Finite Group Databasebeta

← C41×#18414 #23794615

Subgroups — C41×#18414 #23794615

Order 10496.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3534C211yesmaximal, characteristic, complemented
2C41×#3194C211yesmaximal, characteristic, complemented
3C41×#3186C211yesmaximal, characteristic, complemented
4C41×#2661C211yesmaximal, characteristic, complemented
5C41×#1612C211yesmaximal, characteristic, complemented
6C41×#1610C211yesmaximal, characteristic, complemented
7C41×#1609C211yesmaximal, characteristic, complemented
8C41×#1607C211yesmaximal, characteristic, complemented
9C41×#1600C211yesmaximal, characteristic, complemented
10C41×#1598C211yesmaximal, characteristic, complemented
11C41×#1597C211yesmaximal, characteristic, complemented
12C41×#1595C211yesmaximal, characteristic, complemented
13C41×#1507C211yesmaximal, characteristic, complemented
14C41×#1501C211yesmaximal, characteristic, complemented
15C41×#1468C211yesmaximal, characteristic, complemented
16C41×#562—21no—
17C41×#560—21no—
18C41×#553—21no—
19C41×#551—21no—
20C41×#546—21no—
21C41×#546—21no—
22C41×#546—21no—
23D42×C41—21no—
24C41×#540—21no—
25C41×#539—21no—
26C41×#539C2211yescharacteristic
27C41×#538—21no—
28C41×#538C2211yescharacteristic
29C41×#537C2211yescharacteristic
30C41×#534—21no—
31C41×#534C2211yescharacteristic
32C41×#525C2211yescharacteristic
33C2×#123×C41C2211yescharacteristic
34C2×#121×C41C2211yescharacteristic
35C2×#121×C41C2211yescharacteristic, complemented
36C41×#483C2211yescharacteristic, complemented
37C41×#482—21no—
38C41×#480—21no—
39C41×#480C2211yescharacteristic
40C41×#480C2211yescharacteristic, complemented
41C41×#480C2211yescharacteristic, complemented
42C41×#469—21no—
43C41×#468—21no—
44C41×#466—21no—
45C41×#466—21no—
46C41×#450C2211yescharacteristic, complemented
47C41×#449—21no—
48C41×#447—21no—
49C41×#447C2211yescharacteristic
50C41×#447C2211yescharacteristic, complemented
51C41×#447C2211yescharacteristic, complemented
52C41×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C41C2211yescharacteristic, complemented
54C41×#398C2211yescharacteristic, complemented
55C41×#397C2211yescharacteristic, complemented
56C41×#394—21no—
57C41×#394C2211yescharacteristic, complemented
58C41×#392—21no—
59C41×#392C2211yescharacteristic, complemented
60C41×#390—21no—
61C41×#388—21no—
62C4×C22⋊C4×C41C2211yescharacteristic, complemented
63C41×#328C2211yescharacteristic, complemented
64C41×#328C2211yescharacteristic, complemented
65C41×#327C2211yescharacteristic
66C41×#327C2211yescharacteristic
67C41×#327C2211yescharacteristic, complemented
68C41×#327C2211yescharacteristic, complemented
69C41×#327C2211yescharacteristic, complemented
70C41×#327C2211yescharacteristic, complemented
71C41×#324C2211yescharacteristic, complemented
72C41×#324C2211yescharacteristic, complemented
73C41×#323C2211yescharacteristic, complemented
74C41×#323C2211yescharacteristic, complemented
75C2×#41×C41—21no—
76C2×#41×C41D411yescharacteristic, complemented
77C22×D4×C41—21no—
78C22×D4×C41—21no—
79C22×D4×C41—21no—
80C22×D4×C41—21no—
81C22×D4×C41—21no—
82C22×D4×C41D411yescharacteristic
83C22×D4×C41D411yescharacteristic, complemented
84C22×D4×C41C2311yescharacteristic
85C23×C4×C41C2311yescharacteristic
86C2×SD16×C41—21no—
87C2×D8×C41—21no—
88C2×D8×C41—21no—
89C2×D8×C41—21no—
90C2×M16×C41—21no—
91C22×C8×C41—21no—
92#127×C41—21no—
93#126×C41—21no—
94#126×C41—21no—
95#126×C41—21no—
96#126×C41—21no—
97#125×C41—21no—
98#125×C41—21no—
99#124×C41—21no—
100#124×C41—21no—
101#124×C41—21no—
102#123×C41—21no—
103#123×C41—21no—
104#123×C41—21no—
105#123×C41—21no—
106#123×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—
116C22⋊Q8×C41—21no—
117C22⋊Q8×C41—21no—
118C22⋊Q8×C41—21no—
119C22⋊Q8×C41—21no—
120C22⋊Q8×C41—21no—
121C22⋊Q8×C41D411yescharacteristic, complemented
122C22⋊Q8×C41C2311yescharacteristic
123#121×C41—21no—
124#121×C41—21no—
125#121×C41—21no—
126#121×C41—21no—
127#121×C41—21no—
128#121×C41—21no—
129#121×C41—21no—
130#121×C41—21no—
131#121×C41—21no—
132#121×C41—21no—
133#121×C41—21no—
134#121×C41—21no—
135#121×C41—21no—
136#121×C41—21no—
137#121×C41—21no—
138#121×C41—21no—
139#121×C41—21no—
140#121×C41—21no—
141#121×C41—21no—
142#121×C41D411yescharacteristic, complemented
143#121×C41D411yescharacteristic, complemented
144#121×C41D411yescharacteristic, complemented
145#121×C41C2311yescharacteristic
146#121×C41C2311yescharacteristic
147#121×C41C2311yescharacteristic
148#120×C41—21no—
149#120×C41—21no—
150#120×C41—21no—
151#120×C41—21no—
152#120×C41—21no—
153#120×C41—21no—
154#120×C41—21no—
155#120×C41—21no—
156C4×D4×C41—21no—
157C4×D4×C41—21no—
158C4×D4×C41—21no—
159C4×D4×C41—21no—
160C4×D4×C41—21no—
161C4×D4×C41—21no—
162C4×D4×C41—21no—
163C4×D4×C41—21no—
164#117×C41—21no—
165#117×C41D411yescharacteristic, complemented
166C2×C4⋊C4×C41—21no—
167C2×C4⋊C4×C41D411yescharacteristic
168C2×C4⋊C4×C41D411yescharacteristic, complemented
169C2×C4⋊C4×C41C2311yescharacteristic
170C2×C4⋊C4×C41C2311yescharacteristic
171C2×C22⋊C4×C41—21no—
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#107×C41—21no—
186#107×C41—21no—
187#106×C41—21no—
188#103×C41—21no—
189#102×C41—21no—
190#102×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×C41—21no—
208C24×C41—21no—
209C24×C41C2×D411yescharacteristic
210C24×C41C2×D411yescharacteristic
211#41×C41—81no—
212#41×C41—81no—
213#41×C41—81no—
214C2×Q8×C41—21no—
215C2×Q8×C41C2×D411yescharacteristic
216C2×D4×C41—21no—
217C2×D4×C41—21no—
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—21no—
228C2×D4×C41—21no—
229C2×D4×C41—21no—
230C2×D4×C41—21no—
231C2×D4×C41—21no—
232C2×D4×C41—21no—
233C2×D4×C41—21no—
234C2×D4×C41—21no—
235C2×D4×C41—42no—
236C2×D4×C41—41no—
237C2×D4×C41—41no—
238C2×D4×C41—81no—
239C2×D4×C41—81no—
240C2×D4×C41—81no—
241C2×D4×C41—81no—
242C2×D4×C41—81no—
243C2×D4×C41—81no—
244C2×D4×C41—81no—
245C2×D4×C41—81no—
246C2×D4×C41—81no—
247C2×D4×C41—81no—
248C2×D4×C41—81no—
249C2×D4×C41—82no—
250C2×D4×C41C2×D411yescharacteristic
251C2×D4×C41C2×D411yescharacteristic
252C2×D4×C41C2×D411yescharacteristic
253C22×C4×C41—21no—
254C22×C4×C41—21no—
255C22×C4×C41—21no—
256C22×C4×C41—21no—
257C22×C4×C41—21no—
258C22×C4×C41—21no—
259C22×C4×C41—21no—
260C22×C4×C41—21no—
261C22×C4×C41—21no—
262C22×C4×C41—21no—
263C22×C4×C41—81no—
264C22×C4×C41C2×D411yescharacteristic
265C22×C4×C41C2×D411yescharacteristic
266C22×C4×C41C2×D411yescharacteristic
267C22×C4×C41C2×D411yescharacteristic
268C22×C4×C41C2×D411yescharacteristic
269C22×C4×C41C2×D411yescharacteristic
270C22×C4×C41C2×D411yescharacteristic
271C22×C4×C41C2×D411yescharacteristic
272C22×C4×C41C2411yescharacteristic
273SD16×C41—81no—
274D8×C41—81no—
275D8×C41—81no—
276D8×C41—81no—
277M16×C41—81no—
278C2×C8×C41—21no—
279C2×C8×C41—21no—
280C2×C8×C41—21no—
281C2×C8×C41—21no—
282C2×C8×C41—81no—
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—21no—
293C4⋊C4×C41—21no—
294C4⋊C4×C41—21no—
295C4⋊C4×C41—21no—
296C4⋊C4×C41—21no—
297C4⋊C4×C41—21no—
298C4⋊C4×C41—81no—
299C4⋊C4×C41C2×D411yescharacteristic
300C4⋊C4×C41C2×D411yescharacteristic
301C4⋊C4×C41C2×D411yescharacteristic
302C4⋊C4×C41C2×D411yescharacteristic
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—21no—
321C22⋊C4×C41—21no—
322C22⋊C4×C41—21no—
323C22⋊C4×C41—21no—
324C22⋊C4×C41—21no—
325C22⋊C4×C41—21no—
326C22⋊C4×C41—21no—
327C22⋊C4×C41—21no—
328C22⋊C4×C41—42no—
329C22⋊C4×C41—42no—
330C22⋊C4×C41—41no—
331C22⋊C4×C41—41no—
332C22⋊C4×C41—81no—
333C22⋊C4×C41—81no—
334C22⋊C4×C41—81no—
335C42×C41—21no—
336C42×C41—21no—
337C42×C41—21no—
338C42×C41—81no—
339C23×C41—21no—
340C23×C41—21no—
341C23×C41—21no—
342C23×C41—21no—
343C23×C41—21no—
344C23×C41—21no—
345C23×C41—21no—
346C23×C41—21no—
347C23×C41—41no—
348C23×C41—41no—
349C23×C41—42no—
350C23×C41—41no—
351C23×C41—41no—
352C23×C41—41no—
353C23×C41—41no—
354C23×C41—41no—
355C23×C41—41no—
356C23×C41—41no—
357C23×C41—41no—
358C23×C41—41no—
359C23×C41—81no—
360C23×C41—81no—
361C23×C41—81no—
362C23×C41—81no—
363C23×C41—81no—
364C23×C41#12011yescharacteristic
365C23×C41#12011yescharacteristic
366C23×C41C22×D411yescharacteristic
367Q8×C41—41no—
368Q8×C41—81no—
369D4×C41—41no—
370D4×C41—41no—
371D4×C41—41no—
372D4×C41—41no—
373D4×C41—41no—
374D4×C41—41no—
375D4×C41—41no—
376D4×C41—42no—
377D4×C41—42no—
378D4×C41—41no—
379D4×C41—41no—
380D4×C41—41no—
381D4×C41—41no—
382D4×C41—41no—
383D4×C41—41no—
384D4×C41—81no—
385D4×C41—81no—
386D4×C41—81no—
387D4×C41—81no—
388D4×C41—81no—
389D4×C41—81no—
390D4×C41—81no—
391D4×C41—81no—
392D4×C41—81no—
393D4×C41—81no—
394D4×C41—81no—
395D4×C41—81no—
396D4×C41—84no—
397D4×C41—82no—
398D4×C41—82no—
399C2×C4×C41—22no—
400C2×C4×C41—21no—
401C2×C4×C41—21no—
402C2×C4×C41—21no—
403C2×C4×C41—21no—
404C2×C4×C41—21no—
405C2×C4×C41—21no—
406C2×C4×C41—21no—
407C2×C4×C41—21no—
408C2×C4×C41—21no—
409C2×C4×C41—21no—
410C2×C4×C41—41no—
411C2×C4×C41—41no—
412C2×C4×C41—41no—
413C2×C4×C41—41no—
414C2×C4×C41—41no—
415C2×C4×C41—41no—
416C2×C4×C41—41no—
417C2×C4×C41—41no—
418C2×C4×C41—41no—
419C2×C4×C41—41no—
420C2×C4×C41—41no—
421C2×C4×C41—41no—
422C2×C4×C41—41no—
423C2×C4×C41—41no—
424C2×C4×C41—41no—
425C2×C4×C41—41no—
426C2×C4×C41—81no—
427C2×C4×C41—81no—
428C2×C4×C41—81no—
429C2×C4×C41—81no—
430C2×C4×C41—81no—
431C2×C4×C41—81no—
432C2×C4×C41—81no—
433C2×C4×C41#12011yescharacteristic
434C2×C4×C41#12011yescharacteristic
435C2×C4×C41C22×D411yescharacteristic
436C2×C4×C41C22×D411yescharacteristic
437C8×C41—41no—
438C8×C41—41no—
439C8×C41—41no—
440C8×C41—41no—
441#18414C4111yesmaximal, characteristic, direct product factor, Sylow
442C22×C41—21no—
443C22×C41—21no—
444C22×C41—21no—
445C22×C41—21no—
446C22×C41—21no—
447C22×C41—21no—
448C22×C41—21no—
449C22×C41—21no—
450C22×C41—41no—
451C22×C41—41no—
452C22×C41—41no—
453C22×C41—41no—
454C22×C41—41no—
455C22×C41—41no—
456C22×C41—41no—
457C22×C41—41no—
458C22×C41—41no—
459C22×C41—41no—
460C22×C41—41no—
461C22×C41—41no—
462C22×C41—81no—
463C22×C41—81no—
464C22×C41—81no—
465C22×C41—81no—
466C22×C41—81no—
467C22×C41—81no—
468C22×C41—81no—
469C22×C41—81no—
470C22×C41—81no—
471C22×C41—81no—
472C22×C41—81no—
473C22×C41—162no—
474C22×C41—162no—
475C22×C41C2×#12011yescharacteristic
476C22×C41#57611yescharacteristic
477C22×C41#57611yescharacteristic
478C4×C41—21no—
479C4×C41—21no—
480C4×C41—21no—
481C4×C41—21no—
482C4×C41—42no—
483C4×C41—41no—
484C4×C41—41no—
485C4×C41—41no—
486C4×C41—41no—
487C4×C41—41no—
488C4×C41—41no—
489C4×C41—41no—
490C4×C41—41no—
491C4×C41—81no—
492C4×C41—81no—
493#3534C2×C4111yescharacteristic, complemented
494#3194C2×C4111yescharacteristic, complemented
495#3186C2×C4111yescharacteristic, complemented
496#2661C2×C4111yescharacteristic, complemented
497#1612C2×C4111yescharacteristic, complemented
498#1610C2×C4111yescharacteristic, complemented
499#1609C2×C4111yescharacteristic, complemented
500#1607C2×C4111yescharacteristic, complemented
501#1600C2×C4111yescharacteristic, complemented
502#1598C2×C4111yescharacteristic, complemented
503#1597C2×C4111yescharacteristic, complemented
504#1595C2×C4111yescharacteristic, complemented
505#1507C2×C4111yescharacteristic, complemented
506#1501C2×C4111yescharacteristic, complemented
507#1468C2×C4111yescharacteristic, complemented
508C2×C41—21no—
509C2×C41—21no—
510C2×C41—41no—
511C2×C41—41no—
512C2×C41—81no—
513C2×C41—81no—
514C2×C41—81no—
515C2×C41—81no—
516C2×C41—161no—
517C2×C41#300811yescharacteristic
518C2×C41#301811yescharacteristic
519C2×C41#302611yescharacteristic
520#562—21no—
521#560—21no—
522#553—21no—
523#551—21no—
524#546—21no—
525#546—21no—
526#546—21no—
527D42—21no—
528#540—21no—
529#539—21no—
530#539C22×C4111yescharacteristic
531#538—21no—
532#538C22×C4111yescharacteristic
533#537C22×C4111yescharacteristic
534#534—21no—
535#534C22×C4111yescharacteristic
536#525C22×C4111yescharacteristic
537C2×#123C22×C4111yescharacteristic
538C2×#121C22×C4111yescharacteristic
539C2×#121C22×C4111yescharacteristic, complemented
540#483C22×C4111yescharacteristic, complemented
541#482—21no—
542#480—21no—
543#480C22×C4111yescharacteristic
544#480C22×C4111yescharacteristic, complemented
545#480C22×C4111yescharacteristic, complemented
546#469—21no—
547#468—21no—
548#466—21no—
549#466—21no—
550#450C22×C4111yescharacteristic, complemented
551#449—21no—
552#447—21no—
553#447C22×C4111yescharacteristic
554#447C22×C4111yescharacteristic, complemented
555#447C22×C4111yescharacteristic, complemented
556#407C22×C4111yescharacteristic, complemented
557C2×C22⋊C8C22×C4111yescharacteristic, complemented
558#398C22×C4111yescharacteristic, complemented
559#397C22×C4111yescharacteristic, complemented
560#394—21no—
561#394C22×C4111yescharacteristic, complemented
562#392—21no—
563#392C22×C4111yescharacteristic, complemented
564#390—21no—
565#388—21no—
566C4×C22⋊C4C22×C4111yescharacteristic, complemented
567#328C22×C4111yescharacteristic, complemented
568#328C22×C4111yescharacteristic, complemented
569#327C22×C4111yescharacteristic
570#327C22×C4111yescharacteristic
571#327C22×C4111yescharacteristic, complemented
572#327C22×C4111yescharacteristic, complemented
573#327C22×C4111yescharacteristic, complemented
574#327C22×C4111yescharacteristic, complemented
575#324C22×C4111yescharacteristic, complemented
576#324C22×C4111yescharacteristic, complemented
577#323C22×C4111yescharacteristic, complemented
578#323C22×C4111yescharacteristic, complemented
579C41#1841411yescharacteristic, direct product factor, Sylow
580C2×#41—21no—
581C2×#41D4×C4111yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C4111yescharacteristic
588C22×D4D4×C4111yescharacteristic, complemented
589C22×D4C23×C4111yescharacteristic
590C23×C4C23×C4111yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C4111yescharacteristic, complemented
627C22⋊Q8C23×C4111yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C4111yescharacteristic, complemented
648#121D4×C4111yescharacteristic, complemented
649#121D4×C4111yescharacteristic, complemented
650#121C23×C4111yescharacteristic
651#121C23×C4111yescharacteristic
652#121C23×C4111yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C4111yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C4111yescharacteristic
673C2×C4⋊C4D4×C4111yescharacteristic, complemented
674C2×C4⋊C4C23×C4111yescharacteristic
675C2×C4⋊C4C23×C4111yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C4111yescharacteristic
686C2×C22⋊C4D4×C4111yescharacteristic
687C2×C22⋊C4C23×C4111yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C4111yescharacteristic
704C22⋊C8C23×C4111yescharacteristic
705C22⋊C8C23×C4111yescharacteristic
706C22⋊C8C23×C4111yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C4111yescharacteristic
710#95C23×C4111yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C4111yescharacteristic
715C24C2×D4×C4111yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C4111yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C4111yescharacteristic
756C2×D4C2×D4×C4111yescharacteristic
757C2×D4C2×D4×C4111yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C4111yescharacteristic
770C22×C4C2×D4×C4111yescharacteristic
771C22×C4C2×D4×C4111yescharacteristic
772C22×C4C2×D4×C4111yescharacteristic
773C22×C4C2×D4×C4111yescharacteristic
774C22×C4C2×D4×C4111yescharacteristic
775C22×C4C2×D4×C4111yescharacteristic
776C22×C4C2×D4×C4111yescharacteristic
777C22×C4C24×C4111yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C4111yescharacteristic
805C4⋊C4C2×D4×C4111yescharacteristic
806C4⋊C4C2×D4×C4111yescharacteristic
807C4⋊C4C2×D4×C4111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C4111yescharacteristic
870C23#120×C4111yescharacteristic
871C23C22×D4×C4111yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C4111yescharacteristic
939C2×C4#120×C4111yescharacteristic
940C2×C4C22×D4×C4111yescharacteristic
941C2×C4C22×D4×C4111yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C4111yescharacteristic
980C22C41×#57611yescharacteristic
981C22C41×#57611yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C41×#300811yescharacteristic
1007C2C41×#301811yescharacteristic
1008C2C41×#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×#3534C2semidirect
2. C41×#3194C2semidirect
3. C41×#3186C2semidirect
4. C41×#2661C2semidirect
5. C41×#1612C2semidirect
6. C41×#1610C2semidirect
7. C41×#1609C2semidirect
8. C41×#1607C2semidirect
9. C41×#1600C2semidirect
10. C41×#1598C2semidirect
11. C41×#1597C2semidirect
12. C41×#1595C2semidirect
13. C41×#1507C2semidirect
14. C41×#1501C2semidirect
15. C41×#1468C2semidirect
35. C2×#121×C41C22semidirect
36. C41×#483C22semidirect
40. C41×#480C22semidirect
41. C41×#480C22semidirect
46. C41×#450C22semidirect
50. C41×#447C22semidirect
51. C41×#447C22semidirect
52. C41×#407C22semidirect
53. C2×C22⋊C8×C41C22semidirect
54. C41×#398C22semidirect
55. C41×#397C22semidirect
57. C41×#394C22semidirect
59. C41×#392C22semidirect
62. C4×C22⋊C4×C41C22semidirect
63. C41×#328C22semidirect
64. C41×#328C22semidirect
67. C41×#327C22semidirect
68. C41×#327C22semidirect
69. C41×#327C22semidirect
70. C41×#327C22semidirect
71. C41×#324C22semidirect
72. C41×#324C22semidirect
73. C41×#323C22semidirect
74. C41×#323C22semidirect
76. C2×#41×C41D4semidirect
83. C22×D4×C41D4semidirect
121. C22⋊Q8×C41D4semidirect
142. #121×C41D4semidirect
143. #121×C41D4semidirect
144. #121×C41D4semidirect
165. #117×C41D4semidirect
168. C2×C4⋊C4×C41D4semidirect
441. #18414C41direct (N × H)
493. #3534C2×C41semidirect
494. #3194C2×C41semidirect
495. #3186C2×C41semidirect
496. #2661C2×C41semidirect
497. #1612C2×C41semidirect
498. #1610C2×C41semidirect
499. #1609C2×C41semidirect
500. #1607C2×C41semidirect
501. #1600C2×C41semidirect
502. #1598C2×C41semidirect
503. #1597C2×C41semidirect
504. #1595C2×C41semidirect
505. #1507C2×C41semidirect
506. #1501C2×C41semidirect
507. #1468C2×C41semidirect
539. C2×#121C22×C41semidirect
540. #483C22×C41semidirect
544. #480C22×C41semidirect
545. #480C22×C41semidirect
550. #450C22×C41semidirect
554. #447C22×C41semidirect
555. #447C22×C41semidirect
556. #407C22×C41semidirect
557. C2×C22⋊C8C22×C41semidirect
558. #398C22×C41semidirect
559. #397C22×C41semidirect
561. #394C22×C41semidirect
563. #392C22×C41semidirect
566. C4×C22⋊C4C22×C41semidirect
567. #328C22×C41semidirect
568. #328C22×C41semidirect
571. #327C22×C41semidirect
572. #327C22×C41semidirect
573. #327C22×C41semidirect
574. #327C22×C41semidirect
575. #324C22×C41semidirect
576. #324C22×C41semidirect
577. #323C22×C41semidirect
578. #323C22×C41semidirect
579. C41#18414direct (N × H)
581. C2×#41D4×C41semidirect
588. C22×D4D4×C41semidirect
626. C22⋊Q8D4×C41semidirect
647. #121D4×C41semidirect
648. #121D4×C41semidirect
649. #121D4×C41semidirect
670. #117D4×C41semidirect
673. 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×#35342
C41×#31942
C41×#31862
C41×#26612
C41×#16122
C41×#16102
C41×#16092
C41×#16072
C41×#16002
C41×#15982
C41×#15972
C41×#15952
C41×#15072
C41×#15012
C41×#14682
#1841441