Finite Group Databasebeta

← C41×#24469 #23800670

Subgroups — C41×#24469 #23800670

Order 10496.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3489C211yesmaximal, characteristic, complemented
2C41×#3055C211yesmaximal, characteristic, complemented
3C2×C41×#454C211yesmaximal, characteristic, complemented
4C41×#3006C211yesmaximal, characteristic, complemented
5C2×C41×#421C211yesmaximal, characteristic, complemented
6C41×#2620C211yesmaximal, characteristic, complemented
7C41×#2039C211yesmaximal, characteristic, complemented
8C41×#2038C211yesmaximal, characteristic, complemented
9C41×#2006C211yesmaximal, characteristic, complemented
10C41×#2003C211yesmaximal, characteristic, complemented
11C41×#1901C211yesmaximal, characteristic, complemented
12C41×#1897C211yesmaximal, characteristic, complemented
13C41×#1883C211yesmaximal, characteristic, complemented
14C41×#1859C211yesmaximal, characteristic, complemented
15C41×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C41C2211yescharacteristic
17C22×#41×C41C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C41C2211yescharacteristic, complemented
21C22×M16×C41C2211yescharacteristic
22D4×Q8×C41—21no—
23C41×#548—21no—
24C41×#547—21no—
25C41×#547—22no—
26C41×#546—21no—
27C41×#546—22no—
28C41×#537—21no—
29C41×#537C2211yescharacteristic
30C41×#536—21no—
31C41×#536C2211yescharacteristic
32C2×#124×C41C2211yescharacteristic, complemented
33C41×#525—21no—
34C41×#525C2211yescharacteristic
35C2×C22⋊Q8×C41—21no—
36C2×C22⋊Q8×C41C2211yescharacteristic
37C2×#121×C41C2211yescharacteristic
38C41×#520C2211yescharacteristic
39C2×#117×C41C2211yescharacteristic
40C41×#469—21no—
41C41×#468—21no—
42C41×#466—21no—
43C41×#465—21no—
44C41×#454—24no—
45C41×#449—21no—
46C41×#449—21no—
47C41×#448—21no—
48C41×#447—21no—
49C41×#428C2211yescharacteristic, complemented
50C41×#421—24no—
51C2×#104×C41C2211yescharacteristic
52C2×#104×C41C2211yescharacteristic
53C2×#104×C41C2211yescharacteristic
54C2×#104×C41C2211yescharacteristic
55C2×#104×C41C2211yescharacteristic, complemented
56C2×#104×C41C2211yescharacteristic, complemented
57C41×#418C2211yescharacteristic, complemented
58C41×#417C2211yescharacteristic
59C41×#417C2211yescharacteristic
60C41×#417C2211yescharacteristic, complemented
61C2×#101×C41C2211yescharacteristic, complemented
62C2×#101×C41C2211yescharacteristic, complemented
63C41×#407C2211yescharacteristic
64C41×#396—22no—
65C41×#394—22no—
66C41×#391C2211yescharacteristic, complemented
67C41×#390C2211yescharacteristic, complemented
68C41×#384C2211yescharacteristic, complemented
69C41×#343C2211yescharacteristic, complemented
70C41×#343C2211yescharacteristic, complemented
71C41×#339C2211yescharacteristic, complemented
72C41×#339C2211yescharacteristic, complemented
732−1+4×C41—22no—
742−1+4×C41—22no—
752−1+4×C41—41no—
762−1+4×C41—41no—
77C2×#41×C41—21no—
78C2×#41×C41—21no—
79C2×#41×C41—21no—
80C2×#41×C41—22no—
81C2×#41×C41—21no—
82C2×#41×C41—22no—
83C2×#41×C41—22no—
84C2×#41×C41—41no—
85C2×#41×C41—41no—
86C2×#41×C41D411yescharacteristic
87C2×#41×C41D411yescharacteristic
88C2×#41×C41C2311yescharacteristic
89C2×#41×C41C2311yescharacteristic
90C2×#41×C41C2311yescharacteristic
91C22×Q8×C41—21no—
92C22×Q8×C41—21no—
93C22×Q8×C41D411yescharacteristic
94C22×Q8×C41C2311yescharacteristic
95C22×D4×C41—21no—
96C22×D4×C41—21no—
97C22×D4×C41D411yescharacteristic
98C22×D4×C41C2311yescharacteristic
99C23×C4×C41—21no—
100C23×C4×C41C2311yescharacteristic
101AGL(1,ℤ/8)×C41—22no—
102AGL(1,ℤ/8)×C41—22no—
103AGL(1,ℤ/8)×C41—22no—
104AGL(1,ℤ/8)×C41—41no—
105AGL(1,ℤ/8)×C41—41no—
106AGL(1,ℤ/8)×C41—41no—
107C2×SD16×C41—21no—
108C2×SD16×C41—21no—
109C2×SD16×C41—21no—
110C2×D8×C41—21no—
111C2×D8×C41—21no—
112C2×D8×C41—21no—
113C2×M16×C41—21no—
114C2×M16×C41—22no—
115C2×M16×C41—41no—
116C2×M16×C41C2311yescharacteristic
117C2×M16×C41C2311yescharacteristic
118C2×M16×C41C2311yescharacteristic
119C2×M16×C41C2311yescharacteristic
120C22×C8×C41—21no—
121C4⋊Q8×C41—22no—
122C4⋊Q8×C41—21no—
123#124×C41—22no—
124#124×C41—21no—
125#124×C41—22no—
126#124×C41—41no—
127#123×C41—22no—
128#123×C41—22no—
129#123×C41—22no—
130#123×C41—21no—
131#123×C41—22no—
132C22⋊Q8×C41—22no—
133C22⋊Q8×C41—22no—
134C22⋊Q8×C41—22no—
135C22⋊Q8×C41—21no—
136C22⋊Q8×C41—21no—
137C22⋊Q8×C41—21no—
138C22⋊Q8×C41—21no—
139C22⋊Q8×C41—21no—
140C22⋊Q8×C41—21no—
141C22⋊Q8×C41—21no—
142C22⋊Q8×C41—21no—
143C22⋊Q8×C41D411yescharacteristic
144C22⋊Q8×C41D411yescharacteristic
145#121×C41—22no—
146#121×C41—22no—
147#121×C41—22no—
148#121×C41—21no—
149#121×C41—21no—
150#121×C41—22no—
151#121×C41—21no—
152#121×C41—21no—
153#121×C41—21no—
154#121×C41—21no—
155#121×C41D411yescharacteristic
156#121×C41D411yescharacteristic
157#120×C41—22no—
158#120×C41—21no—
159C4×Q8×C41—21no—
160C4×D4×C41—22no—
161C4×D4×C41—22no—
162C4×D4×C41—21no—
163C4×D4×C41—22no—
164C4×D4×C41—21no—
165C4×D4×C41—21no—
166#117×C41—21no—
167#117×C41—22no—
168#117×C41—41no—
169#117×C41C2311yescharacteristic
170C2×C4⋊C4×C41—22no—
171C2×C4⋊C4×C41—21no—
172C2×C4⋊C4×C41—21no—
173C2×C4⋊C4×C41—22no—
174C2×C4⋊C4×C41D412yes—
175C2×C4⋊C4×C41C2311yescharacteristic
176C2×C4⋊C4×C41C2311yescharacteristic
177C2×C22⋊C4×C41—22no—
178C2×C22⋊C4×C41—21no—
179C2×C22⋊C4×C41—21no—
180C2×C22⋊C4×C41—22no—
181C2×C22⋊C4×C41—22no—
182C2×C22⋊C4×C41D412yes—
183C2×C42×C41C2311yescharacteristic
184C2×C42×C41C2311yescharacteristic
185#107×C41—21no—
186#106×C41—21no—
187#104×C41—22no—
188#104×C41—22no—
189#104×C41—22no—
190#104×C41—22no—
191#104×C41—41no—
192#104×C41D414yescomplemented
193#103×C41—21no—
194#103×C41—21no—
195#103×C41—21no—
196#102×C41—21no—
197#102×C41—21no—
198#102×C41—21no—
199#102×C41—21no—
200#102×C41—21no—
201#101×C41—22no—
202#101×C41—41no—
203C22⋊C8×C41—21no—
204C22⋊C8×C41—21no—
205#95×C41—22no—
206C24×C41—21no—
207C24×C41—21no—
208C24×C41C2×D411yescharacteristic
209#41×C41—21no—
210#41×C41—21no—
211#41×C41—22no—
212#41×C41—22no—
213#41×C41—21no—
214#41×C41—21no—
215#41×C41—21no—
216#41×C41—21no—
217#41×C41—21no—
218#41×C41—21no—
219#41×C41—21no—
220#41×C41—21no—
221#41×C41—42no—
222#41×C41—42no—
223#41×C41—41no—
224#41×C41—41no—
225#41×C41—42no—
226#41×C41—42no—
227#41×C41—42no—
228#41×C41—42no—
229#41×C41—44no—
230#41×C41—44no—
231#41×C41—42no—
232#41×C41—42no—
233#41×C41C2×D412yes—
234#41×C41#4112yes—
235C2×Q8×C41—22no—
236C2×Q8×C41—21no—
237C2×Q8×C41—21no—
238C2×Q8×C41—21no—
239C2×Q8×C41—21no—
240C2×Q8×C41—21no—
241C2×Q8×C41—21no—
242C2×Q8×C41—21no—
243C2×Q8×C41—22no—
244C2×Q8×C41—41no—
245C2×Q8×C41—42no—
246C2×Q8×C41—42no—
247C2×Q8×C41—42no—
248C2×Q8×C41—42no—
249C2×Q8×C41C2×D411yescharacteristic
250C2×Q8×C41C2×D411yescharacteristic
251C2×Q8×C41C2×D411yescharacteristic
252C2×D4×C41—21no—
253C2×D4×C41—22no—
254C2×D4×C41—22no—
255C2×D4×C41—21no—
256C2×D4×C41—21no—
257C2×D4×C41—21no—
258C2×D4×C41—21no—
259C2×D4×C41—21no—
260C2×D4×C41—22no—
261C2×D4×C41—21no—
262C2×D4×C41—21no—
263C2×D4×C41—21no—
264C2×D4×C41—21no—
265C2×D4×C41—21no—
266C2×D4×C41—21no—
267C2×D4×C41—21no—
268C2×D4×C41—21no—
269C2×D4×C41—41no—
270C2×D4×C41—42no—
271C2×D4×C41—42no—
272C2×D4×C41—41no—
273C2×D4×C41—41no—
274C2×D4×C41—82no—
275C2×D4×C41C2×D411yescharacteristic
276C2×D4×C41C2×D411yescharacteristic
277C2×D4×C41C2×D411yescharacteristic
278C22×C4×C41—21no—
279C22×C4×C41—21no—
280C22×C4×C41—21no—
281C22×C4×C41—21no—
282C22×C4×C41—21no—
283C22×C4×C41—22no—
284C22×C4×C41—22no—
285C22×C4×C41—21no—
286C22×C4×C41—21no—
287C22×C4×C41—22no—
288C22×C4×C41—21no—
289C22×C4×C41—21no—
290C22×C4×C41—21no—
291C22×C4×C41—21no—
292C22×C4×C41—21no—
293C22×C4×C41—21no—
294C22×C4×C41—42no—
295C22×C4×C41—42no—
296C22×C4×C41C2×D412yes—
297C22×C4×C41C2×D411yescharacteristic
298C22×C4×C41C2×D411yescharacteristic
299C22×C4×C41C2×D411yescharacteristic
300C22×C4×C41C2×D411yescharacteristic
301C22×C4×C41C2×D411yescharacteristic
302C22×C4×C41C2×D412yes—
303C22×C4×C41C2411yescharacteristic
304SD16×C41—42no—
305SD16×C41—42no—
306SD16×C41—42no—
307D8×C41—42no—
308D8×C41—42no—
309D8×C41—42no—
310M16×C41—21no—
311M16×C41—21no—
312M16×C41—21no—
313M16×C41—21no—
314M16×C41—21no—
315M16×C41—21no—
316M16×C41—21no—
317M16×C41—42no—
318M16×C41C2×D412yes—
319C2×C8×C41—21no—
320C2×C8×C41—21no—
321C2×C8×C41—21no—
322C2×C8×C41—21no—
323C2×C8×C41—42no—
324C4⋊C4×C41—22no—
325C4⋊C4×C41—22no—
326C4⋊C4×C41—22no—
327C4⋊C4×C41—22no—
328C4⋊C4×C41—21no—
329C4⋊C4×C41—22no—
330C4⋊C4×C41—22no—
331C4⋊C4×C41—21no—
332C4⋊C4×C41—21no—
333C4⋊C4×C41—21no—
334C4⋊C4×C41—21no—
335C4⋊C4×C41—21no—
336C4⋊C4×C41—42no—
337C4⋊C4×C41—82no—
338C4⋊C4×C41C2×D411yescharacteristic
339C4⋊C4×C41C2×D411yescharacteristic
340C22⋊C4×C41—22no—
341C22⋊C4×C41—22no—
342C22⋊C4×C41—22no—
343C22⋊C4×C41—22no—
344C22⋊C4×C41—22no—
345C22⋊C4×C41—21no—
346C22⋊C4×C41—22no—
347C22⋊C4×C41—22no—
348C22⋊C4×C41—21no—
349C22⋊C4×C41—21no—
350C22⋊C4×C41—21no—
351C22⋊C4×C41—21no—
352C22⋊C4×C41—44no—
353C22⋊C4×C41—42no—
354C22⋊C4×C41—41no—
355C22⋊C4×C41—41no—
356C22⋊C4×C41—82no—
357C42×C41—22no—
358C42×C41—21no—
359C42×C41—21no—
360C42×C41—21no—
361C42×C41—21no—
362C42×C41C2×D412yes—
363C23×C41—21no—
364C23×C41—21no—
365C23×C41—21no—
366C23×C41—21no—
367C23×C41—21no—
368C23×C41—41no—
369C23×C41—41no—
370C23×C41—42no—
371C23×C41—42no—
372C23×C41—42no—
373C23×C41—42no—
374C23×C41—41no—
375C23×C41—41no—
376C23×C41—41no—
377C23×C41—81no—
378C23×C41#12011yescharacteristic
379C23×C41#12011yescharacteristic
380C23×C41C22×D411yescharacteristic
381Q8×C41—21no—
382Q8×C41—21no—
383Q8×C41—21no—
384Q8×C41—21no—
385Q8×C41—21no—
386Q8×C41—42no—
387Q8×C41—44no—
388Q8×C41—41no—
389Q8×C41—41no—
390Q8×C41—41no—
391Q8×C41—41no—
392Q8×C41#12112yes—
393D4×C41—22no—
394D4×C41—22no—
395D4×C41—21no—
396D4×C41—21no—
397D4×C41—21no—
398D4×C41—21no—
399D4×C41—21no—
400D4×C41—42no—
401D4×C41—42no—
402D4×C41—42no—
403D4×C41—42no—
404D4×C41—44no—
405D4×C41—41no—
406D4×C41—41no—
407D4×C41—41no—
408D4×C41—41no—
409D4×C41—41no—
410D4×C41—41no—
411D4×C41—41no—
412D4×C41—41no—
413D4×C41—81no—
414D4×C41—82no—
415D4×C41—82no—
416D4×C41—82no—
417D4×C41#12112yes—
418C2×C4×C41—21no—
419C2×C4×C41—21no—
420C2×C4×C41—21no—
421C2×C4×C41—21no—
422C2×C4×C41—21no—
423C2×C4×C41—21no—
424C2×C4×C41—21no—
425C2×C4×C41—21no—
426C2×C4×C41—21no—
427C2×C4×C41—22no—
428C2×C4×C41—21no—
429C2×C4×C41—21no—
430C2×C4×C41—22no—
431C2×C4×C41—21no—
432C2×C4×C41—22no—
433C2×C4×C41—21no—
434C2×C4×C41—21no—
435C2×C4×C41—22no—
436C2×C4×C41—21no—
437C2×C4×C41—22no—
438C2×C4×C41—22no—
439C2×C4×C41—22no—
440C2×C4×C41—42no—
441C2×C4×C41—42no—
442C2×C4×C41—42no—
443C2×C4×C41—44no—
444C2×C4×C41—41no—
445C2×C4×C41—41no—
446C2×C4×C41—44no—
447C2×C4×C41—41no—
448C2×C4×C41—41no—
449C2×C4×C41—41no—
450C2×C4×C41—41no—
451C2×C4×C41—42no—
452C2×C4×C41—41no—
453C2×C4×C41—42no—
454C2×C4×C41—41no—
455C2×C4×C41—41no—
456C2×C4×C41—41no—
457C2×C4×C41—82no—
458C2×C4×C41#12011yescharacteristic
459C2×C4×C41#12011yescharacteristic
460C2×C4×C41C22×D411yescharacteristic
461C2×C4×C41C22×D411yescharacteristic
462C2×C4×C41C22×D411yescharacteristic
463C2×C4×C41C2×#4111yescharacteristic
464C2×C4×C41H(5,𝔽2)11yescharacteristic
465C2×C4×C41H(5,𝔽2)11yescharacteristic
466C8×C41—22no—
467C8×C41—41no—
468C8×C41—41no—
469C8×C41—41no—
470#24469C4111yesmaximal, characteristic, direct product factor, Sylow
471C22×C41—21no—
472C22×C41—21no—
473C22×C41—21no—
474C22×C41—21no—
475C22×C41—22no—
476C22×C41—21no—
477C22×C41—21no—
478C22×C41—21no—
479C22×C41—21no—
480C22×C41—41no—
481C22×C41—41no—
482C22×C41—41no—
483C22×C41—41no—
484C22×C41—41no—
485C22×C41—41no—
486C22×C41—41no—
487C22×C41—41no—
488C22×C41—81no—
489C22×C41—81no—
490C22×C41—82no—
491C22×C41—82no—
492C22×C41—84no—
493C22×C41—81no—
494C22×C41—81no—
495C22×C41—81no—
496C22×C41C2×#12011yescharacteristic
497C22×C41D4211yescharacteristic
498C22×C41#54611yescharacteristic
499C4×C41—21no—
500C4×C41—21no—
501C4×C41—22no—
502C4×C41—42no—
503C4×C41—42no—
504C4×C41—41no—
505C4×C41—41no—
506C4×C41—41no—
507C4×C41—42no—
508C4×C41—41no—
509C4×C41—81no—
510C4×C41—81no—
511C4×C41C2×#12111yescharacteristic
512C4×C41#53411yescharacteristic
513C4×C41D4211yescharacteristic
514C4×C41#54611yescharacteristic
515#3489C2×C4111yescharacteristic, complemented
516#3055C2×C4111yescharacteristic, complemented
517C2×#454C2×C4111yescharacteristic, complemented
518#3006C2×C4111yescharacteristic, complemented
519C2×#421C2×C4111yescharacteristic, complemented
520#2620C2×C4111yescharacteristic, complemented
521#2039C2×C4111yescharacteristic, complemented
522#2038C2×C4111yescharacteristic, complemented
523#2006C2×C4111yescharacteristic, complemented
524#2003C2×C4111yescharacteristic, complemented
525#1901C2×C4111yescharacteristic, complemented
526#1897C2×C4111yescharacteristic, complemented
527#1883C2×C4111yescharacteristic, complemented
528#1859C2×C4111yescharacteristic, complemented
529#1793C2×C4111yescharacteristic, complemented
530C2×C41—21no—
531C2×C41—21no—
532C2×C41—41no—
533C2×C41—41no—
534C2×C41—42no—
535C2×C41—81no—
536C2×C41—81no—
537C2×C41—161no—
538C2×C41#241011yescharacteristic
539C2×C41#302011yescharacteristic
540C2×C41#302111yescharacteristic
541C2×2−1+4C22×C4111yescharacteristic
542C22×#41C22×C4111yescharacteristic
543C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
544C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
545C2×AGL(1,ℤ/8)C22×C4111yescharacteristic, complemented
546C22×M16C22×C4111yescharacteristic
547D4×Q8—21no—
548#548—21no—
549#547—21no—
550#547—22no—
551#546—21no—
552#546—22no—
553#537—21no—
554#537C22×C4111yescharacteristic
555#536—21no—
556#536C22×C4111yescharacteristic
557C2×#124C22×C4111yescharacteristic, complemented
558#525—21no—
559#525C22×C4111yescharacteristic
560C2×C22⋊Q8—21no—
561C2×C22⋊Q8C22×C4111yescharacteristic
562C2×#121C22×C4111yescharacteristic
563#520C22×C4111yescharacteristic
564C2×#117C22×C4111yescharacteristic
565#469—21no—
566#468—21no—
567#466—21no—
568#465—21no—
569#454—24no—
570#449—21no—
571#449—21no—
572#448—21no—
573#447—21no—
574#428C22×C4111yescharacteristic, complemented
575#421—24no—
576C2×#104C22×C4111yescharacteristic
577C2×#104C22×C4111yescharacteristic
578C2×#104C22×C4111yescharacteristic
579C2×#104C22×C4111yescharacteristic
580C2×#104C22×C4111yescharacteristic, complemented
581C2×#104C22×C4111yescharacteristic, complemented
582#418C22×C4111yescharacteristic, complemented
583#417C22×C4111yescharacteristic
584#417C22×C4111yescharacteristic
585#417C22×C4111yescharacteristic, complemented
586C2×#101C22×C4111yescharacteristic, complemented
587C2×#101C22×C4111yescharacteristic, complemented
588#407C22×C4111yescharacteristic
589#396—22no—
590#394—22no—
591#391C22×C4111yescharacteristic, complemented
592#390C22×C4111yescharacteristic, complemented
593#384C22×C4111yescharacteristic, complemented
594#343C22×C4111yescharacteristic, complemented
595#343C22×C4111yescharacteristic, complemented
596#339C22×C4111yescharacteristic, complemented
597#339C22×C4111yescharacteristic, complemented
598C41#2446911yescharacteristic, direct product factor, Sylow
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C4111yescharacteristic
613C2×#41D4×C4111yescharacteristic
614C2×#41C23×C4111yescharacteristic
615C2×#41C23×C4111yescharacteristic
616C2×#41C23×C4111yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C4111yescharacteristic
620C22×Q8C23×C4111yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C4111yescharacteristic
624C22×D4C23×C4111yescharacteristic
625C23×C4—21no—
626C23×C4C23×C4111yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C4111yescharacteristic
643C2×M16C23×C4111yescharacteristic
644C2×M16C23×C4111yescharacteristic
645C2×M16C23×C4111yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C4111yescharacteristic
670C22⋊Q8D4×C4111yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C4111yescharacteristic
682#121D4×C4111yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C4111yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C4112yes—
701C2×C4⋊C4C23×C4111yescharacteristic
702C2×C4⋊C4C23×C4111yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C4112yes—
709C2×C42C23×C4111yescharacteristic
710C2×C42C23×C4111yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C4114yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C4111yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C4112yes—
760#41#41×C4112yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C4111yescharacteristic
776C2×Q8C2×D4×C4111yescharacteristic
777C2×Q8C2×D4×C4111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C4111yescharacteristic
802C2×D4C2×D4×C4111yescharacteristic
803C2×D4C2×D4×C4111yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C4112yes—
823C22×C4C2×D4×C4111yescharacteristic
824C22×C4C2×D4×C4111yescharacteristic
825C22×C4C2×D4×C4111yescharacteristic
826C22×C4C2×D4×C4111yescharacteristic
827C22×C4C2×D4×C4111yescharacteristic
828C22×C4C2×D4×C4112yes—
829C22×C4C24×C4111yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C4112yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C4111yescharacteristic
865C4⋊C4C2×D4×C4111yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C4112yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C4111yescharacteristic
905C23#120×C4111yescharacteristic
906C23C22×D4×C4111yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C4112yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C4112yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C4111yescharacteristic
985C2×C4#120×C4111yescharacteristic
986C2×C4C22×D4×C4111yescharacteristic
987C2×C4C22×D4×C4111yescharacteristic
988C2×C4C22×D4×C4111yescharacteristic
989C2×C4C2×#41×C4111yescharacteristic
990C2×C4H(5,𝔽2)×C4111yescharacteristic
991C2×C4H(5,𝔽2)×C4111yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C4111yescharacteristic
1022C22D42×C4111yescharacteristic
1023C22C41×#54611yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C4111yescharacteristic
1037C4C41×#53411yescharacteristic
1038C4D42×C4111yescharacteristic
1039C4C41×#54611yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C41×#241011yescharacteristic
1049C2C41×#302011yescharacteristic
1050C2C41×#302111yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ 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×#3489C2semidirect
2. C41×#3055C2semidirect
3. C2×C41×#454C2semidirect
4. C41×#3006C2semidirect
5. C2×C41×#421C2semidirect
6. C41×#2620C2semidirect
7. C41×#2039C2semidirect
8. C41×#2038C2semidirect
9. C41×#2006C2semidirect
10. C41×#2003C2semidirect
11. C41×#1901C2semidirect
12. C41×#1897C2semidirect
13. C41×#1883C2semidirect
14. C41×#1859C2semidirect
15. C41×#1793C2semidirect
20. C2×AGL(1,ℤ/8)×C41C22semidirect
32. C2×#124×C41C22semidirect
49. C41×#428C22semidirect
55. C2×#104×C41C22semidirect
56. C2×#104×C41C22semidirect
57. C41×#418C22semidirect
60. C41×#417C22semidirect
61. C2×#101×C41C22semidirect
62. C2×#101×C41C22semidirect
66. C41×#391C22semidirect
67. C41×#390C22semidirect
68. C41×#384C22semidirect
69. C41×#343C22semidirect
70. C41×#343C22semidirect
71. C41×#339C22semidirect
72. C41×#339C22semidirect
192. #104×C41D4semidirect
470. #24469C41direct (N × H)
515. #3489C2×C41semidirect
516. #3055C2×C41semidirect
517. C2×#454C2×C41semidirect
518. #3006C2×C41semidirect
519. C2×#421C2×C41semidirect
520. #2620C2×C41semidirect
521. #2039C2×C41semidirect
522. #2038C2×C41semidirect
523. #2006C2×C41semidirect
524. #2003C2×C41semidirect
525. #1901C2×C41semidirect
526. #1897C2×C41semidirect
527. #1883C2×C41semidirect
528. #1859C2×C41semidirect
529. #1793C2×C41semidirect
545. C2×AGL(1,ℤ/8)C22×C41semidirect
557. C2×#124C22×C41semidirect
574. #428C22×C41semidirect
580. C2×#104C22×C41semidirect
581. C2×#104C22×C41semidirect
582. #418C22×C41semidirect
585. #417C22×C41semidirect
586. C2×#101C22×C41semidirect
587. C2×#101C22×C41semidirect
591. #391C22×C41semidirect
592. #390C22×C41semidirect
593. #384C22×C41semidirect
594. #343C22×C41semidirect
595. #343C22×C41semidirect
596. #339C22×C41semidirect
597. #339C22×C41semidirect
598. C41#24469direct (N × H)
718. #104D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34892
C41×#30552
C2×C41×#4542
C41×#30062
C2×C41×#4212
C41×#26202
C41×#20392
C41×#20382
C41×#20062
C41×#20032
C41×#19012
C41×#18972
C41×#18832
C41×#18592
C41×#17932
#2446941