Finite Group Databasebeta

← C41×#24390 #23800591

Subgroups — C41×#24390 #23800591

Order 10496.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#535C211yesmaximal, characteristic, complemented
2C2×C41×#469C211yesmaximal, characteristic, complemented
3C2×C41×#466C211yesmaximal, characteristic, complemented
4C2×C41×#447C211yesmaximal, characteristic, complemented
5C2×C41×#408C211yesmaximal, characteristic, complemented
6C41×#2615C211yesmaximal, characteristic, complemented
7C41×#2034C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#1999C211yesmaximal, characteristic, complemented
10C41×#1999C211yesmaximal, characteristic, complemented
11C41×#1895C211yesmaximal, characteristic, complemented
12C41×#1893C211yesmaximal, characteristic, complemented
13C41×#1875C211yesmaximal, characteristic, complemented
14C41×#1854C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C23×D4×C41C2211yescharacteristic
18C22×D8×C41C2211yescharacteristic
19C22×D8×C41C2211yescharacteristic
20C22×M16×C41C2211yescharacteristic, complemented
21C23×C8×C41C2211yescharacteristic, complemented
22C41×#535—24no—
23C41×#535—24no—
24C2×#127×C41—21no—
25C2×#124×C41—21no—
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×#121×C41C2211yescharacteristic
29C2×#121×C41C2211yescharacteristic
30C2×#121×C41C2211yescharacteristic
31C2×#121×C41C2211yescharacteristic, complemented
32C2×#121×C41C2211yescharacteristic, complemented
33C2×#120×C41—21no—
34C2×#120×C41—21no—
35C2×#117×C41C2211yescharacteristic
36C41×#469—24no—
37C41×#466—24no—
38C41×#447—24no—
39C2×#107×C41C2211yescharacteristic, complemented
40C2×#106×C41C2211yescharacteristic, complemented
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×#102×C41C2211yescharacteristic
46C2×#102×C41C2211yescharacteristic
47C2×#102×C41C2211yescharacteristic, complemented
48C2×#102×C41C2211yescharacteristic, complemented
49C41×#408—24no—
50C2×C22⋊C8×C41C2211yescharacteristic
51C2×C22⋊C8×C41C2211yescharacteristic
52C2×C22⋊C8×C41C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic, complemented
54C41×#393—21no—
55C41×#392—21no—
56C41×#392—21no—
57C41×#392—21no—
58C41×#380C2211yescharacteristic
59C41×#380C2211yescharacteristic, complemented
60C41×#380C2211yescharacteristic, complemented
61C41×#340C2211yescharacteristic, complemented
62C41×#340C2211yescharacteristic, complemented
63C41×#340C2211yescharacteristic, complemented
64C41×#340C2211yescharacteristic, complemented
65C25×C41—21no—
66C2×#41×C41—22no—
67C2×#41×C41—22no—
68C2×#41×C41—22no—
69C2×#41×C41—22no—
70C2×#41×C41—41no—
71C2×#41×C41—41no—
72C22×Q8×C41D411yescharacteristic
73C22×D4×C41—21no—
74C22×D4×C41—21no—
75C22×D4×C41—21no—
76C22×D4×C41—21no—
77C22×D4×C41—22no—
78C22×D4×C41—22no—
79C22×D4×C41—21no—
80C22×D4×C41—21no—
81C22×D4×C41—21no—
82C22×D4×C41—21no—
83C22×D4×C41—22no—
84C22×D4×C41—22no—
85C22×D4×C41—41no—
86C22×D4×C41—41no—
87C22×D4×C41D411yescharacteristic
88C22×D4×C41D411yescharacteristic
89C22×D4×C41D411yescharacteristic
90C22×D4×C41C2311yescharacteristic
91C22×D4×C41C2311yescharacteristic
92C22×D4×C41C2311yescharacteristic
93C23×C4×C41C2311yescharacteristic
94C23×C4×C41C2311yescharacteristic
95C23×C4×C41C2311yescharacteristic
96C2×D8×C41—22no—
97C2×D8×C41—22no—
98C2×D8×C41—22no—
99C2×D8×C41—22no—
100C2×D8×C41—41no—
101C2×D8×C41—41no—
102C2×M16×C41—22no—
103C2×M16×C41—22no—
104C2×M16×C41—41no—
105C22×C8×C41—22no—
106C22×C8×C41—22no—
107C22×C8×C41—41no—
108C22×C8×C41C2311yescharacteristic
109C22×C8×C41C2311yescharacteristic
110C22×C8×C41C2311yescharacteristic
111C22×C8×C41C2311yescharacteristic
112#127×C41—28no—
113#124×C41—28no—
114#121×C41—22no—
115#121×C41—22no—
116#121×C41—22no—
117#121×C41—22no—
118#121×C41—22no—
119#121×C41—22no—
120#121×C41—22no—
121#121×C41—22no—
122#121×C41—22no—
123#121×C41—22no—
124#121×C41—41no—
125#121×C41—41no—
126#121×C41D414yescomplemented
127#121×C41D414yescomplemented
128#120×C41—28no—
129#120×C41—28no—
130#117×C41—22no—
131#117×C41—22no—
132C2×C4⋊C4×C41C2311yescharacteristic
133C2×C4⋊C4×C41C2311yescharacteristic
134C2×C4⋊C4×C41C2311yescharacteristic
135C2×C4⋊C4×C41C2311yescharacteristic
136C2×C4⋊C4×C41C2311yescharacteristic
137C2×C22⋊C4×C41—21no—
138C2×C22⋊C4×C41—21no—
139C2×C22⋊C4×C41—21no—
140C2×C22⋊C4×C41—21no—
141C2×C22⋊C4×C41—21no—
142C2×C22⋊C4×C41—21no—
143C2×C22⋊C4×C41—21no—
144C2×C22⋊C4×C41—21no—
145C2×C22⋊C4×C41—21no—
146C2×C22⋊C4×C41—21no—
147C2×C22⋊C4×C41—21no—
148C2×C42×C41—21no—
149#107×C41—22no—
150#106×C41—22no—
151#102×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—41no—
158#102×C41—41no—
159C22⋊C8×C41—22no—
160C22⋊C8×C41—22no—
161C22⋊C8×C41—22no—
162C22⋊C8×C41D414yescomplemented
163#95×C41—21no—
164#95×C41—21no—
165#95×C41—21no—
166C24×C41—24no—
167C24×C41—21no—
168C24×C41—21no—
169C24×C41—21no—
170C24×C41—42no—
171C24×C41—42no—
172C24×C41—81no—
173C24×C41—81no—
174C24×C41—81no—
175C24×C41—81no—
176C24×C41C2×D411yescharacteristic
177C24×C41C2×D411yescharacteristic
178C24×C41C2×D411yescharacteristic
179#41×C41—44no—
180#41×C41—44no—
181#41×C41—44no—
182#41×C41—44no—
183C2×Q8×C41—22no—
184C2×Q8×C41—22no—
185C2×Q8×C41—41no—
186C2×D4×C41—24no—
187C2×D4×C41—22no—
188C2×D4×C41—22no—
189C2×D4×C41—22no—
190C2×D4×C41—22no—
191C2×D4×C41—24no—
192C2×D4×C41—24no—
193C2×D4×C41—24no—
194C2×D4×C41—24no—
195C2×D4×C41—22no—
196C2×D4×C41—22no—
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—21no—
208C2×D4×C41—21no—
209C2×D4×C41—21no—
210C2×D4×C41—21no—
211C2×D4×C41—21no—
212C2×D4×C41—21no—
213C2×D4×C41—44no—
214C2×D4×C41—44no—
215C2×D4×C41—44no—
216C2×D4×C41—44no—
217C2×D4×C41—41no—
218C2×D4×C41—41no—
219C2×D4×C41—41no—
220C2×D4×C41—42no—
221C2×D4×C41—42no—
222C2×D4×C41—42no—
223C2×D4×C41—42no—
224C2×D4×C41—42no—
225C2×D4×C41—81no—
226C2×D4×C41—81no—
227C2×D4×C41—81no—
228C2×D4×C41—81no—
229C2×D4×C41—81no—
230C2×D4×C41—81no—
231C2×D4×C41—81no—
232C2×D4×C41—81no—
233C2×D4×C41—81no—
234C2×D4×C41—81no—
235C2×D4×C41—81no—
236C2×D4×C41—81no—
237C2×D4×C41—81no—
238C2×D4×C41—81no—
239C2×D4×C41C2×D412yes—
240C2×D4×C41C2×D412yes—
241C22×C4×C41—21no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—21no—
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—21no—
258C22×C4×C41—21no—
259C22×C4×C41—21no—
260C22×C4×C41C2×D411yescharacteristic
261C22×C4×C41C2×D411yescharacteristic
262C22×C4×C41C2×D412yes—
263C22×C4×C41C2×D412yes—
264C22×C4×C41C2×D411yescharacteristic
265C22×C4×C41C2×D412yes—
266C22×C4×C41#4112yes—
267C22×C4×C41C2411yescharacteristic
268D8×C41—44no—
269D8×C41—44no—
270M16×C41—44no—
271C2×C8×C41—21no—
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—44no—
282C2×C8×C41C2×D412yes—
283C2×C8×C41C2×D412yes—
284C4⋊C4×C41—21no—
285C4⋊C4×C41—21no—
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×C41C2×D412yes—
293C4⋊C4×C41C2×D412yes—
294C22⋊C4×C41—24no—
295C22⋊C4×C41—24no—
296C22⋊C4×C41—24no—
297C22⋊C4×C41—24no—
298C22⋊C4×C41—24no—
299C22⋊C4×C41—42no—
300C22⋊C4×C41—42no—
301C22⋊C4×C41—42no—
302C22⋊C4×C41—81no—
303C22⋊C4×C41—81no—
304C22⋊C4×C41—81no—
305C42×C41—24no—
306C23×C41—21no—
307C23×C41—21no—
308C23×C41—21no—
309C23×C41—21no—
310C23×C41—21no—
311C23×C41—21no—
312C23×C41—21no—
313C23×C41—21no—
314C23×C41—21no—
315C23×C41—21no—
316C23×C41—21no—
317C23×C41—21no—
318C23×C41—22no—
319C23×C41—22no—
320C23×C41—21no—
321C23×C41—21no—
322C23×C41—21no—
323C23×C41—21no—
324C23×C41—21no—
325C23×C41—21no—
326C23×C41—21no—
327C23×C41—48no—
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—41no—
343C23×C41—41no—
344C23×C41—41no—
345C23×C41—41no—
346C23×C41—41no—
347C23×C41—84no—
348C23×C41—84no—
349C23×C41—84no—
350C23×C41—84no—
351C23×C41—84no—
352C23×C41—84no—
353C23×C41#12012yes—
354C23×C41#12112yes—
355C23×C41C22×D411yescharacteristic
356Q8×C41—44no—
357D4×C41—22no—
358D4×C41—22no—
359D4×C41—22no—
360D4×C41—22no—
361D4×C41—44no—
362D4×C41—44no—
363D4×C41—48no—
364D4×C41—44no—
365D4×C41—41no—
366D4×C41—41no—
367D4×C41—41no—
368D4×C41—41no—
369D4×C41—41no—
370D4×C41—41no—
371D4×C41—41no—
372D4×C41—41no—
373D4×C41—84no—
374D4×C41—84no—
375D4×C41—84no—
376D4×C41—84no—
377D4×C41—84no—
378D4×C41—84no—
379D4×C41—84no—
380C2×C4×C41—21no—
381C2×C4×C41—21no—
382C2×C4×C41—21no—
383C2×C4×C41—21no—
384C2×C4×C41—22no—
385C2×C4×C41—22no—
386C2×C4×C41—22no—
387C2×C4×C41—22no—
388C2×C4×C41—22no—
389C2×C4×C41—22no—
390C2×C4×C41—22no—
391C2×C4×C41—22no—
392C2×C4×C41—22no—
393C2×C4×C41—22no—
394C2×C4×C41—21no—
395C2×C4×C41—21no—
396C2×C4×C41—21no—
397C2×C4×C41—41no—
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#12012yes—
415C2×C4×C41#12112yes—
416C2×C4×C41C22×D411yescharacteristic
417C2×C4×C41C22×D411yescharacteristic
418C2×C4×C41C22×D411yescharacteristic
419C2×C4×C41C2×#4111yescharacteristic
420C2×C4×C41H(5,𝔽2)11yescharacteristic
421C2×C4×C41H(5,𝔽2)11yescharacteristic
422C8×C41—22no—
423C8×C41—22no—
424C8×C41—41no—
425C8×C41—41no—
426#24390C4111yesmaximal, characteristic, direct product factor, Sylow
427C22×C41—22no—
428C22×C41—22no—
429C22×C41—22no—
430C22×C41—22no—
431C22×C41—22no—
432C22×C41—22no—
433C22×C41—41no—
434C22×C41—41no—
435C22×C41—41no—
436C22×C41—41no—
437C22×C41—41no—
438C22×C41—41no—
439C22×C41—41no—
440C22×C41—41no—
441C22×C41—41no—
442C22×C41—42no—
443C22×C41—42no—
444C22×C41—41no—
445C22×C41—41no—
446C22×C41—41no—
447C22×C41—42no—
448C22×C41—42no—
449C22×C41—41no—
450C22×C41—42no—
451C22×C41—42no—
452C22×C41—41no—
453C22×C41—41no—
454C22×C41—816no—
455C22×C41—81no—
456C22×C41—81no—
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—81no—
466C22×C41—81no—
467C22×C41—81no—
468C22×C41—81no—
469C22×C41—81no—
470C22×C41C2×#12011yescharacteristic
471C22×C41C2×#12111yescharacteristic
472C22×C41#53411yescharacteristic
473C22×C41#57611yescharacteristic
474C22×C41#57611yescharacteristic
475C22×C41#57611yescharacteristic
476C22×C41#57711yescharacteristic
477C4×C41—22no—
478C4×C41—22no—
479C4×C41—41no—
480C4×C41—42no—
481C4×C41—42no—
482C4×C41—81no—
483C4×C41—81no—
484C4×C41—81no—
485C4×C41D4211yescharacteristic
486C4×C41D4211yescharacteristic
487C4×C41#54611yescharacteristic
488C4×C41#54611yescharacteristic
489C2×#535C2×C4111yescharacteristic, complemented
490C2×#469C2×C4111yescharacteristic, complemented
491C2×#466C2×C4111yescharacteristic, complemented
492C2×#447C2×C4111yescharacteristic, complemented
493C2×#408C2×C4111yescharacteristic, complemented
494#2615C2×C4111yescharacteristic, complemented
495#2034C2×C4111yescharacteristic, complemented
496#2033C2×C4111yescharacteristic, complemented
497#1999C2×C4111yescharacteristic, complemented
498#1999C2×C4111yescharacteristic, complemented
499#1895C2×C4111yescharacteristic, complemented
500#1893C2×C4111yescharacteristic, complemented
501#1875C2×C4111yescharacteristic, complemented
502#1854C2×C4111yescharacteristic, complemented
503#1786C2×C4111yescharacteristic, complemented
504C2×C41—42no—
505C2×C41—42no—
506C2×C41—81no—
507C2×C41—82no—
508C2×C41—82no—
509C2×C41—161no—
510C2×C41#241011yescharacteristic
511C2×C41#300811yescharacteristic
512C2×C41#301211yescharacteristic
513C2×C41#305811yescharacteristic
514C2×C41#306211yescharacteristic
515C2×C41#319811yescharacteristic
516C2×C41#319911yescharacteristic
517C22×#41C22×C4111yescharacteristic
518C23×D4C22×C4111yescharacteristic
519C22×D8C22×C4111yescharacteristic
520C22×D8C22×C4111yescharacteristic
521C22×M16C22×C4111yescharacteristic, complemented
522C23×C8C22×C4111yescharacteristic, complemented
523#535—24no—
524#535—24no—
525C2×#127—21no—
526C2×#124—21no—
527C2×#121C22×C4111yescharacteristic
528C2×#121C22×C4111yescharacteristic
529C2×#121C22×C4111yescharacteristic
530C2×#121C22×C4111yescharacteristic
531C2×#121C22×C4111yescharacteristic
532C2×#121C22×C4111yescharacteristic, complemented
533C2×#121C22×C4111yescharacteristic, complemented
534C2×#120—21no—
535C2×#120—21no—
536C2×#117C22×C4111yescharacteristic
537#469—24no—
538#466—24no—
539#447—24no—
540C2×#107C22×C4111yescharacteristic, complemented
541C2×#106C22×C4111yescharacteristic, complemented
542C2×#102C22×C4111yescharacteristic
543C2×#102C22×C4111yescharacteristic
544C2×#102C22×C4111yescharacteristic
545C2×#102C22×C4111yescharacteristic
546C2×#102C22×C4111yescharacteristic
547C2×#102C22×C4111yescharacteristic
548C2×#102C22×C4111yescharacteristic, complemented
549C2×#102C22×C4111yescharacteristic, complemented
550#408—24no—
551C2×C22⋊C8C22×C4111yescharacteristic
552C2×C22⋊C8C22×C4111yescharacteristic
553C2×C22⋊C8C22×C4111yescharacteristic, complemented
554C2×C22⋊C8C22×C4111yescharacteristic, complemented
555#393—21no—
556#392—21no—
557#392—21no—
558#392—21no—
559#380C22×C4111yescharacteristic
560#380C22×C4111yescharacteristic, complemented
561#380C22×C4111yescharacteristic, complemented
562#340C22×C4111yescharacteristic, complemented
563#340C22×C4111yescharacteristic, complemented
564#340C22×C4111yescharacteristic, complemented
565#340C22×C4111yescharacteristic, complemented
566C41#2439011yescharacteristic, direct product factor, Sylow
567C25—21no—
568C2×#41—22no—
569C2×#41—22no—
570C2×#41—22no—
571C2×#41—22no—
572C2×#41—41no—
573C2×#41—41no—
574C22×Q8D4×C4111yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—41no—
588C22×D4—41no—
589C22×D4D4×C4111yescharacteristic
590C22×D4D4×C4111yescharacteristic
591C22×D4D4×C4111yescharacteristic
592C22×D4C23×C4111yescharacteristic
593C22×D4C23×C4111yescharacteristic
594C22×D4C23×C4111yescharacteristic
595C23×C4C23×C4111yescharacteristic
596C23×C4C23×C4111yescharacteristic
597C23×C4C23×C4111yescharacteristic
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—41no—
603C2×D8—41no—
604C2×M16—22no—
605C2×M16—22no—
606C2×M16—41no—
607C22×C8—22no—
608C22×C8—22no—
609C22×C8—41no—
610C22×C8C23×C4111yescharacteristic
611C22×C8C23×C4111yescharacteristic
612C22×C8C23×C4111yescharacteristic
613C22×C8C23×C4111yescharacteristic
614#127—28no—
615#124—28no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—41no—
627#121—41no—
628#121D4×C4114yescomplemented
629#121D4×C4114yescomplemented
630#120—28no—
631#120—28no—
632#117—22no—
633#117—22no—
634C2×C4⋊C4C23×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⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C42—21no—
651#107—22no—
652#106—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—41no—
660#102—41no—
661C22⋊C8—22no—
662C22⋊C8—22no—
663C22⋊C8—22no—
664C22⋊C8D4×C4114yescomplemented
665#95—21no—
666#95—21no—
667#95—21no—
668C24—24no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—42no—
673C24—42no—
674C24—81no—
675C24—81no—
676C24—81no—
677C24—81no—
678C24C2×D4×C4111yescharacteristic
679C24C2×D4×C4111yescharacteristic
680C24C2×D4×C4111yescharacteristic
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685C2×Q8—22no—
686C2×Q8—22no—
687C2×Q8—41no—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—21no—
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—21no—
714C2×D4—21no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4C2×D4×C4112yes—
742C2×D4C2×D4×C4112yes—
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—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4C2×D4×C4111yescharacteristic
763C22×C4C2×D4×C4111yescharacteristic
764C22×C4C2×D4×C4112yes—
765C22×C4C2×D4×C4112yes—
766C22×C4C2×D4×C4111yescharacteristic
767C22×C4C2×D4×C4112yes—
768C22×C4#41×C4112yes—
769C22×C4C24×C4111yescharacteristic
770D8—44no—
771D8—44no—
772M16—44no—
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—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C4112yes—
785C2×C8C2×D4×C4112yes—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4C2×D4×C4112yes—
795C4⋊C4C2×D4×C4112yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C42—24no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—48no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23#120×C4112yes—
856C23#121×C4112yes—
857C23C22×D4×C4111yescharacteristic
858Q8—44no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—44no—
864D4—44no—
865D4—48no—
866D4—44no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—84no—
876D4—84no—
877D4—84no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
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—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4#120×C4112yes—
917C2×C4#121×C4112yes—
918C2×C4C22×D4×C4111yescharacteristic
919C2×C4C22×D4×C4111yescharacteristic
920C2×C4C22×D4×C4111yescharacteristic
921C2×C4C2×#41×C4111yescharacteristic
922C2×C4H(5,𝔽2)×C4111yescharacteristic
923C2×C4H(5,𝔽2)×C4111yescharacteristic
924C8—22no—
925C8—22no—
926C8—41no—
927C8—41no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—42no—
954C22—42no—
955C22—816no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×#120×C4111yescharacteristic
972C22C2×#121×C4111yescharacteristic
973C22C41×#53411yescharacteristic
974C22C41×#57611yescharacteristic
975C22C41×#57611yescharacteristic
976C22C41×#57611yescharacteristic
977C22C41×#57711yescharacteristic
978C4—22no—
979C4—22no—
980C4—41no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4D42×C4111yescharacteristic
987C4D42×C4111yescharacteristic
988C4C41×#54611yescharacteristic
989C4C41×#54611yescharacteristic
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2C41×#241011yescharacteristic
997C2C41×#300811yescharacteristic
998C2C41×#301211yescharacteristic
999C2C41×#305811yescharacteristic
1000C2C41×#306211yescharacteristic
1001C2C41×#319811yescharacteristic
1002C2C41×#319911yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C22×#41×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#535C2semidirect
2. C2×C41×#469C2semidirect
3. C2×C41×#466C2semidirect
4. C2×C41×#447C2semidirect
5. C2×C41×#408C2semidirect
6. C41×#2615C2semidirect
7. C41×#2034C2semidirect
8. C41×#2033C2semidirect
9. C41×#1999C2semidirect
10. C41×#1999C2semidirect
11. C41×#1895C2semidirect
12. C41×#1893C2semidirect
13. C41×#1875C2semidirect
14. C41×#1854C2semidirect
15. C41×#1786C2semidirect
20. C22×M16×C41C22semidirect
21. C23×C8×C41C22semidirect
31. C2×#121×C41C22semidirect
32. C2×#121×C41C22semidirect
39. C2×#107×C41C22semidirect
40. C2×#106×C41C22semidirect
47. C2×#102×C41C22semidirect
48. C2×#102×C41C22semidirect
52. C2×C22⋊C8×C41C22semidirect
53. C2×C22⋊C8×C41C22semidirect
59. C41×#380C22semidirect
60. C41×#380C22semidirect
61. C41×#340C22semidirect
62. C41×#340C22semidirect
63. C41×#340C22semidirect
64. C41×#340C22semidirect
126. #121×C41D4semidirect
127. #121×C41D4semidirect
162. C22⋊C8×C41D4semidirect
426. #24390C41direct (N × H)
489. C2×#535C2×C41semidirect
490. C2×#469C2×C41semidirect
491. C2×#466C2×C41semidirect
492. C2×#447C2×C41semidirect
493. C2×#408C2×C41semidirect
494. #2615C2×C41semidirect
495. #2034C2×C41semidirect
496. #2033C2×C41semidirect
497. #1999C2×C41semidirect
498. #1999C2×C41semidirect
499. #1895C2×C41semidirect
500. #1893C2×C41semidirect
501. #1875C2×C41semidirect
502. #1854C2×C41semidirect
503. #1786C2×C41semidirect
521. C22×M16C22×C41semidirect
522. C23×C8C22×C41semidirect
532. C2×#121C22×C41semidirect
533. C2×#121C22×C41semidirect
540. C2×#107C22×C41semidirect
541. C2×#106C22×C41semidirect
548. C2×#102C22×C41semidirect
549. C2×#102C22×C41semidirect
553. C2×C22⋊C8C22×C41semidirect
554. C2×C22⋊C8C22×C41semidirect
560. #380C22×C41semidirect
561. #380C22×C41semidirect
562. #340C22×C41semidirect
563. #340C22×C41semidirect
564. #340C22×C41semidirect
565. #340C22×C41semidirect
566. C41#24390direct (N × H)
628. #121D4×C41semidirect
629. #121D4×C41semidirect
664. C22⋊C8D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5352
C2×C41×#4692
C2×C41×#4662
C2×C41×#4472
C2×C41×#4082
C41×#26152
C41×#20342
C41×#20332
C41×#19992
C41×#18952
C41×#18932
C41×#18752
C41×#18542
C41×#17862
#2439041