Finite Group Databasebeta

← C41×#25390 #23801591

Subgroups — C41×#25390 #23801591

Order 10496.

1084 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#469C211yesmaximal, characteristic, complemented
2C2×C41×#468C211yesmaximal, characteristic, complemented
3C2×C41×#463C211yesmaximal, characteristic, complemented
4C2×C41×#436C211yesmaximal, characteristic, complemented
5C41×#2540C211yesmaximal, characteristic, complemented
6C41×#2535C211yesmaximal, characteristic, complemented
7C41×#2035C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#2000C211yesmaximal, characteristic, complemented
10C41×#1999C211yesmaximal, characteristic, complemented
11C41×#1958C211yesmaximal, characteristic, complemented
12C41×#1949C211yesmaximal, characteristic, complemented
13C41×#1895C211yesmaximal, characteristic, complemented
14C41×#1894C211yesmaximal, characteristic, complemented
15C4×#102×C41C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C22×D8×C41C2211yescharacteristic
18C22×M16×C41C2211yescharacteristic
19C22×M16×C41C2211yescharacteristic
20C2×#124×C41C2211yescharacteristic
21C2×C22⋊Q8×C41C2211yescharacteristic
22C2×C22⋊Q8×C41C2211yescharacteristic
23C2×#121×C41C2211yescharacteristic
24C2×#121×C41C2211yescharacteristic
25C2×#121×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×C4×D4×C41C2211yescharacteristic
28C2×C4×D4×C41C2211yescharacteristic
29C41×#469—24no—
30C41×#468—24no—
31C41×#463—24no—
32C41×#436—24no—
33C2×#107×C41C2211yescharacteristic
34C2×#106×C41C2211yescharacteristic
35C2×C4⋊C8×C41C2211yescharacteristic
36C2×#103×C41C2211yescharacteristic
37C2×#103×C41C2211yescharacteristic
38C2×#103×C41C2211yescharacteristic
39C2×#102×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×C22⋊C8×C41C2211yescharacteristic
45C2×C22⋊C8×C41C2211yescharacteristic
46C2×C4×C8×C41C2211yescharacteristic
47C41×#399—21no—
48C41×#397—21no—
49C41×#392—21no—
50C41×#392—21no—
51C41×#390—21no—
52C41×#390—21no—
53C41×#386—21no—
54C41×#386—21no—
55C41×#382C2211yescharacteristic
56C41×#380C2211yescharacteristic
57C41×#380C2211yescharacteristic
58C4×C4⋊C4×C41C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#340C2211yescharacteristic
62C41×#340C2211yescharacteristic
63C22×Q8×C41C2311yescharacteristic
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41—21no—
68C22×D4×C41D411yescharacteristic
69C22×D4×C41C2311yescharacteristic
70C22×D4×C41C2311yescharacteristic
71C23×C4×C41—21no—
72C23×C4×C41C2311yescharacteristic
73C23×C4×C41C2311yescharacteristic
74C2×SD16×C41—22no—
75C2×SD16×C41—22no—
76C2×SD16×C41—41no—
77C2×D8×C41—22no—
78C2×D8×C41—22no—
79C2×D8×C41—41no—
80C2×M16×C41—22no—
81C2×M16×C41—22no—
82C2×M16×C41—22no—
83C2×M16×C41—22no—
84C2×M16×C41—41no—
85C2×M16×C41—41no—
86C22×C8×C41C2311yescharacteristic
87C22×C8×C41C2311yescharacteristic
88C22×C8×C41C2311yescharacteristic
89C22×C8×C41C2311yescharacteristic
90#124×C41—22no—
91#124×C41—22no—
92C22⋊Q8×C41—22no—
93C22⋊Q8×C41—22no—
94C22⋊Q8×C41—41no—
95C22⋊Q8×C41—41no—
96#121×C41—22no—
97#121×C41—22no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—41no—
101#121×C41—41no—
102#121×C41—41no—
103#121×C41—41no—
104C4×D4×C41—22no—
105C4×D4×C41—22no—
106C4×D4×C41—22no—
107C4×D4×C41—22no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41D411yescharacteristic
111C2×C4⋊C4×C41C2311yescharacteristic
112C2×C4⋊C4×C41C2311yescharacteristic
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C4⋊C4×C41C2311yescharacteristic
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×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41D411yescharacteristic
128C2×C22⋊C4×C41D411yescharacteristic
129C2×C42×C41—21no—
130C2×C42×C41C2311yescharacteristic
131#107×C41—22no—
132#106×C41—22no—
133C4⋊C8×C41D414yescomplemented
134#103×C41—22no—
135#103×C41—22no—
136#103×C41—41no—
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—41no—
141#102×C41D414yescomplemented
142C22⋊C8×C41—22no—
143C22⋊C8×C41—22no—
144C4×C8×C41—22no—
145#95×C41—21no—
146#95×C41—21no—
147#95×C41—21no—
148#95×C41—21no—
149#95×C41—21no—
150C24×C41—21no—
151C24×C41—21no—
152C24×C41C2×D411yescharacteristic
153C24×C41C2×D411yescharacteristic
154C2×Q8×C41—21no—
155C2×Q8×C41—21no—
156C2×Q8×C41—21no—
157C2×Q8×C41—21no—
158C2×Q8×C41—21no—
159C2×Q8×C41—21no—
160C2×D4×C41—22no—
161C2×D4×C41—21no—
162C2×D4×C41—21no—
163C2×D4×C41—21no—
164C2×D4×C41—21no—
165C2×D4×C41—21no—
166C2×D4×C41—21no—
167C2×D4×C41—21no—
168C2×D4×C41—21no—
169C2×D4×C41—21no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41—41no—
173C2×D4×C41—41no—
174C2×D4×C41—42no—
175C2×D4×C41—42no—
176C2×D4×C41—42no—
177C2×D4×C41—42no—
178C2×D4×C41—42no—
179C2×D4×C41—42no—
180C2×D4×C41—42no—
181C2×D4×C41—42no—
182C2×D4×C41—81no—
183C2×D4×C41—81no—
184C2×D4×C41—81no—
185C2×D4×C41—81no—
186C2×D4×C41C2×D412yes—
187C22×C4×C41—21no—
188C22×C4×C41—21no—
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—21no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—42no—
206C22×C4×C41—81no—
207C22×C4×C41—81no—
208C22×C4×C41C2×D411yescharacteristic
209C22×C4×C41C2×D411yescharacteristic
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41C2×D411yescharacteristic
212C22×C4×C41C2411yescharacteristic
213SD16×C41—44no—
214D8×C41—44no—
215M16×C41—44no—
216M16×C41—44no—
217C2×C8×C41—21no—
218C2×C8×C41—21no—
219C2×C8×C41—21no—
220C2×C8×C41—21no—
221C2×C8×C41—21no—
222C2×C8×C41—21no—
223C2×C8×C41—21no—
224C2×C8×C41—21no—
225C2×C8×C41—21no—
226C2×C8×C41C2×D412yes—
227C2×C8×C41C2×D412yes—
228C2×C8×C41C2×D412yes—
229C4⋊C4×C41—22no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—42no—
239C4⋊C4×C41—42no—
240C4⋊C4×C41C2×D412yes—
241C4⋊C4×C41#4112yes—
242C22⋊C4×C41—22no—
243C22⋊C4×C41—22no—
244C22⋊C4×C41—42no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—42no—
247C22⋊C4×C41—42no—
248C22⋊C4×C41—42no—
249C22⋊C4×C41—42no—
250C22⋊C4×C41—42no—
251C22⋊C4×C41—42no—
252C22⋊C4×C41—42no—
253C22⋊C4×C41—81no—
254C22⋊C4×C41—81no—
255C42×C41—81no—
256C42×C41C2×D412yes—
257C42×C41#4112yes—
258C23×C41—21no—
259C23×C41—21no—
260C23×C41—21no—
261C23×C41—22no—
262C23×C41—21no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—21no—
266C23×C41—21no—
267C23×C41—21no—
268C23×C41—21no—
269C23×C41—21no—
270C23×C41—21no—
271C23×C41—21no—
272C23×C41—21no—
273C23×C41—41no—
274C23×C41—41no—
275C23×C41—41no—
276C23×C41—41no—
277C23×C41—41no—
278C23×C41—41no—
279C23×C41—41no—
280C23×C41—41no—
281C23×C41—41no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—41no—
285C23×C41—41no—
286C23×C41C22×D411yescharacteristic
287Q8×C41—41no—
288Q8×C41—41no—
289Q8×C41—41no—
290Q8×C41—41no—
291D4×C41—22no—
292D4×C41—22no—
293D4×C41—44no—
294D4×C41—41no—
295D4×C41—41no—
296D4×C41—41no—
297D4×C41—41no—
298D4×C41—41no—
299D4×C41—41no—
300D4×C41—84no—
301D4×C41—84no—
302D4×C41—84no—
303D4×C41—84no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—21no—
307C2×C4×C41—21no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—22no—
312C2×C4×C41—21no—
313C2×C4×C41—22no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—41no—
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—41no—
335C2×C4×C41—41no—
336C2×C4×C41—41no—
337C2×C4×C41—41no—
338C2×C4×C41—41no—
339C2×C4×C41—41no—
340C2×C4×C41—84no—
341C2×C4×C41#12112yes—
342C2×C4×C41#12112yes—
343C2×C4×C41C22×D411yescharacteristic
344C2×C4×C41C22×D411yescharacteristic
345C2×C4×C41C2×#4111yescharacteristic
346C2×C4×C41C2×#4111yescharacteristic
347C2×C4×C41H(5,𝔽2)11yescharacteristic
348C2×C4×C41H(5,𝔽2)11yescharacteristic
349C8×C41—22no—
350C8×C41—22no—
351C8×C41—22no—
352C8×C41—41no—
353#25390C4111yesmaximal, characteristic, direct product factor, Sylow
354C22×C41—41no—
355C22×C41—41no—
356C22×C41—42no—
357C22×C41—41no—
358C22×C41—41no—
359C22×C41—42no—
360C22×C41—41no—
361C22×C41—42no—
362C22×C41—41no—
363C22×C41—41no—
364C22×C41—41no—
365C22×C41—41no—
366C22×C41—41no—
367C22×C41—41no—
368C22×C41—41no—
369C22×C41—41no—
370C22×C41—41no—
371C22×C41—81no—
372C22×C41—81no—
373C22×C41—81no—
374C22×C41—81no—
375C22×C41—81no—
376C22×C41—81no—
377C22×C41—81no—
378C22×C41—81no—
379C22×C41—81no—
380C22×C41—81no—
381C22×C41—81no—
382C22×C41C2×#12111yescharacteristic
383C22×C41D4211yescharacteristic
384C22×C41#54611yescharacteristic
385C22×C41#57511yescharacteristic
386C22×C41#57511yescharacteristic
387C22×C41#57611yescharacteristic
388C22×C41#57711yescharacteristic
389C4×C41—22no—
390C4×C41—22no—
391C4×C41—41no—
392C4×C41—41no—
393C4×C41—42no—
394C4×C41—42no—
395C4×C41—81no—
396C4×C41—81no—
397C4×C41—81no—
398C4×C41—81no—
399C4×C41#53211yescharacteristic
400C4×C41#54011yescharacteristic
401C4×C41D4211yescharacteristic
402C4×C41#55011yescharacteristic
403C2×#469C2×C4111yescharacteristic, complemented
404C2×#468C2×C4111yescharacteristic, complemented
405C2×#463C2×C4111yescharacteristic, complemented
406C2×#436C2×C4111yescharacteristic, complemented
407#2540C2×C4111yescharacteristic, complemented
408#2535C2×C4111yescharacteristic, complemented
409#2035C2×C4111yescharacteristic, complemented
410#2033C2×C4111yescharacteristic, complemented
411#2000C2×C4111yescharacteristic, complemented
412#1999C2×C4111yescharacteristic, complemented
413#1958C2×C4111yescharacteristic, complemented
414#1949C2×C4111yescharacteristic, complemented
415#1895C2×C4111yescharacteristic, complemented
416#1894C2×C4111yescharacteristic, complemented
417C4×#102C2×C4111yescharacteristic, complemented
418C2×C41—81no—
419C2×C41—81no—
420C2×C41—82no—
421C2×C41—161no—
422C2×C41#242811yescharacteristic
423C2×C41#305411yescharacteristic
424C2×C41#306211yescharacteristic
425C2×C41#327311yescharacteristic
426C2×C41#327511yescharacteristic
427C2×C41#332211yescharacteristic
428C2×C41#332611yescharacteristic
429C22×SD16C22×C4111yescharacteristic
430C22×D8C22×C4111yescharacteristic
431C22×M16C22×C4111yescharacteristic
432C22×M16C22×C4111yescharacteristic
433C2×#124C22×C4111yescharacteristic
434C2×C22⋊Q8C22×C4111yescharacteristic
435C2×C22⋊Q8C22×C4111yescharacteristic
436C2×#121C22×C4111yescharacteristic
437C2×#121C22×C4111yescharacteristic
438C2×#121C22×C4111yescharacteristic
439C2×#121C22×C4111yescharacteristic
440C2×C4×D4C22×C4111yescharacteristic
441C2×C4×D4C22×C4111yescharacteristic
442#469—24no—
443#468—24no—
444#463—24no—
445#436—24no—
446C2×#107C22×C4111yescharacteristic
447C2×#106C22×C4111yescharacteristic
448C2×C4⋊C8C22×C4111yescharacteristic
449C2×#103C22×C4111yescharacteristic
450C2×#103C22×C4111yescharacteristic
451C2×#103C22×C4111yescharacteristic
452C2×#102C22×C4111yescharacteristic
453C2×#102C22×C4111yescharacteristic
454C2×#102C22×C4111yescharacteristic
455C2×#102C22×C4111yescharacteristic
456C2×#102C22×C4111yescharacteristic
457C2×C22⋊C8C22×C4111yescharacteristic
458C2×C22⋊C8C22×C4111yescharacteristic
459C2×C4×C8C22×C4111yescharacteristic
460#399—21no—
461#397—21no—
462#392—21no—
463#392—21no—
464#390—21no—
465#390—21no—
466#386—21no—
467#386—21no—
468#382C22×C4111yescharacteristic
469#380C22×C4111yescharacteristic
470#380C22×C4111yescharacteristic
471C4×C4⋊C4C22×C4111yescharacteristic
472#340C22×C4111yescharacteristic
473#340C22×C4111yescharacteristic
474#340C22×C4111yescharacteristic
475#340C22×C4111yescharacteristic
476C41#2539011yescharacteristic, direct product factor, Sylow
477C22×Q8C23×C4111yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4D4×C4111yescharacteristic
483C22×D4C23×C4111yescharacteristic
484C22×D4C23×C4111yescharacteristic
485C23×C4—21no—
486C23×C4C23×C4111yescharacteristic
487C23×C4C23×C4111yescharacteristic
488C2×SD16—22no—
489C2×SD16—22no—
490C2×SD16—41no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—41no—
494C2×M16—22no—
495C2×M16—22no—
496C2×M16—22no—
497C2×M16—22no—
498C2×M16—41no—
499C2×M16—41no—
500C22×C8C23×C4111yescharacteristic
501C22×C8C23×C4111yescharacteristic
502C22×C8C23×C4111yescharacteristic
503C22×C8C23×C4111yescharacteristic
504#124—22no—
505#124—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—41no—
515#121—41no—
516#121—41no—
517#121—41no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4D4×C4111yescharacteristic
525C2×C4⋊C4C23×C4111yescharacteristic
526C2×C4⋊C4C23×C4111yescharacteristic
527C2×C4⋊C4C23×C4111yescharacteristic
528C2×C4⋊C4C23×C4111yescharacteristic
529C2×C4⋊C4C23×C4111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4D4×C4111yescharacteristic
542C2×C22⋊C4D4×C4111yescharacteristic
543C2×C42—21no—
544C2×C42C23×C4111yescharacteristic
545#107—22no—
546#106—22no—
547C4⋊C8D4×C4114yescomplemented
548#103—22no—
549#103—22no—
550#103—41no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—41no—
555#102D4×C4114yescomplemented
556C22⋊C8—22no—
557C22⋊C8—22no—
558C4×C8—22no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564C24—21no—
565C24—21no—
566C24C2×D4×C4111yescharacteristic
567C24C2×D4×C4111yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4C2×D4×C4112yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C4111yescharacteristic
623C22×C4C2×D4×C4111yescharacteristic
624C22×C4C2×D4×C4111yescharacteristic
625C22×C4C2×D4×C4111yescharacteristic
626C22×C4C24×C4111yescharacteristic
627SD16—44no—
628D8—44no—
629M16—44no—
630M16—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8C2×D4×C4112yes—
641C2×C8C2×D4×C4112yes—
642C2×C8C2×D4×C4112yes—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4C2×D4×C4112yes—
655C4⋊C4#41×C4112yes—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C42—81no—
670C42C2×D4×C4112yes—
671C42#41×C4112yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23C22×D4×C4111yescharacteristic
701Q8—41no—
702Q8—41no—
703Q8—41no—
704Q8—41no—
705D4—22no—
706D4—22no—
707D4—44no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717D4—84no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—84no—
755C2×C4#121×C4112yes—
756C2×C4#121×C4112yes—
757C2×C4C22×D4×C4111yescharacteristic
758C2×C4C22×D4×C4111yescharacteristic
759C2×C4C2×#41×C4111yescharacteristic
760C2×C4C2×#41×C4111yescharacteristic
761C2×C4H(5,𝔽2)×C4111yescharacteristic
762C2×C4H(5,𝔽2)×C4111yescharacteristic
763C8—22no—
764C8—22no—
765C8—22no—
766C8—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—41no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—41no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×#121×C4111yescharacteristic
796C22D42×C4111yescharacteristic
797C22C41×#54611yescharacteristic
798C22C41×#57511yescharacteristic
799C22C41×#57511yescharacteristic
800C22C41×#57611yescharacteristic
801C22C41×#57711yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—41no—
806C4—41no—
807C4—42no—
808C4—81no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C41×#53211yescharacteristic
813C4C41×#54011yescharacteristic
814C4D42×C4111yescharacteristic
815C4C41×#55011yescharacteristic
816C2—81no—
817C2—81no—
818C2—82no—
819C2—161no—
820C2C41×#242811yescharacteristic
821C2C41×#305411yescharacteristic
822C2C41×#306211yescharacteristic
823C2C41×#327311yescharacteristic
824C2C41×#327511yescharacteristic
825C2C41×#332211yescharacteristic
826C2C41×#332611yescharacteristic
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×#469C2semidirect
2. C2×C41×#468C2semidirect
3. C2×C41×#463C2semidirect
4. C2×C41×#436C2semidirect
5. C41×#2540C2semidirect
6. C41×#2535C2semidirect
7. C41×#2035C2semidirect
8. C41×#2033C2semidirect
9. C41×#2000C2semidirect
10. C41×#1999C2semidirect
11. C41×#1958C2semidirect
12. C41×#1949C2semidirect
13. C41×#1895C2semidirect
14. C41×#1894C2semidirect
15. C4×#102×C41C2semidirect
133. C4⋊C8×C41D4semidirect
141. #102×C41D4semidirect
353. #25390C41direct (N × H)
403. C2×#469C2×C41semidirect
404. C2×#468C2×C41semidirect
405. C2×#463C2×C41semidirect
406. C2×#436C2×C41semidirect
407. #2540C2×C41semidirect
408. #2535C2×C41semidirect
409. #2035C2×C41semidirect
410. #2033C2×C41semidirect
411. #2000C2×C41semidirect
412. #1999C2×C41semidirect
413. #1958C2×C41semidirect
414. #1949C2×C41semidirect
415. #1895C2×C41semidirect
416. #1894C2×C41semidirect
417. C4×#102C2×C41semidirect
476. C41#25390direct (N × H)
547. C4⋊C8D4×C41semidirect
555. #102D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4692
C2×C41×#4682
C2×C41×#4632
C2×C41×#4362
C41×#25402
C41×#25352
C41×#20352
C41×#20332
C41×#20002
C41×#19992
C41×#19582
C41×#19492
C41×#18952
C41×#18942
C4×#102×C412
#2539041