Finite Group Databasebeta

← C41×#25575 #23801776

Subgroups — C41×#25575 #23801776

Order 10496.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#553C211yesmaximal, characteristic, complemented
2C2×C41×#488C211yesmaximal, characteristic, complemented
3C2×C41×#463C211yesmaximal, characteristic, complemented
4C41×#2540C211yesmaximal, characteristic, complemented
5C41×#2000C211yesmaximal, characteristic, complemented
6C41×#2000C211yesmaximal, characteristic, complemented
7C41×#1999C211yesmaximal, characteristic, complemented
8C41×#1999C211yesmaximal, characteristic, complemented
9C41×#1989C211yesmaximal, characteristic, complemented
10C41×#1954C211yesmaximal, characteristic, complemented
11C41×#1875C211yesmaximal, characteristic, complemented
12C41×#1874C211yesmaximal, characteristic, complemented
13C41×#1873C211yesmaximal, characteristic, complemented
14C41×#1872C211yesmaximal, characteristic, complemented
15C4×#102×C41C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C22×D8×C41C2211yescharacteristic
18C41×#553—24no—
19C41×#553—24no—
20C2×#126×C41—21no—
21C2×#125×C41C2211yescharacteristic
22C2×#124×C41C2211yescharacteristic
23C2×#123×C41—21no—
24C2×C22⋊Q8×C41C2211yescharacteristic
25C2×C22⋊Q8×C41C2211yescharacteristic
26C2×#121×C41—21no—
27C2×#121×C41C2211yescharacteristic
28C2×#121×C41C2211yescharacteristic
29C2×#121×C41C2211yescharacteristic
30C2×#121×C41C2211yescharacteristic
31C2×C4×D4×C41—21no—
32C2×C4×D4×C41C2211yescharacteristic
33C2×C4×D4×C41C2211yescharacteristic
34C2×#117×C41C2211yescharacteristic
35C22×C4⋊C4×C41C2211yescharacteristic
36C41×#488—24no—
37C41×#463—24no—
38C2×C4⋊C8×C41C2211yescharacteristic
39C2×#103×C41C2211yescharacteristic
40C2×#103×C41C2211yescharacteristic
41C2×#103×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×#102×C41C2211yescharacteristic
46C2×#102×C41C2211yescharacteristic
47C2×C22⋊C8×C41C2211yescharacteristic
48C2×C22⋊C8×C41C2211yescharacteristic
49C2×C22⋊C8×C41C2211yescharacteristic
50C2×C22⋊C8×C41C2211yescharacteristic
51C2×C4×C8×C41C2211yescharacteristic
52C41×#399—21no—
53C41×#392—21no—
54C41×#390—21no—
55C41×#390—21no—
56C4×C4⋊C4×C41C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
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×C41—21no—
73C23×C4×C41C2311yescharacteristic
74C23×C4×C41C2311yescharacteristic
75C2×SD16×C41—22no—
76C2×SD16×C41—41no—
77C2×SD16×C41—41no—
78C2×D8×C41—22no—
79C2×D8×C41—41no—
80C2×D8×C41—41no—
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84C22×C8×C41C2311yescharacteristic
85#126×C41—28no—
86#125×C41—22no—
87#125×C41D414yescomplemented
88#124×C41—22no—
89#124×C41—22no—
90#123×C41—28no—
91C22⋊Q8×C41—22no—
92C22⋊Q8×C41—22no—
93C22⋊Q8×C41—41no—
94C22⋊Q8×C41—41no—
95#121×C41—28no—
96#121×C41—22no—
97#121×C41—22no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—22no—
101#121×C41—22no—
102#121×C41—41no—
103#121×C41—41no—
104C4×D4×C41—28no—
105C4×D4×C41—22no—
106C4×D4×C41—22no—
107C4×D4×C41—22no—
108C4×D4×C41D414yescomplemented
109#117×C41—22no—
110#117×C41—22no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41—21no—
113C2×C4⋊C4×C41—21no—
114C2×C4⋊C4×C41—22no—
115C2×C4⋊C4×C41—22no—
116C2×C4⋊C4×C41—21no—
117C2×C4⋊C4×C41—21no—
118C2×C4⋊C4×C41D411yescharacteristic
119C2×C4⋊C4×C41C2311yescharacteristic
120C2×C4⋊C4×C41C2311yescharacteristic
121C2×C4⋊C4×C41C2311yescharacteristic
122C2×C4⋊C4×C41C2311yescharacteristic
123C2×C4⋊C4×C41C2311yescharacteristic
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41—21no—
128C2×C22⋊C4×C41—21no—
129C2×C22⋊C4×C41—21no—
130C2×C22⋊C4×C41—21no—
131C2×C22⋊C4×C41—21no—
132C2×C22⋊C4×C41—21no—
133C2×C22⋊C4×C41—21no—
134C2×C22⋊C4×C41D411yescharacteristic
135C2×C22⋊C4×C41D411yescharacteristic
136C2×C42×C41—21no—
137C2×C42×C41—21no—
138C2×C42×C41C2311yescharacteristic
139C4⋊C8×C41—22no—
140#103×C41—22no—
141#103×C41—22no—
142#103×C41—22no—
143#102×C41—22no—
144#102×C41—22no—
145#102×C41—22no—
146#102×C41—22no—
147#102×C41—22no—
148C22⋊C8×C41—41no—
149C22⋊C8×C41—41no—
150C22⋊C8×C41—41no—
151C22⋊C8×C41—41no—
152C4×C8×C41—22no—
153#95×C41—21no—
154C24×C41—21no—
155C24×C41—21no—
156C24×C41C2×D411yescharacteristic
157C24×C41C2×D411yescharacteristic
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×D4×C41—24no—
165C2×D4×C41—22no—
166C2×D4×C41—24no—
167C2×D4×C41—22no—
168C2×D4×C41—21no—
169C2×D4×C41—21no—
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—41no—
180C2×D4×C41—42no—
181C2×D4×C41—42no—
182C2×D4×C41—42no—
183C2×D4×C41—42no—
184C2×D4×C41—42no—
185C2×D4×C41—42no—
186C2×D4×C41—81no—
187C2×D4×C41—81no—
188C2×D4×C41—81no—
189C2×D4×C41—81no—
190C2×D4×C41C2×D412yes—
191C22×C4×C41—21no—
192C22×C4×C41—21no—
193C22×C4×C41—21no—
194C22×C4×C41—21no—
195C22×C4×C41—21no—
196C22×C4×C41—24no—
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—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—24no—
210C22×C4×C41—21no—
211C22×C4×C41—81no—
212C22×C4×C41—81no—
213C22×C4×C41—81no—
214C22×C4×C41—81no—
215C22×C4×C41C2×D411yescharacteristic
216C22×C4×C41C2×D411yescharacteristic
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2×D411yescharacteristic
219C22×C4×C41C2411yescharacteristic
220SD16×C41—44no—
221D8×C41—44no—
222C2×C8×C41—21no—
223C2×C8×C41—21no—
224C2×C8×C41—21no—
225C2×C8×C41—21no—
226C2×C8×C41—21no—
227C2×C8×C41—21no—
228C2×C8×C41—21no—
229C2×C8×C41—21no—
230C2×C8×C41—21no—
231C2×C8×C41—21no—
232C2×C8×C41—21no—
233C2×C8×C41—21no—
234C4⋊C4×C41—24no—
235C4⋊C4×C41—24no—
236C4⋊C4×C41—24no—
237C4⋊C4×C41—22no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—21no—
240C4⋊C4×C41—21no—
241C4⋊C4×C41—21no—
242C4⋊C4×C41—21no—
243C4⋊C4×C41—42no—
244C4⋊C4×C41—42no—
245C4⋊C4×C41C2×D412yes—
246C4⋊C4×C41C2×D412yes—
247C4⋊C4×C41C2×D412yes—
248C4⋊C4×C41#4112yes—
249C4⋊C4×C41#4112yes—
250C22⋊C4×C41—24no—
251C22⋊C4×C41—24no—
252C22⋊C4×C41—24no—
253C22⋊C4×C41—24no—
254C22⋊C4×C41—22no—
255C22⋊C4×C41—22no—
256C22⋊C4×C41—42no—
257C22⋊C4×C41—42no—
258C22⋊C4×C41—42no—
259C22⋊C4×C41—42no—
260C22⋊C4×C41—42no—
261C22⋊C4×C41—42no—
262C42×C41—24no—
263C42×C41—81no—
264C42×C41C2×D412yes—
265C42×C41C2×D412yes—
266C23×C41—21no—
267C23×C41—21no—
268C23×C41—21no—
269C23×C41—21no—
270C23×C41—21no—
271C23×C41—21no—
272C23×C41—21no—
273C23×C41—22no—
274C23×C41—21no—
275C23×C41—21no—
276C23×C41—21no—
277C23×C41—21no—
278C23×C41—21no—
279C23×C41—21no—
280C23×C41—41no—
281C23×C41—41no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—41no—
285C23×C41—41no—
286C23×C41—41no—
287C23×C41—41no—
288C23×C41—41no—
289C23×C41—41no—
290C23×C41—41no—
291C23×C41—41no—
292C23×C41—41no—
293C23×C41#13512yes—
294C23×C41C22×D411yescharacteristic
295Q8×C41—41no—
296Q8×C41—41no—
297Q8×C41—41no—
298Q8×C41—41no—
299D4×C41—22no—
300D4×C41—22no—
301D4×C41—44no—
302D4×C41—48no—
303D4×C41—41no—
304D4×C41—41no—
305D4×C41—41no—
306D4×C41—41no—
307D4×C41—41no—
308D4×C41—41no—
309D4×C41—84no—
310D4×C41—84no—
311D4×C41—84no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—21no—
317C2×C4×C41—22no—
318C2×C4×C41—22no—
319C2×C4×C41—21no—
320C2×C4×C41—22no—
321C2×C4×C41—22no—
322C2×C4×C41—22no—
323C2×C4×C41—21no—
324C2×C4×C41—21no—
325C2×C4×C41—21no—
326C2×C4×C41—21no—
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—41no—
341C2×C4×C41—41no—
342C2×C4×C41—41no—
343C2×C4×C41—41no—
344C2×C4×C41—41no—
345C2×C4×C41—41no—
346C2×C4×C41—41no—
347C2×C4×C41—41no—
348C2×C4×C41—84no—
349C2×C4×C41—84no—
350C2×C4×C41#12012yes—
351C2×C4×C41#12012yes—
352C2×C4×C41C22×D411yescharacteristic
353C2×C4×C41C22×D411yescharacteristic
354C2×C4×C41C2×#4111yescharacteristic
355C2×C4×C41C2×#4111yescharacteristic
356C2×C4×C41H(5,𝔽2)11yescharacteristic
357C2×C4×C41H(5,𝔽2)11yescharacteristic
358C8×C41—41no—
359C8×C41—41no—
360C8×C41—41no—
361C8×C41—41no—
362#25575C4111yesmaximal, characteristic, direct product factor, Sylow
363C22×C41—22no—
364C22×C41—22no—
365C22×C41—22no—
366C22×C41—41no—
367C22×C41—41no—
368C22×C41—41no—
369C22×C41—41no—
370C22×C41—41no—
371C22×C41—42no—
372C22×C41—41no—
373C22×C41—42no—
374C22×C41—42no—
375C22×C41—41no—
376C22×C41—41no—
377C22×C41—41no—
378C22×C41—41no—
379C22×C41—41no—
380C22×C41—81no—
381C22×C41—81no—
382C22×C41—81no—
383C22×C41—81no—
384C22×C41—81no—
385C22×C41—81no—
386C22×C41—81no—
387C22×C41—81no—
388C22×C41—81no—
389C22×C41—81no—
390C22×C41—81no—
391C22×C41C2×#12011yescharacteristic
392C22×C41#54611yescharacteristic
393C22×C41#54611yescharacteristic
394C22×C41C2×#13511yescharacteristic
395C22×C41#57511yescharacteristic
396C22×C41#57611yescharacteristic
397C22×C41#57711yescharacteristic
398C4×C41—22no—
399C4×C41—22no—
400C4×C41—41no—
401C4×C41—41no—
402C4×C41—42no—
403C4×C41—42no—
404C4×C41—42no—
405C4×C41—42no—
406C4×C41—42no—
407C4×C41—81no—
408C4×C41#53211yescharacteristic
409C4×C41#53511yescharacteristic
410C4×C41#55011yescharacteristic
411C4×C41#55011yescharacteristic
412C2×#553C2×C4111yescharacteristic, complemented
413C2×#488C2×C4111yescharacteristic, complemented
414C2×#463C2×C4111yescharacteristic, complemented
415#2540C2×C4111yescharacteristic, complemented
416#2000C2×C4111yescharacteristic, complemented
417#2000C2×C4111yescharacteristic, complemented
418#1999C2×C4111yescharacteristic, complemented
419#1999C2×C4111yescharacteristic, complemented
420#1989C2×C4111yescharacteristic, complemented
421#1954C2×C4111yescharacteristic, complemented
422#1875C2×C4111yescharacteristic, complemented
423#1874C2×C4111yescharacteristic, complemented
424#1873C2×C4111yescharacteristic, complemented
425#1872C2×C4111yescharacteristic, complemented
426C4×#102C2×C4111yescharacteristic, complemented
427C2×C41—42no—
428C2×C41—81no—
429C2×C41—82no—
430C2×C41—161no—
431C2×C41#243111yescharacteristic
432C2×C41#300211yescharacteristic
433C2×C41#301211yescharacteristic
434C2×C41#329711yescharacteristic
435C2×C41#330111yescharacteristic
436C2×C41#332211yescharacteristic
437C2×C41#332611yescharacteristic
438C22×SD16C22×C4111yescharacteristic
439C22×D8C22×C4111yescharacteristic
440#553—24no—
441#553—24no—
442C2×#126—21no—
443C2×#125C22×C4111yescharacteristic
444C2×#124C22×C4111yescharacteristic
445C2×#123—21no—
446C2×C22⋊Q8C22×C4111yescharacteristic
447C2×C22⋊Q8C22×C4111yescharacteristic
448C2×#121—21no—
449C2×#121C22×C4111yescharacteristic
450C2×#121C22×C4111yescharacteristic
451C2×#121C22×C4111yescharacteristic
452C2×#121C22×C4111yescharacteristic
453C2×C4×D4—21no—
454C2×C4×D4C22×C4111yescharacteristic
455C2×C4×D4C22×C4111yescharacteristic
456C2×#117C22×C4111yescharacteristic
457C22×C4⋊C4C22×C4111yescharacteristic
458#488—24no—
459#463—24no—
460C2×C4⋊C8C22×C4111yescharacteristic
461C2×#103C22×C4111yescharacteristic
462C2×#103C22×C4111yescharacteristic
463C2×#103C22×C4111yescharacteristic
464C2×#102C22×C4111yescharacteristic
465C2×#102C22×C4111yescharacteristic
466C2×#102C22×C4111yescharacteristic
467C2×#102C22×C4111yescharacteristic
468C2×#102C22×C4111yescharacteristic
469C2×C22⋊C8C22×C4111yescharacteristic
470C2×C22⋊C8C22×C4111yescharacteristic
471C2×C22⋊C8C22×C4111yescharacteristic
472C2×C22⋊C8C22×C4111yescharacteristic
473C2×C4×C8C22×C4111yescharacteristic
474#399—21no—
475#392—21no—
476#390—21no—
477#390—21no—
478C4×C4⋊C4C22×C4111yescharacteristic
479#340C22×C4111yescharacteristic
480#340C22×C4111yescharacteristic
481#340C22×C4111yescharacteristic
482#340C22×C4111yescharacteristic
483#340C22×C4111yescharacteristic
484#340C22×C4111yescharacteristic
485C41#2557511yescharacteristic, direct product factor, Sylow
486C22×Q8C23×C4111yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4D4×C4111yescharacteristic
492C22×D4C23×C4111yescharacteristic
493C22×D4C23×C4111yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C4111yescharacteristic
497C23×C4C23×C4111yescharacteristic
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—41no—
503C2×D8—41no—
504C22×C8C23×C4111yescharacteristic
505C22×C8C23×C4111yescharacteristic
506C22×C8C23×C4111yescharacteristic
507C22×C8C23×C4111yescharacteristic
508#126—28no—
509#125—22no—
510#125D4×C4114yescomplemented
511#124—22no—
512#124—22no—
513#123—28no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—41no—
517C22⋊Q8—41no—
518#121—28no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527C4×D4—28no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4D4×C4114yescomplemented
532#117—22no—
533#117—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C4111yescharacteristic
542C2×C4⋊C4C23×C4111yescharacteristic
543C2×C4⋊C4C23×C4111yescharacteristic
544C2×C4⋊C4C23×C4111yescharacteristic
545C2×C4⋊C4C23×C4111yescharacteristic
546C2×C4⋊C4C23×C4111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4D4×C4111yescharacteristic
558C2×C22⋊C4D4×C4111yescharacteristic
559C2×C42—21no—
560C2×C42—21no—
561C2×C42C23×C4111yescharacteristic
562C4⋊C8—22no—
563#103—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571C22⋊C8—41no—
572C22⋊C8—41no—
573C22⋊C8—41no—
574C22⋊C8—41no—
575C4×C8—22no—
576#95—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C4111yescharacteristic
580C24C2×D4×C4111yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—41no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4C2×D4×C4112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4C2×D4×C4111yescharacteristic
639C22×C4C2×D4×C4111yescharacteristic
640C22×C4C2×D4×C4111yescharacteristic
641C22×C4C2×D4×C4111yescharacteristic
642C22×C4C24×C4111yescharacteristic
643SD16—44no—
644D8—44no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4C2×D4×C4112yes—
669C4⋊C4C2×D4×C4112yes—
670C4⋊C4C2×D4×C4112yes—
671C4⋊C4#41×C4112yes—
672C4⋊C4#41×C4112yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C42—24no—
686C42—81no—
687C42C2×D4×C4112yes—
688C42C2×D4×C4112yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23#135×C4112yes—
717C23C22×D4×C4111yescharacteristic
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—84no—
733D4—84no—
734D4—84no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4#120×C4112yes—
774C2×C4#120×C4112yes—
775C2×C4C22×D4×C4111yescharacteristic
776C2×C4C22×D4×C4111yescharacteristic
777C2×C4C2×#41×C4111yescharacteristic
778C2×C4C2×#41×C4111yescharacteristic
779C2×C4H(5,𝔽2)×C4111yescharacteristic
780C2×C4H(5,𝔽2)×C4111yescharacteristic
781C8—41no—
782C8—41no—
783C8—41no—
784C8—41no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—42no—
801C22—41no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22C2×#120×C4111yescharacteristic
814C22C41×#54611yescharacteristic
815C22C41×#54611yescharacteristic
816C22C2×#135×C4111yescharacteristic
817C22C41×#57511yescharacteristic
818C22C41×#57611yescharacteristic
819C22C41×#57711yescharacteristic
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—81no—
830C4C41×#53211yescharacteristic
831C4C41×#53511yescharacteristic
832C4C41×#55011yescharacteristic
833C4C41×#55011yescharacteristic
834C2—42no—
835C2—81no—
836C2—82no—
837C2—161no—
838C2C41×#243111yescharacteristic
839C2C41×#300211yescharacteristic
840C2C41×#301211yescharacteristic
841C2C41×#329711yescharacteristic
842C2C41×#330111yescharacteristic
843C2C41×#332211yescharacteristic
844C2C41×#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×#553C2semidirect
2. C2×C41×#488C2semidirect
3. C2×C41×#463C2semidirect
4. C41×#2540C2semidirect
5. C41×#2000C2semidirect
6. C41×#2000C2semidirect
7. C41×#1999C2semidirect
8. C41×#1999C2semidirect
9. C41×#1989C2semidirect
10. C41×#1954C2semidirect
11. C41×#1875C2semidirect
12. C41×#1874C2semidirect
13. C41×#1873C2semidirect
14. C41×#1872C2semidirect
15. C4×#102×C41C2semidirect
87. #125×C41D4semidirect
108. C4×D4×C41D4semidirect
362. #25575C41direct (N × H)
412. C2×#553C2×C41semidirect
413. C2×#488C2×C41semidirect
414. C2×#463C2×C41semidirect
415. #2540C2×C41semidirect
416. #2000C2×C41semidirect
417. #2000C2×C41semidirect
418. #1999C2×C41semidirect
419. #1999C2×C41semidirect
420. #1989C2×C41semidirect
421. #1954C2×C41semidirect
422. #1875C2×C41semidirect
423. #1874C2×C41semidirect
424. #1873C2×C41semidirect
425. #1872C2×C41semidirect
426. C4×#102C2×C41semidirect
485. C41#25575direct (N × H)
510. #125D4×C41semidirect
531. C4×D4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5532
C2×C41×#4882
C2×C41×#4632
C41×#25402
C41×#20002
C41×#19992
C41×#19892
C41×#19542
C41×#18752
C41×#18742
C41×#18732
C41×#18722
C4×#102×C412
#2557541