Finite Group Databasebeta

← C41×#24457 #23800658

Subgroups — C41×#24457 #23800658

Order 10496.

1376 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#577C211yesmaximal, characteristic, complemented
2C2×C41×#471C211yesmaximal, characteristic, complemented
3C41×#3045C211yesmaximal, characteristic, complemented
4C2×C41×#453C211yesmaximal, characteristic, complemented
5C41×#3010C211yesmaximal, characteristic, complemented
6C41×#2897C211yesmaximal, characteristic, complemented
7C41×#2051C211yesmaximal, characteristic, complemented
8C41×#2046C211yesmaximal, characteristic, complemented
9C41×#2014C211yesmaximal, characteristic, complemented
10C41×#2002C211yesmaximal, characteristic, complemented
11C41×#1907C211yesmaximal, characteristic, complemented
12C41×#1882C211yesmaximal, characteristic, complemented
13C41×#1876C211yesmaximal, characteristic, complemented
14C41×#1866C211yesmaximal, characteristic, complemented
15C41×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C41C2211yescharacteristic
17C2×H(5,𝔽2)×C41C2211yescharacteristic
18C41×#577—24no—
19C41×#577—24no—
20C2×#137×C41—21no—
21C2×#137×C41C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C41—21no—
23C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
26C2×#135×C41—21no—
27C2×#135×C41C2211yescharacteristic
28C22×SD16×C41—21no—
29C22×SD16×C41C2211yescharacteristic
30C22×SD16×C41C2211yescharacteristic, complemented
31C2×#131×C41C2211yescharacteristic
32C2×#131×C41C2211yescharacteristic
33C41×#535C2211yescharacteristic, complemented
34C2×#127×C41C2211yescharacteristic
35C41×#520C2211yescharacteristic
36C41×#471—24no—
37C41×#464—21no—
38C41×#463—21no—
39C41×#460—21no—
40C41×#459—21no—
41C41×#453—24no—
42C41×#449—21no—
43C41×#449—21no—
44C41×#448—21no—
45C41×#448—21no—
46C2×#108×C41C2211yescharacteristic, complemented
47C41×#424C2211yescharacteristic, complemented
48C2×#104×C41C2211yescharacteristic
49C2×#104×C41C2211yescharacteristic
50C2×#104×C41C2211yescharacteristic, complemented
51C41×#419C2211yescharacteristic, complemented
52C41×#418—21no—
53C41×#418C2211yescharacteristic
54C41×#417—21no—
55C41×#417C2211yescharacteristic
56C41×#417C2211yescharacteristic, complemented
57C41×#416—21no—
58C41×#416C2211yescharacteristic
59C2×#102×C41—21no—
60C2×#102×C41C2211yescharacteristic
61C2×#102×C41C2211yescharacteristic, complemented
62C2×#101×C41C2211yescharacteristic, complemented
63C2×#100×C41C2211yescharacteristic
64C2×#100×C41C2211yescharacteristic, complemented
65C41×#408C2211yescharacteristic, complemented
66C41×#391C2211yescharacteristic, complemented
67C41×#343C2211yescharacteristic, complemented
68C41×#341C2211yescharacteristic, complemented
69C41×#339C2211yescharacteristic, complemented
70C41×#336C2211yescharacteristic, complemented
712−1+4×C41—22no—
722−1+4×C41—22no—
732−1+4×C41—22no—
742−1+4×C41—41no—
75H(5,𝔽2)×C41—22no—
76H(5,𝔽2)×C41—22no—
77H(5,𝔽2)×C41—41no—
78H(5,𝔽2)×C41D414yescomplemented
79C2×#41×C41—21no—
80C2×#41×C41—21no—
81C2×#41×C41—21no—
82C2×#41×C41—21no—
83C2×#41×C41—41no—
84C2×#41×C41C2311yescharacteristic
85C2×#41×C41C2311yescharacteristic
86C2×#41×C41C2311yescharacteristic
87C22×Q8×C41—21no—
88C22×Q8×C41—21no—
89C22×Q8×C41C2311yescharacteristic
90C22×D4×C41—21no—
91C22×D4×C41—21no—
92C22×D4×C41—41no—
93C22×D4×C41—41no—
94C22×D4×C41C2311yescharacteristic
95C22×D4×C41C2311yescharacteristic
96#137×C41—28no—
97#137×C41—22no—
98#137×C41D414yescomplemented
99AGL(1,ℤ/8)×C41—28no—
100AGL(1,ℤ/8)×C41—22no—
101AGL(1,ℤ/8)×C41—22no—
102AGL(1,ℤ/8)×C41—22no—
103AGL(1,ℤ/8)×C41—22no—
104AGL(1,ℤ/8)×C41—22no—
105AGL(1,ℤ/8)×C41—22no—
106#135×C41—28no—
107#135×C41—22no—
108#135×C41—22no—
109C2×Q16×C41—21no—
110C2×Q16×C41D411yescharacteristic, complemented
111C2×SD16×C41—28no—
112C2×SD16×C41—21no—
113C2×SD16×C41—22no—
114C2×SD16×C41—21no—
115C2×SD16×C41—22no—
116C2×SD16×C41—22no—
117C2×SD16×C41—21no—
118C2×SD16×C41—21no—
119C2×SD16×C41—21no—
120C2×SD16×C41—21no—
121C2×SD16×C41—21no—
122C2×SD16×C41—21no—
123C2×SD16×C41—41no—
124C2×SD16×C41D411yescharacteristic, complemented
125C2×SD16×C41D411yescharacteristic, complemented
126C2×D8×C41—21no—
127C2×D8×C41—21no—
128C2×D8×C41—21no—
129C2×D8×C41D411yescharacteristic, complemented
130#131×C41—22no—
131#131×C41—22no—
132#131×C41—22no—
133#131×C41—41no—
134C2×M16×C41—21no—
135C2×M16×C41—21no—
136C2×M16×C41C2311yescharacteristic
137C2×M16×C41C2311yescharacteristic
138C2×M16×C41C2311yescharacteristic
139C2×M16×C41C2311yescharacteristic
140C22×C8×C41—21no—
141C22×C8×C41—21no—
142C22×C8×C41C2311yescharacteristic
143C22×C8×C41C2311yescharacteristic
144#127×C41—22no—
145#127×C41—21no—
146#127×C41—41no—
147#124×C41—21no—
148#121×C41—21no—
149#121×C41—21no—
150#120×C41—41no—
151C4×Q8×C41—21no—
152C4×D4×C41—21no—
153C4×D4×C41—41no—
154#117×C41—21no—
155#117×C41C2311yescharacteristic
156C2×C4⋊C4×C41—21no—
157C2×C4⋊C4×C41C2311yescharacteristic
158C2×C42×C41C2311yescharacteristic
159#108×C41—22no—
160C4⋊C8×C41—21no—
161C4⋊C8×C41—21no—
162#104×C41—22no—
163#104×C41—22no—
164#104×C41—41no—
165#103×C41—21no—
166#103×C41—21no—
167#103×C41—21no—
168#103×C41—21no—
169#103×C41D411yescharacteristic, complemented
170#103×C41D411yescharacteristic, complemented
171#102×C41—21no—
172#102×C41—21no—
173#102×C41—21no—
174#102×C41—21no—
175#102×C41—21no—
176#102×C41—21no—
177#102×C41—21no—
178#102×C41—21no—
179#102×C41D411yescharacteristic, complemented
180#102×C41D411yescharacteristic, complemented
181#101×C41—22no—
182#100×C41—22no—
183#100×C41—22no—
184C22⋊C8×C41—21no—
185C22⋊C8×C41—21no—
186#95×C41—41no—
187C24×C41—21no—
188C24×C41—21no—
189C24×C41—41no—
190#41×C41—21no—
191#41×C41—21no—
192#41×C41—21no—
193#41×C41—21no—
194#41×C41—24no—
195#41×C41—24no—
196#41×C41—24no—
197#41×C41—21no—
198#41×C41—21no—
199#41×C41—21no—
200#41×C41—21no—
201#41×C41—42no—
202#41×C41—44no—
203#41×C41—42no—
204#41×C41—42no—
205#41×C41—42no—
206#41×C41—44no—
207#41×C41—42no—
208#41×C41C2×D412yes—
209#41×C41C2×D412yes—
210#41×C41C2×D412yes—
211#41×C41#4112yes—
212C2×Q8×C41—21no—
213C2×Q8×C41—24no—
214C2×Q8×C41—21no—
215C2×Q8×C41—21no—
216C2×Q8×C41—21no—
217C2×Q8×C41—21no—
218C2×Q8×C41—41no—
219C2×Q8×C41—42no—
220C2×Q8×C41—42no—
221C2×Q8×C41—42no—
222C2×Q8×C41C2×D412yes—
223C2×Q8×C41C2×D411yescharacteristic
224C2×Q8×C41C2×D411yescharacteristic
225C2×Q8×C41C2×D411yescharacteristic
226C2×D4×C41—21no—
227C2×D4×C41—21no—
228C2×D4×C41—24no—
229C2×D4×C41—24no—
230C2×D4×C41—21no—
231C2×D4×C41—21no—
232C2×D4×C41—21no—
233C2×D4×C41—21no—
234C2×D4×C41—21no—
235C2×D4×C41—21no—
236C2×D4×C41—21no—
237C2×D4×C41—21no—
238C2×D4×C41—21no—
239C2×D4×C41—21no—
240C2×D4×C41—21no—
241C2×D4×C41—21no—
242C2×D4×C41—42no—
243C2×D4×C41—42no—
244C2×D4×C41—41no—
245C2×D4×C41—41no—
246C2×D4×C41—41no—
247C2×D4×C41—41no—
248C2×D4×C41—44no—
249C2×D4×C41—44no—
250C2×D4×C41—41no—
251C2×D4×C41—44no—
252C2×D4×C41—82no—
253C2×D4×C41—82no—
254C2×D4×C41C2×D412yes—
255C2×D4×C41C2×D411yescharacteristic
256C2×D4×C41C2×D411yescharacteristic
257C2×D4×C41C2×D411yescharacteristic
258C22×C4×C41—21no—
259C22×C4×C41—21no—
260C22×C4×C41—21no—
261C22×C4×C41—21no—
262C22×C4×C41—21no—
263C22×C4×C41—21no—
264C22×C4×C41—41no—
265C22×C4×C41—41no—
266C22×C4×C41—41no—
267C22×C4×C41—41no—
268C22×C4×C41C2411yescharacteristic
269Q16×C41—24no—
270Q16×C41—22no—
271SD16×C41—24no—
272SD16×C41—24no—
273SD16×C41—24no—
274SD16×C41—22no—
275SD16×C41—22no—
276SD16×C41—24no—
277SD16×C41—42no—
278SD16×C41—42no—
279SD16×C41—42no—
280SD16×C41—42no—
281D8×C41—24no—
282D8×C41—22no—
283D8×C41—42no—
284D8×C41—42no—
285M16×C41—24no—
286M16×C41—21no—
287M16×C41—21no—
288M16×C41—21no—
289M16×C41—21no—
290M16×C41—21no—
291M16×C41—21no—
292M16×C41—21no—
293M16×C41—42no—
294M16×C41C2×D412yes—
295C2×C8×C41—24no—
296C2×C8×C41—21no—
297C2×C8×C41—21no—
298C2×C8×C41—21no—
299C2×C8×C41—21no—
300C2×C8×C41—21no—
301C2×C8×C41—21no—
302C2×C8×C41—21no—
303C2×C8×C41—21no—
304C2×C8×C41—42no—
305C2×C8×C41C2×D411yescharacteristic
306C2×C8×C41C2×D411yescharacteristic
307C2×C8×C41C2×D411yescharacteristic
308C2×C8×C41C2×D411yescharacteristic
309C4⋊C4×C41—21no—
310C4⋊C4×C41—21no—
311C4⋊C4×C41—41no—
312C4⋊C4×C41C2×D411yescharacteristic
313C4⋊C4×C41C2×D411yescharacteristic
314C22⋊C4×C41—21no—
315C22⋊C4×C41—41no—
316C22⋊C4×C41—41no—
317C22⋊C4×C41—41no—
318C42×C41—21no—
319C42×C41—21no—
320C42×C41—21no—
321C42×C41—41no—
322C23×C41—21no—
323C23×C41—21no—
324C23×C41—21no—
325C23×C41—22no—
326C23×C41—44no—
327C23×C41—41no—
328C23×C41—41no—
329C23×C41—41no—
330C23×C41—41no—
331C23×C41—41no—
332C23×C41—81no—
333C23×C41—81no—
334C23×C41—81no—
335C23×C41—81no—
336C23×C41—161no—
337C23×C41—161no—
338C23×C41H(5,𝔽2)11yescharacteristic
339Q8×C41—21no—
340Q8×C41—21no—
341Q8×C41—22no—
342Q8×C41—21no—
343Q8×C41—22no—
344Q8×C41—21no—
345Q8×C41—44no—
346Q8×C41—41no—
347Q8×C41—41no—
348Q8×C41#12012yes—
349Q8×C41#12112yes—
350D4×C41—22no—
351D4×C41—22no—
352D4×C41—22no—
353D4×C41—22no—
354D4×C41—21no—
355D4×C41—22no—
356D4×C41—22no—
357D4×C41—21no—
358D4×C41—21no—
359D4×C41—21no—
360D4×C41—44no—
361D4×C41—44no—
362D4×C41—44no—
363D4×C41—41no—
364D4×C41—41no—
365D4×C41—41no—
366D4×C41—41no—
367D4×C41—41no—
368D4×C41—41no—
369D4×C41—41no—
370D4×C41—41no—
371D4×C41—88no—
372D4×C41—161no—
373D4×C41—161no—
374D4×C41#12012yes—
375D4×C41#12112yes—
376C2×C4×C41—21no—
377C2×C4×C41—21no—
378C2×C4×C41—22no—
379C2×C4×C41—22no—
380C2×C4×C41—22no—
381C2×C4×C41—22no—
382C2×C4×C41—22no—
383C2×C4×C41—21no—
384C2×C4×C41—21no—
385C2×C4×C41—21no—
386C2×C4×C41—22no—
387C2×C4×C41—44no—
388C2×C4×C41—44no—
389C2×C4×C41—41no—
390C2×C4×C41—44no—
391C2×C4×C41—41no—
392C2×C4×C41—41no—
393C2×C4×C41—41no—
394C2×C4×C41—41no—
395C2×C4×C41—41no—
396C2×C4×C41—41no—
397C2×C4×C41—81no—
398C2×C4×C41—161no—
399C2×C4×C41C22×D411yescharacteristic
400C2×C4×C41C22×D411yescharacteristic
401C2×C4×C41C22×D411yescharacteristic
402C2×C4×C41C22×D411yescharacteristic
403C2×C4×C41C2×#4111yescharacteristic
404C2×C4×C41H(5,𝔽2)11yescharacteristic
405C8×C41—21no—
406C8×C41—22no—
407C8×C41—21no—
408C8×C41—21no—
409C8×C41—21no—
410C8×C41—41no—
411C8×C41—41no—
412C8×C41—41no—
413#24457C4111yesmaximal, characteristic, direct product factor, Sylow
414C22×C41—21no—
415C22×C41—21no—
416C22×C41—22no—
417C22×C41—22no—
418C22×C41—41no—
419C22×C41—41no—
420C22×C41—41no—
421C22×C41—41no—
422C22×C41—41no—
423C22×C41—42no—
424C22×C41—41no—
425C22×C41—41no—
426C22×C41—82no—
427C22×C41—82no—
428C22×C41—81no—
429C22×C41—81no—
430C22×C41—81no—
431C22×C41—81no—
432C22×C41—81no—
433C22×C41—161no—
434C22×C41—161no—
435C22×C41—164no—
436C22×C41#53411yescharacteristic
437C22×C41D4211yescharacteristic
438C22×C41#54611yescharacteristic
439C4×C41—22no—
440C4×C41—22no—
441C4×C41—42no—
442C4×C41—41no—
443C4×C41—42no—
444C4×C41—41no—
445C4×C41—41no—
446C4×C41—81no—
447C4×C41C2×#12011yescharacteristic
448C4×C41C2×#12111yescharacteristic
449C4×C41D4211yescharacteristic
450C4×C41#54611yescharacteristic
451C2×#577C2×C4111yescharacteristic, complemented
452C2×#471C2×C4111yescharacteristic, complemented
453#3045C2×C4111yescharacteristic, complemented
454C2×#453C2×C4111yescharacteristic, complemented
455#3010C2×C4111yescharacteristic, complemented
456#2897C2×C4111yescharacteristic, complemented
457#2051C2×C4111yescharacteristic, complemented
458#2046C2×C4111yescharacteristic, complemented
459#2014C2×C4111yescharacteristic, complemented
460#2002C2×C4111yescharacteristic, complemented
461#1907C2×C4111yescharacteristic, complemented
462#1882C2×C4111yescharacteristic, complemented
463#1876C2×C4111yescharacteristic, complemented
464#1866C2×C4111yescharacteristic, complemented
465#1793C2×C4111yescharacteristic, complemented
466C2×C41—21no—
467C2×C41—21no—
468C2×C41—42no—
469C2×C41—42no—
470C2×C41—81no—
471C2×C41—82no—
472C2×C41—161no—
473C2×C41#241011yescharacteristic
474C2×C41#328811yescharacteristic
475C2×C41#329111yescharacteristic
476C2×2−1+4C22×C4111yescharacteristic
477C2×H(5,𝔽2)C22×C4111yescharacteristic
478#577—24no—
479#577—24no—
480C2×#137—21no—
481C2×#137C22×C4111yescharacteristic
482C2×AGL(1,ℤ/8)—21no—
483C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
484C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
485C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
486C2×#135—21no—
487C2×#135C22×C4111yescharacteristic
488C22×SD16—21no—
489C22×SD16C22×C4111yescharacteristic
490C22×SD16C22×C4111yescharacteristic, complemented
491C2×#131C22×C4111yescharacteristic
492C2×#131C22×C4111yescharacteristic
493#535C22×C4111yescharacteristic, complemented
494C2×#127C22×C4111yescharacteristic
495#520C22×C4111yescharacteristic
496#471—24no—
497#464—21no—
498#463—21no—
499#460—21no—
500#459—21no—
501#453—24no—
502#449—21no—
503#449—21no—
504#448—21no—
505#448—21no—
506C2×#108C22×C4111yescharacteristic, complemented
507#424C22×C4111yescharacteristic, complemented
508C2×#104C22×C4111yescharacteristic
509C2×#104C22×C4111yescharacteristic
510C2×#104C22×C4111yescharacteristic, complemented
511#419C22×C4111yescharacteristic, complemented
512#418—21no—
513#418C22×C4111yescharacteristic
514#417—21no—
515#417C22×C4111yescharacteristic
516#417C22×C4111yescharacteristic, complemented
517#416—21no—
518#416C22×C4111yescharacteristic
519C2×#102—21no—
520C2×#102C22×C4111yescharacteristic
521C2×#102C22×C4111yescharacteristic, complemented
522C2×#101C22×C4111yescharacteristic, complemented
523C2×#100C22×C4111yescharacteristic
524C2×#100C22×C4111yescharacteristic, complemented
525#408C22×C4111yescharacteristic, complemented
526#391C22×C4111yescharacteristic, complemented
527#343C22×C4111yescharacteristic, complemented
528#341C22×C4111yescharacteristic, complemented
529#339C22×C4111yescharacteristic, complemented
530#336C22×C4111yescharacteristic, complemented
531C41#2445711yescharacteristic, direct product factor, Sylow
5322−1+4—22no—
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—41no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—41no—
539H(5,𝔽2)D4×C4114yescomplemented
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—41no—
545C2×#41C23×C4111yescharacteristic
546C2×#41C23×C4111yescharacteristic
547C2×#41C23×C4111yescharacteristic
548C22×Q8—21no—
549C22×Q8—21no—
550C22×Q8C23×C4111yescharacteristic
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4—41no—
555C22×D4C23×C4111yescharacteristic
556C22×D4C23×C4111yescharacteristic
557#137—28no—
558#137—22no—
559#137D4×C4114yescomplemented
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567#135—28no—
568#135—22no—
569#135—22no—
570C2×Q16—21no—
571C2×Q16D4×C4111yescharacteristic, complemented
572C2×SD16—28no—
573C2×SD16—21no—
574C2×SD16—22no—
575C2×SD16—21no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×SD16—21no—
581C2×SD16—21no—
582C2×SD16—21no—
583C2×SD16—21no—
584C2×SD16—41no—
585C2×SD16D4×C4111yescharacteristic, complemented
586C2×SD16D4×C4111yescharacteristic, complemented
587C2×D8—21no—
588C2×D8—21no—
589C2×D8—21no—
590C2×D8D4×C4111yescharacteristic, complemented
591#131—22no—
592#131—22no—
593#131—22no—
594#131—41no—
595C2×M16—21no—
596C2×M16—21no—
597C2×M16C23×C4111yescharacteristic
598C2×M16C23×C4111yescharacteristic
599C2×M16C23×C4111yescharacteristic
600C2×M16C23×C4111yescharacteristic
601C22×C8—21no—
602C22×C8—21no—
603C22×C8C23×C4111yescharacteristic
604C22×C8C23×C4111yescharacteristic
605#127—22no—
606#127—21no—
607#127—41no—
608#124—21no—
609#121—21no—
610#121—21no—
611#120—41no—
612C4×Q8—21no—
613C4×D4—21no—
614C4×D4—41no—
615#117—21no—
616#117C23×C4111yescharacteristic
617C2×C4⋊C4—21no—
618C2×C4⋊C4C23×C4111yescharacteristic
619C2×C42C23×C4111yescharacteristic
620#108—22no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623#104—22no—
624#104—22no—
625#104—41no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103D4×C4111yescharacteristic, complemented
631#103D4×C4111yescharacteristic, complemented
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102D4×C4111yescharacteristic, complemented
641#102D4×C4111yescharacteristic, complemented
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647#95—41no—
648C24—21no—
649C24—21no—
650C24—41no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—42no—
663#41—44no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41—44no—
668#41—42no—
669#41C2×D4×C4112yes—
670#41C2×D4×C4112yes—
671#41C2×D4×C4112yes—
672#41#41×C4112yes—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—41no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8—42no—
683C2×Q8C2×D4×C4112yes—
684C2×Q8C2×D4×C4111yescharacteristic
685C2×Q8C2×D4×C4111yescharacteristic
686C2×Q8C2×D4×C4111yescharacteristic
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—21no—
692C2×D4—21no—
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—21no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—41no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—41no—
712C2×D4—44no—
713C2×D4—82no—
714C2×D4—82no—
715C2×D4C2×D4×C4112yes—
716C2×D4C2×D4×C4111yescharacteristic
717C2×D4C2×D4×C4111yescharacteristic
718C2×D4C2×D4×C4111yescharacteristic
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4C24×C4111yescharacteristic
730Q16—24no—
731Q16—22no—
732SD16—24no—
733SD16—24no—
734SD16—24no—
735SD16—22no—
736SD16—22no—
737SD16—24no—
738SD16—42no—
739SD16—42no—
740SD16—42no—
741SD16—42no—
742D8—24no—
743D8—22no—
744D8—42no—
745D8—42no—
746M16—24no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—21no—
753M16—21no—
754M16—42no—
755M16C2×D4×C4112yes—
756C2×C8—24no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—42no—
766C2×C8C2×D4×C4111yescharacteristic
767C2×C8C2×D4×C4111yescharacteristic
768C2×C8C2×D4×C4111yescharacteristic
769C2×C8C2×D4×C4111yescharacteristic
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—41no—
773C4⋊C4C2×D4×C4111yescharacteristic
774C4⋊C4C2×D4×C4111yescharacteristic
775C22⋊C4—21no—
776C22⋊C4—41no—
777C22⋊C4—41no—
778C22⋊C4—41no—
779C42—21no—
780C42—21no—
781C42—21no—
782C42—41no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—81no—
797C23—161no—
798C23—161no—
799C23H(5,𝔽2)×C4111yescharacteristic
800Q8—21no—
801Q8—21no—
802Q8—22no—
803Q8—21no—
804Q8—22no—
805Q8—21no—
806Q8—44no—
807Q8—41no—
808Q8—41no—
809Q8#120×C4112yes—
810Q8#121×C4112yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—21no—
816D4—22no—
817D4—22no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—88no—
833D4—161no—
834D4—161no—
835D4#120×C4112yes—
836D4#121×C4112yes—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—41no—
851C2×C4—44no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—81no—
859C2×C4—161no—
860C2×C4C22×D4×C4111yescharacteristic
861C2×C4C22×D4×C4111yescharacteristic
862C2×C4C22×D4×C4111yescharacteristic
863C2×C4C22×D4×C4111yescharacteristic
864C2×C4C2×#41×C4111yescharacteristic
865C2×C4H(5,𝔽2)×C4111yescharacteristic
866C8—21no—
867C8—22no—
868C8—21no—
869C8—21no—
870C8—21no—
871C8—41no—
872C8—41no—
873C8—41no—
874C22—21no—
875C22—21no—
876C22—22no—
877C22—22no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—41no—
886C22—82no—
887C22—82no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—161no—
894C22—161no—
895C22—164no—
896C22C41×#53411yescharacteristic
897C22D42×C4111yescharacteristic
898C22C41×#54611yescharacteristic
899C4—22no—
900C4—22no—
901C4—42no—
902C4—41no—
903C4—42no—
904C4—41no—
905C4—41no—
906C4—81no—
907C4C2×#120×C4111yescharacteristic
908C4C2×#121×C4111yescharacteristic
909C4D42×C4111yescharacteristic
910C4C41×#54611yescharacteristic
911C2—21no—
912C2—21no—
913C2—42no—
914C2—42no—
915C2—81no—
916C2—82no—
917C2—161no—
918C2C41×#241011yescharacteristic
919C2C41×#328811yescharacteristic
920C2C41×#329111yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#577C2semidirect
2. C2×C41×#471C2semidirect
3. C41×#3045C2semidirect
4. C2×C41×#453C2semidirect
5. C41×#3010C2semidirect
6. C41×#2897C2semidirect
7. C41×#2051C2semidirect
8. C41×#2046C2semidirect
9. C41×#2014C2semidirect
10. C41×#2002C2semidirect
11. C41×#1907C2semidirect
12. C41×#1882C2semidirect
13. C41×#1876C2semidirect
14. C41×#1866C2semidirect
15. C41×#1793C2semidirect
30. C22×SD16×C41C22semidirect
33. C41×#535C22semidirect
46. C2×#108×C41C22semidirect
47. C41×#424C22semidirect
50. C2×#104×C41C22semidirect
51. C41×#419C22semidirect
56. C41×#417C22semidirect
61. C2×#102×C41C22semidirect
62. C2×#101×C41C22semidirect
64. C2×#100×C41C22semidirect
65. C41×#408C22semidirect
66. C41×#391C22semidirect
67. C41×#343C22semidirect
68. C41×#341C22semidirect
69. C41×#339C22semidirect
70. C41×#336C22semidirect
78. H(5,𝔽2)×C41D4semidirect
98. #137×C41D4semidirect
110. C2×Q16×C41D4semidirect
124. C2×SD16×C41D4semidirect
125. C2×SD16×C41D4semidirect
129. C2×D8×C41D4semidirect
169. #103×C41D4semidirect
170. #103×C41D4semidirect
179. #102×C41D4semidirect
180. #102×C41D4semidirect
413. #24457C41direct (N × H)
451. C2×#577C2×C41semidirect
452. C2×#471C2×C41semidirect
453. #3045C2×C41semidirect
454. C2×#453C2×C41semidirect
455. #3010C2×C41semidirect
456. #2897C2×C41semidirect
457. #2051C2×C41semidirect
458. #2046C2×C41semidirect
459. #2014C2×C41semidirect
460. #2002C2×C41semidirect
461. #1907C2×C41semidirect
462. #1882C2×C41semidirect
463. #1876C2×C41semidirect
464. #1866C2×C41semidirect
465. #1793C2×C41semidirect
490. C22×SD16C22×C41semidirect
493. #535C22×C41semidirect
506. C2×#108C22×C41semidirect
507. #424C22×C41semidirect
510. C2×#104C22×C41semidirect
511. #419C22×C41semidirect
516. #417C22×C41semidirect
521. C2×#102C22×C41semidirect
522. C2×#101C22×C41semidirect
524. C2×#100C22×C41semidirect
525. #408C22×C41semidirect
526. #391C22×C41semidirect
527. #343C22×C41semidirect
528. #341C22×C41semidirect
529. #339C22×C41semidirect
530. #336C22×C41semidirect
531. C41#24457direct (N × H)
539. H(5,𝔽2)D4×C41semidirect
559. #137D4×C41semidirect
571. C2×Q16D4×C41semidirect
585. C2×SD16D4×C41semidirect
586. C2×SD16D4×C41semidirect
590. C2×D8D4×C41semidirect
630. #103D4×C41semidirect
631. #103D4×C41semidirect
640. #102D4×C41semidirect
641. #102D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5772
C2×C41×#4712
C41×#30452
C2×C41×#4532
C41×#30102
C41×#28972
C41×#20512
C41×#20462
C41×#20142
C41×#20022
C41×#19072
C41×#18822
C41×#18762
C41×#18662
C41×#17932
#2445741