Finite Group Databasebeta

← #27089317

Subgroups — #27089317

Order 12032.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689744C211yesmaximal, characteristic, complemented
2#20254853C214yesmaximal, complemented
3#20254844C214yesmaximal, complemented
4#20254808C214yesmaximal, complemented
5#20254793C214yesmaximal, complemented
6#20253203C212yesmaximal, complemented
7#20253189C211yesmaximal, characteristic, complemented
8#20253181C211yesmaximal, characteristic, complemented
9#20253020C212yesmaximal, complemented
10#20253009C212yesmaximal, complemented
11#20252882C212yesmaximal, complemented
12#20252856C211yesmaximal, characteristic, complemented
13#20252848C211yesmaximal, characteristic, complemented
14#20251952C211yesmaximal, characteristic, complemented
15C47×#3455C211yesmaximal, characteristic, complemented
16C2×#13094054C2212yes—
17C2×#13094049C2212yes—
18C22×#10625329C2212yes—
19#15689744—22no—
20#15689744—22no—
21#15689744C2214yes—
22#15689744C2214yes—
23C2×#13094024C2211yescharacteristic
24C2×#13094019—21no—
25C2×#13094012C2211yescharacteristic
26C2×#13094010—21no—
27C2×#13094006—21no—
28C2×#13094003C2211yescharacteristic
29C2×#13094002—21no—
30C2×#13093998C2211yescharacteristic
31C2×C4×Dic94C2211yescharacteristic
32C2×C4×D188C2211yescharacteristic
33#15689427C2214yescomplemented
34#15689420C2214yescomplemented
35#15689418C2214yescomplemented
36#15689415C2212yescomplemented
37#15689413C2214yescomplemented
38#15689410C2212yescomplemented
39#15689408C2214yescomplemented
40#15689405C2212yescomplemented
41#15689403C2214yescomplemented
42#15689400C2212yescomplemented
43#15689379C2214yescomplemented
44#15689374C2214yes—
45#15689371C2214yes—
46#15689367C2214yescomplemented
47#15689362C2214yescomplemented
48#15689357C2214yes—
49#15689354C2214yes—
50#15689350C2214yescomplemented
51#15689345C2214yescomplemented
52#15689345C2214yescomplemented
53#15689342C2214yescomplemented
54#15689338C2214yescomplemented
55#15689338C2214yescomplemented
56#15689335C2214yescomplemented
57#15689330C2212yescomplemented
58#15689325C2212yescomplemented
59#15689320C2212yescomplemented
60#15689315C2212yescomplemented
61#15689166C2212yes—
62#15689166C2212yes—
63#15689150C2214yescomplemented
64#15689150C2214yescomplemented
65#15689147C2211yescharacteristic
66#15689147C2212yes—
67#15689147C2211yescharacteristic
68#15689131C2212yes—
69#15689127C2212yes—
70#15689124C2212yes—
71#15689124C2212yes—
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
87C22×Dic94—21no—
88C22×Dic94C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C4×D47—21no—
92#13094054—44no—
93#13094049—44no—
94C2×#10625337C2314yes—
95C2×#10625335C2314yes—
96C2×#10625336C2314yes—
97C2×#10625334C2314yes—
98C2×#10625329—44no—
99C2×#10625329C2312yes—
100C2×#10625329C2312yes—
101C2×#10625329C2314yes—
102C22×C47⋊C8C2314yes—
103#13094024—22no—
104#13094024C2314yes—
105#13094019—24no—
106#13094019—24no—
107#13094012—22no—
108#13094012C2314yes—
109#13094010—24no—
110#13094010—24no—
111#13094006—24no—
112#13094006—24no—
113#13094003—22no—
114#13094003C2314yes—
115#13094002—24no—
116#13094002—24no—
117#13093998—22no—
118#13093998C2314yes—
119C4×Dic94—21no—
120C4×Dic94—21no—
121C4×Dic94C2312yes—
122C4×Dic94C2312yes—
123C4×D188—21no—
124C4×D188—21no—
125C4×D188C2312yes—
126C4×D188C2312yes—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×C22⋊Dic47—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×C4×Dic47—21no—
138#13093957C2314yes—
139#13093957C2314yes—
140#13093955C2314yes—
141#13093955C2314yes—
142C4⋊(C47⋊C8)C2312yes—
143C4⋊(C47⋊C8)C2312yes—
144C4⋊(C47⋊C8)C2312yes—
145C4⋊(C47⋊C8)C2314yes—
146C4⋊(C47⋊C8)C2314yes—
147C4⋊(C47⋊C8)C2312yes—
148#13093948C2314yes—
149#13093948C2314yes—
150#13093947C2314yes—
151#13093947C2314yes—
152#13093945C2314yes—
153#13093945C2314yes—
154#13093944C2314yes—
155#13093944C2314yes—
156C2×#41×C47C2312yes—
157C23×C4×C47C2311yescharacteristic
158C4⋊Q8×C47C2311yescharacteristic
159C4⋊Q8×C47C2311yescharacteristic
160C4⋊Q8×C47C2311yescharacteristic
161#127×C47C2311yescharacteristic
162#126×C47—22no—
163#126×C47—22no—
164#126×C47—22no—
165#126×C47—22no—
166#125×C47—22no—
167#125×C47—22no—
168#125×C47C2312yes—
169#124×C47—22no—
170#124×C47—22no—
171#124×C47C2312yes—
172#123×C47—22no—
173#123×C47—22no—
174#123×C47—22no—
175#123×C47—22no—
176#123×C47—22no—
177C22⋊Q8×C47—21no—
178C22⋊Q8×C47—21no—
179C22⋊Q8×C47—22no—
180C22⋊Q8×C47—22no—
181C22⋊Q8×C47C2312yes—
182C22⋊Q8×C47C2312yes—
183#121×C47—21no—
184#121×C47—21no—
185#121×C47—22no—
186#121×C47—22no—
187#121×C47C2312yes—
188#121×C47C2312yes—
189#120×C47—22no—
190C4×Q8×C47—21no—
191C4×Q8×C47—21no—
192C4×Q8×C47C2312yes—
193C4×Q8×C47C2312yes—
194C4×D4×C47—22no—
195C4×D4×C47—22no—
196C4×D4×C47—22no—
197C4×D4×C47—22no—
198C4×D4×C47—21no—
199C4×D4×C47—21no—
200C4×D4×C47C2312yes—
201C4×D4×C47C2312yes—
202#117×C47—22no—
203#117×C47D412yes—
204#117×C47D412yes—
205#117×C47C2312yes—
206#117×C47C2312yes—
207#117×C47C2312yes—
208C2×C4⋊C4×C47D411yescharacteristic
209C2×C4⋊C4×C47D411yescharacteristic
210C2×C22⋊C4×C47D411yescharacteristic
211C2×C22⋊C4×C47D411yescharacteristic
212C2×C42×C47—22no—
213C2×C42×C47C2311yescharacteristic
214C2×C42×C47C2311yescharacteristic
215C24×C47C2×D411yescharacteristic
216C23×D47—21no—
217#41×C47—24no—
218#41×C47—24no—
219C2×Q8×C47—21no—
220C2×Q8×C47—21no—
221C2×Q8×C47C2412yes—
222C2×D4×C47—22no—
223C2×D4×C47—22no—
224C2×D4×C47—22no—
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47C2412yes—
228C22×C4×C47—22no—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D412yes—
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47C2×D411yescharacteristic
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D411yescharacteristic
239C22×C4×C47C2412yes—
240C22×C4×C47C2411yescharacteristic
241C2×C22⋊D47—24no—
242C2×C22⋊D47—82no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C2×D188—22no—
247C2×D188—22no—
248C2×D188—21no—
249C2×D188C2412yes—
250C2×C4×D47—22no—
251C2×C4×D47—22no—
252C2×C4×D47—82no—
253C2×Dic94—22no—
254C2×Dic94—22no—
255C2×Dic94—21no—
256C2×Dic94—24no—
257C2×Dic94—82no—
258C2×Dic94C2412yes—
259C4⋊C4×C47—22no—
260C4⋊C4×C47—22no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—22no—
264C4⋊C4×C47—22no—
265C4⋊C4×C47—22no—
266C4⋊C4×C47—22no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47C2×D412yes—
270C4⋊C4×C47C2×D412yes—
271C4⋊C4×C47C2×D412yes—
272C4⋊C4×C47C2×D412yes—
273C4⋊C4×C47C2412yes—
274C4⋊C4×C47C2412yes—
275C22⋊C4×C47—22no—
276C22⋊C4×C47—22no—
277C22⋊C4×C47—22no—
278C22⋊C4×C47—22no—
279C22⋊C4×C47—22no—
280C22⋊C4×C47—22no—
281C22⋊C4×C47—22no—
282C22⋊C4×C47—22no—
283C22⋊C4×C47—22no—
284C22⋊C4×C47C2×D412yes—
285C22⋊C4×C47C2×D412yes—
286C22⋊C4×C47C2×D412yes—
287C22⋊C4×C47C2×D412yes—
288C42×C47—22no—
289C42×C47—22no—
290C42×C47—22no—
291C42×C47C2×D412yes—
292C42×C47C2×D411yescharacteristic
293C42×C47C2×D411yescharacteristic
294C42×C47C2412yes—
295C42×C47C2411yescharacteristic
296C42×C47C2411yescharacteristic
297C22⋊Dic47—24no—
298#10625337—44no—
299#10625336—44no—
300#10625335—44no—
301#10625334—44no—
302(C2×D47)⋊C4—22no—
303(C2×D47)⋊C4—22no—
304(C2×D47)⋊C4—24no—
305(C2×D47)⋊C4—24no—
306(C2×D47)⋊C4—24no—
307C4⋊Dic47—24no—
308C4⋊Dic47—21no—
309C4⋊Dic47—21no—
310C4⋊Dic47C2412yes—
311C4⋊Dic47C2412yes—
312Dic47⋊C4—22no—
313Dic47⋊C4—22no—
314Dic47⋊C4—24no—
315C4×Dic47—22no—
316C4×Dic47—22no—
317#10625329—24no—
318#10625329—24no—
319#10625329—44no—
320C2×C47⋊C8—44no—
321C2×C47⋊C8C2414yes—
322C2×C47⋊C8C2414yes—
323C23×C47—22no—
324C23×C47—22no—
325C23×C47—41no—
326C23×C47—41no—
327C23×C47C22×D412yes—
328C23×C47C22×D411yescharacteristic
329C22×D47—22no—
330C22×D47—42no—
331C22×D47—42no—
332C22×D47—42no—
333Q8×C47—22no—
334Q8×C47—22no—
335Q8×C47—81no—
336Q8×C47—81no—
337D4×C47—22no—
338D4×C47—22no—
339D4×C47—44no—
340D4×C47—81no—
341D4×C47—81no—
342D4×C47—82no—
343D4×C47—82no—
344C2×C4×C47—22no—
345C2×C4×C47—24no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—44no—
356C2×C4×C47—82no—
357C2×C4×C47—82no—
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C22×D412yes—
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C22×D412yes—
364C2×C4×C47C22×D412yes—
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47H(5,𝔽2)12yes—
367C2×C4×C472−1+412yes—
368C2×C4×C47C2511yescharacteristic
369C22⋊D47—84no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—42no—
374C2×Dic47—42no—
375C2×Dic47—42no—
376D188—22no—
377D188—22no—
378D188—42no—
379C4×D47—82no—
380C4×D47—82no—
381Dic94—22no—
382Dic94—22no—
383Dic94—42no—
384Dic94—84no—
385C47⋊C8—24no—
386C47⋊C8—24no—
387#60919—471nomaximal, Sylow
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—22no—
391C22×C47—22no—
392C22×C47—22no—
393C22×C47—42no—
394C22×C47—42no—
395C22×C47—42no—
396C22×C47—82no—
397C22×C47#53712yes—
398C22×C47C23×D411yescharacteristic
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—84no—
403C4×C47—22no—
404C4×C47—21no—
405C4×C47—21no—
406C4×C47—22no—
407C4×C47—21no—
408C4×C47—21no—
409C4×C47—22no—
410C4×C47—42no—
411C4×C47—42no—
412C4×C47—42no—
413C4×C47#53712yes—
414C4×C47C2×H(5,𝔽2)11yescharacteristic
415C4×C47C2×2−1+411yescharacteristic
416Dic47—42no—
417Dic47—42no—
418Dic47—42no—
419#3455D4711yescharacteristic, complemented
420C2×#542—471no—
421#3263—474no—
422#3262—474no—
423#3258—474no—
424#3257—474no—
425#3079—472no—
426#3078—471no—
427#3077—471no—
428#3056—472no—
429#3055—472no—
430#3040—472no—
431#3037—471no—
432#3036—471no—
433#2905—471no—
434C2×C47—22no—
435C2×C47—42no—
436C2×C47—82no—
437C2×C47C2×#53711yescharacteristic
438C2×C47#358511yescharacteristic
439C2×C47#358611yescharacteristic
440D47—82no—
441C2×#137—472no—
442C2×AGL(1,ℤ/8)—472no—
443C22×M16—472no—
444#542—474no—
445#542—474no—
446#542—942no—
447#542—942no—
448#542C2×D4712yescomplemented
449#542C2×D4712yescomplemented
450#541C2×D4712yescomplemented
451#540C2×D4712yescomplemented
452#539—21no—
453#539—21no—
454#538—21no—
455#538—21no—
456#533C2×D4711yescharacteristic
457#532C2×D4711yescharacteristic
458C2×C4⋊Q8—471no—
459#529—22no—
460#529—22no—
461C2×#126—941no—
462C2×#124—471no—
463C2×#124—941no—
464#525C2×D4712yes—
465C2×#123—941no—
466C2×C22⋊Q8—471no—
467C2×C22⋊Q8—941no—
468C2×#121—471no—
469C4×#41C2×D4712yes—
470C2×C4×Q8—471no—
471C2×C4×D4—471no—
472C2×#117C2×D4711yescharacteristic
473#479—474no—
474#478—474no—
475#477—472no—
476#477—474no—
477#476—472no—
478#476—474no—
479#475—472no—
480#475—474no—
481#474—472no—
482#474—474no—
483#470—474no—
484#469—474no—
485#468—474no—
486#468—474no—
487#467—474no—
488#466—474no—
489#465—474no—
490#465—474no—
491#464—474no—
492#464—474no—
493#464—474no—
494#463—474no—
495#463—474no—
496#463—474no—
497#462—472no—
498#461—472no—
499#460—472no—
500#459—472no—
501#428—472no—
502#428—472no—
503#424—474no—
504#424—474no—
505#423—471no—
506#423—471no—
507#423—472no—
508#419—472no—
509#418—472no—
510#417—472no—
511#417—472no—
512C47#6091911yescharacteristic, complemented, Sylow
513C2×#41C22×D4712yes—
514C22×Q8—471no—
515C22×Q8—941no—
516C22×D4—471no—
517C22×D4—941no—
518C23×C4—941no—
519C23×C4C22×D4711yescharacteristic
520#137—1884no—
521AGL(1,ℤ/8)—1884no—
522C2×Q16—474no—
523C2×SD16—474no—
524C2×SD16—474no—
525C2×D8—474no—
526C2×M16—472no—
527C2×M16—472no—
528C2×M16—474no—
529C2×M16—1884no—
530C22×C8—474no—
531C4⋊Q8—474no—
532C4⋊Q8—942no—
533C4⋊Q8C22×D4711yescharacteristic
534C4⋊Q8C22×D4711yescharacteristic
535C4⋊Q8C22×D4711yescharacteristic
536#127C22×D4711yescharacteristic
537#126—22no—
538#126—22no—
539#126—22no—
540#126—22no—
541#126—944no—
542#126—944no—
543#125—22no—
544#125—22no—
545#125C22×D4712yes—
546#124—22no—
547#124—22no—
548#124—474no—
549#124—944no—
550#124—944no—
551#124—942no—
552#124C22×D4712yes—
553#123—22no—
554#123—22no—
555#123—22no—
556#123—22no—
557#123—22no—
558#123—944no—
559#123—944no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—474no—
565C22⋊Q8—942no—
566C22⋊Q8—944no—
567C22⋊Q8—944no—
568C22⋊Q8C22×D4712yes—
569C22⋊Q8C22×D4712yes—
570#121—21no—
571#121—21no—
572#121—22no—
573#121—22no—
574#121—474no—
575#121—942no—
576#121C22×D4712yes—
577#121C22×D4712yes—
578#120—22no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—472no—
582C4×Q8—472no—
583C4×Q8—941no—
584C4×Q8—941no—
585C4×Q8C22×D4712yes—
586C4×Q8C22×D4712yes—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—472no—
594C4×D4—472no—
595C4×D4—941no—
596C4×D4—941no—
597C4×D4C22×D4712yes—
598C4×D4C22×D4712yes—
599#117—22no—
600#117C22⋊D4712yes—
601#117C22⋊D4712yes—
602#117C22×D4712yes—
603#117C22×D4712yes—
604#117C22×D4712yes—
605C2×C4⋊C4—471no—
606C2×C4⋊C4—471no—
607C2×C4⋊C4—941no—
608C2×C4⋊C4—941no—
609C2×C4⋊C4—941no—
610C2×C4⋊C4C22⋊D4711yescharacteristic
611C2×C4⋊C4C22⋊D4711yescharacteristic
612C2×C22⋊C4—941no—
613C2×C22⋊C4—941no—
614C2×C22⋊C4—941no—
615C2×C22⋊C4—941no—
616C2×C22⋊C4—941no—
617C2×C22⋊C4C22⋊D4711yescharacteristic
618C2×C22⋊C4C22⋊D4711yescharacteristic
619C2×C42—22no—
620C2×C42—941no—
621C2×C42C22×D4711yescharacteristic
622C2×C42C22×D4711yescharacteristic
623#107—474no—
624#107—474no—
625#106—474no—
626#106—474no—
627C4⋊C8—472no—
628C4⋊C8—472no—
629C4⋊C8—472no—
630C4⋊C8—474no—
631C4⋊C8—474no—
632C4⋊C8—472no—
633#103—474no—
634#103—474no—
635#103—474no—
636#103—474no—
637#102—474no—
638#102—474no—
639#102—474no—
640#102—474no—
641C24—941no—
642C24C2×C22⋊D4711yescharacteristic
643#41—24no—
644#41—24no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—472no—
648C2×Q8—944no—
649C2×Q8—941no—
650C2×Q8—942no—
651C2×Q8—942no—
652C2×Q8—3762no—
653C2×Q8C23×D4712yes—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—472no—
660C2×D4—944no—
661C2×D4—941no—
662C2×D4—942no—
663C2×D4—942no—
664C2×D4—3762no—
665C2×D4C23×D4712yes—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—941no—
672C22×C4—941no—
673C22×C4—941no—
674C22×C4—942no—
675C22×C4—942no—
676C22×C4—3762no—
677C22×C4C2×C22⋊D4711yescharacteristic
678C22×C4C2×C22⋊D4712yes—
679C22×C4C2×C22⋊D4711yescharacteristic
680C22×C4C2×C22⋊D4711yescharacteristic
681C22×C4C2×C22⋊D4711yescharacteristic
682C22×C4C2×C22⋊D4711yescharacteristic
683C22×C4C23×D4712yes—
684C22×C4C23×D4711yescharacteristic
685Q16—1884no—
686SD16—1884no—
687SD16—1884no—
688D8—1884no—
689M16—944no—
690M16—944no—
691M16—1884no—
692C2×C8—474no—
693C2×C8—474no—
694C2×C8—1884no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—472no—
706C4⋊C4—472no—
707C4⋊C4—942no—
708C4⋊C4—942no—
709C4⋊C4—944no—
710C4⋊C4—941no—
711C4⋊C4—941no—
712C4⋊C4—944no—
713C4⋊C4C2×C22⋊D4712yes—
714C4⋊C4C2×C22⋊D4712yes—
715C4⋊C4C2×C22⋊D4712yes—
716C4⋊C4C2×C22⋊D4712yes—
717C4⋊C4C23×D4712yes—
718C4⋊C4C23×D4712yes—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—944no—
729C22⋊C4—942no—
730C22⋊C4—942no—
731C22⋊C4—944no—
732C22⋊C4—944no—
733C22⋊C4—944no—
734C22⋊C4C2×C22⋊D4712yes—
735C22⋊C4C2×C22⋊D4712yes—
736C22⋊C4C2×C22⋊D4712yes—
737C22⋊C4C2×C22⋊D4712yes—
738C42—22no—
739C42—22no—
740C42—22no—
741C42—942no—
742C42—942no—
743C42C2×C22⋊D4712yes—
744C42C2×C22⋊D4711yescharacteristic
745C42C2×C22⋊D4711yescharacteristic
746C42C23×D4711yescharacteristic
747C42C23×D4711yescharacteristic
748C42C23×D4712yes—
749C23—22no—
750C23—22no—
751C23—41no—
752C23—41no—
753C23—942no—
754C23—1882no—
755C23—1882no—
756C23—1882no—
757C23C22×C22⋊D4712yes—
758C23C22×C22⋊D4711yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—81no—
762Q8—81no—
763Q8—942no—
764Q8—942no—
765Q8—3764no—
766Q8—1882no—
767D4—22no—
768D4—22no—
769D4—44no—
770D4—81no—
771D4—81no—
772D4—82no—
773D4—82no—
774D4—942no—
775D4—942no—
776D4—3764no—
777D4—1882no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—44no—
790C2×C4—82no—
791C2×C4—82no—
792C2×C4—942no—
793C2×C4—942no—
794C2×C4—942no—
795C2×C4—3762no—
796C2×C4—3762no—
797C2×C4—1882no—
798C2×C4—1882no—
799C2×C4—1882no—
800C2×C4C22×C22⋊D4712yes—
801C2×C4C22×C22⋊D4712yes—
802C2×C4C22×C22⋊D4711yescharacteristic
803C2×C4C22×C22⋊D4711yescharacteristic
804C2×C4C22×C22⋊D4711yescharacteristic
805C2×C4C22×C22⋊D4711yescharacteristic
806C2×C4C22×C22⋊D4712yes—
807C2×C4C22×C22⋊D4711yescharacteristic
808C2×C4#1309407012yes—
809C2×C4#1309407112yes—
810C2×C4C24×D4711yescharacteristic
811C8—944no—
812C8—944no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—82no—
822C22—3764no—
823C22—1882no—
824C22—1882no—
825C22—1882no—
826C22#1568970112yes—
827C22C23×C22⋊D4711yescharacteristic
828C4—22no—
829C4—21no—
830C4—21no—
831C4—22no—
832C4—21no—
833C4—21no—
834C4—22no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—1882no—
839C4—1882no—
840C4—1882no—
841C4#1568970112yes—
842C4C2×#1309407011yescharacteristic
843C4C2×#1309407111yescharacteristic
844C2—22no—
845C2—42no—
846C2—82no—
847C2—3762no—
848C2C2×#1568970111yescharacteristic
849C2#2025816711yescharacteristic
850C2#2025817411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3455C2
socleC22×C47C23×D4
hypercenter#3455D47
hypocenterC47#60919
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×#15689744C2semidirect
2. #20254853C2semidirect
3. #20254844C2semidirect
4. #20254808C2semidirect
5. #20254793C2semidirect
6. #20253203C2semidirect
7. #20253189C2semidirect
8. #20253181C2semidirect
9. #20253020C2semidirect
10. #20253009C2semidirect
11. #20252882C2semidirect
12. #20252856C2semidirect
13. #20252848C2semidirect
14. #20251952C2semidirect
15. C47×#3455C2semidirect
33. #15689427C22semidirect
34. #15689420C22semidirect
35. #15689418C22semidirect
36. #15689415C22semidirect
37. #15689413C22semidirect
38. #15689410C22semidirect
39. #15689408C22semidirect
40. #15689405C22semidirect
41. #15689403C22semidirect
42. #15689400C22semidirect
43. #15689379C22semidirect
46. #15689367C22semidirect
47. #15689362C22semidirect
50. #15689350C22semidirect
51. #15689345C22semidirect
52. #15689345C22semidirect
53. #15689342C22semidirect
54. #15689338C22semidirect
55. #15689338C22semidirect
56. #15689335C22semidirect
57. #15689330C22semidirect
58. #15689325C22semidirect
59. #15689320C22semidirect
60. #15689315C22semidirect
63. #15689150C22semidirect
64. #15689150C22semidirect
72. C47×#542C22semidirect
73. C47×#542C22semidirect
74. C47×#541C22semidirect
75. C47×#540C22semidirect
419. #3455D47semidirect
448. #542C2×D47semidirect
449. #542C2×D47semidirect
450. #541C2×D47semidirect
451. #540C2×D47semidirect
512. C47#60919semidirect

Maximal subgroups

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

subgroupindex
C2×#156897442
#202548532
#202548442
#202548082
#202547932
#202532032
#202531892
#202531812
#202530202
#202530092
#202528822
#202528562
#202528482
#202519522
C47×#34552
#6091947