Finite Group Databasebeta

← C41×#24432 #23800633

Subgroups — C41×#24432 #23800633

Order 10496.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C41C211yesmaximal, characteristic
2C2×C41×#465C211yesmaximal, characteristic, complemented
3C2×C41×#450C211yesmaximal, characteristic, complemented
4C2×C41×#450C211yesmaximal, characteristic, complemented
5C22×#102×C41C211yesmaximal, characteristic, complemented
6C41×#2417C211yesmaximal, characteristic, complemented
7C41×#2041C211yesmaximal, characteristic, complemented
8C41×#2034C211yesmaximal, characteristic, complemented
9C41×#2014C211yesmaximal, characteristic, complemented
10C41×#2000C211yesmaximal, characteristic, complemented
11C41×#1877C211yesmaximal, characteristic, complemented
12C41×#1874C211yesmaximal, characteristic, complemented
13C41×#1869C211yesmaximal, characteristic, complemented
14C41×#1864C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C41—21no—
17C23×D4×C41C2211yescharacteristic
18C23×D4×C41C2211yescharacteristic
19C22×SD16×C41C2211yescharacteristic
20C22×SD16×C41C2211yescharacteristic, complemented
21C22×SD16×C41C2211yescharacteristic, complemented
22C23×C8×C41C2211yescharacteristic, complemented
23D42×C41—24no—
24D42×C41—24no—
25C2×#127×C41C2211yescharacteristic
26C2×C22⋊Q8×C41C2211yescharacteristic, complemented
27C2×C22⋊Q8×C41C2211yescharacteristic, complemented
28C2×#121×C41—21no—
29C2×#121×C41C2211yescharacteristic
30C2×#121×C41C2211yescharacteristic
31C2×#120×C41—21no—
32C2×#120×C41—21no—
33C2×C4×D4×C41C2211yescharacteristic
34C2×C4×D4×C41C2211yescharacteristic
35C22×C4⋊C4×C41C2211yescharacteristic, complemented
36C41×#465—24no—
37C41×#450—24no—
38C41×#450—24no—
39C2×#106×C41C2211yescharacteristic, complemented
40C2×#103×C41C2211yescharacteristic, complemented
41C2×#102×C41—24no—
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×#102×C41C2211yescharacteristic, complemented
46C2×#102×C41C2211yescharacteristic, complemented
47C2×#102×C41C2211yescharacteristic, complemented
48C2×#102×C41C2211yescharacteristic, complemented
49C2×#102×C41C2211yescharacteristic, complemented
50C2×#102×C41C2211yescharacteristic, complemented
51C2×C22⋊C8×C41C2211yescharacteristic, complemented
52C2×C22⋊C8×C41C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic, complemented
54C41×#398—21no—
55C41×#396—21no—
56C41×#391C2211yescharacteristic, complemented
57C41×#389C2211yescharacteristic, complemented
58C41×#386—21no—
59C41×#380—21no—
60C41×#380C2211yescharacteristic, complemented
61C41×#340C2211yescharacteristic, complemented
62C41×#340C2211yescharacteristic, complemented
63C41×#336C2211yescharacteristic, complemented
64C41×#336C2211yescharacteristic, complemented
65C25×C41—21no—
66C25×C41—21no—
67C22×Q8×C41C2311yescharacteristic
68C22×D4×C41—22no—
69C22×D4×C41—22no—
70C22×D4×C41—28no—
71C22×D4×C41—21no—
72C22×D4×C41—21no—
73C22×D4×C41—22no—
74C22×D4×C41—22no—
75C22×D4×C41—22no—
76C22×D4×C41—22no—
77C22×D4×C41—21no—
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41—22no—
81C22×D4×C41—21no—
82C22×D4×C41—41no—
83C22×D4×C41—41no—
84C22×D4×C41—41no—
85C22×D4×C41—41no—
86C22×D4×C41—44no—
87C22×D4×C41—44no—
88C22×D4×C41D411yescharacteristic
89C22×D4×C41D414yes—
90C22×D4×C41C2311yescharacteristic
91C22×D4×C41C2311yescharacteristic
92C22×D4×C41C2311yescharacteristic
93C23×C4×C41—21no—
94C23×C4×C41—21no—
95C23×C4×C41C2311yescharacteristic
96C23×C4×C41C2311yescharacteristic
97C2×SD16×C41—22no—
98C2×SD16×C41—22no—
99C2×SD16×C41—22no—
100C2×SD16×C41—22no—
101C2×SD16×C41—22no—
102C2×SD16×C41—22no—
103C2×SD16×C41—41no—
104C2×SD16×C41—41no—
105C2×SD16×C41—41no—
106C22×C8×C41—22no—
107C22×C8×C41—22no—
108C22×C8×C41—41no—
109C22×C8×C41C2311yescharacteristic
110C22×C8×C41C2311yescharacteristic
111C22×C8×C41C2311yescharacteristic
112C22×C8×C41C2311yescharacteristic
113#127×C41—22no—
114#127×C41—22no—
115C22⋊Q8×C41—22no—
116C22⋊Q8×C41—22no—
117C22⋊Q8×C41—22no—
118C22⋊Q8×C41—41no—
119#121×C41—28no—
120#121×C41—22no—
121#121×C41—22no—
122#121×C41—22no—
123#121×C41D414yes—
124#120×C41—28no—
125#120×C41—28no—
126C4×D4×C41—22no—
127C4×D4×C41—22no—
128C4×D4×C41—22no—
129C4×D4×C41—22no—
130C2×C4⋊C4×C41—22no—
131C2×C4⋊C4×C41—21no—
132C2×C4⋊C4×C41—21no—
133C2×C4⋊C4×C41—21no—
134C2×C4⋊C4×C41—21no—
135C2×C4⋊C4×C41—41no—
136C2×C4⋊C4×C41D411yescharacteristic
137C2×C4⋊C4×C41C2311yescharacteristic
138C2×C4⋊C4×C41C2311yescharacteristic
139C2×C4⋊C4×C41C2311yescharacteristic
140C2×C4⋊C4×C41C2311yescharacteristic
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×C41D411yescharacteristic
148C2×C22⋊C4×C41D411yescharacteristic
149C2×C42×C41C2311yescharacteristic
150#106×C41—22no—
151#103×C41—22no—
152#102×C41—22no—
153#102×C41—22no—
154#102×C41—22no—
155#102×C41—22no—
156#102×C41—22no—
157#102×C41—22no—
158#102×C41—22no—
159#102×C41—41no—
160#102×C41D414yescomplemented
161C22⋊C8×C41—22no—
162C22⋊C8×C41—22no—
163C22⋊C8×C41—41no—
164#95×C41—21no—
165#95×C41—21no—
166#95×C41—21no—
167#95×C41—21no—
168C24×C41—21no—
169C24×C41—24no—
170C24×C41—21no—
171C24×C41—21no—
172C24×C41—24no—
173C24×C41—42no—
174C24×C41—42no—
175C24×C41—42no—
176C24×C41—42no—
177C24×C41—42no—
178C24×C41—42no—
179C24×C41—42no—
180C24×C41—42no—
181C24×C41—81no—
182C24×C41—81no—
183C24×C41—81no—
184C24×C41—81no—
185C24×C41C2×D411yescharacteristic
186C24×C41C2×D411yescharacteristic
187C2×Q8×C41—21no—
188C2×Q8×C41—21no—
189C2×Q8×C41—21no—
190C2×Q8×C41—21no—
191C2×Q8×C41—21no—
192C2×Q8×C41—21no—
193C2×D4×C41—22no—
194C2×D4×C41—22no—
195C2×D4×C41—28no—
196C2×D4×C41—24no—
197C2×D4×C41—24no—
198C2×D4×C41—24no—
199C2×D4×C41—24no—
200C2×D4×C41—24no—
201C2×D4×C41—24no—
202C2×D4×C41—21no—
203C2×D4×C41—21no—
204C2×D4×C41—21no—
205C2×D4×C41—21no—
206C2×D4×C41—21no—
207C2×D4×C41—21no—
208C2×D4×C41—21no—
209C2×D4×C41—21no—
210C2×D4×C41—21no—
211C2×D4×C41—21no—
212C2×D4×C41—21no—
213C2×D4×C41—21no—
214C2×D4×C41—21no—
215C2×D4×C41—44no—
216C2×D4×C41—44no—
217C2×D4×C41—44no—
218C2×D4×C41—42no—
219C2×D4×C41—42no—
220C2×D4×C41—42no—
221C2×D4×C41—42no—
222C2×D4×C41—42no—
223C2×D4×C41—44no—
224C2×D4×C41—44no—
225C2×D4×C41—432no—
226C2×D4×C41—44no—
227C2×D4×C41—42no—
228C2×D4×C41—42no—
229C2×D4×C41—42no—
230C2×D4×C41—42no—
231C2×D4×C41—44no—
232C2×D4×C41—42no—
233C2×D4×C41—81no—
234C2×D4×C41—81no—
235C2×D4×C41SD1614yescomplemented
236C2×D4×C41C2×D412yes—
237C2×D4×C41C2×D412yes—
238C2×D4×C41C2×D412yes—
239C2×D4×C41C2×D412yes—
240C2×D4×C41#4112yes—
241C22×C4×C41—21no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—24no—
246C22×C4×C41—21no—
247C22×C4×C41—21no—
248C22×C4×C41—21no—
249C22×C4×C41—21no—
250C22×C4×C41—21no—
251C22×C4×C41—21no—
252C22×C4×C41—21no—
253C22×C4×C41—21no—
254C22×C4×C41—21no—
255C22×C4×C41—21no—
256C22×C4×C41—21no—
257C22×C4×C41—42no—
258C22×C4×C41—42no—
259C22×C4×C41—42no—
260C22×C4×C41—42no—
261C22×C4×C41—81no—
262C22×C4×C41C2×D411yescharacteristic
263C22×C4×C41C2×D411yescharacteristic
264C22×C4×C41C2×D411yescharacteristic
265C22×C4×C41C2×D412yes—
266C22×C4×C41C2×D412yes—
267C22×C4×C41C2×D411yescharacteristic
268C22×C4×C41C2411yescharacteristic
269SD16×C41—44no—
270SD16×C41—44no—
271SD16×C41—44no—
272C2×C8×C41—21no—
273C2×C8×C41—21no—
274C2×C8×C41—21no—
275C2×C8×C41—21no—
276C2×C8×C41—21no—
277C2×C8×C41—21no—
278C2×C8×C41—21no—
279C2×C8×C41—21no—
280C2×C8×C41—21no—
281C2×C8×C41—21no—
282C2×C8×C41—21no—
283C2×C8×C41—44no—
284C2×C8×C41C2×D412yescomplemented
285C4⋊C4×C41—22no—
286C4⋊C4×C41—21no—
287C4⋊C4×C41—21no—
288C4⋊C4×C41—21no—
289C4⋊C4×C41—21no—
290C4⋊C4×C41—21no—
291C4⋊C4×C41—21no—
292C4⋊C4×C41—42no—
293C4⋊C4×C41—42no—
294C4⋊C4×C41—42no—
295C4⋊C4×C41—81no—
296C4⋊C4×C41C2×D412yes—
297C4⋊C4×C41C2×D412yescomplemented
298C22⋊C4×C41—24no—
299C22⋊C4×C41—24no—
300C22⋊C4×C41—22no—
301C22⋊C4×C41—24no—
302C22⋊C4×C41—22no—
303C22⋊C4×C41—42no—
304C22⋊C4×C41—42no—
305C22⋊C4×C41—81no—
306C42×C41—21no—
307C42×C41—21no—
308C23×C41—21no—
309C23×C41—21no—
310C23×C41—21no—
311C23×C41—21no—
312C23×C41—21no—
313C23×C41—22no—
314C23×C41—21no—
315C23×C41—22no—
316C23×C41—21no—
317C23×C41—22no—
318C23×C41—21no—
319C23×C41—21no—
320C23×C41—21no—
321C23×C41—22no—
322C23×C41—22no—
323C23×C41—48no—
324C23×C41—48no—
325C23×C41—48no—
326C23×C41—41no—
327C23×C41—41no—
328C23×C41—41no—
329C23×C41—41no—
330C23×C41—41no—
331C23×C41—41no—
332C23×C41—41no—
333C23×C41—41no—
334C23×C41—41no—
335C23×C41—41no—
336C23×C41—41no—
337C23×C41—41no—
338C23×C41—41no—
339C23×C41—41no—
340C23×C41—41no—
341C23×C41—41no—
342C23×C41—48no—
343C23×C41—84no—
344C23×C41—84no—
345C23×C41—84no—
346C23×C41—84no—
347C23×C41—84no—
348C23×C41—84no—
349C23×C41—84no—
350C23×C41—84no—
351C23×C41—84no—
352C23×C41—84no—
353C23×C41#12012yes—
354C23×C41C2×SD1612yes—
355C23×C41C2×SD1612yes—
356C23×C41AGL(1,ℤ/8)12yes—
357C23×C41C22×D411yescharacteristic
358Q8×C41—41no—
359Q8×C41—41no—
360Q8×C41—41no—
361Q8×C41—41no—
362D4×C41—28no—
363D4×C41—22no—
364D4×C41—22no—
365D4×C41—22no—
366D4×C41—22no—
367D4×C41—22no—
368D4×C41—22no—
369D4×C41—22no—
370D4×C41—48no—
371D4×C41—48no—
372D4×C41—48no—
373D4×C41—48no—
374D4×C41—48no—
375D4×C41—41no—
376D4×C41—41no—
377D4×C41—41no—
378D4×C41—41no—
379D4×C41—84no—
380D4×C41#12114yes—
381C2×C4×C41—21no—
382C2×C4×C41—21no—
383C2×C4×C41—21no—
384C2×C4×C41—21no—
385C2×C4×C41—22no—
386C2×C4×C41—22no—
387C2×C4×C41—22no—
388C2×C4×C41—22no—
389C2×C4×C41—21no—
390C2×C4×C41—21no—
391C2×C4×C41—22no—
392C2×C4×C41—22no—
393C2×C4×C41—21no—
394C2×C4×C41—21no—
395C2×C4×C41—21no—
396C2×C4×C41—21no—
397C2×C4×C41—48no—
398C2×C4×C41—41no—
399C2×C4×C41—41no—
400C2×C4×C41—41no—
401C2×C4×C41—41no—
402C2×C4×C41—41no—
403C2×C4×C41—41no—
404C2×C4×C41—41no—
405C2×C4×C41—41no—
406C2×C4×C41—41no—
407C2×C4×C41—41no—
408C2×C4×C41—41no—
409C2×C4×C41—41no—
410C2×C4×C41—41no—
411C2×C4×C41—41no—
412C2×C4×C41—41no—
413C2×C4×C41—41no—
414C2×C4×C41—41no—
415C2×C4×C41—84no—
416C2×C4×C41#12012yes—
417C2×C4×C41C2×SD1612yes—
418C2×C4×C41C22×D411yescharacteristic
419C2×C4×C41C22×D411yescharacteristic
420C2×C4×C41C22×D411yescharacteristic
421C2×C4×C41C2×#4111yescharacteristic
422C2×C4×C41H(5,𝔽2)11yescharacteristic
423C2×C4×C41H(5,𝔽2)11yescharacteristic
424C8×C41—22no—
425C8×C41—41no—
426C8×C41—41no—
427C8×C41—41no—
428#24432C4111yesmaximal, characteristic, direct product factor, Sylow
429C22×C41—22no—
430C22×C41—22no—
431C22×C41—22no—
432C22×C41—22no—
433C22×C41—22no—
434C22×C41—22no—
435C22×C41—24no—
436C22×C41—22no—
437C22×C41—22no—
438C22×C41—22no—
439C22×C41—41no—
440C22×C41—42no—
441C22×C41—41no—
442C22×C41—42no—
443C22×C41—41no—
444C22×C41—42no—
445C22×C41—42no—
446C22×C41—42no—
447C22×C41—41no—
448C22×C41—42no—
449C22×C41—42no—
450C22×C41—42no—
451C22×C41—42no—
452C22×C41—42no—
453C22×C41—42no—
454C22×C41—42no—
455C22×C41—816no—
456C22×C41—816no—
457C22×C41—81no—
458C22×C41—81no—
459C22×C41—81no—
460C22×C41—81no—
461C22×C41—81no—
462C22×C41—81no—
463C22×C41—81no—
464C22×C41—81no—
465C22×C41#45014yescomplemented
466C22×C41C2×#12011yescharacteristic
467C22×C41D4211yescharacteristic
468C22×C41#54611yescharacteristic
469C22×C41C22×SD1611yescharacteristic
470C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
471C22×C41#57611yescharacteristic
472C22×C41#57711yescharacteristic
473C4×C41—22no—
474C4×C41—22no—
475C4×C41—41no—
476C4×C41—42no—
477C4×C41—42no—
478C4×C41—41no—
479C4×C41—81no—
480C4×C41—81no—
481C4×C41—81no—
482C4×C41C2×#12111yescharacteristic
483C4×C41#53411yescharacteristic
484C4×C41D4211yescharacteristic
485C4×C41#54611yescharacteristic
486C2×D42C2×C4111yescharacteristic
487C2×#465C2×C4111yescharacteristic, complemented
488C2×#450C2×C4111yescharacteristic, complemented
489C2×#450C2×C4111yescharacteristic, complemented
490C22×#102C2×C4111yescharacteristic, complemented
491#2417C2×C4111yescharacteristic, complemented
492#2041C2×C4111yescharacteristic, complemented
493#2034C2×C4111yescharacteristic, complemented
494#2014C2×C4111yescharacteristic, complemented
495#2000C2×C4111yescharacteristic, complemented
496#1877C2×C4111yescharacteristic, complemented
497#1874C2×C4111yescharacteristic, complemented
498#1869C2×C4111yescharacteristic, complemented
499#1864C2×C4111yescharacteristic, complemented
500#1786C2×C4111yescharacteristic, complemented
501C2×C41—24no—
502C2×C41—42no—
503C2×C41—44no—
504C2×C41—82no—
505C2×C41—82no—
506C2×C41#241011yescharacteristic
507C2×C41C2×#45011yescharacteristic
508C2×C41#301211yescharacteristic
509C2×C41#326411yescharacteristic
510C2×C41D4×SD1611yescharacteristic
511C2×C41#329511yescharacteristic
512C2×C41#331011yescharacteristic
513C23×D4—21no—
514C23×D4C22×C4111yescharacteristic
515C23×D4C22×C4111yescharacteristic
516C22×SD16C22×C4111yescharacteristic
517C22×SD16C22×C4111yescharacteristic, complemented
518C22×SD16C22×C4111yescharacteristic, complemented
519C23×C8C22×C4111yescharacteristic, complemented
520D42—24no—
521D42—24no—
522C2×#127C22×C4111yescharacteristic
523C2×C22⋊Q8C22×C4111yescharacteristic, complemented
524C2×C22⋊Q8C22×C4111yescharacteristic, complemented
525C2×#121—21no—
526C2×#121C22×C4111yescharacteristic
527C2×#121C22×C4111yescharacteristic
528C2×#120—21no—
529C2×#120—21no—
530C2×C4×D4C22×C4111yescharacteristic
531C2×C4×D4C22×C4111yescharacteristic
532C22×C4⋊C4C22×C4111yescharacteristic, complemented
533#465—24no—
534#450—24no—
535#450—24no—
536C2×#106C22×C4111yescharacteristic, complemented
537C2×#103C22×C4111yescharacteristic, complemented
538C2×#102—24no—
539C2×#102C22×C4111yescharacteristic
540C2×#102C22×C4111yescharacteristic
541C2×#102C22×C4111yescharacteristic
542C2×#102C22×C4111yescharacteristic, complemented
543C2×#102C22×C4111yescharacteristic, complemented
544C2×#102C22×C4111yescharacteristic, complemented
545C2×#102C22×C4111yescharacteristic, complemented
546C2×#102C22×C4111yescharacteristic, complemented
547C2×#102C22×C4111yescharacteristic, complemented
548C2×C22⋊C8C22×C4111yescharacteristic, complemented
549C2×C22⋊C8C22×C4111yescharacteristic, complemented
550C2×C22⋊C8C22×C4111yescharacteristic, complemented
551#398—21no—
552#396—21no—
553#391C22×C4111yescharacteristic, complemented
554#389C22×C4111yescharacteristic, complemented
555#386—21no—
556#380—21no—
557#380C22×C4111yescharacteristic, complemented
558#340C22×C4111yescharacteristic, complemented
559#340C22×C4111yescharacteristic, complemented
560#336C22×C4111yescharacteristic, complemented
561#336C22×C4111yescharacteristic, complemented
562C41#2443211yescharacteristic, direct product factor, Sylow
563C25—21no—
564C25—21no—
565C22×Q8C23×C4111yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C4111yescharacteristic
587C22×D4D4×C4114yes—
588C22×D4C23×C4111yescharacteristic
589C22×D4C23×C4111yescharacteristic
590C22×D4C23×C4111yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C4111yescharacteristic
594C23×C4C23×C4111yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C4111yescharacteristic
608C22×C8C23×C4111yescharacteristic
609C22×C8C23×C4111yescharacteristic
610C22×C8C23×C4111yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C4114yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C4111yescharacteristic
635C2×C4⋊C4C23×C4111yescharacteristic
636C2×C4⋊C4C23×C4111yescharacteristic
637C2×C4⋊C4C23×C4111yescharacteristic
638C2×C4⋊C4C23×C4111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C4111yescharacteristic
646C2×C22⋊C4D4×C4111yescharacteristic
647C2×C42C23×C4111yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C4114yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C4111yescharacteristic
684C24C2×D4×C4111yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C4114yescomplemented
734C2×D4C2×D4×C4112yes—
735C2×D4C2×D4×C4112yes—
736C2×D4C2×D4×C4112yes—
737C2×D4C2×D4×C4112yes—
738C2×D4#41×C4112yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C4111yescharacteristic
761C22×C4C2×D4×C4111yescharacteristic
762C22×C4C2×D4×C4111yescharacteristic
763C22×C4C2×D4×C4112yes—
764C22×C4C2×D4×C4112yes—
765C22×C4C2×D4×C4111yescharacteristic
766C22×C4C24×C4111yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C4112yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C4112yes—
795C4⋊C4C2×D4×C4112yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—48no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C4112yes—
852C23C2×SD16×C4112yes—
853C23C2×SD16×C4112yes—
854C23AGL(1,ℤ/8)×C4112yes—
855C23C22×D4×C4111yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C4114yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C4112yes—
915C2×C4C2×SD16×C4112yes—
916C2×C4C22×D4×C4111yescharacteristic
917C2×C4C22×D4×C4111yescharacteristic
918C2×C4C22×D4×C4111yescharacteristic
919C2×C4C2×#41×C4111yescharacteristic
920C2×C4H(5,𝔽2)×C4111yescharacteristic
921C2×C4H(5,𝔽2)×C4111yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—24no—
934C22—22no—
935C22—22no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—41no—
940C22—42no—
941C22—41no—
942C22—42no—
943C22—41no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22C41×#45014yescomplemented
963C22C2×#120×C4111yescharacteristic
964C22D42×C4111yescharacteristic
965C22C41×#54611yescharacteristic
966C22C22×SD16×C4111yescharacteristic
967C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
968C22C41×#57611yescharacteristic
969C22C41×#57711yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C4111yescharacteristic
980C4C41×#53411yescharacteristic
981C4D42×C4111yescharacteristic
982C4C41×#54611yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C41×#241011yescharacteristic
989C2C2×C41×#45011yescharacteristic
990C2C41×#301211yescharacteristic
991C2C41×#326411yescharacteristic
992C2D4×SD16×C4111yescharacteristic
993C2C41×#329511yescharacteristic
994C2C41×#331011yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×D42×C41C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C4×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#465C2semidirect
3. C2×C41×#450C2semidirect
4. C2×C41×#450C2semidirect
5. C22×#102×C41C2semidirect
6. C41×#2417C2semidirect
7. C41×#2041C2semidirect
8. C41×#2034C2semidirect
9. C41×#2014C2semidirect
10. C41×#2000C2semidirect
11. C41×#1877C2semidirect
12. C41×#1874C2semidirect
13. C41×#1869C2semidirect
14. C41×#1864C2semidirect
15. C41×#1786C2semidirect
20. C22×SD16×C41C22semidirect
21. C22×SD16×C41C22semidirect
22. C23×C8×C41C22semidirect
26. C2×C22⋊Q8×C41C22semidirect
27. C2×C22⋊Q8×C41C22semidirect
35. C22×C4⋊C4×C41C22semidirect
39. C2×#106×C41C22semidirect
40. C2×#103×C41C22semidirect
45. C2×#102×C41C22semidirect
46. C2×#102×C41C22semidirect
47. C2×#102×C41C22semidirect
48. C2×#102×C41C22semidirect
49. C2×#102×C41C22semidirect
50. C2×#102×C41C22semidirect
51. C2×C22⋊C8×C41C22semidirect
52. C2×C22⋊C8×C41C22semidirect
53. C2×C22⋊C8×C41C22semidirect
56. C41×#391C22semidirect
57. C41×#389C22semidirect
60. C41×#380C22semidirect
61. C41×#340C22semidirect
62. C41×#340C22semidirect
63. C41×#336C22semidirect
64. C41×#336C22semidirect
160. #102×C41D4semidirect
235. C2×D4×C41SD16semidirect
284. C2×C8×C41C2×D4semidirect
297. C4⋊C4×C41C2×D4semidirect
428. #24432C41direct (N × H)
465. C22×C41#450semidirect
487. C2×#465C2×C41semidirect
488. C2×#450C2×C41semidirect
489. C2×#450C2×C41semidirect
490. C22×#102C2×C41semidirect
491. #2417C2×C41semidirect
492. #2041C2×C41semidirect
493. #2034C2×C41semidirect
494. #2014C2×C41semidirect
495. #2000C2×C41semidirect
496. #1877C2×C41semidirect
497. #1874C2×C41semidirect
498. #1869C2×C41semidirect
499. #1864C2×C41semidirect
500. #1786C2×C41semidirect
517. C22×SD16C22×C41semidirect
518. C22×SD16C22×C41semidirect
519. C23×C8C22×C41semidirect
523. C2×C22⋊Q8C22×C41semidirect
524. C2×C22⋊Q8C22×C41semidirect
532. C22×C4⋊C4C22×C41semidirect
536. C2×#106C22×C41semidirect
537. C2×#103C22×C41semidirect
542. C2×#102C22×C41semidirect
543. C2×#102C22×C41semidirect
544. C2×#102C22×C41semidirect
545. C2×#102C22×C41semidirect
546. C2×#102C22×C41semidirect
547. C2×#102C22×C41semidirect
548. C2×C22⋊C8C22×C41semidirect
549. C2×C22⋊C8C22×C41semidirect
550. C2×C22⋊C8C22×C41semidirect
553. #391C22×C41semidirect
554. #389C22×C41semidirect
557. #380C22×C41semidirect
558. #340C22×C41semidirect
559. #340C22×C41semidirect
560. #336C22×C41semidirect
561. #336C22×C41semidirect
562. C41#24432direct (N × H)
658. #102D4×C41semidirect
733. C2×D4SD16×C41semidirect
782. C2×C8C2×D4×C41semidirect
795. C4⋊C4C2×D4×C41semidirect
962. C22C41×#450semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C412
C2×C41×#4652
C2×C41×#4502
C22×#102×C412
C41×#24172
C41×#20412
C41×#20342
C41×#20142
C41×#20002
C41×#18772
C41×#18742
C41×#18692
C41×#18642
C41×#17862
#2443241