Finite Group Databasebeta

← #27088590

Subgroups — #27088590

Order 12032.

2036 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689680C211yesmaximal, characteristic, complemented
2C2×#15689673C211yesmaximal, characteristic
3#20254588C214yesmaximal, complemented
4#20254580C214yesmaximal, complemented
5#20254526C214yesmaximal, complemented
6#20254518C212yesmaximal, complemented
7#20254511C212yesmaximal, complemented
8#20253934C212yesmaximal, complemented
9#20253763C212yesmaximal, complemented
10#20253329C214yesmaximal, complemented
11#20253187C214yesmaximal, complemented
12C47×#2920C211yesmaximal, characteristic, complemented
13C22×#10625350—21no—
14#15689680—21no—
15#15689680—21no—
16#15689680—21no—
17#15689680—21no—
18#15689680C2212yes—
19#15689680C2212yes—
20#15689680C2212yescomplemented
21#15689680C2212yescomplemented
22#15689673—21no—
23#15689673—21no—
24#15689673—21no—
25#15689673—21no—
26#15689673C2212yes—
27#15689673C2212yes—
28#15689673C2212yes—
29#15689673C2212yes—
30C2×#13094024C2211yescharacteristic
31C2×#13094024C2211yescharacteristic, complemented
32C2×#13094024C2211yescharacteristic, complemented
33C2×#13094021C2211yescharacteristic
34C2×#13094016C2212yescomplemented
35C2×#13094012—21no—
36C2×#13094003—21no—
37C2×#13094003—21no—
38C2×#13093998—21no—
39C2×#13093998C2212yes—
40C2×C4×Dic94—21no—
41C2×C4×Dic94—21no—
42C2×C4×D188—21no—
43C2×C4×D188C2212yes—
44C2×#13093983C2212yes—
45#15689532C2218yescomplemented
46#15689528C2214yescomplemented
47#15689521C2214yescomplemented
48#15689488C2218yescomplemented
49#15689470C2214yescomplemented
50#15689470C2214yescomplemented
51#15689448C22116yescomplemented
52#15689442C2218yescomplemented
53#15689437C2218yescomplemented
54#15689424C22116yescomplemented
55#15689414C2218yescomplemented
56#15689404C2218yescomplemented
57#15689165C2218yes—
58#15689129C2218yes—
59C22×C42×C47C2211yescharacteristic
60C47×#432C2212yescomplemented
61C47×#432C2212yescomplemented
62C47×#431C2212yescomplemented
63C47×#431C2212yescomplemented
64C47×#423C2212yes—
65C47×#407C2212yes—
66C4×M16×C47C2212yes—
67C2×#10625350—22no—
68C2×#10625350—22no—
69C2×#10625350—22no—
70C2×#10625350—22no—
71C2×#10625350—48no—
72C22×Dic94—21no—
73C22×Dic94—21no—
74C22×Dic94—21no—
75C22×D188—21no—
76C22×D188—21no—
77C22×D188C2312yes—
78C22×C22⋊D47—22no—
79C22×C4×D47—22no—
80#13094024—21no—
81#13094024—21no—
82#13094024—21no—
83#13094024—21no—
84#13094024—21no—
85#13094024—21no—
86#13094024C2312yes—
87#13094024C2312yes—
88#13094024C2312yes—
89#13094024C2312yes—
90#13094024C2312yes—
91#13094024C2312yes—
92#13094021—21no—
93#13094021—21no—
94#13094021C2312yes—
95#13094021C2312yes—
96#13094016—22no—
97#13094016—22no—
98#13094016C2314yes—
99#13094016C2314yes—
100#13094012—22no—
101#13094012—22no—
102#13094012—22no—
103#13094012—22no—
104#13094003—22no—
105#13094003—22no—
106#13094003—22no—
107#13094003—22no—
108#13094003—22no—
109#13094003—22no—
110#13094003—22no—
111#13094003—22no—
112#13093998—22no—
113#13093998—22no—
114#13093998—22no—
115#13093998—22no—
116#13093998—22no—
117#13093998—22no—
118#13093998C2314yes—
119#13093998C2314yes—
120C4×Dic94—22no—
121C4×Dic94—22no—
122C4×Dic94—22no—
123C4×Dic94—22no—
124C4×Dic94—22no—
125C4×Dic94—22no—
126C4×Dic94—22no—
127C4×Dic94—22no—
128C4×D188—22no—
129C4×D188—22no—
130C4×D188—22no—
131C4×D188—22no—
132C4×D188—22no—
133C4×D188—22no—
134C4×D188C2314yes—
135C4×D188C2314yes—
136#13093983—22no—
137#13093983—22no—
138#13093983C2314yes—
139#13093983C2314yes—
140C2×C4⋊Dic47—21no—
141C2×C4⋊Dic47—21no—
142C2×C4⋊Dic47—21no—
143C2×C4⋊Dic47C2312yes—
144C2×C4⋊Dic47C2312yes—
145C2×C4⋊Dic47C2312yes—
146C2×Dic47⋊C4—22no—
147C2×Dic47⋊C4—22no—
148C2×C22⋊Dic47—22no—
149C2×(C2×D47)⋊C4—22no—
150C2×(C2×D47)⋊C4—22no—
151C2×C4×Dic47—22no—
152#13093958C23116yes—
153#13093956C23116yes—
154#13093946C23116yes—
155#13093946C23116yes—
156C23×C4×C47D411yescharacteristic
157C23×C4×C47D411yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C2×M16×C47C2314yes—
160C2×C42×C47D411yescharacteristic
161C2×C42×C47D411yescharacteristic
162C2×C42×C47D411yescharacteristic
163C2×C42×C47D411yescharacteristic
164C2×C42×C47D411yescharacteristic
165C2×C42×C47D411yescharacteristic
166C2×C42×C47C2311yescharacteristic
167C2×C42×C47C2311yescharacteristic
168C2×C42×C47C2311yescharacteristic
169C2×C42×C47C2311yescharacteristic
170C2×C42×C47C2311yescharacteristic
171C2×C42×C47C2311yescharacteristic
172C4⋊C8×C47C2314yes—
173C4⋊C8×C47C2314yes—
174C22⋊C8×C47C2314yes—
175C22⋊C8×C47C2314yes—
176#97×C47C2314yes—
177C4×C8×C47C2314yes—
178C24×C47C2×D411yescharacteristic
179C23×D47—22no—
180C22×C4×C47—24no—
181C22×C4×C47—24no—
182C22×C4×C47—42no—
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×C4×C47C2411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47—48no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207#10625350—48no—
208#10625350—48no—
209#10625350—48no—
210#10625350—48no—
211C2×D188—28no—
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—22no—
217C2×D188—44no—
218C2×D188—44no—
219C2×D188C2414yes—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—48no—
223C2×Dic94—22no—
224C2×Dic94—22no—
225C2×Dic94—22no—
226C2×Dic94—22no—
227C2×Dic94—22no—
228C2×Dic94—22no—
229C2×Dic94—44no—
230C2×Dic94—44no—
231C2×Dic94—44no—
232M16×C47—28no—
233C2×C8×C47C2418yes—
234C42×C47C2×D411yescharacteristic
235C42×C47C2×D411yescharacteristic
236C42×C47C2×D411yescharacteristic
237C42×C47C2×D411yescharacteristic
238C42×C47C2×D411yescharacteristic
239C42×C47C2×D411yescharacteristic
240C42×C47C2×D411yescharacteristic
241C42×C47C2×D411yescharacteristic
242C42×C47C2×D411yescharacteristic
243C42×C47C2×D411yescharacteristic
244C42×C47C2×D411yescharacteristic
245C42×C47C2×D411yescharacteristic
246C42×C47C2411yescharacteristic
247C42×C47C2411yescharacteristic
248C42×C47C2411yescharacteristic
249C42×C47C2411yescharacteristic
250C22⋊Dic47—24no—
251C22⋊Dic47—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256C4⋊Dic47—22no—
257C4⋊Dic47—22no—
258C4⋊Dic47—22no—
259C4⋊Dic47—22no—
260C4⋊Dic47—22no—
261C4⋊Dic47—22no—
262C4⋊Dic47—22no—
263C4⋊Dic47—22no—
264C4⋊Dic47—22no—
265C4⋊Dic47C2414yes—
266C4⋊Dic47C2414yes—
267C4⋊Dic47C2414yes—
268Dic47⋊C4—24no—
269Dic47⋊C4—24no—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272C4×Dic47—24no—
273C4×Dic47—24no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—41no—
277C23×C47C22×D411yescharacteristic
278C23×C47C22×D411yescharacteristic
279C23×C47C22×D411yescharacteristic
280C22×D47—24no—
281C22×D47—44no—
282C22×D47—44no—
283C22×D47—44no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47AGL(1,ℤ/8)14yes—
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C22×D411yescharacteristic
307C2×C4×C47C22×D411yescharacteristic
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47C22×D411yescharacteristic
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C472−1+414yes—
313C2×C4×C47C2511yescharacteristic
314C22⋊D47—48no—
315C22⋊D47—48no—
316C2×Dic47—24no—
317C2×Dic47—24no—
318C2×Dic47—24no—
319C2×Dic47—44no—
320C2×Dic47—44no—
321C2×Dic47—44no—
322D188—28no—
323D188—44no—
324D188—44no—
325D188—44no—
326D188—44no—
327D188—44no—
328C4×D47—48no—
329C4×D47—48no—
330Dic94—44no—
331Dic94—44no—
332Dic94—44no—
333Dic94—44no—
334Dic94—44no—
335Dic94—44no—
336C8×C47—28no—
337#60864—471nomaximal, Sylow
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—21no—
341C22×C47—21no—
342C22×C47—21no—
343C22×C47—21no—
344C22×C47—21no—
345C22×C47—44no—
346C22×C47#53612yes—
347C22×C47C2×AGL(1,ℤ/8)12yes—
348C22×C47C23×D411yescharacteristic
349C2×D47—44no—
350C2×D47—44no—
351C2×D47—44no—
352C2×D47—88no—
353C4×C47—21no—
354C4×C47—21no—
355C4×C47—21no—
356C4×C47—21no—
357C4×C47—21no—
358C4×C47—21no—
359C4×C47—21no—
360C4×C47#53612yes—
361C4×C47C2×AGL(1,ℤ/8)12yes—
362C4×C47C2×AGL(1,ℤ/8)12yes—
363C4×C47#57512yes—
364C4×C47C2×2−1+412yes—
365Dic47—44no—
366Dic47—44no—
367Dic47—44no—
368C2×#533—471no—
369C2×#532—471no—
370#3235—474no—
371#3234—474no—
372#3228—474no—
373#3227—472no—
374#3226—472no—
375#3165—472no—
376#3138—472no—
377#3094—474no—
378#3077—474no—
379#2920D4711yescharacteristic, complemented
380C2×C47—22no—
381C2×C47—22no—
382C2×C47—41no—
383C2×C47C2×#53611yescharacteristic
384C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
385C2×C47C2×#57511yescharacteristic
386D47—84no—
387C22×#41—941no—
388#533—472no—
389#533—472no—
390#533—472no—
391#533—472no—
392#533—941no—
393#533—941no—
394#533—941no—
395#533—941no—
396#532—472no—
397#532—472no—
398#532—472no—
399#532—472no—
400#532—941no—
401#532—941no—
402#532—941no—
403#532—941no—
404C2×C4⋊Q8—471no—
405C2×C4⋊Q8—471no—
406C2×C4⋊Q8—471no—
407C2×#127—471no—
408C2×#125—472no—
409C2×#124—941no—
410C2×C22⋊Q8—941no—
411C2×C22⋊Q8—941no—
412C2×#121—472no—
413C2×#121—941no—
414C2×C4×Q8—941no—
415C2×C4×Q8—941no—
416C2×C4×D4—472no—
417C2×C4×D4—941no—
418C2×#117—472no—
419C22×C42C2×D4711yescharacteristic
420#501—478no—
421#500—474no—
422#498—474no—
423#490—478no—
424#486—474no—
425#486—474no—
426#482—4716no—
427#481—478no—
428#480—478no—
429#478—4716no—
430#476—478no—
431#474—478no—
432#432C2×D4712yescomplemented
433#432C2×D4712yescomplemented
434#431C2×D4712yescomplemented
435#431C2×D4712yescomplemented
436#428—478no—
437#423C2×D4712yes—
438#418—478no—
439#407C2×D4712yes—
440C4×M16C2×D4712yes—
441C47#6086411yescharacteristic, complemented, Sylow
442C2×#41—942no—
443C2×#41—942no—
444C2×#41—942no—
445C2×#41—942no—
446C2×#41—1888no—
447C22×Q8—941no—
448C22×Q8—941no—
449C22×Q8—941no—
450C22×D4—472no—
451C22×D4—942no—
452C22×D4—941no—
453C22×D4—941no—
454C23×C4—942no—
455C23×C4D18811yescharacteristic
456C23×C4D18811yescharacteristic
457C23×C4C22×D4711yescharacteristic
458C2×M16C22×D4714yes—
459C4⋊Q8—472no—
460C4⋊Q8—472no—
461C4⋊Q8—472no—
462C4⋊Q8—472no—
463C4⋊Q8—472no—
464C4⋊Q8—472no—
465C4⋊Q8—941no—
466C4⋊Q8—941no—
467C4⋊Q8—941no—
468C4⋊Q8—941no—
469C4⋊Q8—941no—
470C4⋊Q8—941no—
471#127—472no—
472#127—472no—
473#127—941no—
474#127—941no—
475#125—474no—
476#125—474no—
477#125—942no—
478#125—942no—
479#124—942no—
480#124—942no—
481#124—942no—
482#124—942no—
483C22⋊Q8—942no—
484C22⋊Q8—942no—
485C22⋊Q8—942no—
486C22⋊Q8—942no—
487C22⋊Q8—942no—
488C22⋊Q8—942no—
489C22⋊Q8—942no—
490C22⋊Q8—942no—
491#121—474no—
492#121—474no—
493#121—942no—
494#121—942no—
495#121—942no—
496#121—942no—
497#121—942no—
498#121—942no—
499C4×Q8—942no—
500C4×Q8—942no—
501C4×Q8—942no—
502C4×Q8—942no—
503C4×Q8—942no—
504C4×Q8—942no—
505C4×Q8—942no—
506C4×Q8—942no—
507C4×D4—474no—
508C4×D4—474no—
509C4×D4—942no—
510C4×D4—942no—
511C4×D4—942no—
512C4×D4—942no—
513C4×D4—942no—
514C4×D4—942no—
515#117—474no—
516#117—474no—
517#117—942no—
518#117—942no—
519C2×C4⋊C4—472no—
520C2×C4⋊C4—472no—
521C2×C4⋊C4—472no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—942no—
524C2×C4⋊C4—942no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C22⋊C4—942no—
528C2×C22⋊C4—942no—
529C2×C22⋊C4—942no—
530C2×C42—942no—
531C2×C42D18811yescharacteristic
532C2×C42D18811yescharacteristic
533C2×C42D18811yescharacteristic
534C2×C42D18811yescharacteristic
535C2×C42D18811yescharacteristic
536C2×C42D18811yescharacteristic
537C2×C42C22×D4711yescharacteristic
538C2×C42C22×D4711yescharacteristic
539C2×C42C22×D4711yescharacteristic
540C2×C42C22×D4711yescharacteristic
541C2×C42C22×D4711yescharacteristic
542C2×C42C22×D4711yescharacteristic
543#107—4716no—
544#106—4716no—
545C4⋊C8C22×D4714yes—
546C4⋊C8C22×D4714yes—
547#102—4716no—
548#102—4716no—
549C22⋊C8C22×D4714yes—
550C22⋊C8C22×D4714yes—
551#97C22×D4714yes—
552C4×C8C22×D4714yes—
553C24—942no—
554C24C2×D18811yescharacteristic
555#41—1888no—
556#41—1888no—
557#41—1888no—
558#41—1888no—
559C2×Q8—942no—
560C2×Q8—942no—
561C2×Q8—942no—
562C2×Q8—942no—
563C2×Q8—942no—
564C2×Q8—942no—
565C2×Q8—1884no—
566C2×Q8—1884no—
567C2×Q8—1884no—
568C2×D4—474no—
569C2×D4—944no—
570C2×D4—944no—
571C2×D4—942no—
572C2×D4—942no—
573C2×D4—942no—
574C2×D4—942no—
575C2×D4—942no—
576C2×D4—948no—
577C2×D4—1884no—
578C2×D4—1884no—
579C2×D4—1888no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—42no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—944no—
587C22×C4—944no—
588C22×C4—1888no—
589C22×C4C2×D18811yescharacteristic
590C22×C4C2×D18811yescharacteristic
591C22×C4C2×D18811yescharacteristic
592C22×C4C2×D18811yescharacteristic
593C22×C4C2×D18811yescharacteristic
594C22×C4C2×D18811yescharacteristic
595C22×C4C2×D18811yescharacteristic
596C22×C4C2×D18811yescharacteristic
597C22×C4C2×D18811yescharacteristic
598C22×C4C2×D18811yescharacteristic
599C22×C4C2×D18811yescharacteristic
600C22×C4C2×D18811yescharacteristic
601C22×C4C2×D18811yescharacteristic
602C22×C4C2×D18811yescharacteristic
603C22×C4C2×D18811yescharacteristic
604C22×C4C23×D4711yescharacteristic
605C22×C4C23×D4711yescharacteristic
606C22×C4C23×D4711yescharacteristic
607M16—28no—
608C2×C8C23×D4718yes—
609C4⋊C4—474no—
610C4⋊C4—474no—
611C4⋊C4—474no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—942no—
617C4⋊C4—942no—
618C4⋊C4—942no—
619C4⋊C4—942no—
620C4⋊C4—942no—
621C4⋊C4—942no—
622C4⋊C4—942no—
623C4⋊C4—942no—
624C4⋊C4—942no—
625C22⋊C4—944no—
626C22⋊C4—944no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C42—944no—
632C42—944no—
633C42C2×D18811yescharacteristic
634C42C2×D18811yescharacteristic
635C42C2×D18811yescharacteristic
636C42C2×D18811yescharacteristic
637C42C2×D18811yescharacteristic
638C42C2×D18811yescharacteristic
639C42C2×D18811yescharacteristic
640C42C2×D18811yescharacteristic
641C42C2×D18811yescharacteristic
642C42C2×D18811yescharacteristic
643C42C2×D18811yescharacteristic
644C42C2×D18811yescharacteristic
645C42C23×D4711yescharacteristic
646C42C23×D4711yescharacteristic
647C42C23×D4711yescharacteristic
648C42C23×D4711yescharacteristic
649C23—22no—
650C23—22no—
651C23—41no—
652C23—944no—
653C23—1884no—
654C23—1884no—
655C23—1884no—
656C23C22×D18811yescharacteristic
657C23C22×D18811yescharacteristic
658C23C22×D18811yescharacteristic
659Q8—1884no—
660Q8—1884no—
661Q8—1884no—
662Q8—1884no—
663Q8—1884no—
664Q8—1884no—
665D4—948no—
666D4—1884no—
667D4—1884no—
668D4—1888no—
669D4—1888no—
670D4—1884no—
671D4—1884no—
672D4—1884no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—944no—
690C2×C4—944no—
691C2×C4—944no—
692C2×C4—1888no—
693C2×C4—1884no—
694C2×C4—1884no—
695C2×C4—1884no—
696C2×C4—1888no—
697C2×C4#1309405214yes—
698C2×C4C22×D18811yescharacteristic
699C2×C4C22×D18811yescharacteristic
700C2×C4C22×D18811yescharacteristic
701C2×C4C22×D18811yescharacteristic
702C2×C4C22×D18811yescharacteristic
703C2×C4C22×D18811yescharacteristic
704C2×C4C22×D18811yescharacteristic
705C2×C4C22×D18811yescharacteristic
706C2×C4C22×D18811yescharacteristic
707C2×C4C22×D18811yescharacteristic
708C2×C4C22×D18811yescharacteristic
709C2×C4#1309407114yes—
710C2×C4C24×D4711yescharacteristic
711C8—28no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—44no—
720C22—3768no—
721C22—1884no—
722C22—1884no—
723C22—1884no—
724C22#1568969912yes—
725C22C2×#1309405212yes—
726C22C23×D18811yescharacteristic
727C4—21no—
728C4—21no—
729C4—21no—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—21no—
734C4—1884no—
735C4—1884no—
736C4—1884no—
737C4#1568969912yes—
738C4C2×#1309405212yes—
739C4C2×#1309405212yes—
740C4#1568992312yes—
741C4C2×#1309407112yes—
742C2—22no—
743C2—22no—
744C2—41no—
745C2—3764no—
746C2C2×#1568969911yescharacteristic
747C2C22×#1309405211yescharacteristic
748C2C2×#1568992311yescharacteristic
subgroupG/H
centerC22C23×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#2920C2
socleC22×C47C23×D4
prime radicalC2×#15689673C2
hypercenter#2920D47
hypocenterC47#60864
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. C2×#15689680C2semidirect
3. #20254588C2semidirect
4. #20254580C2semidirect
5. #20254526C2semidirect
6. #20254518C2semidirect
7. #20254511C2semidirect
8. #20253934C2semidirect
9. #20253763C2semidirect
10. #20253329C2semidirect
11. #20253187C2semidirect
12. C47×#2920C2semidirect
20. #15689680C22semidirect
21. #15689680C22semidirect
31. C2×#13094024C22semidirect
32. C2×#13094024C22semidirect
34. C2×#13094016C22semidirect
45. #15689532C22semidirect
46. #15689528C22semidirect
47. #15689521C22semidirect
48. #15689488C22semidirect
49. #15689470C22semidirect
50. #15689470C22semidirect
51. #15689448C22semidirect
52. #15689442C22semidirect
53. #15689437C22semidirect
54. #15689424C22semidirect
55. #15689414C22semidirect
56. #15689404C22semidirect
60. C47×#432C22semidirect
61. C47×#432C22semidirect
62. C47×#431C22semidirect
63. C47×#431C22semidirect
379. #2920D47semidirect
432. #432C2×D47semidirect
433. #432C2×D47semidirect
434. #431C2×D47semidirect
435. #431C2×D47semidirect
441. C47#60864semidirect

Maximal subgroups

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

subgroupindex
C2×#156896802
C2×#156896732
#202545882
#202545802
#202545262
#202545182
#202545112
#202539342
#202537632
#202533292
#202531872
C47×#29202
#6086447