Finite Group Databasebeta

← C41×#23236 #23799437

Subgroups — C41×#23236 #23799437

Order 10496.

710 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3135C211yesmaximal, characteristic
2C41×#2962C211yesmaximal, characteristic, complemented
3C41×#2935C211yesmaximal, characteristic
4C41×#1986C211yesmaximal, characteristic, complemented
5C41×#1980C211yesmaximal, characteristic
6C41×#1938C211yesmaximal, characteristic, complemented
7C41×#1937C211yesmaximal, characteristic, complemented
8C41×#1929C211yesmaximal, characteristic, complemented
9C41×#1929C211yesmaximal, characteristic, complemented
10C41×#1866C211yesmaximal, characteristic, complemented
11C41×#1866C211yesmaximal, characteristic, complemented
12C41×#1778C211yesmaximal, characteristic, complemented
13C41×#1771C211yesmaximal, characteristic, complemented
14C41×#1765C211yesmaximal, characteristic, complemented
15C41×#1764C211yesmaximal, characteristic, complemented
16C2×#131×C41C2211yescharacteristic
17C2×#131×C41C2211yescharacteristic
18C41×#533C2211yescharacteristic
19C41×#532C2211yescharacteristic
20C41×#491C411yescharacteristic, complemented
21C41×#491C411yescharacteristic, complemented
22C41×#490C411yescharacteristic, complemented
23C41×#490C411yescharacteristic, complemented
24C41×#489C411yescharacteristic, complemented
25C41×#489C411yescharacteristic, complemented
26C41×#489C411yescharacteristic, complemented
27C41×#489C411yescharacteristic, complemented
28C41×#446—21no—
29C41×#446—21no—
30C41×#446—21no—
31C8×Q8×C41—21no—
32C41×#436—21no—
33C41×#435—21no—
34C41×#435—21no—
35C8×D4×C41—21no—
36C2×#108×C41C2211yescharacteristic
37C2×#108×C41C2211yescharacteristic
38C41×#424C2211yescharacteristic
39C41×#424C2211yescharacteristic
40C2×C4⋊C8×C41C2211yescharacteristic
41C2×#104×C41C2211yescharacteristic
42C2×#104×C41C2211yescharacteristic
43C2×#104×C41C2211yescharacteristic
44C2×#104×C41C2211yescharacteristic
45C41×#416C2211yescharacteristic
46C41×#416C2211yescharacteristic
47C41×#416C2211yescharacteristic
48C41×#416C2211yescharacteristic
49C41×#408C2211yescharacteristic
50C41×#408C2211yescharacteristic
51C41×#405C2211yescharacteristic
52C41×#405C2211yescharacteristic
53C4×M16×C41C2211yescharacteristic
54C4×M16×C41C2211yescharacteristic
55C2×#97×C41C2211yescharacteristic
56C2×#97×C41C2211yescharacteristic
57C2×C4×C8×C41C2211yescharacteristic
58C4×C4⋊C4×C41C2211yescharacteristic
59C41×#341C2211yescharacteristic
60C41×#341C2211yescharacteristic
61C41×#339C2211yescharacteristic
62C41×#339C2211yescharacteristic
63C41×#339C2211yescharacteristic
64C41×#339C2211yescharacteristic
65C41×#336C2211yescharacteristic
66C41×#336C2211yescharacteristic
67C2×#41×C41C2311yescharacteristic
68C2×#41×C41C2311yescharacteristic
69#131×C41—22no—
70#131×C41—22no—
71#131×C41—41no—
72#131×C41—41no—
73C2×M16×C41—21no—
74C2×M16×C41—21no—
75C2×M16×C41C2311yescharacteristic
76C2×M16×C41C2311yescharacteristic
77C2×M16×C41C2311yescharacteristic
78C2×M16×C41C2311yescharacteristic
79C22×C8×C41—21no—
80C22×C8×C41—21no—
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84C22×C8×C41C2311yescharacteristic
85C4⋊Q8×C41C2×C411yescharacteristic
86C4⋊Q8×C41C2×C411yescharacteristic
87C4⋊Q8×C41C2×C411yescharacteristic
88#127×C41C2×C411yescharacteristic
89#125×C41C2×C411yescharacteristic
90#125×C41C2×C411yescharacteristic
91#124×C41C2×C411yescharacteristic
92#124×C41C2×C411yescharacteristic
93C22⋊Q8×C41—21no—
94C22⋊Q8×C41—21no—
95#121×C41—21no—
96#121×C41—21no—
97C4×Q8×C41—21no—
98C4×Q8×C41—21no—
99C4×D4×C41—21no—
100C4×D4×C41—21no—
101#117×C41C2311yescharacteristic
102#117×C41C2311yescharacteristic
103C2×C4⋊C4×C41—21no—
104C2×C42×C41C2311yescharacteristic
105C2×C42×C41C2311yescharacteristic
106C2×C42×C41C2311yescharacteristic
107#108×C41—22no—
108#108×C41—22no—
109C4⋊C8×C41—21no—
110C4⋊C8×C41—21no—
111C4⋊C8×C41—21no—
112C4⋊C8×C41—21no—
113C4⋊C8×C41D411yescharacteristic
114C4⋊C8×C41D411yescharacteristic
115C4⋊C8×C41D411yescharacteristic
116C4⋊C8×C41D411yescharacteristic
117#104×C41—22no—
118#104×C41—22no—
119#104×C41—41no—
120#104×C41—41no—
121#103×C41C2×C411yescharacteristic
122#103×C41C2×C411yescharacteristic
123#103×C41C2×C411yescharacteristic
124#103×C41C2×C411yescharacteristic
125#103×C41C2×C411yescharacteristic
126#103×C41C2×C411yescharacteristic
127#103×C41C2×C411yescharacteristic
128#103×C41C2×C411yescharacteristic
129#102×C41C2×C411yescharacteristic
130#102×C41C2×C411yescharacteristic
131#102×C41C2×C411yescharacteristic
132#102×C41C2×C411yescharacteristic
133#102×C41C2×C411yescharacteristic
134#102×C41C2×C411yescharacteristic
135#102×C41C2×C411yescharacteristic
136#102×C41C2×C411yescharacteristic
137C22⋊C8×C41—21no—
138C22⋊C8×C41—21no—
139C22⋊C8×C41—21no—
140C22⋊C8×C41—21no—
141#97×C41—21no—
142#97×C41—21no—
143#97×C41—21no—
144#97×C41—21no—
145#97×C41—41no—
146#97×C41C2×C411yescharacteristic
147#97×C41C2×C411yescharacteristic
148#97×C41C2×C411yescharacteristic
149#97×C41C2×C411yescharacteristic
150C4×C8×C41—21no—
151C4×C8×C41—21no—
152C4×C8×C41—21no—
153C4×C8×C41—21no—
154C4×C8×C41—41no—
155#95×C41—21no—
156#41×C41—21no—
157#41×C41—21no—
158#41×C41—21no—
159#41×C41—21no—
160#41×C41—21no—
161#41×C41—21no—
162#41×C41—21no—
163#41×C41—21no—
164C2×Q8×C41—21no—
165C2×Q8×C41—21no—
166C2×Q8×C41C22×C411yescharacteristic
167C2×Q8×C41C22×C411yescharacteristic
168C2×D4×C41—21no—
169C2×D4×C41—21no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41C22×C411yescharacteristic
173C2×D4×C41C22×C411yescharacteristic
174C22×C4×C41—21no—
175C22×C4×C41—21no—
176C22×C4×C41—21no—
177C22×C4×C41—21no—
178C22×C4×C41#4111yescharacteristic
179C22×C4×C41#4111yescharacteristic
180C22×C4×C41C2411yescharacteristic
181M16×C41—21no—
182M16×C41—21no—
183M16×C41—21no—
184M16×C41—21no—
185M16×C41—21no—
186M16×C41—21no—
187M16×C41—42no—
188M16×C41—42no—
189M16×C41#4112yes—
190M16×C41#4112yes—
191C2×C8×C41—21no—
192C2×C8×C41—21no—
193C2×C8×C41—21no—
194C2×C8×C41—21no—
195C2×C8×C41—21no—
196C2×C8×C41—21no—
197C2×C8×C41—21no—
198C2×C8×C41—21no—
199C2×C8×C41—21no—
200C2×C8×C41—21no—
201C2×C8×C41—21no—
202C2×C8×C41—21no—
203C2×C8×C41—42no—
204C2×C8×C41—42no—
205C2×C8×C41C22×C411yescharacteristic
206C2×C8×C41C22×C411yescharacteristic
207C2×C8×C41C22×C411yescharacteristic
208C2×C8×C41C22×C411yescharacteristic
209C2×C8×C41C2×D411yescharacteristic
210C2×C8×C41C2×D411yescharacteristic
211C2×C8×C41C2×D411yescharacteristic
212C2×C8×C41C2×D411yescharacteristic
213C4⋊C4×C41—21no—
214C4⋊C4×C41—21no—
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×C41C22×C411yescharacteristic
223C4⋊C4×C41C22×C411yescharacteristic
224C4⋊C4×C41C22×C411yescharacteristic
225C4⋊C4×C41C22×C411yescharacteristic
226C22⋊C4×C41—21no—
227C22⋊C4×C41—21no—
228C22⋊C4×C41—21no—
229C22⋊C4×C41—21no—
230C22⋊C4×C41—21no—
231C22⋊C4×C41—21no—
232C42×C41—21no—
233C42×C41—21no—
234C42×C41—21no—
235C42×C41—21no—
236C42×C41—21no—
237C42×C41—21no—
238C42×C41C22×C411yescharacteristic
239C42×C41C22×C411yescharacteristic
240C42×C41C2×D411yescharacteristic
241C42×C41C2×D411yescharacteristic
242C23×C41—21no—
243C23×C41—21no—
244C23×C41C2×#4111yescharacteristic
245Q8×C41—21no—
246Q8×C41—21no—
247Q8×C41—21no—
248Q8×C41—21no—
249Q8×C41—42no—
250Q8×C41—81no—
251D4×C41—21no—
252D4×C41—21no—
253D4×C41—21no—
254D4×C41—21no—
255D4×C41—42no—
256D4×C41—41no—
257D4×C41—41no—
258D4×C41—41no—
259D4×C41—41no—
260D4×C41—81no—
261C2×C4×C41—22no—
262C2×C4×C41—21no—
263C2×C4×C41—21no—
264C2×C4×C41—21no—
265C2×C4×C41—21no—
266C2×C4×C41—21no—
267C2×C4×C41—21no—
268C2×C4×C41—41no—
269C2×C4×C41—41no—
270C2×C4×C41—41no—
271C2×C4×C41—41no—
272C2×C4×C41—41no—
273C2×C4×C41—41no—
274C2×C4×C41—41no—
275C2×C4×C41—41no—
276C2×C4×C41—41no—
277C2×C4×C41—41no—
278C2×C4×C41—41no—
279C2×C4×C41C4×D411yescharacteristic
280C2×C4×C41C4×D411yescharacteristic
281C2×C4×C41C4×D411yescharacteristic
282C2×C4×C41C4×D411yescharacteristic
283C2×C4×C41C23×C411yescharacteristic
284C2×C4×C41C22×D411yescharacteristic
285C2×C4×C41C2×#4111yescharacteristic
286C2×C4×C41C2×#4111yescharacteristic
287C2×C4×C41H(5,𝔽2)11yescharacteristic
288C2×C4×C412−1+411yescharacteristic
289C8×C41—21no—
290C8×C41—21no—
291C8×C41—21no—
292C8×C41—21no—
293C8×C41—21no—
294C8×C41—21no—
295C8×C41—21no—
296C8×C41—21no—
297C8×C41—22no—
298C8×C41—22no—
299C8×C41—41no—
300C8×C41—41no—
301#23236C4111yesmaximal, characteristic, direct product factor, Sylow
302C22×C41—21no—
303C22×C41—21no—
304C22×C41—41no—
305C22×C41—41no—
306C22×C41—41no—
307C22×C41—41no—
308C22×C41—41no—
309C22×C41—41no—
310C22×C41C2×C4×D411yescharacteristic
311C22×C41#55611yescharacteristic
312C22×C41#55911yescharacteristic
313C4×C41—21no—
314C4×C41—21no—
315C4×C41—21no—
316C4×C41—21no—
317C4×C41—42no—
318C4×C41—41no—
319C4×C41—41no—
320C4×C41—41no—
321C4×C41—41no—
322C4×C41—41no—
323C4×C41—41no—
324C4×C41—81no—
325C4×C41C4×#4111yescharacteristic
326C4×C41#52011yescharacteristic
327C4×C41#54611yescharacteristic
328C4×C41#54811yescharacteristic
329#3135C2×C4111yescharacteristic
330#2962C2×C4111yescharacteristic, complemented
331#2935C2×C4111yescharacteristic
332#1986C2×C4111yescharacteristic, complemented
333#1980C2×C4111yescharacteristic
334#1938C2×C4111yescharacteristic, complemented
335#1937C2×C4111yescharacteristic, complemented
336#1929C2×C4111yescharacteristic, complemented
337#1929C2×C4111yescharacteristic, complemented
338#1866C2×C4111yescharacteristic, complemented
339#1866C2×C4111yescharacteristic, complemented
340#1778C2×C4111yescharacteristic, complemented
341#1771C2×C4111yescharacteristic, complemented
342#1765C2×C4111yescharacteristic, complemented
343#1764C2×C4111yescharacteristic, complemented
344C2×C41—21no—
345C2×C41—21no—
346C2×C41—81no—
347C2×C41—81no—
348C2×C41#236711yescharacteristic
349C2×C41#295511yescharacteristic
350C2×C41#295611yescharacteristic
351C2×#131C22×C4111yescharacteristic
352C2×#131C22×C4111yescharacteristic
353#533C22×C4111yescharacteristic
354#532C22×C4111yescharacteristic
355#491C4×C4111yescharacteristic, complemented
356#491C4×C4111yescharacteristic, complemented
357#490C4×C4111yescharacteristic, complemented
358#490C4×C4111yescharacteristic, complemented
359#489C4×C4111yescharacteristic, complemented
360#489C4×C4111yescharacteristic, complemented
361#489C4×C4111yescharacteristic, complemented
362#489C4×C4111yescharacteristic, complemented
363#446—21no—
364#446—21no—
365#446—21no—
366C8×Q8—21no—
367#436—21no—
368#435—21no—
369#435—21no—
370C8×D4—21no—
371C2×#108C22×C4111yescharacteristic
372C2×#108C22×C4111yescharacteristic
373#424C22×C4111yescharacteristic
374#424C22×C4111yescharacteristic
375C2×C4⋊C8C22×C4111yescharacteristic
376C2×#104C22×C4111yescharacteristic
377C2×#104C22×C4111yescharacteristic
378C2×#104C22×C4111yescharacteristic
379C2×#104C22×C4111yescharacteristic
380#416C22×C4111yescharacteristic
381#416C22×C4111yescharacteristic
382#416C22×C4111yescharacteristic
383#416C22×C4111yescharacteristic
384#408C22×C4111yescharacteristic
385#408C22×C4111yescharacteristic
386#405C22×C4111yescharacteristic
387#405C22×C4111yescharacteristic
388C4×M16C22×C4111yescharacteristic
389C4×M16C22×C4111yescharacteristic
390C2×#97C22×C4111yescharacteristic
391C2×#97C22×C4111yescharacteristic
392C2×C4×C8C22×C4111yescharacteristic
393C4×C4⋊C4C22×C4111yescharacteristic
394#341C22×C4111yescharacteristic
395#341C22×C4111yescharacteristic
396#339C22×C4111yescharacteristic
397#339C22×C4111yescharacteristic
398#339C22×C4111yescharacteristic
399#339C22×C4111yescharacteristic
400#336C22×C4111yescharacteristic
401#336C22×C4111yescharacteristic
402C41#2323611yescharacteristic, direct product factor, Sylow
403C2×#41C23×C4111yescharacteristic
404C2×#41C23×C4111yescharacteristic
405#131—22no—
406#131—22no—
407#131—41no—
408#131—41no—
409C2×M16—21no—
410C2×M16—21no—
411C2×M16C23×C4111yescharacteristic
412C2×M16C23×C4111yescharacteristic
413C2×M16C23×C4111yescharacteristic
414C2×M16C23×C4111yescharacteristic
415C22×C8—21no—
416C22×C8—21no—
417C22×C8C23×C4111yescharacteristic
418C22×C8C23×C4111yescharacteristic
419C22×C8C23×C4111yescharacteristic
420C22×C8C23×C4111yescharacteristic
421C4⋊Q8C2×C4×C4111yescharacteristic
422C4⋊Q8C2×C4×C4111yescharacteristic
423C4⋊Q8C2×C4×C4111yescharacteristic
424#127C2×C4×C4111yescharacteristic
425#125C2×C4×C4111yescharacteristic
426#125C2×C4×C4111yescharacteristic
427#124C2×C4×C4111yescharacteristic
428#124C2×C4×C4111yescharacteristic
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431#121—21no—
432#121—21no—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×D4—21no—
436C4×D4—21no—
437#117C23×C4111yescharacteristic
438#117C23×C4111yescharacteristic
439C2×C4⋊C4—21no—
440C2×C42C23×C4111yescharacteristic
441C2×C42C23×C4111yescharacteristic
442C2×C42C23×C4111yescharacteristic
443#108—22no—
444#108—22no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8D4×C4111yescharacteristic
450C4⋊C8D4×C4111yescharacteristic
451C4⋊C8D4×C4111yescharacteristic
452C4⋊C8D4×C4111yescharacteristic
453#104—22no—
454#104—22no—
455#104—41no—
456#104—41no—
457#103C2×C4×C4111yescharacteristic
458#103C2×C4×C4111yescharacteristic
459#103C2×C4×C4111yescharacteristic
460#103C2×C4×C4111yescharacteristic
461#103C2×C4×C4111yescharacteristic
462#103C2×C4×C4111yescharacteristic
463#103C2×C4×C4111yescharacteristic
464#103C2×C4×C4111yescharacteristic
465#102C2×C4×C4111yescharacteristic
466#102C2×C4×C4111yescharacteristic
467#102C2×C4×C4111yescharacteristic
468#102C2×C4×C4111yescharacteristic
469#102C2×C4×C4111yescharacteristic
470#102C2×C4×C4111yescharacteristic
471#102C2×C4×C4111yescharacteristic
472#102C2×C4×C4111yescharacteristic
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—21no—
476C22⋊C8—21no—
477#97—21no—
478#97—21no—
479#97—21no—
480#97—21no—
481#97—41no—
482#97C2×C4×C4111yescharacteristic
483#97C2×C4×C4111yescharacteristic
484#97C2×C4×C4111yescharacteristic
485#97C2×C4×C4111yescharacteristic
486C4×C8—21no—
487C4×C8—21no—
488C4×C8—21no—
489C4×C8—21no—
490C4×C8—41no—
491#95—21no—
492#41—21no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8C22×C4×C4111yescharacteristic
503C2×Q8C22×C4×C4111yescharacteristic
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C22×C4×C4111yescharacteristic
509C2×D4C22×C4×C4111yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4#41×C4111yescharacteristic
515C22×C4#41×C4111yescharacteristic
516C22×C4C24×C4111yescharacteristic
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—21no—
522M16—21no—
523M16—42no—
524M16—42no—
525M16#41×C4112yes—
526M16#41×C4112yes—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—42no—
540C2×C8—42no—
541C2×C8C22×C4×C4111yescharacteristic
542C2×C8C22×C4×C4111yescharacteristic
543C2×C8C22×C4×C4111yescharacteristic
544C2×C8C22×C4×C4111yescharacteristic
545C2×C8C2×D4×C4111yescharacteristic
546C2×C8C2×D4×C4111yescharacteristic
547C2×C8C2×D4×C4111yescharacteristic
548C2×C8C2×D4×C4111yescharacteristic
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—42no—
558C4⋊C4C22×C4×C4111yescharacteristic
559C4⋊C4C22×C4×C4111yescharacteristic
560C4⋊C4C22×C4×C4111yescharacteristic
561C4⋊C4C22×C4×C4111yescharacteristic
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42C22×C4×C4111yescharacteristic
575C42C22×C4×C4111yescharacteristic
576C42C2×D4×C4111yescharacteristic
577C42C2×D4×C4111yescharacteristic
578C23—21no—
579C23—21no—
580C23C2×#41×C4111yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—21no—
585Q8—42no—
586Q8—81no—
587D4—21no—
588D4—21no—
589D4—21no—
590D4—21no—
591D4—42no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—81no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4C4×D4×C4111yescharacteristic
616C2×C4C4×D4×C4111yescharacteristic
617C2×C4C4×D4×C4111yescharacteristic
618C2×C4C4×D4×C4111yescharacteristic
619C2×C4C23×C4×C4111yescharacteristic
620C2×C4C22×D4×C4111yescharacteristic
621C2×C4C2×#41×C4111yescharacteristic
622C2×C4C2×#41×C4111yescharacteristic
623C2×C4H(5,𝔽2)×C4111yescharacteristic
624C2×C42−1+4×C4111yescharacteristic
625C8—21no—
626C8—21no—
627C8—21no—
628C8—21no—
629C8—21no—
630C8—21no—
631C8—21no—
632C8—21no—
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C22—21no—
638C22—21no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22C2×C4×D4×C4111yescharacteristic
646C22C41×#55611yescharacteristic
647C22C41×#55911yescharacteristic
648C4—21no—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—81no—
660C4C4×#41×C4111yescharacteristic
661C4C41×#52011yescharacteristic
662C4C41×#54611yescharacteristic
663C4C41×#54811yescharacteristic
664C2—21no—
665C2—21no—
666C2—81no—
667C2—81no—
668C2C41×#236711yescharacteristic
669C2C41×#295511yescharacteristic
670C2C41×#295611yescharacteristic
subgroupG/H
centerC2×C4×C41C22×D4
commutatorC2×C4C23×C4×C41
Frattini, cosocleC22×C4C24×C41
socleC22×C41C2×C4×D4
prime radicalC41×#532C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C2×C4⋊C8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2962C2semidirect
4. C41×#1986C2semidirect
6. C41×#1938C2semidirect
7. C41×#1937C2semidirect
8. C41×#1929C2semidirect
9. C41×#1929C2semidirect
10. C41×#1866C2semidirect
11. C41×#1866C2semidirect
12. C41×#1778C2semidirect
13. C41×#1771C2semidirect
14. C41×#1765C2semidirect
15. C41×#1764C2semidirect
20. C41×#491C4semidirect
21. C41×#491C4semidirect
22. C41×#490C4semidirect
23. C41×#490C4semidirect
24. C41×#489C4semidirect
25. C41×#489C4semidirect
26. C41×#489C4semidirect
27. C41×#489C4semidirect
301. #23236C41direct (N × H)
330. #2962C2×C41semidirect
332. #1986C2×C41semidirect
334. #1938C2×C41semidirect
335. #1937C2×C41semidirect
336. #1929C2×C41semidirect
337. #1929C2×C41semidirect
338. #1866C2×C41semidirect
339. #1866C2×C41semidirect
340. #1778C2×C41semidirect
341. #1771C2×C41semidirect
342. #1765C2×C41semidirect
343. #1764C2×C41semidirect
355. #491C4×C41semidirect
356. #491C4×C41semidirect
357. #490C4×C41semidirect
358. #490C4×C41semidirect
359. #489C4×C41semidirect
360. #489C4×C41semidirect
361. #489C4×C41semidirect
362. #489C4×C41semidirect
402. C41#23236direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31352
C41×#29622
C41×#29352
C41×#19862
C41×#19802
C41×#19382
C41×#19372
C41×#19292
C41×#18662
C41×#17782
C41×#17712
C41×#17652
C41×#17642
#2323641