Finite Group Databasebeta

← #25965113

Subgroups — #25965113

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×#14583520C211yesmaximal, characteristic, complemented
2#19147796C211yesmaximal, characteristic, complemented
3#19144874C214yesmaximal, complemented
4#19144859C214yesmaximal, complemented
5#19144826C214yesmaximal, complemented
6#19144781C214yesmaximal, complemented
7#19144544C211yesmaximal, characteristic, complemented
8#19144536C211yesmaximal, characteristic, complemented
9#19144411C212yesmaximal, complemented
10#19144090C212yesmaximal, complemented
11#19143857C211yesmaximal, characteristic, complemented
12#19143849C211yesmaximal, characteristic
13C4×#13063358C212yesmaximal, complemented
14C4×#13063353C212yesmaximal, complemented
15C43×#2921C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063358C2212yes—
18C2×#13063353C2212yes—
19#14583520—22no—
20#14583520—22no—
21#14583520C2214yes—
22#14583520C2214yescomplemented
23C2×#13063325C2211yescharacteristic, complemented
24C2×#13063320—21no—
25C2×#13063313C2211yescharacteristic, complemented
26C2×#13063311—21no—
27C2×#13063307—21no—
28C2×#13063304C2211yescharacteristic
29C2×#13063303—21no—
30C2×#13063299C2211yescharacteristic
31#14583380—21no—
32#14583380—21no—
33#14583379C2212yescomplemented
34#14583379C2212yescomplemented
35#14583376C2212yescomplemented
36#14583373C2212yescomplemented
37#14583372—21no—
38#14583372—21no—
39C4×#10621898C2212yes—
40C4×#10621898C2212yes—
41#14583367—22no—
42C2×C4×Dic86C2211yescharacteristic, complemented
43C2×C4×D172C2211yescharacteristic, complemented
44C2×#13063284C2211yescharacteristic
45#117×D43—22no—
46#14583241C2214yescomplemented
47#14583235C2212yescomplemented
48#14583230C2212yescomplemented
49#14583224C2214yes—
50#14583218C2212yescomplemented
51#14583213C2212yescomplemented
52#14583195C2214yescomplemented
53#14583190C2214yescomplemented
54#14583185C2214yescomplemented
55#14583180C2214yescomplemented
56#14583122C2214yescomplemented
57#14583122C2214yescomplemented
58#14583115C2214yescomplemented
59#14583115C2214yescomplemented
60#14583063C2214yescomplemented
61#14583057C2212yescomplemented
62#14583052C2212yescomplemented
63#14583046C2214yes—
64#14583040C2212yes—
65#14583035C2212yes—
66#14583012C2214yescomplemented
67#14583007C2214yescomplemented
68#14583001C2214yescomplemented
69#14583001C2214yescomplemented
70C4×Dic172C2214yescomplemented
71C4×#10621873C2214yescomplemented
72C4×#10621873C2214yescomplemented
73C4×D344C2214yescomplemented
74#14582941C2212yescomplemented
75#14582941C2212yescomplemented
76#14582909C2212yescomplemented
77#14582905C2212yescomplemented
78#14582901C2212yes—
79#14582901C2212yes—
80C2×#117×C43C2211yescharacteristic
81C43×#433C2214yescomplemented
82C43×#433C2214yescomplemented
83C43×#423C2212yescomplemented
84C43×#407C2211yescharacteristic
85C43×#407C2211yescharacteristic
86C4×M16×C43C2212yescomplemented
87C2×#10621898—21no—
88C2×#10621898—21no—
89C2×#10621898—28no—
90C2×#10621898C2312yes—
91C2×#10621898C2312yes—
92C22×Dic86—21no—
93C22×Dic86C2311yescharacteristic
94C22×Dic86C2311yescharacteristic
95C22×D172C2311yescharacteristic
96C22×D172C2311yescharacteristic
97C22×C22⋊D43—21no—
98C22×C22⋊D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43—21no—
101#13063358—28no—
102#13063353—28no—
103C2×Dic172C2314yes—
104C2×#10621873C2314yes—
105C2×#10621873C2314yes—
106C2×D344C2314yes—
107#13063325—22no—
108#13063325C2314yes—
109#13063320—24no—
110#13063320—24no—
111#13063313—22no—
112#13063313C2314yes—
113#13063311—24no—
114#13063311—24no—
115#13063307—24no—
116#13063307—24no—
117#13063304—21no—
118#13063304—21no—
119#13063304C2312yes—
120#13063304C2312yes—
121#13063303—24no—
122#13063303—24no—
123#13063299—21no—
124#13063299—21no—
125#13063299C2312yes—
126#13063299C2312yes—
127C4×Dic86—22no—
128C4×Dic86C2314yes—
129C4×Dic86C2312yes—
130C4×Dic86C2312yes—
131C4×Dic86C2312yes—
132C4×Dic86C2312yes—
133#13063290—22no—
134#13063290—22no—
135C4×D172—22no—
136C4×D172C2314yes—
137C4×D172C2312yes—
138C4×D172C2312yes—
139C4×D172C2312yes—
140C4×D172C2312yes—
141#13063287—22no—
142#13063287—22no—
143C4×C22⋊D43—22no—
144C4×C22⋊D43—22no—
145C4×C22⋊D43—22no—
146C4×C22⋊D43—22no—
147(C22⋊D43)⋊C4—22no—
148(C22⋊D43)⋊C4—22no—
149(C22⋊D43)⋊C4—22no—
150(C22⋊D43)⋊C4—22no—
151#13063284—21no—
152#13063284—21no—
153#13063284C2312yes—
154#13063284C2312yes—
155#13063283—22no—
156#13063283—22no—
157#13063282—22no—
158#13063282—22no—
159#13063281—22no—
160#13063281—22no—
161C2×C4⋊Dic43—21no—
162C2×C4⋊Dic43C2311yescharacteristic
163C2×C4⋊Dic43C2311yescharacteristic
164C2×C4⋊Dic43C2311yescharacteristic
165C2×C4⋊Dic43C2311yescharacteristic
166C2×Dic43⋊C4—21no—
167C2×Dic43⋊C4—21no—
168C4⋊C4×D43—22no—
169C4⋊C4×D43—22no—
170C2×C22⋊Dic43—21no—
171C2×C22⋊Dic43—21no—
172C2×(C2×D43)⋊C4—21no—
173C2×(C2×D43)⋊C4—21no—
174C2×(C2×D43)⋊C4—21no—
175C2×(C2×D43)⋊C4—21no—
176C22⋊C4×D43—22no—
177C22⋊C4×D43—22no—
178C2×C4×Dic43—21no—
179C2×C4×Dic43—21no—
180C42×D43—22no—
181C42×D43—22no—
182#13063259C2314yes—
183#13063259C2314yes—
184#13063257C2314yes—
185#13063257C2314yes—
186#13063250C2314yes—
187#13063250C2314yes—
188#13063250C2314yes—
189#13063250C2314yes—
190#13063247C2314yes—
191#13063247C2314yes—
192#13063247C2314yes—
193#13063247C2314yes—
194C23×C4×C43C2311yescharacteristic
195C2×M16×C43C2312yes—
196C2×M16×C43C2312yes—
197#117×C43D412yes—
198#117×C43D412yes—
199#117×C43C2312yes—
200#117×C43C2312yes—
201C2×C4⋊C4×C43D411yescharacteristic
202C2×C4⋊C4×C43D411yescharacteristic
203C2×C22⋊C4×C43D411yescharacteristic
204C2×C22⋊C4×C43D411yescharacteristic
205C2×C42×C43C2311yescharacteristic
206C2×C42×C43C2311yescharacteristic
207C4⋊C8×C43C2314yes—
208C4⋊C8×C43C2314yes—
209C22⋊C8×C43C2312yes—
210C22⋊C8×C43C2312yes—
211C22⋊C8×C43C2312yes—
212C22⋊C8×C43C2312yes—
213#97×C43C2314yes—
214C4×C8×C43C2314yes—
215C24×C43C2×D411yescharacteristic
216C23×D43—21no—
217C23×D43—21no—
218C22×C4×C43—24no—
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2411yescharacteristic
227C22×C4×C43C2411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C2×C22⋊D43—28no—
230C2×C22⋊D43—22no—
231C2×C22⋊D43—22no—
232C2×C22⋊D43—22no—
233C2×C22⋊D43—22no—
234C2×C22⋊D43—82no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241#10621898—28no—
242#10621898—28no—
243#10621898—24no—
244#10621898—24no—
245#10621898—24no—
246#10621898#4118yes—
247C2×D172—21no—
248C2×D172—24no—
249C2×D172—21no—
250C2×D172—24no—
251C2×D172C2412yes—
252C2×D172C2412yes—
253C2×C4×D43—28no—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—22no—
259C2×C4×D43—22no—
260C2×C4×D43—24no—
261C2×C4×D43—82no—
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—
271M16×C43—24no—
272C2×C8×C43C2414yes—
273C2×C8×C43C2414yes—
274C4⋊C4×C43C2×D412yes—
275C4⋊C4×C43C2×D412yes—
276C4⋊C4×C43C2×D412yes—
277C4⋊C4×C43C2×D412yes—
278C22⋊C4×C43C2×D412yes—
279C22⋊C4×C43C2×D412yes—
280C22⋊C4×C43C2×D412yes—
281C22⋊C4×C43C2×D412yes—
282C42×C43C2×D412yes—
283C42×C43C2×D412yes—
284C42×C43C2412yes—
285C42×C43C2412yes—
286C22⋊Dic43—22no—
287C22⋊Dic43—22no—
288C22⋊Dic43—22no—
289C22⋊Dic43—22no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—22no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—22no—
294(C2×D43)⋊C4—24no—
295(C2×D43)⋊C4—22no—
296(C2×D43)⋊C4—22no—
297(C2×D43)⋊C4—24no—
298(C2×D43)⋊C4—24no—
299C4⋊Dic43—21no—
300C4⋊Dic43—21no—
301C4⋊Dic43—24no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43C2412yes—
305C4⋊Dic43C2412yes—
306C4⋊Dic43C2412yes—
307C4⋊Dic43C2412yes—
308Dic43⋊C4—22no—
309Dic43⋊C4—22no—
310Dic43⋊C4—22no—
311Dic43⋊C4—22no—
312Dic43⋊C4—24no—
313Dic43⋊C4—22no—
314Dic43⋊C4—22no—
315C4×Dic43—22no—
316C4×Dic43—22no—
317C4×Dic43—22no—
318C4×Dic43—22no—
319C4×Dic43—22no—
320C4×Dic43—22no—
321C4×Dic43—24no—
322Dic172—28no—
323D344—28no—
324#10621873—28no—
325#10621873—28no—
326C23×C43—22no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43C22×D411yescharacteristic
330C23×C43C22×D411yescharacteristic
331C23×C43C22×D411yescharacteristic
332C22×D43—22no—
333C22×D43—24no—
334C22×D43—22no—
335C22×D43—42no—
336C22×D43—42no—
337C22×D43—42no—
338C22×D43—81no—
339C22×D43—81no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43C22×D412yes—
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D412yes—
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D412yes—
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C2×#4114yes—
357C2×C4×C43C2511yescharacteristic
358C22⋊D43—28no—
359C22⋊D43—28no—
360C22⋊D43—82no—
361C22⋊D43—82no—
362C2×Dic43—24no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—42no—
370C2×Dic43—42no—
371C2×Dic43—42no—
372C2×Dic43—81no—
373C2×Dic43—81no—
374D172—24no—
375D172—22no—
376D172—24no—
377D172—42no—
378D172C2×#4114yes—
379C4×D43—28no—
380C4×D43—28no—
381C4×D43—82no—
382C4×D43—82no—
383C4×D43—82no—
384C4×D43—82no—
385C4×D43—84no—
386Dic86—24no—
387Dic86—22no—
388Dic86—24no—
389Dic86—42no—
390Dic86—84no—
391Dic86C2×#4114yes—
392C8×C43—24no—
393C8×C43—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—82no—
404C22×C43#52512yes—
405C22×C43C23×D411yescharacteristic
406C2×D43—24no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—84no—
413C2×D43—84no—
414C4×C43—22no—
415C4×C43—22no—
416C4×C43—22no—
417C4×C43—22no—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43#52512yes—
421C4×C43C22×#4112yes—
422Dic43—24no—
423Dic43—42no—
424Dic43—42no—
425Dic43—42no—
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#3094—431no—
436#3079—432no—
437#3040—432no—
438#3007—431no—
439#3006—431no—
440C4×#137—432no—
441C4×AGL(1,ℤ/8)—432no—
442#2921D4311yescharacteristic, complemented
443C2×C43—22no—
444C2×C43—41no—
445C2×C43—41no—
446C2×C43C2×#52511yescharacteristic
447C2×C43#358511yescharacteristic
448C2×C43#358611yescharacteristic
449D43—44no—
450D43—82no—
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×#121—431no—
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#482—434no—
486#481—432no—
487#480—432no—
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#433C2×D4314yescomplemented
511#433C2×D4314yescomplemented
512#428—432no—
513#428—432no—
514#423C2×D4312yescomplemented
515#419—432no—
516#418—432no—
517#417—432no—
518#417—432no—
519#407C2×D4311yescharacteristic
520#407C2×D4311yescharacteristic
521C4×M16C2×D4312yescomplemented
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—431no—
532C22×D4—431no—
533C22×D4—861no—
534C22×D4—861no—
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×M16C22×D4312yes—
545C2×M16C22×D4312yes—
546C4⋊Q8—434no—
547C4⋊Q8—862no—
548#126—864no—
549#126—864no—
550#124—434no—
551#124—864no—
552#124—864no—
553#124—862no—
554#123—864no—
555#123—864no—
556C22⋊Q8—432no—
557C22⋊Q8—432no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—864no—
561C22⋊Q8—864no—
562#121—432no—
563#121—432no—
564#121—861no—
565#121—861no—
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—432no—
591#117—432no—
592#117—861no—
593#117—861no—
594#117—862no—
595#117—862no—
596#117—862no—
597#117—862no—
598#117—862no—
599#117—862no—
600#117D17212yes—
601#117D17212yes—
602#117C22×D4312yes—
603#117C22×D4312yes—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—431no—
606C2×C4⋊C4—431no—
607C2×C4⋊C4—431no—
608C2×C4⋊C4—861no—
609C2×C4⋊C4—861no—
610C2×C4⋊C4—861no—
611C2×C4⋊C4—862no—
612C2×C4⋊C4—862no—
613C2×C4⋊C4D17211yescharacteristic
614C2×C4⋊C4D17211yescharacteristic
615C2×C22⋊C4—861no—
616C2×C22⋊C4—861no—
617C2×C22⋊C4—861no—
618C2×C22⋊C4—861no—
619C2×C22⋊C4—861no—
620C2×C22⋊C4—861no—
621C2×C22⋊C4—862no—
622C2×C22⋊C4—862no—
623C2×C22⋊C4D17211yescharacteristic
624C2×C22⋊C4D17211yescharacteristic
625C2×C42—861no—
626C2×C42—861no—
627C2×C42—862no—
628C2×C42—862no—
629C2×C42C22×D4311yescharacteristic
630C2×C42C22×D4311yescharacteristic
631#107—434no—
632#107—434no—
633#106—434no—
634#106—434no—
635C4⋊C8C22×D4314yes—
636C4⋊C8C22×D4314yes—
637#103—434no—
638#103—434no—
639#103—434no—
640#103—434no—
641#102—434no—
642#102—434no—
643#102—434no—
644#102—434no—
645C22⋊C8C22×D4312yes—
646C22⋊C8C22×D4312yes—
647C22⋊C8C22×D4312yes—
648C22⋊C8C22×D4312yes—
649#97C22×D4314yes—
650C4×C8C22×D4314yes—
651C24—861no—
652C24—861no—
653C24C2×D17211yescharacteristic
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—861no—
664C2×Q8—864no—
665C2×Q8—861no—
666C2×Q8—864no—
667C2×Q8—3442no—
668C2×D4—432no—
669C2×D4—432no—
670C2×D4—864no—
671C2×D4—868no—
672C2×D4—862no—
673C2×D4—862no—
674C2×D4—862no—
675C2×D4—862no—
676C2×D4—861no—
677C2×D4—861no—
678C2×D4—864no—
679C2×D4—3442no—
680C22×C4—24no—
681C22×C4—868no—
682C22×C4—861no—
683C22×C4—862no—
684C22×C4—862no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—862no—
691C22×C4—862no—
692C22×C4—862no—
693C22×C4—862no—
694C22×C4—864no—
695C22×C4—3442no—
696C22×C4C2×D17211yescharacteristic
697C22×C4C2×D17211yescharacteristic
698C22×C4C2×D17211yescharacteristic
699C22×C4C2×D17211yescharacteristic
700C22×C4C2×D17211yescharacteristic
701C22×C4C2×D17211yescharacteristic
702C22×C4C2×D17211yescharacteristic
703C22×C4C23×D4311yescharacteristic
704C22×C4C23×D4311yescharacteristic
705C22×C4C23×D4311yescharacteristic
706Q16—868no—
707SD16—868no—
708SD16—868no—
709D8—868no—
710M16—24no—
711M16—24no—
712C2×C8C23×D4314yes—
713C2×C8C23×D4314yes—
714C4⋊C4—432no—
715C4⋊C4—432no—
716C4⋊C4—432no—
717C4⋊C4—432no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—862no—
723C4⋊C4—862no—
724C4⋊C4—862no—
725C4⋊C4—862no—
726C4⋊C4—864no—
727C4⋊C4—862no—
728C4⋊C4—862no—
729C4⋊C4—864no—
730C4⋊C4C2×D17212yes—
731C4⋊C4C2×D17212yes—
732C4⋊C4C2×D17212yes—
733C4⋊C4C2×D17212yes—
734C22⋊C4—862no—
735C22⋊C4—862no—
736C22⋊C4—862no—
737C22⋊C4—862no—
738C22⋊C4—862no—
739C22⋊C4—862no—
740C22⋊C4—862no—
741C22⋊C4—862no—
742C22⋊C4—864no—
743C22⋊C4—862no—
744C22⋊C4—862no—
745C22⋊C4—864no—
746C22⋊C4—864no—
747C22⋊C4C2×D17212yes—
748C22⋊C4C2×D17212yes—
749C22⋊C4C2×D17212yes—
750C22⋊C4C2×D17212yes—
751C42—862no—
752C42—862no—
753C42—862no—
754C42—862no—
755C42—862no—
756C42—862no—
757C42—864no—
758C42C2×D17212yes—
759C42C2×D17212yes—
760C42C23×D4312yes—
761C42C23×D4312yes—
762C23—22no—
763C23—41no—
764C23—41no—
765C23—864no—
766C23—862no—
767C23—862no—
768C23—3441no—
769C23—3441no—
770C23—1722no—
771C23—1722no—
772C23—1722no—
773C23C22×D17211yescharacteristic
774C23C22×D17211yescharacteristic
775C23C22×D17211yescharacteristic
776Q8—434no—
777Q8—864no—
778Q8—862no—
779Q8—864no—
780Q8—3444no—
781Q8—1722no—
782D4—434no—
783D4—864no—
784D4—868no—
785D4—868no—
786D4—862no—
787D4—864no—
788D4—3442no—
789D4—3442no—
790D4—1722no—
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—868no—
801C2×C4—864no—
802C2×C4—862no—
803C2×C4—868no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—3444no—
810C2×C4—3442no—
811C2×C4—3442no—
812C2×C4—3442no—
813C2×C4—3442no—
814C2×C4—3441no—
815C2×C4—3441no—
816C2×C4—1722no—
817C2×C4—1722no—
818C2×C4—1722no—
819C2×C4C22×D17212yes—
820C2×C4C22×D17211yescharacteristic
821C2×C4C22×D17212yes—
822C2×C4C22×D17212yes—
823C2×C4C22×D17212yes—
824C2×C4C22×D17211yescharacteristic
825C2×C4C22×D17211yescharacteristic
826C2×C4#41×D4314yes—
827C2×C4C24×D4311yescharacteristic
828C8—24no—
829C8—24no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—82no—
839C22—864no—
840C22—3444no—
841C22—3444no—
842C22—1722no—
843C22—1722no—
844C22—1722no—
845C22—1722no—
846C22—1722no—
847C22#1458341112yes—
848C22C23×D17211yescharacteristic
849C4—21no—
850C4—21no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—864no—
856C4—1722no—
857C4—1722no—
858C4—1722no—
859C4—1722no—
860C4—1722no—
861C4#1458341112yes—
862C4C2×#41×D4312yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—3442no—
867C2—1724no—
868C2C2×#1458341111yescharacteristic
869C2#1914937611yescharacteristic
870C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2921C2
socleC22×C43C23×D4
prime radical#19143849C2
hypercenter#2921D43
hypocenterC43#60567
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. C2×#14583520C2semidirect
2. #19147796C2semidirect
3. #19144874C2semidirect
4. #19144859C2semidirect
5. #19144826C2semidirect
6. #19144781C2semidirect
7. #19144544C2semidirect
8. #19144536C2semidirect
9. #19144411C2semidirect
10. #19144090C2semidirect
11. #19143857C2semidirect
13. C4×#13063358C2semidirect
14. C4×#13063353C2semidirect
15. C43×#2921C2semidirect
22. #14583520C22semidirect
23. C2×#13063325C22semidirect
25. C2×#13063313C22semidirect
33. #14583379C22semidirect
34. #14583379C22semidirect
35. #14583376C22semidirect
36. #14583373C22semidirect
42. C2×C4×Dic86C22semidirect
43. C2×C4×D172C22semidirect
46. #14583241C22semidirect
47. #14583235C22semidirect
48. #14583230C22semidirect
50. #14583218C22semidirect
51. #14583213C22semidirect
52. #14583195C22semidirect
53. #14583190C22semidirect
54. #14583185C22semidirect
55. #14583180C22semidirect
56. #14583122C22semidirect
57. #14583122C22semidirect
58. #14583115C22semidirect
59. #14583115C22semidirect
60. #14583063C22semidirect
61. #14583057C22semidirect
62. #14583052C22semidirect
66. #14583012C22semidirect
67. #14583007C22semidirect
68. #14583001C22semidirect
69. #14583001C22semidirect
70. C4×Dic172C22semidirect
71. C4×#10621873C22semidirect
72. C4×#10621873C22semidirect
73. C4×D344C22semidirect
74. #14582941C22semidirect
75. #14582941C22semidirect
76. #14582909C22semidirect
77. #14582905C22semidirect
81. C43×#433C22semidirect
82. C43×#433C22semidirect
83. C43×#423C22semidirect
86. C4×M16×C43C22semidirect
442. #2921D43semidirect
510. #433C2×D43semidirect
511. #433C2×D43semidirect
514. #423C2×D43semidirect
521. C4×M16C2×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×#145835202
#191477962
#191448742
#191448592
#191448262
#191447812
#191445442
#191445362
#191444112
#191440902
#191438572
#191438492
C4×#130633582
C4×#130633532
C43×#29212
#6056743