Finite Group Databasebeta

← #27084792

Subgroups — #27084792

Order 12032.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689744C211yesmaximal, characteristic, complemented
2#20253665C214yesmaximal, complemented
3#20253650C214yesmaximal, complemented
4#20253617C214yesmaximal, complemented
5#20253572C214yesmaximal, complemented
6#20253336C211yesmaximal, characteristic, complemented
7#20253328C211yesmaximal, characteristic, complemented
8#20253203C212yesmaximal, complemented
9#20252882C212yesmaximal, complemented
10#20252648C211yesmaximal, characteristic, complemented
11#20252640C211yesmaximal, characteristic
12C4×#13094054C212yesmaximal, complemented
13C4×#13094049C212yesmaximal, complemented
14#20252026C211yesmaximal, characteristic, complemented
15C47×#3428C211yesmaximal, characteristic, complemented
16C2×#13094054C2212yes—
17C2×#13094049C2212yes—
18#15689744—22no—
19#15689744—22no—
20#15689744C2214yes—
21#15689744C2214yescomplemented
22C2×#13094024C2211yescharacteristic, complemented
23C2×#13094019—21no—
24C2×#13094012C2211yescharacteristic, complemented
25C2×#13094010—21no—
26C2×#13094006—21no—
27C2×#13094003C2211yescharacteristic
28C2×#13094002—21no—
29C2×#13093998C2211yescharacteristic
30C2×C4×Dic94C2211yescharacteristic, complemented
31C2×C4×D188C2211yescharacteristic, complemented
32#15689464C2214yescomplemented
33#15689458C2212yescomplemented
34#15689453C2212yescomplemented
35#15689447C2214yes—
36#15689441C2212yescomplemented
37#15689436C2212yescomplemented
38#15689418C2214yescomplemented
39#15689413C2214yescomplemented
40#15689408C2214yescomplemented
41#15689403C2214yescomplemented
42#15689345C2214yescomplemented
43#15689345C2214yescomplemented
44#15689338C2214yescomplemented
45#15689338C2214yescomplemented
46#15689285C2214yescomplemented
47#15689279C2212yescomplemented
48#15689274C2212yescomplemented
49#15689268C2214yes—
50#15689262C2212yes—
51#15689257C2212yes—
52#15689233C2214yescomplemented
53#15689228C2214yescomplemented
54#15689223C2214yescomplemented
55#15689221C2214yescomplemented
56C4×#10625337C2214yescomplemented
57C4×#10625336C2214yescomplemented
58C4×#10625335C2214yescomplemented
59C4×#10625334C2214yescomplemented
60#15689184C2214yescomplemented
61#15689184C2214yescomplemented
62#15689166C2212yescomplemented
63#15689166C2212yescomplemented
64#15689147C2212yescomplemented
65#15689131C2212yescomplemented
66#15689127C2212yescomplemented
67#15689124C2212yes—
68#15689124C2212yes—
69#15689087C2211yescharacteristic
70#15689087C2211yescharacteristic
71C4×#10625329C2212yescomplemented
72C22×#41×C47C2211yescharacteristic
73C47×#520—21no—
74C47×#520—21no—
75C47×#520C2212yescomplemented
76C47×#520C2212yescomplemented
77C47×#519C2212yescomplemented
78C47×#518—21no—
79C47×#518—21no—
80C47×#518C2212yescomplemented
81C4×#41×C47—22no—
82C4×#41×C47C2212yes—
83C4×#41×C47C2212yes—
84C2×#117×C47—22no—
85C2×#117×C47C2211yescharacteristic
86C2×#117×C47C2211yescharacteristic
87C22×Dic94—21no—
88C22×Dic94C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C4×D47—21no—
92#13094054—28no—
93#13094049—28no—
94C2×#10625337C2314yes—
95C2×#10625335C2314yes—
96C2×#10625336C2314yes—
97C2×#10625334C2314yes—
98C2×#10625329C2312yes—
99C2×#10625329C2312yes—
100#13094024—22no—
101#13094024C2314yes—
102#13094019—24no—
103#13094019—24no—
104#13094012—22no—
105#13094012C2314yes—
106#13094010—24no—
107#13094010—24no—
108#13094006—24no—
109#13094006—24no—
110#13094003—21no—
111#13094003—21no—
112#13094003C2312yes—
113#13094003C2312yes—
114#13094002—24no—
115#13094002—24no—
116#13093998—21no—
117#13093998—21no—
118#13093998C2312yes—
119#13093998C2312yes—
120C4×Dic94—22no—
121C4×Dic94C2314yes—
122C4×D188—22no—
123C4×D188C2314yes—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×C22⋊Dic47—21no—
130C2×(C2×D47)⋊C4—21no—
131C2×(C2×D47)⋊C4—21no—
132C2×(C2×D47)⋊C4—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×C4×Dic47—21no—
135#13093957C2314yes—
136#13093957C2314yes—
137#13093955C2314yes—
138#13093955C2314yes—
139C4⋊(C47⋊C8)C2314yes—
140C4⋊(C47⋊C8)C2314yes—
141#13093948C2314yes—
142#13093948C2314yes—
143#13093947C2314yes—
144#13093947C2314yes—
145#13093945C2314yes—
146#13093945C2314yes—
147#13093944C2314yes—
148#13093944C2314yes—
149C22⋊(C47⋊C8)C2312yes—
150C22⋊(C47⋊C8)C2312yes—
151C22⋊(C47⋊C8)C2312yes—
152C22⋊(C47⋊C8)C2312yes—
153#13093935C2314yes—
154C4×C47⋊C8C2314yes—
155C2×#41×C47—28no—
156C2×#41×C47—21no—
157C2×#41×C47—21no—
158C2×#41×C47C2312yes—
159C2×#41×C47C2312yes—
160C22×Q8×C47C2311yescharacteristic
161C22×D4×C47—21no—
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C23×C4×C47C2311yescharacteristic
165C4×Q8×C47—22no—
166C4×Q8×C47—22no—
167C4×Q8×C47C2312yes—
168C4×Q8×C47C2312yes—
169C4×Q8×C47C2312yes—
170C4×Q8×C47C2312yes—
171C4×D4×C47—22no—
172C4×D4×C47—22no—
173C4×D4×C47—22no—
174C4×D4×C47—22no—
175C4×D4×C47—22no—
176C4×D4×C47—22no—
177C4×D4×C47—22no—
178C4×D4×C47—22no—
179C4×D4×C47—22no—
180C4×D4×C47—22no—
181C4×D4×C47C2312yes—
182C4×D4×C47C2312yes—
183C4×D4×C47C2312yes—
184C4×D4×C47C2312yes—
185#117×C47—21no—
186#117×C47—21no—
187#117×C47—22no—
188#117×C47—22no—
189#117×C47—22no—
190#117×C47—22no—
191#117×C47—22no—
192#117×C47—22no—
193#117×C47D412yes—
194#117×C47D412yes—
195#117×C47C2312yes—
196#117×C47C2312yes—
197#117×C47C2312yes—
198#117×C47C2312yes—
199C2×C4⋊C4×C47—22no—
200C2×C4⋊C4×C47—22no—
201C2×C4⋊C4×C47D411yescharacteristic
202C2×C4⋊C4×C47D411yescharacteristic
203C2×C4⋊C4×C47C2311yescharacteristic
204C2×C4⋊C4×C47C2311yescharacteristic
205C2×C22⋊C4×C47—21no—
206C2×C22⋊C4×C47—22no—
207C2×C22⋊C4×C47—22no—
208C2×C22⋊C4×C47D411yescharacteristic
209C2×C22⋊C4×C47D411yescharacteristic
210C2×C42×C47—21no—
211C2×C42×C47—22no—
212C2×C42×C47—22no—
213C2×C42×C47C2311yescharacteristic
214C2×C42×C47C2311yescharacteristic
215C24×C47—21no—
216C24×C47C2×D411yescharacteristic
217C23×D47—21no—
218#41×C47—28no—
219#41×C47—28no—
220#41×C47—24no—
221#41×C47—24no—
222#41×C47—24no—
223#41×C47#4118yes—
224C2×Q8×C47—24no—
225C2×Q8×C47—21no—
226C2×Q8×C47C2412yes—
227C2×D4×C47—28no—
228C2×D4×C47—22no—
229C2×D4×C47—22no—
230C2×D4×C47—24no—
231C2×D4×C47—21no—
232C2×D4×C47C2412yes—
233C22×C4×C47—28no—
234C22×C4×C47—21no—
235C22×C4×C47—22no—
236C22×C4×C47—22no—
237C22×C4×C47—24no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—22no—
241C22×C4×C47—22no—
242C22×C4×C47—22no—
243C22×C4×C47—22no—
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2411yescharacteristic
252C22×C4×C47C2411yescharacteristic
253C22×C4×C47C2411yescharacteristic
254C2×C22⋊D47—22no—
255C2×C22⋊D47—22no—
256C2×C22⋊D47—82no—
257C22×Dic47—21no—
258C22×Dic47—21no—
259C22×Dic47—21no—
260C2×D188—24no—
261C2×D188—21no—
262C2×D188C2412yes—
263C2×C4×D47—24no—
264C2×C4×D47—82no—
265C2×Dic94—24no—
266C2×Dic94—21no—
267C2×Dic94—24no—
268C2×Dic94—82no—
269C2×Dic94C2412yes—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—22no—
273C4⋊C4×C47—22no—
274C4⋊C4×C47—22no—
275C4⋊C4×C47—22no—
276C4⋊C4×C47C2×D412yes—
277C4⋊C4×C47C2×D412yes—
278C4⋊C4×C47C2×D412yes—
279C4⋊C4×C47C2×D412yes—
280C4⋊C4×C47C2412yes—
281C4⋊C4×C47C2412yes—
282C22⋊C4×C47—22no—
283C22⋊C4×C47—22no—
284C22⋊C4×C47—22no—
285C22⋊C4×C47—22no—
286C22⋊C4×C47—22no—
287C22⋊C4×C47—22no—
288C22⋊C4×C47C2×D412yes—
289C22⋊C4×C47C2×D412yes—
290C22⋊C4×C47C2×D412yes—
291C22⋊C4×C47C2×D412yes—
292C42×C47—22no—
293C42×C47—22no—
294C42×C47—22no—
295C42×C47—22no—
296C42×C47—22no—
297C42×C47—22no—
298C42×C47C2×D412yes—
299C42×C47C2×D412yes—
300C42×C47C2412yes—
301C42×C47C2412yes—
302C22⋊Dic47—22no—
303C22⋊Dic47—22no—
304#10625337—28no—
305#10625336—28no—
306#10625335—28no—
307#10625334—28no—
308(C2×D47)⋊C4—24no—
309(C2×D47)⋊C4—22no—
310(C2×D47)⋊C4—22no—
311(C2×D47)⋊C4—24no—
312(C2×D47)⋊C4—24no—
313C4⋊Dic47—24no—
314C4⋊Dic47—21no—
315C4⋊Dic47—21no—
316C4⋊Dic47C2412yes—
317C4⋊Dic47C2412yes—
318Dic47⋊C4—24no—
319Dic47⋊C4—22no—
320Dic47⋊C4—22no—
321C4×Dic47—24no—
322#10625329—24no—
323#10625329—24no—
324C2×C47⋊C8C2414yes—
325C2×C47⋊C8C2414yes—
326C23×C47—24no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—41no—
330C23×C47—41no—
331C23×C47—81no—
332C23×C47—81no—
333C23×C47C22×D411yescharacteristic
334C23×C47C22×D411yescharacteristic
335C23×C47C22×D411yescharacteristic
336C22×D47—22no—
337C22×D47—42no—
338C22×D47—42no—
339C22×D47—42no—
340Q8×C47—24no—
341Q8×C47—22no—
342Q8×C47C2×#4114yes—
343D4×C47—28no—
344D4×C47—24no—
345D4×C47—28no—
346D4×C47—22no—
347D4×C47C2×#4114yes—
348C2×C4×C47—24no—
349C2×C4×C47—28no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—28no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—82no—
364C2×C4×C47—82no—
365C2×C4×C47—82no—
366C2×C4×C47—82no—
367C2×C4×C47—81no—
368C2×C4×C47—81no—
369C2×C4×C47C22×D412yes—
370C2×C4×C47C22×D411yescharacteristic
371C2×C4×C47C22×D411yescharacteristic
372C2×C4×C47C22×D412yes—
373C2×C4×C47C22×D412yes—
374C2×C4×C47C22×D412yes—
375C2×C4×C47C22×D411yescharacteristic
376C2×C4×C47C2×#4114yes—
377C2×C4×C47C2511yescharacteristic
378C22⋊D47—82no—
379C22⋊D47—82no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—42no—
384C2×Dic47—42no—
385C2×Dic47—42no—
386D188—24no—
387D188—42no—
388C4×D47—84no—
389Dic94—24no—
390Dic94—42no—
391Dic94—84no—
392C47⋊C8—24no—
393C47⋊C8—24no—
394#60567—471nomaximal, Sylow
395C22×C47—21no—
396C22×C47—21no—
397C22×C47—21no—
398C22×C47—21no—
399C22×C47—21no—
400C22×C47—21no—
401C22×C47—21no—
402C22×C47—21no—
403C22×C47—24no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—82no—
407C22×C47—84no—
408C22×C47#52512yes—
409C22×C47C23×D411yescharacteristic
410C2×D47—42no—
411C2×D47—42no—
412C2×D47—42no—
413C2×D47—84no—
414C4×C47—22no—
415C4×C47—22no—
416C4×C47—22no—
417C4×C47—22no—
418C4×C47—21no—
419C4×C47—24no—
420C4×C47—21no—
421C4×C47—42no—
422C4×C47—42no—
423C4×C47#52512yes—
424C4×C47C22×#4112yes—
425Dic47—42no—
426Dic47—42no—
427Dic47—42no—
428C2×#542—471no—
429#3428D4711yescharacteristic, complemented
430#3125—474no—
431#3124—474no—
432#3121—474no—
433#3118—474no—
434#3095—471no—
435#3094—471no—
436#3079—472no—
437#3040—472no—
438#3007—471no—
439#3006—471no—
440C4×#137—472no—
441C4×AGL(1,ℤ/8)—472no—
442#2921—471no—
443C2×C47—22no—
444C2×C47—41no—
445C2×C47—41no—
446C2×C47—44no—
447C2×C47C2×#52511yescharacteristic
448C2×C47#358511yescharacteristic
449C2×C47#358611yescharacteristic
450D47—82no—
451C22×#41C2×D4711yescharacteristic
452C2×#137—472no—
453C2×AGL(1,ℤ/8)—472no—
454#542—474no—
455#542—474no—
456#542—942no—
457#542—942no—
458C2×C4⋊Q8—471no—
459C2×#126—941no—
460C2×#124—471no—
461C2×#124—941no—
462C2×#123—941no—
463C2×C22⋊Q8—471no—
464C2×C22⋊Q8—941no—
465C2×#121—471no—
466#520—21no—
467#520—21no—
468#520C2×D4712yescomplemented
469#520C2×D4712yescomplemented
470#519C2×D4712yescomplemented
471#518—21no—
472#518—21no—
473#518C2×D4712yescomplemented
474C4×#41—22no—
475C4×#41C2×D4712yes—
476C4×#41C2×D4712yes—
477C2×C4×Q8—471no—
478C2×C4×D4—471no—
479C2×#117—22no—
480C2×#117C2×D4711yescharacteristic
481C2×#117C2×D4711yescharacteristic
482#485—474no—
483#484—472no—
484#483—472no—
485#482—474no—
486#481—472no—
487#480—472no—
488#477—474no—
489#476—474no—
490#475—474no—
491#474—474no—
492#464—474no—
493#464—474no—
494#463—474no—
495#463—474no—
496#452—474no—
497#451—472no—
498#450—472no—
499#449—474no—
500#448—472no—
501#447—472no—
502#442—474no—
503#441—474no—
504#440—474no—
505#440—474no—
506C4×Q16—474no—
507C4×SD16—474no—
508C4×SD16—474no—
509C4×D8—474no—
510#433—474no—
511#433—474no—
512#428—472no—
513#428—472no—
514#423—472no—
515#419—472no—
516#418—472no—
517#417—472no—
518#417—472no—
519#407—471no—
520#407—471no—
521C4×M16—472no—
522C47#6056711yescharacteristic, complemented, Sylow
523C2×#41—28no—
524C2×#41—21no—
525C2×#41—21no—
526C2×#41C22×D4712yes—
527C2×#41C22×D4712yes—
528C22×Q8—471no—
529C22×Q8—941no—
530C22×Q8C22×D4711yescharacteristic
531C22×D4—21no—
532C22×D4—471no—
533C22×D4—941no—
534C22×D4C22×D4711yescharacteristic
535C23×C4—21no—
536C23×C4—941no—
537C23×C4C22×D4711yescharacteristic
538#137—948no—
539AGL(1,ℤ/8)—948no—
540C2×Q16—474no—
541C2×SD16—474no—
542C2×SD16—474no—
543C2×D8—474no—
544C2×M16—472no—
545C2×M16—472no—
546C4⋊Q8—474no—
547C4⋊Q8—942no—
548#126—944no—
549#126—944no—
550#124—474no—
551#124—944no—
552#124—944no—
553#124—942no—
554#123—944no—
555#123—944no—
556C22⋊Q8—472no—
557C22⋊Q8—472no—
558C22⋊Q8—941no—
559C22⋊Q8—941no—
560C22⋊Q8—944no—
561C22⋊Q8—944no—
562#121—472no—
563#121—472no—
564#121—941no—
565#121—941no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—474no—
569C4×Q8—942no—
570C4×Q8C22×D4712yes—
571C4×Q8C22×D4712yes—
572C4×Q8C22×D4712yes—
573C4×Q8C22×D4712yes—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—474no—
585C4×D4—942no—
586C4×D4C22×D4712yes—
587C4×D4C22×D4712yes—
588C4×D4C22×D4712yes—
589C4×D4C22×D4712yes—
590#117—21no—
591#117—21no—
592#117—22no—
593#117—22no—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—22no—
598#117C22⋊D4712yes—
599#117C22⋊D4712yes—
600#117C22×D4712yes—
601#117C22×D4712yes—
602#117C22×D4712yes—
603#117C22×D4712yes—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—471no—
607C2×C4⋊C4—471no—
608C2×C4⋊C4—941no—
609C2×C4⋊C4—941no—
610C2×C4⋊C4—941no—
611C2×C4⋊C4C22⋊D4711yescharacteristic
612C2×C4⋊C4C22⋊D4711yescharacteristic
613C2×C4⋊C4C22×D4711yescharacteristic
614C2×C4⋊C4C22×D4711yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—941no—
619C2×C22⋊C4—941no—
620C2×C22⋊C4—941no—
621C2×C22⋊C4—941no—
622C2×C22⋊C4—941no—
623C2×C22⋊C4C22⋊D4711yescharacteristic
624C2×C22⋊C4C22⋊D4711yescharacteristic
625C2×C42—21no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—941no—
629C2×C42C22×D4711yescharacteristic
630C2×C42C22×D4711yescharacteristic
631#107—474no—
632#107—474no—
633#106—474no—
634#106—474no—
635C4⋊C8—474no—
636C4⋊C8—474no—
637#103—474no—
638#103—474no—
639#103—474no—
640#103—474no—
641#102—474no—
642#102—474no—
643#102—474no—
644#102—474no—
645C22⋊C8—472no—
646C22⋊C8—472no—
647C22⋊C8—472no—
648C22⋊C8—472no—
649#97—474no—
650C4×C8—474no—
651C24—21no—
652C24—941no—
653C24C2×C22⋊D4711yescharacteristic
654#41—28no—
655#41—28no—
656#41—24no—
657#41—24no—
658#41—24no—
659#41#1062535018yes—
660C2×Q8—24no—
661C2×Q8—21no—
662C2×Q8—472no—
663C2×Q8—944no—
664C2×Q8—941no—
665C2×Q8—944no—
666C2×Q8—3762no—
667C2×Q8C23×D4712yes—
668C2×D4—28no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—21no—
673C2×D4—472no—
674C2×D4—942no—
675C2×D4—942no—
676C2×D4—941no—
677C2×D4—944no—
678C2×D4—3762no—
679C2×D4C23×D4712yes—
680C22×C4—28no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—941no—
692C22×C4—941no—
693C22×C4—941no—
694C22×C4—944no—
695C22×C4—3762no—
696C22×C4C2×C22⋊D4711yescharacteristic
697C22×C4C2×C22⋊D4711yescharacteristic
698C22×C4C2×C22⋊D4711yescharacteristic
699C22×C4C2×C22⋊D4711yescharacteristic
700C22×C4C2×C22⋊D4711yescharacteristic
701C22×C4C2×C22⋊D4711yescharacteristic
702C22×C4C2×C22⋊D4711yescharacteristic
703C22×C4C23×D4711yescharacteristic
704C22×C4C23×D4711yescharacteristic
705C22×C4C23×D4711yescharacteristic
706Q16—948no—
707SD16—948no—
708SD16—948no—
709D8—948no—
710M16—944no—
711M16—944no—
712C2×C8—474no—
713C2×C8—474no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—472no—
721C4⋊C4—472no—
722C4⋊C4—944no—
723C4⋊C4—942no—
724C4⋊C4—942no—
725C4⋊C4—941no—
726C4⋊C4—941no—
727C4⋊C4—944no—
728C4⋊C4C2×C22⋊D4712yes—
729C4⋊C4C2×C22⋊D4712yes—
730C4⋊C4C2×C22⋊D4712yes—
731C4⋊C4C2×C22⋊D4712yes—
732C4⋊C4C23×D4712yes—
733C4⋊C4C23×D4712yes—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—942no—
741C22⋊C4—942no—
742C22⋊C4—944no—
743C22⋊C4—942no—
744C22⋊C4—942no—
745C22⋊C4—944no—
746C22⋊C4—944no—
747C22⋊C4C2×C22⋊D4712yes—
748C22⋊C4C2×C22⋊D4712yes—
749C22⋊C4C2×C22⋊D4712yes—
750C22⋊C4C2×C22⋊D4712yes—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—22no—
757C42—944no—
758C42C2×C22⋊D4712yes—
759C42C2×C22⋊D4712yes—
760C42C23×D4712yes—
761C42C23×D4712yes—
762C23—24no—
763C23—22no—
764C23—22no—
765C23—41no—
766C23—41no—
767C23—81no—
768C23—81no—
769C23—942no—
770C23—1882no—
771C23—1882no—
772C23—1882no—
773C23C22×C22⋊D4711yescharacteristic
774C23C22×C22⋊D4711yescharacteristic
775C23C22×C22⋊D4711yescharacteristic
776Q8—24no—
777Q8—22no—
778Q8—944no—
779Q8—3764no—
780Q8—1882no—
781Q8C2×#1062535014yes—
782D4—28no—
783D4—24no—
784D4—28no—
785D4—22no—
786D4—944no—
787D4—3762no—
788D4—3762no—
789D4—1882no—
790D4C2×#1062535014yes—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—942no—
813C2×C4—942no—
814C2×C4—942no—
815C2×C4—3764no—
816C2×C4—1882no—
817C2×C4—1882no—
818C2×C4—1882no—
819C2×C4C22×C22⋊D4711yescharacteristic
820C2×C4C22×C22⋊D4712yes—
821C2×C4C22×C22⋊D4712yes—
822C2×C4C22×C22⋊D4712yes—
823C2×C4C22×C22⋊D4712yes—
824C2×C4C22×C22⋊D4711yescharacteristic
825C2×C4C22×C22⋊D4711yescharacteristic
826C2×C4C2×#1062535014yes—
827C2×C4C24×D4711yescharacteristic
828C8—944no—
829C8—944no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—24no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—42no—
840C22—42no—
841C22—82no—
842C22—84no—
843C22—3764no—
844C22—1882no—
845C22—1882no—
846C22—1882no—
847C22#1568963412yes—
848C22C23×C22⋊D4711yescharacteristic
849C4—21no—
850C4—24no—
851C4—21no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—42no—
857C4—42no—
858C4—1882no—
859C4—1882no—
860C4—1882no—
861C4#1568963412yes—
862C4C22×#1062535012yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—44no—
867C2—3762no—
868C2C2×#1568963411yescharacteristic
869C2#2025816711yescharacteristic
870C2#2025817411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3428C2
socleC22×C47C23×D4
prime radical#20252640C2
hypercenter#3428D47
hypocenterC47#60567
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. C2×#15689744C2semidirect
2. #20253665C2semidirect
3. #20253650C2semidirect
4. #20253617C2semidirect
5. #20253572C2semidirect
6. #20253336C2semidirect
7. #20253328C2semidirect
8. #20253203C2semidirect
9. #20252882C2semidirect
10. #20252648C2semidirect
12. C4×#13094054C2semidirect
13. C4×#13094049C2semidirect
14. #20252026C2semidirect
15. C47×#3428C2semidirect
21. #15689744C22semidirect
22. C2×#13094024C22semidirect
24. C2×#13094012C22semidirect
30. C2×C4×Dic94C22semidirect
31. C2×C4×D188C22semidirect
32. #15689464C22semidirect
33. #15689458C22semidirect
34. #15689453C22semidirect
36. #15689441C22semidirect
37. #15689436C22semidirect
38. #15689418C22semidirect
39. #15689413C22semidirect
40. #15689408C22semidirect
41. #15689403C22semidirect
42. #15689345C22semidirect
43. #15689345C22semidirect
44. #15689338C22semidirect
45. #15689338C22semidirect
46. #15689285C22semidirect
47. #15689279C22semidirect
48. #15689274C22semidirect
52. #15689233C22semidirect
53. #15689228C22semidirect
54. #15689223C22semidirect
55. #15689221C22semidirect
56. C4×#10625337C22semidirect
57. C4×#10625336C22semidirect
58. C4×#10625335C22semidirect
59. C4×#10625334C22semidirect
60. #15689184C22semidirect
61. #15689184C22semidirect
62. #15689166C22semidirect
63. #15689166C22semidirect
64. #15689147C22semidirect
65. #15689131C22semidirect
66. #15689127C22semidirect
71. C4×#10625329C22semidirect
75. C47×#520C22semidirect
76. C47×#520C22semidirect
77. C47×#519C22semidirect
80. C47×#518C22semidirect
429. #3428D47semidirect
468. #520C2×D47semidirect
469. #520C2×D47semidirect
470. #519C2×D47semidirect
473. #518C2×D47semidirect
522. C47#60567semidirect

Maximal subgroups

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

subgroupindex
C2×#156897442
#202536652
#202536502
#202536172
#202535722
#202533362
#202533282
#202532032
#202528822
#202526482
#202526402
C4×#130940542
C4×#130940492
#202520262
C47×#34282
#6056747