Finite Group Databasebeta

← C41×#25163 #23801364

Subgroups — C41×#25163 #23801364

Order 10496.

1112 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#464C211yesmaximal, characteristic, complemented
2C2×C41×#452C211yesmaximal, characteristic, complemented
3C2×C41×#449C211yesmaximal, characteristic
4C2×C4×Q16×C41C211yesmaximal, characteristic, complemented
5C41×#2426C211yesmaximal, characteristic, complemented
6C41×#2341C211yesmaximal, characteristic, complemented
7C41×#2067C211yesmaximal, characteristic, complemented
8C41×#2036C211yesmaximal, characteristic, complemented
9C41×#2033C211yesmaximal, characteristic, complemented
10C41×#2012C211yesmaximal, characteristic, complemented
11C41×#1970C211yesmaximal, characteristic, complemented
12C41×#1923C211yesmaximal, characteristic, complemented
13C41×#1880C211yesmaximal, characteristic, complemented
14C41×#1880C211yesmaximal, characteristic, complemented
15C41×#1863C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C22×Q16×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic
19C22×SD16×C41C2211yescharacteristic
20C22×D8×C41C2211yescharacteristic
21C2×#124×C41C2211yescharacteristic
22C2×C22⋊Q8×C41C2211yescharacteristic
23C2×#121×C41C2211yescharacteristic
24C2×C4×Q8×C41C2211yescharacteristic
25C2×C4×Q8×C41C2211yescharacteristic
26C2×C4×Q8×C41C2211yescharacteristic
27C41×#464—24no—
28C41×#452—24no—
29C41×#449—24no—
30C4×Q16×C41—24no—
31C2×#107×C41C2211yescharacteristic
32C2×#107×C41C2211yescharacteristic
33C2×C4⋊C8×C41C2211yescharacteristic
34C2×#103×C41C2211yescharacteristic
35C2×#103×C41C2211yescharacteristic
36C2×#103×C41C2211yescharacteristic
37C2×#103×C41C2211yescharacteristic
38C2×#102×C41C2211yescharacteristic
39C2×#102×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×C22⋊C8×C41C2211yescharacteristic
43C2×C22⋊C8×C41C2211yescharacteristic
44C2×C4×C8×C41C2211yescharacteristic
45C41×#396—21no—
46C41×#394—21no—
47C41×#390—21no—
48C41×#390—21no—
49C41×#390—21no—
50C41×#390C2211yescharacteristic
51C41×#390C2211yescharacteristic
52C41×#390C2211yescharacteristic
53C41×#389C2211yescharacteristic
54C41×#388—21no—
55C41×#380—21no—
56C41×#380C2211yescharacteristic
57C4×C22⋊C4×C41—21no—
58C4×C22⋊C4×C41C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#336C2211yescharacteristic
62C41×#336C2211yescharacteristic
63C2×#41×C41—22no—
64C2×#41×C41—22no—
65C2×#41×C41—22no—
66C2×#41×C41—22no—
67C2×#41×C41—41no—
68C2×#41×C41—41no—
69C22×Q8×C41C2311yescharacteristic
70C22×Q8×C41C2311yescharacteristic
71C22×D4×C41—21no—
72C22×D4×C41—21no—
73C22×D4×C41C2311yescharacteristic
74C22×D4×C41C2311yescharacteristic
75C23×C4×C41—21no—
76C23×C4×C41C2311yescharacteristic
77C2×Q16×C41—22no—
78C2×Q16×C41—22no—
79C2×Q16×C41D414yescomplemented
80C2×SD16×C41—22no—
81C2×SD16×C41—22no—
82C2×SD16×C41—22no—
83C2×SD16×C41—22no—
84C2×SD16×C41—22no—
85C2×SD16×C41—41no—
86C2×D8×C41—22no—
87C2×D8×C41—22no—
88C2×D8×C41—41no—
89C22×C8×C41C2311yescharacteristic
90C22×C8×C41C2311yescharacteristic
91C22×C8×C41C2311yescharacteristic
92C22×C8×C41C2311yescharacteristic
93#124×C41—22no—
94#124×C41—41no—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41—41no—
97#121×C41—22no—
98#121×C41—41no—
99C4×Q8×C41—22no—
100C4×Q8×C41—22no—
101C4×Q8×C41—22no—
102C4×Q8×C41—41no—
103C4×Q8×C41—41no—
104C4×Q8×C41—41no—
105C2×C4⋊C4×C41—21no—
106C2×C4⋊C4×C41—21no—
107C2×C4⋊C4×C41—21no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41C2311yescharacteristic
111C2×C4⋊C4×C41C2311yescharacteristic
112C2×C4⋊C4×C41C2311yescharacteristic
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C22⋊C4×C41—21no—
115C2×C22⋊C4×C41—21no—
116C2×C22⋊C4×C41—21no—
117C2×C22⋊C4×C41—21no—
118C2×C22⋊C4×C41—21no—
119C2×C22⋊C4×C41—21no—
120C2×C22⋊C4×C41—21no—
121C2×C22⋊C4×C41—21no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—21no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41D411yescharacteristic
126C2×C22⋊C4×C41D411yescharacteristic
127C2×C42×C41—21no—
128C2×C42×C41—21no—
129C2×C42×C41—21no—
130C2×C42×C41C2311yescharacteristic
131C2×C42×C41C2311yescharacteristic
132#107×C41—22no—
133#107×C41—41no—
134C4⋊C8×C41—22no—
135#103×C41—22no—
136#103×C41—22no—
137#103×C41—22no—
138#103×C41D414yes—
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—22no—
142#102×C41—41no—
143C22⋊C8×C41—22no—
144C22⋊C8×C41—22no—
145C4×C8×C41—22no—
146#95×C41—21no—
147#95×C41—21no—
148#95×C41D411yescharacteristic
149#95×C41D411yescharacteristic
150C24×C41—21no—
151C24×C41—21no—
152C24×C41C2×D411yescharacteristic
153#41×C41—44no—
154#41×C41—44no—
155#41×C41—44no—
156#41×C41—44no—
157C2×Q8×C41—21no—
158C2×Q8×C41—21no—
159C2×Q8×C41—21no—
160C2×Q8×C41—21no—
161C2×Q8×C41—21no—
162C2×Q8×C41—21no—
163C2×Q8×C41—21no—
164C2×Q8×C41—21no—
165C2×Q8×C41C2×D412yes—
166C2×Q8×C41C2×D412yes—
167C2×Q8×C41C2×D412yes—
168C2×Q8×C41#4112yes—
169C2×D4×C41—24no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41—21no—
173C2×D4×C41—21no—
174C2×D4×C41—21no—
175C2×D4×C41—21no—
176C2×D4×C41—21no—
177C2×D4×C41—21no—
178C2×D4×C41—21no—
179C2×D4×C41—21no—
180C2×D4×C41—21no—
181C2×D4×C41—42no—
182C2×D4×C41—42no—
183C2×D4×C41—42no—
184C2×D4×C41—42no—
185C2×D4×C41—81no—
186C2×D4×C41#4112yes—
187C22×C4×C41—21no—
188C22×C4×C41—24no—
189C22×C4×C41—21no—
190C22×C4×C41—21no—
191C22×C4×C41—21no—
192C22×C4×C41—21no—
193C22×C4×C41—21no—
194C22×C4×C41—21no—
195C22×C4×C41—21no—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—21no—
199C22×C4×C41—21no—
200C22×C4×C41—42no—
201C22×C4×C41—42no—
202C22×C4×C41C2×D411yescharacteristic
203C22×C4×C41C2×D411yescharacteristic
204C22×C4×C41C2×D411yescharacteristic
205C22×C4×C41C2×D411yescharacteristic
206C22×C4×C41C2×D411yescharacteristic
207C22×C4×C41C2411yescharacteristic
208Q16×C41—28no—
209SD16×C41—44no—
210SD16×C41—44no—
211D8×C41—44no—
212C2×C8×C41—21no—
213C2×C8×C41—21no—
214C2×C8×C41—21no—
215C2×C8×C41—21no—
216C2×C8×C41—21no—
217C2×C8×C41—21no—
218C2×C8×C41—21no—
219C2×C8×C41—21no—
220C2×C8×C41—21no—
221C2×C8×C41—21no—
222C2×C8×C41C2×D412yes—
223C2×C8×C41C2×D412yes—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—21no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—42no—
232C4⋊C4×C41—42no—
233C4⋊C4×C41—42no—
234C4⋊C4×C41—42no—
235C4⋊C4×C41—81no—
236C4⋊C4×C41C2×D412yes—
237C22⋊C4×C41—22no—
238C22⋊C4×C41—41no—
239C22⋊C4×C41—42no—
240C22⋊C4×C41—42no—
241C22⋊C4×C41—42no—
242C22⋊C4×C41—42no—
243C22⋊C4×C41—42no—
244C22⋊C4×C41—42no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—81no—
247C22⋊C4×C41—81no—
248C22⋊C4×C41—81no—
249C22⋊C4×C41—81no—
250C42×C41—21no—
251C42×C41—21no—
252C42×C41—21no—
253C42×C41—21no—
254C42×C41—42no—
255C42×C41—42no—
256C42×C41—42no—
257C23×C41—21no—
258C23×C41—22no—
259C23×C41—21no—
260C23×C41—21no—
261C23×C41—21no—
262C23×C41—21no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—41no—
266C23×C41—41no—
267C23×C41—41no—
268C23×C41—41no—
269C23×C41—41no—
270C23×C41—41no—
271C23×C41—41no—
272C23×C41—41no—
273C23×C41—41no—
274C23×C41—41no—
275C23×C41—41no—
276C23×C41—41no—
277C23×C41—41no—
278C23×C41C22×D411yescharacteristic
279Q8×C41—22no—
280Q8×C41—22no—
281Q8×C41—22no—
282Q8×C41—22no—
283Q8×C41—22no—
284Q8×C41—41no—
285Q8×C41—41no—
286Q8×C41#12114yes—
287D4×C41—22no—
288D4×C41—22no—
289D4×C41—48no—
290D4×C41—41no—
291D4×C41—41no—
292D4×C41—41no—
293D4×C41—41no—
294D4×C41—41no—
295D4×C41—41no—
296D4×C41—84no—
297C2×C4×C41—22no—
298C2×C4×C41—21no—
299C2×C4×C41—22no—
300C2×C4×C41—22no—
301C2×C4×C41—21no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—22no—
307C2×C4×C41—22no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—48no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—41no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41#13512yes—
335C2×C4×C41C22×D411yescharacteristic
336C2×C4×C41C22×D411yescharacteristic
337C2×C4×C41C2×#4111yescharacteristic
338C2×C4×C41C2×#4111yescharacteristic
339C2×C4×C41H(5,𝔽2)11yescharacteristic
340C2×C4×C41H(5,𝔽2)11yescharacteristic
341C8×C41—22no—
342C8×C41—22no—
343C8×C41—41no—
344C8×C41—41no—
345#25163C4111yesmaximal, characteristic, direct product factor, Sylow
346C22×C41—41no—
347C22×C41—42no—
348C22×C41—41no—
349C22×C41—42no—
350C22×C41—42no—
351C22×C41—41no—
352C22×C41—41no—
353C22×C41—41no—
354C22×C41—41no—
355C22×C41—41no—
356C22×C41—81no—
357C22×C41—81no—
358C22×C41—81no—
359C22×C41—81no—
360C22×C41—81no—
361C22×C41—81no—
362C22×C41—81no—
363C22×C41—81no—
364C22×C41—81no—
365C22×C41—81no—
366C22×C41—81no—
367C22×C41#52511yescharacteristic
368C22×C41D4211yescharacteristic
369C22×C41D4211yescharacteristic
370C22×C41C2×#13511yescharacteristic
371C22×C41#57511yescharacteristic
372C22×C41#57611yescharacteristic
373C22×C41#57811yescharacteristic
374C4×C41—24no—
375C4×C41—22no—
376C4×C41—41no—
377C4×C41—42no—
378C4×C41—41no—
379C4×C41—42no—
380C4×C41—41no—
381C4×C41—41no—
382C4×C41—81no—
383C4×C41—81no—
384C4×C41—81no—
385C4×C41C2×#12111yescharacteristic
386C4×C41#53811yescharacteristic
387C4×C41#54611yescharacteristic
388C4×C41#54611yescharacteristic
389C2×#464C2×C4111yescharacteristic, complemented
390C2×#452C2×C4111yescharacteristic, complemented
391C2×#449C2×C4111yescharacteristic
392C2×C4×Q16C2×C4111yescharacteristic, complemented
393#2426C2×C4111yescharacteristic, complemented
394#2341C2×C4111yescharacteristic, complemented
395#2067C2×C4111yescharacteristic, complemented
396#2036C2×C4111yescharacteristic, complemented
397#2033C2×C4111yescharacteristic, complemented
398#2012C2×C4111yescharacteristic, complemented
399#1970C2×C4111yescharacteristic, complemented
400#1923C2×C4111yescharacteristic, complemented
401#1880C2×C4111yescharacteristic, complemented
402#1880C2×C4111yescharacteristic, complemented
403#1863C2×C4111yescharacteristic, complemented
404C2×C41—81no—
405C2×C41—82no—
406C2×C41—161no—
407C2×C41#242411yescharacteristic
408C2×C41#310211yescharacteristic
409C2×C41#312411yescharacteristic
410C2×C41#326811yescharacteristic
411C2×C41#327711yescharacteristic
412C2×C41#328511yescharacteristic
413C2×C41#328711yescharacteristic
414C22×#41C22×C4111yescharacteristic
415C22×Q16C22×C4111yescharacteristic
416C22×SD16C22×C4111yescharacteristic
417C22×SD16C22×C4111yescharacteristic
418C22×D8C22×C4111yescharacteristic
419C2×#124C22×C4111yescharacteristic
420C2×C22⋊Q8C22×C4111yescharacteristic
421C2×#121C22×C4111yescharacteristic
422C2×C4×Q8C22×C4111yescharacteristic
423C2×C4×Q8C22×C4111yescharacteristic
424C2×C4×Q8C22×C4111yescharacteristic
425#464—24no—
426#452—24no—
427#449—24no—
428C4×Q16—24no—
429C2×#107C22×C4111yescharacteristic
430C2×#107C22×C4111yescharacteristic
431C2×C4⋊C8C22×C4111yescharacteristic
432C2×#103C22×C4111yescharacteristic
433C2×#103C22×C4111yescharacteristic
434C2×#103C22×C4111yescharacteristic
435C2×#103C22×C4111yescharacteristic
436C2×#102C22×C4111yescharacteristic
437C2×#102C22×C4111yescharacteristic
438C2×#102C22×C4111yescharacteristic
439C2×#102C22×C4111yescharacteristic
440C2×C22⋊C8C22×C4111yescharacteristic
441C2×C22⋊C8C22×C4111yescharacteristic
442C2×C4×C8C22×C4111yescharacteristic
443#396—21no—
444#394—21no—
445#390—21no—
446#390—21no—
447#390—21no—
448#390C22×C4111yescharacteristic
449#390C22×C4111yescharacteristic
450#390C22×C4111yescharacteristic
451#389C22×C4111yescharacteristic
452#388—21no—
453#380—21no—
454#380C22×C4111yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4C22×C4111yescharacteristic
457#340C22×C4111yescharacteristic
458#340C22×C4111yescharacteristic
459#336C22×C4111yescharacteristic
460#336C22×C4111yescharacteristic
461C41#2516311yescharacteristic, direct product factor, Sylow
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C22×Q8C23×C4111yescharacteristic
469C22×Q8C23×C4111yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4C23×C4111yescharacteristic
473C22×D4C23×C4111yescharacteristic
474C23×C4—21no—
475C23×C4C23×C4111yescharacteristic
476C2×Q16—22no—
477C2×Q16—22no—
478C2×Q16D4×C4114yescomplemented
479C2×SD16—22no—
480C2×SD16—22no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16—41no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C22×C8C23×C4111yescharacteristic
489C22×C8C23×C4111yescharacteristic
490C22×C8C23×C4111yescharacteristic
491C22×C8C23×C4111yescharacteristic
492#124—22no—
493#124—41no—
494C22⋊Q8—22no—
495C22⋊Q8—41no—
496#121—22no—
497#121—41no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8—41no—
502C4×Q8—41no—
503C4×Q8—41no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4C23×C4111yescharacteristic
510C2×C4⋊C4C23×C4111yescharacteristic
511C2×C4⋊C4C23×C4111yescharacteristic
512C2×C4⋊C4C23×C4111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4D4×C4111yescharacteristic
525C2×C22⋊C4D4×C4111yescharacteristic
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42C23×C4111yescharacteristic
530C2×C42C23×C4111yescharacteristic
531#107—22no—
532#107—41no—
533C4⋊C8—22no—
534#103—22no—
535#103—22no—
536#103—22no—
537#103D4×C4114yes—
538#102—22no—
539#102—22no—
540#102—22no—
541#102—41no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544C4×C8—22no—
545#95—21no—
546#95—21no—
547#95D4×C4111yescharacteristic
548#95D4×C4111yescharacteristic
549C24—21no—
550C24—21no—
551C24C2×D4×C4111yescharacteristic
552#41—44no—
553#41—44no—
554#41—44no—
555#41—44no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8C2×D4×C4112yes—
565C2×Q8C2×D4×C4112yes—
566C2×Q8C2×D4×C4112yes—
567C2×Q8#41×C4112yes—
568C2×D4—24no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—81no—
585C2×D4#41×C4112yes—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4C2×D4×C4111yescharacteristic
602C22×C4C2×D4×C4111yescharacteristic
603C22×C4C2×D4×C4111yescharacteristic
604C22×C4C2×D4×C4111yescharacteristic
605C22×C4C2×D4×C4111yescharacteristic
606C22×C4C24×C4111yescharacteristic
607Q16—28no—
608SD16—44no—
609SD16—44no—
610D8—44no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8C2×D4×C4112yes—
622C2×C8C2×D4×C4112yes—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—81no—
635C4⋊C4C2×D4×C4112yes—
636C22⋊C4—22no—
637C22⋊C4—41no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—42no—
654C42—42no—
655C42—42no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23C22×D4×C4111yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685Q8#121×C4114yes—
686D4—22no—
687D4—22no—
688D4—48no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—84no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—48no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4#135×C4112yes—
734C2×C4C22×D4×C4111yescharacteristic
735C2×C4C22×D4×C4111yescharacteristic
736C2×C4C2×#41×C4111yescharacteristic
737C2×C4C2×#41×C4111yescharacteristic
738C2×C4H(5,𝔽2)×C4111yescharacteristic
739C2×C4H(5,𝔽2)×C4111yescharacteristic
740C8—22no—
741C8—22no—
742C8—41no—
743C8—41no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22C41×#52511yescharacteristic
766C22D42×C4111yescharacteristic
767C22D42×C4111yescharacteristic
768C22C2×#135×C4111yescharacteristic
769C22C41×#57511yescharacteristic
770C22C41×#57611yescharacteristic
771C22C41×#57811yescharacteristic
772C4—24no—
773C4—22no—
774C4—41no—
775C4—42no—
776C4—41no—
777C4—42no—
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4C2×#121×C4111yescharacteristic
784C4C41×#53811yescharacteristic
785C4C41×#54611yescharacteristic
786C4C41×#54611yescharacteristic
787C2—81no—
788C2—82no—
789C2—161no—
790C2C41×#242411yescharacteristic
791C2C41×#310211yescharacteristic
792C2C41×#312411yescharacteristic
793C2C41×#326811yescharacteristic
794C2C41×#327711yescharacteristic
795C2C41×#328511yescharacteristic
796C2C41×#328711yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C4×C22⋊C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#464C2semidirect
2. C2×C41×#452C2semidirect
4. C2×C4×Q16×C41C2semidirect
5. C41×#2426C2semidirect
6. C41×#2341C2semidirect
7. C41×#2067C2semidirect
8. C41×#2036C2semidirect
9. C41×#2033C2semidirect
10. C41×#2012C2semidirect
11. C41×#1970C2semidirect
12. C41×#1923C2semidirect
13. C41×#1880C2semidirect
14. C41×#1880C2semidirect
15. C41×#1863C2semidirect
79. C2×Q16×C41D4semidirect
345. #25163C41direct (N × H)
389. C2×#464C2×C41semidirect
390. C2×#452C2×C41semidirect
392. C2×C4×Q16C2×C41semidirect
393. #2426C2×C41semidirect
394. #2341C2×C41semidirect
395. #2067C2×C41semidirect
396. #2036C2×C41semidirect
397. #2033C2×C41semidirect
398. #2012C2×C41semidirect
399. #1970C2×C41semidirect
400. #1923C2×C41semidirect
401. #1880C2×C41semidirect
402. #1880C2×C41semidirect
403. #1863C2×C41semidirect
461. C41#25163direct (N × H)
478. C2×Q16D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4642
C2×C41×#4522
C2×C41×#4492
C2×C4×Q16×C412
C41×#24262
C41×#23412
C41×#20672
C41×#20362
C41×#20332
C41×#20122
C41×#19702
C41×#19232
C41×#18802
C41×#18632
#2516341