Finite Group Databasebeta

← C41×#14096 #23790297

Subgroups — C41×#14096 #23790297

Order 10496.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C41C211yesmaximal, characteristic
2C2×C41×#388C211yesmaximal, characteristic, complemented
3C2×C41×#386C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C41C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C41C211yesmaximal, characteristic, complemented
6C41×#1445C211yesmaximal, characteristic, complemented
7C41×#1440C211yesmaximal, characteristic, complemented
8C41×#1439C211yesmaximal, characteristic, complemented
9C41×#1438C211yesmaximal, characteristic
10C41×#1437C211yesmaximal, characteristic, complemented
11C41×#1436C211yesmaximal, characteristic, complemented
12C41×#1436C211yesmaximal, characteristic, complemented
13C41×C4⋊#95C211yesmaximal, characteristic, complemented
14C41×C22⋊#95C211yesmaximal, characteristic, complemented
15C41×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C41C2211yescharacteristic
17C24×C4×C41C2211yescharacteristic
18C24×C4×C41C2211yescharacteristic
19C2×#123×C41—24no—
20C2×#123×C41—24no—
21C2×#123×C41C418yescomplemented
22C22×C4⋊C4×C41C2211yescharacteristic
23C22×C4⋊C4×C41C2211yescharacteristic
24C22×C4⋊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
35C22×C42×C41C2211yescharacteristic
36C22×C42×C41C2211yescharacteristic
37C22×C42×C41C2211yescharacteristic
38C41×#388—24no—
39C41×#386—24no—
40C4×C22⋊C4×C41—24no—
41C4×C22⋊C4×C41—24no—
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
55C2×#95×C41C2211yescharacteristic
56C2×#95×C41C2211yescharacteristic
57C2×#95×C41C2211yescharacteristic
58C25×C41C2311yescharacteristic
59C25×C41C2311yescharacteristic
60C22×D4×C41—22no—
61C22×D4×C41—22no—
62C22×D4×C41—22no—
63C22×D4×C41—22no—
64C22×D4×C41—41no—
65C22×D4×C41—41no—
66C22×D4×C41C2×C414yes—
67C23×C4×C41—22no—
68C23×C4×C41—22no—
69C23×C4×C41—22no—
70C23×C4×C41—22no—
71C23×C4×C41—22no—
72C23×C4×C41—22no—
73C23×C4×C41—22no—
74C23×C4×C41—22no—
75C23×C4×C41—22no—
76C23×C4×C41—41no—
77C23×C4×C41—41no—
78C23×C4×C41—41no—
79C23×C4×C41—41no—
80C23×C4×C41C2×C414yescomplemented
81C23×C4×C41C2311yescharacteristic
82C23×C4×C41C2311yescharacteristic
83C23×C4×C41C2311yescharacteristic
84C23×C4×C41C2311yescharacteristic
85C23×C4×C41C2311yescharacteristic
86C23×C4×C41C2311yescharacteristic
87C23×C4×C41C2311yescharacteristic
88C23×C4×C41C2311yescharacteristic
89C23×C4×C41C2311yescharacteristic
90C23×C4×C41C2311yescharacteristic
91C23×C4×C41C2311yescharacteristic
92C23×C4×C41C2311yescharacteristic
93C23×C4×C41C2311yescharacteristic
94#123×C41—232no—
95C2×C4⋊C4×C41—22no—
96C2×C4⋊C4×C41—22no—
97C2×C4⋊C4×C41—22no—
98C2×C4⋊C4×C41—22no—
99C2×C4⋊C4×C41—22no—
100C2×C4⋊C4×C41—22no—
101C2×C4⋊C4×C41—41no—
102C2×C4⋊C4×C41C2×C414yescomplemented
103C2×C4⋊C4×C41C2×C414yescomplemented
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—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—41no—
125C2×C22⋊C4×C41—41no—
126C2×C22⋊C4×C41—41no—
127C2×C22⋊C4×C41—41no—
128C2×C22⋊C4×C41C2×C414yes—
129C2×C22⋊C4×C41C2×C414yes—
130C2×C22⋊C4×C41C2×C414yescomplemented
131C2×C22⋊C4×C41D414yes—
132C2×C22⋊C4×C41D414yes—
133C2×C22⋊C4×C41D414yes—
134C2×C42×C41—22no—
135C2×C42×C41—22no—
136C2×C42×C41—22no—
137C2×C42×C41—22no—
138C2×C42×C41—22no—
139C2×C42×C41—22no—
140C2×C42×C41—41no—
141C2×C42×C41—41no—
142C2×C42×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—22no—
151#95×C41—22no—
152#95×C41—22no—
153#95×C41—22no—
154#95×C41—22no—
155#95×C41—41no—
156#95×C41—41no—
157#95×C41—41no—
158#95×C41—41no—
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×C41C22×C412yes—
184C24×C41C22×C412yes—
185C24×C41C2×D412yes—
186C24×C41C2×D412yes—
187C24×C41C2×D412yes—
188C24×C41#4112yes—
189C24×C41C2411yescharacteristic
190C2×D4×C41—28no—
191C2×D4×C41—28no—
192C2×D4×C41—44no—
193C2×D4×C41—44no—
194C2×D4×C41—44no—
195C2×D4×C41—44no—
196C2×D4×C41—44no—
197C22×C4×C41—21no—
198C22×C4×C41—21no—
199C22×C4×C41—21no—
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—21no—
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—28no—
210C22×C4×C41—28no—
211C22×C4×C41—21no—
212C22×C4×C41—21no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—21no—
216C22×C4×C41—21no—
217C22×C4×C41—21no—
218C22×C4×C41—21no—
219C22×C4×C41—21no—
220C22×C4×C41—21no—
221C22×C4×C41—21no—
222C22×C4×C41—21no—
223C22×C4×C41—21no—
224C22×C4×C41—21no—
225C22×C4×C41—21no—
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—28no—
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—44no—
275C22×C4×C41—44no—
276C22×C4×C41—44no—
277C22×C4×C41—44no—
278C22×C4×C41—44no—
279C22×C4×C41—44no—
280C22×C4×C41—44no—
281C22×C4×C41—44no—
282C22×C4×C41—44no—
283C22×C4×C41—44no—
284C22×C4×C41—44no—
285C22×C4×C41C22×C412yes—
286C22×C4×C41C22×C412yes—
287C22×C4×C41C22×C412yes—
288C22×C4×C41C22×C412yes—
289C22×C4×C41C22×C412yes—
290C22×C4×C41C2×D412yes—
291C22×C4×C41C2×D412yes—
292C22×C4×C41C2×D412yes—
293C22×C4×C41C2×D412yes—
294C22×C4×C41C2×D412yes—
295C22×C4×C41C2×D412yes—
296C22×C4×C41#4112yes—
297C22×C4×C41#4112yes—
298C22×C4×C41#4112yes—
299C22×C4×C41#4112yes—
300C22×C4×C41#4112yes—
301C22×C4×C41#4112yes—
302C4⋊C4×C41—28no—
303C4⋊C4×C41—28no—
304C4⋊C4×C41—44no—
305C22⋊C4×C41—28no—
306C22⋊C4×C41—28no—
307C22⋊C4×C41—28no—
308C22⋊C4×C41—28no—
309C22⋊C4×C41—28no—
310C22⋊C4×C41—44no—
311C22⋊C4×C41—44no—
312C22⋊C4×C41—44no—
313C22⋊C4×C41—44no—
314C22⋊C4×C41C22⋊C4116yescomplemented
315C42×C41—44no—
316C42×C41—44no—
317C42×C41—44no—
318C23×C41—22no—
319C23×C41—22no—
320C23×C41—22no—
321C23×C41—22no—
322C23×C41—22no—
323C23×C41—22no—
324C23×C41—22no—
325C23×C41—22no—
326C23×C41—22no—
327C23×C41—22no—
328C23×C41—22no—
329C23×C41—22no—
330C23×C41—22no—
331C23×C41—22no—
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—41no—
355C23×C41—41no—
356C23×C41—41no—
357C23×C41—41no—
358C23×C41—41no—
359C23×C41—41no—
360C23×C41—41no—
361C23×C41—41no—
362C23×C41—41no—
363C23×C41—41no—
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×C41C2×C22⋊C414yes—
387C23×C41C4×D414yes—
388C23×C41C23×C411yescharacteristic
389C23×C41C22×D411yescharacteristic
390C23×C41C22×D411yescharacteristic
391C23×C41C22×D411yescharacteristic
392C23×C41C2×#4111yescharacteristic
393C23×C41C2×#4111yescharacteristic
394C23×C41C2×#4111yescharacteristic
395C23×C41C2×#4111yescharacteristic
396C23×C41C2×#4111yescharacteristic
397C23×C41C2×#4111yescharacteristic
398C23×C41C2×#4111yescharacteristic
399C23×C41H(5,𝔽2)11yescharacteristic
400C23×C41H(5,𝔽2)11yescharacteristic
401C23×C41H(5,𝔽2)11yescharacteristic
402C23×C412−1+411yescharacteristic
403D4×C41—416no—
404C2×C4×C41—22no—
405C2×C4×C41—22no—
406C2×C4×C41—22no—
407C2×C4×C41—22no—
408C2×C4×C41—22no—
409C2×C4×C41—22no—
410C2×C4×C41—22no—
411C2×C4×C41—22no—
412C2×C4×C41—22no—
413C2×C4×C41—22no—
414C2×C4×C41—22no—
415C2×C4×C41—22no—
416C2×C4×C41—22no—
417C2×C4×C41—22no—
418C2×C4×C41—22no—
419C2×C4×C41—22no—
420C2×C4×C41—22no—
421C2×C4×C41—22no—
422C2×C4×C41—22no—
423C2×C4×C41—22no—
424C2×C4×C41—22no—
425C2×C4×C41—22no—
426C2×C4×C41—22no—
427C2×C4×C41—22no—
428C2×C4×C41—22no—
429C2×C4×C41—22no—
430C2×C4×C41—22no—
431C2×C4×C41—22no—
432C2×C4×C41—22no—
433C2×C4×C41—22no—
434C2×C4×C41—22no—
435C2×C4×C41—22no—
436C2×C4×C41—22no—
437C2×C4×C41—22no—
438C2×C4×C41—22no—
439C2×C4×C41—22no—
440C2×C4×C41—22no—
441C2×C4×C41—22no—
442C2×C4×C41—22no—
443C2×C4×C41—22no—
444C2×C4×C41—22no—
445C2×C4×C41—22no—
446C2×C4×C41—416no—
447C2×C4×C41—416no—
448C2×C4×C41—41no—
449C2×C4×C41—41no—
450C2×C4×C41—41no—
451C2×C4×C41—41no—
452C2×C4×C41—41no—
453C2×C4×C41—41no—
454C2×C4×C41—41no—
455C2×C4×C41—41no—
456C2×C4×C41—41no—
457C2×C4×C41—41no—
458C2×C4×C41—41no—
459C2×C4×C41—41no—
460C2×C4×C41—41no—
461C2×C4×C41—41no—
462C2×C4×C41—41no—
463C2×C4×C41—41no—
464C2×C4×C41—41no—
465C2×C4×C41—41no—
466C2×C4×C41—41no—
467C2×C4×C41—41no—
468C2×C4×C41—41no—
469C2×C4×C41—41no—
470C2×C4×C41—41no—
471C2×C4×C41—41no—
472C2×C4×C41—41no—
473C2×C4×C41—41no—
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×C41C2×C22⋊C414yes—
495C2×C4×C41C2×C22⋊C414yes—
496C2×C4×C41#12314yescomplemented
497#14096C4111yesmaximal, characteristic, direct product factor, Sylow
498C22×C41—24no—
499C22×C41—24no—
500C22×C41—24no—
501C22×C41—24no—
502C22×C41—24no—
503C22×C41—24no—
504C22×C41—42no—
505C22×C41—42no—
506C22×C41—42no—
507C22×C41—42no—
508C22×C41—42no—
509C22×C41—42no—
510C22×C41—42no—
511C22×C41—42no—
512C22×C41—42no—
513C22×C41—42no—
514C22×C41—42no—
515C22×C41—42no—
516C22×C41—42no—
517C22×C41—42no—
518C22×C41—42no—
519C22×C41—42no—
520C22×C41—42no—
521C22×C41—42no—
522C22×C41—42no—
523C22×C41—42no—
524C22×C41—42no—
525C22×C41—42no—
526C22×C41—42no—
527C22×C41—42no—
528C22×C41C22×C22⋊C411yescharacteristic
529C22×C41C2×C4×D411yescharacteristic
530C22×C41C4×#4111yescharacteristic
531C22×C41C4×#4111yescharacteristic
532C22×C41C4×#4111yescharacteristic
533C22×C41#51811yescharacteristic
534C22×C41#52011yescharacteristic
535C22×C41C2×#12311yescharacteristic
536C22×C41#52511yescharacteristic
537C22×C41#52511yescharacteristic
538C22×C41#52511yescharacteristic
539C22×C41#52911yescharacteristic
540C22×C41#52911yescharacteristic
541C22×C41#53211yescharacteristic
542C22×C41#53211yescharacteristic
543C22×C41#53811yescharacteristic
544C22×C41#53911yescharacteristic
545C22×C41#54011yescharacteristic
546C22×C41#54211yescharacteristic
547C22×C41D4211yescharacteristic
548C22×C41D4211yescharacteristic
549C22×C41#54611yescharacteristic
550C22×C41#54611yescharacteristic
551C22×C41#54611yescharacteristic
552C22×C41#54611yescharacteristic
553C22×C41#54611yescharacteristic
554C22×C41#54711yescharacteristic
555C22×C41#54711yescharacteristic
556C22×C41#54711yescharacteristic
557C22×C41#55111yescharacteristic
558C22×C41#55111yescharacteristic
559C22×C41#55211yescharacteristic
560C22×C41#55311yescharacteristic
561C22×C41#55311yescharacteristic
562C22×C41#55911yescharacteristic
563C4×C41—24no—
564C4×C41—24no—
565C4×C41—24no—
566C4×C41—42no—
567C4×C41—42no—
568C4×C41—42no—
569C4×C41—42no—
570C4×C41—42no—
571C4×C41—42no—
572C4×C41—42no—
573C4×C41—42no—
574C4×C41—81no—
575C4×C41—81no—
576C22×#123C2×C4111yescharacteristic
577C2×#388C2×C4111yescharacteristic, complemented
578C2×#386C2×C4111yescharacteristic
579C2×C4×C22⋊C4C2×C4111yescharacteristic, complemented
580C2×C4×C22⋊C4C2×C4111yescharacteristic, complemented
581#1445C2×C4111yescharacteristic, complemented
582#1440C2×C4111yescharacteristic, complemented
583#1439C2×C4111yescharacteristic, complemented
584#1438C2×C4111yescharacteristic
585#1437C2×C4111yescharacteristic, complemented
586#1436C2×C4111yescharacteristic, complemented
587#1436C2×C4111yescharacteristic, complemented
588C4⋊#95C2×C4111yescharacteristic, complemented
589C22⋊#95C2×C4111yescharacteristic, complemented
590C22⋊#95C2×C4111yescharacteristic, complemented
591C2×C41—44no—
592C2×C41—44no—
593C2×C41#229711yescharacteristic
594C2×C41C4×#12311yescharacteristic
595C2×C41#233511yescharacteristic
596C2×C41D4×C22⋊C411yescharacteristic
597C2×C41#233911yescharacteristic
598C2×C41#235911yescharacteristic
599C2×C41#237411yescharacteristic
600C2×C41#241811yescharacteristic
601C2×C41#242211yescharacteristic
602C2×C41#245511yescharacteristic
603C2×C41#245711yescharacteristic
604C2×C41#246411yescharacteristic
605C2×C41#247011yescharacteristic
606C2×C41#255311yescharacteristic
607C2×C41#255711yescharacteristic
608C23×D4C22×C4111yescharacteristic
609C24×C4C22×C4111yescharacteristic
610C24×C4C22×C4111yescharacteristic
611C2×#123—24no—
612C2×#123—24no—
613C2×#123C4×C4118yescomplemented
614C22×C4⋊C4C22×C4111yescharacteristic
615C22×C4⋊C4C22×C4111yescharacteristic
616C22×C4⋊C4C22×C4111yescharacteristic
617C22×C22⋊C4C22×C4111yescharacteristic
618C22×C22⋊C4C22×C4111yescharacteristic
619C22×C22⋊C4C22×C4111yescharacteristic
620C22×C22⋊C4C22×C4111yescharacteristic
621C22×C22⋊C4C22×C4111yescharacteristic
622C22×C22⋊C4C22×C4111yescharacteristic
623C22×C22⋊C4C22×C4111yescharacteristic
624C22×C22⋊C4C22×C4111yescharacteristic
625C22×C22⋊C4C22×C4111yescharacteristic
626C22×C22⋊C4C22×C4111yescharacteristic
627C22×C42C22×C4111yescharacteristic
628C22×C42C22×C4111yescharacteristic
629C22×C42C22×C4111yescharacteristic
630#388—24no—
631#386—24no—
632C4×C22⋊C4—24no—
633C4×C22⋊C4—24no—
634C2×#95C22×C4111yescharacteristic
635C2×#95C22×C4111yescharacteristic
636C2×#95C22×C4111yescharacteristic
637C2×#95C22×C4111yescharacteristic
638C2×#95C22×C4111yescharacteristic
639C2×#95C22×C4111yescharacteristic
640C2×#95C22×C4111yescharacteristic
641C2×#95C22×C4111yescharacteristic
642C2×#95C22×C4111yescharacteristic
643C2×#95C22×C4111yescharacteristic
644C2×#95C22×C4111yescharacteristic
645C2×#95C22×C4111yescharacteristic
646C2×#95C22×C4111yescharacteristic
647C2×#95C22×C4111yescharacteristic
648C2×#95C22×C4111yescharacteristic
649C2×#95C22×C4111yescharacteristic
650C41#1409611yescharacteristic, direct product factor, Sylow
651C25C23×C4111yescharacteristic
652C25C23×C4111yescharacteristic
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—41no—
658C22×D4—41no—
659C22×D4C2×C4×C4114yes—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—41no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4—41no—
673C23×C4C2×C4×C4114yescomplemented
674C23×C4C23×C4111yescharacteristic
675C23×C4C23×C4111yescharacteristic
676C23×C4C23×C4111yescharacteristic
677C23×C4C23×C4111yescharacteristic
678C23×C4C23×C4111yescharacteristic
679C23×C4C23×C4111yescharacteristic
680C23×C4C23×C4111yescharacteristic
681C23×C4C23×C4111yescharacteristic
682C23×C4C23×C4111yescharacteristic
683C23×C4C23×C4111yescharacteristic
684C23×C4C23×C4111yescharacteristic
685C23×C4C23×C4111yescharacteristic
686C23×C4C23×C4111yescharacteristic
687#123—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4C2×C4×C4114yescomplemented
696C2×C4⋊C4C2×C4×C4114yescomplemented
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4C2×C4×C4114yes—
722C2×C22⋊C4C2×C4×C4114yes—
723C2×C22⋊C4C2×C4×C4114yescomplemented
724C2×C22⋊C4D4×C4114yes—
725C2×C22⋊C4D4×C4114yes—
726C2×C22⋊C4D4×C4114yes—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—41no—
734C2×C42—41no—
735C2×C42—41no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—41no—
749#95—41no—
750#95—41no—
751#95—41no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C22×C4×C4112yes—
777C24C22×C4×C4112yes—
778C24C2×D4×C4112yes—
779C24C2×D4×C4112yes—
780C24C2×D4×C4112yes—
781C24#41×C4112yes—
782C24C24×C4111yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—28no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4C22×C4×C4112yes—
879C22×C4C22×C4×C4112yes—
880C22×C4C22×C4×C4112yes—
881C22×C4C22×C4×C4112yes—
882C22×C4C22×C4×C4112yes—
883C22×C4C2×D4×C4112yes—
884C22×C4C2×D4×C4112yes—
885C22×C4C2×D4×C4112yes—
886C22×C4C2×D4×C4112yes—
887C22×C4C2×D4×C4112yes—
888C22×C4C2×D4×C4112yes—
889C22×C4#41×C4112yes—
890C22×C4#41×C4112yes—
891C22×C4#41×C4112yes—
892C22×C4#41×C4112yes—
893C22×C4#41×C4112yes—
894C22×C4#41×C4112yes—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—44no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4C22⋊C4×C41116yescomplemented
908C42—44no—
909C42—44no—
910C42—44no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C2×C22⋊C4×C4114yes—
980C23C4×D4×C4114yes—
981C23C23×C4×C4111yescharacteristic
982C23C22×D4×C4111yescharacteristic
983C23C22×D4×C4111yescharacteristic
984C23C22×D4×C4111yescharacteristic
985C23C2×#41×C4111yescharacteristic
986C23C2×#41×C4111yescharacteristic
987C23C2×#41×C4111yescharacteristic
988C23C2×#41×C4111yescharacteristic
989C23C2×#41×C4111yescharacteristic
990C23C2×#41×C4111yescharacteristic
991C23C2×#41×C4111yescharacteristic
992C23H(5,𝔽2)×C4111yescharacteristic
993C23H(5,𝔽2)×C4111yescharacteristic
994C23H(5,𝔽2)×C4111yescharacteristic
995C232−1+4×C4111yescharacteristic
996D4—416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—416no—
1040C2×C4—416no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4C2×C22⋊C4×C4114yes—
1088C2×C4C2×C22⋊C4×C4114yes—
1089C2×C4#123×C4114yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C22×C22⋊C4×C4111yescharacteristic
1121C22C2×C4×D4×C4111yescharacteristic
1122C22C4×#41×C4111yescharacteristic
1123C22C4×#41×C4111yescharacteristic
1124C22C4×#41×C4111yescharacteristic
1125C22C41×#51811yescharacteristic
1126C22C41×#52011yescharacteristic
1127C22C2×#123×C4111yescharacteristic
1128C22C41×#52511yescharacteristic
1129C22C41×#52511yescharacteristic
1130C22C41×#52511yescharacteristic
1131C22C41×#52911yescharacteristic
1132C22C41×#52911yescharacteristic
1133C22C41×#53211yescharacteristic
1134C22C41×#53211yescharacteristic
1135C22C41×#53811yescharacteristic
1136C22C41×#53911yescharacteristic
1137C22C41×#54011yescharacteristic
1138C22C41×#54211yescharacteristic
1139C22D42×C4111yescharacteristic
1140C22D42×C4111yescharacteristic
1141C22C41×#54611yescharacteristic
1142C22C41×#54611yescharacteristic
1143C22C41×#54611yescharacteristic
1144C22C41×#54611yescharacteristic
1145C22C41×#54611yescharacteristic
1146C22C41×#54711yescharacteristic
1147C22C41×#54711yescharacteristic
1148C22C41×#54711yescharacteristic
1149C22C41×#55111yescharacteristic
1150C22C41×#55111yescharacteristic
1151C22C41×#55211yescharacteristic
1152C22C41×#55311yescharacteristic
1153C22C41×#55311yescharacteristic
1154C22C41×#55911yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—44no—
1170C2C41×#229711yescharacteristic
1171C2C4×#123×C4111yescharacteristic
1172C2C41×#233511yescharacteristic
1173C2D4×C22⋊C4×C4111yescharacteristic
1174C2C41×#233911yescharacteristic
1175C2C41×#235911yescharacteristic
1176C2C41×#237411yescharacteristic
1177C2C41×#241811yescharacteristic
1178C2C41×#242211yescharacteristic
1179C2C41×#245511yescharacteristic
1180C2C41×#245711yescharacteristic
1181C2C41×#246411yescharacteristic
1182C2C41×#247011yescharacteristic
1183C2C41×#255311yescharacteristic
1184C2C41×#255711yescharacteristic
subgroupG/H
center, socleC24×C41C24
commutatorC23C23×C4×C41
Frattini, cosocleC24C24×C41
prime radicalC23×D4×C41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#388C2semidirect
4. C2×C4×C22⋊C4×C41C2semidirect
5. C2×C4×C22⋊C4×C41C2semidirect
6. C41×#1445C2semidirect
7. C41×#1440C2semidirect
8. C41×#1439C2semidirect
10. C41×#1437C2semidirect
11. C41×#1436C2semidirect
12. C41×#1436C2semidirect
13. C41×C4⋊#95C2semidirect
14. C41×C22⋊#95C2semidirect
15. C41×C22⋊#95C2semidirect
21. C2×#123×C41C4semidirect
80. C23×C4×C41C2×C4semidirect
102. C2×C4⋊C4×C41C2×C4semidirect
103. C2×C4⋊C4×C41C2×C4semidirect
130. C2×C22⋊C4×C41C2×C4semidirect
314. C22⋊C4×C41C22⋊C4semidirect
496. C2×C4×C41#123semidirect
497. #14096C41direct (N × H)
577. C2×#388C2×C41semidirect
579. C2×C4×C22⋊C4C2×C41semidirect
580. C2×C4×C22⋊C4C2×C41semidirect
581. #1445C2×C41semidirect
582. #1440C2×C41semidirect
583. #1439C2×C41semidirect
585. #1437C2×C41semidirect
586. #1436C2×C41semidirect
587. #1436C2×C41semidirect
588. C4⋊#95C2×C41semidirect
589. C22⋊#95C2×C41semidirect
590. C22⋊#95C2×C41semidirect
613. C2×#123C4×C41semidirect
650. C41#14096direct (N × H)
673. C23×C4C2×C4×C41semidirect
695. C2×C4⋊C4C2×C4×C41semidirect
696. C2×C4⋊C4C2×C4×C41semidirect
723. C2×C22⋊C4C2×C4×C41semidirect
907. C22⋊C4C22⋊C4×C41semidirect
1089. C2×C4#123×C41semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C412
C2×C41×#3882
C2×C41×#3862
C2×C4×C22⋊C4×C412
C41×#14452
C41×#14402
C41×#14392
C41×#14382
C41×#14372
C41×#14362
C41×C4⋊#952
C41×C22⋊#952
#1409641