Finite Group Databasebeta

← C41×#24403 #23800604

Subgroups — C41×#24403 #23800604

Order 10496.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#575C211yesmaximal, characteristic
2C2×C41×#473C211yesmaximal, characteristic, complemented
3C2×C41×#471C211yesmaximal, characteristic, complemented
4C41×#3007C211yesmaximal, characteristic, complemented
5C2×C41×#452C211yesmaximal, characteristic, complemented
6C41×#2880C211yesmaximal, characteristic, complemented
7C41×#2052C211yesmaximal, characteristic, complemented
8C41×#2051C211yesmaximal, characteristic, complemented
9C41×#2020C211yesmaximal, characteristic, complemented
10C41×#2019C211yesmaximal, characteristic, complemented
11C41×#1908C211yesmaximal, characteristic, complemented
12C41×#1907C211yesmaximal, characteristic, complemented
13C41×#1901C211yesmaximal, characteristic, complemented
14C41×#1855C211yesmaximal, characteristic, complemented
15C41×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C22×#41×C41C2211yescharacteristic
18C41×#575—24no—
19C41×#575—24no—
20C2×#137×C41—21no—
21C2×#137×C41C2211yescharacteristic
22C2×#137×C41C2211yescharacteristic
23C2×#137×C41C2211yescharacteristic
24C2×#137×C41C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C41—21no—
26C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
28C2×#135×C41—21no—
29C2×#135×C41—21no—
30C22×Q16×C41C2211yescharacteristic, complemented
31C22×SD16×C41C2211yescharacteristic, complemented
32C2×#131×C41C2211yescharacteristic
33C2×#131×C41C2211yescharacteristic
34C22×M16×C41C2211yescharacteristic
35C2×C22⋊Q8×C41C2211yescharacteristic
36C41×#473—24no—
37C41×#471—24no—
38C41×#452—21no—
39C41×#452—21no—
40C41×#452—21no—
41C41×#452—21no—
42C41×#452—21no—
43C41×#452—21no—
44C41×#451—21no—
45C41×#450—21no—
46C2×#108×C41C2211yescharacteristic, complemented
47C2×#108×C41C2211yescharacteristic, complemented
48C41×#417C2211yescharacteristic
49C41×#417C2211yescharacteristic
50C2×#103×C41C2211yescharacteristic, complemented
51C2×#102×C41C2211yescharacteristic, complemented
52C2×#101×C41C2211yescharacteristic, complemented
53C2×#101×C41C2211yescharacteristic, complemented
54C2×#101×C41C2211yescharacteristic, complemented
55C2×#101×C41C2211yescharacteristic, complemented
56C2×#100×C41C2211yescharacteristic, complemented
57C2×#100×C41C2211yescharacteristic, complemented
58C41×#408—21no—
59C41×#408—21no—
60C41×#408C2211yescharacteristic
61C41×#408C2211yescharacteristic
62C41×#407—21no—
63C41×#407C2211yescharacteristic
64C41×#407C2211yescharacteristic
65C2×C22⋊C8×C41—21no—
66C2×C22⋊C8×C41C2211yescharacteristic
67C41×#343C2211yescharacteristic, complemented
68C41×#343C2211yescharacteristic, complemented
69C41×#341C2211yescharacteristic, complemented
70C41×#341C2211yescharacteristic, complemented
71C2×#41×C41—21no—
72C2×#41×C41—21no—
73C2×#41×C41—22no—
74C2×#41×C41—22no—
75C2×#41×C41—22no—
76C2×#41×C41—22no—
77C2×#41×C41—21no—
78C2×#41×C41—21no—
79C2×#41×C41—21no—
80C2×#41×C41—21no—
81C2×#41×C41—41no—
82C2×#41×C41—41no—
83C2×#41×C41—41no—
84C2×#41×C41—41no—
85C2×#41×C41D411yescharacteristic
86C2×#41×C41D411yescharacteristic
87C2×#41×C41C2311yescharacteristic
88C2×#41×C41C2311yescharacteristic
89C22×Q8×C41D411yescharacteristic
90C22×Q8×C41C2311yescharacteristic
91C22×Q8×C41C2311yescharacteristic
92C22×D4×C41—21no—
93C22×D4×C41—21no—
94C22×D4×C41D411yescharacteristic
95C22×D4×C41C2311yescharacteristic
96C23×C4×C41—21no—
97C23×C4×C41—21no—
98C23×C4×C41C2311yescharacteristic
99#137×C41—28no—
100#137×C41—22no—
101#137×C41—22no—
102#137×C41—22no—
103#137×C41—22no—
104#137×C41—22no—
105#137×C41—41no—
106#137×C41—41no—
107#137×C41D414yes—
108AGL(1,ℤ/8)×C41—28no—
109AGL(1,ℤ/8)×C41—22no—
110AGL(1,ℤ/8)×C41—22no—
111AGL(1,ℤ/8)×C41—22no—
112AGL(1,ℤ/8)×C41D414yes—
113#135×C41—28no—
114#135×C41—28no—
115C2×Q16×C41—21no—
116C2×Q16×C41—21no—
117C2×Q16×C41—22no—
118C2×Q16×C41—21no—
119C2×Q16×C41—21no—
120C2×Q16×C41—21no—
121C2×Q16×C41—21no—
122C2×Q16×C41—41no—
123C2×SD16×C41—21no—
124C2×SD16×C41—21no—
125C2×SD16×C41—21no—
126C2×SD16×C41—21no—
127C2×SD16×C41—22no—
128C2×SD16×C41—21no—
129C2×SD16×C41—21no—
130C2×SD16×C41—21no—
131C2×SD16×C41—21no—
132C2×SD16×C41—41no—
133C2×D8×C41—21no—
134C2×D8×C41—21no—
135#131×C41—22no—
136#131×C41—22no—
137#131×C41—41no—
138#131×C41—41no—
139C2×M16×C41—21no—
140C2×M16×C41—22no—
141C2×M16×C41—22no—
142C2×M16×C41—21no—
143C2×M16×C41—21no—
144C2×M16×C41C2311yescharacteristic
145C2×M16×C41C2311yescharacteristic
146C2×M16×C41C2311yescharacteristic
147C2×M16×C41C2311yescharacteristic
148C2×M16×C41C2311yescharacteristic
149C2×M16×C41C2311yescharacteristic
150C22×C8×C41—21no—
151C22×C8×C41—21no—
152C22×C8×C41—21no—
153C22×C8×C41C2311yescharacteristic
154C22×C8×C41C2311yescharacteristic
155C22⋊Q8×C41—21no—
156C22⋊Q8×C41—21no—
157C22⋊Q8×C41—21no—
158C22⋊Q8×C41—21no—
159C2×C4⋊C4×C41—21no—
160C2×C4⋊C4×C41C2311yescharacteristic
161C2×C22⋊C4×C41—21no—
162#108×C41—22no—
163#108×C41—22no—
164#103×C41—21no—
165#103×C41—21no—
166#103×C41—21no—
167#103×C41—21no—
168#102×C41—21no—
169#102×C41—21no—
170#102×C41—21no—
171#102×C41—21no—
172#101×C41—22no—
173#101×C41—22no—
174#101×C41—22no—
175#101×C41—41no—
176#100×C41—22no—
177#100×C41—41no—
178C22⋊C8×C41—21no—
179C22⋊C8×C41—21no—
180C22⋊C8×C41—21no—
181C22⋊C8×C41—21no—
182C22⋊C8×C41—21no—
183C22⋊C8×C41—21no—
184C22⋊C8×C41—21no—
185C22⋊C8×C41—21no—
186C22⋊C8×C41D411yescharacteristic
187C22⋊C8×C41D411yescharacteristic
188C22⋊C8×C41D411yescharacteristic
189C22⋊C8×C41D411yescharacteristic
190C24×C41—21no—
191C24×C41—21no—
192C24×C41#4111yescharacteristic
193#41×C41—21no—
194#41×C41—21no—
195#41×C41—24no—
196#41×C41—24no—
197#41×C41—22no—
198#41×C41—22no—
199#41×C41—21no—
200#41×C41—21no—
201#41×C41—21no—
202#41×C41—21no—
203#41×C41—42no—
204#41×C41—42no—
205#41×C41—41no—
206#41×C41—41no—
207#41×C41—42no—
208#41×C41—42no—
209#41×C41—42no—
210#41×C41—42no—
211#41×C41—42no—
212#41×C41—42no—
213#41×C41—42no—
214#41×C41—42no—
215#41×C41C2×D412yes—
216#41×C41C2×D412yes—
217C2×Q8×C41—21no—
218C2×Q8×C41—21no—
219C2×Q8×C41—22no—
220C2×Q8×C41—21no—
221C2×Q8×C41—21no—
222C2×Q8×C41—21no—
223C2×Q8×C41—21no—
224C2×Q8×C41—21no—
225C2×Q8×C41—21no—
226C2×Q8×C41—21no—
227C2×Q8×C41—21no—
228C2×Q8×C41—21no—
229C2×Q8×C41—21no—
230C2×Q8×C41—41no—
231C2×Q8×C41C2×D412yes—
232C2×Q8×C41C2×D411yescharacteristic
233C2×Q8×C41C2×D411yescharacteristic
234C2×D4×C41—21no—
235C2×D4×C41—22no—
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—21no—
243C2×D4×C41—21no—
244C2×D4×C41—21no—
245C2×D4×C41—41no—
246C2×D4×C41—42no—
247C2×D4×C41—42no—
248C2×D4×C41—42no—
249C2×D4×C41—42no—
250C2×D4×C41—41no—
251C2×D4×C41—41no—
252C2×D4×C41C2×D412yes—
253C2×D4×C41C2×D411yescharacteristic
254C2×D4×C41C2×D411yescharacteristic
255C22×C4×C41—21no—
256C22×C4×C41—21no—
257C22×C4×C41—21no—
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—21no—
265C22×C4×C41—21no—
266C22×C4×C41—21no—
267C22×C4×C41—42no—
268C22×C4×C41—42no—
269C22×C4×C41—42no—
270C22×C4×C41—42no—
271C22×C4×C41—41no—
272C22×C4×C41—41no—
273C22×C4×C41C2×D411yescharacteristic
274C22×C4×C41C2×D411yescharacteristic
275C22×C4×C41C2×D411yescharacteristic
276C22×C4×C41C2×D411yescharacteristic
277C22×C4×C41#4111yescharacteristic
278C22×C4×C41C2411yescharacteristic
279Q16×C41—24no—
280Q16×C41—24no—
281Q16×C41—42no—
282Q16×C41—42no—
283Q16×C41—42no—
284Q16×C41—42no—
285SD16×C41—24no—
286SD16×C41—24no—
287SD16×C41—24no—
288SD16×C41—24no—
289SD16×C41—42no—
290SD16×C41—42no—
291SD16×C41—42no—
292SD16×C41—42no—
293D8×C41—24no—
294D8×C41—24no—
295M16×C41—24no—
296M16×C41—21no—
297M16×C41—21no—
298M16×C41—21no—
299M16×C41—21no—
300M16×C41—21no—
301M16×C41—21no—
302M16×C41—21no—
303M16×C41—21no—
304M16×C41—21no—
305M16×C41—21no—
306M16×C41—42no—
307M16×C41—42no—
308M16×C41C2×D412yes—
309M16×C41C2×D412yes—
310C2×C8×C41—24no—
311C2×C8×C41—21no—
312C2×C8×C41—21no—
313C2×C8×C41—21no—
314C2×C8×C41—21no—
315C2×C8×C41—21no—
316C2×C8×C41—21no—
317C2×C8×C41—21no—
318C2×C8×C41—21no—
319C2×C8×C41—21no—
320C2×C8×C41—21no—
321C2×C8×C41—42no—
322C2×C8×C41—42no—
323C2×C8×C41C2×D411yescharacteristic
324C2×C8×C41C2×D411yescharacteristic
325C2×C8×C41C2×D411yescharacteristic
326C2×C8×C41C2×D411yescharacteristic
327C4⋊C4×C41—21no—
328C4⋊C4×C41—21no—
329C4⋊C4×C41—41no—
330C4⋊C4×C41—41no—
331C22⋊C4×C41—41no—
332C22⋊C4×C41—41no—
333C23×C41—21no—
334C23×C41—21no—
335C23×C41—21no—
336C23×C41—21no—
337C23×C41—22no—
338C23×C41—41no—
339C23×C41—41no—
340C23×C41—42no—
341C23×C41—42no—
342C23×C41—41no—
343C23×C41—41no—
344C23×C41—81no—
345C23×C41—81no—
346C23×C41—81no—
347C23×C41#12111yescharacteristic
348C23×C41#12111yescharacteristic
349C23×C41C2×#4111yescharacteristic
350Q8×C41—21no—
351Q8×C41—21no—
352Q8×C41—22no—
353Q8×C41—21no—
354Q8×C41—22no—
355Q8×C41—42no—
356Q8×C41—41no—
357Q8×C41—41no—
358Q8×C41—41no—
359Q8×C41—41no—
360Q8×C41—41no—
361Q8×C41—41no—
362Q8×C41#12012yes—
363D4×C41—22no—
364D4×C41—22no—
365D4×C41—21no—
366D4×C41—22no—
367D4×C41—21no—
368D4×C41—21no—
369D4×C41—22no—
370D4×C41—42no—
371D4×C41—42no—
372D4×C41—42no—
373D4×C41—44no—
374D4×C41—44no—
375D4×C41—41no—
376D4×C41—41no—
377D4×C41—41no—
378D4×C41—41no—
379D4×C41#12012yes—
380C2×C4×C41—21no—
381C2×C4×C41—21no—
382C2×C4×C41—21no—
383C2×C4×C41—21no—
384C2×C4×C41—21no—
385C2×C4×C41—21no—
386C2×C4×C41—21no—
387C2×C4×C41—22no—
388C2×C4×C41—22no—
389C2×C4×C41—21no—
390C2×C4×C41—21no—
391C2×C4×C41—21no—
392C2×C4×C41—21no—
393C2×C4×C41—21no—
394C2×C4×C41—22no—
395C2×C4×C41—42no—
396C2×C4×C41—42no—
397C2×C4×C41—42no—
398C2×C4×C41—44no—
399C2×C4×C41—44no—
400C2×C4×C41—41no—
401C2×C4×C41—41no—
402C2×C4×C41—41no—
403C2×C4×C41—41no—
404C2×C4×C41—41no—
405C2×C4×C41—41no—
406C2×C4×C41—41no—
407C2×C4×C41—41no—
408C2×C4×C41—81no—
409C2×C4×C41#12111yescharacteristic
410C2×C4×C41#12111yescharacteristic
411C2×C4×C41C22×D411yescharacteristic
412C2×C4×C41C22×D411yescharacteristic
413C2×C4×C41C22×D411yescharacteristic
414C2×C4×C41C22×D411yescharacteristic
415C2×C4×C41H(5,𝔽2)11yescharacteristic
416C2×C4×C41H(5,𝔽2)11yescharacteristic
417C8×C41—22no—
418C8×C41—22no—
419C8×C41—21no—
420C8×C41—21no—
421C8×C41—21no—
422C8×C41—21no—
423C8×C41—41no—
424C8×C41—41no—
425C8×C41—41no—
426C8×C41—41no—
427#24403C4111yesmaximal, characteristic, direct product factor, Sylow
428C22×C41—21no—
429C22×C41—21no—
430C22×C41—21no—
431C22×C41—21no—
432C22×C41—22no—
433C22×C41—21no—
434C22×C41—21no—
435C22×C41—21no—
436C22×C41—21no—
437C22×C41—41no—
438C22×C41—41no—
439C22×C41—41no—
440C22×C41—42no—
441C22×C41—41no—
442C22×C41—41no—
443C22×C41—81no—
444C22×C41—81no—
445C22×C41—82no—
446C22×C41—82no—
447C22×C41—84no—
448C22×C41—81no—
449C22×C41—81no—
450C22×C41C2×#12111yescharacteristic
451C22×C41#54611yescharacteristic
452C22×C41#54611yescharacteristic
453C4×C41—21no—
454C4×C41—21no—
455C4×C41—22no—
456C4×C41—41no—
457C4×C41—42no—
458C4×C41—81no—
459C4×C41—81no—
460C4×C41C2×#12011yescharacteristic
461C4×C41#53411yescharacteristic
462C4×C41D4211yescharacteristic
463C4×C41D4211yescharacteristic
464C2×#575C2×C4111yescharacteristic
465C2×#473C2×C4111yescharacteristic, complemented
466C2×#471C2×C4111yescharacteristic, complemented
467#3007C2×C4111yescharacteristic, complemented
468C2×#452C2×C4111yescharacteristic, complemented
469#2880C2×C4111yescharacteristic, complemented
470#2052C2×C4111yescharacteristic, complemented
471#2051C2×C4111yescharacteristic, complemented
472#2020C2×C4111yescharacteristic, complemented
473#2019C2×C4111yescharacteristic, complemented
474#1908C2×C4111yescharacteristic, complemented
475#1907C2×C4111yescharacteristic, complemented
476#1901C2×C4111yescharacteristic, complemented
477#1855C2×C4111yescharacteristic, complemented
478#1785C2×C4111yescharacteristic, complemented
479C2×C41—21no—
480C2×C41—21no—
481C2×C41—41no—
482C2×C41—41no—
483C2×C41—42no—
484C2×C41—81no—
485C2×C41—82no—
486C2×C41#241011yescharacteristic
487C2×C41#306711yescharacteristic
488C2×C41#306911yescharacteristic
489C22×#41C22×C4111yescharacteristic
490C22×#41C22×C4111yescharacteristic
491#575—24no—
492#575—24no—
493C2×#137—21no—
494C2×#137C22×C4111yescharacteristic
495C2×#137C22×C4111yescharacteristic
496C2×#137C22×C4111yescharacteristic
497C2×#137C22×C4111yescharacteristic
498C2×AGL(1,ℤ/8)—21no—
499C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
500C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
501C2×#135—21no—
502C2×#135—21no—
503C22×Q16C22×C4111yescharacteristic, complemented
504C22×SD16C22×C4111yescharacteristic, complemented
505C2×#131C22×C4111yescharacteristic
506C2×#131C22×C4111yescharacteristic
507C22×M16C22×C4111yescharacteristic
508C2×C22⋊Q8C22×C4111yescharacteristic
509#473—24no—
510#471—24no—
511#452—21no—
512#452—21no—
513#452—21no—
514#452—21no—
515#452—21no—
516#452—21no—
517#451—21no—
518#450—21no—
519C2×#108C22×C4111yescharacteristic, complemented
520C2×#108C22×C4111yescharacteristic, complemented
521#417C22×C4111yescharacteristic
522#417C22×C4111yescharacteristic
523C2×#103C22×C4111yescharacteristic, complemented
524C2×#102C22×C4111yescharacteristic, complemented
525C2×#101C22×C4111yescharacteristic, complemented
526C2×#101C22×C4111yescharacteristic, complemented
527C2×#101C22×C4111yescharacteristic, complemented
528C2×#101C22×C4111yescharacteristic, complemented
529C2×#100C22×C4111yescharacteristic, complemented
530C2×#100C22×C4111yescharacteristic, complemented
531#408—21no—
532#408—21no—
533#408C22×C4111yescharacteristic
534#408C22×C4111yescharacteristic
535#407—21no—
536#407C22×C4111yescharacteristic
537#407C22×C4111yescharacteristic
538C2×C22⋊C8—21no—
539C2×C22⋊C8C22×C4111yescharacteristic
540#343C22×C4111yescharacteristic, complemented
541#343C22×C4111yescharacteristic, complemented
542#341C22×C4111yescharacteristic, complemented
543#341C22×C4111yescharacteristic, complemented
544C41#2440311yescharacteristic, direct product factor, Sylow
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—41no—
556C2×#41—41no—
557C2×#41—41no—
558C2×#41—41no—
559C2×#41D4×C4111yescharacteristic
560C2×#41D4×C4111yescharacteristic
561C2×#41C23×C4111yescharacteristic
562C2×#41C23×C4111yescharacteristic
563C22×Q8D4×C4111yescharacteristic
564C22×Q8C23×C4111yescharacteristic
565C22×Q8C23×C4111yescharacteristic
566C22×D4—21no—
567C22×D4—21no—
568C22×D4D4×C4111yescharacteristic
569C22×D4C23×C4111yescharacteristic
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C4111yescharacteristic
573#137—28no—
574#137—22no—
575#137—22no—
576#137—22no—
577#137—22no—
578#137—22no—
579#137—41no—
580#137—41no—
581#137D4×C4114yes—
582AGL(1,ℤ/8)—28no—
583AGL(1,ℤ/8)—22no—
584AGL(1,ℤ/8)—22no—
585AGL(1,ℤ/8)—22no—
586AGL(1,ℤ/8)D4×C4114yes—
587#135—28no—
588#135—28no—
589C2×Q16—21no—
590C2×Q16—21no—
591C2×Q16—22no—
592C2×Q16—21no—
593C2×Q16—21no—
594C2×Q16—21no—
595C2×Q16—21no—
596C2×Q16—41no—
597C2×SD16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—21no—
601C2×SD16—22no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—41no—
607C2×D8—21no—
608C2×D8—21no—
609#131—22no—
610#131—22no—
611#131—41no—
612#131—41no—
613C2×M16—21no—
614C2×M16—22no—
615C2×M16—22no—
616C2×M16—21no—
617C2×M16—21no—
618C2×M16C23×C4111yescharacteristic
619C2×M16C23×C4111yescharacteristic
620C2×M16C23×C4111yescharacteristic
621C2×M16C23×C4111yescharacteristic
622C2×M16C23×C4111yescharacteristic
623C2×M16C23×C4111yescharacteristic
624C22×C8—21no—
625C22×C8—21no—
626C22×C8—21no—
627C22×C8C23×C4111yescharacteristic
628C22×C8C23×C4111yescharacteristic
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4C23×C4111yescharacteristic
635C2×C22⋊C4—21no—
636#108—22no—
637#108—22no—
638#103—21no—
639#103—21no—
640#103—21no—
641#103—21no—
642#102—21no—
643#102—21no—
644#102—21no—
645#102—21no—
646#101—22no—
647#101—22no—
648#101—22no—
649#101—41no—
650#100—22no—
651#100—41no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656C22⋊C8—21no—
657C22⋊C8—21no—
658C22⋊C8—21no—
659C22⋊C8—21no—
660C22⋊C8D4×C4111yescharacteristic
661C22⋊C8D4×C4111yescharacteristic
662C22⋊C8D4×C4111yescharacteristic
663C22⋊C8D4×C4111yescharacteristic
664C24—21no—
665C24—21no—
666C24#41×C4111yescharacteristic
667#41—21no—
668#41—21no—
669#41—24no—
670#41—24no—
671#41—22no—
672#41—22no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—21no—
677#41—42no—
678#41—42no—
679#41—41no—
680#41—41no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41C2×D4×C4112yes—
690#41C2×D4×C4112yes—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—41no—
705C2×Q8C2×D4×C4112yes—
706C2×Q8C2×D4×C4111yescharacteristic
707C2×Q8C2×D4×C4111yescharacteristic
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—41no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4C2×D4×C4112yes—
727C2×D4C2×D4×C4111yescharacteristic
728C2×D4C2×D4×C4111yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4C2×D4×C4111yescharacteristic
748C22×C4C2×D4×C4111yescharacteristic
749C22×C4C2×D4×C4111yescharacteristic
750C22×C4C2×D4×C4111yescharacteristic
751C22×C4#41×C4111yescharacteristic
752C22×C4C24×C4111yescharacteristic
753Q16—24no—
754Q16—24no—
755Q16—42no—
756Q16—42no—
757Q16—42no—
758Q16—42no—
759SD16—24no—
760SD16—24no—
761SD16—24no—
762SD16—24no—
763SD16—42no—
764SD16—42no—
765SD16—42no—
766SD16—42no—
767D8—24no—
768D8—24no—
769M16—24no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—21no—
778M16—21no—
779M16—21no—
780M16—42no—
781M16—42no—
782M16C2×D4×C4112yes—
783M16C2×D4×C4112yes—
784C2×C8—24no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—42no—
796C2×C8—42no—
797C2×C8C2×D4×C4111yescharacteristic
798C2×C8C2×D4×C4111yescharacteristic
799C2×C8C2×D4×C4111yescharacteristic
800C2×C8C2×D4×C4111yescharacteristic
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—41no—
804C4⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—41no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23#121×C4111yescharacteristic
822C23#121×C4111yescharacteristic
823C23C2×#41×C4111yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—22no—
827Q8—21no—
828Q8—22no—
829Q8—42no—
830Q8—41no—
831Q8—41no—
832Q8—41no—
833Q8—41no—
834Q8—41no—
835Q8—41no—
836Q8#120×C4112yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—22no—
841D4—21no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4#120×C4112yes—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—81no—
883C2×C4#121×C4111yescharacteristic
884C2×C4#121×C4111yescharacteristic
885C2×C4C22×D4×C4111yescharacteristic
886C2×C4C22×D4×C4111yescharacteristic
887C2×C4C22×D4×C4111yescharacteristic
888C2×C4C22×D4×C4111yescharacteristic
889C2×C4H(5,𝔽2)×C4111yescharacteristic
890C2×C4H(5,𝔽2)×C4111yescharacteristic
891C8—22no—
892C8—22no—
893C8—21no—
894C8—21no—
895C8—21no—
896C8—21no—
897C8—41no—
898C8—41no—
899C8—41no—
900C8—41no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—22no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—81no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—84no—
921C22—81no—
922C22—81no—
923C22C2×#121×C4111yescharacteristic
924C22C41×#54611yescharacteristic
925C22C41×#54611yescharacteristic
926C4—21no—
927C4—21no—
928C4—22no—
929C4—41no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×#120×C4111yescharacteristic
934C4C41×#53411yescharacteristic
935C4D42×C4111yescharacteristic
936C4D42×C4111yescharacteristic
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C41×#241011yescharacteristic
945C2C41×#306711yescharacteristic
946C2C41×#306911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#575C2
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
2. C2×C41×#473C2semidirect
3. C2×C41×#471C2semidirect
4. C41×#3007C2semidirect
5. C2×C41×#452C2semidirect
6. C41×#2880C2semidirect
7. C41×#2052C2semidirect
8. C41×#2051C2semidirect
9. C41×#2020C2semidirect
10. C41×#2019C2semidirect
11. C41×#1908C2semidirect
12. C41×#1907C2semidirect
13. C41×#1901C2semidirect
14. C41×#1855C2semidirect
15. C41×#1785C2semidirect
30. C22×Q16×C41C22semidirect
31. C22×SD16×C41C22semidirect
46. C2×#108×C41C22semidirect
47. C2×#108×C41C22semidirect
50. C2×#103×C41C22semidirect
51. C2×#102×C41C22semidirect
52. C2×#101×C41C22semidirect
53. C2×#101×C41C22semidirect
54. C2×#101×C41C22semidirect
55. C2×#101×C41C22semidirect
56. C2×#100×C41C22semidirect
57. C2×#100×C41C22semidirect
67. C41×#343C22semidirect
68. C41×#343C22semidirect
69. C41×#341C22semidirect
70. C41×#341C22semidirect
427. #24403C41direct (N × H)
465. C2×#473C2×C41semidirect
466. C2×#471C2×C41semidirect
467. #3007C2×C41semidirect
468. C2×#452C2×C41semidirect
469. #2880C2×C41semidirect
470. #2052C2×C41semidirect
471. #2051C2×C41semidirect
472. #2020C2×C41semidirect
473. #2019C2×C41semidirect
474. #1908C2×C41semidirect
475. #1907C2×C41semidirect
476. #1901C2×C41semidirect
477. #1855C2×C41semidirect
478. #1785C2×C41semidirect
503. C22×Q16C22×C41semidirect
504. C22×SD16C22×C41semidirect
519. C2×#108C22×C41semidirect
520. C2×#108C22×C41semidirect
523. C2×#103C22×C41semidirect
524. C2×#102C22×C41semidirect
525. C2×#101C22×C41semidirect
526. C2×#101C22×C41semidirect
527. C2×#101C22×C41semidirect
528. C2×#101C22×C41semidirect
529. C2×#100C22×C41semidirect
530. C2×#100C22×C41semidirect
540. #343C22×C41semidirect
541. #343C22×C41semidirect
542. #341C22×C41semidirect
543. #341C22×C41semidirect
544. C41#24403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5752
C2×C41×#4732
C2×C41×#4712
C41×#30072
C2×C41×#4522
C41×#28802
C41×#20522
C41×#20512
C41×#20202
C41×#20192
C41×#19082
C41×#19072
C41×#19012
C41×#18552
C41×#17852
#2440341