Finite Group Databasebeta

← C41×#25408 #23801609

Subgroups — C41×#25408 #23801609

Order 10496.

926 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3153C211yesmaximal, characteristic, complemented
2C2×C41×#472C211yesmaximal, characteristic, complemented
3C2×C41×#471C211yesmaximal, characteristic, complemented
4C41×#3036C211yesmaximal, characteristic, complemented
5C2×C41×#463C211yesmaximal, characteristic, complemented
6C41×#2935C211yesmaximal, characteristic, complemented
7C41×#2052C211yesmaximal, characteristic, complemented
8C41×#2051C211yesmaximal, characteristic, complemented
9C41×#2019C211yesmaximal, characteristic, complemented
10C41×#2018C211yesmaximal, characteristic, complemented
11C41×#1967C211yesmaximal, characteristic, complemented
12C41×#1950C211yesmaximal, characteristic, complemented
13C41×#1908C211yesmaximal, characteristic, complemented
14C41×#1907C211yesmaximal, characteristic, complemented
15C4×#100×C41C211yesmaximal, characteristic, complemented
16C2×#137×C41C2211yescharacteristic
17C2×#137×C41C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
22C22×SD16×C41C2211yescharacteristic
23C22×D8×C41C2211yescharacteristic
24C2×#131×C41C2211yescharacteristic
25C2×#131×C41C2211yescharacteristic
26C41×#532C2211yescharacteristic
27C2×#124×C41C2211yescharacteristic
28C2×C4×D4×C41C2211yescharacteristic
29C41×#497—21no—
30C41×#496—21no—
31C41×#495—21no—
32C41×#495—21no—
33C41×#472—24no—
34C41×#471—24no—
35C41×#463—21no—
36C41×#463—21no—
37C41×#463—21no—
38C41×#463—21no—
39C41×#463—21no—
40C41×#463—21no—
41C41×#461—21no—
42C41×#459—21no—
43C41×#436—21no—
44C41×#435—21no—
45C41×#435—21no—
46C8×D4×C41—21no—
47C2×#108×C41C2211yescharacteristic
48C2×#108×C41C2211yescharacteristic
49C41×#423C2211yescharacteristic
50C2×C4⋊C8×C41C2211yescharacteristic
51C41×#417C2211yescharacteristic
52C41×#417C2211yescharacteristic
53C2×#103×C41C2211yescharacteristic
54C2×#102×C41C2211yescharacteristic
55C2×#101×C41C2211yescharacteristic
56C2×#101×C41C2211yescharacteristic
57C2×#100×C41C2211yescharacteristic
58C2×#100×C41C2211yescharacteristic
59C2×#100×C41C2211yescharacteristic
60C2×#100×C41C2211yescharacteristic
61C41×#408C2211yescharacteristic
62C41×#408C2211yescharacteristic
63C4×M16×C41C2211yescharacteristic
64C4×M16×C41C2211yescharacteristic
65C41×#343C2211yescharacteristic
66C41×#343C2211yescharacteristic
67C41×#341C2211yescharacteristic
68C41×#341C2211yescharacteristic
69C2×#41×C41C2311yescharacteristic
70C2×#41×C41C2311yescharacteristic
71C22×Q8×C41C2311yescharacteristic
72C22×D4×C41C2311yescharacteristic
73C22×D4×C41C2311yescharacteristic
74C23×C4×C41—21no—
75#137×C41—22no—
76#137×C41—22no—
77#137×C41—41no—
78#137×C41—41no—
79AGL(1,ℤ/8)×C41—22no—
80AGL(1,ℤ/8)×C41—22no—
81AGL(1,ℤ/8)×C41—22no—
82AGL(1,ℤ/8)×C41—22no—
83AGL(1,ℤ/8)×C41—41no—
84AGL(1,ℤ/8)×C41—41no—
85AGL(1,ℤ/8)×C41—41no—
86AGL(1,ℤ/8)×C41—41no—
87C2×Q16×C41—21no—
88C2×Q16×C41—21no—
89C2×SD16×C41—21no—
90C2×SD16×C41—21no—
91C2×SD16×C41—21no—
92C2×SD16×C41—21no—
93C2×SD16×C41—22no—
94C2×SD16×C41—21no—
95C2×SD16×C41—21no—
96C2×SD16×C41—21no—
97C2×SD16×C41—21no—
98C2×SD16×C41—41no—
99C2×D8×C41—22no—
100C2×D8×C41—21no—
101C2×D8×C41—21no—
102C2×D8×C41—21no—
103C2×D8×C41—21no—
104C2×D8×C41—21no—
105C2×D8×C41—21no—
106C2×D8×C41—41no—
107#131×C41—22no—
108#131×C41—22no—
109#131×C41—41no—
110#131×C41—41no—
111C2×M16×C41—21no—
112C2×M16×C41—21no—
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×C41C2311yescharacteristic
122C22×C8×C41C2311yescharacteristic
123C4⋊Q8×C41D411yescharacteristic
124#127×C41D411yescharacteristic
125#124×C41—21no—
126#124×C41—21no—
127#124×C41—21no—
128#124×C41—21no—
129#124×C41D411yescharacteristic
130#124×C41D411yescharacteristic
131#121×C41—21no—
132#121×C41—21no—
133C4×D4×C41—21no—
134C4×D4×C41—21no—
135C4×D4×C41—21no—
136C4×D4×C41—21no—
137C4×D4×C41—21no—
138C4×D4×C41—21no—
139C2×C4⋊C4×C41C2311yescharacteristic
140C2×C22⋊C4×C41—21no—
141C2×C22⋊C4×C41—21no—
142C2×C22⋊C4×C41—21no—
143C2×C42×C41C2311yescharacteristic
144#108×C41—22no—
145#108×C41—22no—
146C4⋊C8×C41—21no—
147C4⋊C8×C41—21no—
148C4⋊C8×C41D411yescharacteristic
149C4⋊C8×C41D411yescharacteristic
150C4⋊C8×C41D411yescharacteristic
151C4⋊C8×C41D411yescharacteristic
152#103×C41—21no—
153#103×C41—21no—
154#103×C41—21no—
155#103×C41—21no—
156#102×C41—21no—
157#102×C41—21no—
158#102×C41—21no—
159#102×C41—21no—
160#101×C41—22no—
161#101×C41—41no—
162#100×C41—22no—
163#100×C41—22no—
164#100×C41—41no—
165#100×C41D414yescomplemented
166C22⋊C8×C41—21no—
167C22⋊C8×C41—21no—
168C22⋊C8×C41—21no—
169C22⋊C8×C41—21no—
170#97×C41—21no—
171#97×C41—21no—
172C4×C8×C41—21no—
173C4×C8×C41—21no—
174C24×C41—21no—
175C24×C41—21no—
176#41×C41—21no—
177#41×C41—21no—
178#41×C41—21no—
179#41×C41—21no—
180#41×C41—21no—
181#41×C41—21no—
182#41×C41—21no—
183#41×C41—21no—
184C2×Q8×C41—21no—
185C2×Q8×C41—21no—
186C2×Q8×C41—21no—
187C2×Q8×C41—21no—
188C2×Q8×C41—21no—
189C2×Q8×C41—21no—
190C2×Q8×C41C2×D411yescharacteristic
191C2×Q8×C41C2×D411yescharacteristic
192C2×D4×C41—21no—
193C2×D4×C41—21no—
194C2×D4×C41—21no—
195C2×D4×C41—21no—
196C2×D4×C41—21no—
197C2×D4×C41—21no—
198C2×D4×C41—21no—
199C2×D4×C41—21no—
200C2×D4×C41—21no—
201C2×D4×C41—21no—
202C2×D4×C41—21no—
203C2×D4×C41—21no—
204C2×D4×C41—21no—
205C2×D4×C41—21no—
206C2×D4×C41—21no—
207C2×D4×C41C2×D412yes—
208C2×D4×C41C2×D411yescharacteristic
209C2×D4×C41C2×D411yescharacteristic
210C22×C4×C41—21no—
211C22×C4×C41—21no—
212C22×C4×C41—21no—
213C22×C4×C41—21no—
214C22×C4×C41—41no—
215C22×C4×C41—41no—
216C22×C4×C41—82no—
217C22×C4×C41#4111yescharacteristic
218C22×C4×C41#4111yescharacteristic
219C22×C4×C41C2411yescharacteristic
220Q16×C41—42no—
221Q16×C41—42no—
222SD16×C41—42no—
223SD16×C41—42no—
224SD16×C41—42no—
225SD16×C41—42no—
226SD16×C41—42no—
227SD16×C41—42no—
228SD16×C41—42no—
229SD16×C41—42no—
230D8×C41—42no—
231D8×C41—42no—
232D8×C41—42no—
233D8×C41—42no—
234D8×C41—42no—
235D8×C41—42no—
236M16×C41—21no—
237M16×C41—21no—
238M16×C41—21no—
239M16×C41—21no—
240M16×C41—21no—
241M16×C41—21no—
242M16×C41—21no—
243M16×C41—21no—
244M16×C41—21no—
245M16×C41—42no—
246M16×C41—42no—
247M16×C41C2×D412yes—
248M16×C41C2×D412yes—
249M16×C41#4112yes—
250C2×C8×C41—21no—
251C2×C8×C41—21no—
252C2×C8×C41—21no—
253C2×C8×C41—21no—
254C2×C8×C41—21no—
255C2×C8×C41—21no—
256C2×C8×C41—21no—
257C2×C8×C41—21no—
258C2×C8×C41—21no—
259C2×C8×C41—21no—
260C2×C8×C41—42no—
261C2×C8×C41—42no—
262C2×C8×C41C2×D411yescharacteristic
263C2×C8×C41C2×D411yescharacteristic
264C2×C8×C41C2×D411yescharacteristic
265C2×C8×C41C2×D411yescharacteristic
266C4⋊C4×C41—21no—
267C4⋊C4×C41—21no—
268C4⋊C4×C41—21no—
269C4⋊C4×C41—21no—
270C22⋊C4×C41—21no—
271C22⋊C4×C41—21no—
272C22⋊C4×C41—21no—
273C22⋊C4×C41—21no—
274C22⋊C4×C41—41no—
275C22⋊C4×C41—41no—
276C22⋊C4×C41—41no—
277C22⋊C4×C41—41no—
278C22⋊C4×C41—41no—
279C22⋊C4×C41—41no—
280C42×C41C2×D411yescharacteristic
281C42×C41C2×D411yescharacteristic
282C42×C41C2×D411yescharacteristic
283C42×C41C2×D411yescharacteristic
284C23×C41—21no—
285C23×C41—21no—
286C23×C41—22no—
287C23×C41—41no—
288C23×C41—41no—
289C23×C41—41no—
290C23×C41—41no—
291C23×C41—41no—
292C23×C41—81no—
293C23×C41—81no—
294C23×C41—81no—
295C23×C41—81no—
296C23×C41C2×#4111yescharacteristic
297Q8×C41—21no—
298Q8×C41—21no—
299Q8×C41—21no—
300Q8×C41—21no—
301Q8×C41—41no—
302Q8×C41—41no—
303Q8×C41—41no—
304Q8×C41—41no—
305D4×C41—21no—
306D4×C41—22no—
307D4×C41—22no—
308D4×C41—21no—
309D4×C41—21no—
310D4×C41—21no—
311D4×C41—42no—
312D4×C41—41no—
313D4×C41—41no—
314D4×C41—41no—
315D4×C41—41no—
316D4×C41—41no—
317D4×C41—41no—
318D4×C41—41no—
319D4×C41—41no—
320D4×C41—41no—
321D4×C41—41no—
322D4×C41—81no—
323C2×C4×C41—21no—
324C2×C4×C41—21no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—41no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41—41no—
335C2×C4×C41—82no—
336C2×C4×C41—82no—
337C2×C4×C41—81no—
338C2×C4×C41#12111yescharacteristic
339C2×C4×C41#12111yescharacteristic
340C2×C4×C41#12111yescharacteristic
341C2×C4×C41#12111yescharacteristic
342C2×C4×C41C22×D411yescharacteristic
343C2×C4×C41C22×D411yescharacteristic
344C2×C4×C41C22×D411yescharacteristic
345C2×C4×C41C2×#4111yescharacteristic
346C2×C4×C41H(5,𝔽2)11yescharacteristic
347C2×C4×C41H(5,𝔽2)11yescharacteristic
348C8×C41—21no—
349C8×C41—21no—
350C8×C41—21no—
351C8×C41—21no—
352C8×C41—22no—
353C8×C41—22no—
354C8×C41—22no—
355C8×C41—41no—
356C8×C41—41no—
357C8×C41—41no—
358#25408C4111yesmaximal, characteristic, direct product factor, Sylow
359C22×C41—21no—
360C22×C41—21no—
361C22×C41—41no—
362C22×C41—41no—
363C22×C41—42no—
364C22×C41—41no—
365C22×C41—41no—
366C22×C41—41no—
367C22×C41—41no—
368C22×C41—82no—
369C22×C41—82no—
370C22×C41—81no—
371C22×C41—81no—
372C22×C41—81no—
373C22×C41—81no—
374C22×C41—81no—
375C22×C41—161no—
376C22×C41—161no—
377C22×C41C2×#12111yescharacteristic
378C22×C41#53211yescharacteristic
379C22×C41#54011yescharacteristic
380C4×C41—21no—
381C4×C41—21no—
382C4×C41—21no—
383C4×C41—21no—
384C4×C41—41no—
385C4×C41—41no—
386C4×C41—81no—
387C4×C41—81no—
388C4×C41D4211yescharacteristic
389C4×C41D4211yescharacteristic
390C4×C41#54611yescharacteristic
391C4×C41#55011yescharacteristic
392#3153C2×C4111yescharacteristic, complemented
393C2×#472C2×C4111yescharacteristic, complemented
394C2×#471C2×C4111yescharacteristic, complemented
395#3036C2×C4111yescharacteristic, complemented
396C2×#463C2×C4111yescharacteristic, complemented
397#2935C2×C4111yescharacteristic, complemented
398#2052C2×C4111yescharacteristic, complemented
399#2051C2×C4111yescharacteristic, complemented
400#2019C2×C4111yescharacteristic, complemented
401#2018C2×C4111yescharacteristic, complemented
402#1967C2×C4111yescharacteristic, complemented
403#1950C2×C4111yescharacteristic, complemented
404#1908C2×C4111yescharacteristic, complemented
405#1907C2×C4111yescharacteristic, complemented
406C4×#100C2×C4111yescharacteristic, complemented
407C2×C41—21no—
408C2×C41—21no—
409C2×C41—81no—
410C2×C41—81no—
411C2×C41—82no—
412C2×C41—161no—
413C2×C41#242811yescharacteristic
414C2×C41#306711yescharacteristic
415C2×C41#306811yescharacteristic
416C2×#137C22×C4111yescharacteristic
417C2×#137C22×C4111yescharacteristic
418C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
419C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
420C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
421C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
422C22×SD16C22×C4111yescharacteristic
423C22×D8C22×C4111yescharacteristic
424C2×#131C22×C4111yescharacteristic
425C2×#131C22×C4111yescharacteristic
426#532C22×C4111yescharacteristic
427C2×#124C22×C4111yescharacteristic
428C2×C4×D4C22×C4111yescharacteristic
429#497—21no—
430#496—21no—
431#495—21no—
432#495—21no—
433#472—24no—
434#471—24no—
435#463—21no—
436#463—21no—
437#463—21no—
438#463—21no—
439#463—21no—
440#463—21no—
441#461—21no—
442#459—21no—
443#436—21no—
444#435—21no—
445#435—21no—
446C8×D4—21no—
447C2×#108C22×C4111yescharacteristic
448C2×#108C22×C4111yescharacteristic
449#423C22×C4111yescharacteristic
450C2×C4⋊C8C22×C4111yescharacteristic
451#417C22×C4111yescharacteristic
452#417C22×C4111yescharacteristic
453C2×#103C22×C4111yescharacteristic
454C2×#102C22×C4111yescharacteristic
455C2×#101C22×C4111yescharacteristic
456C2×#101C22×C4111yescharacteristic
457C2×#100C22×C4111yescharacteristic
458C2×#100C22×C4111yescharacteristic
459C2×#100C22×C4111yescharacteristic
460C2×#100C22×C4111yescharacteristic
461#408C22×C4111yescharacteristic
462#408C22×C4111yescharacteristic
463C4×M16C22×C4111yescharacteristic
464C4×M16C22×C4111yescharacteristic
465#343C22×C4111yescharacteristic
466#343C22×C4111yescharacteristic
467#341C22×C4111yescharacteristic
468#341C22×C4111yescharacteristic
469C41#2540811yescharacteristic, direct product factor, Sylow
470C2×#41C23×C4111yescharacteristic
471C2×#41C23×C4111yescharacteristic
472C22×Q8C23×C4111yescharacteristic
473C22×D4C23×C4111yescharacteristic
474C22×D4C23×C4111yescharacteristic
475C23×C4—21no—
476#137—22no—
477#137—22no—
478#137—41no—
479#137—41no—
480AGL(1,ℤ/8)—22no—
481AGL(1,ℤ/8)—22no—
482AGL(1,ℤ/8)—22no—
483AGL(1,ℤ/8)—22no—
484AGL(1,ℤ/8)—41no—
485AGL(1,ℤ/8)—41no—
486AGL(1,ℤ/8)—41no—
487AGL(1,ℤ/8)—41no—
488C2×Q16—21no—
489C2×Q16—21no—
490C2×SD16—21no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×SD16—21no—
494C2×SD16—22no—
495C2×SD16—21no—
496C2×SD16—21no—
497C2×SD16—21no—
498C2×SD16—21no—
499C2×SD16—41no—
500C2×D8—22no—
501C2×D8—21no—
502C2×D8—21no—
503C2×D8—21no—
504C2×D8—21no—
505C2×D8—21no—
506C2×D8—21no—
507C2×D8—41no—
508#131—22no—
509#131—22no—
510#131—41no—
511#131—41no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16C23×C4111yescharacteristic
515C2×M16C23×C4111yescharacteristic
516C2×M16C23×C4111yescharacteristic
517C2×M16C23×C4111yescharacteristic
518C2×M16C23×C4111yescharacteristic
519C2×M16C23×C4111yescharacteristic
520C22×C8—21no—
521C22×C8—21no—
522C22×C8C23×C4111yescharacteristic
523C22×C8C23×C4111yescharacteristic
524C4⋊Q8D4×C4111yescharacteristic
525#127D4×C4111yescharacteristic
526#124—21no—
527#124—21no—
528#124—21no—
529#124—21no—
530#124D4×C4111yescharacteristic
531#124D4×C4111yescharacteristic
532#121—21no—
533#121—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C2×C4⋊C4C23×C4111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C42C23×C4111yescharacteristic
545#108—22no—
546#108—22no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8D4×C4111yescharacteristic
550C4⋊C8D4×C4111yescharacteristic
551C4⋊C8D4×C4111yescharacteristic
552C4⋊C8D4×C4111yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#102—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#101—22no—
562#101—41no—
563#100—22no—
564#100—22no—
565#100—41no—
566#100D4×C4114yescomplemented
567C22⋊C8—21no—
568C22⋊C8—21no—
569C22⋊C8—21no—
570C22⋊C8—21no—
571#97—21no—
572#97—21no—
573C4×C8—21no—
574C4×C8—21no—
575C24—21no—
576C24—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580#41—21no—
581#41—21no—
582#41—21no—
583#41—21no—
584#41—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8C2×D4×C4111yescharacteristic
592C2×Q8C2×D4×C4111yescharacteristic
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4C2×D4×C4112yes—
609C2×D4C2×D4×C4111yescharacteristic
610C2×D4C2×D4×C4111yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—82no—
618C22×C4#41×C4111yescharacteristic
619C22×C4#41×C4111yescharacteristic
620C22×C4C24×C4111yescharacteristic
621Q16—42no—
622Q16—42no—
623SD16—42no—
624SD16—42no—
625SD16—42no—
626SD16—42no—
627SD16—42no—
628SD16—42no—
629SD16—42no—
630SD16—42no—
631D8—42no—
632D8—42no—
633D8—42no—
634D8—42no—
635D8—42no—
636D8—42no—
637M16—21no—
638M16—21no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—42no—
647M16—42no—
648M16C2×D4×C4112yes—
649M16C2×D4×C4112yes—
650M16#41×C4112yes—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—42no—
662C2×C8—42no—
663C2×C8C2×D4×C4111yescharacteristic
664C2×C8C2×D4×C4111yescharacteristic
665C2×C8C2×D4×C4111yescharacteristic
666C2×C8C2×D4×C4111yescharacteristic
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C22⋊C4—41no—
681C42C2×D4×C4111yescharacteristic
682C42C2×D4×C4111yescharacteristic
683C42C2×D4×C4111yescharacteristic
684C42C2×D4×C4111yescharacteristic
685C23—21no—
686C23—21no—
687C23—22no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—81no—
694C23—81no—
695C23—81no—
696C23—81no—
697C23C2×#41×C4111yescharacteristic
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—21no—
702Q8—41no—
703Q8—41no—
704Q8—41no—
705Q8—41no—
706D4—21no—
707D4—22no—
708D4—22no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—42no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—81no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—82no—
737C2×C4—82no—
738C2×C4—81no—
739C2×C4#121×C4111yescharacteristic
740C2×C4#121×C4111yescharacteristic
741C2×C4#121×C4111yescharacteristic
742C2×C4#121×C4111yescharacteristic
743C2×C4C22×D4×C4111yescharacteristic
744C2×C4C22×D4×C4111yescharacteristic
745C2×C4C22×D4×C4111yescharacteristic
746C2×C4C2×#41×C4111yescharacteristic
747C2×C4H(5,𝔽2)×C4111yescharacteristic
748C2×C4H(5,𝔽2)×C4111yescharacteristic
749C8—21no—
750C8—21no—
751C8—21no—
752C8—21no—
753C8—22no—
754C8—22no—
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C22—21no—
760C22—21no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—82no—
769C22—82no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—161no—
776C22—161no—
777C22C2×#121×C4111yescharacteristic
778C22C41×#53211yescharacteristic
779C22C41×#54011yescharacteristic
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—41no—
785C4—41no—
786C4—81no—
787C4—81no—
788C4D42×C4111yescharacteristic
789C4D42×C4111yescharacteristic
790C4C41×#54611yescharacteristic
791C4C41×#55011yescharacteristic
792C2—21no—
793C2—21no—
794C2—81no—
795C2—81no—
796C2—82no—
797C2—161no—
798C2C41×#242811yescharacteristic
799C2C41×#306711yescharacteristic
800C2C41×#306811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3153C2semidirect
2. C2×C41×#472C2semidirect
3. C2×C41×#471C2semidirect
4. C41×#3036C2semidirect
5. C2×C41×#463C2semidirect
6. C41×#2935C2semidirect
7. C41×#2052C2semidirect
8. C41×#2051C2semidirect
9. C41×#2019C2semidirect
10. C41×#2018C2semidirect
11. C41×#1967C2semidirect
12. C41×#1950C2semidirect
13. C41×#1908C2semidirect
14. C41×#1907C2semidirect
15. C4×#100×C41C2semidirect
165. #100×C41D4semidirect
358. #25408C41direct (N × H)
392. #3153C2×C41semidirect
393. C2×#472C2×C41semidirect
394. C2×#471C2×C41semidirect
395. #3036C2×C41semidirect
396. C2×#463C2×C41semidirect
397. #2935C2×C41semidirect
398. #2052C2×C41semidirect
399. #2051C2×C41semidirect
400. #2019C2×C41semidirect
401. #2018C2×C41semidirect
402. #1967C2×C41semidirect
403. #1950C2×C41semidirect
404. #1908C2×C41semidirect
405. #1907C2×C41semidirect
406. C4×#100C2×C41semidirect
469. C41#25408direct (N × H)
566. #100D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#31532
C2×C41×#4722
C2×C41×#4712
C41×#30362
C2×C41×#4632
C41×#29352
C41×#20522
C41×#20512
C41×#20192
C41×#20182
C41×#19672
C41×#19502
C41×#19082
C41×#19072
C4×#100×C412
#2540841