Finite Group Databasebeta

← C41×#25423 #23801624

Subgroups — C41×#25423 #23801624

Order 10496.

1006 conjugacy classes of subgroups.

The subgroup lattice has 756 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×#440C211yesmaximal, characteristic, complemented
5C41×#2429C211yesmaximal, characteristic, complemented
6C41×#2427C211yesmaximal, characteristic
7C41×#2043C211yesmaximal, characteristic, complemented
8C41×#2042C211yesmaximal, characteristic, complemented
9C41×#2001C211yesmaximal, characteristic, complemented
10C41×#2000C211yesmaximal, characteristic
11C41×#1971C211yesmaximal, characteristic, complemented
12C41×#1943C211yesmaximal, characteristic, complemented
13C41×#1878C211yesmaximal, characteristic, complemented
14C41×#1877C211yesmaximal, 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×D4×C41C2211yescharacteristic
29C41×#497—24no—
30C41×#467—24no—
31C41×#465—24no—
32C41×#440—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×#397—21no—
48C41×#396—21no—
49C41×#394—21no—
50C41×#391C2211yescharacteristic
51C41×#391C2211yescharacteristic
52C41×#389—21no—
53C41×#389C2211yescharacteristic
54C41×#389C2211yescharacteristic
55C41×#388—21no—
56C41×#386—21no—
57C41×#380—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×C41—21no—
69C23×C4×C41C2311yescharacteristic
70C2×Q16×C41—22no—
71C2×Q16×C41—22no—
72C2×Q16×C41—22no—
73C2×Q16×C41—22no—
74C2×Q16×C41—22no—
75C2×Q16×C41—41no—
76C2×SD16×C41—22no—
77C2×SD16×C41—22no—
78C2×SD16×C41—22no—
79C2×SD16×C41—22no—
80C2×SD16×C41—41no—
81C2×SD16×C41D414yes—
82C22×C8×C41—22no—
83C22×C8×C41—22no—
84C22×C8×C41—22no—
85C22×C8×C41C2311yescharacteristic
86C22×C8×C41C2311yescharacteristic
87C22×C8×C41C2311yescharacteristic
88C22×C8×C41C2311yescharacteristic
89C4⋊Q8×C41—22no—
90C4⋊Q8×C41—41no—
91#124×C41—22no—
92#124×C41—41no—
93C22⋊Q8×C41—22no—
94C22⋊Q8×C41—22no—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41—41no—
97C22⋊Q8×C41—41no—
98C22⋊Q8×C41—41no—
99#121×C41—22no—
100#121×C41—41no—
101C4×Q8×C41—22no—
102C4×Q8×C41—41no—
103C4×D4×C41—22no—
104C4×D4×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×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×C41D411yescharacteristic
125C2×C22⋊C4×C41D411yescharacteristic
126C2×C42×C41—21no—
127C2×C42×C41C2311yescharacteristic
128C2×C42×C41C2311yescharacteristic
129#107×C41D414yescomplemented
130#106×C41—22no—
131#103×C41—22no—
132#103×C41—22no—
133#103×C41—22no—
134#103×C41—22no—
135#103×C41—41no—
136#103×C41—41no—
137#102×C41—22no—
138#102×C41—22no—
139C22⋊C8×C41—22no—
140#97×C41—22no—
141#97×C41—22no—
142#95×C41—21no—
143#95×C41—21no—
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×C41—21no—
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—42no—
176C2×D4×C41—42no—
177C2×D4×C41—81no—
178C2×D4×C41C2×D412yes—
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×C41—42no—
193C22×C4×C41—42no—
194C22×C4×C41—81no—
195C22×C4×C41C2×D411yescharacteristic
196C22×C4×C41C2×D411yescharacteristic
197C22×C4×C41C2×D411yescharacteristic
198C22×C4×C41C2×D411yescharacteristic
199C22×C4×C41C2×D411yescharacteristic
200C22×C4×C41C2411yescharacteristic
201Q16×C41—44no—
202Q16×C41—44no—
203SD16×C41—28no—
204SD16×C41—44no—
205C2×C8×C41—21no—
206C2×C8×C41—21no—
207C2×C8×C41—21no—
208C2×C8×C41—21no—
209C2×C8×C41—21no—
210C2×C8×C41—21no—
211C2×C8×C41—21no—
212C2×C8×C41—21no—
213C2×C8×C41—44no—
214C2×C8×C41C2×D412yes—
215C2×C8×C41C2×D412yes—
216C2×C8×C41#4112yes—
217C2×C8×C41#4112yes—
218C4⋊C4×C41—21no—
219C4⋊C4×C41—21no—
220C4⋊C4×C41—21no—
221C4⋊C4×C41—21no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—42no—
225C4⋊C4×C41—42no—
226C4⋊C4×C41—42no—
227C4⋊C4×C41—42no—
228C4⋊C4×C41—42no—
229C4⋊C4×C41—42no—
230C4⋊C4×C41—42no—
231C4⋊C4×C41—81no—
232C4⋊C4×C41C2×D412yes—
233C4⋊C4×C41C2×D412yes—
234C22⋊C4×C41—22no—
235C22⋊C4×C41—41no—
236C22⋊C4×C41—42no—
237C22⋊C4×C41—42no—
238C22⋊C4×C41—42no—
239C22⋊C4×C41—42no—
240C22⋊C4×C41—42no—
241C22⋊C4×C41—42no—
242C22⋊C4×C41—42no—
243C42×C41—21no—
244C42×C41—21no—
245C42×C41—21no—
246C42×C41—21no—
247C42×C41—42no—
248C23×C41—21no—
249C23×C41—21no—
250C23×C41—21no—
251C23×C41—21no—
252C23×C41—21no—
253C23×C41—21no—
254C23×C41—22no—
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—41no—
266Q8×C41—41no—
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—22no—
276D4×C41—22no—
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—21no—
288C2×C4×C41—22no—
289C2×C4×C41—21no—
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—41no—
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×C41—84no—
321C2×C4×C41C22×D411yescharacteristic
322C2×C4×C41C22×D411yescharacteristic
323C2×C4×C41C2×#4111yescharacteristic
324C2×C4×C41C2×#4111yescharacteristic
325C2×C4×C41H(5,𝔽2)11yescharacteristic
326C2×C4×C41H(5,𝔽2)11yescharacteristic
327C8×C41—22no—
328C8×C41—41no—
329C8×C41—41no—
330C8×C41#12114yes—
331#25423C4111yesmaximal, characteristic, direct product factor, Sylow
332C22×C41—22no—
333C22×C41—22no—
334C22×C41—22no—
335C22×C41—41no—
336C22×C41—41no—
337C22×C41—41no—
338C22×C41—41no—
339C22×C41—42no—
340C22×C41—42no—
341C22×C41—42no—
342C22×C41—81no—
343C22×C41—81no—
344C22×C41—81no—
345C22×C41—81no—
346C22×C41#53211yescharacteristic
347C22×C41D4211yescharacteristic
348C22×C41D4211yescharacteristic
349C22×C41C2×#13711yescharacteristic
350C22×C41#57511yescharacteristic
351C22×C41#57711yescharacteristic
352C22×C41#57811yescharacteristic
353C4×C41—41no—
354C4×C41—42no—
355C4×C41—41no—
356C4×C41—41no—
357C4×C41—42no—
358C4×C41—42no—
359C4×C41—41no—
360C4×C41—41no—
361C4×C41—81no—
362C4×C41—81no—
363C4×C41—81no—
364C4×C41—81no—
365C4×C41C2×#12111yescharacteristic
366C4×C41#54011yescharacteristic
367C4×C41#54611yescharacteristic
368C4×C41#55011yescharacteristic
369C2×#497C2×C4111yescharacteristic, complemented
370C2×#467C2×C4111yescharacteristic, complemented
371C2×#465C2×C4111yescharacteristic
372C2×#440C2×C4111yescharacteristic, complemented
373#2429C2×C4111yescharacteristic, complemented
374#2427C2×C4111yescharacteristic
375#2043C2×C4111yescharacteristic, complemented
376#2042C2×C4111yescharacteristic, complemented
377#2001C2×C4111yescharacteristic, complemented
378#2000C2×C4111yescharacteristic
379#1971C2×C4111yescharacteristic, complemented
380#1943C2×C4111yescharacteristic, complemented
381#1878C2×C4111yescharacteristic, complemented
382#1877C2×C4111yescharacteristic, complemented
383#1752C2×C4111yescharacteristic, complemented
384C2×C41—42no—
385C2×C41—82no—
386C2×C41#242811yescharacteristic
387C2×C41#317811yescharacteristic
388C2×C41#318111yescharacteristic
389C2×C41#326611yescharacteristic
390C2×C41#326711yescharacteristic
391C2×C41#326911yescharacteristic
392C2×C41#327011yescharacteristic
393C22×Q16C22×C4111yescharacteristic
394C22×Q16C22×C4111yescharacteristic
395C22×SD16C22×C4111yescharacteristic
396C22×SD16C22×C4111yescharacteristic
397C23×C8C22×C4111yescharacteristic
398C2×C4⋊Q8C22×C4111yescharacteristic
399C2×#124C22×C4111yescharacteristic
400C2×C22⋊Q8C22×C4111yescharacteristic
401C2×C22⋊Q8C22×C4111yescharacteristic
402C2×C22⋊Q8C22×C4111yescharacteristic
403C2×#121C22×C4111yescharacteristic
404C2×C4×Q8C22×C4111yescharacteristic
405C2×C4×D4C22×C4111yescharacteristic
406#497—24no—
407#467—24no—
408#465—24no—
409#440—24no—
410C2×#107C22×C4111yescharacteristic
411C2×#106C22×C4111yescharacteristic
412C2×#103C22×C4111yescharacteristic
413C2×#103C22×C4111yescharacteristic
414C2×#103C22×C4111yescharacteristic
415C2×#103C22×C4111yescharacteristic
416C2×#103C22×C4111yescharacteristic
417C2×#103C22×C4111yescharacteristic
418C2×#102C22×C4111yescharacteristic
419C2×#102C22×C4111yescharacteristic
420C2×C22⋊C8C22×C4111yescharacteristic
421C2×#97C22×C4111yescharacteristic
422C2×#97C22×C4111yescharacteristic
423#398—21no—
424#397—21no—
425#396—21no—
426#394—21no—
427#391C22×C4111yescharacteristic
428#391C22×C4111yescharacteristic
429#389—21no—
430#389C22×C4111yescharacteristic
431#389C22×C4111yescharacteristic
432#388—21no—
433#386—21no—
434#380—21no—
435C4×C22⋊C4C22×C4111yescharacteristic
436#340C22×C4111yescharacteristic
437#340C22×C4111yescharacteristic
438#336C22×C4111yescharacteristic
439#336C22×C4111yescharacteristic
440C41#2542311yescharacteristic, direct product factor, Sylow
441C22×Q8C23×C4111yescharacteristic
442C22×Q8C23×C4111yescharacteristic
443C22×Q8C23×C4111yescharacteristic
444C22×D4—21no—
445C22×D4C23×C4111yescharacteristic
446C23×C4—21no—
447C23×C4C23×C4111yescharacteristic
448C2×Q16—22no—
449C2×Q16—22no—
450C2×Q16—22no—
451C2×Q16—22no—
452C2×Q16—22no—
453C2×Q16—41no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16—22no—
458C2×SD16—41no—
459C2×SD16D4×C4114yes—
460C22×C8—22no—
461C22×C8—22no—
462C22×C8—22no—
463C22×C8C23×C4111yescharacteristic
464C22×C8C23×C4111yescharacteristic
465C22×C8C23×C4111yescharacteristic
466C22×C8C23×C4111yescharacteristic
467C4⋊Q8—22no—
468C4⋊Q8—41no—
469#124—22no—
470#124—41no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—41no—
475C22⋊Q8—41no—
476C22⋊Q8—41no—
477#121—22no—
478#121—41no—
479C4×Q8—22no—
480C4×Q8—41no—
481C4×D4—22no—
482C4×D4—41no—
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⋊C4—21no—
491C2×C4⋊C4C23×C4111yescharacteristic
492C2×C4⋊C4C23×C4111yescharacteristic
493C2×C4⋊C4C23×C4111yescharacteristic
494C2×C4⋊C4C23×C4111yescharacteristic
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×C42C23×C4111yescharacteristic
506C2×C42C23×C4111yescharacteristic
507#107D4×C4114yescomplemented
508#106—22no—
509#103—22no—
510#103—22no—
511#103—22no—
512#103—22no—
513#103—41no—
514#103—41no—
515#102—22no—
516#102—22no—
517C22⋊C8—22no—
518#97—22no—
519#97—22no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95D4×C4111yescharacteristic
527#95D4×C4111yescharacteristic
528C24—21no—
529C24C2×D4×C4111yescharacteristic
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×Q8—21no—
546C2×Q8—21no—
547C2×Q8C2×D4×C4112yes—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—81no—
556C2×D4C2×D4×C4112yes—
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×C4—21no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—81no—
573C22×C4C2×D4×C4111yescharacteristic
574C22×C4C2×D4×C4111yescharacteristic
575C22×C4C2×D4×C4111yescharacteristic
576C22×C4C2×D4×C4111yescharacteristic
577C22×C4C2×D4×C4111yescharacteristic
578C22×C4C24×C4111yescharacteristic
579Q16—44no—
580Q16—44no—
581SD16—28no—
582SD16—44no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—44no—
592C2×C8C2×D4×C4112yes—
593C2×C8C2×D4×C4112yes—
594C2×C8#41×C4112yes—
595C2×C8#41×C4112yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—81no—
610C4⋊C4C2×D4×C4112yes—
611C4⋊C4C2×D4×C4112yes—
612C22⋊C4—22no—
613C22⋊C4—41no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—42no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23#137×C4112yes—
640C23C22×D4×C4111yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653D4—22no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—84no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
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×C4—41no—
698C2×C4—84no—
699C2×C4C22×D4×C4111yescharacteristic
700C2×C4C22×D4×C4111yescharacteristic
701C2×C4C2×#41×C4111yescharacteristic
702C2×C4C2×#41×C4111yescharacteristic
703C2×C4H(5,𝔽2)×C4111yescharacteristic
704C2×C4H(5,𝔽2)×C4111yescharacteristic
705C8—22no—
706C8—41no—
707C8—41no—
708C8#121×C4114yes—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22C41×#53211yescharacteristic
724C22D42×C4111yescharacteristic
725C22D42×C4111yescharacteristic
726C22C2×#137×C4111yescharacteristic
727C22C41×#57511yescharacteristic
728C22C41×#57711yescharacteristic
729C22C41×#57811yescharacteristic
730C4—41no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4C2×#121×C4111yescharacteristic
743C4C41×#54011yescharacteristic
744C4C41×#54611yescharacteristic
745C4C41×#55011yescharacteristic
746C2—42no—
747C2—82no—
748C2C41×#242811yescharacteristic
749C2C41×#317811yescharacteristic
750C2C41×#318111yescharacteristic
751C2C41×#326611yescharacteristic
752C2C41×#326711yescharacteristic
753C2C41×#326911yescharacteristic
754C2C41×#327011yescharacteristic
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×#440C2semidirect
5. C41×#2429C2semidirect
7. C41×#2043C2semidirect
8. C41×#2042C2semidirect
9. C41×#2001C2semidirect
11. C41×#1971C2semidirect
12. C41×#1943C2semidirect
13. C41×#1878C2semidirect
14. C41×#1877C2semidirect
15. C41×#1752C2semidirect
129. #107×C41D4semidirect
331. #25423C41direct (N × H)
369. C2×#497C2×C41semidirect
370. C2×#467C2×C41semidirect
372. C2×#440C2×C41semidirect
373. #2429C2×C41semidirect
375. #2043C2×C41semidirect
376. #2042C2×C41semidirect
377. #2001C2×C41semidirect
379. #1971C2×C41semidirect
380. #1943C2×C41semidirect
381. #1878C2×C41semidirect
382. #1877C2×C41semidirect
383. #1752C2×C41semidirect
440. C41#25423direct (N × H)
507. #107D4×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×#4402
C41×#24292
C41×#24272
C41×#20432
C41×#20422
C41×#20012
C41×#20002
C41×#19712
C41×#19432
C41×#18782
C41×#18772
C41×#17522
#2542341