Finite Group Databasebeta

← #27084760

Subgroups — #27084760

Order 12032.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689603C211yesmaximal, characteristic, complemented
2#20253659C214yesmaximal, complemented
3#20253644C214yesmaximal, complemented
4#20253596C214yesmaximal, complemented
5#20253581C214yesmaximal, complemented
6#20253308C212yesmaximal, complemented
7#20253189C211yesmaximal, characteristic, complemented
8#20253181C211yesmaximal, characteristic, complemented
9#20252856C211yesmaximal, characteristic, complemented
10#20252848C211yesmaximal, characteristic, complemented
11#20252628C212yesmaximal, complemented
12C4×#13094054C212yesmaximal, complemented
13C4×#13094049C212yesmaximal, complemented
14#20252026C211yesmaximal, characteristic, complemented
15C47×#3455C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C2×#13094054C2212yes—
18C2×#13094049C2212yes—
19#15689603—22no—
20#15689603—22no—
21#15689603C2214yes—
22#15689603C2214yes—
23C2×C4×Dic94C2211yescharacteristic
24C2×C4×Dic94C2211yescharacteristic
25C2×C4×D188C2211yescharacteristic
26C2×C4×D188C2211yescharacteristic
27C2×(C22⋊D47)⋊C4—21no—
28C2×(C22⋊D47)⋊C4—21no—
29C2×#13093982—21no—
30C22×C4⋊Dic47C2211yescharacteristic
31C2×C4⋊C4×D47—21no—
32#15689456C2214yescomplemented
33#15689451C2214yescomplemented
34#15689439C2214yescomplemented
35#15689434C2214yescomplemented
36#15689427C2214yescomplemented
37#15689420C2214yescomplemented
38#15689415C2212yescomplemented
39#15689410C2212yescomplemented
40#15689405C2212yescomplemented
41#15689400C2212yescomplemented
42#15689342C2214yescomplemented
43#15689335C2214yescomplemented
44#15689330C2212yescomplemented
45#15689325C2212yescomplemented
46#15689320C2212yescomplemented
47#15689315C2212yescomplemented
48#15689283C2214yes—
49#15689283C2214yes—
50#15689266C2214yes—
51#15689266C2214yes—
52#15689233C2214yescomplemented
53#15689228C2214yescomplemented
54#15689223C2214yescomplemented
55#15689221C2214yescomplemented
56C4×#10625337C2214yescomplemented
57C4×#10625336C2214yescomplemented
58C4×#10625335C2214yescomplemented
59C4×#10625334C2214yescomplemented
60#15689184C2214yescomplemented
61#15689184C2214yescomplemented
62#15689166C2212yes—
63#15689166C2212yes—
64#15689147C2211yescharacteristic
65#15689147C2211yescharacteristic
66#15689131C2212yes—
67#15689127C2212yes—
68#15689124C2212yes—
69#15689124C2212yes—
70#15689087C2212yes—
71C4×#10625329C2212yes—
72C47×#542C2212yescomplemented
73C47×#542C2212yescomplemented
74C47×#541C2212yescomplemented
75C47×#540C2212yescomplemented
76C47×#539—21no—
77C47×#539—21no—
78C47×#538—21no—
79C47×#538—21no—
80C47×#533C2211yescharacteristic
81C47×#532C2211yescharacteristic
82C47×#529—22no—
83C47×#529—22no—
84C47×#525C2212yes—
85C4×#41×C47C2212yes—
86C2×#117×C47C2211yescharacteristic
87C2×#10625350—22no—
88C2×#10625350—24no—
89C2×#10625350—24no—
90C2×#10625350C2314yes—
91C22×Dic94C2311yescharacteristic
92C22×D188C2311yescharacteristic
93C22×C22⋊D47—21no—
94C23×Dic47—21no—
95C22×C4×D47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98#13094054—28no—
99#13094049—28no—
100C2×#10625337C2314yes—
101C2×#10625335C2314yes—
102C2×#10625336C2314yes—
103C2×#10625334C2314yes—
104C2×#10625329C2312yes—
105C2×#10625329C2312yes—
106C4×Dic94—22no—
107C4×Dic94—21no—
108C4×Dic94—21no—
109C4×Dic94C2314yes—
110C4×Dic94C2312yes—
111C4×Dic94C2312yes—
112C4×D188—22no—
113C4×D188—21no—
114C4×D188—21no—
115C4×D188C2314yes—
116C4×D188C2312yes—
117C4×D188C2312yes—
118(C22⋊D47)⋊C4—24no—
119(C22⋊D47)⋊C4—24no—
120(C22⋊D47)⋊C4—24no—
121(C22⋊D47)⋊C4—24no—
122#13093982—24no—
123#13093982—24no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—22no—
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2314yes—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C4⋊C4×D47—24no—
132C4⋊C4×D47—24no—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×C4×Dic47—21no—
136C2×C4×Dic47—21no—
137#13093957C2314yes—
138#13093957C2314yes—
139#13093955C2314yes—
140#13093955C2314yes—
141C4⋊(C47⋊C8)C2312yes—
142C4⋊(C47⋊C8)C2312yes—
143C4⋊(C47⋊C8)C2312yes—
144C4⋊(C47⋊C8)C2312yes—
145#13093948C2314yes—
146#13093948C2314yes—
147#13093947C2314yes—
148#13093947C2314yes—
149#13093945C2314yes—
150#13093945C2314yes—
151#13093944C2314yes—
152#13093944C2314yes—
153C22⋊(C47⋊C8)C2314yes—
154C22⋊(C47⋊C8)C2314yes—
155#13093935C2314yes—
156C4×C47⋊C8C2314yes—
157C2×#41×C47C2312yes—
158C23×C4×C47C2311yescharacteristic
159C4⋊Q8×C47C2311yescharacteristic
160C4⋊Q8×C47C2311yescharacteristic
161C4⋊Q8×C47C2311yescharacteristic
162#127×C47C2311yescharacteristic
163#126×C47—22no—
164#126×C47—22no—
165#126×C47—22no—
166#126×C47—22no—
167#125×C47—22no—
168#125×C47—22no—
169#125×C47C2312yes—
170#124×C47—22no—
171#124×C47—22no—
172#124×C47C2312yes—
173#123×C47—22no—
174#123×C47—22no—
175#123×C47—22no—
176#123×C47—22no—
177#123×C47—22no—
178C22⋊Q8×C47—21no—
179C22⋊Q8×C47—21no—
180C22⋊Q8×C47—22no—
181C22⋊Q8×C47—22no—
182C22⋊Q8×C47C2312yes—
183C22⋊Q8×C47C2312yes—
184#121×C47—21no—
185#121×C47—21no—
186#121×C47—22no—
187#121×C47—22no—
188#121×C47C2312yes—
189#121×C47C2312yes—
190#120×C47—22no—
191C4×Q8×C47—21no—
192C4×Q8×C47—21no—
193C4×Q8×C47C2312yes—
194C4×Q8×C47C2312yes—
195C4×D4×C47—22no—
196C4×D4×C47—22no—
197C4×D4×C47—22no—
198C4×D4×C47—22no—
199C4×D4×C47—21no—
200C4×D4×C47—21no—
201C4×D4×C47C2312yes—
202C4×D4×C47C2312yes—
203#117×C47—22no—
204#117×C47D412yes—
205#117×C47D412yes—
206#117×C47C2312yes—
207#117×C47C2312yes—
208#117×C47C2312yes—
209C2×C4⋊C4×C47D411yescharacteristic
210C2×C4⋊C4×C47D411yescharacteristic
211C2×C22⋊C4×C47D411yescharacteristic
212C2×C22⋊C4×C47D411yescharacteristic
213C2×C42×C47—22no—
214C2×C42×C47C2311yescharacteristic
215C2×C42×C47C2311yescharacteristic
216C24×C47C2×D411yescharacteristic
217C23×D47—21no—
218#41×C47—24no—
219#41×C47—24no—
220C2×Q8×C47—21no—
221C2×Q8×C47—21no—
222C2×Q8×C47C2412yes—
223C2×D4×C47—22no—
224C2×D4×C47—22no—
225C2×D4×C47—22no—
226C2×D4×C47—21no—
227C2×D4×C47—21no—
228C2×D4×C47C2412yes—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2×D412yes—
236C22×C4×C47C2×D411yescharacteristic
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D411yescharacteristic
239C22×C4×C47C2×D411yescharacteristic
240C22×C4×C47C2412yes—
241C22×C4×C47C2411yescharacteristic
242C2×C22⋊D47—28no—
243C2×C22⋊D47—24no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—24no—
248C22×Dic47—82no—
249#10625350—216no—
250#10625350—28no—
251#10625350—28no—
252C2×D188—21no—
253C2×D188—22no—
254C2×D188#4114yes—
255C2×D188C2412yes—
256C2×C4×D47—28no—
257C2×C4×D47—24no—
258C2×C4×D47—24no—
259C2×C4×D47—22no—
260C2×C4×D47—22no—
261C2×C4×D47—82no—
262C2×C4×D47—82no—
263C2×Dic94—21no—
264C2×Dic94—22no—
265C2×Dic94#4114yes—
266C2×Dic94C2412yes—
267C4⋊C4×C47—22no—
268C4⋊C4×C47—22no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—22no—
272C4⋊C4×C47—22no—
273C4⋊C4×C47—22no—
274C4⋊C4×C47—22no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47C2×D412yes—
278C4⋊C4×C47C2×D412yes—
279C4⋊C4×C47C2×D412yes—
280C4⋊C4×C47C2×D412yes—
281C4⋊C4×C47C2412yes—
282C4⋊C4×C47C2412yes—
283C22⋊C4×C47—22no—
284C22⋊C4×C47—22no—
285C22⋊C4×C47—22no—
286C22⋊C4×C47—22no—
287C22⋊C4×C47—22no—
288C22⋊C4×C47—22no—
289C22⋊C4×C47—22no—
290C22⋊C4×C47—22no—
291C22⋊C4×C47—22no—
292C22⋊C4×C47C2×D412yes—
293C22⋊C4×C47C2×D412yes—
294C22⋊C4×C47C2×D412yes—
295C22⋊C4×C47C2×D412yes—
296C42×C47—22no—
297C42×C47—22no—
298C42×C47—22no—
299C42×C47C2×D412yes—
300C42×C47C2×D411yescharacteristic
301C42×C47C2×D411yescharacteristic
302C42×C47C2412yes—
303C42×C47C2411yescharacteristic
304C42×C47C2411yescharacteristic
305#10625337—28no—
306#10625336—28no—
307#10625335—28no—
308#10625334—28no—
309(C2×D47)⋊C4—24no—
310(C2×D47)⋊C4—22no—
311(C2×D47)⋊C4—22no—
312C4⋊Dic47—24no—
313C4⋊Dic47—21no—
314C4⋊Dic47—21no—
315C4⋊Dic47C2412yes—
316C4⋊Dic47C2412yes—
317Dic47⋊C4—24no—
318Dic47⋊C4—22no—
319Dic47⋊C4—22no—
320C4×Dic47—24no—
321C4×Dic47—22no—
322C4×Dic47—22no—
323#10625329—24no—
324#10625329—24no—
325C2×C47⋊C8C2414yes—
326C2×C47⋊C8C2414yes—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—41no—
330C23×C47—41no—
331C23×C47C22×D412yes—
332C23×C47C22×D411yescharacteristic
333C22×D47—24no—
334C22×D47—22no—
335C22×D47—42no—
336C22×D47—42no—
337Q8×C47—22no—
338Q8×C47—22no—
339Q8×C47—81no—
340Q8×C47—81no—
341D4×C47—22no—
342D4×C47—22no—
343D4×C47—44no—
344D4×C47—81no—
345D4×C47—81no—
346D4×C47—82no—
347D4×C47—82no—
348C2×C4×C47—22no—
349C2×C4×C47—24no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—44no—
360C2×C4×C47—82no—
361C2×C4×C47—82no—
362C2×C4×C47C22×D412yes—
363C2×C4×C47C22×D411yescharacteristic
364C2×C4×C47C22×D411yescharacteristic
365C2×C4×C47C22×D412yes—
366C2×C4×C47C22×D411yescharacteristic
367C2×C4×C47C22×D411yescharacteristic
368C2×C4×C47C22×D412yes—
369C2×C4×C47C22×D411yescharacteristic
370C2×C4×C47C2×#4112yes—
371C2×C4×C47C2×#4112yes—
372C2×C4×C47C2511yescharacteristic
373C22⋊D47—216no—
374C2×Dic47—24no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—42no—
379C2×Dic47—42no—
380C2×Dic47—84no—
381D188—24no—
382D188—22no—
383D188C2×#4114yes—
384C4×D47—216no—
385C4×D47—84no—
386C4×D47—82no—
387C4×D47—82no—
388Dic94—24no—
389Dic94—22no—
390Dic94C2×#4114yes—
391C47⋊C8—24no—
392C47⋊C8—24no—
393#60565—471nomaximal, Sylow
394C22×C47—21no—
395C22×C47—21no—
396C22×C47—22no—
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—44no—
400C22×C47—42no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47#52512yes—
404C22×C47C23×D411yescharacteristic
405C2×D47—24no—
406C2×D47—48no—
407C2×D47—42no—
408C2×D47—42no—
409C4×C47—22no—
410C4×C47—21no—
411C4×C47—21no—
412C4×C47—22no—
413C4×C47—21no—
414C4×C47—21no—
415C4×C47—22no—
416C4×C47—42no—
417C4×C47—42no—
418C4×C47—42no—
419C4×C47#52512yes—
420C4×C47C22×#4111yescharacteristic
421C4×C47C22×#4111yescharacteristic
422Dic47—24no—
423Dic47—42no—
424Dic47—42no—
425#3455D4711yescharacteristic, complemented
426C2×#520—471no—
427#3125—474no—
428#3124—474no—
429#3120—474no—
430#3119—474no—
431#3092—472no—
432#3078—471no—
433#3077—471no—
434#3037—471no—
435#3036—471no—
436#3005—472no—
437C4×#137—472no—
438C4×AGL(1,ℤ/8)—472no—
439#2921—471no—
440C2×C47—22no—
441C2×C47—42no—
442C2×C47—82no—
443C2×C47C2×#52511yescharacteristic
444C2×C47#358511yescharacteristic
445C2×C47#358611yescharacteristic
446D47—44no—
447C22×#41—471no—
448C2×#137—472no—
449C2×AGL(1,ℤ/8)—472no—
450#542C2×D4712yescomplemented
451#542C2×D4712yescomplemented
452#541C2×D4712yescomplemented
453#540C2×D4712yescomplemented
454#539—21no—
455#539—21no—
456#538—21no—
457#538—21no—
458#533C2×D4711yescharacteristic
459#532C2×D4711yescharacteristic
460#529—22no—
461#529—22no—
462#525C2×D4712yes—
463#520—474no—
464#520—474no—
465#520—942no—
466#520—942no—
467C4×#41C2×D4712yes—
468C2×C4×Q8—471no—
469C2×C4×Q8—471no—
470C2×C4×D4—471no—
471C2×C4×D4—471no—
472C2×C4×D4—941no—
473C2×C4×D4—941no—
474C2×#117—941no—
475C2×#117C2×D4711yescharacteristic
476C22×C4⋊C4—471no—
477C22×C4⋊C4—941no—
478#484—474no—
479#483—474no—
480#481—474no—
481#480—474no—
482#479—474no—
483#478—474no—
484#477—472no—
485#476—472no—
486#475—472no—
487#474—472no—
488#464—474no—
489#463—474no—
490#462—472no—
491#461—472no—
492#460—472no—
493#459—472no—
494#452—474no—
495#452—474no—
496#449—474no—
497#449—474no—
498#442—474no—
499#441—474no—
500#440—474no—
501#440—474no—
502C4×Q16—474no—
503C4×SD16—474no—
504C4×SD16—474no—
505C4×D8—474no—
506#433—474no—
507#433—474no—
508#428—472no—
509#428—472no—
510#423—471no—
511#423—471no—
512#419—472no—
513#418—472no—
514#417—472no—
515#417—472no—
516#407—472no—
517C4×M16—472no—
518C47#6056511yescharacteristic, complemented, Sylow
519C2×#41—474no—
520C2×#41—944no—
521C2×#41—944no—
522C2×#41—942no—
523C2×#41C22×D4712yes—
524C22×Q8—471no—
525C22×D4—471no—
526C22×D4—941no—
527C23×C4—941no—
528C23×C4—941no—
529C23×C4—941no—
530C23×C4—941no—
531C23×C4C22×D4711yescharacteristic
532#137—948no—
533AGL(1,ℤ/8)—948no—
534C2×Q16—474no—
535C2×SD16—474no—
536C2×SD16—474no—
537C2×D8—474no—
538C2×M16—472no—
539C2×M16—472no—
540C4⋊Q8C22×D4711yescharacteristic
541C4⋊Q8C22×D4711yescharacteristic
542C4⋊Q8C22×D4711yescharacteristic
543#127C22×D4711yescharacteristic
544#126—22no—
545#126—22no—
546#126—22no—
547#126—22no—
548#125—22no—
549#125—22no—
550#125C22×D4712yes—
551#124—22no—
552#124—22no—
553#124C22×D4712yes—
554#123—22no—
555#123—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8C22×D4712yes—
564C22⋊Q8C22×D4712yes—
565#121—21no—
566#121—21no—
567#121—22no—
568#121—22no—
569#121C22×D4712yes—
570#121C22×D4712yes—
571#120—22no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8—474no—
575C4×Q8—472no—
576C4×Q8—472no—
577C4×Q8—942no—
578C4×Q8—941no—
579C4×Q8—941no—
580C4×Q8C22×D4712yes—
581C4×Q8C22×D4712yes—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—474no—
589C4×D4—472no—
590C4×D4—472no—
591C4×D4—944no—
592C4×D4—944no—
593C4×D4—944no—
594C4×D4—944no—
595C4×D4—942no—
596C4×D4—941no—
597C4×D4—941no—
598C4×D4C22×D4712yes—
599C4×D4C22×D4712yes—
600#117—22no—
601#117—944no—
602#117—944no—
603#117C22⋊D4712yes—
604#117C22⋊D4712yes—
605#117C22×D4712yes—
606#117C22×D4712yes—
607#117C22×D4712yes—
608C2×C4⋊C4—471no—
609C2×C4⋊C4—471no—
610C2×C4⋊C4—474no—
611C2×C4⋊C4—941no—
612C2×C4⋊C4—942no—
613C2×C4⋊C4—941no—
614C2×C4⋊C4—941no—
615C2×C4⋊C4—944no—
616C2×C4⋊C4—944no—
617C2×C4⋊C4C22⋊D4711yescharacteristic
618C2×C4⋊C4C22⋊D4711yescharacteristic
619C2×C22⋊C4—941no—
620C2×C22⋊C4—941no—
621C2×C22⋊C4C22⋊D4711yescharacteristic
622C2×C22⋊C4C22⋊D4711yescharacteristic
623C2×C42—22no—
624C2×C42—941no—
625C2×C42—941no—
626C2×C42C22×D4711yescharacteristic
627C2×C42C22×D4711yescharacteristic
628#107—474no—
629#107—474no—
630#106—474no—
631#106—474no—
632C4⋊C8—472no—
633C4⋊C8—472no—
634C4⋊C8—472no—
635C4⋊C8—472no—
636#103—474no—
637#103—474no—
638#103—474no—
639#103—474no—
640#102—474no—
641#102—474no—
642#102—474no—
643#102—474no—
644C22⋊C8—474no—
645C22⋊C8—474no—
646#97—474no—
647C4×C8—474no—
648C24—941no—
649C24C2×C22⋊D4711yescharacteristic
650#41—24no—
651#41—24no—
652#41—948no—
653#41—948no—
654#41—9416no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—474no—
658C2×Q8—472no—
659C2×Q8—941no—
660C2×Q8—942no—
661C2×Q8C23×D4712yes—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—474no—
668C2×D4—472no—
669C2×D4—948no—
670C2×D4—944no—
671C2×D4—941no—
672C2×D4—942no—
673C2×D4C23×D4712yes—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—948no—
680C22×C4—941no—
681C22×C4—944no—
682C22×C4—944no—
683C22×C4—941no—
684C22×C4—941no—
685C22×C4—944no—
686C22×C4—942no—
687C22×C4—942no—
688C22×C4—3762no—
689C22×C4—3762no—
690C22×C4—3762no—
691C22×C4C2×C22⋊D4711yescharacteristic
692C22×C4C2×C22⋊D4712yes—
693C22×C4C2×C22⋊D4711yescharacteristic
694C22×C4C2×C22⋊D4711yescharacteristic
695C22×C4C2×C22⋊D4711yescharacteristic
696C22×C4C2×C22⋊D4711yescharacteristic
697C22×C4C23×D4712yes—
698C22×C4C23×D4711yescharacteristic
699Q16—948no—
700SD16—948no—
701SD16—948no—
702D8—948no—
703M16—944no—
704M16—944no—
705C2×C8—474no—
706C2×C8—474no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—472no—
718C4⋊C4—472no—
719C4⋊C4—944no—
720C4⋊C4—942no—
721C4⋊C4—942no—
722C4⋊C4—944no—
723C4⋊C4—941no—
724C4⋊C4—941no—
725C4⋊C4C2×C22⋊D4712yes—
726C4⋊C4C2×C22⋊D4712yes—
727C4⋊C4C2×C22⋊D4712yes—
728C4⋊C4C2×C22⋊D4712yes—
729C4⋊C4C23×D4712yes—
730C4⋊C4C23×D4712yes—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—944no—
741C22⋊C4—942no—
742C22⋊C4—942no—
743C22⋊C4C2×C22⋊D4712yes—
744C22⋊C4C2×C22⋊D4712yes—
745C22⋊C4C2×C22⋊D4712yes—
746C22⋊C4C2×C22⋊D4712yes—
747C42—22no—
748C42—22no—
749C42—22no—
750C42—944no—
751C42—942no—
752C42—942no—
753C42C2×C22⋊D4712yes—
754C42C2×C22⋊D4711yescharacteristic
755C42C2×C22⋊D4711yescharacteristic
756C42C23×D4712yes—
757C42C23×D4711yescharacteristic
758C42C23×D4711yescharacteristic
759C23—22no—
760C23—22no—
761C23—41no—
762C23—41no—
763C23—944no—
764C23—942no—
765C23—1882no—
766C23—1882no—
767C23C22×C22⋊D4712yes—
768C23C22×C22⋊D4711yescharacteristic
769Q8—22no—
770Q8—22no—
771Q8—81no—
772Q8—81no—
773Q8—474no—
774Q8—944no—
775Q8—942no—
776D4—22no—
777D4—22no—
778D4—44no—
779D4—81no—
780D4—81no—
781D4—82no—
782D4—82no—
783D4—474no—
784D4—9416no—
785D4—944no—
786D4—942no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—44no—
799C2×C4—82no—
800C2×C4—82no—
801C2×C4—9416no—
802C2×C4—944no—
803C2×C4—942no—
804C2×C4—942no—
805C2×C4—942no—
806C2×C4—3764no—
807C2×C4—3762no—
808C2×C4—3762no—
809C2×C4—3764no—
810C2×C4—1882no—
811C2×C4—1882no—
812C2×C4C22×C22⋊D4712yes—
813C2×C4C22×C22⋊D4712yes—
814C2×C4C22×C22⋊D4711yescharacteristic
815C2×C4C22×C22⋊D4711yescharacteristic
816C2×C4C22×C22⋊D4711yescharacteristic
817C2×C4C22×C22⋊D4711yescharacteristic
818C2×C4C22×C22⋊D4712yes—
819C2×C4C22×C22⋊D4711yescharacteristic
820C2×C4#41×D4712yes—
821C2×C4#41×D4712yes—
822C2×C4C24×D4711yescharacteristic
823C8—944no—
824C8—944no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—44no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—944no—
835C22—1888no—
836C22—1882no—
837C22—1882no—
838C22#1568963012yes—
839C22C23×C22⋊D4711yescharacteristic
840C4—22no—
841C4—22no—
842C4—21no—
843C4—21no—
844C4—22no—
845C4—21no—
846C4—21no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—944no—
851C4—1882no—
852C4—1882no—
853C4#1568963012yes—
854C4C2×#41×D4711yescharacteristic
855C4C2×#41×D4711yescharacteristic
856C2—22no—
857C2—42no—
858C2—82no—
859C2—1884no—
860C2C2×#1568963011yescharacteristic
861C2#2025816711yescharacteristic
862C2#2025817411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3455C2
socleC22×C47C23×D4
hypercenter#3455D47
hypocenterC47#60565
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. C2×#15689603C2semidirect
2. #20253659C2semidirect
3. #20253644C2semidirect
4. #20253596C2semidirect
5. #20253581C2semidirect
6. #20253308C2semidirect
7. #20253189C2semidirect
8. #20253181C2semidirect
9. #20252856C2semidirect
10. #20252848C2semidirect
11. #20252628C2semidirect
12. C4×#13094054C2semidirect
13. C4×#13094049C2semidirect
14. #20252026C2semidirect
15. C47×#3455C2semidirect
32. #15689456C22semidirect
33. #15689451C22semidirect
34. #15689439C22semidirect
35. #15689434C22semidirect
36. #15689427C22semidirect
37. #15689420C22semidirect
38. #15689415C22semidirect
39. #15689410C22semidirect
40. #15689405C22semidirect
41. #15689400C22semidirect
42. #15689342C22semidirect
43. #15689335C22semidirect
44. #15689330C22semidirect
45. #15689325C22semidirect
46. #15689320C22semidirect
47. #15689315C22semidirect
52. #15689233C22semidirect
53. #15689228C22semidirect
54. #15689223C22semidirect
55. #15689221C22semidirect
56. C4×#10625337C22semidirect
57. C4×#10625336C22semidirect
58. C4×#10625335C22semidirect
59. C4×#10625334C22semidirect
60. #15689184C22semidirect
61. #15689184C22semidirect
72. C47×#542C22semidirect
73. C47×#542C22semidirect
74. C47×#541C22semidirect
75. C47×#540C22semidirect
425. #3455D47semidirect
450. #542C2×D47semidirect
451. #542C2×D47semidirect
452. #541C2×D47semidirect
453. #540C2×D47semidirect
518. C47#60565semidirect

Maximal subgroups

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

subgroupindex
C2×#156896032
#202536592
#202536442
#202535962
#202535812
#202533082
#202531892
#202531812
#202528562
#202528482
#202526282
C4×#130940542
C4×#130940492
#202520262
C47×#34552
#6056547