Finite Group Databasebeta

← C41×#25143 #23801344

Subgroups — C41×#25143 #23801344

Order 10496.

996 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#473C211yesmaximal, characteristic, complemented
2C41×#3056C211yesmaximal, characteristic, complemented
3C41×#3005C211yesmaximal, characteristic
4C2×C41×#452C211yesmaximal, characteristic, complemented
5C41×#2933C211yesmaximal, characteristic, complemented
6C2×C41×#413C211yesmaximal, characteristic, complemented
7C41×#2063C211yesmaximal, characteristic, complemented
8C41×#2052C211yesmaximal, characteristic, complemented
9C41×#2047C211yesmaximal, characteristic, complemented
10C41×#2019C211yesmaximal, characteristic, complemented
11C41×#1977C211yesmaximal, characteristic, complemented
12C41×#1930C211yesmaximal, characteristic, complemented
13C41×#1907C211yesmaximal, characteristic, complemented
14C41×#1901C211yesmaximal, characteristic, complemented
15C41×#1855C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C2×#137×C41C2211yescharacteristic
18C2×#137×C41C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
20C22×Q16×C41C2211yescharacteristic
21C22×SD16×C41C2211yescharacteristic
22C2×#131×C41C2211yescharacteristic
23C22×M16×C41C2211yescharacteristic
24C22×M16×C41C2211yescharacteristic
25C41×#525C2211yescharacteristic
26C2×C22⋊Q8×C41C2211yescharacteristic
27C41×#473—24no—
28C41×#470—21no—
29C41×#468—21no—
30C41×#467—21no—
31C41×#465—21no—
32C41×#452—21no—
33C41×#452—21no—
34C41×#452—21no—
35C41×#452—21no—
36C41×#452—21no—
37C41×#452—21no—
38C41×#449—21no—
39C41×#449—21no—
40C41×#436—21no—
41C41×#435—21no—
42C41×#435—21no—
43C8×D4×C41—21no—
44C2×#108×C41C2211yescharacteristic
45C2×#108×C41C2211yescharacteristic
46C41×#428C2211yescharacteristic
47C41×#424C2211yescharacteristic
48C41×#419C2211yescharacteristic
49C41×#419C2211yescharacteristic
50C41×#418C2211yescharacteristic
51C41×#417C2211yescharacteristic
52C2×#103×C41C2211yescharacteristic
53C2×#102×C41C2211yescharacteristic
54C41×#413—24no—
55C2×#101×C41C2211yescharacteristic
56C2×#101×C41C2211yescharacteristic
57C2×#101×C41C2211yescharacteristic
58C2×#101×C41C2211yescharacteristic
59C2×#100×C41C2211yescharacteristic
60C2×#100×C41C2211yescharacteristic
61C41×#408C2211yescharacteristic
62C41×#407C2211yescharacteristic
63C2×C22⋊C8×C41C2211yescharacteristic
64C41×#405C2211yescharacteristic
65C41×#343C2211yescharacteristic
66C41×#343C2211yescharacteristic
67C41×#341C2211yescharacteristic
68C41×#341C2211yescharacteristic
69C2×#41×C41—22no—
70C2×#41×C41—22no—
71C2×#41×C41—21no—
72C2×#41×C41—21no—
73C2×#41×C41—21no—
74C2×#41×C41—21no—
75C2×#41×C41—41no—
76C2×#41×C41—41no—
77C2×#41×C41C2311yescharacteristic
78C22×Q8×C41C2311yescharacteristic
79C22×Q8×C41C2311yescharacteristic
80C22×D4×C41—21no—
81C22×D4×C41C2311yescharacteristic
82C23×C4×C41—21no—
83C23×C4×C41C2311yescharacteristic
84#137×C41—22no—
85#137×C41—22no—
86#137×C41—41no—
87#137×C41—41no—
88AGL(1,ℤ/8)×C41—22no—
89AGL(1,ℤ/8)×C41—41no—
90C2×Q16×C41—22no—
91C2×Q16×C41—21no—
92C2×Q16×C41—21no—
93C2×Q16×C41—21no—
94C2×Q16×C41—21no—
95C2×Q16×C41—41no—
96C2×SD16×C41—21no—
97C2×SD16×C41—21no—
98C2×SD16×C41—21no—
99C2×SD16×C41—22no—
100C2×SD16×C41—21no—
101C2×SD16×C41—21no—
102C2×SD16×C41—41no—
103C2×D8×C41—21no—
104#131×C41—22no—
105#131×C41—41no—
106C2×M16×C41—21no—
107C2×M16×C41—21no—
108C2×M16×C41—21no—
109C2×M16×C41—22no—
110C2×M16×C41—22no—
111C2×M16×C41—41no—
112C2×M16×C41—41no—
113C2×M16×C41C2311yescharacteristic
114C2×M16×C41C2311yescharacteristic
115C2×M16×C41C2311yescharacteristic
116C2×M16×C41C2311yescharacteristic
117C2×M16×C41C2311yescharacteristic
118C2×M16×C41C2311yescharacteristic
119C22×C8×C41—21no—
120C22×C8×C41—21no—
121C22×C8×C41—21no—
122C22×C8×C41C2311yescharacteristic
123C22×C8×C41C2311yescharacteristic
124#123×C41—21no—
125C22⋊Q8×C41—21no—
126C22⋊Q8×C41—21no—
127C22⋊Q8×C41—21no—
128C22⋊Q8×C41—21no—
129C22⋊Q8×C41D411yescharacteristic
130C22⋊Q8×C41D411yescharacteristic
131#121×C41D411yescharacteristic
132#121×C41D411yescharacteristic
133#120×C41—21no—
134C4×D4×C41—21no—
135C4×D4×C41—21no—
136#117×C41C2311yescharacteristic
137C2×C4⋊C4×C41—21no—
138C2×C4⋊C4×C41C2311yescharacteristic
139C2×C22⋊C4×C41—21no—
140#108×C41—22no—
141#108×C41—41no—
142#107×C41—21no—
143#106×C41—21no—
144C4⋊C8×C41—21no—
145C4⋊C8×C41—21no—
146#103×C41—21no—
147#103×C41—21no—
148#103×C41—21no—
149#103×C41—21no—
150#103×C41—21no—
151#103×C41—21no—
152#103×C41—21no—
153#102×C41—21no—
154#102×C41—21no—
155#102×C41—21no—
156#102×C41—21no—
157#102×C41—21no—
158#101×C41—22no—
159#101×C41—22no—
160#101×C41—41no—
161#101×C41D414yescomplemented
162#100×C41—22no—
163#100×C41—22no—
164C22⋊C8×C41—21no—
165C22⋊C8×C41—21no—
166C22⋊C8×C41—21no—
167C22⋊C8×C41—21no—
168C22⋊C8×C41D411yescharacteristic
169C22⋊C8×C41D411yescharacteristic
170C22⋊C8×C41D411yescharacteristic
171C22⋊C8×C41D411yescharacteristic
172#97×C41—21no—
173C4×C8×C41—21no—
174C24×C41—21no—
175C24×C41#4111yescharacteristic
176#41×C41—21no—
177#41×C41—21no—
178#41×C41—21no—
179#41×C41—21no—
180#41×C41—42no—
181#41×C41—42no—
182#41×C41—42no—
183#41×C41—42no—
184#41×C41—42no—
185#41×C41—42no—
186#41×C41—42no—
187#41×C41—42no—
188C2×Q8×C41—21no—
189C2×Q8×C41—21no—
190C2×Q8×C41—21no—
191C2×Q8×C41—21no—
192C2×Q8×C41—21no—
193C2×Q8×C41—21no—
194C2×Q8×C41—21no—
195C2×Q8×C41—21no—
196C2×Q8×C41—21no—
197C2×Q8×C41—21no—
198C2×Q8×C41—21no—
199C2×Q8×C41C2×D412yes—
200C2×Q8×C41C2×D411yescharacteristic
201C2×D4×C41—24no—
202C2×D4×C41—21no—
203C2×D4×C41—21no—
204C2×D4×C41—21no—
205C2×D4×C41—21no—
206C2×D4×C41—21no—
207C2×D4×C41—21no—
208C2×D4×C41—21no—
209C2×D4×C41—21no—
210C2×D4×C41—42no—
211C2×D4×C41—41no—
212C2×D4×C41—41no—
213C2×D4×C41C2×D411yescharacteristic
214C2×D4×C41#4112yes—
215C22×C4×C41—21no—
216C22×C4×C41—21no—
217C22×C4×C41—21no—
218C22×C4×C41—21no—
219C22×C4×C41—24no—
220C22×C4×C41—21no—
221C22×C4×C41—21no—
222C22×C4×C41—21no—
223C22×C4×C41—21no—
224C22×C4×C41—42no—
225C22×C4×C41—41no—
226C22×C4×C41—41no—
227C22×C4×C41C2×D411yescharacteristic
228C22×C4×C41C2×D411yescharacteristic
229C22×C4×C41C2×D411yescharacteristic
230C22×C4×C41C2×D411yescharacteristic
231C22×C4×C41#4111yescharacteristic
232C22×C4×C41C2411yescharacteristic
233Q16×C41—42no—
234Q16×C41—42no—
235Q16×C41—42no—
236Q16×C41—42no—
237SD16×C41—42no—
238SD16×C41—42no—
239SD16×C41—42no—
240SD16×C41—42no—
241SD16×C41—42no—
242D8×C41—42no—
243M16×C41—21no—
244M16×C41—21no—
245M16×C41—21no—
246M16×C41—21no—
247M16×C41—21no—
248M16×C41—21no—
249M16×C41—21no—
250M16×C41—21no—
251M16×C41—21no—
252M16×C41—21no—
253M16×C41—42no—
254M16×C41—42no—
255M16×C41—42no—
256M16×C41C2×D412yes—
257M16×C41C2×D412yes—
258C2×C8×C41—21no—
259C2×C8×C41—21no—
260C2×C8×C41—21no—
261C2×C8×C41—21no—
262C2×C8×C41—21no—
263C2×C8×C41—21no—
264C2×C8×C41—21no—
265C2×C8×C41—21no—
266C2×C8×C41—21no—
267C2×C8×C41—21no—
268C2×C8×C41—42no—
269C2×C8×C41—42no—
270C2×C8×C41—42no—
271C2×C8×C41C2×D411yescharacteristic
272C2×C8×C41C2×D411yescharacteristic
273C2×C8×C41C2×D411yescharacteristic
274C2×C8×C41C2×D411yescharacteristic
275C4⋊C4×C41—21no—
276C4⋊C4×C41—21no—
277C4⋊C4×C41—21no—
278C4⋊C4×C41—21no—
279C4⋊C4×C41—41no—
280C4⋊C4×C41—41no—
281C4⋊C4×C41C2×D411yescharacteristic
282C4⋊C4×C41C2×D411yescharacteristic
283C22⋊C4×C41—21no—
284C22⋊C4×C41—21no—
285C22⋊C4×C41—21no—
286C22⋊C4×C41—21no—
287C22⋊C4×C41—21no—
288C22⋊C4×C41—41no—
289C22⋊C4×C41—41no—
290C42×C41—21no—
291C23×C41—21no—
292C23×C41—21no—
293C23×C41—21no—
294C23×C41—22no—
295C23×C41—41no—
296C23×C41—41no—
297C23×C41—41no—
298C23×C41—41no—
299C23×C41—81no—
300C23×C41—81no—
301C23×C41#12111yescharacteristic
302C23×C41#12111yescharacteristic
303C23×C41C2×#4111yescharacteristic
304Q8×C41—22no—
305Q8×C41—21no—
306Q8×C41—22no—
307Q8×C41—21no—
308Q8×C41—41no—
309Q8×C41—41no—
310Q8×C41—41no—
311Q8×C41—41no—
312Q8×C41—41no—
313Q8×C41—41no—
314D4×C41—21no—
315D4×C41—21no—
316D4×C41—22no—
317D4×C41—22no—
318D4×C41—42no—
319D4×C41—44no—
320D4×C41—44no—
321D4×C41—41no—
322D4×C41—41no—
323D4×C41—41no—
324D4×C41—41no—
325D4×C41—81no—
326C2×C4×C41—21no—
327C2×C4×C41—21no—
328C2×C4×C41—21no—
329C2×C4×C41—21no—
330C2×C4×C41—21no—
331C2×C4×C41—21no—
332C2×C4×C41—21no—
333C2×C4×C41—21no—
334C2×C4×C41—21no—
335C2×C4×C41—21no—
336C2×C4×C41—21no—
337C2×C4×C41—21no—
338C2×C4×C41—21no—
339C2×C4×C41—22no—
340C2×C4×C41—44no—
341C2×C4×C41—44no—
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—81no—
351C2×C4×C41#12111yescharacteristic
352C2×C4×C41#12111yescharacteristic
353C2×C4×C41C22×D411yescharacteristic
354C2×C4×C41C22×D411yescharacteristic
355C2×C4×C41C22×D411yescharacteristic
356C2×C4×C41C2×#4111yescharacteristic
357C2×C4×C41H(5,𝔽2)11yescharacteristic
358C2×C4×C41H(5,𝔽2)11yescharacteristic
359C8×C41—21no—
360C8×C41—21no—
361C8×C41—22no—
362C8×C41—22no—
363C8×C41—21no—
364C8×C41—21no—
365C8×C41—41no—
366C8×C41—41no—
367C8×C41—41no—
368C8×C41—41no—
369#25143C4111yesmaximal, characteristic, direct product factor, Sylow
370C22×C41—21no—
371C22×C41—21no—
372C22×C41—21no—
373C22×C41—21no—
374C22×C41—21no—
375C22×C41—21no—
376C22×C41—21no—
377C22×C41—21no—
378C22×C41—42no—
379C22×C41—41no—
380C22×C41—41no—
381C22×C41—41no—
382C22×C41—81no—
383C22×C41—81no—
384C22×C41—82no—
385C22×C41—82no—
386C22×C41—81no—
387C22×C41—81no—
388C22×C41C2×#12111yescharacteristic
389C22×C41#52511yescharacteristic
390C22×C41#53811yescharacteristic
391C4×C41—21no—
392C4×C41—21no—
393C4×C41—42no—
394C4×C41—41no—
395C4×C41—41no—
396C4×C41—41no—
397C4×C41—81no—
398C4×C41—81no—
399C4×C41D4211yescharacteristic
400C4×C41D4211yescharacteristic
401C4×C41#54611yescharacteristic
402C4×C41#54611yescharacteristic
403C2×#473C2×C4111yescharacteristic, complemented
404#3056C2×C4111yescharacteristic, complemented
405#3005C2×C4111yescharacteristic
406C2×#452C2×C4111yescharacteristic, complemented
407#2933C2×C4111yescharacteristic, complemented
408C2×#413C2×C4111yescharacteristic, complemented
409#2063C2×C4111yescharacteristic, complemented
410#2052C2×C4111yescharacteristic, complemented
411#2047C2×C4111yescharacteristic, complemented
412#2019C2×C4111yescharacteristic, complemented
413#1977C2×C4111yescharacteristic, complemented
414#1930C2×C4111yescharacteristic, complemented
415#1907C2×C4111yescharacteristic, complemented
416#1901C2×C4111yescharacteristic, complemented
417#1855C2×C4111yescharacteristic, complemented
418C2×C41—21no—
419C2×C41—21no—
420C2×C41—41no—
421C2×C41—41no—
422C2×C41—81no—
423C2×C41—82no—
424C2×C41#242411yescharacteristic
425C2×C41#306711yescharacteristic
426C2×C41#306911yescharacteristic
427C22×#41C22×C4111yescharacteristic
428C2×#137C22×C4111yescharacteristic
429C2×#137C22×C4111yescharacteristic
430C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
431C22×Q16C22×C4111yescharacteristic
432C22×SD16C22×C4111yescharacteristic
433C2×#131C22×C4111yescharacteristic
434C22×M16C22×C4111yescharacteristic
435C22×M16C22×C4111yescharacteristic
436#525C22×C4111yescharacteristic
437C2×C22⋊Q8C22×C4111yescharacteristic
438#473—24no—
439#470—21no—
440#468—21no—
441#467—21no—
442#465—21no—
443#452—21no—
444#452—21no—
445#452—21no—
446#452—21no—
447#452—21no—
448#452—21no—
449#449—21no—
450#449—21no—
451#436—21no—
452#435—21no—
453#435—21no—
454C8×D4—21no—
455C2×#108C22×C4111yescharacteristic
456C2×#108C22×C4111yescharacteristic
457#428C22×C4111yescharacteristic
458#424C22×C4111yescharacteristic
459#419C22×C4111yescharacteristic
460#419C22×C4111yescharacteristic
461#418C22×C4111yescharacteristic
462#417C22×C4111yescharacteristic
463C2×#103C22×C4111yescharacteristic
464C2×#102C22×C4111yescharacteristic
465#413—24no—
466C2×#101C22×C4111yescharacteristic
467C2×#101C22×C4111yescharacteristic
468C2×#101C22×C4111yescharacteristic
469C2×#101C22×C4111yescharacteristic
470C2×#100C22×C4111yescharacteristic
471C2×#100C22×C4111yescharacteristic
472#408C22×C4111yescharacteristic
473#407C22×C4111yescharacteristic
474C2×C22⋊C8C22×C4111yescharacteristic
475#405C22×C4111yescharacteristic
476#343C22×C4111yescharacteristic
477#343C22×C4111yescharacteristic
478#341C22×C4111yescharacteristic
479#341C22×C4111yescharacteristic
480C41#2514311yescharacteristic, direct product factor, Sylow
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41C23×C4111yescharacteristic
490C22×Q8C23×C4111yescharacteristic
491C22×Q8C23×C4111yescharacteristic
492C22×D4—21no—
493C22×D4C23×C4111yescharacteristic
494C23×C4—21no—
495C23×C4C23×C4111yescharacteristic
496#137—22no—
497#137—22no—
498#137—41no—
499#137—41no—
500AGL(1,ℤ/8)—22no—
501AGL(1,ℤ/8)—41no—
502C2×Q16—22no—
503C2×Q16—21no—
504C2×Q16—21no—
505C2×Q16—21no—
506C2×Q16—21no—
507C2×Q16—41no—
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×SD16—22no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16—41no—
515C2×D8—21no—
516#131—22no—
517#131—41no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—21no—
521C2×M16—22no—
522C2×M16—22no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16C23×C4111yescharacteristic
526C2×M16C23×C4111yescharacteristic
527C2×M16C23×C4111yescharacteristic
528C2×M16C23×C4111yescharacteristic
529C2×M16C23×C4111yescharacteristic
530C2×M16C23×C4111yescharacteristic
531C22×C8—21no—
532C22×C8—21no—
533C22×C8—21no—
534C22×C8C23×C4111yescharacteristic
535C22×C8C23×C4111yescharacteristic
536#123—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8D4×C4111yescharacteristic
542C22⋊Q8D4×C4111yescharacteristic
543#121D4×C4111yescharacteristic
544#121D4×C4111yescharacteristic
545#120—21no—
546C4×D4—21no—
547C4×D4—21no—
548#117C23×C4111yescharacteristic
549C2×C4⋊C4—21no—
550C2×C4⋊C4C23×C4111yescharacteristic
551C2×C22⋊C4—21no—
552#108—22no—
553#108—41no—
554#107—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558#103—21no—
559#103—21no—
560#103—21no—
561#103—21no—
562#103—21no—
563#103—21no—
564#103—21no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—21no—
569#102—21no—
570#101—22no—
571#101—22no—
572#101—41no—
573#101D4×C4114yescomplemented
574#100—22no—
575#100—22no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8D4×C4111yescharacteristic
581C22⋊C8D4×C4111yescharacteristic
582C22⋊C8D4×C4111yescharacteristic
583C22⋊C8D4×C4111yescharacteristic
584#97—21no—
585C4×C8—21no—
586C24—21no—
587C24#41×C4111yescharacteristic
588#41—21no—
589#41—21no—
590#41—21no—
591#41—21no—
592#41—42no—
593#41—42no—
594#41—42no—
595#41—42no—
596#41—42no—
597#41—42no—
598#41—42no—
599#41—42no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×D4×C4112yes—
612C2×Q8C2×D4×C4111yescharacteristic
613C2×D4—24no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—42no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4C2×D4×C4111yescharacteristic
626C2×D4#41×C4112yes—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—24no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4C2×D4×C4111yescharacteristic
640C22×C4C2×D4×C4111yescharacteristic
641C22×C4C2×D4×C4111yescharacteristic
642C22×C4C2×D4×C4111yescharacteristic
643C22×C4#41×C4111yescharacteristic
644C22×C4C24×C4111yescharacteristic
645Q16—42no—
646Q16—42no—
647Q16—42no—
648Q16—42no—
649SD16—42no—
650SD16—42no—
651SD16—42no—
652SD16—42no—
653SD16—42no—
654D8—42no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—21no—
659M16—21no—
660M16—21no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—42no—
666M16—42no—
667M16—42no—
668M16C2×D4×C4112yes—
669M16C2×D4×C4112yes—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—42no—
681C2×C8—42no—
682C2×C8—42no—
683C2×C8C2×D4×C4111yescharacteristic
684C2×C8C2×D4×C4111yescharacteristic
685C2×C8C2×D4×C4111yescharacteristic
686C2×C8C2×D4×C4111yescharacteristic
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—41no—
692C4⋊C4—41no—
693C4⋊C4C2×D4×C4111yescharacteristic
694C4⋊C4C2×D4×C4111yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C42—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—81no—
712C23—81no—
713C23#121×C4111yescharacteristic
714C23#121×C4111yescharacteristic
715C23C2×#41×C4111yescharacteristic
716Q8—22no—
717Q8—21no—
718Q8—22no—
719Q8—21no—
720Q8—41no—
721Q8—41no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—21no—
727D4—21no—
728D4—22no—
729D4—22no—
730D4—44no—
731D4—44no—
732D4—42no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—81no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—81no—
763C2×C4#121×C4111yescharacteristic
764C2×C4#121×C4111yescharacteristic
765C2×C4C22×D4×C4111yescharacteristic
766C2×C4C22×D4×C4111yescharacteristic
767C2×C4C22×D4×C4111yescharacteristic
768C2×C4C2×#41×C4111yescharacteristic
769C2×C4H(5,𝔽2)×C4111yescharacteristic
770C2×C4H(5,𝔽2)×C4111yescharacteristic
771C8—21no—
772C8—21no—
773C8—22no—
774C8—22no—
775C8—21no—
776C8—21no—
777C8—41no—
778C8—41no—
779C8—41no—
780C8—41no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—81no—
794C22—81no—
795C22—82no—
796C22—82no—
797C22—81no—
798C22—81no—
799C22C2×#121×C4111yescharacteristic
800C22C41×#52511yescharacteristic
801C22C41×#53811yescharacteristic
802C4—21no—
803C4—21no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—41no—
808C4—81no—
809C4—81no—
810C4D42×C4111yescharacteristic
811C4D42×C4111yescharacteristic
812C4C41×#54611yescharacteristic
813C4C41×#54611yescharacteristic
814C2—21no—
815C2—21no—
816C2—41no—
817C2—41no—
818C2—81no—
819C2—82no—
820C2C41×#242411yescharacteristic
821C2C41×#306711yescharacteristic
822C2C41×#306911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#3005C2
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
1. C2×C41×#473C2semidirect
2. C41×#3056C2semidirect
4. C2×C41×#452C2semidirect
5. C41×#2933C2semidirect
6. C2×C41×#413C2semidirect
7. C41×#2063C2semidirect
8. C41×#2052C2semidirect
9. C41×#2047C2semidirect
10. C41×#2019C2semidirect
11. C41×#1977C2semidirect
12. C41×#1930C2semidirect
13. C41×#1907C2semidirect
14. C41×#1901C2semidirect
15. C41×#1855C2semidirect
161. #101×C41D4semidirect
369. #25143C41direct (N × H)
403. C2×#473C2×C41semidirect
404. #3056C2×C41semidirect
406. C2×#452C2×C41semidirect
407. #2933C2×C41semidirect
408. C2×#413C2×C41semidirect
409. #2063C2×C41semidirect
410. #2052C2×C41semidirect
411. #2047C2×C41semidirect
412. #2019C2×C41semidirect
413. #1977C2×C41semidirect
414. #1930C2×C41semidirect
415. #1907C2×C41semidirect
416. #1901C2×C41semidirect
417. #1855C2×C41semidirect
480. C41#25143direct (N × H)
573. #101D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4732
C41×#30562
C41×#30052
C2×C41×#4522
C41×#29332
C2×C41×#4132
C41×#20632
C41×#20522
C41×#20472
C41×#20192
C41×#19772
C41×#19302
C41×#19072
C41×#19012
C41×#18552
#2514341