Finite Group Databasebeta

← C41×#14361 #23790562

Subgroups — C41×#14361 #23790562

Order 10496.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1360 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×#388C211yesmaximal, characteristic, complemented
4C2×C41×#386C211yesmaximal, characteristic, complemented
5C2×C41×#386C211yesmaximal, characteristic, complemented
6C2×C41×#385C211yesmaximal, characteristic, complemented
7C2×C41×#380C211yesmaximal, characteristic, complemented
8C41×#1441C211yesmaximal, characteristic, complemented
9C41×#1439C211yesmaximal, characteristic, complemented
10C41×#1439C211yesmaximal, characteristic, complemented
11C41×#1438C211yesmaximal, characteristic, complemented
12C41×#1438C211yesmaximal, characteristic, complemented
13C41×#1438C211yesmaximal, characteristic, complemented
14C41×#1436C211yesmaximal, 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×C4⋊C4×C41C2211yescharacteristic
27C22×C4⋊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×C22⋊C4×C41C2211yescharacteristic
40C22×C22⋊C4×C41C2211yescharacteristic
41C22×C42×C41C2211yescharacteristic
42C41×#390—24no—
43C41×#388—24no—
44C41×#386—24no—
45C41×#386—24no—
46C41×#385—24no—
47C41×#380—24no—
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
58C2×#95×C41C2211yescharacteristic
59C2×#95×C41C2211yescharacteristic
60C25×C41C2311yescharacteristic
61C25×C41C2311yescharacteristic
62C25×C41C2311yescharacteristic
63C22×D4×C41—22no—
64C22×D4×C41—22no—
65C22×D4×C41—22no—
66C22×D4×C41—22no—
67C22×D4×C41—22no—
68C22×D4×C41—22no—
69C22×D4×C41—22no—
70C22×D4×C41—22no—
71C22×D4×C41—22no—
72C22×D4×C41—22no—
73C22×D4×C41—22no—
74C22×D4×C41—22no—
75C22×D4×C41—41no—
76C22×D4×C41—41no—
77C22×D4×C41—41no—
78C22×D4×C41—41no—
79C22×D4×C41—41no—
80C22×D4×C41—41no—
81C22×D4×C41C2×C414yes—
82C22×D4×C41C2×C414yes—
83C22×D4×C41C2×C414yescomplemented
84C23×C4×C41—22no—
85C23×C4×C41—22no—
86C23×C4×C41—22no—
87C23×C4×C41—22no—
88C23×C4×C41—22no—
89C23×C4×C41—22no—
90C23×C4×C41—22no—
91C23×C4×C41—41no—
92C23×C4×C41—41no—
93C23×C4×C41—41no—
94C23×C4×C41—41no—
95C23×C4×C41—41no—
96C23×C4×C41—41no—
97C23×C4×C41C2×C414yescomplemented
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
108C23×C4×C41C2311yescharacteristic
109C23×C4×C41C2311yescharacteristic
110#121×C41—232no—
111C2×C4⋊C4×C41—22no—
112C2×C4⋊C4×C41—22no—
113C2×C4⋊C4×C41—22no—
114C2×C4⋊C4×C41—22no—
115C2×C4⋊C4×C41—22no—
116C2×C4⋊C4×C41—22no—
117C2×C4⋊C4×C41—22no—
118C2×C4⋊C4×C41—22no—
119C2×C4⋊C4×C41—41no—
120C2×C4⋊C4×C41—41no—
121C2×C4⋊C4×C41—41no—
122C2×C4⋊C4×C41C2×C414yescomplemented
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—22no—
137C2×C22⋊C4×C41—22no—
138C2×C22⋊C4×C41—22no—
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×C41—41no—
153C2×C22⋊C4×C41—41no—
154C2×C22⋊C4×C41—41no—
155C2×C22⋊C4×C41—41no—
156C2×C22⋊C4×C41—41no—
157C2×C22⋊C4×C41C2×C414yes—
158C2×C22⋊C4×C41C2×C414yescomplemented
159C2×C22⋊C4×C41D414yes—
160C2×C22⋊C4×C41D414yes—
161C2×C22⋊C4×C41D414yescomplemented
162C2×C42×C41—22no—
163C2×C42×C41—22no—
164C2×C42×C41—41no—
165#95×C41—22no—
166#95×C41—22no—
167#95×C41—22no—
168#95×C41—22no—
169#95×C41—22no—
170#95×C41—22no—
171#95×C41—22no—
172#95×C41—22no—
173#95×C41—22no—
174#95×C41—41no—
175#95×C41—41no—
176#95×C41D414yescomplemented
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×C41—21no—
210C24×C41—21no—
211C24×C41—21no—
212C24×C41—21no—
213C24×C41—21no—
214C24×C41—21no—
215C24×C41C22×C412yes—
216C24×C41C22×C412yes—
217C24×C41C22×C412yes—
218C24×C41C2×D412yes—
219C24×C41C2×D412yes—
220C24×C41C2×D412yes—
221C24×C41#4112yes—
222C24×C41C2411yescharacteristic
223C2×D4×C41—28no—
224C2×D4×C41—28no—
225C2×D4×C41—28no—
226C2×D4×C41—28no—
227C2×D4×C41—28no—
228C2×D4×C41—28no—
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×C41—44no—
238C2×D4×C41—44no—
239C2×D4×C41—44no—
240C2×D4×C41—44no—
241C2×D4×C41—44no—
242C2×D4×C41—44no—
243C2×D4×C41—44no—
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—28no—
287C22×C4×C41—28no—
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—21no—
313C22×C4×C41—21no—
314C22×C4×C41—21no—
315C22×C4×C41—21no—
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×C41—44no—
325C22×C4×C41—44no—
326C22×C4×C41—44no—
327C22×C4×C41—44no—
328C22×C4×C41C22×C412yes—
329C22×C4×C41C22×C412yes—
330C22×C4×C41C22×C412yes—
331C22×C4×C41C22×C412yes—
332C22×C4×C41C2×D412yes—
333C22×C4×C41C2×D412yes—
334C22×C4×C41C2×D412yes—
335C22×C4×C41C2×D412yes—
336C22×C4×C41C2×D412yes—
337C22×C4×C41C2×D412yes—
338C22×C4×C41C2×D412yes—
339C22×C4×C41C2×D412yes—
340C22×C4×C41C2×D412yes—
341C22×C4×C41#4112yes—
342C4⋊C4×C41—28no—
343C4⋊C4×C41—44no—
344C4⋊C4×C41—44no—
345C4⋊C4×C41—44no—
346C22⋊C4×C41—28no—
347C22⋊C4×C41—44no—
348C22⋊C4×C41—44no—
349C22⋊C4×C41—44no—
350C22⋊C4×C41—44no—
351C22⋊C4×C41—44no—
352C22⋊C4×C41—44no—
353C22⋊C4×C41—44no—
354C22⋊C4×C41—44no—
355C22⋊C4×C41—44no—
356C22⋊C4×C41—44no—
357C22⋊C4×C41—44no—
358C22⋊C4×C41C22⋊C4116yescomplemented
359C42×C41—44no—
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—22no—
396C23×C41—22no—
397C23×C41—22no—
398C23×C41—22no—
399C23×C41—22no—
400C23×C41—22no—
401C23×C41—22no—
402C23×C41—22no—
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×C41—41no—
456C23×C41—41no—
457C23×C41—41no—
458C23×C41—41no—
459C23×C41—41no—
460C23×C41—41no—
461C23×C41—41no—
462C23×C41—41no—
463C23×C41C2×C22⋊C414yes—
464C23×C41C4×D414yes—
465C23×C41C23×C411yescharacteristic
466C23×C41C22×D411yescharacteristic
467C23×C41C22×D411yescharacteristic
468C23×C41C22×D411yescharacteristic
469C23×C41C22×D411yescharacteristic
470C23×C41C2×#4111yescharacteristic
471C23×C41C2×#4111yescharacteristic
472C23×C41H(5,𝔽2)11yescharacteristic
473C23×C41H(5,𝔽2)11yescharacteristic
474C23×C41H(5,𝔽2)11yescharacteristic
475C23×C41H(5,𝔽2)11yescharacteristic
476C23×C41H(5,𝔽2)11yescharacteristic
477C23×C41H(5,𝔽2)11yescharacteristic
478C23×C412−1+411yescharacteristic
479C23×C412−1+411yescharacteristic
480D4×C41—416no—
481D4×C41—416no—
482D4×C41—416no—
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—22no—
506C2×C4×C41—22no—
507C2×C4×C41—22no—
508C2×C4×C41—22no—
509C2×C4×C41—22no—
510C2×C4×C41—22no—
511C2×C4×C41—22no—
512C2×C4×C41—22no—
513C2×C4×C41—22no—
514C2×C4×C41—22no—
515C2×C4×C41—22no—
516C2×C4×C41—416no—
517C2×C4×C41—416no—
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×C41—41no—
560C2×C4×C41—41no—
561C2×C4×C41—41no—
562C2×C4×C41—41no—
563C2×C4×C41—41no—
564C2×C4×C41—41no—
565C2×C4×C41—41no—
566C2×C4×C41C2×C22⋊C414yes—
567C2×C4×C41C2×C22⋊C414yes—
568C2×C4×C41C4×D414yes—
569#14361C4111yesmaximal, characteristic, direct product factor, Sylow
570C22×C41—24no—
571C22×C41—24no—
572C22×C41—24no—
573C22×C41—24no—
574C22×C41—24no—
575C22×C41—24no—
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—42no—
600C22×C41—42no—
601C22×C41—42no—
602C22×C41—42no—
603C22×C41—42no—
604C22×C41—42no—
605C22×C41—42no—
606C22×C41—42no—
607C22×C41—81no—
608C22×C41—81no—
609C22×C41—81no—
610C22×C41—81no—
611C22×C41—81no—
612C22×C41—81no—
613C22×C41—81no—
614C22×C41—81no—
615C22×C41C22×C22⋊C411yescharacteristic
616C22×C41C2×C4×D411yescharacteristic
617C22×C41C2×C4×D411yescharacteristic
618C22×C41#51811yescharacteristic
619C22×C41#51811yescharacteristic
620C22×C41#52011yescharacteristic
621C22×C41#52011yescharacteristic
622C22×C41#53411yescharacteristic
623C22×C41#53511yescharacteristic
624C22×C41#53511yescharacteristic
625C22×C41#53611yescharacteristic
626C22×C41#53711yescharacteristic
627C22×C41#53711yescharacteristic
628C22×C41#53711yescharacteristic
629C22×C41#53711yescharacteristic
630C22×C41#53811yescharacteristic
631C22×C41#53911yescharacteristic
632C22×C41#54011yescharacteristic
633C22×C41#54211yescharacteristic
634C22×C41D4211yescharacteristic
635C22×C41D4211yescharacteristic
636C22×C41D4211yescharacteristic
637C22×C41D4211yescharacteristic
638C22×C41D4211yescharacteristic
639C22×C41#54611yescharacteristic
640C22×C41#54611yescharacteristic
641C22×C41#54611yescharacteristic
642C22×C41#54611yescharacteristic
643C22×C41#54711yescharacteristic
644C22×C41#54811yescharacteristic
645C22×C41#55311yescharacteristic
646C22×C41#56011yescharacteristic
647C22×C41#56011yescharacteristic
648C22×C41#56211yescharacteristic
649C22×C41#56211yescharacteristic
650C4×C41—24no—
651C4×C41—24no—
652C4×C41—24no—
653C4×C41—42no—
654C4×C41—42no—
655C4×C41—42no—
656C4×C41—42no—
657C4×C41—42no—
658C4×C41—81no—
659C4×C41—81no—
660C4×C41—81no—
661C4×C41—81no—
662C22×#121C2×C4111yescharacteristic
663C2×#390C2×C4111yescharacteristic, complemented
664C2×#388C2×C4111yescharacteristic, complemented
665C2×#386C2×C4111yescharacteristic, complemented
666C2×#386C2×C4111yescharacteristic, complemented
667C2×#385C2×C4111yescharacteristic, complemented
668C2×#380C2×C4111yescharacteristic, complemented
669#1441C2×C4111yescharacteristic, complemented
670#1439C2×C4111yescharacteristic, complemented
671#1439C2×C4111yescharacteristic, complemented
672#1438C2×C4111yescharacteristic, complemented
673#1438C2×C4111yescharacteristic, complemented
674#1438C2×C4111yescharacteristic, complemented
675#1436C2×C4111yescharacteristic, complemented
676C22⋊#95C2×C4111yescharacteristic, complemented
677C2×C41—44no—
678C2×C41—44no—
679C2×C41—82no—
680C2×C41#231111yescharacteristic
681C2×C41#232411yescharacteristic
682C2×C41#232511yescharacteristic
683C2×C41D4×C22⋊C411yescharacteristic
684C2×C41D4×C22⋊C411yescharacteristic
685C2×C41#236111yescharacteristic
686C2×C41#237711yescharacteristic
687C2×C41#266911yescharacteristic
688C2×C41#267111yescharacteristic
689C2×C41#267211yescharacteristic
690C2×C41#267511yescharacteristic
691C2×C41#267611yescharacteristic
692C2×C41#268111yescharacteristic
693C2×C41#269111yescharacteristic
694C2×C41#270311yescharacteristic
695C23×D4C22×C4111yescharacteristic
696C23×D4C22×C4111yescharacteristic
697C23×D4C22×C4111yescharacteristic
698C24×C4C22×C4111yescharacteristic
699C24×C4C22×C4111yescharacteristic
700C2×#121—24no—
701C2×#121—24no—
702C2×#121C4×C4118yescomplemented
703C22×C4⋊C4C22×C4111yescharacteristic
704C22×C4⋊C4C22×C4111yescharacteristic
705C22×C4⋊C4C22×C4111yescharacteristic
706C22×C4⋊C4C22×C4111yescharacteristic
707C22×C22⋊C4C22×C4111yescharacteristic
708C22×C22⋊C4C22×C4111yescharacteristic
709C22×C22⋊C4C22×C4111yescharacteristic
710C22×C22⋊C4C22×C4111yescharacteristic
711C22×C22⋊C4C22×C4111yescharacteristic
712C22×C22⋊C4C22×C4111yescharacteristic
713C22×C22⋊C4C22×C4111yescharacteristic
714C22×C22⋊C4C22×C4111yescharacteristic
715C22×C22⋊C4C22×C4111yescharacteristic
716C22×C22⋊C4C22×C4111yescharacteristic
717C22×C22⋊C4C22×C4111yescharacteristic
718C22×C22⋊C4C22×C4111yescharacteristic
719C22×C22⋊C4C22×C4111yescharacteristic
720C22×C42C22×C4111yescharacteristic
721#390—24no—
722#388—24no—
723#386—24no—
724#386—24no—
725#385—24no—
726#380—24no—
727C2×#95C22×C4111yescharacteristic
728C2×#95C22×C4111yescharacteristic
729C2×#95C22×C4111yescharacteristic
730C2×#95C22×C4111yescharacteristic
731C2×#95C22×C4111yescharacteristic
732C2×#95C22×C4111yescharacteristic
733C2×#95C22×C4111yescharacteristic
734C2×#95C22×C4111yescharacteristic
735C2×#95C22×C4111yescharacteristic
736C2×#95C22×C4111yescharacteristic
737C2×#95C22×C4111yescharacteristic
738C2×#95C22×C4111yescharacteristic
739C41#1436111yescharacteristic, direct product factor, Sylow
740C25C23×C4111yescharacteristic
741C25C23×C4111yescharacteristic
742C25C23×C4111yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4—41no—
761C22×D4C2×C4×C4114yes—
762C22×D4C2×C4×C4114yes—
763C22×D4C2×C4×C4114yescomplemented
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—41no—
772C23×C4—41no—
773C23×C4—41no—
774C23×C4—41no—
775C23×C4—41no—
776C23×C4—41no—
777C23×C4C2×C4×C4114yescomplemented
778C23×C4C23×C4111yescharacteristic
779C23×C4C23×C4111yescharacteristic
780C23×C4C23×C4111yescharacteristic
781C23×C4C23×C4111yescharacteristic
782C23×C4C23×C4111yescharacteristic
783C23×C4C23×C4111yescharacteristic
784C23×C4C23×C4111yescharacteristic
785C23×C4C23×C4111yescharacteristic
786C23×C4C23×C4111yescharacteristic
787C23×C4C23×C4111yescharacteristic
788C23×C4C23×C4111yescharacteristic
789C23×C4C23×C4111yescharacteristic
790#121—232no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—22no—
795C2×C4⋊C4—22no—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—22no—
799C2×C4⋊C4—41no—
800C2×C4⋊C4—41no—
801C2×C4⋊C4—41no—
802C2×C4⋊C4C2×C4×C4114yescomplemented
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4—41no—
828C2×C22⋊C4—41no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4—41no—
832C2×C22⋊C4—41no—
833C2×C22⋊C4—41no—
834C2×C22⋊C4—41no—
835C2×C22⋊C4—41no—
836C2×C22⋊C4—41no—
837C2×C22⋊C4C2×C4×C4114yes—
838C2×C22⋊C4C2×C4×C4114yescomplemented
839C2×C22⋊C4D4×C4114yes—
840C2×C22⋊C4D4×C4114yes—
841C2×C22⋊C4D4×C4114yescomplemented
842C2×C42—22no—
843C2×C42—22no—
844C2×C42—41no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—41no—
855#95—41no—
856#95D4×C4114yescomplemented
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—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24C22×C4×C4112yes—
896C24C22×C4×C4112yes—
897C24C22×C4×C4112yes—
898C24C2×D4×C4112yes—
899C24C2×D4×C4112yes—
900C24C2×D4×C4112yes—
901C24#41×C4112yes—
902C24C24×C4111yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
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—21no—
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—28no—
967C22×C4—28no—
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—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4C22×C4×C4112yes—
1009C22×C4C22×C4×C4112yes—
1010C22×C4C22×C4×C4112yes—
1011C22×C4C22×C4×C4112yes—
1012C22×C4C2×D4×C4112yes—
1013C22×C4C2×D4×C4112yes—
1014C22×C4C2×D4×C4112yes—
1015C22×C4C2×D4×C4112yes—
1016C22×C4C2×D4×C4112yes—
1017C22×C4C2×D4×C4112yes—
1018C22×C4C2×D4×C4112yes—
1019C22×C4C2×D4×C4112yes—
1020C22×C4C2×D4×C4112yes—
1021C22×C4#41×C4112yes—
1022C4⋊C4—28no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C22⋊C4—28no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4C22⋊C4×C41116yescomplemented
1039C42—44no—
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—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
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—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23C2×C22⋊C4×C4114yes—
1144C23C4×D4×C4114yes—
1145C23C23×C4×C4111yescharacteristic
1146C23C22×D4×C4111yescharacteristic
1147C23C22×D4×C4111yescharacteristic
1148C23C22×D4×C4111yescharacteristic
1149C23C22×D4×C4111yescharacteristic
1150C23C2×#41×C4111yescharacteristic
1151C23C2×#41×C4111yescharacteristic
1152C23H(5,𝔽2)×C4111yescharacteristic
1153C23H(5,𝔽2)×C4111yescharacteristic
1154C23H(5,𝔽2)×C4111yescharacteristic
1155C23H(5,𝔽2)×C4111yescharacteristic
1156C23H(5,𝔽2)×C4111yescharacteristic
1157C23H(5,𝔽2)×C4111yescharacteristic
1158C232−1+4×C4111yescharacteristic
1159C232−1+4×C4111yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
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—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—416no—
1197C2×C4—416no—
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×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4C2×C22⋊C4×C4114yes—
1247C2×C4C2×C22⋊C4×C4114yes—
1248C2×C4C4×D4×C4114yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
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—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C22⋊C4×C4111yescharacteristic
1295C22C2×C4×D4×C4111yescharacteristic
1296C22C2×C4×D4×C4111yescharacteristic
1297C22C41×#51811yescharacteristic
1298C22C41×#51811yescharacteristic
1299C22C41×#52011yescharacteristic
1300C22C41×#52011yescharacteristic
1301C22C41×#53411yescharacteristic
1302C22C41×#53511yescharacteristic
1303C22C41×#53511yescharacteristic
1304C22C41×#53611yescharacteristic
1305C22C41×#53711yescharacteristic
1306C22C41×#53711yescharacteristic
1307C22C41×#53711yescharacteristic
1308C22C41×#53711yescharacteristic
1309C22C41×#53811yescharacteristic
1310C22C41×#53911yescharacteristic
1311C22C41×#54011yescharacteristic
1312C22C41×#54211yescharacteristic
1313C22D42×C4111yescharacteristic
1314C22D42×C4111yescharacteristic
1315C22D42×C4111yescharacteristic
1316C22D42×C4111yescharacteristic
1317C22D42×C4111yescharacteristic
1318C22C41×#54611yescharacteristic
1319C22C41×#54611yescharacteristic
1320C22C41×#54611yescharacteristic
1321C22C41×#54611yescharacteristic
1322C22C41×#54711yescharacteristic
1323C22C41×#54811yescharacteristic
1324C22C41×#55311yescharacteristic
1325C22C41×#56011yescharacteristic
1326C22C41×#56011yescharacteristic
1327C22C41×#56211yescharacteristic
1328C22C41×#56211yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2C41×#231111yescharacteristic
1345C2C41×#232411yescharacteristic
1346C2C41×#232511yescharacteristic
1347C2D4×C22⋊C4×C4111yescharacteristic
1348C2D4×C22⋊C4×C4111yescharacteristic
1349C2C41×#236111yescharacteristic
1350C2C41×#237711yescharacteristic
1351C2C41×#266911yescharacteristic
1352C2C41×#267111yescharacteristic
1353C2C41×#267211yescharacteristic
1354C2C41×#267511yescharacteristic
1355C2C41×#267611yescharacteristic
1356C2C41×#268111yescharacteristic
1357C2C41×#269111yescharacteristic
1358C2C41×#270311yescharacteristic
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×#388C2semidirect
4. C2×C41×#386C2semidirect
5. C2×C41×#386C2semidirect
6. C2×C41×#385C2semidirect
7. C2×C41×#380C2semidirect
8. C41×#1441C2semidirect
9. C41×#1439C2semidirect
10. C41×#1439C2semidirect
11. C41×#1438C2semidirect
12. C41×#1438C2semidirect
13. C41×#1438C2semidirect
14. C41×#1436C2semidirect
15. C41×C22⋊#95C2semidirect
23. C2×#121×C41C4semidirect
83. C22×D4×C41C2×C4semidirect
97. C23×C4×C41C2×C4semidirect
122. C2×C4⋊C4×C41C2×C4semidirect
158. C2×C22⋊C4×C41C2×C4semidirect
161. C2×C22⋊C4×C41D4semidirect
176. #95×C41D4semidirect
358. C22⋊C4×C41C22⋊C4semidirect
569. #14361C41direct (N × H)
663. C2×#390C2×C41semidirect
664. C2×#388C2×C41semidirect
665. C2×#386C2×C41semidirect
666. C2×#386C2×C41semidirect
667. C2×#385C2×C41semidirect
668. C2×#380C2×C41semidirect
669. #1441C2×C41semidirect
670. #1439C2×C41semidirect
671. #1439C2×C41semidirect
672. #1438C2×C41semidirect
673. #1438C2×C41semidirect
674. #1438C2×C41semidirect
675. #1436C2×C41semidirect
676. C22⋊#95C2×C41semidirect
702. C2×#121C4×C41semidirect
739. C41#14361direct (N × H)
763. C22×D4C2×C4×C41semidirect
777. C23×C4C2×C4×C41semidirect
802. C2×C4⋊C4C2×C4×C41semidirect
838. C2×C22⋊C4C2×C4×C41semidirect
841. C2×C22⋊C4D4×C41semidirect
856. #95D4×C41semidirect
1038. C22⋊C4C22⋊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×#3882
C2×C41×#3862
C2×C41×#3852
C2×C41×#3802
C41×#14412
C41×#14392
C41×#14382
C41×#14362
C41×C22⋊#952
#1436141