Finite Group Databasebeta

← C41×#14363 #23790564

Subgroups — C41×#14363 #23790564

Order 10496.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C41C211yesmaximal, characteristic
2C2×C41×#390C211yesmaximal, characteristic, complemented
3C2×C41×#386C211yesmaximal, characteristic, complemented
4C2×C41×#386C211yesmaximal, characteristic, complemented
5C2×C41×#381C211yesmaximal, characteristic, complemented
6C41×#1441C211yesmaximal, characteristic, complemented
7C41×#1440C211yesmaximal, characteristic, complemented
8C41×#1439C211yesmaximal, characteristic, complemented
9C41×#1438C211yesmaximal, characteristic, complemented
10C41×#1438C211yesmaximal, characteristic, complemented
11C41×#1438C211yesmaximal, characteristic, complemented
12C41×#1437C211yesmaximal, characteristic, complemented
13C41×#1436C211yesmaximal, characteristic, complemented
14C41×C22⋊#95C211yesmaximal, characteristic, complemented
15C41×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C41C2211yescharacteristic
17C23×D4×C41C2211yescharacteristic
18C23×D4×C41C2211yescharacteristic
19C24×C4×C41C2211yescharacteristic
20C24×C4×C41C2211yescharacteristic
21C2×#121×C41—24no—
22C2×#121×C41—24no—
23C2×#121×C41C418yescomplemented
24C22×C4⋊C4×C41C2211yescharacteristic
25C22×C4⋊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
35C22×C22⋊C4×C41C2211yescharacteristic
36C22×C22⋊C4×C41C2211yescharacteristic
37C22×C22⋊C4×C41C2211yescharacteristic
38C22×C22⋊C4×C41C2211yescharacteristic
39C22×C42×C41C2211yescharacteristic
40C41×#390—24no—
41C41×#386—24no—
42C41×#386—24no—
43C41×#381—24no—
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
55C2×#95×C41C2211yescharacteristic
56C2×#95×C41C2211yescharacteristic
57C2×#95×C41C2211yescharacteristic
58C25×C41C2311yescharacteristic
59C25×C41C2311yescharacteristic
60C25×C41C2311yescharacteristic
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—41no—
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×C41C2×C414yes—
78C22×D4×C41C2×C414yes—
79C22×D4×C41C2×C414yescomplemented
80C22×D4×C41D414yes—
81C22×D4×C41D414yes—
82C23×C4×C41—22no—
83C23×C4×C41—22no—
84C23×C4×C41—22no—
85C23×C4×C41—22no—
86C23×C4×C41—22no—
87C23×C4×C41—22no—
88C23×C4×C41—22no—
89C23×C4×C41—41no—
90C23×C4×C41—41no—
91C23×C4×C41—41no—
92C23×C4×C41—41no—
93C23×C4×C41—41no—
94C23×C4×C41—41no—
95C23×C4×C41C2×C414yescomplemented
96C23×C4×C41C2311yescharacteristic
97C23×C4×C41C2311yescharacteristic
98C23×C4×C41C2311yescharacteristic
99C23×C4×C41C2311yescharacteristic
100C23×C4×C41C2311yescharacteristic
101C23×C4×C41C2311yescharacteristic
102C23×C4×C41C2311yescharacteristic
103C23×C4×C41C2311yescharacteristic
104C23×C4×C41C2311yescharacteristic
105C23×C4×C41C2311yescharacteristic
106C23×C4×C41C2311yescharacteristic
107C23×C4×C41C2311yescharacteristic
108#121×C41—232no—
109C2×C4⋊C4×C41—22no—
110C2×C4⋊C4×C41—22no—
111C2×C4⋊C4×C41—22no—
112C2×C4⋊C4×C41—41no—
113C2×C4⋊C4×C41—41no—
114C2×C4⋊C4×C41C2×C414yescomplemented
115C2×C22⋊C4×C41—22no—
116C2×C22⋊C4×C41—22no—
117C2×C22⋊C4×C41—22no—
118C2×C22⋊C4×C41—22no—
119C2×C22⋊C4×C41—22no—
120C2×C22⋊C4×C41—22no—
121C2×C22⋊C4×C41—22no—
122C2×C22⋊C4×C41—22no—
123C2×C22⋊C4×C41—22no—
124C2×C22⋊C4×C41—22no—
125C2×C22⋊C4×C41—22no—
126C2×C22⋊C4×C41—22no—
127C2×C22⋊C4×C41—22no—
128C2×C22⋊C4×C41—22no—
129C2×C22⋊C4×C41—22no—
130C2×C22⋊C4×C41—22no—
131C2×C22⋊C4×C41—22no—
132C2×C22⋊C4×C41—22no—
133C2×C22⋊C4×C41—22no—
134C2×C22⋊C4×C41—22no—
135C2×C22⋊C4×C41—22no—
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—
143C2×C22⋊C4×C41—41no—
144C2×C22⋊C4×C41—41no—
145C2×C22⋊C4×C41—41no—
146C2×C22⋊C4×C41—41no—
147C2×C22⋊C4×C41—41no—
148C2×C22⋊C4×C41—41no—
149C2×C22⋊C4×C41—41no—
150C2×C22⋊C4×C41—41no—
151C2×C22⋊C4×C41—41no—
152C2×C22⋊C4×C41C2×C414yes—
153C2×C22⋊C4×C41C2×C414yescomplemented
154C2×C42×C41—22no—
155C2×C42×C41—41no—
156C2×C42×C41—41no—
157#95×C41—22no—
158#95×C41—22no—
159#95×C41—22no—
160#95×C41—22no—
161#95×C41—22no—
162#95×C41—22no—
163#95×C41—22no—
164#95×C41—41no—
165#95×C41—41no—
166#95×C41—41no—
167#95×C41—41no—
168#95×C41—41no—
169#95×C41—41no—
170#95×C41D414yescomplemented
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×C41—21no—
200C24×C41—21no—
201C24×C41—21no—
202C24×C41—21no—
203C24×C41—21no—
204C24×C41—21no—
205C24×C41—21no—
206C24×C41—21no—
207C24×C41—21no—
208C24×C41—21no—
209C24×C41C22×C412yes—
210C24×C41C22×C412yes—
211C24×C41C22×C412yes—
212C24×C41C2×D412yes—
213C24×C41C2×D412yes—
214C24×C41C2×D412yes—
215C24×C41C2×D412yes—
216C24×C41C2411yescharacteristic
217C2×D4×C41—28no—
218C2×D4×C41—28no—
219C2×D4×C41—28no—
220C2×D4×C41—44no—
221C2×D4×C41—44no—
222C2×D4×C41—44no—
223C2×D4×C41—44no—
224C2×D4×C41—44no—
225C2×D4×C41—44no—
226C2×D4×C41—44no—
227C2×D4×C41—44no—
228C2×D4×C41—44no—
229C2×D4×C41—44no—
230C2×D4×C41—44no—
231C2×D4×C41—44no—
232C2×D4×C41—44no—
233C2×D4×C41—44no—
234C2×D4×C41—44no—
235C2×D4×C41—44no—
236C2×D4×C41—44no—
237C2×D4×C41C22⋊C4116yescomplemented
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—28no—
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—28no—
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—21no—
305C22×C4×C41—21no—
306C22×C4×C41—21no—
307C22×C4×C41—21no—
308C22×C4×C41—21no—
309C22×C4×C41—21no—
310C22×C4×C41—21no—
311C22×C4×C41—21no—
312C22×C4×C41—44no—
313C22×C4×C41—44no—
314C22×C4×C41—44no—
315C22×C4×C41—44no—
316C22×C4×C41—44no—
317C22×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×C41C22×C412yes—
325C22×C4×C41C22×C412yes—
326C22×C4×C41C22×C412yes—
327C22×C4×C41C22×C412yes—
328C22×C4×C41C2×D412yes—
329C22×C4×C41C2×D412yes—
330C22×C4×C41C2×D412yes—
331C22×C4×C41C2×D412yes—
332C22×C4×C41C2×D412yes—
333C22×C4×C41#4112yes—
334C22×C4×C41#4112yes—
335C22×C4×C41#4112yes—
336C4⋊C4×C41—28no—
337C4⋊C4×C41—44no—
338C22⋊C4×C41—28no—
339C22⋊C4×C41—28no—
340C22⋊C4×C41—44no—
341C22⋊C4×C41—44no—
342C22⋊C4×C41—44no—
343C22⋊C4×C41—44no—
344C22⋊C4×C41—44no—
345C22⋊C4×C41—44no—
346C22⋊C4×C41—44no—
347C22⋊C4×C41—44no—
348C22⋊C4×C41—44no—
349C22⋊C4×C41—44no—
350C22⋊C4×C41—44no—
351C42×C41—44no—
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—22no—
365C23×C41—22no—
366C23×C41—22no—
367C23×C41—22no—
368C23×C41—22no—
369C23×C41—22no—
370C23×C41—22no—
371C23×C41—22no—
372C23×C41—22no—
373C23×C41—22no—
374C23×C41—22no—
375C23×C41—22no—
376C23×C41—22no—
377C23×C41—22no—
378C23×C41—22no—
379C23×C41—22no—
380C23×C41—22no—
381C23×C41—22no—
382C23×C41—22no—
383C23×C41—22no—
384C23×C41—22no—
385C23×C41—22no—
386C23×C41—22no—
387C23×C41—22no—
388C23×C41—22no—
389C23×C41—22no—
390C23×C41—22no—
391C23×C41—22no—
392C23×C41—22no—
393C23×C41—22no—
394C23×C41—22no—
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—41no—
437C23×C41—41no—
438C23×C41—41no—
439C23×C41—41no—
440C23×C41—41no—
441C23×C41—41no—
442C23×C41—41no—
443C23×C41—41no—
444C23×C41—41no—
445C23×C41—41no—
446C23×C41—41no—
447C23×C41—41no—
448C23×C41—41no—
449C23×C41—41no—
450C23×C41—41no—
451C23×C41—41no—
452C23×C41—41no—
453C23×C41—41no—
454C23×C41—41no—
455C23×C41C2×C22⋊C414yes—
456C23×C41C2×C22⋊C414yes—
457C23×C41C23×C411yescharacteristic
458C23×C41C22×D411yescharacteristic
459C23×C41C22×D411yescharacteristic
460C23×C41C22×D411yescharacteristic
461C23×C41C2×#4111yescharacteristic
462C23×C41C2×#4111yescharacteristic
463C23×C41C2×#4111yescharacteristic
464C23×C41H(5,𝔽2)11yescharacteristic
465C23×C41H(5,𝔽2)11yescharacteristic
466C23×C41H(5,𝔽2)11yescharacteristic
467C23×C41H(5,𝔽2)11yescharacteristic
468C23×C41H(5,𝔽2)11yescharacteristic
469C23×C41H(5,𝔽2)11yescharacteristic
470C23×C41H(5,𝔽2)11yescharacteristic
471C23×C412−1+411yescharacteristic
472D4×C41—416no—
473D4×C41—416no—
474D4×C41—416no—
475C2×C4×C41—22no—
476C2×C4×C41—22no—
477C2×C4×C41—22no—
478C2×C4×C41—22no—
479C2×C4×C41—22no—
480C2×C4×C41—22no—
481C2×C4×C41—22no—
482C2×C4×C41—22no—
483C2×C4×C41—22no—
484C2×C4×C41—22no—
485C2×C4×C41—22no—
486C2×C4×C41—22no—
487C2×C4×C41—22no—
488C2×C4×C41—22no—
489C2×C4×C41—22no—
490C2×C4×C41—22no—
491C2×C4×C41—22no—
492C2×C4×C41—22no—
493C2×C4×C41—22no—
494C2×C4×C41—22no—
495C2×C4×C41—22no—
496C2×C4×C41—22no—
497C2×C4×C41—22no—
498C2×C4×C41—22no—
499C2×C4×C41—22no—
500C2×C4×C41—22no—
501C2×C4×C41—22no—
502C2×C4×C41—22no—
503C2×C4×C41—22no—
504C2×C4×C41—22no—
505C2×C4×C41—416no—
506C2×C4×C41—416no—
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—
540C2×C4×C41—41no—
541C2×C4×C41—41no—
542C2×C4×C41—41no—
543C2×C4×C41—41no—
544C2×C4×C41—41no—
545C2×C4×C41—41no—
546C2×C4×C41—41no—
547C2×C4×C41—41no—
548C2×C4×C41—41no—
549C2×C4×C41—41no—
550C2×C4×C41—41no—
551C2×C4×C41—41no—
552C2×C4×C41—41no—
553C2×C4×C41—41no—
554C2×C4×C41—41no—
555C2×C4×C41—41no—
556C2×C4×C41—41no—
557C2×C4×C41—41no—
558C2×C4×C41—41no—
559C2×C4×C41C2×C22⋊C414yes—
560C2×C4×C41C4×D414yes—
561#14363C4111yesmaximal, characteristic, direct product factor, Sylow
562C22×C41—24no—
563C22×C41—24no—
564C22×C41—24no—
565C22×C41—24no—
566C22×C41—24no—
567C22×C41—24no—
568C22×C41—42no—
569C22×C41—42no—
570C22×C41—42no—
571C22×C41—42no—
572C22×C41—42no—
573C22×C41—42no—
574C22×C41—42no—
575C22×C41—42no—
576C22×C41—42no—
577C22×C41—42no—
578C22×C41—42no—
579C22×C41—42no—
580C22×C41—42no—
581C22×C41—42no—
582C22×C41—42no—
583C22×C41—42no—
584C22×C41—42no—
585C22×C41—42no—
586C22×C41—42no—
587C22×C41—42no—
588C22×C41—42no—
589C22×C41—42no—
590C22×C41—42no—
591C22×C41—42no—
592C22×C41—42no—
593C22×C41—42no—
594C22×C41—42no—
595C22×C41—42no—
596C22×C41—42no—
597C22×C41—42no—
598C22×C41—42no—
599C22×C41—81no—
600C22×C41—81no—
601C22×C41—81no—
602C22×C41—81no—
603C22×C41—81no—
604C22×C41—81no—
605C22×C41—81no—
606C22×C41—81no—
607C22×C41C22×C22⋊C411yescharacteristic
608C22×C41C2×C4×D411yescharacteristic
609C22×C41C4×#4111yescharacteristic
610C22×C41#51811yescharacteristic
611C22×C41#51811yescharacteristic
612C22×C41#51811yescharacteristic
613C22×C41#52011yescharacteristic
614C22×C41#53411yescharacteristic
615C22×C41#53411yescharacteristic
616C22×C41#53411yescharacteristic
617C22×C41#53411yescharacteristic
618C22×C41#53511yescharacteristic
619C22×C41#53711yescharacteristic
620C22×C41#53811yescharacteristic
621C22×C41#53811yescharacteristic
622C22×C41#54011yescharacteristic
623C22×C41#54011yescharacteristic
624C22×C41#54011yescharacteristic
625C22×C41#54211yescharacteristic
626C22×C41D4211yescharacteristic
627C22×C41D4211yescharacteristic
628C22×C41#54611yescharacteristic
629C22×C41#54611yescharacteristic
630C22×C41#54611yescharacteristic
631C22×C41#54611yescharacteristic
632C22×C41#54611yescharacteristic
633C22×C41#54711yescharacteristic
634C22×C41#54711yescharacteristic
635C22×C41#55011yescharacteristic
636C22×C41#55311yescharacteristic
637C22×C41#55511yescharacteristic
638C22×C41#56011yescharacteristic
639C22×C41#56011yescharacteristic
640C22×C41#56211yescharacteristic
641C22×C41#56211yescharacteristic
642C4×C41—24no—
643C4×C41—24no—
644C4×C41—42no—
645C4×C41—42no—
646C4×C41—42no—
647C4×C41—42no—
648C4×C41—42no—
649C4×C41—42no—
650C4×C41—81no—
651C4×C41—81no—
652C4×C41—81no—
653C4×C41—81no—
654C22×#121C2×C4111yescharacteristic
655C2×#390C2×C4111yescharacteristic, complemented
656C2×#386C2×C4111yescharacteristic, complemented
657C2×#386C2×C4111yescharacteristic, complemented
658C2×#381C2×C4111yescharacteristic, complemented
659#1441C2×C4111yescharacteristic, complemented
660#1440C2×C4111yescharacteristic, complemented
661#1439C2×C4111yescharacteristic, complemented
662#1438C2×C4111yescharacteristic, complemented
663#1438C2×C4111yescharacteristic, complemented
664#1438C2×C4111yescharacteristic, complemented
665#1437C2×C4111yescharacteristic, complemented
666#1436C2×C4111yescharacteristic, complemented
667C22⋊#95C2×C4111yescharacteristic, complemented
668C22⋊#95C2×C4111yescharacteristic, complemented
669C2×C41—44no—
670C2×C41—44no—
671C2×C41—82no—
672C2×C41#230811yescharacteristic
673C2×C41#232411yescharacteristic
674C2×C41#233311yescharacteristic
675C2×C41D4×C22⋊C411yescharacteristic
676C2×C41#233911yescharacteristic
677C2×C41#236311yescharacteristic
678C2×C41#237711yescharacteristic
679C2×C41#267111yescharacteristic
680C2×C41#267311yescharacteristic
681C2×C41#267811yescharacteristic
682C2×C41#268211yescharacteristic
683C2×C41#268611yescharacteristic
684C2×C41#268811yescharacteristic
685C2×C41#269911yescharacteristic
686C2×C41#270111yescharacteristic
687C23×D4C22×C4111yescharacteristic
688C23×D4C22×C4111yescharacteristic
689C23×D4C22×C4111yescharacteristic
690C24×C4C22×C4111yescharacteristic
691C24×C4C22×C4111yescharacteristic
692C2×#121—24no—
693C2×#121—24no—
694C2×#121C4×C4118yescomplemented
695C22×C4⋊C4C22×C4111yescharacteristic
696C22×C4⋊C4C22×C4111yescharacteristic
697C22×C22⋊C4C22×C4111yescharacteristic
698C22×C22⋊C4C22×C4111yescharacteristic
699C22×C22⋊C4C22×C4111yescharacteristic
700C22×C22⋊C4C22×C4111yescharacteristic
701C22×C22⋊C4C22×C4111yescharacteristic
702C22×C22⋊C4C22×C4111yescharacteristic
703C22×C22⋊C4C22×C4111yescharacteristic
704C22×C22⋊C4C22×C4111yescharacteristic
705C22×C22⋊C4C22×C4111yescharacteristic
706C22×C22⋊C4C22×C4111yescharacteristic
707C22×C22⋊C4C22×C4111yescharacteristic
708C22×C22⋊C4C22×C4111yescharacteristic
709C22×C22⋊C4C22×C4111yescharacteristic
710C22×C42C22×C4111yescharacteristic
711#390—24no—
712#386—24no—
713#386—24no—
714#381—24no—
715C2×#95C22×C4111yescharacteristic
716C2×#95C22×C4111yescharacteristic
717C2×#95C22×C4111yescharacteristic
718C2×#95C22×C4111yescharacteristic
719C2×#95C22×C4111yescharacteristic
720C2×#95C22×C4111yescharacteristic
721C2×#95C22×C4111yescharacteristic
722C2×#95C22×C4111yescharacteristic
723C2×#95C22×C4111yescharacteristic
724C2×#95C22×C4111yescharacteristic
725C2×#95C22×C4111yescharacteristic
726C2×#95C22×C4111yescharacteristic
727C2×#95C22×C4111yescharacteristic
728C2×#95C22×C4111yescharacteristic
729C41#1436311yescharacteristic, direct product factor, Sylow
730C25C23×C4111yescharacteristic
731C25C23×C4111yescharacteristic
732C25C23×C4111yescharacteristic
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4C2×C4×C4114yes—
750C22×D4C2×C4×C4114yes—
751C22×D4C2×C4×C4114yescomplemented
752C22×D4D4×C4114yes—
753C22×D4D4×C4114yes—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—41no—
762C23×C4—41no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4C2×C4×C4114yescomplemented
768C23×C4C23×C4111yescharacteristic
769C23×C4C23×C4111yescharacteristic
770C23×C4C23×C4111yescharacteristic
771C23×C4C23×C4111yescharacteristic
772C23×C4C23×C4111yescharacteristic
773C23×C4C23×C4111yescharacteristic
774C23×C4C23×C4111yescharacteristic
775C23×C4C23×C4111yescharacteristic
776C23×C4C23×C4111yescharacteristic
777C23×C4C23×C4111yescharacteristic
778C23×C4C23×C4111yescharacteristic
779C23×C4C23×C4111yescharacteristic
780#121—232no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—41no—
785C2×C4⋊C4—41no—
786C2×C4⋊C4C2×C4×C4114yescomplemented
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4C2×C4×C4114yes—
825C2×C22⋊C4C2×C4×C4114yescomplemented
826C2×C42—22no—
827C2×C42—41no—
828C2×C42—41no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95—41no—
840#95—41no—
841#95—41no—
842#95D4×C4114yescomplemented
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24C22×C4×C4112yes—
882C24C22×C4×C4112yes—
883C24C22×C4×C4112yes—
884C24C2×D4×C4112yes—
885C24C2×D4×C4112yes—
886C24C2×D4×C4112yes—
887C24C2×D4×C4112yes—
888C24C24×C4111yescharacteristic
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4C22⋊C4×C41116yescomplemented
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—28no—
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—28no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4C22×C4×C4112yes—
997C22×C4C22×C4×C4112yes—
998C22×C4C22×C4×C4112yes—
999C22×C4C22×C4×C4112yes—
1000C22×C4C2×D4×C4112yes—
1001C22×C4C2×D4×C4112yes—
1002C22×C4C2×D4×C4112yes—
1003C22×C4C2×D4×C4112yes—
1004C22×C4C2×D4×C4112yes—
1005C22×C4#41×C4112yes—
1006C22×C4#41×C4112yes—
1007C22×C4#41×C4112yes—
1008C4⋊C4—28no—
1009C4⋊C4—44no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C42—44no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
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—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23C2×C22⋊C4×C4114yes—
1128C23C2×C22⋊C4×C4114yes—
1129C23C23×C4×C4111yescharacteristic
1130C23C22×D4×C4111yescharacteristic
1131C23C22×D4×C4111yescharacteristic
1132C23C22×D4×C4111yescharacteristic
1133C23C2×#41×C4111yescharacteristic
1134C23C2×#41×C4111yescharacteristic
1135C23C2×#41×C4111yescharacteristic
1136C23H(5,𝔽2)×C4111yescharacteristic
1137C23H(5,𝔽2)×C4111yescharacteristic
1138C23H(5,𝔽2)×C4111yescharacteristic
1139C23H(5,𝔽2)×C4111yescharacteristic
1140C23H(5,𝔽2)×C4111yescharacteristic
1141C23H(5,𝔽2)×C4111yescharacteristic
1142C23H(5,𝔽2)×C4111yescharacteristic
1143C232−1+4×C4111yescharacteristic
1144D4—416no—
1145D4—416no—
1146D4—416no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—416no—
1178C2×C4—416no—
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—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4C2×C22⋊C4×C4114yes—
1232C2×C4C4×D4×C4114yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22C22×C22⋊C4×C4111yescharacteristic
1279C22C2×C4×D4×C4111yescharacteristic
1280C22C4×#41×C4111yescharacteristic
1281C22C41×#51811yescharacteristic
1282C22C41×#51811yescharacteristic
1283C22C41×#51811yescharacteristic
1284C22C41×#52011yescharacteristic
1285C22C41×#53411yescharacteristic
1286C22C41×#53411yescharacteristic
1287C22C41×#53411yescharacteristic
1288C22C41×#53411yescharacteristic
1289C22C41×#53511yescharacteristic
1290C22C41×#53711yescharacteristic
1291C22C41×#53811yescharacteristic
1292C22C41×#53811yescharacteristic
1293C22C41×#54011yescharacteristic
1294C22C41×#54011yescharacteristic
1295C22C41×#54011yescharacteristic
1296C22C41×#54211yescharacteristic
1297C22D42×C4111yescharacteristic
1298C22D42×C4111yescharacteristic
1299C22C41×#54611yescharacteristic
1300C22C41×#54611yescharacteristic
1301C22C41×#54611yescharacteristic
1302C22C41×#54611yescharacteristic
1303C22C41×#54611yescharacteristic
1304C22C41×#54711yescharacteristic
1305C22C41×#54711yescharacteristic
1306C22C41×#55011yescharacteristic
1307C22C41×#55311yescharacteristic
1308C22C41×#55511yescharacteristic
1309C22C41×#56011yescharacteristic
1310C22C41×#56011yescharacteristic
1311C22C41×#56211yescharacteristic
1312C22C41×#56211yescharacteristic
1313C4—24no—
1314C4—24no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C2—44no—
1326C2—44no—
1327C2—82no—
1328C2C41×#230811yescharacteristic
1329C2C41×#232411yescharacteristic
1330C2C41×#233311yescharacteristic
1331C2D4×C22⋊C4×C4111yescharacteristic
1332C2C41×#233911yescharacteristic
1333C2C41×#236311yescharacteristic
1334C2C41×#237711yescharacteristic
1335C2C41×#267111yescharacteristic
1336C2C41×#267311yescharacteristic
1337C2C41×#267811yescharacteristic
1338C2C41×#268211yescharacteristic
1339C2C41×#268611yescharacteristic
1340C2C41×#268811yescharacteristic
1341C2C41×#269911yescharacteristic
1342C2C41×#270111yescharacteristic
subgroupG/H
center, socleC24×C41C24
commutatorC23C23×C4×C41
Frattini, cosocleC24C24×C41
prime radicalC22×#121×C41C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#390C2semidirect
3. C2×C41×#386C2semidirect
4. C2×C41×#386C2semidirect
5. C2×C41×#381C2semidirect
6. C41×#1441C2semidirect
7. C41×#1440C2semidirect
8. C41×#1439C2semidirect
9. C41×#1438C2semidirect
10. C41×#1438C2semidirect
11. C41×#1438C2semidirect
12. C41×#1437C2semidirect
13. C41×#1436C2semidirect
14. C41×C22⋊#95C2semidirect
15. C41×C22⋊#95C2semidirect
23. C2×#121×C41C4semidirect
79. C22×D4×C41C2×C4semidirect
95. C23×C4×C41C2×C4semidirect
114. C2×C4⋊C4×C41C2×C4semidirect
153. C2×C22⋊C4×C41C2×C4semidirect
170. #95×C41D4semidirect
237. C2×D4×C41C22⋊C4semidirect
561. #14363C41direct (N × H)
655. C2×#390C2×C41semidirect
656. C2×#386C2×C41semidirect
657. C2×#386C2×C41semidirect
658. C2×#381C2×C41semidirect
659. #1441C2×C41semidirect
660. #1440C2×C41semidirect
661. #1439C2×C41semidirect
662. #1438C2×C41semidirect
663. #1438C2×C41semidirect
664. #1438C2×C41semidirect
665. #1437C2×C41semidirect
666. #1436C2×C41semidirect
667. C22⋊#95C2×C41semidirect
668. C22⋊#95C2×C41semidirect
694. C2×#121C4×C41semidirect
729. C41#14363direct (N × H)
751. C22×D4C2×C4×C41semidirect
767. C23×C4C2×C4×C41semidirect
786. C2×C4⋊C4C2×C4×C41semidirect
825. C2×C22⋊C4C2×C4×C41semidirect
842. #95D4×C41semidirect
909. C2×D4C22⋊C4×C41semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C412
C2×C41×#3902
C2×C41×#3862
C2×C41×#3812
C41×#14412
C41×#14402
C41×#14392
C41×#14382
C41×#14372
C41×#14362
C41×C22⋊#952
#1436341