Finite Group Databasebeta

← #27084794

Subgroups — #27084794

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#20256589C211yesmaximal, characteristic, complemented
3#20253667C214yesmaximal, complemented
4#20253652C214yesmaximal, complemented
5#20253619C214yesmaximal, complemented
6#20253574C214yesmaximal, complemented
7#20253337C211yesmaximal, characteristic, complemented
8#20253329C211yesmaximal, characteristic, complemented
9#20253204C212yesmaximal, complemented
10#20252883C212yesmaximal, complemented
11#20252650C211yesmaximal, characteristic, complemented
12#20252642C211yesmaximal, characteristic
13C4×#13094057C212yesmaximal, complemented
14C4×#13094052C212yesmaximal, complemented
15C47×#2921C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C2×#13094057C2212yes—
18C2×#13094052C2212yes—
19#15689744—22no—
20#15689744—22no—
21#15689744C2214yes—
22#15689744C2214yescomplemented
23C2×#13094024C2211yescharacteristic, complemented
24C2×#13094019—21no—
25C2×#13094012C2211yescharacteristic, complemented
26C2×#13094010—21no—
27C2×#13094006—21no—
28C2×#13094003C2211yescharacteristic
29C2×#13094002—21no—
30C2×#13093998C2211yescharacteristic
31#15689604—21no—
32#15689604—21no—
33#15689603C2212yescomplemented
34#15689603C2212yescomplemented
35#15689600C2212yescomplemented
36#15689597C2212yescomplemented
37#15689596—21no—
38#15689596—21no—
39C4×#10625350C2212yes—
40C4×#10625350C2212yes—
41#15689591—22no—
42C2×C4×Dic94C2211yescharacteristic, complemented
43C2×C4×D188C2211yescharacteristic, complemented
44C2×#13093983C2211yescharacteristic
45#117×D47—22no—
46#15689465C2214yescomplemented
47#15689459C2212yescomplemented
48#15689454C2212yescomplemented
49#15689448C2214yes—
50#15689442C2212yescomplemented
51#15689437C2212yescomplemented
52#15689419C2214yescomplemented
53#15689414C2214yescomplemented
54#15689409C2214yescomplemented
55#15689404C2214yescomplemented
56#15689346C2214yescomplemented
57#15689346C2214yescomplemented
58#15689339C2214yescomplemented
59#15689339C2214yescomplemented
60#15689287C2214yescomplemented
61#15689281C2212yescomplemented
62#15689276C2212yescomplemented
63#15689270C2214yes—
64#15689264C2212yes—
65#15689259C2212yes—
66#15689236C2214yescomplemented
67#15689231C2214yescomplemented
68#15689225C2214yescomplemented
69#15689225C2214yescomplemented
70C4×Dic188C2214yescomplemented
71C4×#10625325C2214yescomplemented
72C4×#10625325C2214yescomplemented
73C4×D376C2214yescomplemented
74#15689165C2212yescomplemented
75#15689165C2212yescomplemented
76#15689133C2212yescomplemented
77#15689129C2212yescomplemented
78#15689125C2212yes—
79#15689125C2212yes—
80C2×#117×C47C2211yescharacteristic
81C47×#433C2214yescomplemented
82C47×#433C2214yescomplemented
83C47×#423C2212yescomplemented
84C47×#407C2211yescharacteristic
85C47×#407C2211yescharacteristic
86C4×M16×C47C2212yescomplemented
87C2×#10625350—21no—
88C2×#10625350—21no—
89C2×#10625350—28no—
90C2×#10625350C2312yes—
91C2×#10625350C2312yes—
92C22×Dic94—21no—
93C22×Dic94C2311yescharacteristic
94C22×Dic94C2311yescharacteristic
95C22×D188C2311yescharacteristic
96C22×D188C2311yescharacteristic
97C22×C22⋊D47—21no—
98C22×C22⋊D47—21no—
99C22×C4×D47—21no—
100C22×C4×D47—21no—
101#13094057—28no—
102#13094052—28no—
103C2×Dic188C2314yes—
104C2×#10625325C2314yes—
105C2×#10625325C2314yes—
106C2×D376C2314yes—
107#13094024—22no—
108#13094024C2314yes—
109#13094019—24no—
110#13094019—24no—
111#13094012—22no—
112#13094012C2314yes—
113#13094010—24no—
114#13094010—24no—
115#13094006—24no—
116#13094006—24no—
117#13094003—21no—
118#13094003—21no—
119#13094003C2312yes—
120#13094003C2312yes—
121#13094002—24no—
122#13094002—24no—
123#13093998—21no—
124#13093998—21no—
125#13093998C2312yes—
126#13093998C2312yes—
127C4×Dic94—22no—
128C4×Dic94C2312yes—
129C4×Dic94C2314yes—
130C4×Dic94C2312yes—
131C4×Dic94C2312yes—
132C4×Dic94C2312yes—
133#13093989—22no—
134#13093989—22no—
135C4×D188—22no—
136C4×D188C2312yes—
137C4×D188C2314yes—
138C4×D188C2312yes—
139C4×D188C2312yes—
140C4×D188C2312yes—
141#13093986—22no—
142#13093986—22no—
143C4×C22⋊D47—22no—
144C4×C22⋊D47—22no—
145C4×C22⋊D47—22no—
146C4×C22⋊D47—22no—
147(C22⋊D47)⋊C4—22no—
148(C22⋊D47)⋊C4—22no—
149(C22⋊D47)⋊C4—22no—
150(C22⋊D47)⋊C4—22no—
151#13093983—21no—
152#13093983—21no—
153#13093983C2312yes—
154#13093983C2312yes—
155#13093982—22no—
156#13093982—22no—
157#13093981—22no—
158#13093981—22no—
159#13093980—22no—
160#13093980—22no—
161C2×C4⋊Dic47—21no—
162C2×C4⋊Dic47C2311yescharacteristic
163C2×C4⋊Dic47C2311yescharacteristic
164C2×C4⋊Dic47C2311yescharacteristic
165C2×C4⋊Dic47C2311yescharacteristic
166C2×Dic47⋊C4—21no—
167C2×Dic47⋊C4—21no—
168C4⋊C4×D47—22no—
169C4⋊C4×D47—22no—
170C2×C22⋊Dic47—21no—
171C2×C22⋊Dic47—21no—
172C2×(C2×D47)⋊C4—21no—
173C2×(C2×D47)⋊C4—21no—
174C2×(C2×D47)⋊C4—21no—
175C2×(C2×D47)⋊C4—21no—
176C22⋊C4×D47—22no—
177C22⋊C4×D47—22no—
178C2×C4×Dic47—21no—
179C2×C4×Dic47—21no—
180C42×D47—22no—
181C42×D47—22no—
182#13093958C2314yes—
183#13093958C2314yes—
184#13093956C2314yes—
185#13093956C2314yes—
186#13093949C2314yes—
187#13093949C2314yes—
188#13093949C2314yes—
189#13093949C2314yes—
190#13093946C2314yes—
191#13093946C2314yes—
192#13093946C2314yes—
193#13093946C2314yes—
194C23×C4×C47C2311yescharacteristic
195C2×M16×C47C2312yes—
196C2×M16×C47C2312yes—
197#117×C47D412yes—
198#117×C47D412yes—
199#117×C47C2312yes—
200#117×C47C2312yes—
201C2×C4⋊C4×C47D411yescharacteristic
202C2×C4⋊C4×C47D411yescharacteristic
203C2×C22⋊C4×C47D411yescharacteristic
204C2×C22⋊C4×C47D411yescharacteristic
205C2×C42×C47C2311yescharacteristic
206C2×C42×C47C2311yescharacteristic
207C4⋊C8×C47C2314yes—
208C4⋊C8×C47C2314yes—
209C22⋊C8×C47C2312yes—
210C22⋊C8×C47C2312yes—
211C22⋊C8×C47C2312yes—
212C22⋊C8×C47C2312yes—
213#97×C47C2314yes—
214C4×C8×C47C2314yes—
215C24×C47C2×D411yescharacteristic
216C23×D47—21no—
217C23×D47—21no—
218C22×C4×C47—24no—
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2411yescharacteristic
227C22×C4×C47C2411yescharacteristic
228C22×C4×C47C2411yescharacteristic
229C2×C22⋊D47—28no—
230C2×C22⋊D47—22no—
231C2×C22⋊D47—22no—
232C2×C22⋊D47—22no—
233C2×C22⋊D47—22no—
234C2×C22⋊D47—82no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241#10625350—28no—
242#10625350—28no—
243#10625350—24no—
244#10625350—24no—
245#10625350—24no—
246#10625350#4118yes—
247C2×D188—21no—
248C2×D188—24no—
249C2×D188—24no—
250C2×D188—21no—
251C2×D188C2412yes—
252C2×D188C2412yes—
253C2×C4×D47—28no—
254C2×C4×D47—22no—
255C2×C4×D47—22no—
256C2×C4×D47—22no—
257C2×C4×D47—22no—
258C2×C4×D47—22no—
259C2×C4×D47—22no—
260C2×C4×D47—24no—
261C2×C4×D47—82no—
262C2×Dic94—21no—
263C2×Dic94—24no—
264C2×Dic94—24no—
265C2×Dic94—21no—
266C2×Dic94—24no—
267C2×Dic94—82no—
268C2×Dic94C2412yes—
269C2×Dic94C2412yes—
270M16×C47—24no—
271M16×C47—24no—
272C2×C8×C47C2414yes—
273C2×C8×C47C2414yes—
274C4⋊C4×C47C2×D412yes—
275C4⋊C4×C47C2×D412yes—
276C4⋊C4×C47C2×D412yes—
277C4⋊C4×C47C2×D412yes—
278C22⋊C4×C47C2×D412yes—
279C22⋊C4×C47C2×D412yes—
280C22⋊C4×C47C2×D412yes—
281C22⋊C4×C47C2×D412yes—
282C42×C47C2×D412yes—
283C42×C47C2×D412yes—
284C42×C47C2412yes—
285C42×C47C2412yes—
286C22⋊Dic47—22no—
287C22⋊Dic47—22no—
288C22⋊Dic47—22no—
289C22⋊Dic47—22no—
290(C2×D47)⋊C4—22no—
291(C2×D47)⋊C4—22no—
292(C2×D47)⋊C4—22no—
293(C2×D47)⋊C4—22no—
294(C2×D47)⋊C4—24no—
295(C2×D47)⋊C4—22no—
296(C2×D47)⋊C4—22no—
297(C2×D47)⋊C4—24no—
298(C2×D47)⋊C4—24no—
299C4⋊Dic47—21no—
300C4⋊Dic47—21no—
301C4⋊Dic47—24no—
302C4⋊Dic47—21no—
303C4⋊Dic47—21no—
304C4⋊Dic47C2412yes—
305C4⋊Dic47C2412yes—
306C4⋊Dic47C2412yes—
307C4⋊Dic47C2412yes—
308Dic47⋊C4—22no—
309Dic47⋊C4—22no—
310Dic47⋊C4—22no—
311Dic47⋊C4—22no—
312Dic47⋊C4—24no—
313Dic47⋊C4—22no—
314Dic47⋊C4—22no—
315C4×Dic47—22no—
316C4×Dic47—22no—
317C4×Dic47—22no—
318C4×Dic47—22no—
319C4×Dic47—22no—
320C4×Dic47—22no—
321C4×Dic47—24no—
322Dic188—28no—
323D376—28no—
324#10625325—28no—
325#10625325—28no—
326C23×C47—22no—
327C23×C47—41no—
328C23×C47—41no—
329C23×C47C22×D411yescharacteristic
330C23×C47C22×D411yescharacteristic
331C23×C47C22×D411yescharacteristic
332C22×D47—22no—
333C22×D47—24no—
334C22×D47—22no—
335C22×D47—42no—
336C22×D47—42no—
337C22×D47—42no—
338C22×D47—81no—
339C22×D47—81no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47C22×D412yes—
350C2×C4×C47C22×D411yescharacteristic
351C2×C4×C47C22×D412yes—
352C2×C4×C47C22×D412yes—
353C2×C4×C47C22×D412yes—
354C2×C4×C47C22×D411yescharacteristic
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C2×#4114yes—
357C2×C4×C47C2511yescharacteristic
358C22⋊D47—28no—
359C22⋊D47—28no—
360C22⋊D47—82no—
361C22⋊D47—82no—
362C2×Dic47—24no—
363C2×Dic47—22no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—42no—
370C2×Dic47—42no—
371C2×Dic47—42no—
372C2×Dic47—81no—
373C2×Dic47—81no—
374D188—24no—
375D188—22no—
376D188—24no—
377D188—42no—
378D188C2×#4114yes—
379C4×D47—28no—
380C4×D47—28no—
381C4×D47—82no—
382C4×D47—82no—
383C4×D47—82no—
384C4×D47—82no—
385C4×D47—84no—
386Dic94—24no—
387Dic94—22no—
388Dic94—24no—
389Dic94—42no—
390Dic94—84no—
391Dic94C2×#4114yes—
392C8×C47—24no—
393C8×C47—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—82no—
404C22×C47#52512yes—
405C22×C47C23×D411yescharacteristic
406C2×D47—24no—
407C2×D47—42no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—42no—
412C2×D47—84no—
413C2×D47—84no—
414C4×C47—22no—
415C4×C47—22no—
416C4×C47—22no—
417C4×C47—22no—
418C4×C47—21no—
419C4×C47—21no—
420C4×C47#52512yes—
421C4×C47C22×#4112yes—
422Dic47—24no—
423Dic47—42no—
424Dic47—42no—
425Dic47—42no—
426Dic47—42no—
427Dic47—42no—
428C2×#542—471no—
429#3428—471no—
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#2921D4711yescharacteristic, complemented
443C2×C47—22no—
444C2×C47—41no—
445C2×C47—41no—
446C2×C47C2×#52511yescharacteristic
447C2×C47#358511yescharacteristic
448C2×C47#358611yescharacteristic
449D47—44no—
450D47—82no—
451C22×#41—471no—
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—472no—
467#520—472no—
468#520—941no—
469#520—941no—
470#519—472no—
471#518—472no—
472#518—941no—
473#518—941no—
474C4×#41—472no—
475C4×#41—472no—
476C4×#41—942no—
477C2×C4×Q8—471no—
478C2×C4×D4—471no—
479C2×#117—471no—
480C2×#117—942no—
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#433C2×D4714yescomplemented
511#433C2×D4714yescomplemented
512#428—472no—
513#428—472no—
514#423C2×D4712yescomplemented
515#419—472no—
516#418—472no—
517#417—472no—
518#417—472no—
519#407C2×D4711yescharacteristic
520#407C2×D4711yescharacteristic
521C4×M16C2×D4712yescomplemented
522C47#6056711yescharacteristic, complemented, Sylow
523C2×#41—472no—
524C2×#41—472no—
525C2×#41—948no—
526C2×#41—941no—
527C2×#41—941no—
528C22×Q8—471no—
529C22×Q8—471no—
530C22×Q8—941no—
531C22×D4—471no—
532C22×D4—471no—
533C22×D4—941no—
534C22×D4—941no—
535C23×C4—941no—
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×M16C22×D4712yes—
545C2×M16C22×D4712yes—
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—474no—
567C4×Q8—472no—
568C4×Q8—472no—
569C4×Q8—472no—
570C4×Q8—472no—
571C4×Q8—942no—
572C4×Q8—942no—
573C4×Q8—942no—
574C4×D4—474no—
575C4×D4—472no—
576C4×D4—472no—
577C4×D4—472no—
578C4×D4—472no—
579C4×D4—942no—
580C4×D4—942no—
581C4×D4—942no—
582C4×D4—942no—
583C4×D4—942no—
584C4×D4—942no—
585C4×D4—942no—
586C4×D4—942no—
587C4×D4—942no—
588C4×D4—942no—
589C4×D4—942no—
590#117—472no—
591#117—472no—
592#117—941no—
593#117—941no—
594#117—942no—
595#117—942no—
596#117—942no—
597#117—942no—
598#117—942no—
599#117—942no—
600#117D18812yes—
601#117D18812yes—
602#117C22×D4712yes—
603#117C22×D4712yes—
604C2×C4⋊C4—471no—
605C2×C4⋊C4—471no—
606C2×C4⋊C4—471no—
607C2×C4⋊C4—471no—
608C2×C4⋊C4—941no—
609C2×C4⋊C4—941no—
610C2×C4⋊C4—941no—
611C2×C4⋊C4—942no—
612C2×C4⋊C4—942no—
613C2×C4⋊C4D18811yescharacteristic
614C2×C4⋊C4D18811yescharacteristic
615C2×C22⋊C4—941no—
616C2×C22⋊C4—941no—
617C2×C22⋊C4—941no—
618C2×C22⋊C4—941no—
619C2×C22⋊C4—941no—
620C2×C22⋊C4—941no—
621C2×C22⋊C4—942no—
622C2×C22⋊C4—942no—
623C2×C22⋊C4D18811yescharacteristic
624C2×C22⋊C4D18811yescharacteristic
625C2×C42—941no—
626C2×C42—941no—
627C2×C42—942no—
628C2×C42—942no—
629C2×C42C22×D4711yescharacteristic
630C2×C42C22×D4711yescharacteristic
631#107—474no—
632#107—474no—
633#106—474no—
634#106—474no—
635C4⋊C8C22×D4714yes—
636C4⋊C8C22×D4714yes—
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⋊C8C22×D4712yes—
646C22⋊C8C22×D4712yes—
647C22⋊C8C22×D4712yes—
648C22⋊C8C22×D4712yes—
649#97C22×D4714yes—
650C4×C8C22×D4714yes—
651C24—941no—
652C24—941no—
653C24C2×D18811yescharacteristic
654#41—478no—
655#41—944no—
656#41—944no—
657#41—948no—
658#41—948no—
659#41—944no—
660C2×Q8—472no—
661C2×Q8—472no—
662C2×Q8—944no—
663C2×Q8—941no—
664C2×Q8—944no—
665C2×Q8—941no—
666C2×Q8—944no—
667C2×Q8—3762no—
668C2×D4—472no—
669C2×D4—472no—
670C2×D4—944no—
671C2×D4—948no—
672C2×D4—942no—
673C2×D4—942no—
674C2×D4—942no—
675C2×D4—942no—
676C2×D4—941no—
677C2×D4—941no—
678C2×D4—944no—
679C2×D4—3762no—
680C22×C4—24no—
681C22×C4—948no—
682C22×C4—941no—
683C22×C4—942no—
684C22×C4—942no—
685C22×C4—941no—
686C22×C4—941no—
687C22×C4—941no—
688C22×C4—941no—
689C22×C4—941no—
690C22×C4—942no—
691C22×C4—942no—
692C22×C4—942no—
693C22×C4—942no—
694C22×C4—944no—
695C22×C4—3762no—
696C22×C4C2×D18811yescharacteristic
697C22×C4C2×D18811yescharacteristic
698C22×C4C2×D18811yescharacteristic
699C22×C4C2×D18811yescharacteristic
700C22×C4C2×D18811yescharacteristic
701C22×C4C2×D18811yescharacteristic
702C22×C4C2×D18811yescharacteristic
703C22×C4C23×D4711yescharacteristic
704C22×C4C23×D4711yescharacteristic
705C22×C4C23×D4711yescharacteristic
706Q16—948no—
707SD16—948no—
708SD16—948no—
709D8—948no—
710M16—24no—
711M16—24no—
712C2×C8C23×D4714yes—
713C2×C8C23×D4714yes—
714C4⋊C4—472no—
715C4⋊C4—472no—
716C4⋊C4—472no—
717C4⋊C4—472no—
718C4⋊C4—942no—
719C4⋊C4—942no—
720C4⋊C4—942no—
721C4⋊C4—942no—
722C4⋊C4—944no—
723C4⋊C4—942no—
724C4⋊C4—942no—
725C4⋊C4—941no—
726C4⋊C4—941no—
727C4⋊C4—941no—
728C4⋊C4—941no—
729C4⋊C4—944no—
730C4⋊C4C2×D18812yes—
731C4⋊C4C2×D18812yes—
732C4⋊C4C2×D18812yes—
733C4⋊C4C2×D18812yes—
734C22⋊C4—942no—
735C22⋊C4—942no—
736C22⋊C4—942no—
737C22⋊C4—942no—
738C22⋊C4—942no—
739C22⋊C4—942no—
740C22⋊C4—942no—
741C22⋊C4—942no—
742C22⋊C4—944no—
743C22⋊C4—942no—
744C22⋊C4—942no—
745C22⋊C4—944no—
746C22⋊C4—944no—
747C22⋊C4C2×D18812yes—
748C22⋊C4C2×D18812yes—
749C22⋊C4C2×D18812yes—
750C22⋊C4C2×D18812yes—
751C42—942no—
752C42—942no—
753C42—942no—
754C42—942no—
755C42—942no—
756C42—942no—
757C42—944no—
758C42C2×D18812yes—
759C42C2×D18812yes—
760C42C23×D4712yes—
761C42C23×D4712yes—
762C23—22no—
763C23—41no—
764C23—41no—
765C23—944no—
766C23—942no—
767C23—942no—
768C23—3761no—
769C23—3761no—
770C23—1882no—
771C23—1882no—
772C23—1882no—
773C23C22×D18811yescharacteristic
774C23C22×D18811yescharacteristic
775C23C22×D18811yescharacteristic
776Q8—474no—
777Q8—944no—
778Q8—942no—
779Q8—944no—
780Q8—3764no—
781Q8—1882no—
782D4—474no—
783D4—944no—
784D4—948no—
785D4—948no—
786D4—942no—
787D4—944no—
788D4—3762no—
789D4—3762no—
790D4—1882no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—948no—
801C2×C4—944no—
802C2×C4—942no—
803C2×C4—948no—
804C2×C4—942no—
805C2×C4—942no—
806C2×C4—942no—
807C2×C4—942no—
808C2×C4—942no—
809C2×C4—3762no—
810C2×C4—3762no—
811C2×C4—3762no—
812C2×C4—3762no—
813C2×C4—3764no—
814C2×C4—3761no—
815C2×C4—3761no—
816C2×C4—1882no—
817C2×C4—1882no—
818C2×C4—1882no—
819C2×C4C22×D18812yes—
820C2×C4C22×D18811yescharacteristic
821C2×C4C22×D18812yes—
822C2×C4C22×D18812yes—
823C2×C4C22×D18812yes—
824C2×C4C22×D18811yescharacteristic
825C2×C4C22×D18811yescharacteristic
826C2×C4#41×D4714yes—
827C2×C4C24×D4711yescharacteristic
828C8—24no—
829C8—24no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—82no—
839C22—944no—
840C22—3764no—
841C22—3764no—
842C22—1882no—
843C22—1882no—
844C22—1882no—
845C22—1882no—
846C22—1882no—
847C22#1568963512yes—
848C22C23×D18811yescharacteristic
849C4—21no—
850C4—21no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—944no—
856C4—1882no—
857C4—1882no—
858C4—1882no—
859C4—1882no—
860C4—1882no—
861C4#1568963512yes—
862C4C2×#41×D4712yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—3762no—
867C2—1884no—
868C2C2×#1568963511yescharacteristic
869C2#2025816911yescharacteristic
870C2#2025817611yescharacteristic
subgroupG/H
centerC22C23×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#2921C2
socleC22×C47C23×D4
prime radical#20252642C2
hypercenter#2921D47
hypocenterC47#60567
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. C2×#15689744C2semidirect
2. #20256589C2semidirect
3. #20253667C2semidirect
4. #20253652C2semidirect
5. #20253619C2semidirect
6. #20253574C2semidirect
7. #20253337C2semidirect
8. #20253329C2semidirect
9. #20253204C2semidirect
10. #20252883C2semidirect
11. #20252650C2semidirect
13. C4×#13094057C2semidirect
14. C4×#13094052C2semidirect
15. C47×#2921C2semidirect
22. #15689744C22semidirect
23. C2×#13094024C22semidirect
25. C2×#13094012C22semidirect
33. #15689603C22semidirect
34. #15689603C22semidirect
35. #15689600C22semidirect
36. #15689597C22semidirect
42. C2×C4×Dic94C22semidirect
43. C2×C4×D188C22semidirect
46. #15689465C22semidirect
47. #15689459C22semidirect
48. #15689454C22semidirect
50. #15689442C22semidirect
51. #15689437C22semidirect
52. #15689419C22semidirect
53. #15689414C22semidirect
54. #15689409C22semidirect
55. #15689404C22semidirect
56. #15689346C22semidirect
57. #15689346C22semidirect
58. #15689339C22semidirect
59. #15689339C22semidirect
60. #15689287C22semidirect
61. #15689281C22semidirect
62. #15689276C22semidirect
66. #15689236C22semidirect
67. #15689231C22semidirect
68. #15689225C22semidirect
69. #15689225C22semidirect
70. C4×Dic188C22semidirect
71. C4×#10625325C22semidirect
72. C4×#10625325C22semidirect
73. C4×D376C22semidirect
74. #15689165C22semidirect
75. #15689165C22semidirect
76. #15689133C22semidirect
77. #15689129C22semidirect
81. C47×#433C22semidirect
82. C47×#433C22semidirect
83. C47×#423C22semidirect
86. C4×M16×C47C22semidirect
442. #2921D47semidirect
510. #433C2×D47semidirect
511. #433C2×D47semidirect
514. #423C2×D47semidirect
521. C4×M16C2×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
#202565892
#202536672
#202536522
#202536192
#202535742
#202533372
#202533292
#202532042
#202528832
#202526502
#202526422
C4×#130940572
C4×#130940522
C47×#29212
#6056747