharacteristic
861C2×C4C2×#41×C4111yescharacteristic
862C2×C4H(5,𝔽2)×C4111yescharacteristic
863C2×C4H(5,𝔽2)×C4111yescharacteristic
864C8—22no—
865C8—22no—
866C8—41no—
867C8—41no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—416no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22C2×#120×C4111yescharacteristic
898C22C2×#121×C4111yescharacteristic
899C22C41×#53411yescharacteristic
900C22C2×#137×C4111yescharacteristic
901C22C41×#57511yescharacteristic
902C22C41×#57511yescharacteristic
903C22C41×#57511yescharacteristic
904C4—22no—
905C4—22no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4D42×C4111yescharacteristic
915C4D42×C4111yescharacteristic
916C4C41×#54611yescharacteristic
917C4C41×#54611yescharacteristic
918C2—42no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2C41×#241011yescharacteristic
923C2C41×#300511yescharacteristic
924C2C41×#300711yescharacteristic
925C2C41×#305411yescharacteristic
926C2C41×#305611yescharacteristic
927C2C41×#319611yescharacteristic
928C2C41×#319711yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C24×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#470C2semidirect
3. C2×C41×#468C2semidirect
4. C2×C41×#452C2semidirect
5. C2×C41×#407C2semidirect
6. C41×#2848C2semidirect
7. C41×#2036C2semidirect
8. C41×#2034C2semidirect
9. C41×#2001C2semidirect
10. C41×#2000C2semidirect
11. C41×#1895C2semidirect
12. C41×#1894C2semidirect
13. C41×#1873C2semidirect
14. C41×#1854C2semidirect
15. C41×#1788C2semidirect
18. C22×Q16×C41C22semidirect
19. C22×SD16×C41C22semidirect
39. C2×#107×C41C22semidirect
40. C2×#106×C41C22semidirect
41. C2×#103×C41C22semidirect
42. C2×#103×C41C22semidirect
43. C2×#103×C41C22semidirect
44. C2×#103×C41C22semidirect
45. C2×#103×C41C22semidirect
46. C2×#102×C41C22semidirect
47. C2×#102×C41C22semidirect
48. C2×#102×C41C22semidirect
61. C41×#340C22semidirect
62. C41×#340C22semidirect
63. C41×#340C22semidirect
64. C41×#340C22semidirect
162. C22⋊C8×C41D4semidirect
403. #24389C41direct (N × H)
455. C2×#470C2×C41semidirect
456. C2×#468C2×C41semidirect
457. C2×#452C2×C41semidirect
458. C2×#407C2×C41semidirect
459. #2848C2×C41semidirect
460. #2036C2×C41semidirect
461. #2034C2×C41semidirect
462. #2001C2×C41semidirect
463. #2000C2×C41semidirect
464. #1895C2×C41semidirect
465. #1894C2×C41semidirect
466. #1873C2×C41semidirect
467. #1854C2×C41semidirect
468. #1788C2×C41semidirect
482. C22×Q16C22×C41semidirect
483. C22×SD16C22×C41semidirect
503. C2×#107C22×C41semidirect
504. C2×#106C22×C41semidirect
505. C2×#103C22×C41semidirect
506. C2×#103C22×C41semidirect
507. C2×#103C22×C41semidirect
508. C2×#103C22×C41semidirect
509. C2×#103C22×C41semidirect
510. C2×#102C22×C41semidirect
511. C2×#102C22×C41semidirect
512. C2×#102C22×C41semidirect
525. #340C22×C41semidirect
526. #340C22×C41semidirect
527. #340C22×C41semidirect
528. #340C22×C41semidirect
529. C41#24389direct (N × H)
627. C22⋊C8D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5252
C2×C41×#4702
C2×C41×#4682
C2×C41×#4522
C2×C41×#4072
C41×#28482
C41×#20362
C41×#20342
C41×#20012
C41×#20002
C41×#18952
C41×#18942
C41×#18732
C41×#18542
C41×#17882
#2438941