Finite Group Databasebeta

← C41×#16270 #23792471

Subgroups — C41×#16270 #23792471

Order 10496.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#397C211yesmaximal, characteristic, complemented
2C2×C41×#392C211yesmaximal, characteristic
3C2×C41×#386C211yesmaximal, characteristic, complemented
4C2×C41×#386C211yesmaximal, characteristic, complemented
5C41×#1443C211yesmaximal, characteristic, complemented
6C41×#1443C211yesmaximal, characteristic, complemented
7C41×#1440C211yesmaximal, characteristic, complemented
8C41×#1440C211yesmaximal, characteristic, complemented
9C41×#1439C211yesmaximal, characteristic, complemented
10C41×#1439C211yesmaximal, characteristic, complemented
11C41×#1438C211yesmaximal, characteristic, complemented
12C41×#1438C211yesmaximal, characteristic, complemented
13C41×#1438C211yesmaximal, characteristic, complemented
14C41×#1438C211yesmaximal, characteristic, complemented
15C41×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C41C2211yescharacteristic
17C23×D4×C41C2211yescharacteristic
18C23×D4×C41C2211yescharacteristic
19C24×C4×C41C2211yescharacteristic
20C22×C4⋊C4×C41C2211yescharacteristic
21C22×C22⋊C4×C41C2211yescharacteristic
22C22×C22⋊C4×C41C2211yescharacteristic
23C22×C22⋊C4×C41C2211yescharacteristic
24C22×C22⋊C4×C41C2211yescharacteristic
25C22×C22⋊C4×C41C2211yescharacteristic
26C22×C22⋊C4×C41C2211yescharacteristic
27C22×C22⋊C4×C41C2211yescharacteristic
28C22×C22⋊C4×C41C2211yescharacteristic
29C22×C22⋊C4×C41C2211yescharacteristic
30C22×C22⋊C4×C41C2211yescharacteristic
31C22×C22⋊C4×C41C2211yescharacteristic
32C22×C22⋊C4×C41C2211yescharacteristic
33C22×C22⋊C4×C41C2211yescharacteristic
34C22×C22⋊C4×C41C2211yescharacteristic
35C41×#397—24no—
36C41×#392—24no—
37C41×#386—24no—
38C41×#386—24no—
39C2×#95×C41C2211yescharacteristic
40C2×#95×C41C2211yescharacteristic
41C2×#95×C41C2211yescharacteristic
42C2×#95×C41C2211yescharacteristic
43C2×#95×C41C2211yescharacteristic
44C2×#95×C41C2211yescharacteristic
45C2×#95×C41C2211yescharacteristic
46C2×#95×C41C2211yescharacteristic
47C2×#95×C41C2211yescharacteristic
48C2×#95×C41C2211yescharacteristic
49C2×#95×C41C2211yescharacteristic
50C2×#95×C41C2211yescharacteristic
51C2×#95×C41C2211yescharacteristic
52C2×#95×C41C2211yescharacteristic
53C2×#95×C41C2211yescharacteristic
54C2×#95×C41C2211yescharacteristic
55C25×C41C2311yescharacteristic
56C25×C41C2311yescharacteristic
57C25×C41C2311yescharacteristic
58C22×D4×C41—22no—
59C22×D4×C41—22no—
60C22×D4×C41—22no—
61C22×D4×C41—22no—
62C22×D4×C41—22no—
63C22×D4×C41—22no—
64C22×D4×C41—22no—
65C22×D4×C41—22no—
66C22×D4×C41—22no—
67C22×D4×C41—22no—
68C22×D4×C41—41no—
69C22×D4×C41—41no—
70C22×D4×C41—41no—
71C22×D4×C41—41no—
72C22×D4×C41—41no—
73C22×D4×C41—41no—
74C22×D4×C41—41no—
75C22×D4×C41—41no—
76C22×D4×C41—41no—
77C22×D4×C41—41no—
78C22×D4×C41D414yes—
79C23×C4×C41—22no—
80C23×C4×C41—22no—
81C23×C4×C41—22no—
82C23×C4×C41—41no—
83C23×C4×C41—41no—
84C23×C4×C41—41no—
85C23×C4×C41—41no—
86C23×C4×C41C2311yescharacteristic
87C23×C4×C41C2311yescharacteristic
88C23×C4×C41C2311yescharacteristic
89C23×C4×C41C2311yescharacteristic
90C23×C4×C41C2311yescharacteristic
91C23×C4×C41C2311yescharacteristic
92C23×C4×C41C2311yescharacteristic
93C23×C4×C41C2311yescharacteristic
94C23×C4×C41C2311yescharacteristic
95C23×C4×C41C2311yescharacteristic
96C23×C4×C41C2311yescharacteristic
97C23×C4×C41C2311yescharacteristic
98C2×C4⋊C4×C41—22no—
99C2×C4⋊C4×C41—41no—
100C2×C4⋊C4×C41—41no—
101C2×C22⋊C4×C41—22no—
102C2×C22⋊C4×C41—22no—
103C2×C22⋊C4×C41—22no—
104C2×C22⋊C4×C41—22no—
105C2×C22⋊C4×C41—22no—
106C2×C22⋊C4×C41—22no—
107C2×C22⋊C4×C41—22no—
108C2×C22⋊C4×C41—22no—
109C2×C22⋊C4×C41—22no—
110C2×C22⋊C4×C41—22no—
111C2×C22⋊C4×C41—22no—
112C2×C22⋊C4×C41—22no—
113C2×C22⋊C4×C41—22no—
114C2×C22⋊C4×C41—22no—
115C2×C22⋊C4×C41—22no—
116C2×C22⋊C4×C41—22no—
117C2×C22⋊C4×C41—22no—
118C2×C22⋊C4×C41—22no—
119C2×C22⋊C4×C41—41no—
120C2×C22⋊C4×C41—41no—
121C2×C22⋊C4×C41—41no—
122C2×C22⋊C4×C41—41no—
123C2×C22⋊C4×C41—41no—
124C2×C22⋊C4×C41—41no—
125C2×C22⋊C4×C41—41no—
126C2×C22⋊C4×C41—41no—
127C2×C22⋊C4×C41—41no—
128C2×C22⋊C4×C41—41no—
129C2×C22⋊C4×C41—41no—
130C2×C22⋊C4×C41—41no—
131C2×C22⋊C4×C41—41no—
132C2×C22⋊C4×C41—41no—
133C2×C22⋊C4×C41—41no—
134C2×C22⋊C4×C41—41no—
135C2×C22⋊C4×C41—41no—
136C2×C22⋊C4×C41—41no—
137C2×C22⋊C4×C41—41no—
138C2×C22⋊C4×C41—41no—
139C2×C22⋊C4×C41—41no—
140C2×C22⋊C4×C41—41no—
141C2×C22⋊C4×C41—41no—
142C2×C22⋊C4×C41—41no—
143#95×C41—22no—
144#95×C41—22no—
145#95×C41—22no—
146#95×C41—22no—
147#95×C41—22no—
148#95×C41—22no—
149#95×C41—22no—
150#95×C41—41no—
151#95×C41—41no—
152#95×C41—41no—
153#95×C41—41no—
154#95×C41—41no—
155#95×C41—41no—
156#95×C41—41no—
157#95×C41—41no—
158#95×C41D414yescomplemented
159C24×C41—21no—
160C24×C41—21no—
161C24×C41—21no—
162C24×C41—21no—
163C24×C41—21no—
164C24×C41—21no—
165C24×C41—21no—
166C24×C41—21no—
167C24×C41—21no—
168C24×C41—21no—
169C24×C41—21no—
170C24×C41—21no—
171C24×C41—21no—
172C24×C41—21no—
173C24×C41—21no—
174C24×C41—21no—
175C24×C41—21no—
176C24×C41—21no—
177C24×C41—21no—
178C24×C41—21no—
179C24×C41—21no—
180C24×C41—21no—
181C24×C41—21no—
182C24×C41—21no—
183C24×C41—21no—
184C24×C41—21no—
185C24×C41—21no—
186C24×C41—21no—
187C24×C41—21no—
188C24×C41—21no—
189C24×C41—21no—
190C24×C41—21no—
191C24×C41—21no—
192C24×C41—21no—
193C24×C41—21no—
194C24×C41—21no—
195C24×C41—21no—
196C24×C41—21no—
197C24×C41—21no—
198C24×C41—21no—
199C24×C41C2×D412yes—
200C24×C41C2×D412yes—
201C24×C41#4112yes—
202C24×C41#4112yes—
203C24×C41#4112yes—
204C24×C41C2411yescharacteristic
205C2×D4×C41—28no—
206C2×D4×C41—28no—
207C2×D4×C41—44no—
208C2×D4×C41—44no—
209C2×D4×C41—44no—
210C2×D4×C41—44no—
211C2×D4×C41—44no—
212C2×D4×C41—44no—
213C2×D4×C41—44no—
214C2×D4×C41—44no—
215C2×D4×C41—44no—
216C2×D4×C41—44no—
217C2×D4×C41—44no—
218C2×D4×C41—44no—
219C2×D4×C41—44no—
220C2×D4×C41—44no—
221C2×D4×C41—44no—
222C2×D4×C41—44no—
223C2×D4×C41—44no—
224C2×D4×C41—44no—
225C2×D4×C41—44no—
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×C41—21no—
233C22×C4×C41—21no—
234C22×C4×C41—21no—
235C22×C4×C41—21no—
236C22×C4×C41—21no—
237C22×C4×C41—21no—
238C22×C4×C41—21no—
239C22×C4×C41—21no—
240C22×C4×C41—21no—
241C22×C4×C41—21no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—21no—
245C22×C4×C41—21no—
246C22×C4×C41—21no—
247C22×C4×C41—21no—
248C22×C4×C41—21no—
249C22×C4×C41—21no—
250C22×C4×C41—21no—
251C22×C4×C41—21no—
252C22×C4×C41—21no—
253C22×C4×C41—21no—
254C22×C4×C41—21no—
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—21no—
268C22×C4×C41—21no—
269C22×C4×C41—21no—
270C22×C4×C41—21no—
271C22×C4×C41—21no—
272C22×C4×C41—21no—
273C22×C4×C41—21no—
274C22×C4×C41—21no—
275C22×C4×C41—21no—
276C22×C4×C41—21no—
277C22×C4×C41—21no—
278C22×C4×C41—21no—
279C22×C4×C41—21no—
280C22×C4×C41—21no—
281C22×C4×C41—21no—
282C22×C4×C41—21no—
283C22×C4×C41—21no—
284C22×C4×C41—21no—
285C22×C4×C41—21no—
286C22×C4×C41—21no—
287C22×C4×C41—21no—
288C22×C4×C41—21no—
289C22×C4×C41—21no—
290C22×C4×C41—21no—
291C22×C4×C41—21no—
292C22×C4×C41—21no—
293C22×C4×C41—21no—
294C22×C4×C41—21no—
295C22×C4×C41—21no—
296C22×C4×C41—21no—
297C22×C4×C41—21no—
298C22×C4×C41—21no—
299C22×C4×C41—21no—
300C22×C4×C41—21no—
301C22×C4×C41—21no—
302C22×C4×C41—21no—
303C22×C4×C41—21no—
304C22×C4×C41—44no—
305C22×C4×C41—44no—
306C22×C4×C41—44no—
307C22×C4×C41—44no—
308C22×C4×C41—44no—
309C22×C4×C41—44no—
310C22×C4×C41—44no—
311C22×C4×C41C2×D412yes—
312C22×C4×C41C2×D412yes—
313C22×C4×C41C2×D412yes—
314C22×C4×C41C2×D412yes—
315C22×C4×C41#4112yes—
316C22×C4×C41#4112yes—
317C4⋊C4×C41—44no—
318C22⋊C4×C41—44no—
319C22⋊C4×C41—44no—
320C22⋊C4×C41—44no—
321C22⋊C4×C41—44no—
322C22⋊C4×C41—44no—
323C22⋊C4×C41—44no—
324C22⋊C4×C41—44no—
325C22⋊C4×C41—44no—
326C22⋊C4×C41—44no—
327C22⋊C4×C41—44no—
328C22⋊C4×C41—44no—
329C22⋊C4×C41—44no—
330C22⋊C4×C41—44no—
331C22⋊C4×C41—44no—
332C23×C41—22no—
333C23×C41—22no—
334C23×C41—22no—
335C23×C41—22no—
336C23×C41—22no—
337C23×C41—22no—
338C23×C41—22no—
339C23×C41—22no—
340C23×C41—22no—
341C23×C41—22no—
342C23×C41—22no—
343C23×C41—22no—
344C23×C41—22no—
345C23×C41—22no—
346C23×C41—22no—
347C23×C41—22no—
348C23×C41—22no—
349C23×C41—22no—
350C23×C41—22no—
351C23×C41—22no—
352C23×C41—22no—
353C23×C41—22no—
354C23×C41—22no—
355C23×C41—22no—
356C23×C41—22no—
357C23×C41—22no—
358C23×C41—22no—
359C23×C41—22no—
360C23×C41—22no—
361C23×C41—22no—
362C23×C41—22no—
363C23×C41—22no—
364C23×C41—41no—
365C23×C41—41no—
366C23×C41—41no—
367C23×C41—41no—
368C23×C41—41no—
369C23×C41—41no—
370C23×C41—41no—
371C23×C41—41no—
372C23×C41—41no—
373C23×C41—41no—
374C23×C41—41no—
375C23×C41—41no—
376C23×C41—41no—
377C23×C41—41no—
378C23×C41—41no—
379C23×C41—41no—
380C23×C41—41no—
381C23×C41—41no—
382C23×C41—41no—
383C23×C41—41no—
384C23×C41—41no—
385C23×C41—41no—
386C23×C41—41no—
387C23×C41—41no—
388C23×C41—41no—
389C23×C41—41no—
390C23×C41—41no—
391C23×C41—41no—
392C23×C41—41no—
393C23×C41—41no—
394C23×C41—41no—
395C23×C41—41no—
396C23×C41—41no—
397C23×C41—41no—
398C23×C41—41no—
399C23×C41—41no—
400C23×C41—41no—
401C23×C41—41no—
402C23×C41—41no—
403C23×C41—41no—
404C23×C41—41no—
405C23×C41—41no—
406C23×C41—41no—
407C23×C41—41no—
408C23×C41—41no—
409C23×C41—41no—
410C23×C41—41no—
411C23×C41—41no—
412C23×C41—41no—
413C23×C41—41no—
414C23×C41—41no—
415C23×C41—41no—
416C23×C41—41no—
417C23×C41—41no—
418C23×C41—41no—
419C23×C41—41no—
420C23×C41—41no—
421C23×C41—41no—
422C23×C41—41no—
423C23×C41—41no—
424C23×C41—41no—
425C23×C41—41no—
426C23×C41—41no—
427C23×C41—41no—
428C23×C41—41no—
429C23×C41—41no—
430C23×C41—41no—
431C23×C41—41no—
432C23×C41—41no—
433C23×C41—41no—
434C23×C41—41no—
435C23×C41—41no—
436C23×C41#12314yes—
437C23×C41C22×D411yescharacteristic
438C23×C41C22×D411yescharacteristic
439C23×C41C2×#4111yescharacteristic
440C23×C41C2×#4111yescharacteristic
441C23×C41C2×#4111yescharacteristic
442C23×C41C2×#4111yescharacteristic
443C23×C41C2×#4111yescharacteristic
444C23×C41H(5,𝔽2)11yescharacteristic
445C23×C41H(5,𝔽2)11yescharacteristic
446C23×C41H(5,𝔽2)11yescharacteristic
447C23×C41H(5,𝔽2)11yescharacteristic
448C23×C41H(5,𝔽2)11yescharacteristic
449C23×C41H(5,𝔽2)11yescharacteristic
450C23×C41H(5,𝔽2)11yescharacteristic
451C23×C41H(5,𝔽2)11yescharacteristic
452D4×C41—416no—
453D4×C41—416no—
454D4×C41—416no—
455C2×C4×C41—22no—
456C2×C4×C41—22no—
457C2×C4×C41—22no—
458C2×C4×C41—22no—
459C2×C4×C41—22no—
460C2×C4×C41—22no—
461C2×C4×C41—22no—
462C2×C4×C41—22no—
463C2×C4×C41—22no—
464C2×C4×C41—22no—
465C2×C4×C41—22no—
466C2×C4×C41—22no—
467C2×C4×C41—22no—
468C2×C4×C41—22no—
469C2×C4×C41—22no—
470C2×C4×C41—22no—
471C2×C4×C41—22no—
472C2×C4×C41—22no—
473C2×C4×C41—416no—
474C2×C4×C41—41no—
475C2×C4×C41—41no—
476C2×C4×C41—41no—
477C2×C4×C41—41no—
478C2×C4×C41—41no—
479C2×C4×C41—41no—
480C2×C4×C41—41no—
481C2×C4×C41—41no—
482C2×C4×C41—41no—
483C2×C4×C41—41no—
484C2×C4×C41—41no—
485C2×C4×C41—41no—
486C2×C4×C41—41no—
487C2×C4×C41—41no—
488C2×C4×C41—41no—
489C2×C4×C41—41no—
490C2×C4×C41—41no—
491C2×C4×C41—41no—
492C2×C4×C41—41no—
493C2×C4×C41—41no—
494C2×C4×C41—41no—
495C2×C4×C41—41no—
496C2×C4×C41—41no—
497C2×C4×C41—41no—
498C2×C4×C41—41no—
499C2×C4×C41—41no—
500C2×C4×C41—41no—
501C2×C4×C41—41no—
502C2×C4×C41—41no—
503C2×C4×C41—41no—
504C2×C4×C41—41no—
505C2×C4×C41—41no—
506C2×C4×C41—41no—
507C2×C4×C41—41no—
508C2×C4×C41—41no—
509C2×C4×C41—41no—
510C2×C4×C41—41no—
511C2×C4×C41—41no—
512C2×C4×C41—41no—
513C2×C4×C41—41no—
514C2×C4×C41—41no—
515C2×C4×C41—41no—
516C2×C4×C41—41no—
517C2×C4×C41—41no—
518C2×C4×C41—41no—
519C2×C4×C41—41no—
520C2×C4×C41—41no—
521C2×C4×C41—41no—
522C2×C4×C41—41no—
523C2×C4×C41—41no—
524C2×C4×C41—41no—
525C2×C4×C41—41no—
526C2×C4×C41—41no—
527C2×C4×C41—41no—
528C2×C4×C41—41no—
529C2×C4×C41—41no—
530C2×C4×C41—41no—
531C2×C4×C41—41no—
532C2×C4×C41—41no—
533C2×C4×C41—41no—
534C2×C4×C41—41no—
535C2×C4×C41—41no—
536C2×C4×C41—41no—
537C2×C4×C41—41no—
538C2×C4×C41—41no—
539C2×C4×C41—41no—
540#16270C4111yesmaximal, characteristic, direct product factor, Sylow
541C22×C41—24no—
542C22×C41—24no—
543C22×C41—24no—
544C22×C41—42no—
545C22×C41—42no—
546C22×C41—42no—
547C22×C41—42no—
548C22×C41—42no—
549C22×C41—42no—
550C22×C41—42no—
551C22×C41—42no—
552C22×C41—42no—
553C22×C41—42no—
554C22×C41—42no—
555C22×C41—42no—
556C22×C41—42no—
557C22×C41—42no—
558C22×C41—42no—
559C22×C41—42no—
560C22×C41—42no—
561C22×C41—42no—
562C22×C41—42no—
563C22×C41—42no—
564C22×C41—42no—
565C22×C41—42no—
566C22×C41—42no—
567C22×C41—42no—
568C22×C41—42no—
569C22×C41—42no—
570C22×C41—81no—
571C22×C41—81no—
572C22×C41—81no—
573C22×C41—81no—
574C22×C41—81no—
575C22×C41—81no—
576C22×C41—81no—
577C22×C41—81no—
578C22×C41—81no—
579C22×C41—81no—
580C22×C41—81no—
581C22×C41—81no—
582C22×C41—81no—
583C22×C41—81no—
584C22×C41—81no—
585C22×C41—81no—
586C22×C41C2×#12311yescharacteristic
587C22×C41#52511yescharacteristic
588C22×C41#52911yescharacteristic
589C22×C41#53411yescharacteristic
590C22×C41#53411yescharacteristic
591C22×C41#53511yescharacteristic
592C22×C41#53511yescharacteristic
593C22×C41#53811yescharacteristic
594C22×C41#53811yescharacteristic
595C22×C41#53811yescharacteristic
596C22×C41#53811yescharacteristic
597C22×C41#53811yescharacteristic
598C22×C41#53811yescharacteristic
599C22×C41#53811yescharacteristic
600C22×C41#53811yescharacteristic
601C22×C41#53811yescharacteristic
602C22×C41#53811yescharacteristic
603C22×C41#54011yescharacteristic
604C22×C41#54011yescharacteristic
605C22×C41D4211yescharacteristic
606C22×C41#54611yescharacteristic
607C22×C41#54611yescharacteristic
608C22×C41#54611yescharacteristic
609C22×C41#54611yescharacteristic
610C22×C41#54611yescharacteristic
611C22×C41#55011yescharacteristic
612C22×C41#55111yescharacteristic
613C22×C41#55111yescharacteristic
614C22×C41#55311yescharacteristic
615C22×C41#55311yescharacteristic
616C22×C41#55311yescharacteristic
617C22×C41#56011yescharacteristic
618C22×C41#56011yescharacteristic
619C22×C41#56011yescharacteristic
620C22×C41#56011yescharacteristic
621C4×C41—42no—
622C4×C41—42no—
623C4×C41—42no—
624C4×C41—42no—
625C4×C41—42no—
626C4×C41—42no—
627C4×C41—81no—
628C4×C41—81no—
629C4×C41—81no—
630C4×C41—81no—
631C4×C41—81no—
632C4×C41—81no—
633C2×#397C2×C4111yescharacteristic, complemented
634C2×#392C2×C4111yescharacteristic
635C2×#386C2×C4111yescharacteristic, complemented
636C2×#386C2×C4111yescharacteristic, complemented
637#1443C2×C4111yescharacteristic, complemented
638#1443C2×C4111yescharacteristic, complemented
639#1440C2×C4111yescharacteristic, complemented
640#1440C2×C4111yescharacteristic, complemented
641#1439C2×C4111yescharacteristic, complemented
642#1439C2×C4111yescharacteristic, complemented
643#1438C2×C4111yescharacteristic, complemented
644#1438C2×C4111yescharacteristic, complemented
645#1438C2×C4111yescharacteristic, complemented
646#1438C2×C4111yescharacteristic, complemented
647C22⋊#95C2×C4111yescharacteristic, complemented
648C2×C41—44no—
649C2×C41—82no—
650C2×C41—82no—
651C2×C41#241811yescharacteristic
652C2×C41#244411yescharacteristic
653C2×C41#246711yescharacteristic
654C2×C41#262211yescharacteristic
655C2×C41#263111yescharacteristic
656C2×C41#264811yescharacteristic
657C2×C41#267311yescharacteristic
658C2×C41#267811yescharacteristic
659C2×C41#268811yescharacteristic
660C2×C41#269711yescharacteristic
661C2×C41#270311yescharacteristic
662C2×C41#271411yescharacteristic
663C2×C41#274911yescharacteristic
664C2×C41#277811yescharacteristic
665C2×C41#282511yescharacteristic
666C23×D4C22×C4111yescharacteristic
667C23×D4C22×C4111yescharacteristic
668C23×D4C22×C4111yescharacteristic
669C24×C4C22×C4111yescharacteristic
670C22×C4⋊C4C22×C4111yescharacteristic
671C22×C22⋊C4C22×C4111yescharacteristic
672C22×C22⋊C4C22×C4111yescharacteristic
673C22×C22⋊C4C22×C4111yescharacteristic
674C22×C22⋊C4C22×C4111yescharacteristic
675C22×C22⋊C4C22×C4111yescharacteristic
676C22×C22⋊C4C22×C4111yescharacteristic
677C22×C22⋊C4C22×C4111yescharacteristic
678C22×C22⋊C4C22×C4111yescharacteristic
679C22×C22⋊C4C22×C4111yescharacteristic
680C22×C22⋊C4C22×C4111yescharacteristic
681C22×C22⋊C4C22×C4111yescharacteristic
682C22×C22⋊C4C22×C4111yescharacteristic
683C22×C22⋊C4C22×C4111yescharacteristic
684C22×C22⋊C4C22×C4111yescharacteristic
685#397—24no—
686#392—24no—
687#386—24no—
688#386—24no—
689C2×#95C22×C4111yescharacteristic
690C2×#95C22×C4111yescharacteristic
691C2×#95C22×C4111yescharacteristic
692C2×#95C22×C4111yescharacteristic
693C2×#95C22×C4111yescharacteristic
694C2×#95C22×C4111yescharacteristic
695C2×#95C22×C4111yescharacteristic
696C2×#95C22×C4111yescharacteristic
697C2×#95C22×C4111yescharacteristic
698C2×#95C22×C4111yescharacteristic
699C2×#95C22×C4111yescharacteristic
700C2×#95C22×C4111yescharacteristic
701C2×#95C22×C4111yescharacteristic
702C2×#95C22×C4111yescharacteristic
703C2×#95C22×C4111yescharacteristic
704C2×#95C22×C4111yescharacteristic
705C41#1627011yescharacteristic, direct product factor, Sylow
706C25C23×C4111yescharacteristic
707C25C23×C4111yescharacteristic
708C25C23×C4111yescharacteristic
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4D4×C4114yes—
730C23×C4—22no—
731C23×C4—22no—
732C23×C4—22no—
733C23×C4—41no—
734C23×C4—41no—
735C23×C4—41no—
736C23×C4—41no—
737C23×C4C23×C4111yescharacteristic
738C23×C4C23×C4111yescharacteristic
739C23×C4C23×C4111yescharacteristic
740C23×C4C23×C4111yescharacteristic
741C23×C4C23×C4111yescharacteristic
742C23×C4C23×C4111yescharacteristic
743C23×C4C23×C4111yescharacteristic
744C23×C4C23×C4111yescharacteristic
745C23×C4C23×C4111yescharacteristic
746C23×C4C23×C4111yescharacteristic
747C23×C4C23×C4111yescharacteristic
748C23×C4C23×C4111yescharacteristic
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C4⋊C4—41no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95—41no—
805#95—41no—
806#95—41no—
807#95—41no—
808#95—41no—
809#95D4×C4114yescomplemented
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24C2×D4×C4112yes—
851C24C2×D4×C4112yes—
852C24#41×C4112yes—
853C24#41×C4112yes—
854C24#41×C4112yes—
855C24C24×C4111yescharacteristic
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4C2×D4×C4112yes—
963C22×C4C2×D4×C4112yes—
964C22×C4C2×D4×C4112yes—
965C22×C4C2×D4×C4112yes—
966C22×C4#41×C4112yes—
967C22×C4#41×C4112yes—
968C4⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23#123×C4114yes—
1088C23C22×D4×C4111yescharacteristic
1089C23C22×D4×C4111yescharacteristic
1090C23C2×#41×C4111yescharacteristic
1091C23C2×#41×C4111yescharacteristic
1092C23C2×#41×C4111yescharacteristic
1093C23C2×#41×C4111yescharacteristic
1094C23C2×#41×C4111yescharacteristic
1095C23H(5,𝔽2)×C4111yescharacteristic
1096C23H(5,𝔽2)×C4111yescharacteristic
1097C23H(5,𝔽2)×C4111yescharacteristic
1098C23H(5,𝔽2)×C4111yescharacteristic
1099C23H(5,𝔽2)×C4111yescharacteristic
1100C23H(5,𝔽2)×C4111yescharacteristic
1101C23H(5,𝔽2)×C4111yescharacteristic
1102C23H(5,𝔽2)×C4111yescharacteristic
1103D4—416no—
1104D4—416no—
1105D4—416no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—416no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22C2×#123×C4111yescharacteristic
1237C22C41×#52511yescharacteristic
1238C22C41×#52911yescharacteristic
1239C22C41×#53411yescharacteristic
1240C22C41×#53411yescharacteristic
1241C22C41×#53511yescharacteristic
1242C22C41×#53511yescharacteristic
1243C22C41×#53811yescharacteristic
1244C22C41×#53811yescharacteristic
1245C22C41×#53811yescharacteristic
1246C22C41×#53811yescharacteristic
1247C22C41×#53811yescharacteristic
1248C22C41×#53811yescharacteristic
1249C22C41×#53811yescharacteristic
1250C22C41×#53811yescharacteristic
1251C22C41×#53811yescharacteristic
1252C22C41×#53811yescharacteristic
1253C22C41×#54011yescharacteristic
1254C22C41×#54011yescharacteristic
1255C22D42×C4111yescharacteristic
1256C22C41×#54611yescharacteristic
1257C22C41×#54611yescharacteristic
1258C22C41×#54611yescharacteristic
1259C22C41×#54611yescharacteristic
1260C22C41×#54611yescharacteristic
1261C22C41×#55011yescharacteristic
1262C22C41×#55111yescharacteristic
1263C22C41×#55111yescharacteristic
1264C22C41×#55311yescharacteristic
1265C22C41×#55311yescharacteristic
1266C22C41×#55311yescharacteristic
1267C22C41×#56011yescharacteristic
1268C22C41×#56011yescharacteristic
1269C22C41×#56011yescharacteristic
1270C22C41×#56011yescharacteristic
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C2—44no—
1284C2—82no—
1285C2—82no—
1286C2C41×#241811yescharacteristic
1287C2C41×#244411yescharacteristic
1288C2C41×#246711yescharacteristic
1289C2C41×#262211yescharacteristic
1290C2C41×#263111yescharacteristic
1291C2C41×#264811yescharacteristic
1292C2C41×#267311yescharacteristic
1293C2C41×#267811yescharacteristic
1294C2C41×#268811yescharacteristic
1295C2C41×#269711yescharacteristic
1296C2C41×#270311yescharacteristic
1297C2C41×#271411yescharacteristic
1298C2C41×#274911yescharacteristic
1299C2C41×#277811yescharacteristic
1300C2C41×#282511yescharacteristic
subgroupG/H
center, socleC24×C41C24
commutator, Frattini, cosocleC24C24×C41
prime radicalC2×C41×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#397C2semidirect
3. C2×C41×#386C2semidirect
4. C2×C41×#386C2semidirect
5. C41×#1443C2semidirect
6. C41×#1443C2semidirect
7. C41×#1440C2semidirect
8. C41×#1440C2semidirect
9. C41×#1439C2semidirect
10. C41×#1439C2semidirect
11. C41×#1438C2semidirect
12. C41×#1438C2semidirect
13. C41×#1438C2semidirect
14. C41×#1438C2semidirect
15. C41×C22⋊#95C2semidirect
158. #95×C41D4semidirect
540. #16270C41direct (N × H)
633. C2×#397C2×C41semidirect
635. C2×#386C2×C41semidirect
636. C2×#386C2×C41semidirect
637. #1443C2×C41semidirect
638. #1443C2×C41semidirect
639. #1440C2×C41semidirect
640. #1440C2×C41semidirect
641. #1439C2×C41semidirect
642. #1439C2×C41semidirect
643. #1438C2×C41semidirect
644. #1438C2×C41semidirect
645. #1438C2×C41semidirect
646. #1438C2×C41semidirect
647. C22⋊#95C2×C41semidirect
705. C41#16270direct (N × H)
809. #95D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#3972
C2×C41×#3922
C2×C41×#3862
C41×#14432
C41×#14402
C41×#14392
C41×#14382
C41×C22⋊#952
#1627041