Finite Group Databasebeta

← C41×#24394 #23800595

Subgroups — C41×#24394 #23800595

Order 10496.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#535C211yesmaximal, characteristic
2C2×C41×#468C211yesmaximal, characteristic, complemented
3C2×C41×#465C211yesmaximal, characteristic, complemented
4C2×C41×#450C211yesmaximal, characteristic, complemented
5C2×C41×#408C211yesmaximal, characteristic, complemented
6C41×#2616C211yesmaximal, characteristic, complemented
7C41×#2034C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#2000C211yesmaximal, characteristic, complemented
10C41×#2000C211yesmaximal, characteristic, complemented
11C41×#1895C211yesmaximal, characteristic, complemented
12C41×#1893C211yesmaximal, characteristic, complemented
13C41×#1873C211yesmaximal, characteristic, complemented
14C41×#1854C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C23×D4×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic
19C22×SD16×C41C2211yescharacteristic
20C22×M16×C41C2211yescharacteristic, complemented
21C23×C8×C41C2211yescharacteristic, complemented
22C41×#535—24no—
23C41×#535—24no—
24C2×#127×C41—21no—
25C2×#124×C41—21no—
26C2×C22⋊Q8×C41C2211yescharacteristic
27C2×C22⋊Q8×C41C2211yescharacteristic, complemented
28C2×C22⋊Q8×C41C2211yescharacteristic, complemented
29C2×#121×C41C2211yescharacteristic
30C2×#121×C41C2211yescharacteristic
31C2×#121×C41C2211yescharacteristic
32C2×#121×C41C2211yescharacteristic
33C2×#120×C41—21no—
34C2×#120×C41—21no—
35C2×#117×C41C2211yescharacteristic
36C41×#468—24no—
37C41×#465—24no—
38C41×#450—24no—
39C2×#107×C41C2211yescharacteristic, complemented
40C2×#106×C41C2211yescharacteristic, complemented
41C2×#103×C41C2211yescharacteristic, complemented
42C2×#103×C41C2211yescharacteristic, complemented
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×#102×C41C2211yescharacteristic
46C2×#102×C41C2211yescharacteristic
47C2×#102×C41C2211yescharacteristic
48C2×#102×C41C2211yescharacteristic
49C41×#408—24no—
50C2×C22⋊C8×C41C2211yescharacteristic
51C2×C22⋊C8×C41C2211yescharacteristic
52C2×C22⋊C8×C41C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic, complemented
54C41×#395—21no—
55C41×#394—21no—
56C41×#394—21no—
57C41×#394—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×Q8×C41C2311yescharacteristic
74C22×D4×C41—21no—
75C22×D4×C41—21no—
76C22×D4×C41—21no—
77C22×D4×C41—21no—
78C22×D4×C41—22no—
79C22×D4×C41—22no—
80C22×D4×C41—21no—
81C22×D4×C41—22no—
82C22×D4×C41—22no—
83C22×D4×C41—41no—
84C22×D4×C41—41no—
85C22×D4×C41D411yescharacteristic
86C22×D4×C41D411yescharacteristic
87C22×D4×C41D411yescharacteristic
88C22×D4×C41C2311yescharacteristic
89C22×D4×C41C2311yescharacteristic
90C23×C4×C41C2311yescharacteristic
91C23×C4×C41C2311yescharacteristic
92C23×C4×C41C2311yescharacteristic
93C2×SD16×C41—22no—
94C2×SD16×C41—22no—
95C2×SD16×C41—22no—
96C2×SD16×C41—22no—
97C2×SD16×C41—41no—
98C2×SD16×C41—41no—
99C2×M16×C41—22no—
100C2×M16×C41—22no—
101C2×M16×C41—41no—
102C22×C8×C41—22no—
103C22×C8×C41—22no—
104C22×C8×C41—41no—
105C22×C8×C41C2311yescharacteristic
106C22×C8×C41C2311yescharacteristic
107C22×C8×C41C2311yescharacteristic
108C22×C8×C41C2311yescharacteristic
109#127×C41—28no—
110#124×C41—28no—
111C22⋊Q8×C41—22no—
112C22⋊Q8×C41—22no—
113C22⋊Q8×C41—22no—
114C22⋊Q8×C41—22no—
115C22⋊Q8×C41—41no—
116C22⋊Q8×C41—41no—
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×C41D414yes—
124#121×C41D414yes—
125#120×C41—28no—
126#120×C41—28no—
127#117×C41—22no—
128#117×C41—22no—
129C2×C4⋊C4×C41—21no—
130C2×C4⋊C4×C41—21no—
131C2×C4⋊C4×C41—21no—
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#103×C41—22no—
152#103×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—42no—
170C24×C41—42no—
171C24×C41—81no—
172C24×C41—81no—
173C24×C41—81no—
174C24×C41—81no—
175C24×C41C2×D411yescharacteristic
176C24×C41C2×D411yescharacteristic
177C24×C41C2×D411yescharacteristic
178#41×C41—44no—
179#41×C41—44no—
180#41×C41—44no—
181#41×C41—44no—
182C2×Q8×C41—22no—
183C2×Q8×C41—22no—
184C2×Q8×C41—21no—
185C2×Q8×C41—21no—
186C2×Q8×C41—21no—
187C2×Q8×C41—21no—
188C2×Q8×C41—21no—
189C2×Q8×C41—21no—
190C2×Q8×C41—41no—
191C2×D4×C41—24no—
192C2×D4×C41—22no—
193C2×D4×C41—22no—
194C2×D4×C41—22no—
195C2×D4×C41—22no—
196C2×D4×C41—24no—
197C2×D4×C41—24no—
198C2×D4×C41—24no—
199C2×D4×C41—24no—
200C2×D4×C41—22no—
201C2×D4×C41—22no—
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—44no—
213C2×D4×C41—44no—
214C2×D4×C41—44no—
215C2×D4×C41—44no—
216C2×D4×C41—41no—
217C2×D4×C41—41no—
218C2×D4×C41—41no—
219C2×D4×C41—42no—
220C2×D4×C41—42no—
221C2×D4×C41—81no—
222C2×D4×C41—81no—
223C2×D4×C41—81no—
224C2×D4×C41—81no—
225C2×D4×C41—81no—
226C2×D4×C41—81no—
227C2×D4×C41—81no—
228C2×D4×C41—81no—
229C2×D4×C41C2×D412yes—
230C2×D4×C41C2×D412yes—
231C22×C4×C41—21no—
232C22×C4×C41—21no—
233C22×C4×C41—21no—
234C22×C4×C41—21no—
235C22×C4×C41—21no—
236C22×C4×C41—21no—
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—21no—
246C22×C4×C41—21no—
247C22×C4×C41—21no—
248C22×C4×C41—21no—
249C22×C4×C41—21no—
250C22×C4×C41—21no—
251C22×C4×C41C2×D411yescharacteristic
252C22×C4×C41C2×D411yescharacteristic
253C22×C4×C41C2×D412yes—
254C22×C4×C41C2×D412yes—
255C22×C4×C41C2×D411yescharacteristic
256C22×C4×C41C2×D412yes—
257C22×C4×C41#4112yes—
258C22×C4×C41C2411yescharacteristic
259SD16×C41—44no—
260SD16×C41—44no—
261M16×C41—44no—
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—21no—
271C2×C8×C41—21no—
272C2×C8×C41—44no—
273C2×C8×C41C2×D412yes—
274C2×C8×C41C2×D412yes—
275C4⋊C4×C41—21no—
276C4⋊C4×C41—21no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—21no—
280C4⋊C4×C41—21no—
281C4⋊C4×C41—21no—
282C4⋊C4×C41—21no—
283C4⋊C4×C41—42no—
284C4⋊C4×C41—42no—
285C4⋊C4×C41—42no—
286C4⋊C4×C41C2×D412yes—
287C4⋊C4×C41C2×D412yes—
288C22⋊C4×C41—24no—
289C22⋊C4×C41—24no—
290C22⋊C4×C41—24no—
291C22⋊C4×C41—24no—
292C22⋊C4×C41—24no—
293C22⋊C4×C41—42no—
294C22⋊C4×C41—42no—
295C22⋊C4×C41—42no—
296C22⋊C4×C41—81no—
297C22⋊C4×C41—81no—
298C22⋊C4×C41—81no—
299C42×C41—24no—
300C23×C41—21no—
301C23×C41—21no—
302C23×C41—21no—
303C23×C41—21no—
304C23×C41—21no—
305C23×C41—21no—
306C23×C41—21no—
307C23×C41—21no—
308C23×C41—21no—
309C23×C41—21no—
310C23×C41—21no—
311C23×C41—21no—
312C23×C41—22no—
313C23×C41—22no—
314C23×C41—21no—
315C23×C41—21no—
316C23×C41—21no—
317C23×C41—21no—
318C23×C41—21no—
319C23×C41—21no—
320C23×C41—21no—
321C23×C41—48no—
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—84no—
340C23×C41#12012yes—
341C23×C41#12112yes—
342C23×C41C22×D411yescharacteristic
343Q8×C41—44no—
344Q8×C41—41no—
345Q8×C41—41no—
346Q8×C41—41no—
347Q8×C41—41no—
348D4×C41—22no—
349D4×C41—22no—
350D4×C41—22no—
351D4×C41—22no—
352D4×C41—44no—
353D4×C41—44no—
354D4×C41—48no—
355D4×C41—44no—
356D4×C41—41no—
357D4×C41—41no—
358D4×C41—41no—
359D4×C41—41no—
360D4×C41—84no—
361D4×C41—84no—
362D4×C41—84no—
363D4×C41—84no—
364C2×C4×C41—21no—
365C2×C4×C41—21no—
366C2×C4×C41—21no—
367C2×C4×C41—21no—
368C2×C4×C41—22no—
369C2×C4×C41—22no—
370C2×C4×C41—22no—
371C2×C4×C41—22no—
372C2×C4×C41—22no—
373C2×C4×C41—22no—
374C2×C4×C41—22no—
375C2×C4×C41—22no—
376C2×C4×C41—22no—
377C2×C4×C41—22no—
378C2×C4×C41—21no—
379C2×C4×C41—21no—
380C2×C4×C41—21no—
381C2×C4×C41—41no—
382C2×C4×C41—41no—
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—41no—
400C2×C4×C41—41no—
401C2×C4×C41#12012yes—
402C2×C4×C41#12112yes—
403C2×C4×C41C22×D411yescharacteristic
404C2×C4×C41C22×D411yescharacteristic
405C2×C4×C41C22×D411yescharacteristic
406C2×C4×C41C2×#4111yescharacteristic
407C2×C4×C41H(5,𝔽2)11yescharacteristic
408C2×C4×C41H(5,𝔽2)11yescharacteristic
409C8×C41—22no—
410C8×C41—22no—
411C8×C41—41no—
412C8×C41—41no—
413#24394C4111yesmaximal, characteristic, direct product factor, Sylow
414C22×C41—22no—
415C22×C41—22no—
416C22×C41—22no—
417C22×C41—22no—
418C22×C41—22no—
419C22×C41—22no—
420C22×C41—41no—
421C22×C41—41no—
422C22×C41—41no—
423C22×C41—41no—
424C22×C41—41no—
425C22×C41—41no—
426C22×C41—41no—
427C22×C41—41no—
428C22×C41—41no—
429C22×C41—42no—
430C22×C41—42no—
431C22×C41—41no—
432C22×C41—41no—
433C22×C41—41no—
434C22×C41—42no—
435C22×C41—42no—
436C22×C41—41no—
437C22×C41—42no—
438C22×C41—42no—
439C22×C41—41no—
440C22×C41—41no—
441C22×C41—816no—
442C22×C41—81no—
443C22×C41—81no—
444C22×C41—81no—
445C22×C41—81no—
446C22×C41—81no—
447C22×C41—81no—
448C22×C41—81no—
449C22×C41—81no—
450C22×C41C2×#12011yescharacteristic
451C22×C41C2×#12111yescharacteristic
452C22×C41#53411yescharacteristic
453C22×C41#57611yescharacteristic
454C22×C41#57711yescharacteristic
455C22×C41#57711yescharacteristic
456C22×C41#57711yescharacteristic
457C4×C41—22no—
458C4×C41—22no—
459C4×C41—41no—
460C4×C41—42no—
461C4×C41—42no—
462C4×C41—81no—
463C4×C41—81no—
464C4×C41—81no—
465C4×C41—81no—
466C4×C41D4211yescharacteristic
467C4×C41D4211yescharacteristic
468C4×C41#54611yescharacteristic
469C4×C41#54611yescharacteristic
470C2×#535C2×C4111yescharacteristic
471C2×#468C2×C4111yescharacteristic, complemented
472C2×#465C2×C4111yescharacteristic, complemented
473C2×#450C2×C4111yescharacteristic, complemented
474C2×#408C2×C4111yescharacteristic, complemented
475#2616C2×C4111yescharacteristic, complemented
476#2034C2×C4111yescharacteristic, complemented
477#2033C2×C4111yescharacteristic, complemented
478#2000C2×C4111yescharacteristic, complemented
479#2000C2×C4111yescharacteristic, complemented
480#1895C2×C4111yescharacteristic, complemented
481#1893C2×C4111yescharacteristic, complemented
482#1873C2×C4111yescharacteristic, complemented
483#1854C2×C4111yescharacteristic, complemented
484#1786C2×C4111yescharacteristic, complemented
485C2×C41—42no—
486C2×C41—42no—
487C2×C41—81no—
488C2×C41—82no—
489C2×C41—82no—
490C2×C41#241011yescharacteristic
491C2×C41#300911yescharacteristic
492C2×C41#301211yescharacteristic
493C2×C41#305711yescharacteristic
494C2×C41#306211yescharacteristic
495C2×C41#319811yescharacteristic
496C2×C41#320011yescharacteristic
497C22×#41C22×C4111yescharacteristic
498C23×D4C22×C4111yescharacteristic
499C22×SD16C22×C4111yescharacteristic
500C22×SD16C22×C4111yescharacteristic
501C22×M16C22×C4111yescharacteristic, complemented
502C23×C8C22×C4111yescharacteristic, complemented
503#535—24no—
504#535—24no—
505C2×#127—21no—
506C2×#124—21no—
507C2×C22⋊Q8C22×C4111yescharacteristic
508C2×C22⋊Q8C22×C4111yescharacteristic, complemented
509C2×C22⋊Q8C22×C4111yescharacteristic, complemented
510C2×#121C22×C4111yescharacteristic
511C2×#121C22×C4111yescharacteristic
512C2×#121C22×C4111yescharacteristic
513C2×#121C22×C4111yescharacteristic
514C2×#120—21no—
515C2×#120—21no—
516C2×#117C22×C4111yescharacteristic
517#468—24no—
518#465—24no—
519#450—24no—
520C2×#107C22×C4111yescharacteristic, complemented
521C2×#106C22×C4111yescharacteristic, complemented
522C2×#103C22×C4111yescharacteristic, complemented
523C2×#103C22×C4111yescharacteristic, complemented
524C2×#102C22×C4111yescharacteristic
525C2×#102C22×C4111yescharacteristic
526C2×#102C22×C4111yescharacteristic
527C2×#102C22×C4111yescharacteristic
528C2×#102C22×C4111yescharacteristic
529C2×#102C22×C4111yescharacteristic
530#408—24no—
531C2×C22⋊C8C22×C4111yescharacteristic
532C2×C22⋊C8C22×C4111yescharacteristic
533C2×C22⋊C8C22×C4111yescharacteristic, complemented
534C2×C22⋊C8C22×C4111yescharacteristic, complemented
535#395—21no—
536#394—21no—
537#394—21no—
538#394—21no—
539#380C22×C4111yescharacteristic
540#380C22×C4111yescharacteristic, complemented
541#380C22×C4111yescharacteristic, complemented
542#340C22×C4111yescharacteristic, complemented
543#340C22×C4111yescharacteristic, complemented
544#340C22×C4111yescharacteristic, complemented
545#340C22×C4111yescharacteristic, complemented
546C41#2439411yescharacteristic, direct product factor, Sylow
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C4111yescharacteristic
555C22×Q8C23×C4111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C4111yescharacteristic
568C22×D4D4×C4111yescharacteristic
569C22×D4D4×C4111yescharacteristic
570C22×D4C23×C4111yescharacteristic
571C22×D4C23×C4111yescharacteristic
572C23×C4C23×C4111yescharacteristic
573C23×C4C23×C4111yescharacteristic
574C23×C4C23×C4111yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—41no—
587C22×C8C23×C4111yescharacteristic
588C22×C8C23×C4111yescharacteristic
589C22×C8C23×C4111yescharacteristic
590C22×C8C23×C4111yescharacteristic
591#127—28no—
592#124—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121D4×C4114yes—
606#121D4×C4114yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C23×C4111yescharacteristic
615C2×C4⋊C4C23×C4111yescharacteristic
616C2×C4⋊C4C23×C4111yescharacteristic
617C2×C4⋊C4C23×C4111yescharacteristic
618C2×C4⋊C4C23×C4111yescharacteristic
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⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C42—21no—
631#107—22no—
632#106—22no—
633#103—22no—
634#103—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8D4×C4114yescomplemented
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C4111yescharacteristic
658C24C2×D4×C4111yescharacteristic
659C24C2×D4×C4111yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C4112yes—
712C2×D4C2×D4×C4112yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
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—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C4111yescharacteristic
734C22×C4C2×D4×C4111yescharacteristic
735C22×C4C2×D4×C4112yes—
736C22×C4C2×D4×C4112yes—
737C22×C4C2×D4×C4111yescharacteristic
738C22×C4C2×D4×C4112yes—
739C22×C4#41×C4112yes—
740C22×C4C24×C4111yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—44no—
755C2×C8C2×D4×C4112yes—
756C2×C8C2×D4×C4112yes—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C4112yes—
769C4⋊C4C2×D4×C4112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#120×C4112yes—
823C23#121×C4112yes—
824C23C22×D4×C4111yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
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—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4#120×C4112yes—
884C2×C4#121×C4112yes—
885C2×C4C22×D4×C4111yescharacteristic
886C2×C4C22×D4×C4111yescharacteristic
887C2×C4C22×D4×C4111yescharacteristic
888C2×C4C2×#41×C4111yescharacteristic
889C2×C4H(5,𝔽2)×C4111yescharacteristic
890C2×C4H(5,𝔽2)×C4111yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—42no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C4111yescharacteristic
932C22C2×#121×C4111yescharacteristic
933C22C41×#53411yescharacteristic
934C22C41×#57611yescharacteristic
935C22C41×#57711yescharacteristic
936C22C41×#57711yescharacteristic
937C22C41×#57711yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C4111yescharacteristic
948C4D42×C4111yescharacteristic
949C4C41×#54611yescharacteristic
950C4C41×#54611yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C41×#241011yescharacteristic
957C2C41×#300911yescharacteristic
958C2C41×#301211yescharacteristic
959C2C41×#305711yescharacteristic
960C2C41×#306211yescharacteristic
961C2C41×#319811yescharacteristic
962C2C41×#320011yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#535C2
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
2. C2×C41×#468C2semidirect
3. C2×C41×#465C2semidirect
4. C2×C41×#450C2semidirect
5. C2×C41×#408C2semidirect
6. C41×#2616C2semidirect
7. C41×#2034C2semidirect
8. C41×#2033C2semidirect
9. C41×#2000C2semidirect
10. C41×#2000C2semidirect
11. C41×#1895C2semidirect
12. C41×#1893C2semidirect
13. C41×#1873C2semidirect
14. C41×#1854C2semidirect
15. C41×#1786C2semidirect
20. C22×M16×C41C22semidirect
21. C23×C8×C41C22semidirect
27. C2×C22⋊Q8×C41C22semidirect
28. C2×C22⋊Q8×C41C22semidirect
39. C2×#107×C41C22semidirect
40. C2×#106×C41C22semidirect
41. C2×#103×C41C22semidirect
42. C2×#103×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
162. C22⋊C8×C41D4semidirect
413. #24394C41direct (N × H)
471. C2×#468C2×C41semidirect
472. C2×#465C2×C41semidirect
473. C2×#450C2×C41semidirect
474. C2×#408C2×C41semidirect
475. #2616C2×C41semidirect
476. #2034C2×C41semidirect
477. #2033C2×C41semidirect
478. #2000C2×C41semidirect
479. #2000C2×C41semidirect
480. #1895C2×C41semidirect
481. #1893C2×C41semidirect
482. #1873C2×C41semidirect
483. #1854C2×C41semidirect
484. #1786C2×C41semidirect
501. C22×M16C22×C41semidirect
502. C23×C8C22×C41semidirect
508. C2×C22⋊Q8C22×C41semidirect
509. C2×C22⋊Q8C22×C41semidirect
520. C2×#107C22×C41semidirect
521. C2×#106C22×C41semidirect
522. C2×#103C22×C41semidirect
523. C2×#103C22×C41semidirect
533. C2×C22⋊C8C22×C41semidirect
534. C2×C22⋊C8C22×C41semidirect
540. #380C22×C41semidirect
541. #380C22×C41semidirect
542. #340C22×C41semidirect
543. #340C22×C41semidirect
544. #340C22×C41semidirect
545. #340C22×C41semidirect
546. C41#24394direct (N × H)
644. 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×#4682
C2×C41×#4652
C2×C41×#4502
C2×C41×#4082
C41×#26162
C41×#20342
C41×#20332
C41×#20002
C41×#18952
C41×#18932
C41×#18732
C41×#18542
C41×#17862
#2439441