Finite Group Databasebeta

← #27081473

Subgroups — #27081473

Order 12032.

1864 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256683C211yesmaximal, characteristic
2#20252554C214yesmaximal, complemented
3#20252523C214yesmaximal, complemented
4#20252508C214yesmaximal, complemented
5#20252500C214yesmaximal, complemented
6#20252328C211yesmaximal, characteristic, complemented
7#20252325C211yesmaximal, characteristic, complemented
8#20252118C212yesmaximal, complemented
9#20252110C212yesmaximal, complemented
10#20252106C211yesmaximal, characteristic, complemented
11#20252050C212yesmaximal, complemented
12C2×#15689178C211yesmaximal, characteristic, complemented
13#20251954C212yesmaximal, complemented
14#423×D47C211yesmaximal, characteristic, complemented
15C47×#2932C211yesmaximal, characteristic, complemented
16C2×#13094031C2212yes—
17C2×M16×D47C2212yes—
18#15689680C2211yescharacteristic
19#15689678C411yescharacteristic
20#15689678C411yescharacteristic
21#15689671C411yescharacteristic
22#15689671C411yescharacteristic
23#15689655C2212yes—
24#15689655C2212yes—
25#15689654C412yes—
26#15689654C412yes—
27#15689652C412yes—
28#15689652C412yes—
29#15689633C412yes—
30#15689633C412yes—
31#15689630C2212yes—
32#41×Dic47C2212yes—
33C4×#10625352C2212yes—
34C4×#10625352C2212yes—
35C2×C42×D47C2211yescharacteristic
36#15689252C2214yescomplemented
37#15689252C2214yescomplemented
38#15689251C2214yescomplemented
39#15689251C2214yescomplemented
40#15689199C2214yes—
41#15689198C2214yes—
42#15689197C2214yes—
43#15689195C2214yescomplemented
44#15689195C2214yescomplemented
45#15689194C2214yes—
46#15689192C2214yes—
47#15689191C2214yes—
48C8×C22⋊D47C2214yes—
49(C22⋊D47)⋊C8C2214yes—
50#15689181C2214yescomplemented
51#15689181C2214yescomplemented
52#15689178C2212yes—
53#15689178C2212yes—
54#15689178C2212yes—
55#15689178C2212yes—
56#15689177C2214yescomplemented
57#15689173C2214yescomplemented
58#15689151C2212yes—
59#15689151C2214yescomplemented
60#15689149C2212yes—
61#15689149C2214yescomplemented
62#15689147C2211yescharacteristic
63#15689146C2212yes—
64#15689146C2214yescomplemented
65#15689145C2212yes—
66#15689145C2212yes—
67C2×Dic47⋊C8C2211yescharacteristic
68C2×Dic47⋊C8C2211yescharacteristic
69C2×Dic47⋊C8C2214yescomplemented
70C4⋊C8×D47C2212yes—
71C4⋊C8×D47C2212yes—
72#15689090C2212yes—
73C2×(C2×D47)⋊C8C2211yescharacteristic
74C2×(C2×D47)⋊C8C2211yescharacteristic
75#15689081C2212yes—
76#15689078C2212yes—
77C2×#13093935C2211yescharacteristic
78C2×#131×C47C2212yes—
79C47×#532C2211yescharacteristic
80C47×#435C2214yescomplemented
81C47×#435C2214yescomplemented
82C47×#423C2211yescharacteristic
83C47×#408C2212yes—
84C2×#97×C47C2211yescharacteristic
85C2×#10625352C2×C412yes—
86C2×#10625352C2×C412yes—
87C22×C4×D47C2×C411yescharacteristic
88C22×C4×D47C2×C411yescharacteristic
89C22×C4×D47C2311yescharacteristic
90#13094031—44no—
91C2×#10625329C2312yes—
92C2×#10625329C2314yes—
93C2×#10625324C2314yes—
94M16×D47—44no—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2314yes—
98C2×C8×D47C2314yes—
99#13094024C2×C411yescharacteristic
100#13094024C2×C411yescharacteristic
101#13094017C2×C414yes—
102#13094017C2×C414yes—
103#13094016C2×C412yes—
104#13094015C2×C412yes—
105#13094015C2×C412yes—
106#13094011C2×C412yes—
107#13094011C2×C412yes—
108#13094006C2×C414yes—
109#13094006C2×C414yes—
110#13094005C2×C414yes—
111#13094004C2×C412yes—
112#13094004C2×C412yes—
113#13094003C2×C412yes—
114#13094003C2×C412yes—
115#13094000C2×C412yes—
116#13094000C2×C412yes—
117#13093995C2×C412yes—
118#13093995C2×C412yes—
119#13093995C2×C412yes—
120#13093995C2×C412yes—
121#13093992C2×C414yes—
122Q8×Dic47C2×C412yes—
123Q8×Dic47C2×C412yes—
124C4×Dic94C2312yes—
125C4×Dic94C2312yes—
126#13093989C2×C412yes—
127#13093989C2×C412yes—
128D4×Dic47C2×C412yes—
129D4×Dic47C2×C412yes—
130D4×Dic47C2×C414yes—
131D4×Dic47C2×C414yes—
132D4×Dic47C2×C412yes—
133D4×Dic47C2×C412yes—
134C4×C22⋊D47C2314yes—
135C4×C22⋊D47C2314yes—
136(C22⋊D47)⋊C4C2×C414yes—
137(C22⋊D47)⋊C4C2×C414yes—
138#13093983C2312yes—
139#13093983C2314yes—
140#13093982C2×C412yes—
141#13093982C2×C412yes—
142#13093980C2×C414yes—
143#13093980C2×C414yes—
144C2×C4×Dic47C2×C411yescharacteristic
145C2×C4×Dic47C2×C411yescharacteristic
146C2×C4×Dic47C2311yescharacteristic
147C2×C4×Dic47C2314yes—
148C42×D47C2×C411yescharacteristic
149C42×D47C2×C411yescharacteristic
150C42×D47C2×C411yescharacteristic
151C42×D47C2×C411yescharacteristic
152C42×D47C2311yescharacteristic
153C42×D47C2311yescharacteristic
154C42×D47C2311yescharacteristic
155C42×D47C2311yescharacteristic
156C4⋊(C47⋊C8)C2312yes—
157C4⋊(C47⋊C8)C2312yes—
158Dic47⋊C8C2314yes—
159Dic47⋊C8C2314yes—
160Dic47⋊C8C2314yes—
161Dic47⋊C8C2314yes—
162Dic47⋊C8C2314yes—
163Dic47⋊C8C2314yes—
164Dic47⋊C8C2312yes—
165Dic47⋊C8C2312yes—
166Dic47⋊C8C2312yes—
167Dic47⋊C8C2312yes—
168C22⋊(C47⋊C8)C2314yes—
169C22⋊(C47⋊C8)C2314yes—
170(C2×D47)⋊C8C2312yes—
171(C2×D47)⋊C8C2312yes—
172(C2×D47)⋊C8C2312yes—
173(C2×D47)⋊C8C2312yes—
174#13093935C2312yes—
175#13093935C2312yes—
176#13093934C2314yes—
177#13093934C2314yes—
178C8×Dic47C2314yes—
179C8×Dic47C2314yes—
180C2×#41×C47C2312yes—
181#131×C47—44no—
182C2×M16×C47C2312yes—
183C2×M16×C47C2314yes—
184C22×C8×C47C2311yescharacteristic
185C22×C8×C47C2311yescharacteristic
186C22×C8×C47C2314yes—
187C4⋊Q8×C47C2×C411yescharacteristic
188#127×C47C2×C411yescharacteristic
189#124×C47C2×C412yes—
190#121×C47C2×C412yes—
191#121×C47C2×C412yes—
192C4×D4×C47C2312yes—
193C4×D4×C47C2312yes—
194C2×C42×C47C2311yescharacteristic
195C4⋊C8×C47C2312yes—
196C4⋊C8×C47C2312yes—
197C22⋊C8×C47C2314yes—
198C22⋊C8×C47C2314yes—
199#97×C47C2312yes—
200#97×C47C2312yes—
201C23×D47C22×C411yescharacteristic
202#41×C47—24no—
203#41×C47—24no—
204C2×Q8×C47C22×C412yes—
205C2×D4×C47C22×C414yes—
206C2×D4×C47C22×C412yes—
207C2×D4×C47C22×C412yes—
208C2×D4×C47C22×C412yes—
209C22×C4×C47C22×C411yescharacteristic
210C22×C4×C47C22×C411yescharacteristic
211C22×C4×C47C2414yes—
212C22×C4×C47C2411yescharacteristic
213C2×C22⋊D47C22×C414yes—
214C2×C22⋊D47C22×C414yes—
215C22×Dic47C22×C411yescharacteristic
216C22×Dic47C22×C411yescharacteristic
217C22×Dic47C22×C414yes—
218C22×Dic47C22×C411yescharacteristic
219C22×Dic47C22×C414yes—
220#10625352—44no—
221#10625352—44no—
222C2×C4×D47—22no—
223C2×C4×D47—22no—
224C2×C4×D47—42no—
225C2×C4×D47—42no—
226C2×C4×D47C22×C411yescharacteristic
227C2×C4×D47C22×C411yescharacteristic
228C2×C4×D47C22×C411yescharacteristic
229C2×C4×D47C22×C411yescharacteristic
230C2×C4×D47C22×C411yescharacteristic
231C2×C4×D47C22×C411yescharacteristic
232C2×C4×D47C22×C411yescharacteristic
233C2×C4×D47C22×C411yescharacteristic
234C2×C4×D47C22×C411yescharacteristic
235C2×C4×D47C22×C411yescharacteristic
236C2×C4×D47C2411yescharacteristic
237C2×C4×D47C2411yescharacteristic
238C2×Dic94C22×C412yes—
239C2×Dic94C22×C412yes—
240M16×C47—24no—
241M16×C47—44no—
242C2×C8×C47—22no—
243C2×C8×C47—22no—
244C2×C8×C47—44no—
245C2×C8×C47C2414yes—
246C2×C8×C47C2412yes—
247C2×C8×C47C2412yes—
248C4⋊C4×C47C22×C412yes—
249C4⋊C4×C47C22×C412yes—
250C22⋊C4×C47C22×C414yes—
251C22⋊C4×C47C22×C414yes—
252C42×C47C22×C411yescharacteristic
253C42×C47C22×C411yescharacteristic
254C42×C47C2411yescharacteristic
255C42×C47C2411yescharacteristic
256C22⋊Dic47C22×C414yes—
257C22⋊Dic47C22×C414yes—
258C22⋊Dic47C22×C414yes—
259C22⋊Dic47C22×C414yes—
260C22⋊Dic47C22×C414yes—
261(C2×D47)⋊C4C22×C414yes—
262(C2×D47)⋊C4C22×C414yes—
263C4⋊Dic47C22×C412yes—
264C4⋊Dic47C22×C412yes—
265C4⋊Dic47C22×C412yes—
266C4⋊Dic47C22×C412yes—
267C4⋊Dic47C22×C414yes—
268C4⋊Dic47C22×C414yes—
269Dic47⋊C4C22×C414yes—
270Dic47⋊C4C22×C414yes—
271Dic47⋊C4C22×C414yes—
272Dic47⋊C4C22×C414yes—
273C4×Dic47C22×C411yescharacteristic
274C4×Dic47C22×C411yescharacteristic
275C4×Dic47C22×C411yescharacteristic
276C4×Dic47C22×C411yescharacteristic
277C4×Dic47C22×C411yescharacteristic
278C4×Dic47C22×C411yescharacteristic
279C4×Dic47C22×C411yescharacteristic
280C4×Dic47C22×C411yescharacteristic
281C4×Dic47C22×C411yescharacteristic
282C4×Dic47C22×C411yescharacteristic
283C4×Dic47C22×C414yes—
284C4×Dic47C22×C414yes—
285C4×Dic47C2414yes—
286C4×Dic47C2411yescharacteristic
287C4×Dic47C2411yescharacteristic
288#10625329—24no—
289#10625329—44no—
290C2×C47⋊C8—22no—
291C2×C47⋊C8—22no—
292C2×C47⋊C8—44no—
293C2×C47⋊C8C2412yes—
294C2×C47⋊C8C2414yes—
295C2×C47⋊C8C2412yes—
296#10625324—44no—
297C8×D47—44no—
298C23×C47C23×C414yes—
299C23×C47C23×C411yescharacteristic
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—41no—
303C22×D47C23×C411yescharacteristic
304C22×D47C23×C411yescharacteristic
305Q8×C47—24no—
306D4×C47—28no—
307D4×C47—24no—
308D4×C47—42no—
309D4×C47—42no—
310C2×C4×C47—24no—
311C2×C4×C47—24no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47C23×C411yescharacteristic
315C2×C4×C47C23×C411yescharacteristic
316C2×C4×C47C23×C414yes—
317C2×C4×C47C23×C411yescharacteristic
318C2×C4×C47C23×C411yescharacteristic
319C2×C4×C47C23×C411yescharacteristic
320C2×C4×C47H(5,𝔽2)12yes—
321C2×C4×C472−1+412yes—
322C2×C4×C47C2511yescharacteristic
323C22⋊D47—28no—
324C22⋊D47—44no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—28no—
328C2×Dic47—41no—
329C2×Dic47—44no—
330C2×Dic47C23×C411yescharacteristic
331C2×Dic47C23×C411yescharacteristic
332C2×Dic47C23×C411yescharacteristic
333C2×Dic47C23×C411yescharacteristic
334C2×Dic47C23×C411yescharacteristic
335C2×Dic47C23×C414yes—
336C2×Dic47C23×C414yes—
337C2×Dic47C23×C411yescharacteristic
338C4×D47—22no—
339C4×D47—22no—
340C4×D47—22no—
341C4×D47—22no—
342C4×D47—21no—
343C4×D47—21no—
344C4×D47—21no—
345C4×D47—21no—
346C4×D47—22no—
347C4×D47—22no—
348C4×D47—41no—
349C4×D47—41no—
350C4×D47—41no—
351C4×D47—41no—
352Dic94—42no—
353Dic94—42no—
354C8×C47—24no—
355C8×C47—22no—
356C8×C47—22no—
357C47⋊C8—24no—
358C47⋊C8—22no—
359C47⋊C8—22no—
360#60269—471nomaximal, Sylow
361C22×C47—21no—
362C22×C47—21no—
363C22×C47—24no—
364C22×C47—24no—
365C22×C47—24no—
366C22×C47#52012yes—
367C22×C47C24×C411yescharacteristic
368C2×D47—21no—
369C2×D47—21no—
370C2×D47—21no—
371C2×D47—21no—
372C2×D47—21no—
373C2×D47—44no—
374C2×D47#56812yes—
375C4×C47—24no—
376C4×C47—21no—
377C4×C47—21no—
378C4×C47—21no—
379C4×C47—21no—
380C4×C47#52012yes—
381C4×C47C2×H(5,𝔽2)11yescharacteristic
382C4×C47C2×2−1+411yescharacteristic
383Dic47—21no—
384Dic47—21no—
385Dic47—24no—
386Dic47—24no—
387Dic47—21no—
388Dic47—21no—
389Dic47—21no—
390Dic47#56812yes—
391#3444—471no—
392#2995—474no—
393#2992—474no—
394#2990—474no—
395#2989—474no—
396#2961—471no—
397#2961—471no—
398#2933—472no—
399#2933—472no—
400#2932—471no—
401#2932D4711yescharacteristic, complemented
402#2925—472no—
403C2×#432—471no—
404#2906—472no—
405C2×#423—471no—
406C2×C47—22no—
407C2×C47—44no—
408C2×C47C2×#52011yescharacteristic
409C2×C47C2×#56811yescharacteristic
410C2×C47C2×#56811yescharacteristic
411D47—22no—
412D47—41no—
413C2×#131—472no—
414C2×#131C2×D4712yes—
415C22×M16—472no—
416#533—471no—
417#533—471no—
418#533—471no—
419#532—471no—
420#532—471no—
421#532C2×D4711yescharacteristic
422#529—472no—
423#529—472no—
424#529—472no—
425#529—472no—
426#529—472no—
427#529—472no—
428#525—472no—
429#525—472no—
430#525—472no—
431C4×#41—472no—
432C4×#41—472no—
433C4×#41—472no—
434C22×C42—471no—
435#446—474no—
436#446—474no—
437#446—474no—
438#446—474no—
439#436—474no—
440#436—474no—
441#435—474no—
442#435—474no—
443#435—474no—
444#435—474no—
445#435—474no—
446#435—474no—
447#435C2×D4714yescomplemented
448#435C2×D4714yescomplemented
449C8×D4—474no—
450C8×D4—474no—
451#433—474no—
452#433—474no—
453#432—474no—
454#432—472no—
455#432—472no—
456#432—472no—
457#432—472no—
458#431—474no—
459#424—472no—
460#424—474no—
461#424—472no—
462#424—474no—
463#423—472no—
464#423—474no—
465#423—471no—
466#423—472no—
467#423—472no—
468#423C2×D4711yescharacteristic
469C2×C4⋊C8—471no—
470C2×C4⋊C8—474no—
471C2×C4⋊C8—471no—
472C2×C4⋊C8—472no—
473C2×C4⋊C8—472no—
474#408—472no—
475#408C2×D4712yes—
476C2×C22⋊C8—471no—
477C2×C22⋊C8—471no—
478#405—472no—
479#405—472no—
480C2×#97—471no—
481C2×#97C2×D4711yescharacteristic
482C47#6026911yescharacteristic, complemented, Sylow
483C2×#41—472no—
484C2×#41—472no—
485C2×#41C22×D4712yes—
486C23×C4—471no—
487C23×C4—471no—
488C23×C4—471no—
489#131—44no—
490#131—1884no—
491C2×M16—472no—
492C2×M16—474no—
493C2×M16—474no—
494C2×M16—1884no—
495C2×M16C22×D4712yes—
496C2×M16C22×D4714yes—
497C22×C8—471no—
498C22×C8—471no—
499C22×C8—474no—
500C22×C8—474no—
501C22×C8C22×D4711yescharacteristic
502C22×C8C22×D4711yescharacteristic
503C22×C8C22×D4714yes—
504C4⋊Q8—471no—
505C4⋊Q8—471no—
506C4⋊Q8C4×D4711yescharacteristic
507#127C4×D4711yescharacteristic
508#126—474no—
509#126—474no—
510#125—472no—
511#125—472no—
512#125—472no—
513#124—472no—
514#124—472no—
515#124C4×D4712yes—
516#123—474no—
517#123—474no—
518#123—474no—
519C22⋊Q8—472no—
520C22⋊Q8—472no—
521C22⋊Q8—472no—
522C22⋊Q8—472no—
523C22⋊Q8—472no—
524C22⋊Q8—472no—
525#121—472no—
526#121—472no—
527#121—472no—
528#121—472no—
529#121C4×D4712yes—
530#121C4×D4712yes—
531#120—474no—
532C4×Q8—472no—
533C4×Q8—472no—
534C4×Q8—472no—
535C4×Q8—472no—
536C4×Q8—472no—
537C4×Q8—472no—
538C4×D4—474no—
539C4×D4—474no—
540C4×D4—472no—
541C4×D4—472no—
542C4×D4—472no—
543C4×D4—472no—
544C4×D4—474no—
545C4×D4—474no—
546C4×D4—474no—
547C4×D4—474no—
548C4×D4C22×D4712yes—
549C4×D4C22×D4712yes—
550#117—472no—
551#117—474no—
552#117—472no—
553#117—472no—
554#117—474no—
555#117—474no—
556C2×C42—471no—
557C2×C42—471no—
558C2×C42—474no—
559C2×C42—471no—
560C2×C42—471no—
561C2×C42—471no—
562C2×C42—471no—
563C2×C42—471no—
564C2×C42—471no—
565C2×C42—471no—
566C2×C42—471no—
567C2×C42—471no—
568C2×C42C22×D4711yescharacteristic
569C4⋊C8—472no—
570C4⋊C8—474no—
571C4⋊C8—474no—
572C4⋊C8—472no—
573C4⋊C8—474no—
574C4⋊C8—474no—
575C4⋊C8—472no—
576C4⋊C8—472no—
577C4⋊C8—474no—
578C4⋊C8—474no—
579C4⋊C8—472no—
580C4⋊C8—472no—
581C4⋊C8C22×D4712yes—
582C4⋊C8C22×D4712yes—
583C22⋊C8—474no—
584C22⋊C8—474no—
585C22⋊C8—472no—
586C22⋊C8—472no—
587C22⋊C8—472no—
588C22⋊C8—472no—
589C22⋊C8C22×D4714yes—
590C22⋊C8C22×D4714yes—
591#97—474no—
592#97—474no—
593#97—472no—
594#97—472no—
595#97C22×D4712yes—
596#97C22×D4712yes—
597C4×C8—474no—
598C4×C8—474no—
599C24—471no—
600#41—24no—
601#41—24no—
602#41—1884no—
603#41—1884no—
604C2×Q8—472no—
605C2×Q8—472no—
606C2×Q8C2×C4×D4712yes—
607C2×D4—474no—
608C2×D4—474no—
609C2×D4C2×C4×D4714yes—
610C2×D4C2×C4×D4712yes—
611C2×D4C2×C4×D4712yes—
612C2×D4C2×C4×D4712yes—
613C22×C4—471no—
614C22×C4—471no—
615C22×C4—474no—
616C22×C4—471no—
617C22×C4—474no—
618C22×C4—471no—
619C22×C4—471no—
620C22×C4—471no—
621C22×C4—471no—
622C22×C4—471no—
623C22×C4—471no—
624C22×C4—471no—
625C22×C4—471no—
626C22×C4—471no—
627C22×C4—471no—
628C22×C4—471no—
629C22×C4—471no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—1882no—
633C22×C4—1882no—
634C22×C4C2×C4×D4711yescharacteristic
635C22×C4C2×C4×D4711yescharacteristic
636C22×C4C23×D4714yes—
637C22×C4C23×D4711yescharacteristic
638M16—24no—
639M16—44no—
640M16—944no—
641M16—1884no—
642M16—1884no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—44no—
646C2×C8—472no—
647C2×C8—474no—
648C2×C8—472no—
649C2×C8—942no—
650C2×C8—942no—
651C2×C8—1884no—
652C2×C8—1884no—
653C2×C8C23×D4712yes—
654C2×C8C23×D4714yes—
655C2×C8C23×D4712yes—
656C4⋊C4—474no—
657C4⋊C4—474no—
658C4⋊C4—474no—
659C4⋊C4—474no—
660C4⋊C4—472no—
661C4⋊C4—472no—
662C4⋊C4—472no—
663C4⋊C4—472no—
664C4⋊C4—474no—
665C4⋊C4—474no—
666C4⋊C4C2×C4×D4712yes—
667C4⋊C4C2×C4×D4712yes—
668C22⋊C4—474no—
669C22⋊C4—474no—
670C22⋊C4—474no—
671C22⋊C4—474no—
672C22⋊C4—474no—
673C22⋊C4—474no—
674C22⋊C4—474no—
675C22⋊C4C2×C4×D4714yes—
676C22⋊C4C2×C4×D4714yes—
677C42—471no—
678C42—471no—
679C42—471no—
680C42—471no—
681C42—471no—
682C42—471no—
683C42—471no—
684C42—471no—
685C42—471no—
686C42—471no—
687C42—474no—
688C42—474no—
689C42—474no—
690C42—471no—
691C42—471no—
692C42C2×C4×D4711yescharacteristic
693C42C2×C4×D4711yescharacteristic
694C42C23×D4711yescharacteristic
695C42C23×D4711yescharacteristic
696C23—471no—
697C23—471no—
698C23—942no—
699C23—942no—
700C23—1881no—
701C23C22×C4×D4714yes—
702C23C22×C4×D4711yescharacteristic
703Q8—24no—
704Q8—1882no—
705Q8—1882no—
706D4—28no—
707D4—24no—
708D4—42no—
709D4—42no—
710D4—948no—
711D4—1884no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—471no—
717C2×C4—471no—
718C2×C4—471no—
719C2×C4—471no—
720C2×C4—471no—
721C2×C4—471no—
722C2×C4—474no—
723C2×C4—474no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—948no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—941no—
734C2×C4—941no—
735C2×C4—941no—
736C2×C4—941no—
737C2×C4—1881no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1881no—
741C2×C4—1881no—
742C2×C4—1884no—
743C2×C4C22×C4×D4711yescharacteristic
744C2×C4C22×C4×D4711yescharacteristic
745C2×C4C22×C4×D4711yescharacteristic
746C2×C4C22×C4×D4711yescharacteristic
747C2×C4C22×C4×D4714yes—
748C2×C4C22×C4×D4711yescharacteristic
749C2×C4#1309406912yes—
750C2×C4#1309407112yes—
751C2×C4C24×D4711yescharacteristic
752C8—22no—
753C8—24no—
754C8—22no—
755C8—942no—
756C8—944no—
757C8—942no—
758C22—21no—
759C22—21no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—472no—
764C22—941no—
765C22—941no—
766C22—941no—
767C22—941no—
768C22—941no—
769C22—1884no—
770C22#1568960212yes—
771C22C23×C4×D4711yescharacteristic
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—24no—
777C4—472no—
778C4—941no—
779C4—941no—
780C4—941no—
781C4—944no—
782C4—944no—
783C4—941no—
784C4—941no—
785C4#1568960212yes—
786C4C2×#1309406911yescharacteristic
787C4C2×#1309407111yescharacteristic
788C2—22no—
789C2—44no—
790C2—942no—
791C2—1881no—
792C2C2×#1568960211yescharacteristic
793C2#568×D4711yescharacteristic
794C2#568×D4711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2932C2
prime radical#20256683C2
cosocleC2×C4×C47C25
hypercenter#2932D47
hypocenterC47#60269
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #20252554C2semidirect
3. #20252523C2semidirect
4. #20252508C2semidirect
5. #20252500C2semidirect
6. #20252328C2semidirect
7. #20252325C2semidirect
8. #20252118C2semidirect
9. #20252110C2semidirect
10. #20252106C2semidirect
11. #20252050C2semidirect
12. C2×#15689178C2semidirect
13. #20251954C2semidirect
14. #423×D47C2semidirect
15. C47×#2932C2semidirect
36. #15689252C22semidirect
37. #15689252C22semidirect
38. #15689251C22semidirect
39. #15689251C22semidirect
43. #15689195C22semidirect
44. #15689195C22semidirect
50. #15689181C22semidirect
51. #15689181C22semidirect
56. #15689177C22semidirect
57. #15689173C22semidirect
59. #15689151C22semidirect
61. #15689149C22semidirect
64. #15689146C22semidirect
69. C2×Dic47⋊C8C22semidirect
80. C47×#435C22semidirect
81. C47×#435C22semidirect
401. #2932D47semidirect
447. #435C2×D47semidirect
448. #435C2×D47semidirect
482. C47#60269semidirect

Maximal subgroups

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

subgroupindex
#202566832
#202525542
#202525232
#202525082
#202525002
#202523282
#202523252
#202521182
#202521102
#202521062
#202520502
C2×#156891782
#202519542
#423×D472
C47×#29322
#6026947