Finite Group Databasebeta

← C41×#25140 #23801341

Subgroups — C41×#25140 #23801341

Order 10496.

1140 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#472C211yesmaximal, characteristic, complemented
2C41×#3055C211yesmaximal, characteristic, complemented
3C41×#3003C211yesmaximal, characteristic, complemented
4C2×C41×#447C211yesmaximal, characteristic, complemented
5C41×#2933C211yesmaximal, characteristic, complemented
6C22×#100×C41C211yesmaximal, characteristic, complemented
7C41×#2063C211yesmaximal, characteristic, complemented
8C41×#2051C211yesmaximal, characteristic, complemented
9C41×#2045C211yesmaximal, characteristic, complemented
10C41×#2018C211yesmaximal, characteristic, complemented
11C41×#1978C211yesmaximal, characteristic, complemented
12C41×#1931C211yesmaximal, characteristic, complemented
13C41×#1907C211yesmaximal, characteristic, complemented
14C41×#1900C211yesmaximal, characteristic, complemented
15C41×#1855C211yesmaximal, characteristic, complemented
16C23×D4×C41C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C41C2211yescharacteristic, complemented
20C22×D8×C41C2211yescharacteristic
21C22×D8×C41C2211yescharacteristic
22C2×#131×C41C2211yescharacteristic, complemented
23C22×M16×C41C2211yescharacteristic
24C22×M16×C41C2211yescharacteristic
25C41×#525C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C41×#472—24no—
28C41×#469—21no—
29C41×#468—21no—
30C41×#466—21no—
31C41×#465—21no—
32C41×#450—21no—
33C41×#450—21no—
34C41×#447—21no—
35C41×#447—21no—
36C41×#447—21no—
37C41×#447—21no—
38C41×#447—21no—
39C41×#447—21no—
40C41×#436—21no—
41C41×#435—21no—
42C41×#435—21no—
43C8×D4×C41—21no—
44C2×#108×C41C2211yescharacteristic, complemented
45C2×#108×C41C2211yescharacteristic, complemented
46C41×#428C2211yescharacteristic, complemented
47C41×#424C2211yescharacteristic, complemented
48C41×#418C2211yescharacteristic
49C41×#418C2211yescharacteristic
50C41×#418C2211yescharacteristic, complemented
51C41×#417C2211yescharacteristic, complemented
52C2×#102×C41C2211yescharacteristic
53C2×#102×C41C2211yescharacteristic
54C2×#100×C41—24no—
55C2×#100×C41C2211yescharacteristic
56C2×#100×C41C2211yescharacteristic
57C2×#100×C41C2211yescharacteristic
58C2×#100×C41C2211yescharacteristic
59C2×#100×C41C2211yescharacteristic, complemented
60C2×#100×C41C2211yescharacteristic, complemented
61C41×#408C2211yescharacteristic, complemented
62C41×#407C2211yescharacteristic
63C2×C22⋊C8×C41C2211yescharacteristic
64C41×#405C2211yescharacteristic, complemented
65C41×#343C2211yescharacteristic, complemented
66C41×#343C2211yescharacteristic, complemented
67C41×#341C2211yescharacteristic, complemented
68C41×#341C2211yescharacteristic, complemented
69C25×C41—21no—
70C2×#41×C41C2311yescharacteristic
71C22×D4×C41—22no—
72C22×D4×C41—22no—
73C22×D4×C41—21no—
74C22×D4×C41—21no—
75C22×D4×C41—21no—
76C22×D4×C41—21no—
77C22×D4×C41—21no—
78C22×D4×C41—21no—
79C22×D4×C41—41no—
80C22×D4×C41—41no—
81C22×D4×C41C2311yescharacteristic
82C22×D4×C41C2311yescharacteristic
83C22×D4×C41C2311yescharacteristic
84C23×C4×C41C2311yescharacteristic
85AGL(1,ℤ/8)×C41—22no—
86AGL(1,ℤ/8)×C41—22no—
87AGL(1,ℤ/8)×C41—22no—
88AGL(1,ℤ/8)×C41—41no—
89AGL(1,ℤ/8)×C41—41no—
90AGL(1,ℤ/8)×C41—41no—
91C2×SD16×C41—21no—
92C2×SD16×C41—21no—
93C2×SD16×C41—21no—
94C2×D8×C41—22no—
95C2×D8×C41—21no—
96C2×D8×C41—21no—
97C2×D8×C41—21no—
98C2×D8×C41—22no—
99C2×D8×C41—21no—
100C2×D8×C41—21no—
101C2×D8×C41—21no—
102C2×D8×C41—21no—
103C2×D8×C41—41no—
104C2×D8×C41—41no—
105#131×C41—22no—
106#131×C41—41no—
107C2×M16×C41—21no—
108C2×M16×C41—21no—
109C2×M16×C41—21no—
110C2×M16×C41—22no—
111C2×M16×C41—22no—
112C2×M16×C41—41no—
113C2×M16×C41—41no—
114C2×M16×C41C2311yescharacteristic
115C2×M16×C41C2311yescharacteristic
116C2×M16×C41C2311yescharacteristic
117C2×M16×C41C2311yescharacteristic
118C2×M16×C41C2311yescharacteristic
119C2×M16×C41C2311yescharacteristic
120C22×C8×C41—21no—
121C22×C8×C41—21no—
122C22×C8×C41—21no—
123C22×C8×C41C2311yescharacteristic
124C22×C8×C41C2311yescharacteristic
125#123×C41—21no—
126C22⋊Q8×C41D411yescharacteristic
127C22⋊Q8×C41D411yescharacteristic
128#121×C41—21no—
129#121×C41—21no—
130#121×C41—21no—
131#121×C41—21no—
132#121×C41D411yescharacteristic
133#121×C41D411yescharacteristic
134#120×C41—21no—
135C4×D4×C41—21no—
136C4×D4×C41—21no—
137#117×C41C2311yescharacteristic
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#102×C41—21no—
148#102×C41—21no—
149#102×C41—21no—
150#102×C41—21no—
151#102×C41—21no—
152#102×C41—21no—
153#102×C41—21no—
154#102×C41—21no—
155#102×C41—21no—
156#102×C41—21no—
157#102×C41—21no—
158#100×C41—22no—
159#100×C41—22no—
160#100×C41—22no—
161#100×C41—22no—
162#100×C41—41no—
163#100×C41D414yescomplemented
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—24no—
175C24×C41—21no—
176C24×C41—21no—
177C24×C41—21no—
178C24×C41—42no—
179C24×C41—41no—
180C24×C41—41no—
181C24×C41—82no—
182C24×C41—82no—
183C24×C41#4111yescharacteristic
184#41×C41—21no—
185#41×C41—21no—
186#41×C41—21no—
187#41×C41—21no—
188C2×Q8×C41C2×D411yescharacteristic
189C2×D4×C41—24no—
190C2×D4×C41—21no—
191C2×D4×C41—21no—
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×C41—21no—
208C2×D4×C41—21no—
209C2×D4×C41—42no—
210C2×D4×C41—42no—
211C2×D4×C41—42no—
212C2×D4×C41—42no—
213C2×D4×C41—42no—
214C2×D4×C41—42no—
215C2×D4×C41—42no—
216C2×D4×C41—42no—
217C2×D4×C41—42no—
218C2×D4×C41—41no—
219C2×D4×C41—41no—
220C2×D4×C41—41no—
221C2×D4×C41—41no—
222C2×D4×C41—82no—
223C2×D4×C41C2×D412yes—
224C2×D4×C41C2×D411yescharacteristic
225C2×D4×C41#4112yes—
226C22×C4×C41—21no—
227C22×C4×C41—21no—
228C22×C4×C41—21no—
229C22×C4×C41—21no—
230C22×C4×C41—21no—
231C22×C4×C41—21no—
232C22×C4×C41C2×D411yescharacteristic
233C22×C4×C41C2×D411yescharacteristic
234C22×C4×C41C2×D411yescharacteristic
235C22×C4×C41C2×D411yescharacteristic
236C22×C4×C41#4111yescharacteristic
237C22×C4×C41C2411yescharacteristic
238SD16×C41—42no—
239SD16×C41—42no—
240SD16×C41—42no—
241D8×C41—42no—
242D8×C41—42no—
243D8×C41—42no—
244D8×C41—42no—
245D8×C41—42no—
246D8×C41—42no—
247D8×C41—42no—
248M16×C41—21no—
249M16×C41—21no—
250M16×C41—21no—
251M16×C41—21no—
252M16×C41—21no—
253M16×C41—21no—
254M16×C41—21no—
255M16×C41—21no—
256M16×C41—21no—
257M16×C41—21no—
258M16×C41—42no—
259M16×C41—42no—
260M16×C41—42no—
261M16×C41C2×D412yes—
262M16×C41C2×D412yes—
263C2×C8×C41—21no—
264C2×C8×C41—21no—
265C2×C8×C41—21no—
266C2×C8×C41—21no—
267C2×C8×C41—21no—
268C2×C8×C41—21no—
269C2×C8×C41—21no—
270C2×C8×C41—21no—
271C2×C8×C41—21no—
272C2×C8×C41—21no—
273C2×C8×C41—42no—
274C2×C8×C41—42no—
275C2×C8×C41—42no—
276C2×C8×C41C2×D411yescharacteristic
277C2×C8×C41C2×D411yescharacteristic
278C2×C8×C41C2×D411yescharacteristic
279C2×C8×C41C2×D411yescharacteristic
280C4⋊C4×C41—21no—
281C4⋊C4×C41—21no—
282C4⋊C4×C41—21no—
283C4⋊C4×C41—21no—
284C4⋊C4×C41C2×D411yescharacteristic
285C4⋊C4×C41C2×D411yescharacteristic
286C22⋊C4×C41—21no—
287C22⋊C4×C41—21no—
288C22⋊C4×C41—21no—
289C22⋊C4×C41—21no—
290C22⋊C4×C41—21no—
291C22⋊C4×C41—41no—
292C22⋊C4×C41—41no—
293C42×C41—21no—
294C23×C41—21no—
295C23×C41—21no—
296C23×C41—22no—
297C23×C41—21no—
298C23×C41—22no—
299C23×C41—22no—
300C23×C41—41no—
301C23×C41—44no—
302C23×C41—44no—
303C23×C41—41no—
304C23×C41—41no—
305C23×C41—41no—
306C23×C41—41no—
307C23×C41—41no—
308C23×C41—41no—
309C23×C41—41no—
310C23×C41—81no—
311C23×C41—81no—
312C23×C41—81no—
313C23×C41—81no—
314C23×C41—82no—
315C23×C41—82no—
316C23×C41—82no—
317C23×C41—81no—
318C23×C41—81no—
319C23×C41—88no—
320C23×C41—88no—
321C23×C41—82no—
322C23×C41#12111yescharacteristic
323C23×C41#12111yescharacteristic
324C23×C41C2×#4111yescharacteristic
325Q8×C41—21no—
326Q8×C41—21no—
327D4×C41—21no—
328D4×C41—22no—
329D4×C41—22no—
330D4×C41—22no—
331D4×C41—21no—
332D4×C41—22no—
333D4×C41—44no—
334D4×C41—44no—
335D4×C41—41no—
336D4×C41—41no—
337D4×C41—42no—
338D4×C41—41no—
339D4×C41—41no—
340D4×C41—41no—
341D4×C41—41no—
342D4×C41—41no—
343D4×C41—41no—
344D4×C41—41no—
345D4×C41—41no—
346D4×C41—81no—
347D4×C41—82no—
348D4×C41—82no—
349C2×C4×C41—21no—
350C2×C4×C41—21no—
351C2×C4×C41—21no—
352C2×C4×C41—21no—
353C2×C4×C41—21no—
354C2×C4×C41—21no—
355C2×C4×C41—21no—
356C2×C4×C41—21no—
357C2×C4×C41—21no—
358C2×C4×C41—21no—
359C2×C4×C41—21no—
360C2×C4×C41—21no—
361C2×C4×C41—21no—
362C2×C4×C41—41no—
363C2×C4×C41—41no—
364C2×C4×C41—41no—
365C2×C4×C41—81no—
366C2×C4×C41#12111yescharacteristic
367C2×C4×C41#12111yescharacteristic
368C2×C4×C41C22×D411yescharacteristic
369C2×C4×C41C22×D411yescharacteristic
370C2×C4×C41C22×D411yescharacteristic
371C2×C4×C41C2×#4111yescharacteristic
372C2×C4×C41H(5,𝔽2)11yescharacteristic
373C2×C4×C41H(5,𝔽2)11yescharacteristic
374C8×C41—21no—
375C8×C41—21no—
376C8×C41—22no—
377C8×C41—22no—
378C8×C41—21no—
379C8×C41—21no—
380C8×C41—41no—
381C8×C41—41no—
382C8×C41—41no—
383C8×C41—41no—
384#25140C4111yesmaximal, characteristic, direct product factor, Sylow
385C22×C41—21no—
386C22×C41—21no—
387C22×C41—21no—
388C22×C41—21no—
389C22×C41—21no—
390C22×C41—21no—
391C22×C41—21no—
392C22×C41—42no—
393C22×C41—42no—
394C22×C41—41no—
395C22×C41—42no—
396C22×C41—42no—
397C22×C41—41no—
398C22×C41—41no—
399C22×C41—82no—
400C22×C41—82no—
401C22×C41—88no—
402C22×C41—82no—
403C22×C41—82no—
404C22×C41—88no—
405C22×C41—81no—
406C22×C41—81no—
407C22×C41—81no—
408C22×C41—81no—
409C22×C41—81no—
410C22×C41—81no—
411C22×C41—81no—
412C22×C41—161no—
413C22×C41—161no—
414C22×C41#47212yescomplemented
415C22×C41C2×#12111yescharacteristic
416C22×C41#52511yescharacteristic
417C22×C41#53811yescharacteristic
418C4×C41—21no—
419C4×C41—21no—
420C4×C41—41no—
421C4×C41—41no—
422C4×C41—41no—
423C4×C41—81no—
424C4×C41D4211yescharacteristic
425C4×C41D4211yescharacteristic
426C4×C41#54611yescharacteristic
427C4×C41#54611yescharacteristic
428C2×#472C2×C4111yescharacteristic, complemented
429#3055C2×C4111yescharacteristic, complemented
430#3003C2×C4111yescharacteristic, complemented
431C2×#447C2×C4111yescharacteristic, complemented
432#2933C2×C4111yescharacteristic, complemented
433C22×#100C2×C4111yescharacteristic, complemented
434#2063C2×C4111yescharacteristic, complemented
435#2051C2×C4111yescharacteristic, complemented
436#2045C2×C4111yescharacteristic, complemented
437#2018C2×C4111yescharacteristic, complemented
438#1978C2×C4111yescharacteristic, complemented
439#1931C2×C4111yescharacteristic, complemented
440#1907C2×C4111yescharacteristic, complemented
441#1900C2×C4111yescharacteristic, complemented
442#1855C2×C4111yescharacteristic, complemented
443C2×C41—21no—
444C2×C41—21no—
445C2×C41—22no—
446C2×C41—41no—
447C2×C41—81no—
448C2×C41—82no—
449C2×C41—82no—
450C2×C41—161no—
451C2×C41#242411yescharacteristic
452C2×C41C2×#47211yescharacteristic
453C2×C41#306811yescharacteristic
454C23×D4C22×C4111yescharacteristic
455C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
456C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
457C2×AGL(1,ℤ/8)C22×C4111yescharacteristic, complemented
458C22×D8C22×C4111yescharacteristic
459C22×D8C22×C4111yescharacteristic
460C2×#131C22×C4111yescharacteristic, complemented
461C22×M16C22×C4111yescharacteristic
462C22×M16C22×C4111yescharacteristic
463#525C22×C4111yescharacteristic
464C2×#121C22×C4111yescharacteristic
465#472—24no—
466#469—21no—
467#468—21no—
468#466—21no—
469#465—21no—
470#450—21no—
471#450—21no—
472#447—21no—
473#447—21no—
474#447—21no—
475#447—21no—
476#447—21no—
477#447—21no—
478#436—21no—
479#435—21no—
480#435—21no—
481C8×D4—21no—
482C2×#108C22×C4111yescharacteristic, complemented
483C2×#108C22×C4111yescharacteristic, complemented
484#428C22×C4111yescharacteristic, complemented
485#424C22×C4111yescharacteristic, complemented
486#418C22×C4111yescharacteristic
487#418C22×C4111yescharacteristic
488#418C22×C4111yescharacteristic, complemented
489#417C22×C4111yescharacteristic, complemented
490C2×#102C22×C4111yescharacteristic
491C2×#102C22×C4111yescharacteristic
492C2×#100—24no—
493C2×#100C22×C4111yescharacteristic
494C2×#100C22×C4111yescharacteristic
495C2×#100C22×C4111yescharacteristic
496C2×#100C22×C4111yescharacteristic
497C2×#100C22×C4111yescharacteristic, complemented
498C2×#100C22×C4111yescharacteristic, complemented
499#408C22×C4111yescharacteristic, complemented
500#407C22×C4111yescharacteristic
501C2×C22⋊C8C22×C4111yescharacteristic
502#405C22×C4111yescharacteristic, complemented
503#343C22×C4111yescharacteristic, complemented
504#343C22×C4111yescharacteristic, complemented
505#341C22×C4111yescharacteristic, complemented
506#341C22×C4111yescharacteristic, complemented
507C41#2514011yescharacteristic, direct product factor, Sylow
508C25—21no—
509C2×#41C23×C4111yescharacteristic
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C23×C4111yescharacteristic
521C22×D4C23×C4111yescharacteristic
522C22×D4C23×C4111yescharacteristic
523C23×C4C23×C4111yescharacteristic
524AGL(1,ℤ/8)—22no—
525AGL(1,ℤ/8)—22no—
526AGL(1,ℤ/8)—22no—
527AGL(1,ℤ/8)—41no—
528AGL(1,ℤ/8)—41no—
529AGL(1,ℤ/8)—41no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×SD16—21no—
533C2×D8—22no—
534C2×D8—21no—
535C2×D8—21no—
536C2×D8—21no—
537C2×D8—22no—
538C2×D8—21no—
539C2×D8—21no—
540C2×D8—21no—
541C2×D8—21no—
542C2×D8—41no—
543C2×D8—41no—
544#131—22no—
545#131—41no—
546C2×M16—21no—
547C2×M16—21no—
548C2×M16—21no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16C23×C4111yescharacteristic
554C2×M16C23×C4111yescharacteristic
555C2×M16C23×C4111yescharacteristic
556C2×M16C23×C4111yescharacteristic
557C2×M16C23×C4111yescharacteristic
558C2×M16C23×C4111yescharacteristic
559C22×C8—21no—
560C22×C8—21no—
561C22×C8—21no—
562C22×C8C23×C4111yescharacteristic
563C22×C8C23×C4111yescharacteristic
564#123—21no—
565C22⋊Q8D4×C4111yescharacteristic
566C22⋊Q8D4×C4111yescharacteristic
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121D4×C4111yescharacteristic
572#121D4×C4111yescharacteristic
573#120—21no—
574C4×D4—21no—
575C4×D4—21no—
576#117C23×C4111yescharacteristic
577C2×C4⋊C4C23×C4111yescharacteristic
578C2×C22⋊C4—21no—
579#108—22no—
580#108—41no—
581#107—21no—
582#106—21no—
583C4⋊C8—21no—
584C4⋊C8—21no—
585#103—21no—
586#102—21no—
587#102—21no—
588#102—21no—
589#102—21no—
590#102—21no—
591#102—21no—
592#102—21no—
593#102—21no—
594#102—21no—
595#102—21no—
596#102—21no—
597#100—22no—
598#100—22no—
599#100—22no—
600#100—22no—
601#100—41no—
602#100D4×C4114yescomplemented
603C22⋊C8—21no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8D4×C4111yescharacteristic
608C22⋊C8D4×C4111yescharacteristic
609C22⋊C8D4×C4111yescharacteristic
610C22⋊C8D4×C4111yescharacteristic
611#97—21no—
612C4×C8—21no—
613C24—24no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—42no—
618C24—41no—
619C24—41no—
620C24—82no—
621C24—82no—
622C24#41×C4111yescharacteristic
623#41—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627C2×Q8C2×D4×C4111yescharacteristic
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—41no—
658C2×D4—41no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—82no—
662C2×D4C2×D4×C4112yes—
663C2×D4C2×D4×C4111yescharacteristic
664C2×D4#41×C4112yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4C2×D4×C4111yescharacteristic
672C22×C4C2×D4×C4111yescharacteristic
673C22×C4C2×D4×C4111yescharacteristic
674C22×C4C2×D4×C4111yescharacteristic
675C22×C4#41×C4111yescharacteristic
676C22×C4C24×C4111yescharacteristic
677SD16—42no—
678SD16—42no—
679SD16—42no—
680D8—42no—
681D8—42no—
682D8—42no—
683D8—42no—
684D8—42no—
685D8—42no—
686D8—42no—
687M16—21no—
688M16—21no—
689M16—21no—
690M16—21no—
691M16—21no—
692M16—21no—
693M16—21no—
694M16—21no—
695M16—21no—
696M16—21no—
697M16—42no—
698M16—42no—
699M16—42no—
700M16C2×D4×C4112yes—
701M16C2×D4×C4112yes—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—42no—
713C2×C8—42no—
714C2×C8—42no—
715C2×C8C2×D4×C4111yescharacteristic
716C2×C8C2×D4×C4111yescharacteristic
717C2×C8C2×D4×C4111yescharacteristic
718C2×C8C2×D4×C4111yescharacteristic
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4C2×D4×C4111yescharacteristic
724C4⋊C4C2×D4×C4111yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—41no—
731C22⋊C4—41no—
732C42—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—41no—
740C23—44no—
741C23—44no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—82no—
754C23—82no—
755C23—82no—
756C23—81no—
757C23—81no—
758C23—88no—
759C23—88no—
760C23—82no—
761C23#121×C4111yescharacteristic
762C23#121×C4111yescharacteristic
763C23C2×#41×C4111yescharacteristic
764Q8—21no—
765Q8—21no—
766D4—21no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—21no—
771D4—22no—
772D4—44no—
773D4—44no—
774D4—41no—
775D4—41no—
776D4—42no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—81no—
786D4—82no—
787D4—82no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—81no—
805C2×C4#121×C4111yescharacteristic
806C2×C4#121×C4111yescharacteristic
807C2×C4C22×D4×C4111yescharacteristic
808C2×C4C22×D4×C4111yescharacteristic
809C2×C4C22×D4×C4111yescharacteristic
810C2×C4C2×#41×C4111yescharacteristic
811C2×C4H(5,𝔽2)×C4111yescharacteristic
812C2×C4H(5,𝔽2)×C4111yescharacteristic
813C8—21no—
814C8—21no—
815C8—22no—
816C8—22no—
817C8—21no—
818C8—21no—
819C8—41no—
820C8—41no—
821C8—41no—
822C8—41no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—88no—
842C22—88no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—161no—
851C22—161no—
852C22C41×#47212yescomplemented
853C22C2×#121×C4111yescharacteristic
854C22C41×#52511yescharacteristic
855C22C41×#53811yescharacteristic
856C4—21no—
857C4—21no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—81no—
862C4D42×C4111yescharacteristic
863C4D42×C4111yescharacteristic
864C4C41×#54611yescharacteristic
865C4C41×#54611yescharacteristic
866C2—21no—
867C2—21no—
868C2—22no—
869C2—41no—
870C2—81no—
871C2—82no—
872C2—82no—
873C2—161no—
874C2C41×#242411yescharacteristic
875C2C2×C41×#47211yescharacteristic
876C2C41×#306811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC22×C4C24×C41
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×#472C2semidirect
2. C41×#3055C2semidirect
3. C41×#3003C2semidirect
4. C2×C41×#447C2semidirect
5. C41×#2933C2semidirect
6. C22×#100×C41C2semidirect
7. C41×#2063C2semidirect
8. C41×#2051C2semidirect
9. C41×#2045C2semidirect
10. C41×#2018C2semidirect
11. C41×#1978C2semidirect
12. C41×#1931C2semidirect
13. C41×#1907C2semidirect
14. C41×#1900C2semidirect
15. C41×#1855C2semidirect
19. C2×AGL(1,ℤ/8)×C41C22semidirect
22. C2×#131×C41C22semidirect
44. C2×#108×C41C22semidirect
45. C2×#108×C41C22semidirect
46. C41×#428C22semidirect
47. C41×#424C22semidirect
50. C41×#418C22semidirect
51. C41×#417C22semidirect
59. C2×#100×C41C22semidirect
60. C2×#100×C41C22semidirect
61. C41×#408C22semidirect
64. C41×#405C22semidirect
65. C41×#343C22semidirect
66. C41×#343C22semidirect
67. C41×#341C22semidirect
68. C41×#341C22semidirect
163. #100×C41D4semidirect
384. #25140C41direct (N × H)
414. C22×C41#472semidirect
428. C2×#472C2×C41semidirect
429. #3055C2×C41semidirect
430. #3003C2×C41semidirect
431. C2×#447C2×C41semidirect
432. #2933C2×C41semidirect
433. C22×#100C2×C41semidirect
434. #2063C2×C41semidirect
435. #2051C2×C41semidirect
436. #2045C2×C41semidirect
437. #2018C2×C41semidirect
438. #1978C2×C41semidirect
439. #1931C2×C41semidirect
440. #1907C2×C41semidirect
441. #1900C2×C41semidirect
442. #1855C2×C41semidirect
457. C2×AGL(1,ℤ/8)C22×C41semidirect
460. C2×#131C22×C41semidirect
482. C2×#108C22×C41semidirect
483. C2×#108C22×C41semidirect
484. #428C22×C41semidirect
485. #424C22×C41semidirect
488. #418C22×C41semidirect
489. #417C22×C41semidirect
497. C2×#100C22×C41semidirect
498. C2×#100C22×C41semidirect
499. #408C22×C41semidirect
502. #405C22×C41semidirect
503. #343C22×C41semidirect
504. #343C22×C41semidirect
505. #341C22×C41semidirect
506. #341C22×C41semidirect
507. C41#25140direct (N × H)
602. #100D4×C41semidirect
852. C22C41×#472semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4722
C41×#30552
C41×#30032
C2×C41×#4472
C41×#29332
C22×#100×C412
C41×#20632
C41×#20512
C41×#20452
C41×#20182
C41×#19782
C41×#19312
C41×#19072
C41×#19002
C41×#18552
#2514041