Finite Group Databasebeta

← C41×#24471 #23800672

Subgroups — C41×#24471 #23800672

Order 10496.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3488C211yesmaximal, characteristic
2C41×#3056C211yesmaximal, characteristic, complemented
3C2×C41×#455C211yesmaximal, characteristic, complemented
4C41×#3007C211yesmaximal, characteristic, complemented
5C2×C41×#421C211yesmaximal, characteristic, complemented
6C41×#2620C211yesmaximal, characteristic, complemented
7C41×#2039C211yesmaximal, characteristic, complemented
8C41×#2037C211yesmaximal, characteristic, complemented
9C41×#2007C211yesmaximal, characteristic, complemented
10C41×#2004C211yesmaximal, characteristic, complemented
11C41×#1900C211yesmaximal, characteristic, complemented
12C41×#1897C211yesmaximal, characteristic, complemented
13C41×#1882C211yesmaximal, characteristic, complemented
14C41×#1859C211yesmaximal, characteristic, complemented
15C41×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C41C2211yescharacteristic
17C22×#41×C41C2211yescharacteristic
18C2×#137×C41C2211yescharacteristic
19C2×#137×C41C2211yescharacteristic, complemented
20C2×#137×C41C2211yescharacteristic, complemented
21C22×M16×C41C2211yescharacteristic, complemented
22C41×#550—21no—
23C41×#548—21no—
24C41×#546—21no—
25C41×#546—22no—
26D42×C41—22no—
27D42×C41—21no—
28C41×#537—21no—
29C41×#537C2211yescharacteristic
30C41×#535—21no—
31C41×#535C2211yescharacteristic
32C2×#124×C41C2211yescharacteristic, complemented
33C41×#525—21no—
34C41×#525C2211yescharacteristic
35C2×C22⋊Q8×C41C2211yescharacteristic, complemented
36C2×#121×C41—21no—
37C2×#121×C41C2211yescharacteristic
38C41×#520C2211yescharacteristic
39C2×#117×C41C2211yescharacteristic, complemented
40C41×#470—21no—
41C41×#468—21no—
42C41×#467—21no—
43C41×#465—21no—
44C41×#455—24no—
45C41×#452—21no—
46C41×#452—21no—
47C41×#451—21no—
48C41×#450—21no—
49C41×#428C2211yescharacteristic, complemented
50C41×#421—24no—
51C2×#104×C41C2211yescharacteristic
52C2×#104×C41C2211yescharacteristic
53C2×#104×C41C2211yescharacteristic, complemented
54C2×#104×C41C2211yescharacteristic, complemented
55C2×#104×C41C2211yescharacteristic, complemented
56C2×#104×C41C2211yescharacteristic, complemented
57C41×#419C2211yescharacteristic, complemented
58C41×#417C2211yescharacteristic
59C41×#417C2211yescharacteristic, complemented
60C41×#417C2211yescharacteristic, complemented
61C2×#100×C41C2211yescharacteristic, complemented
62C2×#100×C41C2211yescharacteristic, complemented
63C41×#407C2211yescharacteristic, complemented
64C41×#396—22no—
65C41×#394—22no—
66C41×#391C2211yescharacteristic, complemented
67C41×#390C2211yescharacteristic, complemented
68C41×#384C2211yescharacteristic, complemented
69C41×#343C2211yescharacteristic, complemented
70C41×#343C2211yescharacteristic, complemented
71C41×#339C2211yescharacteristic, complemented
72C41×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C41—22no—
74H(5,𝔽2)×C41—22no—
75H(5,𝔽2)×C41—41no—
76H(5,𝔽2)×C41—41no—
77C2×#41×C41—21no—
78C2×#41×C41—21no—
79C2×#41×C41—21no—
80C2×#41×C41—21no—
81C2×#41×C41—22no—
82C2×#41×C41—22no—
83C2×#41×C41—41no—
84C2×#41×C41—41no—
85C2×#41×C41D411yescharacteristic
86C2×#41×C41D411yescharacteristic
87C2×#41×C41C2311yescharacteristic
88C2×#41×C41C2311yescharacteristic
89C2×#41×C41C2311yescharacteristic
90C22×Q8×C41D411yescharacteristic
91C22×Q8×C41C2311yescharacteristic
92C22×D4×C41—21no—
93C22×D4×C41—22no—
94C22×D4×C41—22no—
95C22×D4×C41—21no—
96C22×D4×C41—21no—
97C22×D4×C41D411yescharacteristic
98C22×D4×C41D412yes—
99C22×D4×C41C2311yescharacteristic
100C23×C4×C41—21no—
101C23×C4×C41C2311yescharacteristic
102#137×C41—22no—
103#137×C41—22no—
104#137×C41—22no—
105#137×C41—41no—
106#137×C41—41no—
107#137×C41—41no—
108C2×Q16×C41—21no—
109C2×Q16×C41—21no—
110C2×Q16×C41—21no—
111C2×SD16×C41—21no—
112C2×SD16×C41—21no—
113C2×SD16×C41—21no—
114C2×M16×C41—21no—
115C2×M16×C41—22no—
116C2×M16×C41—41no—
117C2×M16×C41C2311yescharacteristic
118C2×M16×C41C2311yescharacteristic
119C2×M16×C41C2311yescharacteristic
120C2×M16×C41C2311yescharacteristic
121C22×C8×C41—21no—
122#127×C41—22no—
123#127×C41—21no—
124#124×C41—22no—
125#124×C41—21no—
126#124×C41—22no—
127#124×C41—41no—
128#123×C41—22no—
129#123×C41—21no—
130C22⋊Q8×C41—22no—
131C22⋊Q8×C41—21no—
132C22⋊Q8×C41—21no—
133C22⋊Q8×C41—21no—
134C22⋊Q8×C41—21no—
135C22⋊Q8×C41—21no—
136C22⋊Q8×C41—21no—
137C22⋊Q8×C41D411yescharacteristic
138C22⋊Q8×C41D411yescharacteristic
139#121×C41—22no—
140#121×C41—22no—
141#121×C41—22no—
142#121×C41—22no—
143#121×C41—22no—
144#121×C41—21no—
145#121×C41—21no—
146#121×C41—21no—
147#121×C41—21no—
148#121×C41—21no—
149#121×C41—21no—
150#121×C41—22no—
151#121×C41—21no—
152#121×C41—21no—
153#121×C41D411yescharacteristic
154#121×C41D411yescharacteristic
155#120×C41—22no—
156#120×C41—22no—
157#120×C41—22no—
158#120×C41—21no—
159#120×C41—22no—
160C4×Q8×C41—21no—
161C4×D4×C41—22no—
162C4×D4×C41—22no—
163C4×D4×C41—21no—
164C4×D4×C41—22no—
165C4×D4×C41—21no—
166C4×D4×C41—21no—
167#117×C41—21no—
168#117×C41—22no—
169#117×C41—41no—
170#117×C41C2311yescharacteristic
171C2×C4⋊C4×C41—21no—
172C2×C4⋊C4×C41—21no—
173C2×C4⋊C4×C41—21no—
174C2×C4⋊C4×C41—22no—
175C2×C4⋊C4×C41C2311yescharacteristic
176C2×C4⋊C4×C41C2311yescharacteristic
177C2×C22⋊C4×C41—22no—
178C2×C22⋊C4×C41—21no—
179C2×C22⋊C4×C41—21no—
180C2×C22⋊C4×C41—22no—
181C2×C22⋊C4×C41—22no—
182C2×C22⋊C4×C41D412yes—
183C2×C42×C41C2311yescharacteristic
184C2×C42×C41C2311yescharacteristic
185#107×C41—21no—
186#106×C41—21no—
187#104×C41—22no—
188#104×C41—22no—
189#104×C41—22no—
190#104×C41—22no—
191#104×C41—41no—
192#104×C41D414yescomplemented
193#103×C41—21no—
194#103×C41—21no—
195#103×C41—21no—
196#103×C41—21no—
197#103×C41—21no—
198#102×C41—21no—
199#102×C41—21no—
200#102×C41—21no—
201#100×C41—22no—
202#100×C41—41no—
203C22⋊C8×C41—21no—
204C22⋊C8×C41—21no—
205#95×C41—22no—
206C24×C41—22no—
207C24×C41—21no—
208C24×C41C2×D412yes—
209C24×C41C2×D411yescharacteristic
210#41×C41—21no—
211#41×C41—21no—
212#41×C41—22no—
213#41×C41—22no—
214#41×C41—21no—
215#41×C41—21no—
216#41×C41—21no—
217#41×C41—21no—
218#41×C41—21no—
219#41×C41—21no—
220#41×C41—21no—
221#41×C41—21no—
222#41×C41—42no—
223#41×C41—42no—
224#41×C41—41no—
225#41×C41—41no—
226#41×C41—42no—
227#41×C41—42no—
228#41×C41—42no—
229#41×C41—42no—
230#41×C41—42no—
231#41×C41—42no—
232#41×C41C2×D412yes—
233#41×C41#4112yes—
234C2×Q8×C41—21no—
235C2×Q8×C41—22no—
236C2×Q8×C41—21no—
237C2×Q8×C41—21no—
238C2×Q8×C41—21no—
239C2×Q8×C41—21no—
240C2×Q8×C41—21no—
241C2×Q8×C41—21no—
242C2×Q8×C41—41no—
243C2×Q8×C41C2×D411yescharacteristic
244C2×Q8×C41C2×D411yescharacteristic
245C2×Q8×C41C2×D411yescharacteristic
246C2×D4×C41—21no—
247C2×D4×C41—22no—
248C2×D4×C41—22no—
249C2×D4×C41—22no—
250C2×D4×C41—22no—
251C2×D4×C41—21no—
252C2×D4×C41—21no—
253C2×D4×C41—21no—
254C2×D4×C41—21no—
255C2×D4×C41—21no—
256C2×D4×C41—22no—
257C2×D4×C41—22no—
258C2×D4×C41—22no—
259C2×D4×C41—21no—
260C2×D4×C41—22no—
261C2×D4×C41—21no—
262C2×D4×C41—21no—
263C2×D4×C41—21no—
264C2×D4×C41—21no—
265C2×D4×C41—21no—
266C2×D4×C41—21no—
267C2×D4×C41—21no—
268C2×D4×C41—41no—
269C2×D4×C41—42no—
270C2×D4×C41—42no—
271C2×D4×C41—42no—
272C2×D4×C41—42no—
273C2×D4×C41—44no—
274C2×D4×C41—44no—
275C2×D4×C41—42no—
276C2×D4×C41—42no—
277C2×D4×C41—82no—
278C2×D4×C41—84no—
279C2×D4×C41C2×D411yescharacteristic
280C2×D4×C41C2×D411yescharacteristic
281C2×D4×C41C2×D411yescharacteristic
282C22×C4×C41—21no—
283C22×C4×C41—21no—
284C22×C4×C41—21no—
285C22×C4×C41—21no—
286C22×C4×C41—21no—
287C22×C4×C41—22no—
288C22×C4×C41—21no—
289C22×C4×C41—21no—
290C22×C4×C41—22no—
291C22×C4×C41—21no—
292C22×C4×C41—21no—
293C22×C4×C41—21no—
294C22×C4×C41—21no—
295C22×C4×C41—21no—
296C22×C4×C41—21no—
297C22×C4×C41—21no—
298C22×C4×C41—42no—
299C22×C4×C41—42no—
300C22×C4×C41C2×D411yescharacteristic
301C22×C4×C41C2×D411yescharacteristic
302C22×C4×C41C2×D411yescharacteristic
303C22×C4×C41C2×D411yescharacteristic
304C22×C4×C41C2×D411yescharacteristic
305C22×C4×C41C2×D412yes—
306C22×C4×C41C2411yescharacteristic
307Q16×C41—42no—
308Q16×C41—42no—
309Q16×C41—42no—
310SD16×C41—42no—
311SD16×C41—42no—
312SD16×C41—42no—
313M16×C41—21no—
314M16×C41—21no—
315M16×C41—21no—
316M16×C41—21no—
317M16×C41—21no—
318M16×C41—21no—
319M16×C41—21no—
320M16×C41—42no—
321M16×C41C2×D412yescomplemented
322C2×C8×C41—21no—
323C2×C8×C41—21no—
324C2×C8×C41—21no—
325C2×C8×C41—21no—
326C2×C8×C41—42no—
327C4⋊C4×C41—22no—
328C4⋊C4×C41—22no—
329C4⋊C4×C41—21no—
330C4⋊C4×C41—21no—
331C4⋊C4×C41—21no—
332C4⋊C4×C41—21no—
333C4⋊C4×C41—21no—
334C4⋊C4×C41—21no—
335C4⋊C4×C41—42no—
336C4⋊C4×C41—41no—
337C4⋊C4×C41—41no—
338C4⋊C4×C41—82no—
339C4⋊C4×C41C2×D411yescharacteristic
340C4⋊C4×C41C2×D411yescharacteristic
341C22⋊C4×C41—22no—
342C22⋊C4×C41—22no—
343C22⋊C4×C41—22no—
344C22⋊C4×C41—22no—
345C22⋊C4×C41—22no—
346C22⋊C4×C41—21no—
347C22⋊C4×C41—21no—
348C22⋊C4×C41—21no—
349C22⋊C4×C41—21no—
350C22⋊C4×C41—22no—
351C22⋊C4×C41—22no—
352C22⋊C4×C41—21no—
353C22⋊C4×C41—42no—
354C22⋊C4×C41—44no—
355C22⋊C4×C41—41no—
356C22⋊C4×C41—41no—
357C22⋊C4×C41—82no—
358C42×C41—22no—
359C42×C41—21no—
360C42×C41—21no—
361C42×C41—21no—
362C42×C41—21no—
363C42×C41C2×D412yescomplemented
364C23×C41—21no—
365C23×C41—21no—
366C23×C41—21no—
367C23×C41—22no—
368C23×C41—21no—
369C23×C41—21no—
370C23×C41—22no—
371C23×C41—22no—
372C23×C41—41no—
373C23×C41—41no—
374C23×C41—42no—
375C23×C41—42no—
376C23×C41—44no—
377C23×C41—42no—
378C23×C41—42no—
379C23×C41—81no—
380C23×C41—82no—
381C23×C41—82no—
382C23×C41#12011yescharacteristic
383C23×C41#12011yescharacteristic
384C23×C41C22×D411yescharacteristic
385Q8×C41—21no—
386Q8×C41—21no—
387Q8×C41—21no—
388Q8×C41—21no—
389Q8×C41—21no—
390Q8×C41—42no—
391Q8×C41—41no—
392Q8×C41—41no—
393Q8×C41—41no—
394Q8×C41—41no—
395Q8×C41#12112yes—
396D4×C41—22no—
397D4×C41—22no—
398D4×C41—21no—
399D4×C41—21no—
400D4×C41—21no—
401D4×C41—21no—
402D4×C41—21no—
403D4×C41—42no—
404D4×C41—42no—
405D4×C41—44no—
406D4×C41—42no—
407D4×C41—44no—
408D4×C41—44no—
409D4×C41—42no—
410D4×C41—41no—
411D4×C41—41no—
412D4×C41—41no—
413D4×C41—41no—
414D4×C41—41no—
415D4×C41—41no—
416D4×C41—41no—
417D4×C41—41no—
418D4×C41—81no—
419D4×C41—82no—
420D4×C41—82no—
421D4×C41—82no—
422D4×C41—82no—
423D4×C41#12112yes—
424C2×C4×C41—21no—
425C2×C4×C41—21no—
426C2×C4×C41—21no—
427C2×C4×C41—21no—
428C2×C4×C41—21no—
429C2×C4×C41—21no—
430C2×C4×C41—21no—
431C2×C4×C41—21no—
432C2×C4×C41—21no—
433C2×C4×C41—22no—
434C2×C4×C41—21no—
435C2×C4×C41—21no—
436C2×C4×C41—22no—
437C2×C4×C41—21no—
438C2×C4×C41—22no—
439C2×C4×C41—21no—
440C2×C4×C41—21no—
441C2×C4×C41—21no—
442C2×C4×C41—22no—
443C2×C4×C41—42no—
444C2×C4×C41—42no—
445C2×C4×C41—42no—
446C2×C4×C41—44no—
447C2×C4×C41—41no—
448C2×C4×C41—41no—
449C2×C4×C41—41no—
450C2×C4×C41—41no—
451C2×C4×C41—41no—
452C2×C4×C41—41no—
453C2×C4×C41—42no—
454C2×C4×C41—41no—
455C2×C4×C41—42no—
456C2×C4×C41—41no—
457C2×C4×C41—41no—
458C2×C4×C41—41no—
459C2×C4×C41—41no—
460C2×C4×C41—41no—
461C2×C4×C41—41no—
462C2×C4×C41—82no—
463C2×C4×C41#12011yescharacteristic
464C2×C4×C41#12011yescharacteristic
465C2×C4×C41C22×D411yescharacteristic
466C2×C4×C41C22×D411yescharacteristic
467C2×C4×C41C22×D411yescharacteristic
468C2×C4×C41C2×#4111yescharacteristic
469C2×C4×C41H(5,𝔽2)11yescharacteristic
470C2×C4×C41H(5,𝔽2)11yescharacteristic
471C8×C41—22no—
472C8×C41—41no—
473C8×C41—41no—
474C8×C41—41no—
475#24471C4111yesmaximal, characteristic, direct product factor, Sylow
476C22×C41—21no—
477C22×C41—21no—
478C22×C41—21no—
479C22×C41—21no—
480C22×C41—22no—
481C22×C41—21no—
482C22×C41—21no—
483C22×C41—21no—
484C22×C41—21no—
485C22×C41—41no—
486C22×C41—41no—
487C22×C41—41no—
488C22×C41—41no—
489C22×C41—42no—
490C22×C41—42no—
491C22×C41—41no—
492C22×C41—41no—
493C22×C41—41no—
494C22×C41—42no—
495C22×C41—41no—
496C22×C41—81no—
497C22×C41—81no—
498C22×C41—82no—
499C22×C41—82no—
500C22×C41—84no—
501C22×C41—164no—
502C22×C41C2×#12011yescharacteristic
503C22×C41D4211yescharacteristic
504C22×C41#54611yescharacteristic
505C4×C41—21no—
506C4×C41—21no—
507C4×C41—22no—
508C4×C41—42no—
509C4×C41—41no—
510C4×C41—41no—
511C4×C41—42no—
512C4×C41—41no—
513C4×C41—41no—
514C4×C41—81no—
515C4×C41—81no—
516C4×C41—81no—
517C4×C41C2×#12111yescharacteristic
518C4×C41#53411yescharacteristic
519C4×C41D4211yescharacteristic
520C4×C41#54611yescharacteristic
521#3488C2×C4111yescharacteristic
522#3056C2×C4111yescharacteristic, complemented
523C2×#455C2×C4111yescharacteristic, complemented
524#3007C2×C4111yescharacteristic, complemented
525C2×#421C2×C4111yescharacteristic, complemented
526#2620C2×C4111yescharacteristic, complemented
527#2039C2×C4111yescharacteristic, complemented
528#2037C2×C4111yescharacteristic, complemented
529#2007C2×C4111yescharacteristic, complemented
530#2004C2×C4111yescharacteristic, complemented
531#1900C2×C4111yescharacteristic, complemented
532#1897C2×C4111yescharacteristic, complemented
533#1882C2×C4111yescharacteristic, complemented
534#1859C2×C4111yescharacteristic, complemented
535#1792C2×C4111yescharacteristic, complemented
536C2×C41—21no—
537C2×C41—21no—
538C2×C41—41no—
539C2×C41—41no—
540C2×C41—42no—
541C2×C41—81no—
542C2×C41—82no—
543C2×C41—81no—
544C2×C41#241011yescharacteristic
545C2×C41#301911yescharacteristic
546C2×C41#302211yescharacteristic
547C2×H(5,𝔽2)C22×C4111yescharacteristic
548C22×#41C22×C4111yescharacteristic
549C2×#137C22×C4111yescharacteristic
550C2×#137C22×C4111yescharacteristic, complemented
551C2×#137C22×C4111yescharacteristic, complemented
552C22×M16C22×C4111yescharacteristic, complemented
553#550—21no—
554#548—21no—
555#546—21no—
556#546—22no—
557D42—22no—
558D42—21no—
559#537—21no—
560#537C22×C4111yescharacteristic
561#535—21no—
562#535C22×C4111yescharacteristic
563C2×#124C22×C4111yescharacteristic, complemented
564#525—21no—
565#525C22×C4111yescharacteristic
566C2×C22⋊Q8C22×C4111yescharacteristic, complemented
567C2×#121—21no—
568C2×#121C22×C4111yescharacteristic
569#520C22×C4111yescharacteristic
570C2×#117C22×C4111yescharacteristic, complemented
571#470—21no—
572#468—21no—
573#467—21no—
574#465—21no—
575#455—24no—
576#452—21no—
577#452—21no—
578#451—21no—
579#450—21no—
580#428C22×C4111yescharacteristic, complemented
581#421—24no—
582C2×#104C22×C4111yescharacteristic
583C2×#104C22×C4111yescharacteristic
584C2×#104C22×C4111yescharacteristic, complemented
585C2×#104C22×C4111yescharacteristic, complemented
586C2×#104C22×C4111yescharacteristic, complemented
587C2×#104C22×C4111yescharacteristic, complemented
588#419C22×C4111yescharacteristic, complemented
589#417C22×C4111yescharacteristic
590#417C22×C4111yescharacteristic, complemented
591#417C22×C4111yescharacteristic, complemented
592C2×#100C22×C4111yescharacteristic, complemented
593C2×#100C22×C4111yescharacteristic, complemented
594#407C22×C4111yescharacteristic, complemented
595#396—22no—
596#394—22no—
597#391C22×C4111yescharacteristic, complemented
598#390C22×C4111yescharacteristic, complemented
599#384C22×C4111yescharacteristic, complemented
600#343C22×C4111yescharacteristic, complemented
601#343C22×C4111yescharacteristic, complemented
602#339C22×C4111yescharacteristic, complemented
603#339C22×C4111yescharacteristic, complemented
604C41#2447111yescharacteristic, direct product factor, Sylow
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C4111yescharacteristic
618C2×#41D4×C4111yescharacteristic
619C2×#41C23×C4111yescharacteristic
620C2×#41C23×C4111yescharacteristic
621C2×#41C23×C4111yescharacteristic
622C22×Q8D4×C4111yescharacteristic
623C22×Q8C23×C4111yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C4111yescharacteristic
630C22×D4D4×C4112yes—
631C22×D4C23×C4111yescharacteristic
632C23×C4—21no—
633C23×C4C23×C4111yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C4111yescharacteristic
650C2×M16C23×C4111yescharacteristic
651C2×M16C23×C4111yescharacteristic
652C2×M16C23×C4111yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C4111yescharacteristic
670C22⋊Q8D4×C4111yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C4111yescharacteristic
686#121D4×C4111yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C4111yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C4111yescharacteristic
708C2×C4⋊C4C23×C4111yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C4112yes—
715C2×C42C23×C4111yescharacteristic
716C2×C42C23×C4111yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C4114yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C4112yes—
741C24C2×D4×C4111yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C4112yes—
765#41#41×C4112yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C4111yescharacteristic
776C2×Q8C2×D4×C4111yescharacteristic
777C2×Q8C2×D4×C4111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C4111yescharacteristic
812C2×D4C2×D4×C4111yescharacteristic
813C2×D4C2×D4×C4111yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C4111yescharacteristic
833C22×C4C2×D4×C4111yescharacteristic
834C22×C4C2×D4×C4111yescharacteristic
835C22×C4C2×D4×C4111yescharacteristic
836C22×C4C2×D4×C4111yescharacteristic
837C22×C4C2×D4×C4112yes—
838C22×C4C24×C4111yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C4112yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C4111yescharacteristic
872C4⋊C4C2×D4×C4111yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C4112yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C4111yescharacteristic
915C23#120×C4111yescharacteristic
916C23C22×D4×C4111yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C4112yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C4112yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C4111yescharacteristic
996C2×C4#120×C4111yescharacteristic
997C2×C4C22×D4×C4111yescharacteristic
998C2×C4C22×D4×C4111yescharacteristic
999C2×C4C22×D4×C4111yescharacteristic
1000C2×C4C2×#41×C4111yescharacteristic
1001C2×C4H(5,𝔽2)×C4111yescharacteristic
1002C2×C4H(5,𝔽2)×C4111yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C4111yescharacteristic
1034C22D42×C4111yescharacteristic
1035C22C41×#54611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C4111yescharacteristic
1049C4C41×#53411yescharacteristic
1050C4D42×C4111yescharacteristic
1051C4C41×#54611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C41×#241011yescharacteristic
1061C2C41×#301911yescharacteristic
1062C2C41×#302211yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#3056C2semidirect
3. C2×C41×#455C2semidirect
4. C41×#3007C2semidirect
5. C2×C41×#421C2semidirect
6. C41×#2620C2semidirect
7. C41×#2039C2semidirect
8. C41×#2037C2semidirect
9. C41×#2007C2semidirect
10. C41×#2004C2semidirect
11. C41×#1900C2semidirect
12. C41×#1897C2semidirect
13. C41×#1882C2semidirect
14. C41×#1859C2semidirect
15. C41×#1792C2semidirect
19. C2×#137×C41C22semidirect
20. C2×#137×C41C22semidirect
21. C22×M16×C41C22semidirect
32. C2×#124×C41C22semidirect
35. C2×C22⋊Q8×C41C22semidirect
39. C2×#117×C41C22semidirect
49. C41×#428C22semidirect
53. C2×#104×C41C22semidirect
54. C2×#104×C41C22semidirect
55. C2×#104×C41C22semidirect
56. C2×#104×C41C22semidirect
57. C41×#419C22semidirect
59. C41×#417C22semidirect
60. C41×#417C22semidirect
61. C2×#100×C41C22semidirect
62. C2×#100×C41C22semidirect
63. C41×#407C22semidirect
66. C41×#391C22semidirect
67. C41×#390C22semidirect
68. C41×#384C22semidirect
69. C41×#343C22semidirect
70. C41×#343C22semidirect
71. C41×#339C22semidirect
72. C41×#339C22semidirect
192. #104×C41D4semidirect
321. M16×C41C2×D4semidirect
363. C42×C41C2×D4semidirect
475. #24471C41direct (N × H)
522. #3056C2×C41semidirect
523. C2×#455C2×C41semidirect
524. #3007C2×C41semidirect
525. C2×#421C2×C41semidirect
526. #2620C2×C41semidirect
527. #2039C2×C41semidirect
528. #2037C2×C41semidirect
529. #2007C2×C41semidirect
530. #2004C2×C41semidirect
531. #1900C2×C41semidirect
532. #1897C2×C41semidirect
533. #1882C2×C41semidirect
534. #1859C2×C41semidirect
535. #1792C2×C41semidirect
550. C2×#137C22×C41semidirect
551. C2×#137C22×C41semidirect
552. C22×M16C22×C41semidirect
563. C2×#124C22×C41semidirect
566. C2×C22⋊Q8C22×C41semidirect
570. C2×#117C22×C41semidirect
580. #428C22×C41semidirect
584. C2×#104C22×C41semidirect
585. C2×#104C22×C41semidirect
586. C2×#104C22×C41semidirect
587. C2×#104C22×C41semidirect
588. #419C22×C41semidirect
590. #417C22×C41semidirect
591. #417C22×C41semidirect
592. C2×#100C22×C41semidirect
593. C2×#100C22×C41semidirect
594. #407C22×C41semidirect
597. #391C22×C41semidirect
598. #390C22×C41semidirect
599. #384C22×C41semidirect
600. #343C22×C41semidirect
601. #343C22×C41semidirect
602. #339C22×C41semidirect
603. #339C22×C41semidirect
604. C41#24471direct (N × H)
724. #104D4×C41semidirect
853. M16C2×D4×C41semidirect
895. C42C2×D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34882
C41×#30562
C2×C41×#4552
C41×#30072
C2×C41×#4212
C41×#26202
C41×#20392
C41×#20372
C41×#20072
C41×#20042
C41×#19002
C41×#18972
C41×#18822
C41×#18592
C41×#17922
#2447141