Finite Group Databasebeta

← #25965106

Subgroups — #25965106

Order 11008.

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×#14583516C211yesmaximal, characteristic, complemented
2#19147796C211yesmaximal, characteristic, complemented
3#19144875C214yesmaximal, complemented
4#19144852C214yesmaximal, complemented
5#19144819C214yesmaximal, complemented
6#19144774C214yesmaximal, complemented
7#19144543C211yesmaximal, characteristic, complemented
8#19144408C212yesmaximal, complemented
9#19144088C212yesmaximal, complemented
10#19143857C211yesmaximal, characteristic, complemented
11#19143845C211yesmaximal, characteristic
12#19143413C212yesmaximal, complemented
13#19143399C212yesmaximal, complemented
14#19143230C211yesmaximal, characteristic, complemented
15C43×#3094C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063358C2212yes—
18C2×#13063351C2212yes—
19#14583516—22no—
20#14583516—22no—
21#14583516C2214yes—
22#14583516C2214yescomplemented
23C2×#13063324C2211yescharacteristic, complemented
24C2×#13063318—21no—
25C2×#13063312—21no—
26C2×#13063312C2211yescharacteristic, complemented
27C2×#13063306—21no—
28C2×#13063304C2211yescharacteristic
29C2×#13063302—21no—
30#14583380C2212yescomplemented
31#14583380C2212yescomplemented
32#14583379—21no—
33#14583379—21no—
34#14583376C2212yescomplemented
35#14583373C2212yescomplemented
36#14583372—21no—
37#14583372—21no—
38C4×#10621898—22no—
39#14583367C2212yes—
40#14583367C2212yes—
41C2×#13063290C2211yescharacteristic, complemented
42C2×D4×Dic43C2211yescharacteristic, complemented
43C2×#13063284C2211yescharacteristic
44#117×D43—22no—
45#14583240C2214yescomplemented
46#14583234C2212yescomplemented
47#14583229C2212yescomplemented
48#14583193C2214yescomplemented
49#14583188C2214yescomplemented
50#14583183C2214yescomplemented
51#14583178C2214yescomplemented
52#14583120C2214yescomplemented
53#14583120C2214yescomplemented
54#14583113C2214yescomplemented
55#14583113C2214yescomplemented
56#14583063C2214yescomplemented
57#14583057C2212yescomplemented
58#14583052C2212yescomplemented
59#14583042C2214yes—
60#14583037C2212yes—
61#14583032C2212yes—
62#14583008C2214yescomplemented
63#14583005C2214yescomplemented
64#14582998C2214yescomplemented
65#14582996C2214yescomplemented
66#14582993C2214yescomplemented
67#14582990C2214yescomplemented
68#14582986C2214yescomplemented
69#14582979C2214yescomplemented
70#14582957C2214yescomplemented
71#14582957C2214yescomplemented
72#14582942C2212yescomplemented
73#14582922C2212yescomplemented
74#14582907C2212yescomplemented
75#14582901C2212yes—
76#14582898C2212yes—
77#14582863C2211yescharacteristic
78M16×Dic43C2212yescomplemented
79C2×#121×C43C2211yescharacteristic
80C2×#117×C43C2211yescharacteristic
81C43×#482C2214yes—
82C43×#481C2212yescomplemented
83C43×#480C2212yescomplemented
84C43×#428C2212yescomplemented
85C43×#418C2212yescomplemented
86C43×#407C2211yescharacteristic
87C2×#10621898—21no—
88C2×#10621898—21no—
89C2×#10621898—28no—
90C2×#10621898C2312yes—
91C2×#10621898C2312yes—
92C22×Dic86—21no—
93C22×Dic86C2311yescharacteristic
94C22×Dic86C2311yescharacteristic
95C22×D172C2311yescharacteristic
96C22×C22⋊D43—21no—
97C23×Dic43—21no—
98C22×C4×D43—21no—
99#13063358—28no—
100#13063351—28no—
101C2×Dic172C2314yes—
102C2×#10621873C2314yes—
103C2×#10621883C2314yes—
104C2×#10621882C2314yes—
105C2×#10621877C2312yes—
106#13063324—22no—
107#13063324C2314yes—
108#13063318—24no—
109#13063318—24no—
110#13063312—24no—
111#13063312—24no—
112#13063312—22no—
113#13063312C2314yes—
114#13063306—24no—
115#13063306—24no—
116#13063304—21no—
117#13063304—21no—
118#13063304C2312yes—
119#13063304C2312yes—
120#13063302—24no—
121#13063302—24no—
122C4×Dic86—22no—
123C4×Dic86—22no—
124#13063290—22no—
125#13063290C2314yes—
126#13063290C2312yes—
127#13063290C2312yes—
128#13063290C2312yes—
129#13063290C2312yes—
130C4×D172—22no—
131C4×D172—22no—
132D4×Dic43—22no—
133D4×Dic43C2314yes—
134#13063287C2312yes—
135#13063287C2312yes—
136#13063287C2312yes—
137#13063287C2312yes—
138C4×C22⋊D43—22no—
139C4×C22⋊D43—22no—
140C4×C22⋊D43—22no—
141C4×C22⋊D43—22no—
142(C22⋊D43)⋊C4—22no—
143(C22⋊D43)⋊C4—22no—
144(C22⋊D43)⋊C4—22no—
145(C22⋊D43)⋊C4—22no—
146#13063284D412yes—
147#13063284D412yes—
148#13063284C2312yes—
149#13063284C2312yes—
150#13063283—22no—
151#13063283—22no—
152#13063282—22no—
153#13063282—22no—
154#13063281—22no—
155#13063281—22no—
156C2×C4⋊Dic43D411yescharacteristic
157C2×C4⋊Dic43D411yescharacteristic
158C2×C4⋊Dic43C2311yescharacteristic
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4—21no—
162C4⋊C4×D43—22no—
163C4⋊C4×D43—22no—
164C2×C22⋊Dic43—21no—
165C2×C22⋊Dic43—21no—
166C2×C22⋊Dic43—21no—
167C2×C22⋊Dic43—21no—
168C2×C22⋊Dic43D411yescharacteristic
169C2×C22⋊Dic43D411yescharacteristic
170C22⋊C4×D43—22no—
171C22⋊C4×D43—22no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43C2311yescharacteristic
174C2×C4×Dic43C2311yescharacteristic
175C42×D43—22no—
176C42×D43—22no—
177#13063258C2314yes—
178#13063256C2314yes—
179Dic43⋊C8C2314yes—
180Dic43⋊C8C2314yes—
181#13063250C2314yes—
182#13063248C2314yes—
183#13063248C2314yes—
184#13063248C2314yes—
185#13063247C2314yes—
186#13063245C2314yes—
187C22⋊(C43⋊C8)C2312yes—
188C22⋊(C43⋊C8)C2312yes—
189#13063235C2314yes—
190C8×Dic43C2314yes—
191C22×D4×C43—21no—
192C22×D4×C43C2311yescharacteristic
193C23×C4×C43C2311yescharacteristic
194C2×M16×C43C2312yes—
195#121×C43—21no—
196#121×C43—21no—
197#121×C43C2312yes—
198#121×C43C2312yes—
199#117×C43—21no—
200#117×C43—21no—
201#117×C43C2312yes—
202#117×C43C2312yes—
203C2×C4⋊C4×C43C2311yescharacteristic
204C2×C4⋊C4×C43C2311yescharacteristic
205C2×C4⋊C4×C43C2311yescharacteristic
206C2×C22⋊C4×C43—21no—
207C2×C22⋊C4×C43—21no—
208C2×C42×C43—21no—
209#107×C43C2314yes—
210#106×C43C2314yes—
211#102×C43C2314yes—
212#102×C43C2314yes—
213C22⋊C8×C43C2312yes—
214C22⋊C8×C43C2312yes—
215C24×C43—21no—
216C24×C43C2×D411yescharacteristic
217C23×D43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—22no—
220C2×D4×C43—22no—
221C2×D4×C43—24no—
222C2×D4×C43—82no—
223C2×D4×C43C2412yes—
224C22×C4×C43—24no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C2×C22⋊D43—28no—
235C2×C22⋊D43—22no—
236C2×C22⋊D43—22no—
237C22×Dic43—24no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—82no—
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244C22×Dic43C2×D411yescharacteristic
245C22×Dic43C2×D411yescharacteristic
246#10621898—28no—
247#10621898—28no—
248#10621898—24no—
249#10621898—24no—
250#10621898—24no—
251#10621898#4118yes—
252C2×D172—21no—
253C2×D172—24no—
254C2×D172C2412yes—
255C2×C4×D43—28no—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—22no—
259C2×C4×D43—22no—
260C2×C4×D43—22no—
261C2×C4×D43—22no—
262C2×Dic86—21no—
263C2×Dic86—24no—
264C2×Dic86—24no—
265C2×Dic86—21no—
266C2×Dic86—24no—
267C2×Dic86—82no—
268C2×Dic86C2412yes—
269C2×Dic86C2412yes—
270M16×C43—24no—
271C2×C8×C43C2414yes—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43C2412yes—
276C4⋊C4×C43C2412yes—
277C4⋊C4×C43C2412yes—
278C22⋊C4×C43—22no—
279C22⋊C4×C43—22no—
280C22⋊C4×C43—22no—
281C22⋊C4×C43—22no—
282C42×C43—22no—
283C42×C43—22no—
284C22⋊Dic43—24no—
285C22⋊Dic43—24no—
286C22⋊Dic43—24no—
287C22⋊Dic43—22no—
288C22⋊Dic43—22no—
289C22⋊Dic43C2×D412yes—
290C22⋊Dic43C2×D412yes—
291C22⋊Dic43C2×D412yes—
292C22⋊Dic43C2×D412yes—
293#10621883—28no—
294#10621882—28no—
295(C2×D43)⋊C4—22no—
296(C2×D43)⋊C4—22no—
297(C2×D43)⋊C4—22no—
298(C2×D43)⋊C4—22no—
299C4⋊Dic43—21no—
300C4⋊Dic43C2×D412yes—
301C4⋊Dic43C2×D412yes—
302C4⋊Dic43C2×D412yes—
303C4⋊Dic43C2×D412yes—
304C4⋊Dic43C2412yes—
305Dic43⋊C4—22no—
306Dic43⋊C4—22no—
307Dic43⋊C4—22no—
308Dic43⋊C4—22no—
309Dic43⋊C4—22no—
310Dic43⋊C4—22no—
311Dic43⋊C4—24no—
312Dic43⋊C4—24no—
313C4×Dic43—22no—
314C4×Dic43—22no—
315C4×Dic43—22no—
316C4×Dic43—22no—
317C4×Dic43—24no—
318C4×Dic43C2×D412yes—
319C4×Dic43C2×D412yes—
320C4×Dic43C2412yes—
321C4×Dic43C2412yes—
322#10621877—24no—
323C2×C43⋊C8C2414yes—
324Dic172—28no—
325#10621873—28no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—42no—
331C23×C43—42no—
332C23×C43—42no—
333C23×C43C22×D411yescharacteristic
334C23×C43C22×D411yescharacteristic
335C23×C43C22×D411yescharacteristic
336C22×D43—22no—
337C22×D43—24no—
338C22×D43—81no—
339C22×D43—81no—
340D4×C43—24no—
341D4×C43—42no—
342D4×C43—82no—
343D4×C43—82no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—42no—
353C2×C4×C43—81no—
354C2×C4×C43—81no—
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C2×#4114yes—
359C2×C4×C43C2511yescharacteristic
360C22⋊D43—28no—
361C22⋊D43—28no—
362C2×Dic43—24no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—42no—
371C2×Dic43—42no—
372C2×Dic43—84no—
373C2×Dic43C22×D412yes—
374C2×Dic43C22×D412yes—
375C2×Dic43C22×D412yes—
376C2×Dic43C22×D412yes—
377D172—24no—
378D172—22no—
379D172C2×#4114yes—
380C4×D43—28no—
381C4×D43—28no—
382C4×D43—82no—
383C4×D43—82no—
384C4×D43—82no—
385C4×D43—82no—
386Dic86—24no—
387Dic86—22no—
388Dic86—24no—
389Dic86—42no—
390Dic86—84no—
391Dic86C2×#4114yes—
392C8×C43—24no—
393C43⋊C8—24no—
394#60567—431nomaximal, Sylow
395C22×C43—21no—
396C22×C43—21no—
397C22×C43—21no—
398C22×C43—21no—
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—82no—
407C22×C43—84no—
408C22×C43#52512yes—
409C22×C43C23×D411yescharacteristic
410C2×D43—24no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—84no—
414C4×C43—21no—
415C4×C43—21no—
416C4×C43—42no—
417C4×C43—42no—
418C4×C43—42no—
419C4×C43#52512yes—
420C4×C43C22×#4112yes—
421Dic43—22no—
422Dic43—22no—
423Dic43—22no—
424Dic43—22no—
425Dic43—24no—
426Dic43—42no—
427Dic43—42no—
428C2×#542—431no—
429#3428—431no—
430#3125—434no—
431#3124—434no—
432#3121—434no—
433#3118—434no—
434#3095—431no—
435#3094D4311yescharacteristic, complemented
436#3079—432no—
437#3040—432no—
438#3007—431no—
439#3006—431no—
440C4×#137—432no—
441C4×AGL(1,ℤ/8)—432no—
442#2921—431no—
443C2×C43—22no—
444C2×C43—41no—
445C2×C43—41no—
446C2×C43—82no—
447C2×C43C2×#52511yescharacteristic
448C2×C43#358511yescharacteristic
449C2×C43#358611yescharacteristic
450D43—44no—
451C22×#41—431no—
452C2×#137—432no—
453C2×AGL(1,ℤ/8)—432no—
454#542—434no—
455#542—434no—
456#542—862no—
457#542—862no—
458C2×C4⋊Q8—431no—
459C2×#126—861no—
460C2×#124—431no—
461C2×#124—861no—
462C2×#123—861no—
463C2×C22⋊Q8—431no—
464C2×C22⋊Q8—861no—
465C2×#121C2×D4311yescharacteristic
466#520—432no—
467#520—432no—
468#520—861no—
469#520—861no—
470#519—432no—
471#518—432no—
472#518—861no—
473#518—861no—
474C4×#41—432no—
475C4×#41—432no—
476C4×#41—862no—
477C2×C4×Q8—431no—
478C2×C4×D4—431no—
479C2×#117—431no—
480C2×#117—862no—
481C2×#117C2×D4311yescharacteristic
482#485—434no—
483#484—432no—
484#483—432no—
485#482C2×D4314yes—
486#481C2×D4312yescomplemented
487#480C2×D4312yescomplemented
488#477—434no—
489#476—434no—
490#475—434no—
491#474—434no—
492#464—434no—
493#464—434no—
494#463—434no—
495#463—434no—
496#452—434no—
497#451—432no—
498#450—432no—
499#449—434no—
500#448—432no—
501#447—432no—
502#442—434no—
503#441—434no—
504#440—434no—
505#440—434no—
506C4×Q16—434no—
507C4×SD16—434no—
508C4×SD16—434no—
509C4×D8—434no—
510#433—434no—
511#433—434no—
512#428—432no—
513#428C2×D4312yescomplemented
514#423—432no—
515#419—432no—
516#418C2×D4312yescomplemented
517#417—432no—
518#417—432no—
519#407—431no—
520#407C2×D4311yescharacteristic
521C4×M16—432no—
522C43#6056711yescharacteristic, complemented, Sylow
523C2×#41—432no—
524C2×#41—432no—
525C2×#41—868no—
526C2×#41—861no—
527C2×#41—861no—
528C22×Q8—431no—
529C22×Q8—431no—
530C22×Q8—861no—
531C22×D4—21no—
532C22×D4—431no—
533C22×D4—861no—
534C22×D4C22×D4311yescharacteristic
535C23×C4—861no—
536C23×C4—861no—
537C23×C4C22×D4311yescharacteristic
538#137—868no—
539AGL(1,ℤ/8)—868no—
540C2×Q16—434no—
541C2×SD16—434no—
542C2×SD16—434no—
543C2×D8—434no—
544C2×M16—432no—
545C2×M16C22×D4312yes—
546C4⋊Q8—434no—
547C4⋊Q8—862no—
548#126—864no—
549#126—864no—
550#124—434no—
551#124—862no—
552#124—864no—
553#124—864no—
554#123—864no—
555#123—864no—
556C22⋊Q8—432no—
557C22⋊Q8—432no—
558C22⋊Q8—864no—
559C22⋊Q8—864no—
560C22⋊Q8—861no—
561C22⋊Q8—861no—
562#121—21no—
563#121—21no—
564#121C22×D4312yes—
565#121C22×D4312yes—
566C4×Q8—434no—
567C4×Q8—432no—
568C4×Q8—432no—
569C4×Q8—432no—
570C4×Q8—432no—
571C4×Q8—862no—
572C4×Q8—862no—
573C4×Q8—862no—
574C4×D4—434no—
575C4×D4—432no—
576C4×D4—432no—
577C4×D4—432no—
578C4×D4—432no—
579C4×D4—862no—
580C4×D4—862no—
581C4×D4—862no—
582C4×D4—862no—
583C4×D4—862no—
584C4×D4—862no—
585C4×D4—862no—
586C4×D4—862no—
587C4×D4—862no—
588C4×D4—862no—
589C4×D4—862no—
590#117—21no—
591#117—21no—
592#117—432no—
593#117—432no—
594#117—432no—
595#117—432no—
596#117—862no—
597#117—862no—
598#117—862no—
599#117—862no—
600#117—862no—
601#117—862no—
602#117C22×D4312yes—
603#117C22×D4312yes—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—431no—
606C2×C4⋊C4—431no—
607C2×C4⋊C4—862no—
608C2×C4⋊C4—862no—
609C2×C4⋊C4—861no—
610C2×C4⋊C4—861no—
611C2×C4⋊C4—861no—
612C2×C4⋊C4C22×D4311yescharacteristic
613C2×C4⋊C4C22×D4311yescharacteristic
614C2×C4⋊C4C22×D4311yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—431no—
618C2×C22⋊C4—431no—
619C2×C22⋊C4—862no—
620C2×C22⋊C4—862no—
621C2×C22⋊C4—861no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C42—21no—
626C2×C42—431no—
627C2×C42—431no—
628C2×C42—862no—
629C2×C42—862no—
630C2×C42—861no—
631#107—434no—
632#107C22×D4314yes—
633#106—434no—
634#106C22×D4314yes—
635C4⋊C8—434no—
636C4⋊C8—434no—
637#103—434no—
638#103—434no—
639#103—434no—
640#103—434no—
641#102—434no—
642#102—434no—
643#102C22×D4314yes—
644#102C22×D4314yes—
645C22⋊C8—432no—
646C22⋊C8—432no—
647C22⋊C8C22×D4312yes—
648C22⋊C8C22×D4312yes—
649#97—434no—
650C4×C8—434no—
651C24—21no—
652C24—861no—
653C24D4×D4311yescharacteristic
654#41—438no—
655#41—864no—
656#41—864no—
657#41—868no—
658#41—868no—
659#41—864no—
660C2×Q8—432no—
661C2×Q8—432no—
662C2×Q8—864no—
663C2×Q8—864no—
664C2×Q8—861no—
665C2×Q8—861no—
666C2×Q8—864no—
667C2×Q8—3442no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—24no—
672C2×D4—82no—
673C2×D4—432no—
674C2×D4—864no—
675C2×D4—868no—
676C2×D4—862no—
677C2×D4—862no—
678C2×D4—861no—
679C2×D4C23×D4312yes—
680C22×C4—24no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—431no—
685C22×C4—431no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—862no—
689C22×C4—862no—
690C22×C4—862no—
691C22×C4—862no—
692C22×C4—868no—
693C22×C4—864no—
694C22×C4—861no—
695C22×C4—862no—
696C22×C4—862no—
697C22×C4—861no—
698C22×C4—861no—
699C22×C4—3442no—
700C22×C4D4×D4311yescharacteristic
701C22×C4D4×D4311yescharacteristic
702C22×C4D4×D4311yescharacteristic
703C22×C4C23×D4311yescharacteristic
704C22×C4C23×D4311yescharacteristic
705C22×C4C23×D4311yescharacteristic
706Q16—868no—
707SD16—868no—
708SD16—868no—
709D8—868no—
710M16—24no—
711M16—864no—
712C2×C8—434no—
713C2×C8C23×D4314yes—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—432no—
718C4⋊C4—432no—
719C4⋊C4—432no—
720C4⋊C4—432no—
721C4⋊C4—432no—
722C4⋊C4—862no—
723C4⋊C4—862no—
724C4⋊C4—862no—
725C4⋊C4—862no—
726C4⋊C4—864no—
727C4⋊C4—864no—
728C4⋊C4—861no—
729C4⋊C4—862no—
730C4⋊C4—862no—
731C4⋊C4C23×D4312yes—
732C4⋊C4C23×D4312yes—
733C4⋊C4C23×D4312yes—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—432no—
739C22⋊C4—432no—
740C22⋊C4—432no—
741C22⋊C4—432no—
742C22⋊C4—862no—
743C22⋊C4—862no—
744C22⋊C4—862no—
745C22⋊C4—862no—
746C22⋊C4—864no—
747C22⋊C4—864no—
748C22⋊C4—864no—
749C22⋊C4—862no—
750C22⋊C4—862no—
751C42—22no—
752C42—22no—
753C42—432no—
754C42—432no—
755C42—432no—
756C42—432no—
757C42—862no—
758C42—862no—
759C42—862no—
760C42—862no—
761C42—864no—
762C23—22no—
763C23—22no—
764C23—41no—
765C23—41no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—864no—
770C23—862no—
771C23—3441no—
772C23—3441no—
773C23C2×D4×D4311yescharacteristic
774C23C2×D4×D4311yescharacteristic
775C23C2×D4×D4311yescharacteristic
776Q8—434no—
777Q8—864no—
778Q8—862no—
779Q8—864no—
780Q8—3444no—
781Q8—1722no—
782D4—24no—
783D4—42no—
784D4—82no—
785D4—82no—
786D4—434no—
787D4—864no—
788D4—868no—
789D4—868no—
790D4—862no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—42no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—432no—
803C2×C4—432no—
804C2×C4—432no—
805C2×C4—432no—
806C2×C4—868no—
807C2×C4—864no—
808C2×C4—862no—
809C2×C4—868no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—3442no—
813C2×C4—3442no—
814C2×C4—3442no—
815C2×C4—3442no—
816C2×C4—3444no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1722no—
822C2×C4—1722no—
823C2×C4C2×D4×D4311yescharacteristic
824C2×C4C2×D4×D4311yescharacteristic
825C2×C4C2×D4×D4311yescharacteristic
826C2×C4#41×D4314yes—
827C2×C4C24×D4311yescharacteristic
828C8—24no—
829C8—864no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—82no—
842C22—84no—
843C22—864no—
844C22—3444no—
845C22—1722no—
846C22—1722no—
847C22#1458340712yes—
848C22C22×D4×D4311yescharacteristic
849C4—21no—
850C4—21no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—864no—
855C4—862no—
856C4—862no—
857C4—862no—
858C4—862no—
859C4—1722no—
860C4—1722no—
861C4#1458340712yes—
862C4C2×#41×D4312yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—82no—
867C2—1724no—
868C2C2×#1458340711yescharacteristic
869C2#1914937111yescharacteristic
870C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3094C2
socleC22×C43C23×D4
prime radical#19143845C2
hypercenter#3094D43
hypocenterC43#60567
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. C2×#14583516C2semidirect
2. #19147796C2semidirect
3. #19144875C2semidirect
4. #19144852C2semidirect
5. #19144819C2semidirect
6. #19144774C2semidirect
7. #19144543C2semidirect
8. #19144408C2semidirect
9. #19144088C2semidirect
10. #19143857C2semidirect
12. #19143413C2semidirect
13. #19143399C2semidirect
14. #19143230C2semidirect
15. C43×#3094C2semidirect
22. #14583516C22semidirect
23. C2×#13063324C22semidirect
26. C2×#13063312C22semidirect
30. #14583380C22semidirect
31. #14583380C22semidirect
34. #14583376C22semidirect
35. #14583373C22semidirect
41. C2×#13063290C22semidirect
42. C2×D4×Dic43C22semidirect
45. #14583240C22semidirect
46. #14583234C22semidirect
47. #14583229C22semidirect
48. #14583193C22semidirect
49. #14583188C22semidirect
50. #14583183C22semidirect
51. #14583178C22semidirect
52. #14583120C22semidirect
53. #14583120C22semidirect
54. #14583113C22semidirect
55. #14583113C22semidirect
56. #14583063C22semidirect
57. #14583057C22semidirect
58. #14583052C22semidirect
62. #14583008C22semidirect
63. #14583005C22semidirect
64. #14582998C22semidirect
65. #14582996C22semidirect
66. #14582993C22semidirect
67. #14582990C22semidirect
68. #14582986C22semidirect
69. #14582979C22semidirect
70. #14582957C22semidirect
71. #14582957C22semidirect
72. #14582942C22semidirect
73. #14582922C22semidirect
74. #14582907C22semidirect
78. M16×Dic43C22semidirect
82. C43×#481C22semidirect
83. C43×#480C22semidirect
84. C43×#428C22semidirect
85. C43×#418C22semidirect
435. #3094D43semidirect
486. #481C2×D43semidirect
487. #480C2×D43semidirect
513. #428C2×D43semidirect
516. #418C2×D43semidirect
522. C43#60567semidirect

Maximal subgroups

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

subgroupindex
C2×#145835162
#191477962
#191448752
#191448522
#191448192
#191447742
#191445432
#191444082
#191440882
#191438572
#191438452
#191434132
#191433992
#191432302
C43×#30942
#6056743