Finite Group Databasebeta

← C41×#23975 #23800176

Subgroups — C41×#23975 #23800176

Order 10496.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#553C211yesmaximal, characteristic, complemented
2C2×C41×#449C211yesmaximal, characteristic, complemented
3C2×C41×#417C211yesmaximal, characteristic, complemented
4C41×#2407C211yesmaximal, characteristic, complemented
5C41×#2026C211yesmaximal, characteristic, complemented
6C41×#2025C211yesmaximal, characteristic, complemented
7C41×#2000C211yesmaximal, characteristic, complemented
8C41×#1999C211yesmaximal, characteristic, complemented
9C41×#1895C211yesmaximal, characteristic, complemented
10C41×#1879C211yesmaximal, characteristic, complemented
11C41×#1877C211yesmaximal, characteristic, complemented
12C41×#1875C211yesmaximal, characteristic, complemented
13C41×#1873C211yesmaximal, characteristic, complemented
14C41×#1870C211yesmaximal, characteristic, complemented
15C41×#1823C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C22×SD16×C41C2211yescharacteristic
18C22×D8×C41C2211yescharacteristic
19C22×M16×C41C2211yescharacteristic
20C41×#553—24no—
21C41×#553—24no—
22C2×#126×C41—21no—
23C2×#125×C41C2211yescharacteristic
24C2×#123×C41—21no—
25C2×C22⋊Q8×C41C2211yescharacteristic
26C2×#121×C41—21no—
27C2×#121×C41C2211yescharacteristic
28C2×#121×C41C2211yescharacteristic
29C2×#121×C41C2211yescharacteristic
30C2×C4×D4×C41—21no—
31C2×C4×D4×C41C2211yescharacteristic
32C2×C4×D4×C41C2211yescharacteristic
33C2×#117×C41C2211yescharacteristic
34C22×C4⋊C4×C41C2211yescharacteristic
35C41×#449—24no—
36C41×#417—24no—
37C2×#103×C41C2211yescharacteristic
38C2×#103×C41C2211yescharacteristic
39C2×#103×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×#102×C41C2211yescharacteristic
45C2×C22⋊C8×C41C2211yescharacteristic
46C2×C22⋊C8×C41C2211yescharacteristic
47C2×C22⋊C8×C41C2211yescharacteristic
48C41×#394—21no—
49C41×#392—21no—
50C41×#391C2211yescharacteristic
51C41×#390C2211yescharacteristic
52C41×#386—21no—
53C41×#385—21no—
54C41×#380C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#336C2211yescharacteristic
62C41×#336C2211yescharacteristic
63C2×#41×C41—22no—
64C2×#41×C41—22no—
65C2×#41×C41—22no—
66C2×#41×C41—22no—
67C2×#41×C41—41no—
68C2×#41×C41—41no—
69C22×Q8×C41C2311yescharacteristic
70C22×D4×C41—21no—
71C22×D4×C41—21no—
72C22×D4×C41—21no—
73C22×D4×C41—21no—
74C22×D4×C41D411yescharacteristic
75C22×D4×C41C2311yescharacteristic
76C22×D4×C41C2311yescharacteristic
77C23×C4×C41—21no—
78C23×C4×C41—21no—
79C23×C4×C41—21no—
80C23×C4×C41C2311yescharacteristic
81C23×C4×C41C2311yescharacteristic
82C2×SD16×C41—22no—
83C2×SD16×C41—22no—
84C2×SD16×C41—41no—
85C2×D8×C41—22no—
86C2×D8×C41—22no—
87C2×D8×C41—41no—
88C2×M16×C41—22no—
89C2×M16×C41—41no—
90C2×M16×C41—41no—
91C22×C8×C41C2311yescharacteristic
92C22×C8×C41C2311yescharacteristic
93C22×C8×C41C2311yescharacteristic
94C22×C8×C41C2311yescharacteristic
95#126×C41—28no—
96#125×C41—22no—
97#125×C41—22no—
98#123×C41—28no—
99C22⋊Q8×C41—22no—
100C22⋊Q8×C41—41no—
101#121×C41—28no—
102#121×C41—22no—
103#121×C41—22no—
104#121×C41—22no—
105#121×C41—22no—
106#121×C41—41no—
107#121×C41D414yescomplemented
108C4×D4×C41—28no—
109C4×D4×C41—22no—
110C4×D4×C41—22no—
111C4×D4×C41—22no—
112C4×D4×C41—22no—
113#117×C41—22no—
114#117×C41—22no—
115C2×C4⋊C4×C41—21no—
116C2×C4⋊C4×C41—22no—
117C2×C4⋊C4×C41—21no—
118C2×C4⋊C4×C41—21no—
119C2×C4⋊C4×C41—21no—
120C2×C4⋊C4×C41D411yescharacteristic
121C2×C4⋊C4×C41D414yescomplemented
122C2×C4⋊C4×C41C2311yescharacteristic
123C2×C4⋊C4×C41C2311yescharacteristic
124C2×C4⋊C4×C41C2311yescharacteristic
125C2×C4⋊C4×C41C2311yescharacteristic
126C2×C4⋊C4×C41C2311yescharacteristic
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×C41—21no—
135C2×C22⋊C4×C41—21no—
136C2×C22⋊C4×C41D411yescharacteristic
137C2×C22⋊C4×C41D411yescharacteristic
138C2×C42×C41—21no—
139C2×C42×C41C2311yescharacteristic
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—41no—
147#102×C41—41no—
148C22⋊C8×C41—22no—
149C22⋊C8×C41—41no—
150C22⋊C8×C41—41no—
151#95×C41—21no—
152#95×C41—21no—
153#95×C41—21no—
154C24×C41—21no—
155C24×C41—21no—
156C24×C41C2×D411yescharacteristic
157C24×C41C2×D411yescharacteristic
158#41×C41—28no—
159#41×C41—44no—
160#41×C41—44no—
161#41×C41—44no—
162C2×Q8×C41—21no—
163C2×Q8×C41—21no—
164C2×Q8×C41—21no—
165C2×Q8×C41—21no—
166C2×Q8×C41—21no—
167C2×Q8×C41#4112yes—
168C2×D4×C41—22no—
169C2×D4×C41—24no—
170C2×D4×C41—24no—
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—21no—
180C2×D4×C41—21no—
181C2×D4×C41—41no—
182C2×D4×C41—41no—
183C2×D4×C41—42no—
184C2×D4×C41—42no—
185C2×D4×C41—42no—
186C2×D4×C41—42no—
187C2×D4×C41—42no—
188C2×D4×C41—42no—
189C2×D4×C41—42no—
190C2×D4×C41—81no—
191C2×D4×C41—81no—
192C2×D4×C41—81no—
193C2×D4×C41C2×D412yes—
194C2×D4×C41#4112yes—
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—24no—
204C22×C4×C41—24no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—21no—
212C22×C4×C41—21no—
213C22×C4×C41—42no—
214C22×C4×C41—42no—
215C22×C4×C41—42no—
216C22×C4×C41—81no—
217C22×C4×C41—81no—
218C22×C4×C41—81no—
219C22×C4×C41—81no—
220C22×C4×C41C2×D411yescharacteristic
221C22×C4×C41C2×D411yescharacteristic
222C22×C4×C41C2×D411yescharacteristic
223C22×C4×C41C2×D411yescharacteristic
224C22×C4×C41C2×D412yes—
225C22×C4×C41C2×D412yes—
226C22×C4×C41C2411yescharacteristic
227SD16×C41—44no—
228D8×C41—44no—
229M16×C41—44no—
230C2×C8×C41—21no—
231C2×C8×C41—21no—
232C2×C8×C41—21no—
233C2×C8×C41—21no—
234C2×C8×C41—21no—
235C2×C8×C41—21no—
236C2×C8×C41—21no—
237C2×C8×C41—21no—
238C2×C8×C41—21no—
239C2×C8×C41—21no—
240C2×C8×C41—21no—
241C2×C8×C41—21no—
242C4⋊C4×C41—24no—
243C4⋊C4×C41—24no—
244C4⋊C4×C41—24no—
245C4⋊C4×C41—22no—
246C4⋊C4×C41—21no—
247C4⋊C4×C41—21no—
248C4⋊C4×C41—21no—
249C4⋊C4×C41—21no—
250C4⋊C4×C41—21no—
251C4⋊C4×C41—21no—
252C4⋊C4×C41—21no—
253C4⋊C4×C41—42no—
254C4⋊C4×C41C2×D412yes—
255C4⋊C4×C41C2×D412yes—
256C4⋊C4×C41C2×D412yes—
257C22⋊C4×C41—24no—
258C22⋊C4×C41—24no—
259C22⋊C4×C41—24no—
260C22⋊C4×C41—22no—
261C22⋊C4×C41—24no—
262C22⋊C4×C41—22no—
263C22⋊C4×C41—42no—
264C22⋊C4×C41—42no—
265C22⋊C4×C41—42no—
266C22⋊C4×C41—81no—
267C22⋊C4×C41—81no—
268C42×C41—24no—
269C42×C41—21no—
270C42×C41—21no—
271C23×C41—21no—
272C23×C41—21no—
273C23×C41—21no—
274C23×C41—21no—
275C23×C41—21no—
276C23×C41—21no—
277C23×C41—21no—
278C23×C41—22no—
279C23×C41—21no—
280C23×C41—22no—
281C23×C41—21no—
282C23×C41—21no—
283C23×C41—21no—
284C23×C41—21no—
285C23×C41—21no—
286C23×C41—41no—
287C23×C41—41no—
288C23×C41—41no—
289C23×C41—41no—
290C23×C41—41no—
291C23×C41—41no—
292C23×C41—41no—
293C23×C41—41no—
294C23×C41—41no—
295C23×C41—41no—
296C23×C41—41no—
297C23×C41—41no—
298C23×C41#12012yes—
299C23×C41C22×D411yescharacteristic
300Q8×C41—22no—
301Q8×C41—22no—
302Q8×C41—41no—
303Q8×C41—41no—
304D4×C41—22no—
305D4×C41—22no—
306D4×C41—22no—
307D4×C41—22no—
308D4×C41—44no—
309D4×C41—48no—
310D4×C41—48no—
311D4×C41—41no—
312D4×C41—41no—
313D4×C41—41no—
314D4×C41—41no—
315D4×C41—84no—
316D4×C41—84no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—22no—
320C2×C4×C41—22no—
321C2×C4×C41—22no—
322C2×C4×C41—22no—
323C2×C4×C41—21no—
324C2×C4×C41—21no—
325C2×C4×C41—22no—
326C2×C4×C41—21no—
327C2×C4×C41—22no—
328C2×C4×C41—22no—
329C2×C4×C41—21no—
330C2×C4×C41—22no—
331C2×C4×C41—21no—
332C2×C4×C41—21no—
333C2×C4×C41—21no—
334C2×C4×C41—21no—
335C2×C4×C41—21no—
336C2×C4×C41—48no—
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—41no—
349C2×C4×C41—41no—
350C2×C4×C41—41no—
351C2×C4×C41—41no—
352C2×C4×C41—41no—
353C2×C4×C41—41no—
354C2×C4×C41—41no—
355C2×C4×C41—84no—
356C2×C4×C41—84no—
357C2×C4×C41#12012yes—
358C2×C4×C41C22×D411yescharacteristic
359C2×C4×C41C22×D411yescharacteristic
360C2×C4×C41C2×#4111yescharacteristic
361C2×C4×C41C2×#4111yescharacteristic
362C2×C4×C41H(5,𝔽2)11yescharacteristic
363C2×C4×C41H(5,𝔽2)11yescharacteristic
364C8×C41—41no—
365C8×C41—41no—
366C8×C41—41no—
367C8×C41—41no—
368#23975C4111yesmaximal, characteristic, direct product factor, Sylow
369C22×C41—22no—
370C22×C41—22no—
371C22×C41—22no—
372C22×C41—41no—
373C22×C41—41no—
374C22×C41—41no—
375C22×C41—41no—
376C22×C41—42no—
377C22×C41—41no—
378C22×C41—42no—
379C22×C41—41no—
380C22×C41—42no—
381C22×C41—42no—
382C22×C41—41no—
383C22×C41—41no—
384C22×C41—42no—
385C22×C41—41no—
386C22×C41—41no—
387C22×C41—42no—
388C22×C41—41no—
389C22×C41—81no—
390C22×C41—81no—
391C22×C41—81no—
392C22×C41—81no—
393C22×C41—81no—
394C22×C41—81no—
395C22×C41—81no—
396C22×C41—81no—
397C22×C41C2×#12011yescharacteristic
398C22×C41#54611yescharacteristic
399C22×C41#54611yescharacteristic
400C22×C41#57511yescharacteristic
401C22×C41#57511yescharacteristic
402C22×C41#57611yescharacteristic
403C22×C41#57711yescharacteristic
404C4×C41—22no—
405C4×C41—41no—
406C4×C41—42no—
407C4×C41—41no—
408C4×C41—42no—
409C4×C41—41no—
410C4×C41—42no—
411C4×C41—42no—
412C4×C41—81no—
413C4×C41—81no—
414C4×C41#52511yescharacteristic
415C4×C41#53511yescharacteristic
416C4×C41#54611yescharacteristic
417C4×C41#54611yescharacteristic
418C2×#553C2×C4111yescharacteristic, complemented
419C2×#449C2×C4111yescharacteristic, complemented
420C2×#417C2×C4111yescharacteristic, complemented
421#2407C2×C4111yescharacteristic, complemented
422#2026C2×C4111yescharacteristic, complemented
423#2025C2×C4111yescharacteristic, complemented
424#2000C2×C4111yescharacteristic, complemented
425#1999C2×C4111yescharacteristic, complemented
426#1895C2×C4111yescharacteristic, complemented
427#1879C2×C4111yescharacteristic, complemented
428#1877C2×C4111yescharacteristic, complemented
429#1875C2×C4111yescharacteristic, complemented
430#1873C2×C4111yescharacteristic, complemented
431#1870C2×C4111yescharacteristic, complemented
432#1823C2×C4111yescharacteristic, complemented
433C2×C41—42no—
434C2×C41—81no—
435C2×C41—82no—
436C2×C41—82no—
437C2×C41#240411yescharacteristic
438C2×C41#300511yescharacteristic
439C2×C41#301211yescharacteristic
440C2×C41#330711yescharacteristic
441C2×C41#330911yescharacteristic
442C2×C41#332211yescharacteristic
443C2×C41#332611yescharacteristic
444C22×#41C22×C4111yescharacteristic
445C22×SD16C22×C4111yescharacteristic
446C22×D8C22×C4111yescharacteristic
447C22×M16C22×C4111yescharacteristic
448#553—24no—
449#553—24no—
450C2×#126—21no—
451C2×#125C22×C4111yescharacteristic
452C2×#123—21no—
453C2×C22⋊Q8C22×C4111yescharacteristic
454C2×#121—21no—
455C2×#121C22×C4111yescharacteristic
456C2×#121C22×C4111yescharacteristic
457C2×#121C22×C4111yescharacteristic
458C2×C4×D4—21no—
459C2×C4×D4C22×C4111yescharacteristic
460C2×C4×D4C22×C4111yescharacteristic
461C2×#117C22×C4111yescharacteristic
462C22×C4⋊C4C22×C4111yescharacteristic
463#449—24no—
464#417—24no—
465C2×#103C22×C4111yescharacteristic
466C2×#103C22×C4111yescharacteristic
467C2×#103C22×C4111yescharacteristic
468C2×#102C22×C4111yescharacteristic
469C2×#102C22×C4111yescharacteristic
470C2×#102C22×C4111yescharacteristic
471C2×#102C22×C4111yescharacteristic
472C2×#102C22×C4111yescharacteristic
473C2×C22⋊C8C22×C4111yescharacteristic
474C2×C22⋊C8C22×C4111yescharacteristic
475C2×C22⋊C8C22×C4111yescharacteristic
476#394—21no—
477#392—21no—
478#391C22×C4111yescharacteristic
479#390C22×C4111yescharacteristic
480#386—21no—
481#385—21no—
482#380C22×C4111yescharacteristic
483#340C22×C4111yescharacteristic
484#340C22×C4111yescharacteristic
485#340C22×C4111yescharacteristic
486#340C22×C4111yescharacteristic
487#340C22×C4111yescharacteristic
488#340C22×C4111yescharacteristic
489#336C22×C4111yescharacteristic
490#336C22×C4111yescharacteristic
491C41#2397511yescharacteristic, direct product factor, Sylow
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C23×C4111yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4D4×C4111yescharacteristic
504C22×D4C23×C4111yescharacteristic
505C22×D4C23×C4111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C23×C4111yescharacteristic
510C23×C4C23×C4111yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8C23×C4111yescharacteristic
521C22×C8C23×C4111yescharacteristic
522C22×C8C23×C4111yescharacteristic
523C22×C8C23×C4111yescharacteristic
524#126—28no—
525#125—22no—
526#125—22no—
527#123—28no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—41no—
536#121D4×C4114yescomplemented
537C4×D4—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C4111yescharacteristic
550C2×C4⋊C4D4×C4114yescomplemented
551C2×C4⋊C4C23×C4111yescharacteristic
552C2×C4⋊C4C23×C4111yescharacteristic
553C2×C4⋊C4C23×C4111yescharacteristic
554C2×C4⋊C4C23×C4111yescharacteristic
555C2×C4⋊C4C23×C4111yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C4111yescharacteristic
566C2×C22⋊C4D4×C4111yescharacteristic
567C2×C42—21no—
568C2×C42C23×C4111yescharacteristic
569#103—22no—
570#103—22no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—41no—
579C22⋊C8—41no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—21no—
585C24C2×D4×C4111yescharacteristic
586C24C2×D4×C4111yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#41×C4112yes—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4C2×D4×C4112yes—
623C2×D4#41×C4112yes—
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—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—81no—
649C22×C4C2×D4×C4111yescharacteristic
650C22×C4C2×D4×C4111yescharacteristic
651C22×C4C2×D4×C4111yescharacteristic
652C22×C4C2×D4×C4111yescharacteristic
653C22×C4C2×D4×C4112yes—
654C22×C4C2×D4×C4112yes—
655C22×C4C24×C4111yescharacteristic
656SD16—44no—
657D8—44no—
658M16—44no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4C2×D4×C4112yes—
684C4⋊C4C2×D4×C4112yes—
685C4⋊C4C2×D4×C4112yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23#120×C4112yes—
728C23C22×D4×C4111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—44no—
738D4—48no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—48no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4#120×C4112yes—
787C2×C4C22×D4×C4111yescharacteristic
788C2×C4C22×D4×C4111yescharacteristic
789C2×C4C2×#41×C4111yescharacteristic
790C2×C4C2×#41×C4111yescharacteristic
791C2×C4H(5,𝔽2)×C4111yescharacteristic
792C2×C4H(5,𝔽2)×C4111yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×#120×C4111yescharacteristic
826C22C41×#54611yescharacteristic
827C22C41×#54611yescharacteristic
828C22C41×#57511yescharacteristic
829C22C41×#57511yescharacteristic
830C22C41×#57611yescharacteristic
831C22C41×#57711yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4C41×#52511yescharacteristic
843C4C41×#53511yescharacteristic
844C4C41×#54611yescharacteristic
845C4C41×#54611yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2C41×#240411yescharacteristic
851C2C41×#300511yescharacteristic
852C2C41×#301211yescharacteristic
853C2C41×#330711yescharacteristic
854C2C41×#330911yescharacteristic
855C2C41×#332211yescharacteristic
856C2C41×#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×#449C2semidirect
3. C2×C41×#417C2semidirect
4. C41×#2407C2semidirect
5. C41×#2026C2semidirect
6. C41×#2025C2semidirect
7. C41×#2000C2semidirect
8. C41×#1999C2semidirect
9. C41×#1895C2semidirect
10. C41×#1879C2semidirect
11. C41×#1877C2semidirect
12. C41×#1875C2semidirect
13. C41×#1873C2semidirect
14. C41×#1870C2semidirect
15. C41×#1823C2semidirect
107. #121×C41D4semidirect
121. C2×C4⋊C4×C41D4semidirect
368. #23975C41direct (N × H)
418. C2×#553C2×C41semidirect
419. C2×#449C2×C41semidirect
420. C2×#417C2×C41semidirect
421. #2407C2×C41semidirect
422. #2026C2×C41semidirect
423. #2025C2×C41semidirect
424. #2000C2×C41semidirect
425. #1999C2×C41semidirect
426. #1895C2×C41semidirect
427. #1879C2×C41semidirect
428. #1877C2×C41semidirect
429. #1875C2×C41semidirect
430. #1873C2×C41semidirect
431. #1870C2×C41semidirect
432. #1823C2×C41semidirect
491. C41#23975direct (N × H)
536. #121D4×C41semidirect
550. C2×C4⋊C4D4×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×#4492
C2×C41×#4172
C41×#24072
C41×#20262
C41×#20252
C41×#20002
C41×#19992
C41×#18952
C41×#18792
C41×#18772
C41×#18752
C41×#18732
C41×#18702
C41×#18232
#2397541