Finite Group Databasebeta

← C41×#14725 #23790926

Subgroups — C41×#14725 #23790926

Order 10496.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C41C211yesmaximal, characteristic
2C23×C22⋊C4×C41C211yesmaximal, characteristic, complemented
3C2×C41×#394C212yesmaximal, complemented
4C2×C41×#386C211yesmaximal, characteristic, complemented
5C2×C41×#386C211yesmaximal, characteristic, complemented
6C2×C41×#380C211yesmaximal, characteristic, complemented
7C2×C41×#379C211yesmaximal, characteristic, complemented
8C41×#1440C212yesmaximal, complemented
9C41×#1439C212yesmaximal, complemented
10C41×#1438C212yesmaximal, complemented
11C41×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C41C2211yescharacteristic
13C23×D4×C41C2211yescharacteristic
14C23×D4×C41C2212yes—
15C24×C4×C41C2211yescharacteristic
16C24×C4×C41C2211yescharacteristic
17C2×#120×C41—24no—
18C2×#120×C41—24no—
19C2×#120×C41—24no—
20C22×C4⋊C4×C41C2212yescomplemented
21C22×C22⋊C4×C41—24no—
22C22×C22⋊C4×C41—28no—
23C22×C22⋊C4×C41C2211yescharacteristic
24C22×C22⋊C4×C41C2211yescharacteristic
25C22×C22⋊C4×C41C2212yes—
26C22×C22⋊C4×C41C2212yes—
27C22×C22⋊C4×C41C2212yes—
28C22×C22⋊C4×C41C2211yescharacteristic
29C22×C22⋊C4×C41C2212yes—
30C22×C22⋊C4×C41C2212yes—
31C22×C22⋊C4×C41C2211yescharacteristic, complemented
32C22×C22⋊C4×C41C2212yescomplemented
33C22×C22⋊C4×C41C2211yescharacteristic, complemented
34C41×#394—28no—
35C41×#386—24no—
36C41×#386—24no—
37C41×#380—24no—
38C41×#379—24no—
39C2×#95×C41C2212yescomplemented
40C2×#95×C41C2211yescharacteristic, complemented
41C2×#95×C41C2212yescomplemented
42C2×#95×C41C2211yescharacteristic, complemented
43C2×#95×C41C2212yescomplemented
44C2×#95×C41C2212yescomplemented
45C25×C41—24no—
46C25×C41—22no—
47C25×C41—24no—
48C25×C41—22no—
49C25×C41—22no—
50C25×C41—22no—
51C25×C41—22no—
52C25×C41—22no—
53C25×C41—42no—
54C25×C41—42no—
55C25×C41D414yes—
56C25×C41C2311yescharacteristic
57C25×C41C2312yes—
58C25×C41C2311yescharacteristic
59C22×D4×C41—24no—
60C22×D4×C41—24no—
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—24no—
68C22×D4×C41—24no—
69C22×D4×C41—24no—
70C22×D4×C41—42no—
71C22×D4×C41—42no—
72C22×D4×C41D414yes—
73C23×C4×C41—22no—
74C23×C4×C41—22no—
75C23×C4×C41—22no—
76C23×C4×C41—24no—
77C23×C4×C41—24no—
78C23×C4×C41—22no—
79C23×C4×C41—22no—
80C23×C4×C41—42no—
81C23×C4×C41—42no—
82C23×C4×C41D414yescomplemented
83C23×C4×C41C2312yes—
84C23×C4×C41C2311yescharacteristic
85C23×C4×C41C2311yescharacteristic
86C23×C4×C41C2311yescharacteristic
87C23×C4×C41C2312yes—
88C23×C4×C41C2312yes—
89C23×C4×C41C2311yescharacteristic
90C23×C4×C41C2311yescharacteristic
91#120×C41—232no—
92C2×C4⋊C4×C41—24no—
93C2×C4⋊C4×C41—24no—
94C2×C4⋊C4×C41—42no—
95C2×C22⋊C4×C41—232no—
96C2×C22⋊C4×C41—24no—
97C2×C22⋊C4×C41—24no—
98C2×C22⋊C4×C41—22no—
99C2×C22⋊C4×C41—22no—
100C2×C22⋊C4×C41—24no—
101C2×C22⋊C4×C41—24no—
102C2×C22⋊C4×C41—24no—
103C2×C22⋊C4×C41—24no—
104C2×C22⋊C4×C41—24no—
105C2×C22⋊C4×C41—24no—
106C2×C22⋊C4×C41—24no—
107C2×C22⋊C4×C41—22no—
108C2×C22⋊C4×C41—24no—
109C2×C22⋊C4×C41—22no—
110C2×C22⋊C4×C41—22no—
111C2×C22⋊C4×C41—22no—
112C2×C22⋊C4×C41—22no—
113C2×C22⋊C4×C41—24no—
114C2×C22⋊C4×C41—24no—
115C2×C22⋊C4×C41—24no—
116C2×C22⋊C4×C41—22no—
117C2×C22⋊C4×C41—22no—
118C2×C22⋊C4×C41—22no—
119C2×C22⋊C4×C41—24no—
120C2×C22⋊C4×C41—24no—
121C2×C22⋊C4×C41—42no—
122C2×C22⋊C4×C41—42no—
123C2×C22⋊C4×C41—42no—
124C2×C22⋊C4×C41—42no—
125C2×C22⋊C4×C41D414yes—
126C2×C22⋊C4×C41D418yescomplemented
127#95×C41—24no—
128#95×C41—22no—
129#95×C41—22no—
130#95×C41—24no—
131#95×C41—24no—
132#95×C41—42no—
133C24×C41—22no—
134C24×C41—22no—
135C24×C41—22no—
136C24×C41—22no—
137C24×C41—28no—
138C24×C41—28no—
139C24×C41—216no—
140C24×C41—216no—
141C24×C41—28no—
142C24×C41—22no—
143C24×C41—22no—
144C24×C41—22no—
145C24×C41—22no—
146C24×C41—22no—
147C24×C41—22no—
148C24×C41—22no—
149C24×C41—22no—
150C24×C41—22no—
151C24×C41—22no—
152C24×C41—22no—
153C24×C41—22no—
154C24×C41—28no—
155C24×C41—28no—
156C24×C41—21no—
157C24×C41—22no—
158C24×C41—21no—
159C24×C41—21no—
160C24×C41—21no—
161C24×C41—21no—
162C24×C41—21no—
163C24×C41—22no—
164C24×C41—22no—
165C24×C41—22no—
166C24×C41—48no—
167C24×C41—48no—
168C24×C41—48no—
169C24×C41—48no—
170C24×C41—48no—
171C24×C41—48no—
172C24×C41—48no—
173C24×C41—48no—
174C24×C41—48no—
175C24×C41—44no—
176C24×C41—44no—
177C24×C41—48no—
178C24×C41—44no—
179C24×C41—44no—
180C24×C41—44no—
181C24×C41—44no—
182C24×C41C2×D412yes—
183C24×C41C2×D414yes—
184C24×C41C2×D414yes—
185C24×C41C2×D412yes—
186C24×C41C2×D412yes—
187C24×C41C2×D412yes—
188C24×C41C2×D412yes—
189C24×C41#4114yes—
190C24×C41#4112yes—
191C24×C41#4112yes—
192C24×C41#4112yes—
193C24×C41C2411yescharacteristic
194C2×D4×C41—216no—
195C2×D4×C41—28no—
196C2×D4×C41—28no—
197C2×D4×C41—28no—
198C2×D4×C41—48no—
199C2×D4×C41—48no—
200C2×D4×C41—48no—
201C2×D4×C41—48no—
202C2×D4×C41—48no—
203C2×D4×C41—48no—
204C2×D4×C41—44no—
205C2×D4×C41—44no—
206C2×D4×C41—44no—
207C2×D4×C41—44no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—22no—
211C22×C4×C41—28no—
212C22×C4×C41—28no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—22no—
216C22×C4×C41—22no—
217C22×C4×C41—22no—
218C22×C4×C41—22no—
219C22×C4×C41—22no—
220C22×C4×C41—21no—
221C22×C4×C41—21no—
222C22×C4×C41—22no—
223C22×C4×C41—22no—
224C22×C4×C41—21no—
225C22×C4×C41—22no—
226C22×C4×C41—21no—
227C22×C4×C41—21no—
228C22×C4×C41—21no—
229C22×C4×C41—22no—
230C22×C4×C41—22no—
231C22×C4×C41—22no—
232C22×C4×C41—22no—
233C22×C4×C41—22no—
234C22×C4×C41—22no—
235C22×C4×C41—28no—
236C22×C4×C41—21no—
237C22×C4×C41—22no—
238C22×C4×C41—22no—
239C22×C4×C41—21no—
240C22×C4×C41—22no—
241C22×C4×C41—22no—
242C22×C4×C41—21no—
243C22×C4×C41—21no—
244C22×C4×C41—22no—
245C22×C4×C41—21no—
246C22×C4×C41—22no—
247C22×C4×C41—21no—
248C22×C4×C41—22no—
249C22×C4×C41—22no—
250C22×C4×C41—22no—
251C22×C4×C41—22no—
252C22×C4×C41—22no—
253C22×C4×C41—44no—
254C22×C4×C41—48no—
255C22×C4×C41—48no—
256C22×C4×C41—48no—
257C22×C4×C41—48no—
258C22×C4×C41—44no—
259C22×C4×C41—44no—
260C22×C4×C41C2×D412yes—
261C22×C4×C41C2×D412yes—
262C22×C4×C41C2×D414yes—
263C22×C4×C41C2×D414yes—
264C22×C4×C41C2×D412yes—
265C22×C4×C41C2×D414yes—
266C4⋊C4×C41—48no—
267C22⋊C4×C41—216no—
268C22⋊C4×C41—216no—
269C22⋊C4×C41—28no—
270C22⋊C4×C41—216no—
271C22⋊C4×C41—48no—
272C22⋊C4×C41—44no—
273C22⋊C4×C41—48no—
274C22⋊C4×C41—44no—
275C22⋊C4×C41—48no—
276C22⋊C4×C41—44no—
277C22⋊C4×C41—44no—
278C23×C41—22no—
279C23×C41—24no—
280C23×C41—22no—
281C23×C41—24no—
282C23×C41—22no—
283C23×C41—24no—
284C23×C41—22no—
285C23×C41—24no—
286C23×C41—24no—
287C23×C41—24no—
288C23×C41—24no—
289C23×C41—24no—
290C23×C41—24no—
291C23×C41—24no—
292C23×C41—24no—
293C23×C41—24no—
294C23×C41—232no—
295C23×C41—24no—
296C23×C41—24no—
297C23×C41—24no—
298C23×C41—24no—
299C23×C41—24no—
300C23×C41—24no—
301C23×C41—24no—
302C23×C41—24no—
303C23×C41—24no—
304C23×C41—24no—
305C23×C41—24no—
306C23×C41—24no—
307C23×C41—24no—
308C23×C41—24no—
309C23×C41—24no—
310C23×C41—24no—
311C23×C41—24no—
312C23×C41—24no—
313C23×C41—22no—
314C23×C41—22no—
315C23×C41—22no—
316C23×C41—24no—
317C23×C41—24no—
318C23×C41—432no—
319C23×C41—432no—
320C23×C41—416no—
321C23×C41—416no—
322C23×C41—416no—
323C23×C41—416no—
324C23×C41—432no—
325C23×C41—432no—
326C23×C41—416no—
327C23×C41—42no—
328C23×C41—42no—
329C23×C41—42no—
330C23×C41—42no—
331C23×C41—42no—
332C23×C41—42no—
333C23×C41—42no—
334C23×C41—42no—
335C23×C41—42no—
336C23×C41—42no—
337C23×C41—42no—
338C23×C41—42no—
339C23×C41—42no—
340C23×C41—42no—
341C23×C41—42no—
342C23×C41—42no—
343C23×C41—416no—
344C23×C41—41no—
345C23×C41—41no—
346C23×C41—41no—
347C23×C41—42no—
348C23×C41—41no—
349C23×C41—42no—
350C23×C41—41no—
351C23×C41—41no—
352C23×C41—41no—
353C23×C41—42no—
354C23×C41—41no—
355C23×C41—42no—
356C23×C41—42no—
357C23×C41—42no—
358C23×C41—42no—
359C23×C41—42no—
360C23×C41—42no—
361C23×C41—42no—
362C23×C41#12014yes—
363C23×C41#12118yes—
364C23×C41#12114yes—
365C23×C41#12114yes—
366C23×C41#12114yes—
367C23×C41#12314yes—
368C23×C41#12314yes—
369C23×C41#12414yes—
370C23×C41C22×D411yescharacteristic
371C23×C41C22×D411yescharacteristic
372C23×C41C22×D411yescharacteristic
373C23×C41C22×D412yes—
374C23×C41C22×D411yescharacteristic
375C23×C41C2×#4111yescharacteristic
376C23×C41C2×#4111yescharacteristic
377C23×C41C2×#4111yescharacteristic
378C23×C41C2×#4112yes—
379C23×C41H(5,𝔽2)12yes—
380C23×C41H(5,𝔽2)12yes—
381D4×C41—432no—
382D4×C41—416no—
383C2×C4×C41—22no—
384C2×C4×C41—22no—
385C2×C4×C41—24no—
386C2×C4×C41—24no—
387C2×C4×C41—24no—
388C2×C4×C41—22no—
389C2×C4×C41—22no—
390C2×C4×C41—24no—
391C2×C4×C41—22no—
392C2×C4×C41—22no—
393C2×C4×C41—22no—
394C2×C4×C41—22no—
395C2×C4×C41—24no—
396C2×C4×C41—24no—
397C2×C4×C41—24no—
398C2×C4×C41—24no—
399C2×C4×C41—416no—
400C2×C4×C41—416no—
401C2×C4×C41—42no—
402C2×C4×C41—41no—
403C2×C4×C41—41no—
404C2×C4×C41—42no—
405C2×C4×C41—41no—
406C2×C4×C41—41no—
407C2×C4×C41—42no—
408C2×C4×C41—42no—
409C2×C4×C41—42no—
410C2×C4×C41—42no—
411C2×C4×C41—42no—
412C2×C4×C41—42no—
413C2×C4×C41—42no—
414C2×C4×C41—42no—
415C2×C4×C41—41no—
416C2×C4×C41—42no—
417C2×C4×C41—41no—
418C2×C4×C41—42no—
419C2×C4×C41—41no—
420C2×C4×C41—42no—
421C2×C4×C41—41no—
422C2×C4×C41—42no—
423C2×C4×C41—42no—
424C2×C4×C41—41no—
425C2×C4×C41—42no—
426C2×C4×C41—41no—
427C2×C4×C41—42no—
428C2×C4×C41—42no—
429C2×C4×C41—42no—
430C2×C4×C41—42no—
431C2×C4×C41—42no—
432C2×C4×C41#12014yescomplemented
433#14725C4111yesmaximal, characteristic, direct product factor, Sylow
434C22×C41—24no—
435C22×C41—24no—
436C22×C41—24no—
437C22×C41—24no—
438C22×C41—28no—
439C22×C41—24no—
440C22×C41—28no—
441C22×C41—28no—
442C22×C41—28no—
443C22×C41—24no—
444C22×C41—28no—
445C22×C41—28no—
446C22×C41—28no—
447C22×C41—464no—
448C22×C41—44no—
449C22×C41—44no—
450C22×C41—44no—
451C22×C41—44no—
452C22×C41—44no—
453C22×C41—44no—
454C22×C41—44no—
455C22×C41—44no—
456C22×C41—44no—
457C22×C41—44no—
458C22×C41—44no—
459C22×C41—44no—
460C22×C41—42no—
461C22×C41—42no—
462C22×C41—44no—
463C22×C41—44no—
464C22×C41—42no—
465C22×C41—81no—
466C22×C41—81no—
467C22×C41—81no—
468C22×C41—81no—
469C22×C41—82no—
470C22×C41—82no—
471C22×C41#39418yescomplemented
472C22×C41C2×#12011yescharacteristic
473C22×C41C2×#12011yescharacteristic
474C22×C41C2×#12111yescharacteristic
475C22×C41C2×#12112yes—
476C22×C41C2×#12111yescharacteristic
477C22×C41C2×#12111yescharacteristic
478C22×C41C2×#12311yescharacteristic
479C22×C41C2×#12311yescharacteristic
480C22×C41#52511yescharacteristic
481C22×C41#52512yes—
482C22×C41C2×#12411yescharacteristic
483C22×C41#53412yes—
484C22×C41#53411yescharacteristic
485C22×C41#53511yescharacteristic
486C22×C41#53812yes—
487C22×C41D4212yes—
488C22×C41D4212yes—
489C22×C41#54612yes—
490C22×C41#54612yes—
491C22×C41#54612yes—
492C22×C41#54612yes—
493C22×C41#55112yes—
494C22×C41#55112yes—
495C4×C41—24no—
496C4×C41—42no—
497C4×C41—44no—
498C4×C41—42no—
499C4×C41—44no—
500C4×C41—81no—
501C4×C41—81no—
502C4×C41—82no—
503C22×#120C2×C4111yescharacteristic
504C23×C22⋊C4C2×C4111yescharacteristic, complemented
505C2×#394C2×C4112yescomplemented
506C2×#386C2×C4111yescharacteristic, complemented
507C2×#386C2×C4111yescharacteristic, complemented
508C2×#380C2×C4111yescharacteristic, complemented
509C2×#379C2×C4111yescharacteristic, complemented
510#1440C2×C4112yescomplemented
511#1439C2×C4112yescomplemented
512#1438C2×C4112yescomplemented
513C22⋊#95C2×C4111yescharacteristic, complemented
514C2×C41—28no—
515C2×C41—48no—
516C2×C41—82no—
517C2×C41C2×#39411yescharacteristic
518C2×C41#240811yescharacteristic
519C2×C41#241011yescharacteristic
520C2×C41#241012yes—
521C2×C41#241111yescharacteristic
522C2×C41#241212yes—
523C2×C41#241812yes—
524C2×C41#247212yes—
525C2×C41#253411yescharacteristic
526C2×C41#261711yescharacteristic
527C2×C41#284711yescharacteristic
528C26C22×C4111yescharacteristic
529C23×D4C22×C4111yescharacteristic
530C23×D4C22×C4112yes—
531C24×C4C22×C4111yescharacteristic
532C24×C4C22×C4111yescharacteristic
533C2×#120—24no—
534C2×#120—24no—
535C2×#120—24no—
536C22×C4⋊C4C22×C4112yescomplemented
537C22×C22⋊C4—24no—
538C22×C22⋊C4—28no—
539C22×C22⋊C4C22×C4112yes—
540C22×C22⋊C4C22×C4112yes—
541C22×C22⋊C4C22×C4112yes—
542C22×C22⋊C4C22×C4111yescharacteristic
543C22×C22⋊C4C22×C4111yescharacteristic
544C22×C22⋊C4C22×C4111yescharacteristic
545C22×C22⋊C4C22×C4112yes—
546C22×C22⋊C4C22×C4112yes—
547C22×C22⋊C4C22×C4111yescharacteristic, complemented
548C22×C22⋊C4C22×C4112yescomplemented
549C22×C22⋊C4C22×C4111yescharacteristic, complemented
550#394—28no—
551#386—24no—
552#386—24no—
553#380—24no—
554#379—24no—
555C2×#95C22×C4112yescomplemented
556C2×#95C22×C4112yescomplemented
557C2×#95C22×C4111yescharacteristic, complemented
558C2×#95C22×C4112yescomplemented
559C2×#95C22×C4111yescharacteristic, complemented
560C2×#95C22×C4112yescomplemented
561C41#1472511yescharacteristic, direct product factor, Sylow
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C4114yes—
573C25C23×C4111yescharacteristic
574C25C23×C4112yes—
575C25C23×C4111yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C4114yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C4114yescomplemented
600C23×C4C23×C4112yes—
601C23×C4C23×C4111yescharacteristic
602C23×C4C23×C4111yescharacteristic
603C23×C4C23×C4111yescharacteristic
604C23×C4C23×C4112yes—
605C23×C4C23×C4112yes—
606C23×C4C23×C4111yescharacteristic
607C23×C4C23×C4111yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C4114yes—
643C2×C22⋊C4D4×C4118yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C4112yes—
700C24C2×D4×C4114yes—
701C24C2×D4×C4114yes—
702C24C2×D4×C4112yes—
703C24C2×D4×C4112yes—
704C24C2×D4×C4112yes—
705C24C2×D4×C4112yes—
706C24#41×C4114yes—
707C24#41×C4112yes—
708C24#41×C4112yes—
709C24#41×C4112yes—
710C24C24×C4111yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C4112yes—
778C22×C4C2×D4×C4112yes—
779C22×C4C2×D4×C4114yes—
780C22×C4C2×D4×C4114yes—
781C22×C4C2×D4×C4112yes—
782C22×C4C2×D4×C4114yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—432no—
843C23—432no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C4114yes—
880C23#121×C4118yes—
881C23#121×C4114yes—
882C23#121×C4114yes—
883C23#121×C4114yes—
884C23#123×C4114yes—
885C23#123×C4114yes—
886C23#124×C4114yes—
887C23C22×D4×C4111yescharacteristic
888C23C22×D4×C4111yescharacteristic
889C23C22×D4×C4111yescharacteristic
890C23C22×D4×C4112yes—
891C23C22×D4×C4111yescharacteristic
892C23C2×#41×C4111yescharacteristic
893C23C2×#41×C4111yescharacteristic
894C23C2×#41×C4111yescharacteristic
895C23C2×#41×C4112yes—
896C23H(5,𝔽2)×C4112yes—
897C23H(5,𝔽2)×C4112yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C4114yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22C41×#39418yescomplemented
988C22C2×#120×C4111yescharacteristic
989C22C2×#120×C4111yescharacteristic
990C22C2×#121×C4111yescharacteristic
991C22C2×#121×C4111yescharacteristic
992C22C2×#121×C4112yes—
993C22C2×#121×C4111yescharacteristic
994C22C2×#123×C4111yescharacteristic
995C22C2×#123×C4111yescharacteristic
996C22C41×#52511yescharacteristic
997C22C41×#52512yes—
998C22C2×#124×C4111yescharacteristic
999C22C41×#53411yescharacteristic
1000C22C41×#53412yes—
1001C22C41×#53511yescharacteristic
1002C22C41×#53812yes—
1003C22D42×C4112yes—
1004C22D42×C4112yes—
1005C22C41×#54612yes—
1006C22C41×#54612yes—
1007C22C41×#54612yes—
1008C22C41×#54612yes—
1009C22C41×#55112yes—
1010C22C41×#55112yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×C41×#39411yescharacteristic
1023C2C41×#240811yescharacteristic
1024C2C41×#241011yescharacteristic
1025C2C41×#241012yes—
1026C2C41×#241111yescharacteristic
1027C2C41×#241212yes—
1028C2C41×#241812yes—
1029C2C41×#247212yes—
1030C2C41×#253411yescharacteristic
1031C2C41×#261711yescharacteristic
1032C2C41×#284711yescharacteristic
subgroupG/H
center, socleC24×C41C24
commutator, Frattini, cosocleC24C24×C41
prime radicalC22×#120×C41C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C41C2semidirect
3. C2×C41×#394C2semidirect
4. C2×C41×#386C2semidirect
5. C2×C41×#386C2semidirect
6. C2×C41×#380C2semidirect
7. C2×C41×#379C2semidirect
8. C41×#1440C2semidirect
9. C41×#1439C2semidirect
10. C41×#1438C2semidirect
11. C41×C22⋊#95C2semidirect
20. C22×C4⋊C4×C41C22semidirect
31. C22×C22⋊C4×C41C22semidirect
32. C22×C22⋊C4×C41C22semidirect
33. C22×C22⋊C4×C41C22semidirect
39. C2×#95×C41C22semidirect
40. C2×#95×C41C22semidirect
41. C2×#95×C41C22semidirect
42. C2×#95×C41C22semidirect
43. C2×#95×C41C22semidirect
44. C2×#95×C41C22semidirect
82. C23×C4×C41D4semidirect
126. C2×C22⋊C4×C41D4semidirect
432. C2×C4×C41#120semidirect
433. #14725C41direct (N × H)
471. C22×C41#394semidirect
504. C23×C22⋊C4C2×C41semidirect
505. C2×#394C2×C41semidirect
506. C2×#386C2×C41semidirect
507. C2×#386C2×C41semidirect
508. C2×#380C2×C41semidirect
509. C2×#379C2×C41semidirect
510. #1440C2×C41semidirect
511. #1439C2×C41semidirect
512. #1438C2×C41semidirect
513. C22⋊#95C2×C41semidirect
536. C22×C4⋊C4C22×C41semidirect
547. C22×C22⋊C4C22×C41semidirect
548. C22×C22⋊C4C22×C41semidirect
549. C22×C22⋊C4C22×C41semidirect
555. C2×#95C22×C41semidirect
556. C2×#95C22×C41semidirect
557. C2×#95C22×C41semidirect
558. C2×#95C22×C41semidirect
559. C2×#95C22×C41semidirect
560. C2×#95C22×C41semidirect
561. C41#14725direct (N × H)
599. C23×C4D4×C41semidirect
643. C2×C22⋊C4D4×C41semidirect
949. C2×C4#120×C41semidirect
987. C22C41×#394semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C412
C23×C22⋊C4×C412
C2×C41×#3942
C2×C41×#3862
C2×C41×#3802
C2×C41×#3792
C41×#14402
C41×#14392
C41×#14382
C41×C22⋊#952
#1472541