Finite Group Databasebeta

← C41×#24402 #23800603

Subgroups — C41×#24402 #23800603

Order 10496.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#575C211yesmaximal, characteristic, complemented
2C2×C41×#472C211yesmaximal, characteristic, complemented
3C2×C41×#471C211yesmaximal, characteristic, complemented
4C41×#3006C211yesmaximal, characteristic, complemented
5C2×C41×#449C211yesmaximal, characteristic, complemented
6C41×#2880C211yesmaximal, characteristic, complemented
7C41×#2052C211yesmaximal, characteristic, complemented
8C41×#2051C211yesmaximal, characteristic, complemented
9C41×#2019C211yesmaximal, characteristic, complemented
10C41×#2018C211yesmaximal, characteristic, complemented
11C41×#1908C211yesmaximal, characteristic, complemented
12C41×#1907C211yesmaximal, characteristic, complemented
13C41×#1900C211yesmaximal, characteristic, complemented
14C41×#1855C211yesmaximal, characteristic, complemented
15C41×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C22×#41×C41C2211yescharacteristic
18C41×#575—24no—
19C41×#575—24no—
20C2×#137×C41—21no—
21C2×#137×C41C2211yescharacteristic
22C2×#137×C41C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C41—21no—
24C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
28C2×#135×C41—21no—
29C2×#135×C41—21no—
30C22×SD16×C41C2211yescharacteristic, complemented
31C22×D8×C41C2211yescharacteristic, complemented
32C2×#131×C41C2211yescharacteristic
33C2×#131×C41C2211yescharacteristic
34C22×M16×C41C2211yescharacteristic
35C2×#121×C41C2211yescharacteristic
36C41×#472—24no—
37C41×#471—24no—
38C41×#449—21no—
39C41×#449—21no—
40C41×#449—21no—
41C41×#449—21no—
42C41×#449—21no—
43C41×#449—21no—
44C41×#448—21no—
45C41×#447—21no—
46C2×#108×C41C2211yescharacteristic, complemented
47C2×#108×C41C2211yescharacteristic, complemented
48C41×#417C2211yescharacteristic
49C41×#417C2211yescharacteristic
50C2×#103×C41C2211yescharacteristic, complemented
51C2×#102×C41C2211yescharacteristic, complemented
52C2×#101×C41C2211yescharacteristic, complemented
53C2×#101×C41C2211yescharacteristic, complemented
54C2×#100×C41C2211yescharacteristic, complemented
55C2×#100×C41C2211yescharacteristic, complemented
56C2×#100×C41C2211yescharacteristic, complemented
57C2×#100×C41C2211yescharacteristic, complemented
58C41×#408—21no—
59C41×#408—21no—
60C41×#408C2211yescharacteristic
61C41×#408C2211yescharacteristic
62C41×#407—21no—
63C41×#407C2211yescharacteristic
64C41×#407C2211yescharacteristic
65C2×C22⋊C8×C41—21no—
66C2×C22⋊C8×C41C2211yescharacteristic
67C41×#343C2211yescharacteristic, complemented
68C41×#343C2211yescharacteristic, complemented
69C41×#341C2211yescharacteristic, complemented
70C41×#341C2211yescharacteristic, complemented
71C2×#41×C41—21no—
72C2×#41×C41—21no—
73C2×#41×C41—22no—
74C2×#41×C41—22no—
75C2×#41×C41—22no—
76C2×#41×C41—22no—
77C2×#41×C41—21no—
78C2×#41×C41—21no—
79C2×#41×C41—21no—
80C2×#41×C41—21no—
81C2×#41×C41—41no—
82C2×#41×C41—41no—
83C2×#41×C41—41no—
84C2×#41×C41—41no—
85C2×#41×C41D411yescharacteristic
86C2×#41×C41D411yescharacteristic
87C2×#41×C41C2311yescharacteristic
88C2×#41×C41C2311yescharacteristic
89C22×Q8×C41D411yescharacteristic
90C22×Q8×C41C2311yescharacteristic
91C22×D4×C41—21no—
92C22×D4×C41—21no—
93C22×D4×C41—21no—
94C22×D4×C41D411yescharacteristic
95C22×D4×C41C2311yescharacteristic
96C22×D4×C41C2311yescharacteristic
97C23×C4×C41—21no—
98C23×C4×C41—21no—
99C23×C4×C41C2311yescharacteristic
100#137×C41—28no—
101#137×C41—22no—
102#137×C41—22no—
103#137×C41—22no—
104#137×C41D414yescomplemented
105AGL(1,ℤ/8)×C41—28no—
106AGL(1,ℤ/8)×C41—22no—
107AGL(1,ℤ/8)×C41—22no—
108AGL(1,ℤ/8)×C41—22no—
109AGL(1,ℤ/8)×C41—22no—
110AGL(1,ℤ/8)×C41—22no—
111AGL(1,ℤ/8)×C41—41no—
112AGL(1,ℤ/8)×C41—41no—
113AGL(1,ℤ/8)×C41D414yescomplemented
114#135×C41—28no—
115#135×C41—28no—
116C2×Q16×C41—21no—
117C2×Q16×C41—21no—
118C2×SD16×C41—21no—
119C2×SD16×C41—21no—
120C2×SD16×C41—21no—
121C2×SD16×C41—21no—
122C2×SD16×C41—22no—
123C2×SD16×C41—21no—
124C2×SD16×C41—21no—
125C2×SD16×C41—21no—
126C2×SD16×C41—21no—
127C2×SD16×C41—41no—
128C2×D8×C41—21no—
129C2×D8×C41—21no—
130C2×D8×C41—22no—
131C2×D8×C41—21no—
132C2×D8×C41—21no—
133C2×D8×C41—21no—
134C2×D8×C41—21no—
135C2×D8×C41—41no—
136#131×C41—22no—
137#131×C41—22no—
138#131×C41—41no—
139#131×C41—41no—
140C2×M16×C41—21no—
141C2×M16×C41—22no—
142C2×M16×C41—22no—
143C2×M16×C41—21no—
144C2×M16×C41—21no—
145C2×M16×C41C2311yescharacteristic
146C2×M16×C41C2311yescharacteristic
147C2×M16×C41C2311yescharacteristic
148C2×M16×C41C2311yescharacteristic
149C2×M16×C41C2311yescharacteristic
150C2×M16×C41C2311yescharacteristic
151C22×C8×C41—21no—
152C22×C8×C41—21no—
153C22×C8×C41—21no—
154C22×C8×C41C2311yescharacteristic
155C22×C8×C41C2311yescharacteristic
156#121×C41—21no—
157#121×C41—21no—
158#121×C41—21no—
159#121×C41—21no—
160C2×C4⋊C4×C41C2311yescharacteristic
161C2×C22⋊C4×C41—21no—
162#108×C41—22no—
163#108×C41—22no—
164#103×C41—21no—
165#103×C41—21no—
166#103×C41—21no—
167#103×C41—21no—
168#102×C41—21no—
169#102×C41—21no—
170#102×C41—21no—
171#102×C41—21no—
172#101×C41—22no—
173#101×C41—41no—
174#100×C41—22no—
175#100×C41—22no—
176#100×C41—22no—
177#100×C41—41no—
178C22⋊C8×C41—21no—
179C22⋊C8×C41—21no—
180C22⋊C8×C41—21no—
181C22⋊C8×C41—21no—
182C22⋊C8×C41—21no—
183C22⋊C8×C41—21no—
184C22⋊C8×C41—21no—
185C22⋊C8×C41—21no—
186C22⋊C8×C41D411yescharacteristic
187C22⋊C8×C41D411yescharacteristic
188C22⋊C8×C41D411yescharacteristic
189C22⋊C8×C41D411yescharacteristic
190C24×C41—21no—
191C24×C41—21no—
192C24×C41—21no—
193C24×C41#4111yescharacteristic
194#41×C41—21no—
195#41×C41—21no—
196#41×C41—24no—
197#41×C41—24no—
198#41×C41—22no—
199#41×C41—22no—
200#41×C41—21no—
201#41×C41—21no—
202#41×C41—21no—
203#41×C41—21no—
204#41×C41—42no—
205#41×C41—42no—
206#41×C41—41no—
207#41×C41—41no—
208#41×C41—42no—
209#41×C41—42no—
210#41×C41—42no—
211#41×C41—42no—
212#41×C41—42no—
213#41×C41—42no—
214#41×C41—42no—
215#41×C41—42no—
216#41×C41C2×D412yes—
217#41×C41C2×D412yes—
218C2×Q8×C41—21no—
219C2×Q8×C41—21no—
220C2×Q8×C41—22no—
221C2×Q8×C41—21no—
222C2×Q8×C41—21no—
223C2×Q8×C41—21no—
224C2×Q8×C41—21no—
225C2×Q8×C41—41no—
226C2×Q8×C41C2×D412yes—
227C2×Q8×C41C2×D411yescharacteristic
228C2×Q8×C41C2×D411yescharacteristic
229C2×D4×C41—21no—
230C2×D4×C41—22no—
231C2×D4×C41—21no—
232C2×D4×C41—21no—
233C2×D4×C41—21no—
234C2×D4×C41—21no—
235C2×D4×C41—21no—
236C2×D4×C41—21no—
237C2×D4×C41—21no—
238C2×D4×C41—21no—
239C2×D4×C41—21no—
240C2×D4×C41—21no—
241C2×D4×C41—21no—
242C2×D4×C41—21no—
243C2×D4×C41—21no—
244C2×D4×C41—21no—
245C2×D4×C41—21no—
246C2×D4×C41—41no—
247C2×D4×C41—42no—
248C2×D4×C41—42no—
249C2×D4×C41—42no—
250C2×D4×C41—42no—
251C2×D4×C41—41no—
252C2×D4×C41—41no—
253C2×D4×C41—41no—
254C2×D4×C41—41no—
255C2×D4×C41—82no—
256C2×D4×C41C2×D412yes—
257C2×D4×C41C2×D411yescharacteristic
258C2×D4×C41C2×D411yescharacteristic
259C22×C4×C41—21no—
260C22×C4×C41—21no—
261C22×C4×C41—21no—
262C22×C4×C41—21no—
263C22×C4×C41—21no—
264C22×C4×C41—21no—
265C22×C4×C41—21no—
266C22×C4×C41—21no—
267C22×C4×C41—21no—
268C22×C4×C41—21no—
269C22×C4×C41—21no—
270C22×C4×C41—42no—
271C22×C4×C41—42no—
272C22×C4×C41—42no—
273C22×C4×C41—42no—
274C22×C4×C41—41no—
275C22×C4×C41—41no—
276C22×C4×C41C2×D411yescharacteristic
277C22×C4×C41C2×D411yescharacteristic
278C22×C4×C41C2×D411yescharacteristic
279C22×C4×C41C2×D411yescharacteristic
280C22×C4×C41#4111yescharacteristic
281C22×C4×C41C2411yescharacteristic
282Q16×C41—24no—
283Q16×C41—24no—
284SD16×C41—24no—
285SD16×C41—24no—
286SD16×C41—24no—
287SD16×C41—24no—
288SD16×C41—42no—
289SD16×C41—42no—
290SD16×C41—42no—
291SD16×C41—42no—
292D8×C41—24no—
293D8×C41—24no—
294D8×C41—42no—
295D8×C41—42no—
296D8×C41—42no—
297D8×C41—42no—
298M16×C41—24no—
299M16×C41—21no—
300M16×C41—21no—
301M16×C41—21no—
302M16×C41—21no—
303M16×C41—21no—
304M16×C41—21no—
305M16×C41—21no—
306M16×C41—21no—
307M16×C41—21no—
308M16×C41—21no—
309M16×C41—42no—
310M16×C41—42no—
311M16×C41C2×D412yes—
312M16×C41C2×D412yes—
313C2×C8×C41—24no—
314C2×C8×C41—21no—
315C2×C8×C41—21no—
316C2×C8×C41—21no—
317C2×C8×C41—21no—
318C2×C8×C41—21no—
319C2×C8×C41—21no—
320C2×C8×C41—21no—
321C2×C8×C41—21no—
322C2×C8×C41—21no—
323C2×C8×C41—21no—
324C2×C8×C41—42no—
325C2×C8×C41—42no—
326C2×C8×C41C2×D411yescharacteristic
327C2×C8×C41C2×D411yescharacteristic
328C2×C8×C41C2×D411yescharacteristic
329C2×C8×C41C2×D411yescharacteristic
330C4⋊C4×C41—21no—
331C4⋊C4×C41—21no—
332C22⋊C4×C41—41no—
333C22⋊C4×C41—41no—
334C23×C41—21no—
335C23×C41—21no—
336C23×C41—21no—
337C23×C41—21no—
338C23×C41—22no—
339C23×C41—41no—
340C23×C41—41no—
341C23×C41—42no—
342C23×C41—42no—
343C23×C41—41no—
344C23×C41—41no—
345C23×C41—41no—
346C23×C41—41no—
347C23×C41—41no—
348C23×C41—81no—
349C23×C41—81no—
350C23×C41—81no—
351C23×C41—81no—
352C23×C41—81no—
353C23×C41#12111yescharacteristic
354C23×C41#12111yescharacteristic
355C23×C41C2×#4111yescharacteristic
356Q8×C41—21no—
357Q8×C41—21no—
358Q8×C41—22no—
359Q8×C41—21no—
360Q8×C41—22no—
361Q8×C41—42no—
362Q8×C41—41no—
363Q8×C41—41no—
364Q8×C41#12012yes—
365D4×C41—22no—
366D4×C41—22no—
367D4×C41—21no—
368D4×C41—22no—
369D4×C41—21no—
370D4×C41—21no—
371D4×C41—22no—
372D4×C41—42no—
373D4×C41—42no—
374D4×C41—42no—
375D4×C41—44no—
376D4×C41—44no—
377D4×C41—41no—
378D4×C41—41no—
379D4×C41—41no—
380D4×C41—41no—
381D4×C41—41no—
382D4×C41—41no—
383D4×C41—41no—
384D4×C41—41no—
385D4×C41—82no—
386D4×C41—82no—
387D4×C41#12012yes—
388C2×C4×C41—21no—
389C2×C4×C41—21no—
390C2×C4×C41—21no—
391C2×C4×C41—21no—
392C2×C4×C41—21no—
393C2×C4×C41—21no—
394C2×C4×C41—21no—
395C2×C4×C41—22no—
396C2×C4×C41—22no—
397C2×C4×C41—21no—
398C2×C4×C41—21no—
399C2×C4×C41—21no—
400C2×C4×C41—21no—
401C2×C4×C41—21no—
402C2×C4×C41—22no—
403C2×C4×C41—42no—
404C2×C4×C41—42no—
405C2×C4×C41—42no—
406C2×C4×C41—44no—
407C2×C4×C41—44no—
408C2×C4×C41—41no—
409C2×C4×C41—41no—
410C2×C4×C41—41no—
411C2×C4×C41—41no—
412C2×C4×C41—41no—
413C2×C4×C41—81no—
414C2×C4×C41#12111yescharacteristic
415C2×C4×C41#12111yescharacteristic
416C2×C4×C41C22×D411yescharacteristic
417C2×C4×C41C22×D411yescharacteristic
418C2×C4×C41C22×D411yescharacteristic
419C2×C4×C41C22×D411yescharacteristic
420C2×C4×C41H(5,𝔽2)11yescharacteristic
421C2×C4×C41H(5,𝔽2)11yescharacteristic
422C8×C41—22no—
423C8×C41—22no—
424C8×C41—21no—
425C8×C41—21no—
426C8×C41—21no—
427C8×C41—21no—
428C8×C41—41no—
429C8×C41—41no—
430C8×C41—41no—
431C8×C41—41no—
432#24402C4111yesmaximal, characteristic, direct product factor, Sylow
433C22×C41—21no—
434C22×C41—21no—
435C22×C41—21no—
436C22×C41—21no—
437C22×C41—22no—
438C22×C41—21no—
439C22×C41—21no—
440C22×C41—21no—
441C22×C41—21no—
442C22×C41—41no—
443C22×C41—41no—
444C22×C41—41no—
445C22×C41—42no—
446C22×C41—41no—
447C22×C41—41no—
448C22×C41—81no—
449C22×C41—81no—
450C22×C41—82no—
451C22×C41—82no—
452C22×C41—84no—
453C22×C41—81no—
454C22×C41—81no—
455C22×C41—81no—
456C22×C41—81no—
457C22×C41—81no—
458C22×C41—161no—
459C22×C41—161no—
460C22×C41C2×#12111yescharacteristic
461C22×C41#54611yescharacteristic
462C22×C41#54611yescharacteristic
463C4×C41—21no—
464C4×C41—21no—
465C4×C41—22no—
466C4×C41—41no—
467C4×C41—42no—
468C4×C41—81no—
469C4×C41C2×#12011yescharacteristic
470C4×C41#53411yescharacteristic
471C4×C41D4211yescharacteristic
472C4×C41D4211yescharacteristic
473C2×#575C2×C4111yescharacteristic, complemented
474C2×#472C2×C4111yescharacteristic, complemented
475C2×#471C2×C4111yescharacteristic, complemented
476#3006C2×C4111yescharacteristic, complemented
477C2×#449C2×C4111yescharacteristic, complemented
478#2880C2×C4111yescharacteristic, complemented
479#2052C2×C4111yescharacteristic, complemented
480#2051C2×C4111yescharacteristic, complemented
481#2019C2×C4111yescharacteristic, complemented
482#2018C2×C4111yescharacteristic, complemented
483#1908C2×C4111yescharacteristic, complemented
484#1907C2×C4111yescharacteristic, complemented
485#1900C2×C4111yescharacteristic, complemented
486#1855C2×C4111yescharacteristic, complemented
487#1785C2×C4111yescharacteristic, complemented
488C2×C41—21no—
489C2×C41—21no—
490C2×C41—41no—
491C2×C41—41no—
492C2×C41—42no—
493C2×C41—81no—
494C2×C41—82no—
495C2×C41—161no—
496C2×C41#241011yescharacteristic
497C2×C41#306711yescharacteristic
498C2×C41#306811yescharacteristic
499C22×#41C22×C4111yescharacteristic
500C22×#41C22×C4111yescharacteristic
501#575—24no—
502#575—24no—
503C2×#137—21no—
504C2×#137C22×C4111yescharacteristic
505C2×#137C22×C4111yescharacteristic
506C2×AGL(1,ℤ/8)—21no—
507C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
508C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
509C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
510C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
511C2×#135—21no—
512C2×#135—21no—
513C22×SD16C22×C4111yescharacteristic, complemented
514C22×D8C22×C4111yescharacteristic, complemented
515C2×#131C22×C4111yescharacteristic
516C2×#131C22×C4111yescharacteristic
517C22×M16C22×C4111yescharacteristic
518C2×#121C22×C4111yescharacteristic
519#472—24no—
520#471—24no—
521#449—21no—
522#449—21no—
523#449—21no—
524#449—21no—
525#449—21no—
526#449—21no—
527#448—21no—
528#447—21no—
529C2×#108C22×C4111yescharacteristic, complemented
530C2×#108C22×C4111yescharacteristic, complemented
531#417C22×C4111yescharacteristic
532#417C22×C4111yescharacteristic
533C2×#103C22×C4111yescharacteristic, complemented
534C2×#102C22×C4111yescharacteristic, complemented
535C2×#101C22×C4111yescharacteristic, complemented
536C2×#101C22×C4111yescharacteristic, complemented
537C2×#100C22×C4111yescharacteristic, complemented
538C2×#100C22×C4111yescharacteristic, complemented
539C2×#100C22×C4111yescharacteristic, complemented
540C2×#100C22×C4111yescharacteristic, complemented
541#408—21no—
542#408—21no—
543#408C22×C4111yescharacteristic
544#408C22×C4111yescharacteristic
545#407—21no—
546#407C22×C4111yescharacteristic
547#407C22×C4111yescharacteristic
548C2×C22⋊C8—21no—
549C2×C22⋊C8C22×C4111yescharacteristic
550#343C22×C4111yescharacteristic, complemented
551#343C22×C4111yescharacteristic, complemented
552#341C22×C4111yescharacteristic, complemented
553#341C22×C4111yescharacteristic, complemented
554C41#2440211yescharacteristic, direct product factor, Sylow
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C4111yescharacteristic
570C2×#41D4×C4111yescharacteristic
571C2×#41C23×C4111yescharacteristic
572C2×#41C23×C4111yescharacteristic
573C22×Q8D4×C4111yescharacteristic
574C22×Q8C23×C4111yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C4111yescharacteristic
579C22×D4C23×C4111yescharacteristic
580C22×D4C23×C4111yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C23×C4111yescharacteristic
584#137—28no—
585#137—22no—
586#137—22no—
587#137—22no—
588#137D4×C4114yescomplemented
589AGL(1,ℤ/8)—28no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—22no—
595AGL(1,ℤ/8)—41no—
596AGL(1,ℤ/8)—41no—
597AGL(1,ℤ/8)D4×C4114yescomplemented
598#135—28no—
599#135—28no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—22no—
607C2×SD16—21no—
608C2×SD16—21no—
609C2×SD16—21no—
610C2×SD16—21no—
611C2×SD16—41no—
612C2×D8—21no—
613C2×D8—21no—
614C2×D8—22no—
615C2×D8—21no—
616C2×D8—21no—
617C2×D8—21no—
618C2×D8—21no—
619C2×D8—41no—
620#131—22no—
621#131—22no—
622#131—41no—
623#131—41no—
624C2×M16—21no—
625C2×M16—22no—
626C2×M16—22no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16C23×C4111yescharacteristic
630C2×M16C23×C4111yescharacteristic
631C2×M16C23×C4111yescharacteristic
632C2×M16C23×C4111yescharacteristic
633C2×M16C23×C4111yescharacteristic
634C2×M16C23×C4111yescharacteristic
635C22×C8—21no—
636C22×C8—21no—
637C22×C8—21no—
638C22×C8C23×C4111yescharacteristic
639C22×C8C23×C4111yescharacteristic
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644C2×C4⋊C4C23×C4111yescharacteristic
645C2×C22⋊C4—21no—
646#108—22no—
647#108—22no—
648#103—21no—
649#103—21no—
650#103—21no—
651#103—21no—
652#102—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#101—22no—
657#101—41no—
658#100—22no—
659#100—22no—
660#100—22no—
661#100—41no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8D4×C4111yescharacteristic
671C22⋊C8D4×C4111yescharacteristic
672C22⋊C8D4×C4111yescharacteristic
673C22⋊C8D4×C4111yescharacteristic
674C24—21no—
675C24—21no—
676C24—21no—
677C24#41×C4111yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×D4×C4112yes—
701#41C2×D4×C4112yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×D4×C4112yes—
711C2×Q8C2×D4×C4111yescharacteristic
712C2×Q8C2×D4×C4111yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—82no—
740C2×D4C2×D4×C4112yes—
741C2×D4C2×D4×C4111yescharacteristic
742C2×D4C2×D4×C4111yescharacteristic
743C22×C4—21no—
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—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4C2×D4×C4111yescharacteristic
761C22×C4C2×D4×C4111yescharacteristic
762C22×C4C2×D4×C4111yescharacteristic
763C22×C4C2×D4×C4111yescharacteristic
764C22×C4#41×C4111yescharacteristic
765C22×C4C24×C4111yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776D8—24no—
777D8—24no—
778D8—42no—
779D8—42no—
780D8—42no—
781D8—42no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—21no—
786M16—21no—
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—42no—
794M16—42no—
795M16C2×D4×C4112yes—
796M16C2×D4×C4112yes—
797C2×C8—24no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—42no—
809C2×C8—42no—
810C2×C8C2×D4×C4111yescharacteristic
811C2×C8C2×D4×C4111yescharacteristic
812C2×C8C2×D4×C4111yescharacteristic
813C2×C8C2×D4×C4111yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—21no—
816C22⋊C4—41no—
817C22⋊C4—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23#121×C4111yescharacteristic
838C23#121×C4111yescharacteristic
839C23C2×#41×C4111yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8#120×C4112yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—22no—
853D4—21no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—41no—
866D4—41no—
867D4—41no—
868D4—41no—
869D4—82no—
870D4—82no—
871D4#120×C4112yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4#121×C4111yescharacteristic
899C2×C4#121×C4111yescharacteristic
900C2×C4C22×D4×C4111yescharacteristic
901C2×C4C22×D4×C4111yescharacteristic
902C2×C4C22×D4×C4111yescharacteristic
903C2×C4C22×D4×C4111yescharacteristic
904C2×C4H(5,𝔽2)×C4111yescharacteristic
905C2×C4H(5,𝔽2)×C4111yescharacteristic
906C8—22no—
907C8—22no—
908C8—21no—
909C8—21no—
910C8—21no—
911C8—21no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—41no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—42no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—161no—
942C22—161no—
943C22C2×#121×C4111yescharacteristic
944C22C41×#54611yescharacteristic
945C22C41×#54611yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—41no—
950C4—42no—
951C4—81no—
952C4C2×#120×C4111yescharacteristic
953C4C41×#53411yescharacteristic
954C4D42×C4111yescharacteristic
955C4D42×C4111yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2C41×#241011yescharacteristic
965C2C41×#306711yescharacteristic
966C2C41×#306811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
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. C2×C41×#575C2semidirect
2. C2×C41×#472C2semidirect
3. C2×C41×#471C2semidirect
4. C41×#3006C2semidirect
5. C2×C41×#449C2semidirect
6. C41×#2880C2semidirect
7. C41×#2052C2semidirect
8. C41×#2051C2semidirect
9. C41×#2019C2semidirect
10. C41×#2018C2semidirect
11. C41×#1908C2semidirect
12. C41×#1907C2semidirect
13. C41×#1900C2semidirect
14. C41×#1855C2semidirect
15. C41×#1785C2semidirect
30. C22×SD16×C41C22semidirect
31. C22×D8×C41C22semidirect
46. C2×#108×C41C22semidirect
47. C2×#108×C41C22semidirect
50. C2×#103×C41C22semidirect
51. C2×#102×C41C22semidirect
52. C2×#101×C41C22semidirect
53. C2×#101×C41C22semidirect
54. C2×#100×C41C22semidirect
55. C2×#100×C41C22semidirect
56. C2×#100×C41C22semidirect
57. C2×#100×C41C22semidirect
67. C41×#343C22semidirect
68. C41×#343C22semidirect
69. C41×#341C22semidirect
70. C41×#341C22semidirect
104. #137×C41D4semidirect
113. AGL(1,ℤ/8)×C41D4semidirect
432. #24402C41direct (N × H)
473. C2×#575C2×C41semidirect
474. C2×#472C2×C41semidirect
475. C2×#471C2×C41semidirect
476. #3006C2×C41semidirect
477. C2×#449C2×C41semidirect
478. #2880C2×C41semidirect
479. #2052C2×C41semidirect
480. #2051C2×C41semidirect
481. #2019C2×C41semidirect
482. #2018C2×C41semidirect
483. #1908C2×C41semidirect
484. #1907C2×C41semidirect
485. #1900C2×C41semidirect
486. #1855C2×C41semidirect
487. #1785C2×C41semidirect
513. C22×SD16C22×C41semidirect
514. C22×D8C22×C41semidirect
529. C2×#108C22×C41semidirect
530. C2×#108C22×C41semidirect
533. C2×#103C22×C41semidirect
534. C2×#102C22×C41semidirect
535. C2×#101C22×C41semidirect
536. C2×#101C22×C41semidirect
537. C2×#100C22×C41semidirect
538. C2×#100C22×C41semidirect
539. C2×#100C22×C41semidirect
540. C2×#100C22×C41semidirect
550. #343C22×C41semidirect
551. #343C22×C41semidirect
552. #341C22×C41semidirect
553. #341C22×C41semidirect
554. C41#24402direct (N × H)
588. #137D4×C41semidirect
597. AGL(1,ℤ/8)D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5752
C2×C41×#4722
C2×C41×#4712
C41×#30062
C2×C41×#4492
C41×#28802
C41×#20522
C41×#20512
C41×#20192
C41×#20182
C41×#19082
C41×#19072
C41×#19002
C41×#18552
C41×#17852
#2440241