Finite Group Databasebeta

← C41×#18416 #23794617

Subgroups — C41×#18416 #23794617

Order 10496.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3535C211yesmaximal, characteristic, complemented
2C41×#3194C211yesmaximal, characteristic, complemented
3C41×#3187C211yesmaximal, characteristic, complemented
4C41×#2661C211yesmaximal, characteristic, complemented
5C41×#1612C211yesmaximal, characteristic, complemented
6C41×#1611C211yesmaximal, characteristic, complemented
7C41×#1609C211yesmaximal, characteristic, complemented
8C41×#1608C211yesmaximal, characteristic, complemented
9C41×#1600C211yesmaximal, characteristic, complemented
10C41×#1599C211yesmaximal, characteristic, complemented
11C41×#1597C211yesmaximal, characteristic, complemented
12C41×#1596C211yesmaximal, characteristic, complemented
13C41×#1508C211yesmaximal, characteristic, complemented
14C41×#1501C211yesmaximal, characteristic, complemented
15C41×#1468C211yesmaximal, characteristic, complemented
16C41×#563—21no—
17C41×#562—21no—
18C41×#554—21no—
19C41×#552—21no—
20C41×#551—21no—
21C41×#551—21no—
22C41×#547—21no—
23C41×#546—21no—
24C41×#544C2211yescharacteristic
25C41×#543C2211yescharacteristic
26C41×#542—21no—
27C41×#539—21no—
28C41×#539—21no—
29C41×#539C2211yescharacteristic
30C41×#538C2211yescharacteristic
31C41×#536—21no—
32C41×#525C2211yescharacteristic
33C2×#123×C41C2211yescharacteristic
34C2×C22⋊Q8×C41C2211yescharacteristic
35C2×#121×C41C2211yescharacteristic
36C41×#483C2211yescharacteristic
37C41×#483C2211yescharacteristic
38C41×#483C2211yescharacteristic
39C41×#482—21no—
40C41×#481—21no—
41C41×#480C2211yescharacteristic
42C41×#469—21no—
43C41×#468—21no—
44C41×#465—21no—
45C41×#465—21no—
46C41×#450C2211yescharacteristic
47C41×#450C2211yescharacteristic
48C41×#450C2211yescharacteristic
49C41×#449—21no—
50C41×#448—21no—
51C41×#447C2211yescharacteristic
52C41×#407C2211yescharacteristic
53C2×C22⋊C8×C41C2211yescharacteristic
54C41×#398C2211yescharacteristic
55C41×#397C2211yescharacteristic
56C41×#394—21no—
57C41×#394C2211yescharacteristic
58C41×#392—21no—
59C41×#392C2211yescharacteristic
60C41×#390—21no—
61C41×#388—21no—
62C4×C22⋊C4×C41C2211yescharacteristic
63C41×#328C2211yescharacteristic
64C41×#328C2211yescharacteristic
65C41×#328C2211yescharacteristic
66C41×#328C2211yescharacteristic
67C41×#328C2211yescharacteristic
68C41×#328C2211yescharacteristic
69C41×#327C2211yescharacteristic
70C41×#327C2211yescharacteristic
71C41×#324C2211yescharacteristic
72C41×#324C2211yescharacteristic
73C41×#323C2211yescharacteristic
74C41×#323C2211yescharacteristic
75C2×#41×C41—21no—
76C2×#41×C41D411yescharacteristic, complemented
77C22×Q8×C41D411yescharacteristic, complemented
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41D411yescharacteristic
81C22×D4×C41C2311yescharacteristic
82C23×C4×C41C2311yescharacteristic
83C2×SD16×C41—21no—
84C2×SD16×C41—21no—
85C2×SD16×C41—21no—
86C2×D8×C41—21no—
87C2×M16×C41—21no—
88C22×C8×C41—21no—
89C4⋊Q8×C41—21no—
90C4⋊Q8×C41—21no—
91C4⋊Q8×C41—21no—
92#126×C41—21no—
93#126×C41—21no—
94#126×C41—21no—
95#126×C41—21no—
96#126×C41—21no—
97#126×C41—21no—
98#125×C41—21no—
99#125×C41—21no—
100#125×C41—21no—
101#125×C41—21no—
102#125×C41—21no—
103#124×C41—21no—
104#124×C41—21no—
105#124×C41—21no—
106#124×C41—21no—
107#123×C41—21no—
108#123×C41—21no—
109#123×C41—21no—
110#123×C41—21no—
111#123×C41—21no—
112#123×C41—21no—
113#123×C41—21no—
114#123×C41—21no—
115#123×C41—21no—
116#123×C41—21no—
117#123×C41—21no—
118#123×C41—21no—
119#123×C41—21no—
120#123×C41—21no—
121C22⋊Q8×C41—21no—
122C22⋊Q8×C41—21no—
123C22⋊Q8×C41—21no—
124C22⋊Q8×C41—21no—
125C22⋊Q8×C41—21no—
126C22⋊Q8×C41—21no—
127C22⋊Q8×C41—21no—
128C22⋊Q8×C41—21no—
129C22⋊Q8×C41—21no—
130C22⋊Q8×C41—21no—
131C22⋊Q8×C41—21no—
132C22⋊Q8×C41—21no—
133C22⋊Q8×C41—21no—
134C22⋊Q8×C41—21no—
135C22⋊Q8×C41D411yescharacteristic, complemented
136C22⋊Q8×C41D411yescharacteristic, complemented
137C22⋊Q8×C41D411yescharacteristic, complemented
138C22⋊Q8×C41C2311yescharacteristic
139C22⋊Q8×C41C2311yescharacteristic
140C22⋊Q8×C41C2311yescharacteristic
141#121×C41—21no—
142#121×C41—21no—
143#121×C41—21no—
144#121×C41—21no—
145#121×C41—21no—
146#121×C41—21no—
147#121×C41—21no—
148#121×C41—21no—
149#121×C41D411yescharacteristic, complemented
150#121×C41C2311yescharacteristic
151#120×C41—21no—
152#120×C41—21no—
153C4×Q8×C41—21no—
154C4×D4×C41—21no—
155C4×D4×C41—21no—
156C4×D4×C41—21no—
157C4×D4×C41—21no—
158C4×D4×C41—21no—
159C4×D4×C41—21no—
160C4×D4×C41—21no—
161#117×C41—21no—
162#117×C41—21no—
163#117×C41—21no—
164#117×C41D411yescharacteristic, complemented
165C2×C4⋊C4×C41—21no—
166C2×C4⋊C4×C41—21no—
167C2×C4⋊C4×C41—21no—
168C2×C4⋊C4×C41D411yescharacteristic
169C2×C4⋊C4×C41D411yescharacteristic, complemented
170C2×C4⋊C4×C41C2311yescharacteristic
171C2×C4⋊C4×C41C2311yescharacteristic
172C2×C22⋊C4×C41—21no—
173C2×C22⋊C4×C41—21no—
174C2×C22⋊C4×C41—21no—
175C2×C22⋊C4×C41—21no—
176C2×C22⋊C4×C41—21no—
177C2×C22⋊C4×C41—21no—
178C2×C22⋊C4×C41—21no—
179C2×C22⋊C4×C41—21no—
180C2×C22⋊C4×C41D411yescharacteristic
181C2×C22⋊C4×C41D411yescharacteristic
182C2×C22⋊C4×C41C2311yescharacteristic
183C2×C42×C41—21no—
184#107×C41—21no—
185#106×C41—21no—
186#106×C41—21no—
187#106×C41—21no—
188#103×C41—21no—
189#103×C41—21no—
190#103×C41—21no—
191#102×C41—21no—
192#102×C41—21no—
193#102×C41—21no—
194#102×C41—21no—
195#102×C41—21no—
196C22⋊C8×C41—21no—
197C22⋊C8×C41—21no—
198C22⋊C8×C41C2311yescharacteristic
199C22⋊C8×C41C2311yescharacteristic
200C22⋊C8×C41C2311yescharacteristic
201C22⋊C8×C41C2311yescharacteristic
202#95×C41—21no—
203#95×C41—21no—
204#95×C41C2311yescharacteristic
205#95×C41C2311yescharacteristic
206C24×C41—21no—
207C24×C41C2×D411yescharacteristic
208C24×C41C2×D411yescharacteristic
209#41×C41—82no—
210#41×C41—81no—
211C2×Q8×C41—21no—
212C2×Q8×C41—21no—
213C2×Q8×C41—21no—
214C2×Q8×C41—81no—
215C2×Q8×C41C2×D411yescharacteristic
216C2×Q8×C41C2×D411yescharacteristic
217C2×Q8×C41C2×D411yescharacteristic
218C2×D4×C41—21no—
219C2×D4×C41—21no—
220C2×D4×C41—21no—
221C2×D4×C41—21no—
222C2×D4×C41—21no—
223C2×D4×C41—21no—
224C2×D4×C41—21no—
225C2×D4×C41—21no—
226C2×D4×C41—21no—
227C2×D4×C41—42no—
228C2×D4×C41—41no—
229C2×D4×C41—41no—
230C2×D4×C41—81no—
231C2×D4×C41—81no—
232C2×D4×C41—81no—
233C2×D4×C41—81no—
234C2×D4×C41—81no—
235C2×D4×C41—81no—
236C2×D4×C41C2×D411yescharacteristic
237C22×C4×C41—21no—
238C22×C4×C41—21no—
239C22×C4×C41—21no—
240C22×C4×C41—21no—
241C22×C4×C41—21no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—21no—
246C22×C4×C41—21no—
247C22×C4×C41—81no—
248C22×C4×C41C2×D411yescharacteristic
249C22×C4×C41C2×D411yescharacteristic
250C22×C4×C41C2×D411yescharacteristic
251C22×C4×C41C2×D411yescharacteristic
252C22×C4×C41C2×D411yescharacteristic
253C22×C4×C41C2×D411yescharacteristic
254C22×C4×C41C2×D411yescharacteristic
255C22×C4×C41C2×D411yescharacteristic
256C22×C4×C41C2411yescharacteristic
257SD16×C41—81no—
258SD16×C41—81no—
259SD16×C41—81no—
260D8×C41—81no—
261M16×C41—81no—
262C2×C8×C41—21no—
263C2×C8×C41—21no—
264C2×C8×C41—21no—
265C2×C8×C41—21no—
266C2×C8×C41—81no—
267C4⋊C4×C41—21no—
268C4⋊C4×C41—21no—
269C4⋊C4×C41—21no—
270C4⋊C4×C41—21no—
271C4⋊C4×C41—21no—
272C4⋊C4×C41—21no—
273C4⋊C4×C41—21no—
274C4⋊C4×C41—21no—
275C4⋊C4×C41—21no—
276C4⋊C4×C41—21no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—21no—
280C4⋊C4×C41—21no—
281C4⋊C4×C41—21no—
282C4⋊C4×C41—21no—
283C4⋊C4×C41—21no—
284C4⋊C4×C41—21no—
285C4⋊C4×C41—21no—
286C4⋊C4×C41—21no—
287C4⋊C4×C41—21no—
288C4⋊C4×C41—21no—
289C4⋊C4×C41—21no—
290C4⋊C4×C41—21no—
291C4⋊C4×C41—21no—
292C4⋊C4×C41—81no—
293C4⋊C4×C41C2×D411yescharacteristic
294C4⋊C4×C41C2×D411yescharacteristic
295C4⋊C4×C41C2×D411yescharacteristic
296C4⋊C4×C41C2×D411yescharacteristic
297C22⋊C4×C41—21no—
298C22⋊C4×C41—21no—
299C22⋊C4×C41—21no—
300C22⋊C4×C41—21no—
301C22⋊C4×C41—21no—
302C22⋊C4×C41—21no—
303C22⋊C4×C41—21no—
304C22⋊C4×C41—21no—
305C22⋊C4×C41—21no—
306C22⋊C4×C41—21no—
307C22⋊C4×C41—21no—
308C22⋊C4×C41—21no—
309C22⋊C4×C41—21no—
310C22⋊C4×C41—21no—
311C22⋊C4×C41—21no—
312C22⋊C4×C41—21no—
313C22⋊C4×C41—21no—
314C22⋊C4×C41—21no—
315C22⋊C4×C41—21no—
316C22⋊C4×C41—21no—
317C22⋊C4×C41—21no—
318C22⋊C4×C41—21no—
319C22⋊C4×C41—21no—
320C22⋊C4×C41—42no—
321C22⋊C4×C41—42no—
322C22⋊C4×C41—41no—
323C22⋊C4×C41—41no—
324C22⋊C4×C41—81no—
325C22⋊C4×C41—81no—
326C22⋊C4×C41—81no—
327C42×C41—21no—
328C42×C41—21no—
329C42×C41—21no—
330C42×C41—21no—
331C42×C41—21no—
332C42×C41—81no—
333C23×C41—21no—
334C23×C41—21no—
335C23×C41—21no—
336C23×C41—21no—
337C23×C41—21no—
338C23×C41—21no—
339C23×C41—41no—
340C23×C41—41no—
341C23×C41—41no—
342C23×C41—41no—
343C23×C41—41no—
344C23×C41—41no—
345C23×C41—41no—
346C23×C41—41no—
347C23×C41—41no—
348C23×C41—41no—
349C23×C41—41no—
350C23×C41#12011yescharacteristic
351C23×C41#12011yescharacteristic
352C23×C41C22×D411yescharacteristic
353Q8×C41—41no—
354Q8×C41—41no—
355Q8×C41—41no—
356Q8×C41—81no—
357Q8×C41—81no—
358Q8×C41—81no—
359D4×C41—41no—
360D4×C41—41no—
361D4×C41—41no—
362D4×C41—41no—
363D4×C41—41no—
364D4×C41—42no—
365D4×C41—42no—
366D4×C41—41no—
367D4×C41—41no—
368D4×C41—81no—
369D4×C41—81no—
370D4×C41—81no—
371D4×C41—81no—
372D4×C41—84no—
373D4×C41—82no—
374D4×C41—82no—
375C2×C4×C41—22no—
376C2×C4×C41—21no—
377C2×C4×C41—21no—
378C2×C4×C41—21no—
379C2×C4×C41—21no—
380C2×C4×C41—21no—
381C2×C4×C41—21no—
382C2×C4×C41—21no—
383C2×C4×C41—21no—
384C2×C4×C41—21no—
385C2×C4×C41—21no—
386C2×C4×C41—21no—
387C2×C4×C41—21no—
388C2×C4×C41—41no—
389C2×C4×C41—41no—
390C2×C4×C41—41no—
391C2×C4×C41—41no—
392C2×C4×C41—41no—
393C2×C4×C41—41no—
394C2×C4×C41—41no—
395C2×C4×C41—42no—
396C2×C4×C41—41no—
397C2×C4×C41—41no—
398C2×C4×C41—41no—
399C2×C4×C41—41no—
400C2×C4×C41—41no—
401C2×C4×C41—41no—
402C2×C4×C41—41no—
403C2×C4×C41—41no—
404C2×C4×C41—41no—
405C2×C4×C41—81no—
406C2×C4×C41—81no—
407C2×C4×C41—81no—
408C2×C4×C41—81no—
409C2×C4×C41—81no—
410C2×C4×C41—81no—
411C2×C4×C41#12011yescharacteristic
412C2×C4×C41#12011yescharacteristic
413C2×C4×C41C22×D411yescharacteristic
414C2×C4×C41C22×D411yescharacteristic
415C8×C41—41no—
416C8×C41—41no—
417C8×C41—41no—
418C8×C41—41no—
419#18416C4111yesmaximal, characteristic, direct product factor, Sylow
420C22×C41—21no—
421C22×C41—21no—
422C22×C41—21no—
423C22×C41—21no—
424C22×C41—21no—
425C22×C41—21no—
426C22×C41—21no—
427C22×C41—21no—
428C22×C41—41no—
429C22×C41—41no—
430C22×C41—41no—
431C22×C41—41no—
432C22×C41—41no—
433C22×C41—41no—
434C22×C41—81no—
435C22×C41—81no—
436C22×C41—81no—
437C22×C41—81no—
438C22×C41—81no—
439C22×C41—81no—
440C22×C41—81no—
441C22×C41—81no—
442C22×C41—81no—
443C22×C41—81no—
444C22×C41—81no—
445C22×C41C2×#12011yescharacteristic
446C22×C41#57711yescharacteristic
447C22×C41#57711yescharacteristic
448C4×C41—21no—
449C4×C41—21no—
450C4×C41—21no—
451C4×C41—21no—
452C4×C41—42no—
453C4×C41—41no—
454C4×C41—41no—
455C4×C41—41no—
456C4×C41—41no—
457C4×C41—41no—
458C4×C41—41no—
459C4×C41—41no—
460C4×C41—41no—
461C4×C41—41no—
462C4×C41—41no—
463C4×C41—81no—
464C4×C41—81no—
465#3535C2×C4111yescharacteristic, complemented
466#3194C2×C4111yescharacteristic, complemented
467#3187C2×C4111yescharacteristic, complemented
468#2661C2×C4111yescharacteristic, complemented
469#1612C2×C4111yescharacteristic, complemented
470#1611C2×C4111yescharacteristic, complemented
471#1609C2×C4111yescharacteristic, complemented
472#1608C2×C4111yescharacteristic, complemented
473#1600C2×C4111yescharacteristic, complemented
474#1599C2×C4111yescharacteristic, complemented
475#1597C2×C4111yescharacteristic, complemented
476#1596C2×C4111yescharacteristic, complemented
477#1508C2×C4111yescharacteristic, complemented
478#1501C2×C4111yescharacteristic, complemented
479#1468C2×C4111yescharacteristic, complemented
480C2×C41—21no—
481C2×C41—21no—
482C2×C41—41no—
483C2×C41—41no—
484C2×C41—81no—
485C2×C41—81no—
486C2×C41—161no—
487C2×C41#301011yescharacteristic
488C2×C41#301811yescharacteristic
489C2×C41#302611yescharacteristic
490#563—21no—
491#562—21no—
492#554—21no—
493#552—21no—
494#551—21no—
495#551—21no—
496#547—21no—
497#546—21no—
498#544C22×C4111yescharacteristic
499#543C22×C4111yescharacteristic
500#542—21no—
501#539—21no—
502#539—21no—
503#539C22×C4111yescharacteristic
504#538C22×C4111yescharacteristic
505#536—21no—
506#525C22×C4111yescharacteristic
507C2×#123C22×C4111yescharacteristic
508C2×C22⋊Q8C22×C4111yescharacteristic
509C2×#121C22×C4111yescharacteristic
510#483C22×C4111yescharacteristic
511#483C22×C4111yescharacteristic
512#483C22×C4111yescharacteristic
513#482—21no—
514#481—21no—
515#480C22×C4111yescharacteristic
516#469—21no—
517#468—21no—
518#465—21no—
519#465—21no—
520#450C22×C4111yescharacteristic
521#450C22×C4111yescharacteristic
522#450C22×C4111yescharacteristic
523#449—21no—
524#448—21no—
525#447C22×C4111yescharacteristic
526#407C22×C4111yescharacteristic
527C2×C22⋊C8C22×C4111yescharacteristic
528#398C22×C4111yescharacteristic
529#397C22×C4111yescharacteristic
530#394—21no—
531#394C22×C4111yescharacteristic
532#392—21no—
533#392C22×C4111yescharacteristic
534#390—21no—
535#388—21no—
536C4×C22⋊C4C22×C4111yescharacteristic
537#328C22×C4111yescharacteristic
538#328C22×C4111yescharacteristic
539#328C22×C4111yescharacteristic
540#328C22×C4111yescharacteristic
541#328C22×C4111yescharacteristic
542#328C22×C4111yescharacteristic
543#327C22×C4111yescharacteristic
544#327C22×C4111yescharacteristic
545#324C22×C4111yescharacteristic
546#324C22×C4111yescharacteristic
547#323C22×C4111yescharacteristic
548#323C22×C4111yescharacteristic
549C41#1841611yescharacteristic, direct product factor, Sylow
550C2×#41—21no—
551C2×#41D4×C4111yescharacteristic, complemented
552C22×Q8D4×C4111yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C4111yescharacteristic
556C22×D4C23×C4111yescharacteristic
557C23×C4C23×C4111yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C4111yescharacteristic, complemented
611C22⋊Q8D4×C4111yescharacteristic, complemented
612C22⋊Q8D4×C4111yescharacteristic, complemented
613C22⋊Q8C23×C4111yescharacteristic
614C22⋊Q8C23×C4111yescharacteristic
615C22⋊Q8C23×C4111yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C4111yescharacteristic, complemented
625#121C23×C4111yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C4111yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C4111yescharacteristic
644C2×C4⋊C4D4×C4111yescharacteristic, complemented
645C2×C4⋊C4C23×C4111yescharacteristic
646C2×C4⋊C4C23×C4111yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C4111yescharacteristic
656C2×C22⋊C4D4×C4111yescharacteristic
657C2×C22⋊C4C23×C4111yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C4111yescharacteristic
674C22⋊C8C23×C4111yescharacteristic
675C22⋊C8C23×C4111yescharacteristic
676C22⋊C8C23×C4111yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C4111yescharacteristic
680#95C23×C4111yescharacteristic
681C24—21no—
682C24C2×D4×C4111yescharacteristic
683C24C2×D4×C4111yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C4111yescharacteristic
691C2×Q8C2×D4×C4111yescharacteristic
692C2×Q8C2×D4×C4111yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C4111yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C4111yescharacteristic
724C22×C4C2×D4×C4111yescharacteristic
725C22×C4C2×D4×C4111yescharacteristic
726C22×C4C2×D4×C4111yescharacteristic
727C22×C4C2×D4×C4111yescharacteristic
728C22×C4C2×D4×C4111yescharacteristic
729C22×C4C2×D4×C4111yescharacteristic
730C22×C4C2×D4×C4111yescharacteristic
731C22×C4C24×C4111yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C4111yescharacteristic
769C4⋊C4C2×D4×C4111yescharacteristic
770C4⋊C4C2×D4×C4111yescharacteristic
771C4⋊C4C2×D4×C4111yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C4111yescharacteristic
826C23#120×C4111yescharacteristic
827C23C22×D4×C4111yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C4111yescharacteristic
887C2×C4#120×C4111yescharacteristic
888C2×C4C22×D4×C4111yescharacteristic
889C2×C4C22×D4×C4111yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C4111yescharacteristic
920C22C41×#57711yescharacteristic
921C22C41×#57711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C41×#301011yescharacteristic
947C2C41×#301811yescharacteristic
948C2C41×#302611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3535C2semidirect
2. C41×#3194C2semidirect
3. C41×#3187C2semidirect
4. C41×#2661C2semidirect
5. C41×#1612C2semidirect
6. C41×#1611C2semidirect
7. C41×#1609C2semidirect
8. C41×#1608C2semidirect
9. C41×#1600C2semidirect
10. C41×#1599C2semidirect
11. C41×#1597C2semidirect
12. C41×#1596C2semidirect
13. C41×#1508C2semidirect
14. C41×#1501C2semidirect
15. C41×#1468C2semidirect
76. C2×#41×C41D4semidirect
77. C22×Q8×C41D4semidirect
135. C22⋊Q8×C41D4semidirect
136. C22⋊Q8×C41D4semidirect
137. C22⋊Q8×C41D4semidirect
149. #121×C41D4semidirect
164. #117×C41D4semidirect
169. C2×C4⋊C4×C41D4semidirect
419. #18416C41direct (N × H)
465. #3535C2×C41semidirect
466. #3194C2×C41semidirect
467. #3187C2×C41semidirect
468. #2661C2×C41semidirect
469. #1612C2×C41semidirect
470. #1611C2×C41semidirect
471. #1609C2×C41semidirect
472. #1608C2×C41semidirect
473. #1600C2×C41semidirect
474. #1599C2×C41semidirect
475. #1597C2×C41semidirect
476. #1596C2×C41semidirect
477. #1508C2×C41semidirect
478. #1501C2×C41semidirect
479. #1468C2×C41semidirect
549. C41#18416direct (N × H)
551. C2×#41D4×C41semidirect
552. C22×Q8D4×C41semidirect
610. C22⋊Q8D4×C41semidirect
611. C22⋊Q8D4×C41semidirect
612. C22⋊Q8D4×C41semidirect
624. #121D4×C41semidirect
639. #117D4×C41semidirect
644. C2×C4⋊C4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35352
C41×#31942
C41×#31872
C41×#26612
C41×#16122
C41×#16112
C41×#16092
C41×#16082
C41×#16002
C41×#15992
C41×#15972
C41×#15962
C41×#15082
C41×#15012
C41×#14682
#1841641