Finite Group Databasebeta

← #25965085

Subgroups — #25965085

Order 11008.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147984C211yesmaximal, characteristic, complemented
2C2×#14583381C211yesmaximal, characteristic, complemented
3#19144871C214yesmaximal, complemented
4#19144856C214yesmaximal, complemented
5#19144808C214yesmaximal, complemented
6#19144793C214yesmaximal, complemented
7#19144516C212yesmaximal, complemented
8#19144400C211yesmaximal, characteristic, complemented
9#19144394C211yesmaximal, characteristic, complemented
10#19144055C211yesmaximal, characteristic, complemented
11#19143836C212yesmaximal, complemented
12#137×Dic43C212yesmaximal, complemented
13#19143408C212yesmaximal, complemented
14#19143232C211yesmaximal, characteristic, complemented
15C43×#3037C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C2×#13063350C2212yes—
18#14583518C2212yescomplemented
19#14583518C2212yescomplemented
20#14583510C2212yescomplemented
21#14583503C2212yescomplemented
22#14583494—21no—
23#14583494—21no—
24#14583486—21no—
25#14583486—21no—
26#14583456C2211yescharacteristic
27#14583429—22no—
28#14583429—22no—
29#14583406C2212yes—
30#14583381—22no—
31#14583381—22no—
32#14583381C2214yes—
33#14583381C2214yes—
34#41×Dic43C2212yes—
35C2×Q8×Dic43C2211yescharacteristic
36C2×C4×D172—21no—
37C2×C4×D172C2211yescharacteristic
38C2×#13063287—21no—
39C2×#13063287C2211yescharacteristic
40C2×#13063282—21no—
41C2×#13063282C2211yescharacteristic
42C2×C4⋊C4×D43—21no—
43C2×C4⋊C4×D43C2211yescharacteristic
44#14583233C2214yescomplemented
45#14583228C2214yescomplemented
46#14583216C2214yescomplemented
47#14583211C2214yescomplemented
48#14583206C2214yescomplemented
49#14583200C2214yescomplemented
50#14583194C2212yescomplemented
51#14583190C2212yescomplemented
52#14583184C2212yescomplemented
53#14583180C2212yescomplemented
54#14583111C2214yescomplemented
55#14583101C2212yescomplemented
56#14583091C2212yescomplemented
57#14583060C2214yes—
58#14583060C2214yes—
59#14583043C2214yes—
60#14583043C2214yes—
61#14583008C2214yescomplemented
62#14583006C2214yescomplemented
63#14583002C2214yescomplemented
64#14583000C2214yescomplemented
65Q16×Dic43C2214yescomplemented
66SD16×Dic43C2214yescomplemented
67#14582984C2214yescomplemented
68#14582979C2214yescomplemented
69#14582959C2214yescomplemented
70#14582959C2214yescomplemented
71#14582941C2212yes—
72#14582939C2212yes—
73#14582923C2211yescharacteristic
74#14582908C2212yes—
75#14582905C2212yes—
76#14582900C2212yes—
77#14582862C2212yes—
78M16×Dic43C2212yes—
79C2×#137×C43C2212yes—
80C43×#532C2211yescharacteristic
81C2×C4×Q8×C43C2211yescharacteristic
82C43×#464C2214yescomplemented
83C43×#462C2212yescomplemented
84C43×#460C2212yescomplemented
85C43×#423C2211yescharacteristic
86C43×#417C2212yes—
87C2×#10621902—24no—
88C2×#10621902—24no—
89C2×#10621902—22no—
90C2×#10621902C2314yes—
91C22×D172—21no—
92C22×D172C2311yescharacteristic
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98#13063350—28no—
99C2×#10621884C2314yes—
100C2×#10621882C2314yes—
101C2×#10621877C2312yes—
102#13063325C2311yescharacteristic
103#13063325C2311yescharacteristic
104#13063320—22no—
105#13063320—22no—
106#13063318—22no—
107#13063318—22no—
108#13063317C2312yes—
109#13063315—22no—
110#13063315—22no—
111#13063311—22no—
112#13063311—22no—
113#13063309—22no—
114#13063309—22no—
115#13063306—22no—
116#13063306—22no—
117#13063306—22no—
118#13063304—21no—
119#13063304—21no—
120#13063302—22no—
121#13063302—22no—
122#13063301C2312yes—
123#13063301C2312yes—
124#13063297—22no—
125#13063297—22no—
126#13063296C2312yes—
127#13063296C2312yes—
128#13063293—22no—
129Q8×Dic43—22no—
130Q8×Dic43C2314yes—
131Q8×Dic43C2312yes—
132Q8×Dic43C2312yes—
133C4×Dic86—21no—
134C4×Dic86—21no—
135C4×D172—21no—
136C4×D172—21no—
137C4×D172—24no—
138C4×D172—24no—
139C4×D172C2312yes—
140C4×D172C2312yes—
141D4×Dic43—22no—
142D4×Dic43—22no—
143D4×Dic43C2312yes—
144D4×Dic43C2312yes—
145#13063287—24no—
146#13063287—24no—
147#13063287—22no—
148#13063287C2314yes—
149C4×C22⋊D43—22no—
150C4×C22⋊D43—22no—
151#13063284—22no—
152#13063284C2312yes—
153#13063282—24no—
154#13063282—24no—
155#13063282D412yes—
156#13063282D412yes—
157#13063282C2312yes—
158#13063282C2312yes—
159C2×C4⋊Dic43—21no—
160C2×C4⋊Dic43C2311yescharacteristic
161C2×Dic43⋊C4—21no—
162C2×Dic43⋊C4D411yescharacteristic
163C2×Dic43⋊C4D411yescharacteristic
164C4⋊C4×D43—22no—
165C4⋊C4×D43—24no—
166C4⋊C4×D43—24no—
167C4⋊C4×D43C2314yes—
168C2×(C2×D43)⋊C4—21no—
169C2×(C2×D43)⋊C4—21no—
170C2×(C2×D43)⋊C4D411yescharacteristic
171C2×(C2×D43)⋊C4D411yescharacteristic
172C2×C4×Dic43—21no—
173C2×C4×Dic43—22no—
174C2×C4×Dic43C2311yescharacteristic
175#13063259C2314yes—
176#13063258C2314yes—
177#13063257C2314yes—
178#13063256C2314yes—
179C4⋊(C43⋊C8)C2312yes—
180C4⋊(C43⋊C8)C2312yes—
181#13063249C2314yes—
182#13063249C2314yes—
183#13063249C2314yes—
184#13063247C2314yes—
185#13063247C2314yes—
186#13063246C2314yes—
187(C2×D43)⋊C8C2314yes—
188(C2×D43)⋊C8C2314yes—
189#13063235C2314yes—
190C8×Dic43C2314yes—
191C2×#41×C43C2312yes—
192C22×Q8×C43C2311yescharacteristic
193#137×C43—28no—
194C2×Q16×C43C2314yes—
195C2×SD16×C43C2314yes—
196C2×M16×C43C2312yes—
197C4⋊Q8×C43C2311yescharacteristic
198#127×C43C2311yescharacteristic
199#124×C43C2312yes—
200#121×C43—21no—
201#121×C43—21no—
202C4×Q8×C43—21no—
203C4×Q8×C43—21no—
204C4×Q8×C43C2312yes—
205C4×Q8×C43C2312yes—
206C4×D4×C43—21no—
207C4×D4×C43—21no—
208C2×C4⋊C4×C43—21no—
209C2×C4⋊C4×C43C2311yescharacteristic
210C2×C42×C43—21no—
211C2×C42×C43C2311yescharacteristic
212C4⋊C8×C43C2312yes—
213C4⋊C8×C43C2312yes—
214#103×C43C2314yes—
215#102×C43C2314yes—
216C23×D43—21no—
217C23×D43C2×D411yescharacteristic
218#41×C43—24no—
219#41×C43—24no—
220C2×Q8×C43—21no—
221C2×Q8×C43—22no—
222C2×Q8×C43#4114yes—
223C2×Q8×C43C2412yes—
224C2×Q8×C43C2412yes—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—22no—
228C2×D4×C43C2412yes—
229C22×C4×C43—22no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C2×C22⋊D43—22no—
236C2×C22⋊D43—22no—
237C22×Dic43—22no—
238C22×Dic43—22no—
239C22×Dic43—21no—
240C22×Dic43C2×D411yescharacteristic
241C22×Dic43C2×D411yescharacteristic
242C22×Dic43C2×D411yescharacteristic
243#10621902—216no—
244#10621902—28no—
245#10621902—28no—
246C2×D172—28no—
247C2×D172—21no—
248C2×D172—22no—
249C2×D172—24no—
250C2×D172#4114yes—
251C2×D172C2412yes—
252C2×C4×D43—28no—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—24no—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—24no—
259C2×C4×D43—24no—
260C2×C4×D43—82no—
261C2×C4×D43—82no—
262C2×C4×D43—82no—
263C2×C4×D43C2×D412yes—
264C2×C4×D43C2412yes—
265C2×Dic86—21no—
266C2×Dic86—21no—
267Q16×C43—28no—
268SD16×C43—28no—
269M16×C43—24no—
270C2×C8×C43C2414yes—
271C4⋊C4×C43—22no—
272C4⋊C4×C43—22no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43C2412yes—
277C22⋊C4×C43—22no—
278C22⋊C4×C43—22no—
279C42×C43—22no—
280C42×C43—22no—
281C42×C43C2×D411yescharacteristic
282C42×C43C2×D411yescharacteristic
283C42×C43C2411yescharacteristic
284C42×C43C2411yescharacteristic
285C22⋊Dic43—22no—
286C22⋊Dic43—22no—
287C22⋊Dic43—22no—
288C22⋊Dic43—22no—
289C22⋊Dic43—22no—
290#10621884—28no—
291#10621882—28no—
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)⋊C4C2×D412yes—
298(C2×D43)⋊C4C2×D412yes—
299(C2×D43)⋊C4C2×D412yes—
300(C2×D43)⋊C4C2×D412yes—
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43—24no—
305C4⋊Dic43—22no—
306C4⋊Dic43—22no—
307C4⋊Dic43C2412yes—
308C4⋊Dic43C2412yes—
309C4⋊Dic43C2412yes—
310Dic43⋊C4—22no—
311Dic43⋊C4—22no—
312Dic43⋊C4—24no—
313Dic43⋊C4—22no—
314Dic43⋊C4—22no—
315Dic43⋊C4C2×D412yes—
316Dic43⋊C4C2×D412yes—
317Dic43⋊C4C2×D412yes—
318Dic43⋊C4C2×D412yes—
319C4×Dic43—22no—
320C4×Dic43—24no—
321C4×Dic43—22no—
322C4×Dic43—22no—
323C4×Dic43C2×D412yes—
324C4×Dic43C2412yes—
325#10621877—24no—
326C2×C43⋊C8C2414yes—
327C23×C43—22no—
328C23×C43C22×D411yescharacteristic
329C22×D43—22no—
330C22×D43—24no—
331C22×D43—22no—
332C22×D43—41no—
333C22×D43—41no—
334C22×D43—42no—
335C22×D43—42no—
336C22×D43C22×D412yes—
337Q8×C43—24no—
338Q8×C43—22no—
339Q8×C43—22no—
340Q8×C43—22no—
341Q8×C43C2×#4114yes—
342D4×C43—22no—
343D4×C43—22no—
344D4×C43—44no—
345D4×C43—81no—
346D4×C43—81no—
347C2×C4×C43—24no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—42no—
354C2×C4×C43—44no—
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C2×#4112yes—
361C2×C4×C43C2×#4112yes—
362C2×C4×C43C2511yescharacteristic
363C22⋊D43—82no—
364C22⋊D43—82no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—42no—
372C2×Dic43—82no—
373C2×Dic43—82no—
374C2×Dic43C22×D412yes—
375C2×Dic43C22×D412yes—
376C2×Dic43C22×D412yes—
377D172—216no—
378D172—24no—
379D172—22no—
380D172C2×#4114yes—
381C4×D43—216no—
382C4×D43—24no—
383C4×D43—22no—
384C4×D43—22no—
385C4×D43—84no—
386C4×D43—82no—
387C4×D43—82no—
388C4×D43—84no—
389Dic86—81no—
390Dic86—81no—
391C8×C43—24no—
392C43⋊C8—24no—
393#60565—431nomaximal, Sylow
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43#52512yes—
400C22×C43C23×D411yescharacteristic
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—24no—
404C2×D43—22no—
405C2×D43—44no—
406C2×D43—48no—
407C2×D43—42no—
408C2×D43—42no—
409C4×C43—21no—
410C4×C43—21no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—24no—
414C4×C43—42no—
415C4×C43—42no—
416C4×C43#52512yes—
417C4×C43C22×#4111yescharacteristic
418C4×C43C22×#4111yescharacteristic
419Dic43—22no—
420Dic43—22no—
421Dic43—22no—
422Dic43—42no—
423Dic43—42no—
424Dic43—42no—
425#3455—431no—
426C2×#520—431no—
427#3125—434no—
428#3124—434no—
429#3120—434no—
430#3119—434no—
431#3092—432no—
432#3078—431no—
433#3077—431no—
434#3037D4311yescharacteristic, complemented
435#3036—431no—
436#3005—432no—
437C4×#137—432no—
438C4×AGL(1,ℤ/8)—432no—
439#2921—431no—
440C2×C43—22no—
441C2×C43—82no—
442C2×C43C2×#52511yescharacteristic
443C2×C43#358511yescharacteristic
444C2×C43#358611yescharacteristic
445D43—42no—
446D43—44no—
447C22×#41—431no—
448C2×#137C2×D4312yes—
449C2×AGL(1,ℤ/8)—432no—
450#542—432no—
451#542—432no—
452#541—432no—
453#540—432no—
454#539—861no—
455#539—861no—
456#538—861no—
457#538—861no—
458#533—431no—
459#532C2×D4311yescharacteristic
460#529—862no—
461#529—862no—
462#525—432no—
463#520—434no—
464#520—434no—
465#520—862no—
466#520—862no—
467C4×#41—432no—
468C2×C4×Q8—431no—
469C2×C4×Q8C2×D4311yescharacteristic
470C2×C4×D4—431no—
471C2×C4×D4—431no—
472C2×C4×D4—861no—
473C2×C4×D4—861no—
474C2×#117—431no—
475C2×#117—861no—
476C22×C4⋊C4—431no—
477C22×C4⋊C4—861no—
478#484—434no—
479#483—434no—
480#481—434no—
481#480—434no—
482#479—434no—
483#478—434no—
484#477—432no—
485#476—432no—
486#475—432no—
487#474—432no—
488#464C2×D4314yescomplemented
489#463—434no—
490#462C2×D4312yescomplemented
491#461—432no—
492#460C2×D4312yescomplemented
493#459—432no—
494#452—434no—
495#452—434no—
496#449—434no—
497#449—434no—
498#442—434no—
499#441—434no—
500#440—434no—
501#440—434no—
502C4×Q16—434no—
503C4×SD16—434no—
504C4×SD16—434no—
505C4×D8—434no—
506#433—434no—
507#433—434no—
508#428—432no—
509#428—432no—
510#423—431no—
511#423C2×D4311yescharacteristic
512#419—432no—
513#418—432no—
514#417—432no—
515#417C2×D4312yes—
516#407—432no—
517C4×M16—432no—
518C43#6056511yescharacteristic, complemented, Sylow
519C2×#41—434no—
520C2×#41—862no—
521C2×#41—864no—
522C2×#41—864no—
523C2×#41C22×D4312yes—
524C22×Q8C22×D4311yescharacteristic
525C22×D4—431no—
526C22×D4—861no—
527C23×C4—431no—
528C23×C4—861no—
529C23×C4—861no—
530C23×C4—861no—
531C23×C4—861no—
532#137—28no—
533AGL(1,ℤ/8)—868no—
534C2×Q16C22×D4314yes—
535C2×SD16—434no—
536C2×SD16C22×D4314yes—
537C2×D8—434no—
538C2×M16—432no—
539C2×M16C22×D4312yes—
540C4⋊Q8—431no—
541C4⋊Q8—431no—
542C4⋊Q8C22×D4311yescharacteristic
543#127C22×D4311yescharacteristic
544#126—862no—
545#126—862no—
546#126—862no—
547#126—862no—
548#125—432no—
549#125—862no—
550#125—862no—
551#124—862no—
552#124—862no—
553#124C22×D4312yes—
554#123—862no—
555#123—862no—
556#123—862no—
557#123—862no—
558#123—862no—
559C22⋊Q8—432no—
560C22⋊Q8—432no—
561C22⋊Q8—862no—
562C22⋊Q8—862no—
563C22⋊Q8—861no—
564C22⋊Q8—861no—
565#121—21no—
566#121—21no—
567#121—432no—
568#121—432no—
569#121—862no—
570#121—862no—
571#120—862no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8—434no—
575C4×Q8—432no—
576C4×Q8—432no—
577C4×Q8—862no—
578C4×Q8—861no—
579C4×Q8—861no—
580C4×Q8C22×D4312yes—
581C4×Q8C22×D4312yes—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—432no—
585C4×D4—432no—
586C4×D4—434no—
587C4×D4—432no—
588C4×D4—432no—
589C4×D4—864no—
590C4×D4—864no—
591C4×D4—862no—
592C4×D4—864no—
593C4×D4—864no—
594C4×D4—862no—
595C4×D4—862no—
596C4×D4—862no—
597C4×D4—862no—
598C4×D4—861no—
599C4×D4—861no—
600#117—432no—
601#117—432no—
602#117—432no—
603#117—432no—
604#117—432no—
605#117—864no—
606#117—864no—
607#117—862no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—431no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—434no—
613C2×C4⋊C4—864no—
614C2×C4⋊C4—864no—
615C2×C4⋊C4—862no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4C22×D4311yescharacteristic
619C2×C22⋊C4—431no—
620C2×C22⋊C4—431no—
621C2×C22⋊C4—861no—
622C2×C22⋊C4—861no—
623C2×C42—21no—
624C2×C42—431no—
625C2×C42—862no—
626C2×C42—861no—
627C2×C42C22×D4311yescharacteristic
628#107—434no—
629#107—434no—
630#106—434no—
631#106—434no—
632C4⋊C8—432no—
633C4⋊C8—432no—
634C4⋊C8C22×D4312yes—
635C4⋊C8C22×D4312yes—
636#103—434no—
637#103—434no—
638#103—434no—
639#103C22×D4314yes—
640#102—434no—
641#102—434no—
642#102—434no—
643#102C22×D4314yes—
644C22⋊C8—434no—
645C22⋊C8—434no—
646#97—434no—
647C4×C8—434no—
648C24—431no—
649C24—861no—
650#41—24no—
651#41—24no—
652#41—868no—
653#41—8616no—
654#41—868no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—861no—
658C2×Q8—861no—
659C2×Q8#1062190014yes—
660C2×Q8C23×D4312yes—
661C2×Q8C23×D4312yes—
662C2×D4—22no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—434no—
666C2×D4—432no—
667C2×D4—864no—
668C2×D4—868no—
669C2×D4—862no—
670C2×D4—862no—
671C2×D4—861no—
672C2×D4—862no—
673C2×D4C23×D4312yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—431no—
678C22×C4—431no—
679C22×C4—431no—
680C22×C4—432no—
681C22×C4—432no—
682C22×C4—864no—
683C22×C4—864no—
684C22×C4—868no—
685C22×C4—864no—
686C22×C4—862no—
687C22×C4—862no—
688C22×C4—862no—
689C22×C4—862no—
690C22×C4—861no—
691C22×C4—862no—
692C22×C4—862no—
693C22×C4—3442no—
694C22×C4—3442no—
695C22×C4—3442no—
696C22×C4D4×D4311yescharacteristic
697C22×C4D4×D4311yescharacteristic
698C22×C4C23×D4311yescharacteristic
699Q16—28no—
700SD16—28no—
701SD16—868no—
702D8—868no—
703M16—24no—
704M16—864no—
705C2×C8—434no—
706C2×C8C23×D4314yes—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—432no—
713C4⋊C4—432no—
714C4⋊C4—432no—
715C4⋊C4—432no—
716C4⋊C4—432no—
717C4⋊C4—432no—
718C4⋊C4—432no—
719C4⋊C4—864no—
720C4⋊C4—864no—
721C4⋊C4—862no—
722C4⋊C4—862no—
723C4⋊C4—862no—
724C4⋊C4—862no—
725C4⋊C4—861no—
726C4⋊C4—862no—
727C4⋊C4—862no—
728C4⋊C4—861no—
729C4⋊C4—861no—
730C4⋊C4C23×D4312yes—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—432no—
734C22⋊C4—432no—
735C22⋊C4—432no—
736C22⋊C4—432no—
737C22⋊C4—864no—
738C22⋊C4—862no—
739C22⋊C4—862no—
740C22⋊C4—862no—
741C22⋊C4—862no—
742C22⋊C4—862no—
743C22⋊C4—862no—
744C22⋊C4—862no—
745C22⋊C4—862no—
746C22⋊C4—862no—
747C42—22no—
748C42—22no—
749C42—432no—
750C42—432no—
751C42—864no—
752C42—862no—
753C42—862no—
754C42—862no—
755C42D4×D4311yescharacteristic
756C42D4×D4311yescharacteristic
757C42C23×D4311yescharacteristic
758C42C23×D4311yescharacteristic
759C23—22no—
760C23—432no—
761C23—864no—
762C23—862no—
763C23—862no—
764C23—1721no—
765C23—1721no—
766C23—1722no—
767C23—1722no—
768C23C2×D4×D4311yescharacteristic
769Q8—24no—
770Q8—22no—
771Q8—22no—
772Q8—22no—
773Q8—3441no—
774Q8—3441no—
775Q8C2×#1062190014yes—
776D4—22no—
777D4—22no—
778D4—44no—
779D4—81no—
780D4—81no—
781D4—434no—
782D4—8616no—
783D4—864no—
784D4—862no—
785D4—3442no—
786D4—3442no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—432no—
796C2×C4—432no—
797C2×C4—432no—
798C2×C4—8616no—
799C2×C4—862no—
800C2×C4—864no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—3442no—
807C2×C4—3442no—
808C2×C4—3444no—
809C2×C4—3444no—
810C2×C4—3442no—
811C2×C4—3442no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1722no—
815C2×C4C2×D4×D4311yescharacteristic
816C2×C4C2×D4×D4311yescharacteristic
817C2×C4C2×D4×D4311yescharacteristic
818C2×C4C2×D4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4#41×D4312yes—
821C2×C4C2×#1062190012yes—
822C2×C4C24×D4311yescharacteristic
823C8—24no—
824C8—864no—
825C22—21no—
826C22—21no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—864no—
831C22—862no—
832C22—862no—
833C22—862no—
834C22—1724no—
835C22—1728no—
836C22—1722no—
837C22—1722no—
838C22#1458340912yes—
839C22C22×D4×D4311yescharacteristic
840C4—24no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—42no—
846C4—42no—
847C4—862no—
848C4—862no—
849C4—862no—
850C4—1722no—
851C4—1722no—
852C4—1722no—
853C4#1458340912yes—
854C4C2×#41×D4311yescharacteristic
855C4C22×#1062190011yescharacteristic
856C2—22no—
857C2—82no—
858C2—1722no—
859C2—1724no—
860C2C2×#1458340911yescharacteristic
861C2#1914937211yescharacteristic
862C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3037C2
socleC22×C43C23×D4
hypercenter#3037D43
hypocenterC43#60565
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
1. #19147984C2semidirect
2. C2×#14583381C2semidirect
3. #19144871C2semidirect
4. #19144856C2semidirect
5. #19144808C2semidirect
6. #19144793C2semidirect
7. #19144516C2semidirect
8. #19144400C2semidirect
9. #19144394C2semidirect
10. #19144055C2semidirect
11. #19143836C2semidirect
12. #137×Dic43C2semidirect
13. #19143408C2semidirect
14. #19143232C2semidirect
15. C43×#3037C2semidirect
18. #14583518C22semidirect
19. #14583518C22semidirect
20. #14583510C22semidirect
21. #14583503C22semidirect
44. #14583233C22semidirect
45. #14583228C22semidirect
46. #14583216C22semidirect
47. #14583211C22semidirect
48. #14583206C22semidirect
49. #14583200C22semidirect
50. #14583194C22semidirect
51. #14583190C22semidirect
52. #14583184C22semidirect
53. #14583180C22semidirect
54. #14583111C22semidirect
55. #14583101C22semidirect
56. #14583091C22semidirect
61. #14583008C22semidirect
62. #14583006C22semidirect
63. #14583002C22semidirect
64. #14583000C22semidirect
65. Q16×Dic43C22semidirect
66. SD16×Dic43C22semidirect
67. #14582984C22semidirect
68. #14582979C22semidirect
69. #14582959C22semidirect
70. #14582959C22semidirect
82. C43×#464C22semidirect
83. C43×#462C22semidirect
84. C43×#460C22semidirect
434. #3037D43semidirect
488. #464C2×D43semidirect
490. #462C2×D43semidirect
492. #460C2×D43semidirect
518. C43#60565semidirect

Maximal subgroups

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

subgroupindex
#191479842
C2×#145833812
#191448712
#191448562
#191448082
#191447932
#191445162
#191444002
#191443942
#191440552
#191438362
#137×Dic432
#191434082
#191432322
C43×#30372
#6056543