Finite Group Databasebeta

← C2×#20257257 #27124631

Subgroups — C2×#20257257 #27124631

Order 12032.

8622 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257257C2132yesmaximal, direct product factor
2C2×#15689856C212yesmaximal, complemented
3C2×#15689855C212yesmaximal, complemented
4C2×#15689792C212yesmaximal, complemented
5C2×#15689791C212yesmaximal, complemented
6C2×#15689770C212yesmaximal, complemented
7C2×#15689768C212yesmaximal, complemented
8C2×#15689766C212yesmaximal, complemented
9C2×#15689761C212yesmaximal, complemented
10C2×#15689726C212yesmaximal, complemented
11C2×#15689724C212yesmaximal, complemented
12C2×#15689689C212yesmaximal, complemented
13C2×#15689678C211yesmaximal, characteristic, complemented
14C2×#15689674C211yesmaximal, characteristic, complemented
15C2×#15689673C211yesmaximal, characteristic, complemented
16C2×#15689671C211yesmaximal, characteristic, complemented
17C2×#127×D47C211yesmaximal, characteristic, complemented
18C2×#15689595C212yesmaximal, complemented
19C2×C4×#10625350C211yesmaximal, characteristic, complemented
20C2×C47×#532C211yesmaximal, characteristic, complemented
21C22×#10625354C2212yescomplemented
22C22×#10625350C2211yescharacteristic
23C22×#10625350C2212yescomplemented
24C22×#10625352C2212yescomplemented
25C22×D4×D47C2212yes—
26C22×D4×D47C2212yes—
27C22×D4×D47C2212yes—
28#15689856C22132yescomplemented
29#15689855C22132yescomplemented
30#15689792C22132yescomplemented
31#15689791C22132yescomplemented
32#15689770C22132yescomplemented
33#15689768C22132yescomplemented
34#15689766C22132yescomplemented
35#15689761C22132yescomplemented
36#15689726C22132yescomplemented
37#15689724C22132yescomplemented
38#15689689C22132yescomplemented
39#15689678C22116yescomplemented
40#15689674C22116yescomplemented
41#15689673C22116yescomplemented
42#15689671C22116yescomplemented
43C2×#13094024C2211yescharacteristic, complemented
44C2×#13094021C2211yescharacteristic
45C2×#13094020C2212yes—
46C2×#13094020C2212yes—
47C2×#13094020C2212yes—
48C2×#13094020C2214yescomplemented
49#127×D47C22116yescomplemented
50C2×#13094015C2212yescomplemented
51C2×#13094013C2212yescomplemented
52C2×#13094012C2212yescomplemented
53C2×#13094011C2212yescomplemented
54C2×#13094010C2214yescomplemented
55C2×#13094008C2214yescomplemented
56C2×#13094007C2214yescomplemented
57C2×#13094006C2214yescomplemented
58C2×#13094006C2214yescomplemented
59C2×#13094004C2212yes—
60C2×#13094000C2212yes—
61C2×#13093999C2212yescomplemented
62C2×#13093999C2212yescomplemented
63C2×#13093998C2212yescomplemented
64C2×#13093998C2214yescomplemented
65C2×#13093998C2212yescomplemented
66C2×#13093997C2214yescomplemented
67C2×#13093996C2214yescomplemented
68C2×#13093995C2212yescomplemented
69C2×#13093995C2214yescomplemented
70C2×#13093995C2212yescomplemented
71C2×#13093994C2214yes—
72C2×#13093992C2214yes—
73#15689595C22132yescomplemented
74C4×#10625350C22116yescomplemented
75C2×Q8×Dic47C2212yescomplemented
76C2×C4×Dic94C2211yescharacteristic, complemented
77C2×C4×Dic94C2211yescharacteristic, complemented
78C2×#13093989C2212yescomplemented
79C2×C4×D188C2211yescharacteristic
80C2×C4×D188C2211yescharacteristic
81C2×C4×D188C2212yescomplemented
82C2×C4×D188C2212yescomplemented
83C2×D4×Dic47C2212yescomplemented
84C2×D4×Dic47C2212yescomplemented
85C2×#13093986C2212yescomplemented
86C2×#13093986C2212yescomplemented
87C2×C4×C22⋊D47C2211yescharacteristic
88C2×C4×C22⋊D47C2211yescharacteristic
89C2×C4×C22⋊D47C2211yescharacteristic, complemented
90C2×C4×C22⋊D47C2211yescharacteristic, complemented
91C2×C4×C22⋊D47C2214yescomplemented
92C2×(C22⋊D47)⋊C4C2214yescomplemented
93C2×#13093983C2211yescharacteristic, complemented
94C2×#13093982C2212yes—
95C2×#13093981C2211yescharacteristic
96C2×#13093981C2211yescharacteristic, complemented
97C22×(C2×D47)⋊C4C2214yes—
98C2×C22⋊C4×D47C2214yes—
99C2×C42×D47C2211yescharacteristic
100C2×C42×D47C2211yescharacteristic, complemented
101C22×#41×C47C2212yescomplemented
102C47×#532C22116yescomplemented
103C2×C4⋊Q8×C47C2211yescharacteristic, complemented
104C2×#127×C47C2211yescharacteristic
105C2×#124×C47C2212yescomplemented
106C2×#121×C47C2212yescomplemented
107C2×#121×C47C2212yescomplemented
108C2×C4×D4×C47C2212yescomplemented
109C2×C4×D4×C47C2212yescomplemented
110C22×C42×C47C2211yescharacteristic, complemented
111C24×D47C2314yes—
112C2×#10625354—48no—
113C2×#10625354C23116yescomplemented
114C2×#10625350—28no—
115C2×#10625350—48no—
116C2×#10625350C2318yes—
117C2×#10625350C23116yescomplemented
118C2×#10625352—48no—
119C2×#10625352C23116yescomplemented
120C22×Dic94C2312yes—
121C22×Dic94C2311yescharacteristic
122C22×D188C2312yes—
123C22×D188C2312yes—
124C22×D188C2311yescharacteristic
125C22×D188C2312yes—
126C22×D188C2314yes—
127C22×C22⋊D47C2314yes—
128C22×C22⋊D47C2311yescharacteristic
129C22×C22⋊D47C2311yescharacteristic
130C22×C22⋊D47C2314yes—
131C22×C22⋊D47C2314yes—
132C22×C22⋊D47C2314yes—
133C22×C22⋊D47C2314yes—
134C2×D4×D47—216no—
135C2×D4×D47—48no—
136C2×D4×D47—48no—
137C2×D4×D47C23116yes—
138C2×D4×D47C23116yes—
139C2×D4×D47C23116yes—
140C23×Dic47C2314yes—
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2314yes—
147C22×C4×D47C2314yes—
148C22×C4×D47C2311yescharacteristic
149#13094024C2318yescomplemented
150#13094021C2318yes—
151#13094020C23116yes—
152#13094020C23116yes—
153#13094020C23116yes—
154#13094020C23132yescomplemented
155#13094015C23116yescomplemented
156#13094013C23116yescomplemented
157#13094012C23116yescomplemented
158#13094011C23116yescomplemented
159#13094010C23132yescomplemented
160#13094008C23132yescomplemented
161#13094007C23132yescomplemented
162#13094006C23132yescomplemented
163#13094006C23132yescomplemented
164#13094004C23116yes—
165#13094000C23116yes—
166#13093999C23116yescomplemented
167#13093999C23116yescomplemented
168#13093998C23116yescomplemented
169#13093998C23132yescomplemented
170#13093998C23116yescomplemented
171#13093997C23132yescomplemented
172#13093996C23132yescomplemented
173#13093995C23116yescomplemented
174#13093995C23132yescomplemented
175#13093995C23116yescomplemented
176#13093994C23132yes—
177#13093992C23132yes—
178Q8×Dic47C23116yescomplemented
179C4×Dic94C2318yescomplemented
180C4×Dic94C2318yescomplemented
181#13093989C23116yescomplemented
182C4×D188C2318yes—
183C4×D188C2318yes—
184C4×D188C23116yescomplemented
185C4×D188C23116yescomplemented
186D4×Dic47C23116yescomplemented
187D4×Dic47C23116yescomplemented
188#13093986C23116yescomplemented
189#13093986C23116yescomplemented
190C4×C22⋊D47C2318yes—
191C4×C22⋊D47C2318yes—
192C4×C22⋊D47C2318yescomplemented
193C4×C22⋊D47C2318yescomplemented
194C4×C22⋊D47C23132yescomplemented
195(C22⋊D47)⋊C4C23132yescomplemented
196#13093983C2318yescomplemented
197#13093982C23116yes—
198#13093981C2318yes—
199#13093981C2318yescomplemented
200C2×C4⋊Dic47C2312yes—
201C2×C4⋊Dic47C2311yescharacteristic
202C2×C4⋊Dic47C2311yescharacteristic
203C2×C4⋊Dic47C2312yes—
204C2×C4⋊Dic47C2314yes—
205C2×Dic47⋊C4C2311yescharacteristic
206C2×Dic47⋊C4C2311yescharacteristic
207C2×Dic47⋊C4C2311yescharacteristic
208C2×Dic47⋊C4C2311yescharacteristic
209C2×Dic47⋊C4C2314yes—
210C2×C22⋊Dic47C2314yes—
211C2×C22⋊Dic47C2311yescharacteristic
212C2×C22⋊Dic47C2311yescharacteristic
213C2×C22⋊Dic47C2314yes—
214C2×(C2×D47)⋊C4C23132yes—
215C2×(C2×D47)⋊C4C2311yescharacteristic
216C2×(C2×D47)⋊C4C2314yes—
217C2×(C2×D47)⋊C4C2311yescharacteristic
218C2×(C2×D47)⋊C4C2314yes—
219C2×(C2×D47)⋊C4C2314yes—
220C2×(C2×D47)⋊C4C2311yescharacteristic
221C2×(C2×D47)⋊C4C2311yescharacteristic
222C2×(C2×D47)⋊C4C2314yes—
223C2×(C2×D47)⋊C4C2314yes—
224C22⋊C4×D47C23132yes—
225C2×C4×Dic47C2311yescharacteristic
226C2×C4×Dic47C2311yescharacteristic
227C2×C4×Dic47C2311yescharacteristic
228C2×C4×Dic47C2311yescharacteristic
229C2×C4×Dic47C2311yescharacteristic
230C2×C4×Dic47C2311yescharacteristic
231C2×C4×Dic47C2314yes—
232C42×D47C2318yes—
233C42×D47C2318yescomplemented
234C2×#41×C47—48no—
235C2×#41×C47C23116yescomplemented
236C22×Q8×C47C2312yes—
237C22×D4×C47C2312yes—
238C22×D4×C47C2312yes—
239C22×D4×C47C2312yes—
240C22×D4×C47C2314yes—
241C23×C4×C47C2311yescharacteristic
242C23×C4×C47C2311yescharacteristic
243C23×C4×C47C2311yescharacteristic
244C23×C4×C47C2314yes—
245C4⋊Q8×C47C2318yescomplemented
246#127×C47C2318yes—
247#124×C47C23116yescomplemented
248#121×C47C23116yescomplemented
249#121×C47C23116yescomplemented
250C4×D4×C47C23116yescomplemented
251C4×D4×C47C23116yescomplemented
252C2×C4⋊C4×C47C2312yes—
253C2×C4⋊C4×C47C2312yes—
254C2×C22⋊C4×C47C2314yes—
255C2×C22⋊C4×C47C2314yes—
256C2×C42×C47C2311yescharacteristic
257C2×C42×C47C2311yescharacteristic
258C2×C42×C47C2311yescharacteristic
259C2×C42×C47C2311yescharacteristic
260C2×C42×C47C2318yescomplemented
261C24×C47C2414yes—
262C24×C47C2411yescharacteristic
263C23×D47—216no—
264C23×D47—48no—
265C23×D47—48no—
266C23×D47C2414yes—
267C23×D47C2411yescharacteristic
268C23×D47C2411yescharacteristic
269C23×D47C24116yes—
270#41×C47—432no—
271C2×Q8×C47—28no—
272C2×Q8×C47C2418yes—
273C2×D4×C47—28no—
274C2×D4×C47—28no—
275C2×D4×C47—28no—
276C2×D4×C47—48no—
277C2×D4×C47C2418yes—
278C2×D4×C47C2418yes—
279C2×D4×C47C2418yes—
280C2×D4×C47C24116yes—
281C22×C4×C47—24no—
282C22×C4×C47—24no—
283C22×C4×C47—24no—
284C22×C4×C47—48no—
285C22×C4×C47C2411yescharacteristic
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2414yes—
289C22×C4×C47C2414yes—
290C22×C4×C47C2414yes—
291C22×C4×C47C2414yes—
292C22×C4×C47C24116yes—
293C22×C4×C47C2411yescharacteristic
294C22×C4×C47C2411yescharacteristic
295C22×C4×C47C2411yescharacteristic
296C2×C22⋊D47—24no—
297C2×C22⋊D47—216no—
298C2×C22⋊D47—24no—
299C2×C22⋊D47—48no—
300C2×C22⋊D47—48no—
301C2×C22⋊D47—48no—
302C2×C22⋊D47—48no—
303C2×C22⋊D47C24116yes—
304C2×C22⋊D47C2414yes—
305C2×C22⋊D47C2414yes—
306C2×C22⋊D47C24116yes—
307C2×C22⋊D47C24116yes—
308C2×C22⋊D47C24116yes—
309C2×C22⋊D47C24116yes—
310C22×Dic47—48no—
311C22×Dic47C2411yescharacteristic
312C22×Dic47C2411yescharacteristic
313C22×Dic47C2411yescharacteristic
314C22×Dic47C2411yescharacteristic
315C22×Dic47C2411yescharacteristic
316C22×Dic47C2414yes—
317C22×Dic47C24116yes—
318C22×Dic47C2411yescharacteristic
319#10625354—432no—
320#10625352—432no—
321D4×D47—264no—
322D4×D47—432no—
323D4×D47—432no—
324#10625350—232no—
325#10625350—432no—
326C2×D188—24no—
327C2×D188—28no—
328C2×D188—28no—
329C2×D188—28no—
330C2×D188—48no—
331C2×D188C2418yes—
332C2×D188C2418yes—
333C2×D188C2414yes—
334C2×D188C2418yes—
335C2×D188C24116yes—
336C2×C4×D47—24no—
337C2×C4×D47—24no—
338C2×C4×D47—24no—
339C2×C4×D47—24no—
340C2×C4×D47—24no—
341C2×C4×D47—48no—
342C2×C4×D47—48no—
343C2×C4×D47#4118yescomplemented
344C2×C4×D47C2414yes—
345C2×C4×D47C2414yes—
346C2×C4×D47C2414yes—
347C2×C4×D47C2414yes—
348C2×C4×D47C2414yes—
349C2×C4×D47C24116yes—
350C2×C4×D47C24116yes—
351C2×C4×D47C2414yes—
352C2×Dic94—28no—
353C2×Dic94—24no—
354C2×Dic94C2418yes—
355C2×Dic94C2414yes—
356C4⋊C4×C47C2418yes—
357C4⋊C4×C47C2418yes—
358C22⋊C4×C47C24116yes—
359C22⋊C4×C47C24116yes—
360C42×C47C2414yes—
361C42×C47C2414yes—
362C42×C47C2414yes—
363C42×C47C2414yes—
364C22⋊Dic47C24116yes—
365C22⋊Dic47C2414yes—
366C22⋊Dic47C2414yes—
367C22⋊Dic47C24116yes—
368(C2×D47)⋊C4C2414yes—
369(C2×D47)⋊C4C24116yes—
370(C2×D47)⋊C4C2414yes—
371(C2×D47)⋊C4C24116yes—
372(C2×D47)⋊C4C24116yes—
373(C2×D47)⋊C4C2414yes—
374(C2×D47)⋊C4C2414yes—
375(C2×D47)⋊C4C24116yes—
376(C2×D47)⋊C4C24116yes—
377C4⋊Dic47C2418yes—
378C4⋊Dic47C2414yes—
379C4⋊Dic47C2414yes—
380C4⋊Dic47C2418yes—
381C4⋊Dic47C24116yes—
382Dic47⋊C4C2414yes—
383Dic47⋊C4C2414yes—
384Dic47⋊C4C2414yes—
385Dic47⋊C4C2414yes—
386Dic47⋊C4C24116yes—
387C4×Dic47C2414yes—
388C4×Dic47C2414yes—
389C4×Dic47C2414yes—
390C4×Dic47C2414yes—
391C4×Dic47C2414yes—
392C4×Dic47C2414yes—
393C4×Dic47C24116yes—
394C23×C47—22no—
395C23×C47—28no—
396C23×C47—28no—
397C23×C47—22no—
398C23×C47—28no—
399C23×C47—22no—
400C23×C47C2518yes—
401C23×C47C2512yes—
402C23×C47C2511yescharacteristic
403C22×D47—22no—
404C22×D47—22no—
405C22×D47—22no—
406C22×D47—28no—
407C22×D47—22no—
408C22×D47—22no—
409C22×D47—28no—
410C22×D47—28no—
411C22×D47—232no—
412C22×D47—416no—
413C22×D47—416no—
414C22×D47—832no—
415C22×D47C2×#4114yes—
416C22×D47C2518yes—
417C22×D47C2512yes—
418C22×D47C2512yes—
419Q8×C47—216no—
420D4×C47—216no—
421D4×C47—216no—
422D4×C47—216no—
423D4×C47—416no—
424C2×C4×C47—22no—
425C2×C4×C47—22no—
426C2×C4×C47—28no—
427C2×C4×C47—22no—
428C2×C4×C47—28no—
429C2×C4×C47—28no—
430C2×C4×C47—28no—
431C2×C4×C47—416no—
432C2×C4×C47C2×#4114yes—
433C2×C4×C47H(5,𝔽2)14yes—
434C2×C4×C47H(5,𝔽2)14yes—
435C2×C4×C47C2518yes—
436C2×C4×C47C2512yes—
437C2×C4×C47C2512yes—
438C2×C4×C47C2512yes—
439C2×C4×C47C2512yes—
440C2×C4×C47C2512yes—
441C2×C4×C47C2512yes—
442C22⋊D47—28no—
443C22⋊D47—28no—
444C22⋊D47—232no—
445C22⋊D47—416no—
446C22⋊D47—416no—
447C22⋊D47—416no—
448C22⋊D47—416no—
449C2×Dic47—22no—
450C2×Dic47—28no—
451C2×Dic47—22no—
452C2×Dic47—22no—
453C2×Dic47—22no—
454C2×Dic47—22no—
455C2×Dic47—416no—
456C2×Dic47C2×#4114yes—
457C2×Dic47C2512yes—
458C2×Dic47C2512yes—
459C2×Dic47C2512yes—
460C2×Dic47C2512yes—
461C2×Dic47C2512yes—
462C2×Dic47C2518yes—
463C2×Dic47C2512yes—
464D188—28no—
465D188—216no—
466D188—216no—
467D188—216no—
468D188—416no—
469C4×D47—28no—
470C4×D47—28no—
471C4×D47—28no—
472C4×D47—28no—
473C4×D47—28no—
474C4×D47—416no—
475C4×D47—416no—
476C4×D47C2×#41116yescomplemented
477Dic94—216no—
478Dic94—28no—
479C2×#3508—471nomaximal, Sylow
480C22×C47—22no—
481C22×C47—28no—
482C22×C47—28no—
483C22×C47—22no—
484C22×C47—28no—
485C22×C47—22no—
486C22×C47—416no—
487C22×C47—44no—
488C22×C47C22×#4112yes—
489C22×C47C2×H(5,𝔽2)12yes—
490C22×C47C2×H(5,𝔽2)12yes—
491C22×C47C2611yescharacteristic
492C2×D47—22no—
493C2×D47—22no—
494C2×D47—28no—
495C2×D47—22no—
496C2×D47—28no—
497C2×D47—22no—
498C2×D47—22no—
499C2×D47—28no—
500C2×D47—28no—
501C2×D47—44no—
502C2×D47—416no—
503C2×D47—832no—
504C2×D47C22×#4114yes—
505C4×C47—22no—
506C4×C47—22no—
507C4×C47—28no—
508C4×C47—22no—
509C4×C47C22×#4114yes—
510C4×C47C2×H(5,𝔽2)14yes—
511C4×C47C2×H(5,𝔽2)14yes—
512Dic47—22no—
513Dic47—28no—
514Dic47—22no—
515Dic47—22no—
516Dic47—22no—
517Dic47—22no—
518Dic47C22×#4114yes—
519#3508—4732no—
520C2×#559—472no—
521C2×#559—472no—
522C2×#550—472no—
523C2×#550—472no—
524C2×#546—472no—
525C2×#546—472no—
526C2×#546—472no—
527C2×#546—472no—
528C2×#540—472no—
529C2×#540—472no—
530C2×#535—472no—
531C2×#533—471no—
532C2×#532—471no—
533C2×#532—471no—
534C2×#532—471no—
535C2×#532D4711yescharacteristic, complemented
536C22×#127—471no—
537C2×#518—472no—
538C2×C4×#41—471no—
539C2×C47—48no—
540C2×C47—42no—
541C2×C47#350814yescomplemented
542C2×C47C23×#4111yescharacteristic
543C2×C47C22×H(5,𝔽2)11yescharacteristic
544C2×C47C22×H(5,𝔽2)11yescharacteristic
545D47—24no—
546D47—42no—
547D47—48no—
548C22×#41—472no—
549C22×#41—472no—
550C22×#41—471no—
551C22×#41—472no—
552C22×#41C2×D4712yescomplemented
553C23×D4—472no—
554C23×D4—472no—
555C23×D4—472no—
556#559—4732no—
557#559—4732no—
558#550—4732no—
559#550—4732no—
560#546—4732no—
561#546—4732no—
562#546—4732no—
563#546—4732no—
564#540—4732no—
565#540—4732no—
566#535—4732no—
567#533—4716no—
568#532—4716no—
569#532—4716no—
570#532—4716no—
571#532C2×D47116yescomplemented
572C2×C4⋊Q8—471no—
573C2×C4⋊Q8C2×D4711yescharacteristic, complemented
574C2×#127—472no—
575C2×#127—472no—
576C2×#127—472no—
577C2×#127—474no—
578C2×#127—4716no—
579C2×#127—471no—
580C2×#127C2×D4711yescharacteristic
581C2×#125—472no—
582C2×#124—472no—
583C2×#124—472no—
584C2×#124—474no—
585C2×#124—472no—
586C2×#124C2×D4712yescomplemented
587C2×#123—474no—
588C2×#123—474no—
589C2×#123—474no—
590C2×#123—474no—
591C2×C22⋊Q8—472no—
592C2×C22⋊Q8—472no—
593C2×#121—472no—
594C2×#121—472no—
595C2×#121—474no—
596C2×#121—474no—
597C2×#121—472no—
598C2×#121—472no—
599C2×#121—474no—
600C2×#121—472no—
601C2×#121—472no—
602C2×#121—474no—
603C2×#121C2×D4712yescomplemented
604C2×#121C2×D4712yescomplemented
605C2×#120—474no—
606C2×#120—474no—
607#518—4732no—
608C4×#41—4716no—
609C2×C4×Q8—472no—
610C2×C4×Q8—472no—
611C2×C4×Q8—471no—
612C2×C4×Q8—471no—
613C2×C4×D4—472no—
614C2×C4×D4—472no—
615C2×C4×D4—471no—
616C2×C4×D4—471no—
617C2×C4×D4—471no—
618C2×C4×D4—471no—
619C2×C4×D4—474no—
620C2×C4×D4—472no—
621C2×C4×D4—472no—
622C2×C4×D4—474no—
623C2×C4×D4—471no—
624C2×C4×D4—471no—
625C2×C4×D4—472no—
626C2×C4×D4—472no—
627C2×C4×D4C2×D4712yescomplemented
628C2×C4×D4C2×D4712yescomplemented
629C2×#117—471no—
630C2×#117—472no—
631C2×#117—471no—
632C2×#117—471no—
633C22×C22⋊C4—474no—
634C22×C22⋊C4—474no—
635C22×C42—471no—
636C22×C42—471no—
637C22×C42C2×D4711yescharacteristic, complemented
638C47C2×#350811yescharacteristic, complemented, Sylow
639C25—474no—
640C2×#41—48no—
641C2×#41—4716no—
642C2×#41—4716no—
643C2×#41—478no—
644C2×#41—4716no—
645C2×#41—948no—
646C2×#41—1888no—
647C2×#41—1888no—
648C2×#41—1888no—
649C2×#41C22×D47116yescomplemented
650C22×Q8—471no—
651C22×Q8—472no—
652C22×Q8C22×D4712yes—
653C22×D4—471no—
654C22×D4—474no—
655C22×D4—471no—
656C22×D4—474no—
657C22×D4—474no—
658C22×D4—474no—
659C22×D4—474no—
660C22×D4—4716no—
661C22×D4—4716no—
662C22×D4—4716no—
663C22×D4—471no—
664C22×D4—472no—
665C22×D4—472no—
666C22×D4—472no—
667C22×D4—474no—
668C22×D4—9416no—
669C22×D4—1888no—
670C22×D4—1888no—
671C22×D4C22×D4712yes—
672C22×D4C22×D4712yes—
673C22×D4C22×D4712yes—
674C22×D4C22×D4714yes—
675C23×C4—471no—
676C23×C4—474no—
677C23×C4—471no—
678C23×C4—471no—
679C23×C4—471no—
680C23×C4—471no—
681C23×C4—471no—
682C23×C4—474no—
683C23×C4—474no—
684C23×C4C22×D4711yescharacteristic
685C23×C4C22×D4711yescharacteristic
686C23×C4C22×D4711yescharacteristic
687C23×C4C22×D4714yes—
688C4⋊Q8—478no—
689C4⋊Q8C22×D4718yescomplemented
690#127—4716no—
691#127—4716no—
692#127—4716no—
693#127—4732no—
694#127—478no—
695#127C22×D4718yes—
696#125—4716no—
697#124—4716no—
698#124—4716no—
699#124—4732no—
700#124—4716no—
701#124C22×D47116yescomplemented
702#123—4732no—
703#123—4732no—
704#123—4732no—
705#123—4732no—
706C22⋊Q8—4716no—
707C22⋊Q8—4716no—
708#121—4716no—
709#121—4716no—
710#121—4732no—
711#121—4732no—
712#121—4716no—
713#121—4716no—
714#121—4732no—
715#121—4716no—
716#121—4716no—
717#121—4732no—
718#121C22×D47116yescomplemented
719#121C22×D47116yescomplemented
720#120—4732no—
721#120—4732no—
722C4×Q8—4716no—
723C4×Q8—4716no—
724C4×Q8—478no—
725C4×Q8—478no—
726C4×D4—4716no—
727C4×D4—4716no—
728C4×D4—478no—
729C4×D4—478no—
730C4×D4—478no—
731C4×D4—478no—
732C4×D4—4732no—
733C4×D4—4716no—
734C4×D4—4716no—
735C4×D4—4732no—
736C4×D4—478no—
737C4×D4—478no—
738C4×D4—4716no—
739C4×D4—4716no—
740C4×D4C22×D47116yescomplemented
741C4×D4C22×D47116yescomplemented
742#117—478no—
743#117—4716no—
744#117—478no—
745#117—478no—
746C2×C4⋊C4—471no—
747C2×C4⋊C4—471no—
748C2×C4⋊C4—472no—
749C2×C4⋊C4—471no—
750C2×C4⋊C4—471no—
751C2×C4⋊C4—471no—
752C2×C4⋊C4—471no—
753C2×C4⋊C4—472no—
754C2×C4⋊C4—474no—
755C2×C4⋊C4—474no—
756C2×C4⋊C4C22×D4712yes—
757C2×C4⋊C4C22×D4712yes—
758C2×C22⋊C4—474no—
759C2×C22⋊C4—471no—
760C2×C22⋊C4—471no—
761C2×C22⋊C4—474no—
762C2×C22⋊C4—471no—
763C2×C22⋊C4—471no—
764C2×C22⋊C4—474no—
765C2×C22⋊C4—474no—
766C2×C22⋊C4—474no—
767C2×C22⋊C4—4732no—
768C2×C22⋊C4—471no—
769C2×C22⋊C4—471no—
770C2×C22⋊C4—474no—
771C2×C22⋊C4—474no—
772C2×C22⋊C4—4732no—
773C2×C22⋊C4C22×D4714yes—
774C2×C22⋊C4C22×D4714yes—
775C2×C42—471no—
776C2×C42—471no—
777C2×C42—474no—
778C2×C42—471no—
779C2×C42—471no—
780C2×C42—471no—
781C2×C42—471no—
782C2×C42—478no—
783C2×C42—478no—
784C2×C42C22×D4711yescharacteristic
785C2×C42C22×D4711yescharacteristic
786C2×C42C22×D4711yescharacteristic
787C2×C42C22×D4711yescharacteristic
788C2×C42C22×D4718yescomplemented
789C24—471no—
790C24—474no—
791C24—471no—
792C24—4716no—
793C24—9416no—
794C24—1888no—
795C24—1888no—
796C24C23×D4714yes—
797C24C23×D4711yescharacteristic
798#41—432no—
799#41—9432no—
800#41—18832no—
801#41—18832no—
802#41—18832no—
803C2×Q8—28no—
804C2×Q8—474no—
805C2×Q8—478no—
806C2×Q8—944no—
807C2×Q8—948no—
808C2×Q8C23×D4718yes—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—48no—
813C2×D4—474no—
814C2×D4—4716no—
815C2×D4—474no—
816C2×D4—4716no—
817C2×D4—4716no—
818C2×D4—4716no—
819C2×D4—4716no—
820C2×D4—474no—
821C2×D4—478no—
822C2×D4—478no—
823C2×D4—478no—
824C2×D4—4716no—
825C2×D4—944no—
826C2×D4—9464no—
827C2×D4—9416no—
828C2×D4—944no—
829C2×D4—944no—
830C2×D4—948no—
831C2×D4—948no—
832C2×D4—948no—
833C2×D4—1888no—
834C2×D4—18832no—
835C2×D4—18832no—
836C2×D4—1888no—
837C2×D4—1888no—
838C2×D4—1888no—
839C2×D4—1888no—
840C2×D4C23×D4718yes—
841C2×D4C23×D4718yes—
842C2×D4C23×D4718yes—
843C2×D4C23×D47116yes—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—48no—
848C22×C4—471no—
849C22×C4—478no—
850C22×C4—474no—
851C22×C4—471no—
852C22×C4—471no—
853C22×C4—471no—
854C22×C4—471no—
855C22×C4—471no—
856C22×C4—474no—
857C22×C4—4716no—
858C22×C4—474no—
859C22×C4—474no—
860C22×C4—474no—
861C22×C4—474no—
862C22×C4—474no—
863C22×C4—4716no—
864C22×C4—4716no—
865C22×C4—944no—
866C22×C4—944no—
867C22×C4—944no—
868C22×C4—944no—
869C22×C4—944no—
870C22×C4—1888no—
871C22×C4—1888no—
872C22×C4—1888no—
873C22×C4C23×D4714yes—
874C22×C4C23×D4714yes—
875C22×C4C23×D4714yes—
876C22×C4C23×D4714yes—
877C22×C4C23×D4711yescharacteristic
878C22×C4C23×D4711yescharacteristic
879C22×C4C23×D4711yescharacteristic
880C22×C4C23×D47116yes—
881C22×C4C23×D4711yescharacteristic
882C22×C4C23×D4711yescharacteristic
883C22×C4C23×D4711yescharacteristic
884C4⋊C4—474no—
885C4⋊C4—474no—
886C4⋊C4—474no—
887C4⋊C4—474no—
888C4⋊C4—4716no—
889C4⋊C4—478no—
890C4⋊C4—474no—
891C4⋊C4—474no—
892C4⋊C4—478no—
893C4⋊C4—4716no—
894C4⋊C4C23×D4718yes—
895C4⋊C4C23×D4718yes—
896C22⋊C4—4716no—
897C22⋊C4—474no—
898C22⋊C4—474no—
899C22⋊C4—4716no—
900C22⋊C4—474no—
901C22⋊C4—474no—
902C22⋊C4—4716no—
903C22⋊C4—4716no—
904C22⋊C4—4716no—
905C22⋊C4—474no—
906C22⋊C4—474no—
907C22⋊C4—4716no—
908C22⋊C4—4716no—
909C22⋊C4C23×D47116yes—
910C22⋊C4C23×D47116yes—
911C42—474no—
912C42—474no—
913C42—474no—
914C42—474no—
915C42—474no—
916C42—474no—
917C42—4716no—
918C42C23×D4714yes—
919C42C23×D4714yes—
920C42C23×D4714yes—
921C42C23×D4714yes—
922C23—22no—
923C23—28no—
924C23—22no—
925C23—28no—
926C23—22no—
927C23—28no—
928C23—474no—
929C23—472no—
930C23—478no—
931C23—472no—
932C23—9432no—
933C23—942no—
934C23—942no—
935C23—942no—
936C23—948no—
937C23—942no—
938C23—948no—
939C23—942no—
940C23—948no—
941C23—37632no—
942C23—18816no—
943C23—18816no—
944C23C24×D4718yes—
945C23C24×D4712yes—
946C23C24×D4711yescharacteristic
947Q8—216no—
948Q8—948no—
949Q8—9416no—
950D4—216no—
951D4—216no—
952D4—216no—
953D4—416no—
954D4—948no—
955D4—9432no—
956D4—948no—
957D4—948no—
958D4—9416no—
959D4—9416no—
960D4—9416no—
961D4—18816no—
962D4—18816no—
963D4—18816no—
964D4—18816no—
965D4—18816no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—28no—
969C2×C4—22no—
970C2×C4—28no—
971C2×C4—28no—
972C2×C4—28no—
973C2×C4—416no—
974C2×C4—474no—
975C2×C4—472no—
976C2×C4—4716no—
977C2×C4—472no—
978C2×C4—472no—
979C2×C4—472no—
980C2×C4—472no—
981C2×C4—472no—
982C2×C4—478no—
983C2×C4—942no—
984C2×C4—942no—
985C2×C4—942no—
986C2×C4—942no—
987C2×C4—942no—
988C2×C4—948no—
989C2×C4—948no—
990C2×C4—948no—
991C2×C4—948no—
992C2×C4—948no—
993C2×C4—948no—
994C2×C4—18816no—
995C2×C4—18816no—
996C2×C4—18816no—
997C2×C4#41×D4714yes—
998C2×C4#1309406914yes—
999C2×C4#1309407014yes—
1000C2×C4C24×D4718yes—
1001C2×C4C24×D4712yes—
1002C2×C4C24×D4712yes—
1003C2×C4C24×D4712yes—
1004C2×C4C24×D4712yes—
1005C2×C4C24×D4712yes—
1006C2×C4C24×D4712yes—
1007C22—22no—
1008C22—28no—
1009C22—22no—
1010C22—28no—
1011C22—22no—
1012C22—28no—
1013C22—416no—
1014C22—44no—
1015C22—474no—
1016C22—942no—
1017C22—942no—
1018C22—948no—
1019C22—942no—
1020C22—948no—
1021C22—942no—
1022C22—948no—
1023C22—942no—
1024C22—948no—
1025C22—37632no—
1026C22—18816no—
1027C22—1884no—
1028C22C2×#41×D4712yes—
1029C22C2×#1309406912yes—
1030C22C2×#1309407012yes—
1031C22C25×D4711yescharacteristic
1032C4—22no—
1033C4—22no—
1034C4—28no—
1035C4—22no—
1036C4—474no—
1037C4—942no—
1038C4—942no—
1039C4—942no—
1040C4—942no—
1041C4—942no—
1042C4—948no—
1043C4C2×#41×D4714yes—
1044C4C2×#1309406914yes—
1045C4C2×#1309407014yes—
1046C2—48no—
1047C2—42no—
1048C2—944no—
1049C2—1888no—
1050C2—1882no—
1051C2#2025725714yesdirect product factor
1052C2C22×#41×D4711yescharacteristic
1053C2C22×#1309406911yescharacteristic
1054C2C22×#1309407011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#532C2
socleC23×C47C25
hypercenterC2×#532D47
hypocenterC47C2×#3508
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #20257257C2direct (N × H)
2. C2×#15689856C2semidirect
3. C2×#15689855C2semidirect
4. C2×#15689792C2semidirect
5. C2×#15689791C2semidirect
6. C2×#15689770C2semidirect
7. C2×#15689768C2semidirect
8. C2×#15689766C2semidirect
9. C2×#15689761C2semidirect
10. C2×#15689726C2semidirect
11. C2×#15689724C2semidirect
12. C2×#15689689C2semidirect
13. C2×#15689678C2semidirect
14. C2×#15689674C2semidirect
15. C2×#15689673C2semidirect
16. C2×#15689671C2semidirect
17. C2×#127×D47C2semidirect
18. C2×#15689595C2semidirect
19. C2×C4×#10625350C2semidirect
20. C2×C47×#532C2semidirect
21. C22×#10625354C22semidirect
23. C22×#10625350C22semidirect
24. C22×#10625352C22semidirect
28. #15689856C22semidirect
29. #15689855C22semidirect
30. #15689792C22semidirect
31. #15689791C22semidirect
32. #15689770C22semidirect
33. #15689768C22semidirect
34. #15689766C22semidirect
35. #15689761C22semidirect
36. #15689726C22semidirect
37. #15689724C22semidirect
38. #15689689C22semidirect
39. #15689678C22semidirect
40. #15689674C22semidirect
41. #15689673C22semidirect
42. #15689671C22semidirect
43. C2×#13094024C22semidirect
48. C2×#13094020C22semidirect
49. #127×D47C22semidirect
50. C2×#13094015C22semidirect
51. C2×#13094013C22semidirect
52. C2×#13094012C22semidirect
53. C2×#13094011C22semidirect
54. C2×#13094010C22semidirect
55. C2×#13094008C22semidirect
56. C2×#13094007C22semidirect
57. C2×#13094006C22semidirect
58. C2×#13094006C22semidirect
61. C2×#13093999C22semidirect
62. C2×#13093999C22semidirect
63. C2×#13093998C22semidirect
64. C2×#13093998C22semidirect
65. C2×#13093998C22semidirect
66. C2×#13093997C22semidirect
67. C2×#13093996C22semidirect
68. C2×#13093995C22semidirect
69. C2×#13093995C22semidirect
70. C2×#13093995C22semidirect
73. #15689595C22semidirect
74. C4×#10625350C22semidirect
75. C2×Q8×Dic47C22semidirect
76. C2×C4×Dic94C22semidirect
77. C2×C4×Dic94C22semidirect
78. C2×#13093989C22semidirect
81. C2×C4×D188C22semidirect
82. C2×C4×D188C22semidirect
83. C2×D4×Dic47C22semidirect
84. C2×D4×Dic47C22semidirect
85. C2×#13093986C22semidirect
86. C2×#13093986C22semidirect
89. C2×C4×C22⋊D47C22semidirect
90. C2×C4×C22⋊D47C22semidirect
91. C2×C4×C22⋊D47C22semidirect
92. C2×(C22⋊D47)⋊C4C22semidirect
93. C2×#13093983C22semidirect
96. C2×#13093981C22semidirect
100. C2×C42×D47C22semidirect
101. C22×#41×C47C22semidirect
102. C47×#532C22semidirect
103. C2×C4⋊Q8×C47C22semidirect
105. C2×#124×C47C22semidirect
106. C2×#121×C47C22semidirect
107. C2×#121×C47C22semidirect
108. C2×C4×D4×C47C22semidirect
109. C2×C4×D4×C47C22semidirect
110. C22×C42×C47C22semidirect
113. C2×#10625354C23semidirect
117. C2×#10625350C23semidirect
119. C2×#10625352C23semidirect
149. #13094024C23semidirect
154. #13094020C23semidirect
155. #13094015C23semidirect
156. #13094013C23semidirect
157. #13094012C23semidirect
158. #13094011C23semidirect
159. #13094010C23semidirect
160. #13094008C23semidirect
161. #13094007C23semidirect
162. #13094006C23semidirect
163. #13094006C23semidirect
166. #13093999C23semidirect
167. #13093999C23semidirect
168. #13093998C23semidirect
169. #13093998C23semidirect
170. #13093998C23semidirect
171. #13093997C23semidirect
172. #13093996C23semidirect
173. #13093995C23semidirect
174. #13093995C23semidirect
175. #13093995C23semidirect
178. Q8×Dic47C23semidirect
179. C4×Dic94C23semidirect
180. C4×Dic94C23semidirect
181. #13093989C23semidirect
184. C4×D188C23semidirect
185. C4×D188C23semidirect
186. D4×Dic47C23semidirect
187. D4×Dic47C23semidirect
188. #13093986C23semidirect
189. #13093986C23semidirect
192. C4×C22⋊D47C23semidirect
193. C4×C22⋊D47C23semidirect
194. C4×C22⋊D47C23semidirect
195. (C22⋊D47)⋊C4C23semidirect
196. #13093983C23semidirect
199. #13093981C23semidirect
233. C42×D47C23semidirect
235. C2×#41×C47C23semidirect
245. C4⋊Q8×C47C23semidirect
247. #124×C47C23semidirect
248. #121×C47C23semidirect
249. #121×C47C23semidirect
250. C4×D4×C47C23semidirect
251. C4×D4×C47C23semidirect
260. C2×C42×C47C23semidirect
343. C2×C4×D47#41semidirect
476. C4×D47C2×#41semidirect
535. C2×#532D47semidirect
541. C2×C47#3508semidirect
552. C22×#41C2×D47semidirect
571. #532C2×D47semidirect
573. C2×C4⋊Q8C2×D47semidirect
586. C2×#124C2×D47semidirect
603. C2×#121C2×D47semidirect
604. C2×#121C2×D47semidirect
627. C2×C4×D4C2×D47semidirect
628. C2×C4×D4C2×D47semidirect
637. C22×C42C2×D47semidirect
638. C47C2×#3508semidirect
649. C2×#41C22×D47semidirect
689. C4⋊Q8C22×D47semidirect
701. #124C22×D47semidirect
718. #121C22×D47semidirect
719. #121C22×D47semidirect
740. C4×D4C22×D47semidirect
741. C4×D4C22×D47semidirect
788. C2×C42C22×D47semidirect
1051. C2#20257257direct (N × H)

Maximal subgroups

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

subgroupindex
#202572572
C2×#156898562
C2×#156898552
C2×#156897922
C2×#156897912
C2×#156897702
C2×#156897682
C2×#156897662
C2×#156897612
C2×#156897262
C2×#156897242
C2×#156896892
C2×#156896782
C2×#156896742
C2×#156896732
C2×#156896712
C2×#127×D472
C2×#156895952
C2×C4×#106253502
C2×C47×#5322
C2×#350847