Finite Group Databasebeta

← C41×#26246 #23802447

Subgroups — C41×#26246 #23802447

Order 10496.

1006 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#481C211yesmaximal, characteristic, complemented
2C2×C41×#482C211yesmaximal, characteristic, complemented
3C41×#2541C211yesmaximal, characteristic
4C41×#2352C211yesmaximal, characteristic, complemented
5C41×#2034C211yesmaximal, characteristic, complemented
6C41×#2033C211yesmaximal, characteristic, complemented
7C41×#2033C211yesmaximal, characteristic, complemented
8C41×#2033C211yesmaximal, characteristic, complemented
9C41×#1982C211yesmaximal, characteristic, complemented
10C41×#1961C211yesmaximal, characteristic, complemented
11C41×#1955C211yesmaximal, characteristic, complemented
12C41×#1949C211yesmaximal, characteristic, complemented
13C41×#1875C211yesmaximal, characteristic, complemented
14C41×#1874C211yesmaximal, characteristic, complemented
15C41×#1776C211yesmaximal, characteristic, complemented
16C2×#127×C41—21no—
17C2×#127×C41C2211yescharacteristic
18C2×#121×C41C2211yescharacteristic
19C2×#121×C41C2211yescharacteristic
20C2×#121×C41C2211yescharacteristic
21C2×#121×C41C2211yescharacteristic
22C2×C4×D4×C41C2211yescharacteristic
23C2×#117×C41C2211yescharacteristic
24C22×C4⋊C4×C41C2211yescharacteristic
25C41×#482—24no—
26C41×#481—24no—
27C2×#107×C41C2211yescharacteristic
28C2×#107×C41C2211yescharacteristic
29C2×#106×C41C2211yescharacteristic
30C2×#106×C41C2211yescharacteristic
31C2×C4⋊C8×C41C2211yescharacteristic
32C2×#102×C41C2211yescharacteristic
33C2×#102×C41C2211yescharacteristic
34C2×#102×C41C2211yescharacteristic
35C2×#102×C41C2211yescharacteristic
36C2×#102×C41C2211yescharacteristic
37C2×#102×C41C2211yescharacteristic
38C2×#102×C41C2211yescharacteristic
39C2×#102×C41C2211yescharacteristic
40C2×C22⋊C8×C41C2211yescharacteristic
41C2×C22⋊C8×C41C2211yescharacteristic
42C2×C22⋊C8×C41C2211yescharacteristic
43C2×C22⋊C8×C41C2211yescharacteristic
44C2×#97×C41C2211yescharacteristic
45C41×#392—21no—
46C41×#392—21no—
47C41×#390—21no—
48C41×#388—21no—
49C41×#387—21no—
50C41×#386—21no—
51C41×#382C2211yescharacteristic
52C41×#380C2211yescharacteristic
53C41×#380C2211yescharacteristic
54C4×C4⋊C4×C41C2211yescharacteristic
55C4×C4⋊C4×C41C2211yescharacteristic
56C4×C22⋊C4×C41—21no—
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C22×D4×C41—21no—
62C22×D4×C41—21no—
63C22×D4×C41—21no—
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41D411yescharacteristic
68C22×D4×C41C2311yescharacteristic
69C22×D4×C41C2311yescharacteristic
70C23×C4×C41—21no—
71C23×C4×C41C2311yescharacteristic
72C23×C4×C41C2311yescharacteristic
73C22×C8×C41C2311yescharacteristic
74C22×C8×C41C2311yescharacteristic
75C22×C8×C41C2311yescharacteristic
76C22×C8×C41C2311yescharacteristic
77#127×C41—22no—
78#127×C41—22no—
79#127×C41—44no—
80#121×C41—22no—
81#121×C41—22no—
82#121×C41—22no—
83#121×C41—22no—
84#121×C41—41no—
85#121×C41—41no—
86#121×C41—41no—
87#121×C41—41no—
88C4×D4×C41—22no—
89C4×D4×C41—22no—
90#117×C41—22no—
91#117×C41—41no—
92C2×C4⋊C4×C41—22no—
93C2×C4⋊C4×C41—21no—
94C2×C4⋊C4×C41—41no—
95C2×C4⋊C4×C41D411yescharacteristic
96C2×C4⋊C4×C41C2311yescharacteristic
97C2×C4⋊C4×C41C2311yescharacteristic
98C2×C4⋊C4×C41C2311yescharacteristic
99C2×C4⋊C4×C41C2311yescharacteristic
100C2×C4⋊C4×C41C2311yescharacteristic
101C2×C4⋊C4×C41C2311yescharacteristic
102C2×C22⋊C4×C41—21no—
103C2×C22⋊C4×C41—21no—
104C2×C22⋊C4×C41—21no—
105C2×C22⋊C4×C41—21no—
106C2×C22⋊C4×C41—21no—
107C2×C22⋊C4×C41—21no—
108C2×C22⋊C4×C41—21no—
109C2×C22⋊C4×C41D411yescharacteristic
110C2×C22⋊C4×C41D411yescharacteristic
111C2×C42×C41—21no—
112C2×C42×C41—21no—
113C2×C42×C41—21no—
114C2×C42×C41C2311yescharacteristic
115#107×C41—22no—
116#107×C41—22no—
117#106×C41—22no—
118#106×C41D414yescomplemented
119C4⋊C8×C41—22no—
120#102×C41—22no—
121#102×C41—22no—
122#102×C41—22no—
123#102×C41—22no—
124#102×C41—41no—
125#102×C41—41no—
126#102×C41—41no—
127#102×C41—41no—
128C22⋊C8×C41—22no—
129C22⋊C8×C41—22no—
130C22⋊C8×C41—41no—
131C22⋊C8×C41—41no—
132#97×C41—22no—
133#95×C41—21no—
134#95×C41—21no—
135#95×C41—21no—
136#95×C41—21no—
137#95×C41—21no—
138#95×C41—21no—
139C24×C41—21no—
140C24×C41—21no—
141C24×C41C2×D411yescharacteristic
142C24×C41C2×D411yescharacteristic
143C2×D4×C41—22no—
144C2×D4×C41—22no—
145C2×D4×C41—21no—
146C2×D4×C41—21no—
147C2×D4×C41—21no—
148C2×D4×C41—21no—
149C2×D4×C41—21no—
150C2×D4×C41—21no—
151C2×D4×C41—21no—
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—21no—
157C2×D4×C41—41no—
158C2×D4×C41—42no—
159C2×D4×C41—42no—
160C2×D4×C41—42no—
161C2×D4×C41—42no—
162C2×D4×C41—42no—
163C2×D4×C41—42no—
164C2×D4×C41—42no—
165C2×D4×C41—42no—
166C2×D4×C41—42no—
167C2×D4×C41—42no—
168C2×D4×C41—42no—
169C2×D4×C41—42no—
170C2×D4×C41—81no—
171C2×D4×C41—81no—
172C2×D4×C41—81no—
173C2×D4×C41—81no—
174C2×D4×C41—81no—
175C2×D4×C41—81no—
176C22×C4×C41—21no—
177C22×C4×C41—21no—
178C22×C4×C41—21no—
179C22×C4×C41—21no—
180C22×C4×C41—21no—
181C22×C4×C41—21no—
182C22×C4×C41—21no—
183C22×C4×C41—21no—
184C22×C4×C41—21no—
185C22×C4×C41—21no—
186C22×C4×C41—21no—
187C22×C4×C41—21no—
188C22×C4×C41—21no—
189C22×C4×C41—21no—
190C22×C4×C41—21no—
191C22×C4×C41—21no—
192C22×C4×C41—21no—
193C22×C4×C41—21no—
194C22×C4×C41—42no—
195C22×C4×C41—42no—
196C22×C4×C41—81no—
197C22×C4×C41C2×D411yescharacteristic
198C22×C4×C41C2×D411yescharacteristic
199C22×C4×C41C2×D411yescharacteristic
200C22×C4×C41C2×D411yescharacteristic
201C22×C4×C41C2411yescharacteristic
202C2×C8×C41—21no—
203C2×C8×C41—21no—
204C2×C8×C41—21no—
205C2×C8×C41—21no—
206C2×C8×C41—21no—
207C2×C8×C41—21no—
208C2×C8×C41—21no—
209C2×C8×C41—21no—
210C2×C8×C41—21no—
211C2×C8×C41—21no—
212C2×C8×C41—21no—
213C2×C8×C41C2×D412yes—
214C4⋊C4×C41—22no—
215C4⋊C4×C41—21no—
216C4⋊C4×C41—21no—
217C4⋊C4×C41—21no—
218C4⋊C4×C41—21no—
219C4⋊C4×C41—21no—
220C4⋊C4×C41—21no—
221C4⋊C4×C41—21no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—42no—
225C4⋊C4×C41C2×D412yes—
226C4⋊C4×C41C2×D412yes—
227C4⋊C4×C41#4112yes—
228C22⋊C4×C41—22no—
229C22⋊C4×C41—22no—
230C22⋊C4×C41—42no—
231C22⋊C4×C41—42no—
232C22⋊C4×C41—42no—
233C22⋊C4×C41—42no—
234C22⋊C4×C41—42no—
235C22⋊C4×C41—42no—
236C22⋊C4×C41—81no—
237C42×C41—42no—
238C42×C41—42no—
239C42×C41—81no—
240C42×C41#4112yes—
241C42×C41#4112yes—
242C23×C41—21no—
243C23×C41—21no—
244C23×C41—21no—
245C23×C41—21no—
246C23×C41—21no—
247C23×C41—21no—
248C23×C41—21no—
249C23×C41—21no—
250C23×C41—21no—
251C23×C41—21no—
252C23×C41—21no—
253C23×C41—21no—
254C23×C41—21no—
255C23×C41—41no—
256C23×C41—41no—
257C23×C41—41no—
258C23×C41—41no—
259C23×C41—41no—
260C23×C41—41no—
261C23×C41—41no—
262C23×C41—41no—
263C23×C41—41no—
264C23×C41—41no—
265C23×C41—41no—
266C23×C41—41no—
267C23×C41—41no—
268C23×C41—41no—
269C23×C41AGL(1,ℤ/8)12yes—
270C23×C41C22×D411yescharacteristic
271D4×C41—44no—
272D4×C41—41no—
273D4×C41—41no—
274D4×C41—41no—
275D4×C41—41no—
276D4×C41—41no—
277D4×C41—41no—
278D4×C41—41no—
279D4×C41—41no—
280D4×C41—84no—
281D4×C41—84no—
282D4×C41—84no—
283D4×C41—84no—
284D4×C41—84no—
285D4×C41—84no—
286C2×C4×C41—21no—
287C2×C4×C41—21no—
288C2×C4×C41—21no—
289C2×C4×C41—21no—
290C2×C4×C41—21no—
291C2×C4×C41—21no—
292C2×C4×C41—21no—
293C2×C4×C41—22no—
294C2×C4×C41—22no—
295C2×C4×C41—21no—
296C2×C4×C41—22no—
297C2×C4×C41—21no—
298C2×C4×C41—21no—
299C2×C4×C41—41no—
300C2×C4×C41—41no—
301C2×C4×C41—41no—
302C2×C4×C41—41no—
303C2×C4×C41—41no—
304C2×C4×C41—41no—
305C2×C4×C41—41no—
306C2×C4×C41—41no—
307C2×C4×C41—41no—
308C2×C4×C41—41no—
309C2×C4×C41—41no—
310C2×C4×C41—41no—
311C2×C4×C41—41no—
312C2×C4×C41—41no—
313C2×C4×C41—41no—
314C2×C4×C41—41no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—84no—
323C2×C4×C41#12312yes—
324C2×C4×C41#12312yes—
325C2×C4×C41C22×D411yescharacteristic
326C2×C4×C41C2×#4111yescharacteristic
327C2×C4×C41C2×#4111yescharacteristic
328C2×C4×C41C2×#4111yescharacteristic
329C2×C4×C41H(5,𝔽2)11yescharacteristic
330C2×C4×C41H(5,𝔽2)11yescharacteristic
331C8×C41—22no—
332C8×C41—41no—
333C8×C41—41no—
334C8×C41—41no—
335#26246C4111yesmaximal, characteristic, direct product factor, Sylow
336C22×C41—22no—
337C22×C41—22no—
338C22×C41—22no—
339C22×C41—41no—
340C22×C41—41no—
341C22×C41—41no—
342C22×C41—41no—
343C22×C41—41no—
344C22×C41—41no—
345C22×C41—41no—
346C22×C41—41no—
347C22×C41—41no—
348C22×C41—41no—
349C22×C41—41no—
350C22×C41—81no—
351C22×C41—81no—
352C22×C41—81no—
353C22×C41—81no—
354C22×C41—81no—
355C22×C41—81no—
356C22×C41—81no—
357C22×C41—81no—
358C22×C41—81no—
359C22×C41—81no—
360C22×C41—81no—
361C22×C41—81no—
362C22×C41—81no—
363C22×C41—81no—
364C22×C41C2×#12311yescharacteristic
365C22×C41D4211yescharacteristic
366C22×C41#54611yescharacteristic
367C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C41#57511yescharacteristic
369C22×C41#57611yescharacteristic
370C22×C41#57711yescharacteristic
371C4×C41—22no—
372C4×C41—22no—
373C4×C41—41no—
374C4×C41—41no—
375C4×C41—42no—
376C4×C41—42no—
377C4×C41—42no—
378C4×C41—81no—
379C4×C41—81no—
380C4×C41—81no—
381C4×C41#53211yescharacteristic
382C4×C41#54011yescharacteristic
383C4×C41#55011yescharacteristic
384C4×C41#55911yescharacteristic
385C2×#481C2×C4111yescharacteristic, complemented
386C2×#482C2×C4111yescharacteristic, complemented
387#2541C2×C4111yescharacteristic
388#2352C2×C4111yescharacteristic, complemented
389#2034C2×C4111yescharacteristic, complemented
390#2033C2×C4111yescharacteristic, complemented
391#2033C2×C4111yescharacteristic, complemented
392#2033C2×C4111yescharacteristic, complemented
393#1982C2×C4111yescharacteristic, complemented
394#1961C2×C4111yescharacteristic, complemented
395#1955C2×C4111yescharacteristic, complemented
396#1949C2×C4111yescharacteristic, complemented
397#1875C2×C4111yescharacteristic, complemented
398#1874C2×C4111yescharacteristic, complemented
399#1776C2×C4111yescharacteristic, complemented
400C2×C41—42no—
401C2×C41—81no—
402C2×C41—161no—
403C2×C41—161no—
404C2×C41#244511yescharacteristic
405C2×C41#309411yescharacteristic
406C2×C41#309611yescharacteristic
407C2×C41#326511yescharacteristic
408C2×C41#326811yescharacteristic
409C2×C41#331711yescharacteristic
410C2×C41#331811yescharacteristic
411C2×#127—21no—
412C2×#127C22×C4111yescharacteristic
413C2×#121C22×C4111yescharacteristic
414C2×#121C22×C4111yescharacteristic
415C2×#121C22×C4111yescharacteristic
416C2×#121C22×C4111yescharacteristic
417C2×C4×D4C22×C4111yescharacteristic
418C2×#117C22×C4111yescharacteristic
419C22×C4⋊C4C22×C4111yescharacteristic
420#482—24no—
421#481—24no—
422C2×#107C22×C4111yescharacteristic
423C2×#107C22×C4111yescharacteristic
424C2×#106C22×C4111yescharacteristic
425C2×#106C22×C4111yescharacteristic
426C2×C4⋊C8C22×C4111yescharacteristic
427C2×#102C22×C4111yescharacteristic
428C2×#102C22×C4111yescharacteristic
429C2×#102C22×C4111yescharacteristic
430C2×#102C22×C4111yescharacteristic
431C2×#102C22×C4111yescharacteristic
432C2×#102C22×C4111yescharacteristic
433C2×#102C22×C4111yescharacteristic
434C2×#102C22×C4111yescharacteristic
435C2×C22⋊C8C22×C4111yescharacteristic
436C2×C22⋊C8C22×C4111yescharacteristic
437C2×C22⋊C8C22×C4111yescharacteristic
438C2×C22⋊C8C22×C4111yescharacteristic
439C2×#97C22×C4111yescharacteristic
440#392—21no—
441#392—21no—
442#390—21no—
443#388—21no—
444#387—21no—
445#386—21no—
446#382C22×C4111yescharacteristic
447#380C22×C4111yescharacteristic
448#380C22×C4111yescharacteristic
449C4×C4⋊C4C22×C4111yescharacteristic
450C4×C4⋊C4C22×C4111yescharacteristic
451C4×C22⋊C4—21no—
452#340C22×C4111yescharacteristic
453#340C22×C4111yescharacteristic
454#340C22×C4111yescharacteristic
455#340C22×C4111yescharacteristic
456C41#2624611yescharacteristic, direct product factor, Sylow
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4D4×C4111yescharacteristic
464C22×D4C23×C4111yescharacteristic
465C22×D4C23×C4111yescharacteristic
466C23×C4—21no—
467C23×C4C23×C4111yescharacteristic
468C23×C4C23×C4111yescharacteristic
469C22×C8C23×C4111yescharacteristic
470C22×C8C23×C4111yescharacteristic
471C22×C8C23×C4111yescharacteristic
472C22×C8C23×C4111yescharacteristic
473#127—22no—
474#127—22no—
475#127—44no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—41no—
481#121—41no—
482#121—41no—
483#121—41no—
484C4×D4—22no—
485C4×D4—22no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4D4×C4111yescharacteristic
492C2×C4⋊C4C23×C4111yescharacteristic
493C2×C4⋊C4C23×C4111yescharacteristic
494C2×C4⋊C4C23×C4111yescharacteristic
495C2×C4⋊C4C23×C4111yescharacteristic
496C2×C4⋊C4C23×C4111yescharacteristic
497C2×C4⋊C4C23×C4111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C4111yescharacteristic
506C2×C22⋊C4D4×C4111yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42C23×C4111yescharacteristic
511#107—22no—
512#107—22no—
513#106—22no—
514#106D4×C4114yescomplemented
515C4⋊C8—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102—41no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—41no—
527C22⋊C8—41no—
528#97—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C4111yescharacteristic
538C24C2×D4×C4111yescharacteristic
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—81no—
593C22×C4C2×D4×C4111yescharacteristic
594C22×C4C2×D4×C4111yescharacteristic
595C22×C4C2×D4×C4111yescharacteristic
596C22×C4C2×D4×C4111yescharacteristic
597C22×C4C24×C4111yescharacteristic
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8C2×D4×C4112yes—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4C2×D4×C4112yes—
622C4⋊C4C2×D4×C4112yes—
623C4⋊C4#41×C4112yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—81no—
633C42—42no—
634C42—42no—
635C42—81no—
636C42#41×C4112yes—
637C42#41×C4112yes—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23AGL(1,ℤ/8)×C4112yes—
666C23C22×D4×C4111yescharacteristic
667D4—44no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—84no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4#123×C4112yes—
720C2×C4#123×C4112yes—
721C2×C4C22×D4×C4111yescharacteristic
722C2×C4C2×#41×C4111yescharacteristic
723C2×C4C2×#41×C4111yescharacteristic
724C2×C4C2×#41×C4111yescharacteristic
725C2×C4H(5,𝔽2)×C4111yescharacteristic
726C2×C4H(5,𝔽2)×C4111yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C2×#123×C4111yescharacteristic
760C22D42×C4111yescharacteristic
761C22C41×#54611yescharacteristic
762C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
763C22C41×#57511yescharacteristic
764C22C41×#57611yescharacteristic
765C22C41×#57711yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—42no—
772C4—42no—
773C4—81no—
774C4—81no—
775C4—81no—
776C4C41×#53211yescharacteristic
777C4C41×#54011yescharacteristic
778C4C41×#55011yescharacteristic
779C4C41×#55911yescharacteristic
780C2—42no—
781C2—81no—
782C2—161no—
783C2—161no—
784C2C41×#244511yescharacteristic
785C2C41×#309411yescharacteristic
786C2C41×#309611yescharacteristic
787C2C41×#326511yescharacteristic
788C2C41×#326811yescharacteristic
789C2C41×#331711yescharacteristic
790C2C41×#331811yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#2541C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C4×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#481C2semidirect
2. C2×C41×#482C2semidirect
4. C41×#2352C2semidirect
5. C41×#2034C2semidirect
6. C41×#2033C2semidirect
7. C41×#2033C2semidirect
8. C41×#2033C2semidirect
9. C41×#1982C2semidirect
10. C41×#1961C2semidirect
11. C41×#1955C2semidirect
12. C41×#1949C2semidirect
13. C41×#1875C2semidirect
14. C41×#1874C2semidirect
15. C41×#1776C2semidirect
118. #106×C41D4semidirect
335. #26246C41direct (N × H)
385. C2×#481C2×C41semidirect
386. C2×#482C2×C41semidirect
388. #2352C2×C41semidirect
389. #2034C2×C41semidirect
390. #2033C2×C41semidirect
391. #2033C2×C41semidirect
392. #2033C2×C41semidirect
393. #1982C2×C41semidirect
394. #1961C2×C41semidirect
395. #1955C2×C41semidirect
396. #1949C2×C41semidirect
397. #1875C2×C41semidirect
398. #1874C2×C41semidirect
399. #1776C2×C41semidirect
456. C41#26246direct (N × H)
514. #106D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4812
C2×C41×#4822
C41×#25412
C41×#23522
C41×#20342
C41×#20332
C41×#19822
C41×#19612
C41×#19552
C41×#19492
C41×#18752
C41×#18742
C41×#17762
#2624641