Finite Group Databasebeta

← C41×#25420 #23801621

Subgroups — C41×#25420 #23801621

Order 10496.

992 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#497C211yesmaximal, characteristic, complemented
2C2×C41×#467C211yesmaximal, characteristic, complemented
3C2×C41×#465C211yesmaximal, characteristic
4C2×C41×#441C211yesmaximal, characteristic, complemented
5C41×#2429C211yesmaximal, characteristic, complemented
6C41×#2426C211yesmaximal, characteristic
7C41×#2043C211yesmaximal, characteristic, complemented
8C41×#2042C211yesmaximal, characteristic, complemented
9C41×#2001C211yesmaximal, characteristic, complemented
10C41×#2000C211yesmaximal, characteristic
11C41×#1973C211yesmaximal, characteristic, complemented
12C41×#1944C211yesmaximal, characteristic, complemented
13C41×#1880C211yesmaximal, characteristic, complemented
14C41×#1878C211yesmaximal, characteristic, complemented
15C41×#1752C211yesmaximal, characteristic, complemented
16C22×Q16×C41C2211yescharacteristic
17C22×Q16×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic
19C22×SD16×C41C2211yescharacteristic
20C23×C8×C41C2211yescharacteristic
21C2×C4⋊Q8×C41C2211yescharacteristic
22C2×#124×C41C2211yescharacteristic
23C2×C22⋊Q8×C41C2211yescharacteristic
24C2×C22⋊Q8×C41C2211yescharacteristic
25C2×C22⋊Q8×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×C4×Q8×C41C2211yescharacteristic
28C2×C4×Q8×C41C2211yescharacteristic
29C41×#497—24no—
30C41×#467—24no—
31C41×#465—24no—
32C41×#441—24no—
33C2×#107×C41C2211yescharacteristic
34C2×#106×C41C2211yescharacteristic
35C2×#103×C41C2211yescharacteristic
36C2×#103×C41C2211yescharacteristic
37C2×#103×C41C2211yescharacteristic
38C2×#103×C41C2211yescharacteristic
39C2×#103×C41C2211yescharacteristic
40C2×#103×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×C22⋊C8×C41C2211yescharacteristic
44C2×#97×C41C2211yescharacteristic
45C2×#97×C41C2211yescharacteristic
46C41×#398—21no—
47C41×#396—21no—
48C41×#396—21no—
49C41×#394—21no—
50C41×#391C2211yescharacteristic
51C41×#390—21no—
52C41×#390C2211yescharacteristic
53C41×#389—21no—
54C41×#389C2211yescharacteristic
55C41×#389C2211yescharacteristic
56C41×#388—21no—
57C41×#388—21no—
58C4×C22⋊C4×C41C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#336C2211yescharacteristic
62C41×#336C2211yescharacteristic
63C22×Q8×C41C2311yescharacteristic
64C22×Q8×C41C2311yescharacteristic
65C22×Q8×C41C2311yescharacteristic
66C22×D4×C41—21no—
67C22×D4×C41C2311yescharacteristic
68C23×C4×C41C2311yescharacteristic
69C2×Q16×C41—22no—
70C2×Q16×C41—22no—
71C2×Q16×C41—22no—
72C2×Q16×C41—22no—
73C2×Q16×C41—41no—
74C2×Q16×C41D414yescomplemented
75C2×SD16×C41—22no—
76C2×SD16×C41—22no—
77C2×SD16×C41—22no—
78C2×SD16×C41—22no—
79C2×SD16×C41—22no—
80C2×SD16×C41—41no—
81C22×C8×C41—22no—
82C22×C8×C41—22no—
83C22×C8×C41—22no—
84C22×C8×C41C2311yescharacteristic
85C22×C8×C41C2311yescharacteristic
86C22×C8×C41C2311yescharacteristic
87C22×C8×C41C2311yescharacteristic
88C4⋊Q8×C41—22no—
89C4⋊Q8×C41—41no—
90#124×C41—22no—
91#124×C41—41no—
92C22⋊Q8×C41—22no—
93C22⋊Q8×C41—22no—
94C22⋊Q8×C41—22no—
95C22⋊Q8×C41—41no—
96C22⋊Q8×C41—41no—
97C22⋊Q8×C41—41no—
98#121×C41—22no—
99#121×C41—41no—
100C4×Q8×C41—22no—
101C4×Q8×C41—22no—
102C4×Q8×C41—41no—
103C4×Q8×C41—41no—
104C2×C4⋊C4×C41—21no—
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×C41—21no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41—21no—
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C4⋊C4×C41C2311yescharacteristic
116C2×C4⋊C4×C41C2311yescharacteristic
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×C41C2311yescharacteristic
130C2×C42×C41C2311yescharacteristic
131#107×C41—22no—
132#106×C41D414yes—
133#103×C41—22no—
134#103×C41—22no—
135#103×C41—22no—
136#103×C41—22no—
137#103×C41—22no—
138#103×C41—41no—
139#102×C41—22no—
140#102×C41—41no—
141C22⋊C8×C41—22no—
142#97×C41—22no—
143#97×C41—22no—
144#95×C41—21no—
145#95×C41—21no—
146#95×C41—21no—
147#95×C41—21no—
148#95×C41D411yescharacteristic
149#95×C41D411yescharacteristic
150C24×C41—21no—
151C24×C41C2×D411yescharacteristic
152C2×Q8×C41—21no—
153C2×Q8×C41—21no—
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×Q8×C41—21no—
161C2×Q8×C41—21no—
162C2×Q8×C41—21no—
163C2×Q8×C41—21no—
164C2×Q8×C41—21no—
165C2×Q8×C41—21no—
166C2×Q8×C41—21no—
167C2×Q8×C41—21no—
168C2×Q8×C41C2×D412yes—
169C2×Q8×C41C2×D412yes—
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—42no—
177C2×D4×C41—42no—
178C2×D4×C41—81no—
179C22×C4×C41—21no—
180C22×C4×C41—21no—
181C22×C4×C41—21no—
182C22×C4×C41—21no—
183C22×C4×C41—21no—
184C22×C4×C41—21no—
185C22×C4×C41—21no—
186C22×C4×C41—21no—
187C22×C4×C41—21no—
188C22×C4×C41—21no—
189C22×C4×C41—21no—
190C22×C4×C41—21no—
191C22×C4×C41—21no—
192C22×C4×C41C2×D411yescharacteristic
193C22×C4×C41C2×D411yescharacteristic
194C22×C4×C41C2×D411yescharacteristic
195C22×C4×C41C2×D411yescharacteristic
196C22×C4×C41C2×D411yescharacteristic
197C22×C4×C41C2411yescharacteristic
198Q16×C41—28no—
199Q16×C41—44no—
200SD16×C41—44no—
201SD16×C41—44no—
202C2×C8×C41—21no—
203C2×C8×C41—21no—
204C2×C8×C41—21no—
205C2×C8×C41—21no—
206C2×C8×C41—21no—
207C2×C8×C41—21no—
208C2×C8×C41—21no—
209C2×C8×C41—21no—
210C2×C8×C41—44no—
211C2×C8×C41C2×D412yes—
212C2×C8×C41C2×D412yes—
213C2×C8×C41#4112yes—
214C2×C8×C41#4112yes—
215C4⋊C4×C41—21no—
216C4⋊C4×C41—21no—
217C4⋊C4×C41—21no—
218C4⋊C4×C41—21no—
219C4⋊C4×C41—21no—
220C4⋊C4×C41—21no—
221C4⋊C4×C41—42no—
222C4⋊C4×C41—42no—
223C4⋊C4×C41—42no—
224C4⋊C4×C41—42no—
225C4⋊C4×C41—42no—
226C4⋊C4×C41—42no—
227C4⋊C4×C41—42no—
228C4⋊C4×C41—42no—
229C4⋊C4×C41—81no—
230C4⋊C4×C41C2×D412yes—
231C4⋊C4×C41C2×D412yes—
232C22⋊C4×C41—22no—
233C22⋊C4×C41—41no—
234C22⋊C4×C41—42no—
235C22⋊C4×C41—42no—
236C22⋊C4×C41—42no—
237C22⋊C4×C41—42no—
238C22⋊C4×C41—42no—
239C22⋊C4×C41—42no—
240C22⋊C4×C41—42no—
241C22⋊C4×C41—81no—
242C42×C41—21no—
243C42×C41—21no—
244C42×C41—21no—
245C42×C41—21no—
246C42×C41—42no—
247C42×C41—42no—
248C23×C41—21no—
249C23×C41—21no—
250C23×C41—21no—
251C23×C41—21no—
252C23×C41—21no—
253C23×C41—21no—
254C23×C41—41no—
255C23×C41—41no—
256C23×C41—41no—
257C23×C41—41no—
258C23×C41—41no—
259C23×C41—41no—
260C23×C41—41no—
261C23×C41#13712yes—
262C23×C41C22×D411yescharacteristic
263Q8×C41—22no—
264Q8×C41—22no—
265Q8×C41—22no—
266Q8×C41—22no—
267Q8×C41—41no—
268Q8×C41—41no—
269Q8×C41—41no—
270Q8×C41—41no—
271Q8×C41—41no—
272Q8×C41—41no—
273Q8×C41—41no—
274Q8×C41—41no—
275D4×C41—41no—
276D4×C41—41no—
277D4×C41—41no—
278D4×C41—41no—
279D4×C41—84no—
280C2×C4×C41—21no—
281C2×C4×C41—21no—
282C2×C4×C41—21no—
283C2×C4×C41—21no—
284C2×C4×C41—21no—
285C2×C4×C41—22no—
286C2×C4×C41—22no—
287C2×C4×C41—22no—
288C2×C4×C41—21no—
289C2×C4×C41—22no—
290C2×C4×C41—21no—
291C2×C4×C41—21no—
292C2×C4×C41—21no—
293C2×C4×C41—21no—
294C2×C4×C41—21no—
295C2×C4×C41—21no—
296C2×C4×C41—21no—
297C2×C4×C41—21no—
298C2×C4×C41—21no—
299C2×C4×C41—41no—
300C2×C4×C41—41no—
301C2×C4×C41—41no—
302C2×C4×C41—41no—
303C2×C4×C41—41no—
304C2×C4×C41—41no—
305C2×C4×C41—41no—
306C2×C4×C41—41no—
307C2×C4×C41—41no—
308C2×C4×C41—41no—
309C2×C4×C41—41no—
310C2×C4×C41—41no—
311C2×C4×C41—41no—
312C2×C4×C41—41no—
313C2×C4×C41—41no—
314C2×C4×C41—41no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41C22×D411yescharacteristic
321C2×C4×C41C22×D411yescharacteristic
322C2×C4×C41C2×#4111yescharacteristic
323C2×C4×C41C2×#4111yescharacteristic
324C2×C4×C41H(5,𝔽2)11yescharacteristic
325C2×C4×C41H(5,𝔽2)11yescharacteristic
326C8×C41—22no—
327C8×C41—41no—
328C8×C41—41no—
329C8×C41#12114yes—
330#25420C4111yesmaximal, characteristic, direct product factor, Sylow
331C22×C41—22no—
332C22×C41—22no—
333C22×C41—22no—
334C22×C41—41no—
335C22×C41—41no—
336C22×C41—41no—
337C22×C41—41no—
338C22×C41—81no—
339C22×C41—81no—
340C22×C41—81no—
341C22×C41—81no—
342C22×C41—81no—
343C22×C41—81no—
344C22×C41—81no—
345C22×C41#53211yescharacteristic
346C22×C41D4211yescharacteristic
347C22×C41D4211yescharacteristic
348C22×C41C2×#13711yescharacteristic
349C22×C41#57511yescharacteristic
350C22×C41#57711yescharacteristic
351C22×C41#57811yescharacteristic
352C4×C41—41no—
353C4×C41—42no—
354C4×C41—42no—
355C4×C41—41no—
356C4×C41—42no—
357C4×C41—41no—
358C4×C41—42no—
359C4×C41—41no—
360C4×C41—41no—
361C4×C41—81no—
362C4×C41—81no—
363C4×C41—81no—
364C4×C41C2×#12111yescharacteristic
365C4×C41#54011yescharacteristic
366C4×C41#54611yescharacteristic
367C4×C41#55011yescharacteristic
368C2×#497C2×C4111yescharacteristic, complemented
369C2×#467C2×C4111yescharacteristic, complemented
370C2×#465C2×C4111yescharacteristic
371C2×#441C2×C4111yescharacteristic, complemented
372#2429C2×C4111yescharacteristic, complemented
373#2426C2×C4111yescharacteristic
374#2043C2×C4111yescharacteristic, complemented
375#2042C2×C4111yescharacteristic, complemented
376#2001C2×C4111yescharacteristic, complemented
377#2000C2×C4111yescharacteristic
378#1973C2×C4111yescharacteristic, complemented
379#1944C2×C4111yescharacteristic, complemented
380#1880C2×C4111yescharacteristic, complemented
381#1878C2×C4111yescharacteristic, complemented
382#1752C2×C4111yescharacteristic, complemented
383C2×C41—42no—
384C2×C41—161no—
385C2×C41#242811yescharacteristic
386C2×C41#317811yescharacteristic
387C2×C41#318111yescharacteristic
388C2×C41#326611yescharacteristic
389C2×C41#326911yescharacteristic
390C2×C41#327011yescharacteristic
391C2×C41#327111yescharacteristic
392C22×Q16C22×C4111yescharacteristic
393C22×Q16C22×C4111yescharacteristic
394C22×SD16C22×C4111yescharacteristic
395C22×SD16C22×C4111yescharacteristic
396C23×C8C22×C4111yescharacteristic
397C2×C4⋊Q8C22×C4111yescharacteristic
398C2×#124C22×C4111yescharacteristic
399C2×C22⋊Q8C22×C4111yescharacteristic
400C2×C22⋊Q8C22×C4111yescharacteristic
401C2×C22⋊Q8C22×C4111yescharacteristic
402C2×#121C22×C4111yescharacteristic
403C2×C4×Q8C22×C4111yescharacteristic
404C2×C4×Q8C22×C4111yescharacteristic
405#497—24no—
406#467—24no—
407#465—24no—
408#441—24no—
409C2×#107C22×C4111yescharacteristic
410C2×#106C22×C4111yescharacteristic
411C2×#103C22×C4111yescharacteristic
412C2×#103C22×C4111yescharacteristic
413C2×#103C22×C4111yescharacteristic
414C2×#103C22×C4111yescharacteristic
415C2×#103C22×C4111yescharacteristic
416C2×#103C22×C4111yescharacteristic
417C2×#102C22×C4111yescharacteristic
418C2×#102C22×C4111yescharacteristic
419C2×C22⋊C8C22×C4111yescharacteristic
420C2×#97C22×C4111yescharacteristic
421C2×#97C22×C4111yescharacteristic
422#398—21no—
423#396—21no—
424#396—21no—
425#394—21no—
426#391C22×C4111yescharacteristic
427#390—21no—
428#390C22×C4111yescharacteristic
429#389—21no—
430#389C22×C4111yescharacteristic
431#389C22×C4111yescharacteristic
432#388—21no—
433#388—21no—
434C4×C22⋊C4C22×C4111yescharacteristic
435#340C22×C4111yescharacteristic
436#340C22×C4111yescharacteristic
437#336C22×C4111yescharacteristic
438#336C22×C4111yescharacteristic
439C41#2542011yescharacteristic, direct product factor, Sylow
440C22×Q8C23×C4111yescharacteristic
441C22×Q8C23×C4111yescharacteristic
442C22×Q8C23×C4111yescharacteristic
443C22×D4—21no—
444C22×D4C23×C4111yescharacteristic
445C23×C4C23×C4111yescharacteristic
446C2×Q16—22no—
447C2×Q16—22no—
448C2×Q16—22no—
449C2×Q16—22no—
450C2×Q16—41no—
451C2×Q16D4×C4114yescomplemented
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16—41no—
458C22×C8—22no—
459C22×C8—22no—
460C22×C8—22no—
461C22×C8C23×C4111yescharacteristic
462C22×C8C23×C4111yescharacteristic
463C22×C8C23×C4111yescharacteristic
464C22×C8C23×C4111yescharacteristic
465C4⋊Q8—22no—
466C4⋊Q8—41no—
467#124—22no—
468#124—41no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—41no—
473C22⋊Q8—41no—
474C22⋊Q8—41no—
475#121—22no—
476#121—41no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—41no—
480C4×Q8—41no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4C23×C4111yescharacteristic
491C2×C4⋊C4C23×C4111yescharacteristic
492C2×C4⋊C4C23×C4111yescharacteristic
493C2×C4⋊C4C23×C4111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4D4×C4111yescharacteristic
503C2×C22⋊C4D4×C4111yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42C23×C4111yescharacteristic
507C2×C42C23×C4111yescharacteristic
508#107—22no—
509#106D4×C4114yes—
510#103—22no—
511#103—22no—
512#103—22no—
513#103—22no—
514#103—22no—
515#103—41no—
516#102—22no—
517#102—41no—
518C22⋊C8—22no—
519#97—22no—
520#97—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95D4×C4111yescharacteristic
526#95D4×C4111yescharacteristic
527C24—21no—
528C24C2×D4×C4111yescharacteristic
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8C2×D4×C4112yes—
546C2×Q8C2×D4×C4112yes—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—81no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4C2×D4×C4111yescharacteristic
570C22×C4C2×D4×C4111yescharacteristic
571C22×C4C2×D4×C4111yescharacteristic
572C22×C4C2×D4×C4111yescharacteristic
573C22×C4C2×D4×C4111yescharacteristic
574C22×C4C24×C4111yescharacteristic
575Q16—28no—
576Q16—44no—
577SD16—44no—
578SD16—44no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—44no—
588C2×C8C2×D4×C4112yes—
589C2×C8C2×D4×C4112yes—
590C2×C8#41×C4112yes—
591C2×C8#41×C4112yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—81no—
607C4⋊C4C2×D4×C4112yes—
608C4⋊C4C2×D4×C4112yes—
609C22⋊C4—22no—
610C22⋊C4—41no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—81no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—42no—
624C42—42no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23#137×C4112yes—
639C23C22×D4×C4111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4C22×D4×C4111yescharacteristic
698C2×C4C22×D4×C4111yescharacteristic
699C2×C4C2×#41×C4111yescharacteristic
700C2×C4C2×#41×C4111yescharacteristic
701C2×C4H(5,𝔽2)×C4111yescharacteristic
702C2×C4H(5,𝔽2)×C4111yescharacteristic
703C8—22no—
704C8—41no—
705C8—41no—
706C8#121×C4114yes—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22C41×#53211yescharacteristic
722C22D42×C4111yescharacteristic
723C22D42×C4111yescharacteristic
724C22C2×#137×C4111yescharacteristic
725C22C41×#57511yescharacteristic
726C22C41×#57711yescharacteristic
727C22C41×#57811yescharacteristic
728C4—41no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—41no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4C2×#121×C4111yescharacteristic
741C4C41×#54011yescharacteristic
742C4C41×#54611yescharacteristic
743C4C41×#55011yescharacteristic
744C2—42no—
745C2—161no—
746C2C41×#242811yescharacteristic
747C2C41×#317811yescharacteristic
748C2C41×#318111yescharacteristic
749C2C41×#326611yescharacteristic
750C2C41×#326911yescharacteristic
751C2C41×#327011yescharacteristic
752C2C41×#327111yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×#121×C41C22
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×#497C2semidirect
2. C2×C41×#467C2semidirect
4. C2×C41×#441C2semidirect
5. C41×#2429C2semidirect
7. C41×#2043C2semidirect
8. C41×#2042C2semidirect
9. C41×#2001C2semidirect
11. C41×#1973C2semidirect
12. C41×#1944C2semidirect
13. C41×#1880C2semidirect
14. C41×#1878C2semidirect
15. C41×#1752C2semidirect
74. C2×Q16×C41D4semidirect
330. #25420C41direct (N × H)
368. C2×#497C2×C41semidirect
369. C2×#467C2×C41semidirect
371. C2×#441C2×C41semidirect
372. #2429C2×C41semidirect
374. #2043C2×C41semidirect
375. #2042C2×C41semidirect
376. #2001C2×C41semidirect
378. #1973C2×C41semidirect
379. #1944C2×C41semidirect
380. #1880C2×C41semidirect
381. #1878C2×C41semidirect
382. #1752C2×C41semidirect
439. C41#25420direct (N × H)
451. 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×#4972
C2×C41×#4672
C2×C41×#4652
C2×C41×#4412
C41×#24292
C41×#24262
C41×#20432
C41×#20422
C41×#20012
C41×#20002
C41×#19732
C41×#19442
C41×#18802
C41×#18782
C41×#17522
#2542041