Finite Group Databasebeta

← #27081477

Subgroups — #27081477

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#20256685C211yesmaximal, characteristic
2#20252557C214yesmaximal, complemented
3#20252526C214yesmaximal, complemented
4#20252512C214yesmaximal, complemented
5#20252504C214yesmaximal, complemented
6#20252329C211yesmaximal, characteristic, complemented
7#20252116C212yesmaximal, complemented
8#20252112C212yesmaximal, complemented
9#20252107C211yesmaximal, characteristic, complemented
10#20252105C211yesmaximal, characteristic, complemented
11#20252052C212yesmaximal, complemented
12C2×#15689178C211yesmaximal, characteristic, complemented
13#20251955C212yesmaximal, complemented
14#423×D47C211yesmaximal, characteristic, complemented
15C47×#2961C211yesmaximal, characteristic, complemented
16C2×#13094032C2212yes—
17C2×#13094030C2212yes—
18C2×M16×D47C2212yes—
19#15689678C411yescharacteristic
20#15689678C411yescharacteristic
21#15689674C411yescharacteristic
22#15689674C411yescharacteristic
23#15689673C2211yescharacteristic
24#15689660C2212yes—
25#15689660C2212yes—
26#15689659C412yes—
27#15689659C412yes—
28#15689658C412yes—
29#15689658C412yes—
30#15689636C412yes—
31#15689636C412yes—
32#15689635C2212yes—
33C4×#10625354C2212yes—
34C4×#10625354C2212yes—
35#15689591C2212yes—
36C2×C42×D47C2211yescharacteristic
37#15689254C2214yescomplemented
38#15689254C2214yescomplemented
39#15689202C2214yes—
40#15689200C2214yes—
41#15689196C2214yes—
42#15689196C2214yes—
43#15689196C2214yescomplemented
44#15689196C2214yescomplemented
45#15689193C2214yes—
46#15689193C2214yes—
47#15689193C2214yescomplemented
48#15689193C2214yescomplemented
49C8×D188C2214yes—
50#15689188C2214yes—
51#15689185C2214yescomplemented
52#15689182C2214yescomplemented
53#15689178C2212yes—
54#15689178C2212yes—
55#15689178C2212yes—
56#15689178C2212yes—
57#15689178C2214yescomplemented
58#15689174C2214yescomplemented
59#15689150C2212yes—
60#15689148C2214yescomplemented
61#15689148C2214yescomplemented
62#15689147C2211yescharacteristic
63#15689146C2212yes—
64#15689145C2212yes—
65#15689145C2212yes—
66#15689145C2214yescomplemented
67C2×Dic47⋊C8C2211yescharacteristic
68C2×Dic47⋊C8C2211yescharacteristic
69C4⋊C8×D47C2212yes—
70C4⋊C8×D47C2212yes—
71C4⋊C8×D47C2214yescomplemented
72#15689091C2212yes—
73#15689089C2212yes—
74C2×(C2×D47)⋊C8C2211yescharacteristic
75C2×(C2×D47)⋊C8C2211yescharacteristic
76#15689079C2212yes—
77C2×#13093935C2211yescharacteristic
78C47×#533C2211yescharacteristic
79C47×#446C2214yescomplemented
80C47×#446C2214yescomplemented
81C47×#424C2212yes—
82C47×#423C2211yescharacteristic
83C47×#405C2212yes—
84C2×#97×C47C2211yescharacteristic
85C2×#10625354C2×C412yes—
86C2×#10625354C2×C412yes—
87C2×#10625350C2312yes—
88C22×C4×D47C2×C411yescharacteristic
89C22×C4×D47C2×C411yescharacteristic
90C22×C4×D47C2311yescharacteristic
91#13094032—44no—
92#13094030—44no—
93C2×#10625329C2312yes—
94C2×#10625324C2314yes—
95C2×#10625324C2314yes—
96C2×#10625324C2314yes—
97M16×D47—44no—
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100C2×C8×D47C2314yes—
101C2×C8×D47C2314yes—
102C2×C8×D47C2314yes—
103#13094024C2×C411yescharacteristic
104#13094021C2×C411yescharacteristic
105#13094019C2×C414yes—
106#13094019C2×C414yes—
107#13094015C2×C412yes—
108#13094015C2×C412yes—
109#13094013C2×C412yes—
110#13094013C2×C412yes—
111#13094012C2×C412yes—
112#13094009C2×C414yes—
113#13094009C2×C414yes—
114#13094008C2×C414yes—
115#13094004C2×C412yes—
116#13094004C2×C412yes—
117#13094000C2×C412yes—
118#13094000C2×C412yes—
119#13093999C2×C412yes—
120#13093999C2×C412yes—
121#13093999C2×C412yes—
122#13093999C2×C412yes—
123#13093998C2×C412yes—
124#13093998C2×C412yes—
125#13093994C2×C414yes—
126Q8×Dic47C2×C412yes—
127Q8×Dic47C2×C412yes—
128#13093989C2×C412yes—
129#13093989C2×C412yes—
130C4×D188C2314yes—
131C4×D188C2314yes—
132C4×D188C2312yes—
133C4×D188C2312yes—
134#13093986C2×C412yes—
135#13093986C2×C412yes—
136#13093986C2×C414yes—
137#13093986C2×C414yes—
138#13093986C2×C412yes—
139#13093986C2×C412yes—
140(C22⋊D47)⋊C4C2×C414yes—
141(C22⋊D47)⋊C4C2×C414yes—
142#13093982C2×C412yes—
143#13093982C2×C412yes—
144#13093982C2×C414yes—
145#13093982C2×C414yes—
146#13093981C2314yes—
147C2×C4×Dic47C2×C411yescharacteristic
148C2×C4×Dic47C2×C411yescharacteristic
149C2×C4×Dic47C2311yescharacteristic
150C42×D47C2×C411yescharacteristic
151C42×D47C2×C411yescharacteristic
152C42×D47C2×C411yescharacteristic
153C42×D47C2×C411yescharacteristic
154C42×D47C2311yescharacteristic
155C42×D47C2311yescharacteristic
156C42×D47C2311yescharacteristic
157C42×D47C2311yescharacteristic
158C42×D47C2314yes—
159C4⋊(C47⋊C8)C2312yes—
160C4⋊(C47⋊C8)C2312yes—
161C4⋊(C47⋊C8)C2314yes—
162C4⋊(C47⋊C8)C2314yes—
163Dic47⋊C8C2314yes—
164Dic47⋊C8C2314yes—
165Dic47⋊C8C2312yes—
166Dic47⋊C8C2312yes—
167Dic47⋊C8C2312yes—
168Dic47⋊C8C2312yes—
169(C2×D47)⋊C8C2312yes—
170(C2×D47)⋊C8C2312yes—
171(C2×D47)⋊C8C2312yes—
172(C2×D47)⋊C8C2312yes—
173(C2×D47)⋊C8C2314yes—
174(C2×D47)⋊C8C2314yes—
175(C2×D47)⋊C8C2314yes—
176(C2×D47)⋊C8C2314yes—
177#13093935C2312yes—
178#13093935C2312yes—
179#13093935C2314yes—
180C4×C47⋊C8C2314yes—
181C2×M16×C47C2312yes—
182C22×C8×C47C2311yescharacteristic
183C22×C8×C47C2311yescharacteristic
184C4⋊Q8×C47C2×C411yescharacteristic
185C4⋊Q8×C47C2×C411yescharacteristic
186#125×C47C2×C412yes—
187C22⋊Q8×C47C2×C412yes—
188C22⋊Q8×C47C2×C412yes—
189C4×Q8×C47C2312yes—
190C4×Q8×C47C2312yes—
191#117×C47C2312yes—
192C2×C42×C47C2311yescharacteristic
193C4⋊C8×C47C2312yes—
194C4⋊C8×C47C2312yes—
195C4⋊C8×C47C2314yes—
196C4⋊C8×C47C2314yes—
197#97×C47C2312yes—
198#97×C47C2312yes—
199#97×C47C2314yes—
200C4×C8×C47C2314yes—
201C23×D47C22×C411yescharacteristic
202C2×Q8×C47C22×C412yes—
203C2×Q8×C47C22×C412yes—
204C22×C4×C47C22×C411yescharacteristic
205C22×C4×C47C22×C411yescharacteristic
206C22×C4×C47C2411yescharacteristic
207C2×C22⋊D47C22×C414yes—
208C22×Dic47C22×C411yescharacteristic
209C22×Dic47C22×C411yescharacteristic
210C22×Dic47C22×C411yescharacteristic
211#10625354—44no—
212#10625354—44no—
213#10625350—24no—
214#10625350—24no—
215C2×D188C22×C412yes—
216C2×D188C22×C414yes—
217C2×D188C22×C414yes—
218C2×D188C22×C412yes—
219C2×D188C22×C412yes—
220C2×C4×D47—22no—
221C2×C4×D47—22no—
222C2×C4×D47—42no—
223C2×C4×D47—42no—
224C2×C4×D47C22×C411yescharacteristic
225C2×C4×D47C22×C411yescharacteristic
226C2×C4×D47C22×C411yescharacteristic
227C2×C4×D47C22×C411yescharacteristic
228C2×C4×D47C22×C411yescharacteristic
229C2×C4×D47C22×C411yescharacteristic
230C2×C4×D47C22×C414yes—
231C2×C4×D47C22×C411yescharacteristic
232C2×C4×D47C22×C411yescharacteristic
233C2×C4×D47C22×C411yescharacteristic
234C2×C4×D47C22×C411yescharacteristic
235C2×C4×D47C22×C414yes—
236C2×C4×D47C2411yescharacteristic
237C2×C4×D47C2411yescharacteristic
238C2×C4×D47C2414yes—
239C2×Dic94C22×C412yes—
240M16×C47—24no—
241C2×C8×C47—22no—
242C2×C8×C47—22no—
243C2×C8×C47C2412yes—
244C2×C8×C47C2414yes—
245C2×C8×C47C2412yes—
246C4⋊C4×C47C22×C412yes—
247C4⋊C4×C47C22×C412yes—
248C4⋊C4×C47C22×C414yes—
249C4⋊C4×C47C22×C414yes—
250C4⋊C4×C47C22×C412yes—
251C4⋊C4×C47C22×C412yes—
252C22⋊C4×C47C22×C414yes—
253C42×C47C22×C411yescharacteristic
254C42×C47C22×C411yescharacteristic
255C42×C47C2411yescharacteristic
256C42×C47C2411yescharacteristic
257C42×C47C2414yes—
258(C2×D47)⋊C4C22×C414yes—
259(C2×D47)⋊C4C22×C414yes—
260(C2×D47)⋊C4C22×C414yes—
261(C2×D47)⋊C4C22×C414yes—
262(C2×D47)⋊C4C22×C414yes—
263(C2×D47)⋊C4C22×C414yes—
264(C2×D47)⋊C4C22×C414yes—
265(C2×D47)⋊C4C22×C414yes—
266C4⋊Dic47C22×C412yes—
267C4⋊Dic47C22×C412yes—
268C4⋊Dic47C22×C414yes—
269C4⋊Dic47C22×C414yes—
270Dic47⋊C4C22×C414yes—
271Dic47⋊C4C22×C414yes—
272C4×Dic47C22×C411yescharacteristic
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×C414yes—
283C4×Dic47C22×C414yes—
284C4×Dic47C2411yescharacteristic
285C4×Dic47C2411yescharacteristic
286#10625329—24no—
287C2×C47⋊C8—22no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8C2412yes—
290C2×C47⋊C8C2414yes—
291C2×C47⋊C8C2412yes—
292#10625324—44no—
293#10625324—44no—
294#10625324—44no—
295C8×D47—44no—
296C8×D47—44no—
297C8×D47—44no—
298C23×C47C23×C411yescharacteristic
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—41no—
302C22×D47C23×C414yes—
303C22×D47C23×C411yescharacteristic
304C22×D47C23×C411yescharacteristic
305Q8×C47—42no—
306Q8×C47—42no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47C23×C411yescharacteristic
310C2×C4×C47C23×C411yescharacteristic
311C2×C4×C47C23×C411yescharacteristic
312C2×C4×C47C23×C411yescharacteristic
313C2×C4×C47C23×C414yes—
314C2×C4×C47C23×C414yes—
315C2×C4×C47C23×C411yescharacteristic
316C2×C4×C47H(5,𝔽2)12yes—
317C2×C4×C472−1+412yes—
318C2×C4×C47C2511yescharacteristic
319C22⋊D47—28no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—41no—
323C2×Dic47C23×C411yescharacteristic
324C2×Dic47C23×C411yescharacteristic
325C2×Dic47C23×C411yescharacteristic
326C2×Dic47C23×C411yescharacteristic
327C2×Dic47C23×C411yescharacteristic
328C2×Dic47C23×C414yes—
329C2×Dic47C23×C411yescharacteristic
330D188—28no—
331D188—24no—
332D188—42no—
333D188—42no—
334D188—44no—
335C4×D47—22no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—22no—
339C4×D47—21no—
340C4×D47—24no—
341C4×D47—21no—
342C4×D47—21no—
343C4×D47—21no—
344C4×D47—24no—
345C4×D47—22no—
346C4×D47—22no—
347C4×D47—28no—
348C4×D47—41no—
349C4×D47—41no—
350C4×D47—41no—
351C4×D47—41no—
352C4×D47—44no—
353Dic94—24no—
354C8×C47—22no—
355C8×C47—24no—
356C8×C47—22no—
357C47⋊C8—22no—
358C47⋊C8—24no—
359C47⋊C8—22no—
360#60269—471nomaximal, Sylow
361C22×C47—21no—
362C22×C47—21no—
363C22×C47#52012yes—
364C22×C47C24×C411yescharacteristic
365C2×D47—21no—
366C2×D47—21no—
367C2×D47—21no—
368C2×D47—24no—
369C2×D47—21no—
370C2×D47—24no—
371C2×D47—21no—
372C2×D47—24no—
373C2×D47—44no—
374C2×D47#56812yes—
375C4×C47—21no—
376C4×C47—21no—
377C4×C47—21no—
378C4×C47—21no—
379C4×C47—24no—
380C4×C47—24no—
381C4×C47#52012yes—
382C4×C47C2×H(5,𝔽2)11yescharacteristic
383C4×C47C2×2−1+411yescharacteristic
384Dic47—24no—
385Dic47—21no—
386Dic47—21no—
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#2961D4711yescharacteristic, complemented
398#2933—472no—
399#2933—472no—
400#2932—471no—
401#2932—471no—
402#2925—472no—
403C2×#432—471no—
404#2906—472no—
405C2×#423—471no—
406C2×C47—22no—
407C2×C47C2×#52011yescharacteristic
408C2×C47C2×#56811yescharacteristic
409C2×C47C2×#56811yescharacteristic
410D47—22no—
411D47—44no—
412D47—41no—
413C2×#131—472no—
414C2×#131—472no—
415C22×M16—472no—
416#533—471no—
417#533—471no—
418#533C2×D4711yescharacteristic
419#532—471no—
420#532—471no—
421#532—471no—
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#446C2×D4714yescomplemented
438#446C2×D4714yescomplemented
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#435—474no—
448#435—474no—
449C8×D4—474no—
450C8×D4—474no—
451#433—474no—
452#433—474no—
453#432—472no—
454#432—472no—
455#432—472no—
456#432—472no—
457#432—474no—
458#431—474no—
459#424—472no—
460#424—474no—
461#424—474no—
462#424C2×D4712yes—
463#423—472no—
464#423—471no—
465#423—472no—
466#423—472no—
467#423—474no—
468#423C2×D4711yescharacteristic
469C2×C4⋊C8—471no—
470C2×C4⋊C8—471no—
471C2×C4⋊C8—472no—
472C2×C4⋊C8—472no—
473C2×C4⋊C8—474no—
474#408—472no—
475#408—472no—
476C2×C22⋊C8—471no—
477C2×C22⋊C8—471no—
478#405—472no—
479#405C2×D4712yes—
480C2×#97—471no—
481C2×#97C2×D4711yescharacteristic
482C47#6026911yescharacteristic, complemented, Sylow
483C2×#41—472no—
484C2×#41—472no—
485C2×#41—472no—
486C23×C4—471no—
487C23×C4—471no—
488C23×C4—471no—
489#131—1884no—
490#131—1884no—
491C2×M16—472no—
492C2×M16—474no—
493C2×M16—474no—
494C2×M16—474no—
495C2×M16—1884no—
496C2×M16C22×D4712yes—
497C22×C8—471no—
498C22×C8—471no—
499C22×C8—474no—
500C22×C8—474no—
501C22×C8—474no—
502C22×C8C22×D4711yescharacteristic
503C22×C8C22×D4711yescharacteristic
504C4⋊Q8—471no—
505C4⋊Q8C4×D4711yescharacteristic
506C4⋊Q8C4×D4711yescharacteristic
507#127—471no—
508#126—474no—
509#126—474no—
510#125—472no—
511#125—472no—
512#125C4×D4712yes—
513#124—472no—
514#124—472no—
515#124—472no—
516#123—474no—
517#123—474no—
518#123—474no—
519C22⋊Q8—472no—
520C22⋊Q8—472no—
521C22⋊Q8—472no—
522C22⋊Q8—472no—
523C22⋊Q8C4×D4712yes—
524C22⋊Q8C4×D4712yes—
525#121—472no—
526#121—472no—
527#121—472no—
528#121—472no—
529#121—472no—
530#121—472no—
531#120—474no—
532C4×Q8—472no—
533C4×Q8—472no—
534C4×Q8—472no—
535C4×Q8—472no—
536C4×Q8C22×D4712yes—
537C4×Q8C22×D4712yes—
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×D4—472no—
549C4×D4—472no—
550#117—472no—
551#117—472no—
552#117—474no—
553#117—474no—
554#117—474no—
555#117C22×D4712yes—
556C2×C42—471no—
557C2×C42—471no—
558C2×C42—471no—
559C2×C42—471no—
560C2×C42—471no—
561C2×C42—471no—
562C2×C42—471no—
563C2×C42—474no—
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—472no—
574C4⋊C8—472no—
575C4⋊C8—472no—
576C4⋊C8—472no—
577C4⋊C8—474no—
578C4⋊C8—474no—
579C4⋊C8C22×D4712yes—
580C4⋊C8C22×D4712yes—
581C4⋊C8C22×D4714yes—
582C4⋊C8C22×D4714yes—
583C22⋊C8—472no—
584C22⋊C8—472no—
585C22⋊C8—472no—
586C22⋊C8—472no—
587C22⋊C8—474no—
588C22⋊C8—474no—
589C22⋊C8—474no—
590C22⋊C8—474no—
591#97—472no—
592#97—472no—
593#97—474no—
594#97C22×D4712yes—
595#97C22×D4712yes—
596#97C22×D4714yes—
597C4×C8—474no—
598C4×C8C22×D4714yes—
599C24—471no—
600#41—944no—
601#41—944no—
602#41—1884no—
603#41—1884no—
604C2×Q8—472no—
605C2×Q8C2×C4×D4712yes—
606C2×Q8C2×C4×D4712yes—
607C2×D4—474no—
608C2×D4—474no—
609C2×D4—472no—
610C2×D4—474no—
611C2×D4—472no—
612C2×D4—472no—
613C22×C4—471no—
614C22×C4—471no—
615C22×C4—471no—
616C22×C4—471no—
617C22×C4—471no—
618C22×C4—471no—
619C22×C4—471no—
620C22×C4—471no—
621C22×C4—471no—
622C22×C4—474no—
623C22×C4—471no—
624C22×C4—471no—
625C22×C4—474no—
626C22×C4—471no—
627C22×C4—471no—
628C22×C4—471no—
629C22×C4—471no—
630C22×C4—474no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—1882no—
634C22×C4—1882no—
635C22×C4C2×C4×D4711yescharacteristic
636C22×C4C2×C4×D4711yescharacteristic
637C22×C4C23×D4711yescharacteristic
638M16—24no—
639M16—944no—
640M16—1884no—
641M16—1884no—
642M16—1884no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—472no—
646C2×C8—474no—
647C2×C8—472no—
648C2×C8—942no—
649C2×C8—942no—
650C2×C8—1884no—
651C2×C8—1884no—
652C2×C8—1884no—
653C2×C8C23×D4712yes—
654C2×C8C23×D4714yes—
655C2×C8C23×D4712yes—
656C4⋊C4—474no—
657C4⋊C4—474no—
658C4⋊C4—472no—
659C4⋊C4—472no—
660C4⋊C4—474no—
661C4⋊C4—474no—
662C4⋊C4C2×C4×D4712yes—
663C4⋊C4C2×C4×D4712yes—
664C4⋊C4C2×C4×D4714yes—
665C4⋊C4C2×C4×D4714yes—
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⋊C4—474no—
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—471no—
690C42—471no—
691C42C2×C4×D4711yescharacteristic
692C42C2×C4×D4711yescharacteristic
693C42C23×D4714yes—
694C42C23×D4711yescharacteristic
695C42C23×D4711yescharacteristic
696C23—471no—
697C23—474no—
698C23—471no—
699C23—942no—
700C23—942no—
701C23—1881no—
702C23C22×C4×D4711yescharacteristic
703Q8—42no—
704Q8—42no—
705Q8—944no—
706D4—948no—
707D4—948no—
708D4—944no—
709D4—1882no—
710D4—1882no—
711D4—1884no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—471no—
715C2×C4—471no—
716C2×C4—471no—
717C2×C4—471no—
718C2×C4—471no—
719C2×C4—471no—
720C2×C4—474no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—948no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—941no—
731C2×C4—944no—
732C2×C4—941no—
733C2×C4—941no—
734C2×C4—941no—
735C2×C4—944no—
736C2×C4—1881no—
737C2×C4—1881no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1884no—
741C2×C4—1881no—
742C2×C4C22×C4×D4711yescharacteristic
743C2×C4C22×C4×D4711yescharacteristic
744C2×C4C22×C4×D4711yescharacteristic
745C2×C4C22×C4×D4711yescharacteristic
746C2×C4C22×C4×D4714yes—
747C2×C4C22×C4×D4714yes—
748C2×C4C22×C4×D4711yescharacteristic
749C2×C4#1309407012yes—
750C2×C4#1309407212yes—
751C2×C4C24×D4711yescharacteristic
752C8—22no—
753C8—24no—
754C8—22no—
755C8—942no—
756C8—944no—
757C8—942no—
758C22—21no—
759C22—21no—
760C22—472no—
761C22—941no—
762C22—941no—
763C22—941no—
764C22—944no—
765C22—941no—
766C22—944no—
767C22—941no—
768C22—944no—
769C22—1884no—
770C22#1568960512yes—
771C22C23×C4×D4711yescharacteristic
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—24no—
777C4—24no—
778C4—472no—
779C4—941no—
780C4—941no—
781C4—941no—
782C4—941no—
783C4—941no—
784C4—944no—
785C4#1568960512yes—
786C4C2×#1309407011yescharacteristic
787C4C2×#1309407211yescharacteristic
788C2—22no—
789C2—942no—
790C2—1881no—
791C2—1884no—
792C2C2×#1568960511yescharacteristic
793C2#568×D4711yescharacteristic
794C2#568×D4711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2961C2
prime radical#20256685C2
cosocleC2×C4×C47C25
hypercenter#2961D47
hypocenterC47#60269
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #20252557C2semidirect
3. #20252526C2semidirect
4. #20252512C2semidirect
5. #20252504C2semidirect
6. #20252329C2semidirect
7. #20252116C2semidirect
8. #20252112C2semidirect
9. #20252107C2semidirect
10. #20252105C2semidirect
11. #20252052C2semidirect
12. C2×#15689178C2semidirect
13. #20251955C2semidirect
14. #423×D47C2semidirect
15. C47×#2961C2semidirect
37. #15689254C22semidirect
38. #15689254C22semidirect
43. #15689196C22semidirect
44. #15689196C22semidirect
47. #15689193C22semidirect
48. #15689193C22semidirect
51. #15689185C22semidirect
52. #15689182C22semidirect
57. #15689178C22semidirect
58. #15689174C22semidirect
60. #15689148C22semidirect
61. #15689148C22semidirect
66. #15689145C22semidirect
71. C4⋊C8×D47C22semidirect
79. C47×#446C22semidirect
80. C47×#446C22semidirect
397. #2961D47semidirect
437. #446C2×D47semidirect
438. #446C2×D47semidirect
482. C47#60269semidirect

Maximal subgroups

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

subgroupindex
#202566852
#202525572
#202525262
#202525122
#202525042
#202523292
#202521162
#202521122
#202521072
#202521052
#202520522
C2×#156891782
#202519552
#423×D472
C47×#29612
#6026947