Finite Group Databasebeta

← C41×#24428 #23800629

Subgroups — C41×#24428 #23800629

Order 10496.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#546C211yesmaximal, characteristic, complemented
2C2×C41×#466C211yesmaximal, characteristic, complemented
3C2×C41×#449C211yesmaximal, characteristic, complemented
4C2×C41×#447C211yesmaximal, characteristic, complemented
5C2×C41×#416C211yesmaximal, characteristic, complemented
6C41×#2414C211yesmaximal, characteristic, complemented
7C41×#2042C211yesmaximal, characteristic, complemented
8C41×#2036C211yesmaximal, characteristic, complemented
9C41×#2012C211yesmaximal, characteristic, complemented
10C41×#2000C211yesmaximal, characteristic, complemented
11C41×#1879C211yesmaximal, characteristic, complemented
12C41×#1875C211yesmaximal, characteristic, complemented
13C41×#1869C211yesmaximal, characteristic, complemented
14C41×#1862C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C23×D4×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic, complemented
19C22×D8×C41C2211yescharacteristic
20C22×D8×C41C2211yescharacteristic
21C23×C8×C41C2211yescharacteristic, complemented
22C41×#546—24no—
23C41×#546—24no—
24C2×#124×C41C2211yescharacteristic
25C2×#123×C41—21no—
26C2×C22⋊Q8×C41C2211yescharacteristic
27C2×#121×C41—21no—
28C2×#121×C41C2211yescharacteristic
29C2×#121×C41C2211yescharacteristic
30C2×#121×C41C2211yescharacteristic, complemented
31C2×#120×C41—21no—
32C2×C4×D4×C41C2211yescharacteristic
33C2×C4×D4×C41C2211yescharacteristic
34C2×#117×C41C2211yescharacteristic, complemented
35C22×C22⋊C4×C41—21no—
36C41×#466—24no—
37C41×#449—24no—
38C41×#447—24no—
39C2×#107×C41C2211yescharacteristic, complemented
40C41×#416—24no—
41C2×#103×C41C2211yescharacteristic, complemented
42C2×#103×C41C2211yescharacteristic, complemented
43C2×#103×C41C2211yescharacteristic, complemented
44C2×#102×C41C2211yescharacteristic
45C2×#102×C41C2211yescharacteristic
46C2×#102×C41C2211yescharacteristic
47C2×#102×C41C2211yescharacteristic
48C2×#102×C41C2211yescharacteristic
49C2×#102×C41C2211yescharacteristic
50C2×#102×C41C2211yescharacteristic, complemented
51C2×C22⋊C8×C41C2211yescharacteristic
52C2×C22⋊C8×C41C2211yescharacteristic
53C2×C22⋊C8×C41C2211yescharacteristic, complemented
54C41×#394—21no—
55C41×#392—21no—
56C41×#390—21no—
57C41×#390C2211yescharacteristic, complemented
58C41×#389C2211yescharacteristic, complemented
59C41×#388—21no—
60C41×#380C2211yescharacteristic
61C41×#340C2211yescharacteristic, complemented
62C41×#340C2211yescharacteristic, complemented
63C41×#336C2211yescharacteristic, complemented
64C41×#336C2211yescharacteristic, complemented
65C25×C41—21no—
66C2×#41×C41—22no—
67C2×#41×C41—22no—
68C2×#41×C41—22no—
69C2×#41×C41—41no—
70C2×#41×C41—41no—
71C2×#41×C41D414yescomplemented
72C22×Q8×C41C2311yescharacteristic
73C22×D4×C41—21no—
74C22×D4×C41—21no—
75C22×D4×C41—22no—
76C22×D4×C41—22no—
77C22×D4×C41—22no—
78C22×D4×C41—22no—
79C22×D4×C41—21no—
80C22×D4×C41—21no—
81C22×D4×C41—21no—
82C22×D4×C41—41no—
83C22×D4×C41—41no—
84C22×D4×C41D411yescharacteristic
85C22×D4×C41C2311yescharacteristic
86C22×D4×C41C2311yescharacteristic
87C22×D4×C41C2311yescharacteristic
88C23×C4×C41—21no—
89C23×C4×C41—21no—
90C23×C4×C41C2311yescharacteristic
91C23×C4×C41C2311yescharacteristic
92C2×SD16×C41—22no—
93C2×SD16×C41—41no—
94C2×SD16×C41—41no—
95C2×D8×C41—22no—
96C2×D8×C41—22no—
97C2×D8×C41—22no—
98C2×D8×C41—22no—
99C2×D8×C41—22no—
100C2×D8×C41—41no—
101C22×C8×C41—22no—
102C22×C8×C41—22no—
103C22×C8×C41—41no—
104C22×C8×C41C2311yescharacteristic
105C22×C8×C41C2311yescharacteristic
106C22×C8×C41C2311yescharacteristic
107C22×C8×C41C2311yescharacteristic
108#124×C41—22no—
109#124×C41—22no—
110#123×C41—28no—
111C22⋊Q8×C41—22no—
112C22⋊Q8×C41—22no—
113#121×C41—28no—
114#121×C41—22no—
115#121×C41—22no—
116#121×C41—22no—
117#121×C41—22no—
118#121×C41—41no—
119#121×C41D414yescomplemented
120#120×C41—28no—
121C4×D4×C41—22no—
122C4×D4×C41—22no—
123C4×D4×C41—22no—
124C4×D4×C41—22no—
125#117×C41—22no—
126#117×C41—41no—
127C2×C4⋊C4×C41—21no—
128C2×C4⋊C4×C41—21no—
129C2×C4⋊C4×C41D411yescharacteristic
130C2×C4⋊C4×C41C2311yescharacteristic
131C2×C4⋊C4×C41C2311yescharacteristic
132C2×C4⋊C4×C41C2311yescharacteristic
133C2×C4⋊C4×C41C2311yescharacteristic
134C2×C22⋊C4×C41—28no—
135C2×C22⋊C4×C41—21no—
136C2×C22⋊C4×C41—21no—
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×C41D411yescharacteristic
147C2×C22⋊C4×C41D411yescharacteristic
148C2×C42×C41—21no—
149C2×C42×C41C2311yescharacteristic
150#107×C41—22no—
151#103×C41—22no—
152#103×C41—22no—
153#103×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—
166C24×C41—21no—
167C24×C41—24no—
168C24×C41—21no—
169C24×C41—21no—
170C24×C41—42no—
171C24×C41—42no—
172C24×C41—42no—
173C24×C41—42no—
174C24×C41—81no—
175C24×C41—81no—
176C24×C41C2×D411yescharacteristic
177C24×C41C2×D411yescharacteristic
178#41×C41—28no—
179#41×C41—44no—
180#41×C41—44no—
181#41×C41—44no—
182C2×Q8×C41—21no—
183C2×Q8×C41—21no—
184C2×Q8×C41—21no—
185C2×Q8×C41—21no—
186C2×Q8×C41—21no—
187C2×Q8×C41C2×D412yes—
188C2×D4×C41—24no—
189C2×D4×C41—22no—
190C2×D4×C41—24no—
191C2×D4×C41—22no—
192C2×D4×C41—24no—
193C2×D4×C41—21no—
194C2×D4×C41—21no—
195C2×D4×C41—21no—
196C2×D4×C41—21no—
197C2×D4×C41—21no—
198C2×D4×C41—21no—
199C2×D4×C41—21no—
200C2×D4×C41—21no—
201C2×D4×C41—21no—
202C2×D4×C41—21no—
203C2×D4×C41—21no—
204C2×D4×C41—21no—
205C2×D4×C41—21no—
206C2×D4×C41—21no—
207C2×D4×C41—41no—
208C2×D4×C41—42no—
209C2×D4×C41—42no—
210C2×D4×C41—42no—
211C2×D4×C41—44no—
212C2×D4×C41—44no—
213C2×D4×C41—44no—
214C2×D4×C41—42no—
215C2×D4×C41—42no—
216C2×D4×C41—44no—
217C2×D4×C41—42no—
218C2×D4×C41—42no—
219C2×D4×C41—81no—
220C2×D4×C41—81no—
221C2×D4×C41—81no—
222C2×D4×C41—81no—
223C2×D4×C41—81no—
224C2×D4×C41C2×D412yes—
225C2×D4×C41C2×D412yes—
226C2×D4×C41C2×D412yes—
227C2×D4×C41#4112yes—
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—24no—
236C22×C4×C41—24no—
237C22×C4×C41—21no—
238C22×C4×C41—21no—
239C22×C4×C41—21no—
240C22×C4×C41—21no—
241C22×C4×C41—21no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—42no—
246C22×C4×C41—42no—
247C22×C4×C41—81no—
248C22×C4×C41—81no—
249C22×C4×C41C2×D411yescharacteristic
250C22×C4×C41C2×D411yescharacteristic
251C22×C4×C41C2×D411yescharacteristic
252C22×C4×C41C2×D411yescharacteristic
253C22×C4×C41C2×D412yes—
254C22×C4×C41C2×D412yes—
255C22×C4×C41C2411yescharacteristic
256SD16×C41—44no—
257D8×C41—44no—
258D8×C41—44no—
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×C41—21no—
268C2×C8×C41—21no—
269C2×C8×C41—21no—
270C2×C8×C41—44no—
271C2×C8×C41C2×D412yes—
272C4⋊C4×C41—24no—
273C4⋊C4×C41—22no—
274C4⋊C4×C41—21no—
275C4⋊C4×C41—21no—
276C4⋊C4×C41—21no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—21no—
280C4⋊C4×C41—81no—
281C4⋊C4×C41C2×D412yes—
282C4⋊C4×C41C2×D412yes—
283C22⋊C4×C41—24no—
284C22⋊C4×C41—24no—
285C22⋊C4×C41—24no—
286C22⋊C4×C41—24no—
287C22⋊C4×C41—22no—
288C22⋊C4×C41—22no—
289C22⋊C4×C41—24no—
290C22⋊C4×C41—42no—
291C22⋊C4×C41—42no—
292C22⋊C4×C41—42no—
293C22⋊C4×C41—42no—
294C22⋊C4×C41—81no—
295C22⋊C4×C41—81no—
296C42×C41—21no—
297C42×C41—21no—
298C42×C41—42no—
299C23×C41—21no—
300C23×C41—22no—
301C23×C41—21no—
302C23×C41—21no—
303C23×C41—22no—
304C23×C41—21no—
305C23×C41—21no—
306C23×C41—22no—
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—48no—
316C23×C41—48no—
317C23×C41—41no—
318C23×C41—41no—
319C23×C41—41no—
320C23×C41—41no—
321C23×C41—41no—
322C23×C41—41no—
323C23×C41—41no—
324C23×C41—41no—
325C23×C41—41no—
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—84no—
335C23×C41—84no—
336C23×C41—84no—
337C23×C41—84no—
338C23×C41—84no—
339C23×C41#12012yes—
340C23×C41#13512yes—
341C23×C41C22×D411yescharacteristic
342Q8×C41—22no—
343Q8×C41—22no—
344Q8×C41—41no—
345Q8×C41—41no—
346D4×C41—22no—
347D4×C41—22no—
348D4×C41—22no—
349D4×C41—22no—
350D4×C41—22no—
351D4×C41—44no—
352D4×C41—48no—
353D4×C41—48no—
354D4×C41—41no—
355D4×C41—41no—
356D4×C41—41no—
357D4×C41—41no—
358D4×C41—41no—
359D4×C41—41no—
360D4×C41—84no—
361D4×C41—84no—
362D4×C41—84no—
363D4×C41#12114yes—
364C2×C4×C41—21no—
365C2×C4×C41—21no—
366C2×C4×C41—22no—
367C2×C4×C41—22no—
368C2×C4×C41—22no—
369C2×C4×C41—22no—
370C2×C4×C41—21no—
371C2×C4×C41—21no—
372C2×C4×C41—22no—
373C2×C4×C41—22no—
374C2×C4×C41—21no—
375C2×C4×C41—22no—
376C2×C4×C41—21no—
377C2×C4×C41—21no—
378C2×C4×C41—21no—
379C2×C4×C41—21no—
380C2×C4×C41—21no—
381C2×C4×C41—21no—
382C2×C4×C41—48no—
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—41no—
392C2×C4×C41—41no—
393C2×C4×C41—41no—
394C2×C4×C41—41no—
395C2×C4×C41—41no—
396C2×C4×C41—41no—
397C2×C4×C41—41no—
398C2×C4×C41—41no—
399C2×C4×C41—84no—
400C2×C4×C41#12012yes—
401C2×C4×C41C22×D411yescharacteristic
402C2×C4×C41C22×D411yescharacteristic
403C2×C4×C41C22×D411yescharacteristic
404C2×C4×C41C2×#4111yescharacteristic
405C2×C4×C41H(5,𝔽2)11yescharacteristic
406C2×C4×C41H(5,𝔽2)11yescharacteristic
407C8×C41—22no—
408C8×C41—41no—
409C8×C41—41no—
410C8×C41—41no—
411#24428C4111yesmaximal, characteristic, direct product factor, Sylow
412C22×C41—22no—
413C22×C41—24no—
414C22×C41—22no—
415C22×C41—22no—
416C22×C41—22no—
417C22×C41—22no—
418C22×C41—22no—
419C22×C41—41no—
420C22×C41—42no—
421C22×C41—42no—
422C22×C41—41no—
423C22×C41—41no—
424C22×C41—41no—
425C22×C41—42no—
426C22×C41—41no—
427C22×C41—42no—
428C22×C41—41no—
429C22×C41—42no—
430C22×C41—41no—
431C22×C41—41no—
432C22×C41—42no—
433C22×C41—42no—
434C22×C41—42no—
435C22×C41—42no—
436C22×C41—816no—
437C22×C41—81no—
438C22×C41—81no—
439C22×C41—81no—
440C22×C41—81no—
441C22×C41—81no—
442C22×C41—81no—
443C22×C41—81no—
444C22×C41—81no—
445C22×C41—81no—
446C22×C41—81no—
447C22×C41—81no—
448C22×C41C2×#12011yescharacteristic
449C22×C41D4211yescharacteristic
450C22×C41#54611yescharacteristic
451C22×C41C2×#13511yescharacteristic
452C22×C41#57511yescharacteristic
453C22×C41#57611yescharacteristic
454C22×C41#57611yescharacteristic
455C4×C41—22no—
456C4×C41—41no—
457C4×C41—42no—
458C4×C41—41no—
459C4×C41—41no—
460C4×C41—42no—
461C4×C41—42no—
462C4×C41—81no—
463C4×C41—81no—
464C4×C41C2×#12111yescharacteristic
465C4×C41#53411yescharacteristic
466C4×C41D4211yescharacteristic
467C4×C41#54611yescharacteristic
468C2×#546C2×C4111yescharacteristic, complemented
469C2×#466C2×C4111yescharacteristic, complemented
470C2×#449C2×C4111yescharacteristic, complemented
471C2×#447C2×C4111yescharacteristic, complemented
472C2×#416C2×C4111yescharacteristic, complemented
473#2414C2×C4111yescharacteristic, complemented
474#2042C2×C4111yescharacteristic, complemented
475#2036C2×C4111yescharacteristic, complemented
476#2012C2×C4111yescharacteristic, complemented
477#2000C2×C4111yescharacteristic, complemented
478#1879C2×C4111yescharacteristic, complemented
479#1875C2×C4111yescharacteristic, complemented
480#1869C2×C4111yescharacteristic, complemented
481#1862C2×C4111yescharacteristic, complemented
482#1786C2×C4111yescharacteristic, complemented
483C2×C41—42no—
484C2×C41—42no—
485C2×C41—44no—
486C2×C41—82no—
487C2×C41—161no—
488C2×C41#241011yescharacteristic
489C2×C41#300211yescharacteristic
490C2×C41#300811yescharacteristic
491C2×C41#326811yescharacteristic
492C2×C41#328011yescharacteristic
493C2×C41#329711yescharacteristic
494C2×C41#331911yescharacteristic
495C22×#41C22×C4111yescharacteristic
496C23×D4C22×C4111yescharacteristic
497C22×SD16C22×C4111yescharacteristic, complemented
498C22×D8C22×C4111yescharacteristic
499C22×D8C22×C4111yescharacteristic
500C23×C8C22×C4111yescharacteristic, complemented
501#546—24no—
502#546—24no—
503C2×#124C22×C4111yescharacteristic
504C2×#123—21no—
505C2×C22⋊Q8C22×C4111yescharacteristic
506C2×#121—21no—
507C2×#121C22×C4111yescharacteristic
508C2×#121C22×C4111yescharacteristic
509C2×#121C22×C4111yescharacteristic, complemented
510C2×#120—21no—
511C2×C4×D4C22×C4111yescharacteristic
512C2×C4×D4C22×C4111yescharacteristic
513C2×#117C22×C4111yescharacteristic, complemented
514C22×C22⋊C4—21no—
515#466—24no—
516#449—24no—
517#447—24no—
518C2×#107C22×C4111yescharacteristic, complemented
519#416—24no—
520C2×#103C22×C4111yescharacteristic, complemented
521C2×#103C22×C4111yescharacteristic, complemented
522C2×#103C22×C4111yescharacteristic, complemented
523C2×#102C22×C4111yescharacteristic
524C2×#102C22×C4111yescharacteristic
525C2×#102C22×C4111yescharacteristic
526C2×#102C22×C4111yescharacteristic
527C2×#102C22×C4111yescharacteristic
528C2×#102C22×C4111yescharacteristic
529C2×#102C22×C4111yescharacteristic, complemented
530C2×C22⋊C8C22×C4111yescharacteristic
531C2×C22⋊C8C22×C4111yescharacteristic
532C2×C22⋊C8C22×C4111yescharacteristic, complemented
533#394—21no—
534#392—21no—
535#390—21no—
536#390C22×C4111yescharacteristic, complemented
537#389C22×C4111yescharacteristic, complemented
538#388—21no—
539#380C22×C4111yescharacteristic
540#340C22×C4111yescharacteristic, complemented
541#340C22×C4111yescharacteristic, complemented
542#336C22×C4111yescharacteristic, complemented
543#336C22×C4111yescharacteristic, complemented
544C41#2442811yescharacteristic, direct product factor, Sylow
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41D4×C4114yescomplemented
552C22×Q8C23×C4111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C4111yescharacteristic
565C22×D4C23×C4111yescharacteristic
566C22×D4C23×C4111yescharacteristic
567C22×D4C23×C4111yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C23×C4111yescharacteristic
571C23×C4C23×C4111yescharacteristic
572C2×SD16—22no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C4111yescharacteristic
585C22×C8C23×C4111yescharacteristic
586C22×C8C23×C4111yescharacteristic
587C22×C8C23×C4111yescharacteristic
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—41no—
599#121D4×C4114yescomplemented
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—22no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C4111yescharacteristic
610C2×C4⋊C4C23×C4111yescharacteristic
611C2×C4⋊C4C23×C4111yescharacteristic
612C2×C4⋊C4C23×C4111yescharacteristic
613C2×C4⋊C4C23×C4111yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C4111yescharacteristic
627C2×C22⋊C4D4×C4111yescharacteristic
628C2×C42—21no—
629C2×C42C23×C4111yescharacteristic
630#107—22no—
631#103—22no—
632#103—22no—
633#103—22no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102D4×C4114yescomplemented
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C4111yescharacteristic
657C24C2×D4×C4111yescharacteristic
658#41—28no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C4112yes—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C4112yes—
705C2×D4C2×D4×C4112yes—
706C2×D4C2×D4×C4112yes—
707C2×D4#41×C4112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C4111yescharacteristic
730C22×C4C2×D4×C4111yescharacteristic
731C22×C4C2×D4×C4111yescharacteristic
732C22×C4C2×D4×C4111yescharacteristic
733C22×C4C2×D4×C4112yes—
734C22×C4C2×D4×C4112yes—
735C22×C4C24×C4111yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—44no—
751C2×C8C2×D4×C4112yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C4112yes—
762C4⋊C4C2×D4×C4112yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—24no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—48no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#120×C4112yes—
820C23#135×C4112yes—
821C23C22×D4×C4111yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4#121×C4114yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4#120×C4112yes—
881C2×C4C22×D4×C4111yescharacteristic
882C2×C4C22×D4×C4111yescharacteristic
883C2×C4C22×D4×C4111yescharacteristic
884C2×C4C2×#41×C4111yescharacteristic
885C2×C4H(5,𝔽2)×C4111yescharacteristic
886C2×C4H(5,𝔽2)×C4111yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—22no—
893C22—24no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—42no—
910C22—41no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C4111yescharacteristic
928C22D42×C4111yescharacteristic
929C22C41×#54611yescharacteristic
930C22C2×#135×C4111yescharacteristic
931C22C41×#57511yescharacteristic
932C22C41×#57611yescharacteristic
933C22C41×#57611yescharacteristic
934C4—22no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×#121×C4111yescharacteristic
944C4C41×#53411yescharacteristic
945C4D42×C4111yescharacteristic
946C4C41×#54611yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—161no—
952C2C41×#241011yescharacteristic
953C2C41×#300211yescharacteristic
954C2C41×#300811yescharacteristic
955C2C41×#326811yescharacteristic
956C2C41×#328011yescharacteristic
957C2C41×#329711yescharacteristic
958C2C41×#331911yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
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
1. C2×C41×#546C2semidirect
2. C2×C41×#466C2semidirect
3. C2×C41×#449C2semidirect
4. C2×C41×#447C2semidirect
5. C2×C41×#416C2semidirect
6. C41×#2414C2semidirect
7. C41×#2042C2semidirect
8. C41×#2036C2semidirect
9. C41×#2012C2semidirect
10. C41×#2000C2semidirect
11. C41×#1879C2semidirect
12. C41×#1875C2semidirect
13. C41×#1869C2semidirect
14. C41×#1862C2semidirect
15. C41×#1786C2semidirect
18. C22×SD16×C41C22semidirect
21. C23×C8×C41C22semidirect
30. C2×#121×C41C22semidirect
34. C2×#117×C41C22semidirect
39. C2×#107×C41C22semidirect
41. C2×#103×C41C22semidirect
42. C2×#103×C41C22semidirect
43. C2×#103×C41C22semidirect
50. C2×#102×C41C22semidirect
53. C2×C22⋊C8×C41C22semidirect
57. C41×#390C22semidirect
58. C41×#389C22semidirect
61. C41×#340C22semidirect
62. C41×#340C22semidirect
63. C41×#336C22semidirect
64. C41×#336C22semidirect
71. C2×#41×C41D4semidirect
119. #121×C41D4semidirect
160. #102×C41D4semidirect
411. #24428C41direct (N × H)
468. C2×#546C2×C41semidirect
469. C2×#466C2×C41semidirect
470. C2×#449C2×C41semidirect
471. C2×#447C2×C41semidirect
472. C2×#416C2×C41semidirect
473. #2414C2×C41semidirect
474. #2042C2×C41semidirect
475. #2036C2×C41semidirect
476. #2012C2×C41semidirect
477. #2000C2×C41semidirect
478. #1879C2×C41semidirect
479. #1875C2×C41semidirect
480. #1869C2×C41semidirect
481. #1862C2×C41semidirect
482. #1786C2×C41semidirect
497. C22×SD16C22×C41semidirect
500. C23×C8C22×C41semidirect
509. C2×#121C22×C41semidirect
513. C2×#117C22×C41semidirect
518. C2×#107C22×C41semidirect
520. C2×#103C22×C41semidirect
521. C2×#103C22×C41semidirect
522. C2×#103C22×C41semidirect
529. C2×#102C22×C41semidirect
532. C2×C22⋊C8C22×C41semidirect
536. #390C22×C41semidirect
537. #389C22×C41semidirect
540. #340C22×C41semidirect
541. #340C22×C41semidirect
542. #336C22×C41semidirect
543. #336C22×C41semidirect
544. C41#24428direct (N × H)
551. C2×#41D4×C41semidirect
599. #121D4×C41semidirect
640. #102D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5462
C2×C41×#4662
C2×C41×#4492
C2×C41×#4472
C2×C41×#4162
C41×#24142
C41×#20422
C41×#20362
C41×#20122
C41×#20002
C41×#18792
C41×#18752
C41×#18692
C41×#18622
C41×#17862
#2442841