Finite Group Databasebeta

← #25965075

Subgroups — #25965075

Order 11008.

2218 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147987C211yesmaximal, characteristic, complemented
2C2×#14583371C211yesmaximal, characteristic, complemented
3#19144849C214yesmaximal, complemented
4#19144840C214yesmaximal, complemented
5#19144786C214yesmaximal, complemented
6#19144784C214yesmaximal, complemented
7#19144529C212yesmaximal, complemented
8#19144388C211yesmaximal, characteristic, complemented
9#19144061C211yesmaximal, characteristic, complemented
10#19144059C211yesmaximal, characteristic, complemented
11#19143824C212yesmaximal, complemented
12#19143402C212yesmaximal, complemented
13#19143399C212yesmaximal, complemented
14#19143232C211yesmaximal, characteristic, complemented
15C43×#3077C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C2×#13063353C2212yes—
18C2×#13063351C2212yes—
19#14583523C2212yescomplemented
20#14583523C2212yescomplemented
21#14583512C2212yescomplemented
22#14583505C2212yescomplemented
23#14583498—21no—
24#14583498—21no—
25#14583489—21no—
26#14583489—21no—
27#14583449C2211yescharacteristic, complemented
28#14583436—22no—
29#14583436—22no—
30#14583411C2212yes—
31#14583371—22no—
32#14583371—22no—
33#14583371C2214yes—
34#14583371C2214yes—
35#14583367C2212yescomplemented
36C2×C4×D172C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×C4×C22⋊D43—21no—
40C2×(C22⋊D43)⋊C4—21no—
41C2×#13063283C2211yescharacteristic
42C2×#13063282C2211yescharacteristic
43C22×(C2×D43)⋊C4—21no—
44C2×C22⋊C4×D43—21no—
45#14583243C2214yescomplemented
46#14583242C2214yescomplemented
47#14583226C2214yescomplemented
48#14583225C2214yescomplemented
49#14583196C2214yescomplemented
50#14583186C2212yescomplemented
51#14583176C2212yescomplemented
52#14583115C2214yescomplemented
53#14583114C2214yescomplemented
54#14583105C2212yescomplemented
55#14583104C2212yescomplemented
56#14583095C2212yescomplemented
57#14583094C2212yescomplemented
58#14583051C2214yes—
59#14583051C2214yes—
60#14583034C2214yes—
61#14583034C2214yes—
62#14583010C2214yescomplemented
63#14583008C2214yescomplemented
64#14582998C2214yescomplemented
65#14582996C2214yescomplemented
66#14582990C2214yescomplemented
67#14582986C2214yescomplemented
68#14582981C2214yescomplemented
69#14582979C2214yescomplemented
70#14582959C2214yescomplemented
71#14582959C2214yescomplemented
72#14582942C2212yescomplemented
73#14582923C2211yescharacteristic, complemented
74#14582903C2212yes—
75#14582901C2212yescomplemented
76#14582898C2212yescomplemented
77#14582862C2212yes—
78M16×Dic43C2212yescomplemented
79C43×#533C2211yescharacteristic, complemented
80C2×C4×D4×C43C2211yescharacteristic
81C43×#478C2214yescomplemented
82C43×#476C2212yescomplemented
83C43×#474C2212yescomplemented
84C43×#428C2212yescomplemented
85C43×#423C2211yescharacteristic, complemented
86C43×#418C2212yes—
87C24×D43—21no—
88C2×#10621898C2312yes—
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91C2×D4×D43—24no—
92C2×D4×D43—24no—
93C2×D4×D43—22no—
94C2×D4×D43C2314yes—
95C23×Dic43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C22×C4×D43C2311yescharacteristic
99#13063353—28no—
100#13063351—28no—
101C2×#10621873C2314yes—
102C2×#10621883C2314yes—
103C2×D344C2314yes—
104C2×#10621882C2314yes—
105C2×#10621877C2312yes—
106#13063325C2311yescharacteristic, complemented
107#13063322C2311yescharacteristic, complemented
108#13063320—22no—
109#13063320—22no—
110#13063320—22no—
111#13063320—22no—
112#13063316—22no—
113#13063316—22no—
114#13063314—22no—
115#13063314—22no—
116#13063313C2312yescomplemented
117#13063310—22no—
118#13063310—22no—
119#13063310—22no—
120#13063310—22no—
121#13063309—22no—
122#13063305C2312yes—
123#13063305C2312yes—
124#13063301—22no—
125#13063301—22no—
126#13063300—22no—
127#13063300—22no—
128#13063300C2312yes—
129#13063300C2312yes—
130#13063299—21no—
131#13063299—21no—
132#13063295—22no—
133#13063290C2312yescomplemented
134#13063290C2312yescomplemented
135C4×D172—22no—
136C4×D172—22no—
137C4×D172—21no—
138C4×D172—21no—
139C4×D172—21no—
140C4×D172—21no—
141C4×D172C2312yes—
142C4×D172C2312yes—
143D4×Dic43—22no—
144D4×Dic43C2314yes—
145#13063287—22no—
146#13063287C2314yes—
147#13063287C2312yescomplemented
148#13063287C2312yescomplemented
149C4×C22⋊D43—24no—
150C4×C22⋊D43—24no—
151(C22⋊D43)⋊C4—22no—
152(C22⋊D43)⋊C4—22no—
153(C22⋊D43)⋊C4—24no—
154(C22⋊D43)⋊C4—24no—
155#13063283—22no—
156#13063283C2314yes—
157#13063282—22no—
158#13063282D412yes—
159#13063282D412yes—
160#13063282C2312yes—
161#13063282C2312yes—
162C2×C4⋊Dic43C2311yescharacteristic
163C2×Dic43⋊C4D411yescharacteristic
164C2×Dic43⋊C4D411yescharacteristic
165C2×C22⋊Dic43—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4—21no—
169C2×(C2×D43)⋊C4—24no—
170C2×(C2×D43)⋊C4—24no—
171C2×(C2×D43)⋊C4D411yescharacteristic
172C2×(C2×D43)⋊C4D411yescharacteristic
173C22⋊C4×D43—24no—
174C22⋊C4×D43—24no—
175C2×C4×Dic43—21no—
176C2×C4×Dic43C2311yescharacteristic
177C42×D43—22no—
178#13063258C2314yescomplemented
179#13063256C2314yescomplemented
180C4⋊(C43⋊C8)C2312yescomplemented
181C4⋊(C43⋊C8)C2312yescomplemented
182#13063250C2314yescomplemented
183#13063248C2314yescomplemented
184#13063247C2314yescomplemented
185#13063245C2314yes—
186#13063245C2314yes—
187#13063245C2314yescomplemented
188(C2×D43)⋊C8C2314yes—
189(C2×D43)⋊C8C2314yes—
190#13063235C2314yescomplemented
191C8×Dic43C2314yescomplemented
192C22×D4×C43C2311yescharacteristic
193C23×C4×C43—21no—
194C2×M16×C43C2312yes—
195C4⋊Q8×C43C2311yescharacteristic, complemented
196C4⋊Q8×C43C2311yescharacteristic, complemented
197#125×C43C2312yescomplemented
198C22⋊Q8×C43—21no—
199C22⋊Q8×C43—21no—
200C4×Q8×C43—21no—
201C4×Q8×C43—21no—
202C4×D4×C43—21no—
203C4×D4×C43—21no—
204C4×D4×C43C2312yes—
205C4×D4×C43C2312yes—
206#117×C43C2312yes—
207C2×C4⋊C4×C43C2311yescharacteristic
208C2×C22⋊C4×C43—21no—
209C2×C42×C43C2311yescharacteristic
210#107×C43C2314yescomplemented
211#106×C43C2314yescomplemented
212C4⋊C8×C43C2312yescomplemented
213C4⋊C8×C43C2312yescomplemented
214#102×C43C2314yes—
215#102×C43C2314yes—
216C24×C43—21no—
217C23×D43—21no—
218C23×D43—28no—
219C23×D43—24no—
220C23×D43—82no—
221C23×D43—82no—
222C23×D43C2×D411yescharacteristic
223C2×Q8×C43—21no—
224C2×Q8×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—22no—
227C2×D4×C43#4114yes—
228C2×D4×C43C2412yes—
229C22×C4×C43—22no—
230C22×C4×C43—22no—
231C22×C4×C43—21no—
232C22×C4×C43—82no—
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2411yescharacteristic
236C2×C22⋊D43—28no—
237C2×C22⋊D43—24no—
238C2×C22⋊D43—22no—
239C22×Dic43—24no—
240C22×Dic43—21no—
241C22×Dic43—82no—
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244C22×Dic43C2×D411yescharacteristic
245D4×D43—216no—
246D4×D43—28no—
247D4×D43—28no—
248#10621898—24no—
249#10621898—24no—
250C2×D172—21no—
251C2×D172—22no—
252C2×D172—21no—
253C2×D172—21no—
254C2×D172—22no—
255C2×D172—22no—
256C2×D172#4114yes—
257C2×D172C2412yes—
258C2×D172C2412yes—
259C2×C4×D43—22no—
260C2×C4×D43—22no—
261C2×C4×D43—22no—
262C2×C4×D43—22no—
263C2×C4×D43—22no—
264C2×C4×D43—22no—
265C2×C4×D43—22no—
266C2×C4×D43—24no—
267C2×C4×D43—82no—
268C2×C4×D43—82no—
269C2×C4×D43C2×D412yes—
270C2×C4×D43C2412yes—
271C2×Dic86C2412yes—
272M16×C43—24no—
273C2×C8×C43C2414yes—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—22no—
276C4⋊C4×C43—22no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43C2412yes—
280C4⋊C4×C43C2412yes—
281C4⋊C4×C43C2412yes—
282C22⋊C4×C43—22no—
283C22⋊C4×C43—22no—
284C22⋊C4×C43—22no—
285C42×C43—22no—
286C42×C43C2×D411yescharacteristic
287C42×C43C2×D411yescharacteristic
288C42×C43C2411yescharacteristic
289C42×C43C2411yescharacteristic
290C22⋊Dic43—24no—
291#10621883—28no—
292#10621882—28no—
293(C2×D43)⋊C4—22no—
294(C2×D43)⋊C4—22no—
295(C2×D43)⋊C4—22no—
296(C2×D43)⋊C4—22no—
297(C2×D43)⋊C4—24no—
298(C2×D43)⋊C4—22no—
299(C2×D43)⋊C4—22no—
300(C2×D43)⋊C4—22no—
301(C2×D43)⋊C4—22no—
302(C2×D43)⋊C4—24no—
303(C2×D43)⋊C4—22no—
304(C2×D43)⋊C4—22no—
305(C2×D43)⋊C4C2×D412yes—
306(C2×D43)⋊C4C2×D412yes—
307(C2×D43)⋊C4C2×D412yes—
308(C2×D43)⋊C4C2×D412yes—
309C4⋊Dic43—21no—
310C4⋊Dic43—21no—
311C4⋊Dic43—21no—
312C4⋊Dic43—22no—
313C4⋊Dic43—22no—
314C4⋊Dic43C2412yes—
315Dic43⋊C4—22no—
316Dic43⋊C4—22no—
317Dic43⋊C4C2×D412yes—
318Dic43⋊C4C2×D412yes—
319Dic43⋊C4C2×D412yes—
320Dic43⋊C4C2×D412yes—
321C4×Dic43—22no—
322C4×Dic43—22no—
323C4×Dic43—24no—
324C4×Dic43C2×D412yes—
325C4×Dic43C2412yes—
326#10621877—24no—
327C2×C43⋊C8C2414yes—
328D344—28no—
329#10621873—28no—
330C23×C43—24no—
331C23×C43—22no—
332C23×C43—42no—
333C23×C43—42no—
334C23×C43C22×D411yescharacteristic
335C22×D43—22no—
336C22×D43—24no—
337C22×D43—22no—
338C22×D43—216no—
339C22×D43—22no—
340C22×D43—41no—
341C22×D43—41no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—84no—
345C22×D43—84no—
346C22×D43—816no—
347C22×D43C22×D412yes—
348Q8×C43—81no—
349Q8×C43—81no—
350D4×C43—24no—
351D4×C43—22no—
352D4×C43C2×#4114yes—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—42no—
359C2×C4×C43—82no—
360C2×C4×C43—82no—
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C2×#4112yes—
367C2×C4×C43C2×#4112yes—
368C2×C4×C43C2511yescharacteristic
369C22⋊D43—216no—
370C22⋊D43—44no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43—41no—
375C2×Dic43—41no—
376C2×Dic43—42no—
377C2×Dic43—84no—
378C2×Dic43C22×D412yes—
379C2×Dic43C22×D412yes—
380C2×Dic43C22×D412yes—
381D172—24no—
382D172—22no—
383D172—22no—
384D172—22no—
385D172—81no—
386D172—81no—
387D172—82no—
388D172—82no—
389D172C2×#4114yes—
390C4×D43—24no—
391C4×D43—22no—
392C4×D43—22no—
393C4×D43—44no—
394C4×D43—82no—
395C4×D43—82no—
396C4×D43—84no—
397C4×D43—82no—
398C4×D43—82no—
399Dic86—22no—
400Dic86—22no—
401C8×C43—24no—
402C43⋊C8—24no—
403#60564—431nomaximal, Sylow
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—24no—
407C22×C43—48no—
408C22×C43—42no—
409C22×C43—42no—
410C22×C43#52512yes—
411C22×C43C23×D411yescharacteristic
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—24no—
416C2×D43—48no—
417C2×D43—44no—
418C2×D43—42no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—42no—
423C2×D43—816no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—42no—
429C4×C43—42no—
430C4×C43—42no—
431C4×C43#52512yes—
432C4×C43C22×#4111yescharacteristic
433C4×C43C22×#4111yescharacteristic
434Dic43—22no—
435Dic43—22no—
436Dic43—22no—
437Dic43—42no—
438Dic43—42no—
439#3455—431no—
440C2×#518—431no—
441#3123—434no—
442#3122—434no—
443#3118—434no—
444#3118—434no—
445#3093—432no—
446#3077—431no—
447#3077D4311yescharacteristic, complemented
448#3036—431no—
449#3036—431no—
450#3003—432no—
451C4×AGL(1,ℤ/8)—432no—
452C4×AGL(1,ℤ/8)—432no—
453#2921—431no—
454C2×C43—22no—
455C2×C43—44no—
456C2×C43C2×#52511yescharacteristic
457C2×C43#358511yescharacteristic
458C2×C43#358511yescharacteristic
459D43—42no—
460D43—44no—
461D43—82no—
462C23×D4—431no—
463C2×AGL(1,ℤ/8)—432no—
464C2×AGL(1,ℤ/8)—432no—
465#542—432no—
466#542—432no—
467#541—432no—
468#540—432no—
469#539—861no—
470#539—861no—
471#538—861no—
472#538—861no—
473#533C2×D4311yescharacteristic, complemented
474#532—431no—
475#529—862no—
476#529—862no—
477#525—432no—
478#518—434no—
479#518—434no—
480#518—862no—
481#518—862no—
482C4×#41—432no—
483C2×C4×D4—431no—
484C2×C4×D4—431no—
485C2×C4×D4—431no—
486C2×C4×D4—861no—
487C2×C4×D4—861no—
488C2×C4×D4C2×D4311yescharacteristic
489C2×#117—431no—
490C2×#117—431no—
491C22×C22⋊C4—861no—
492C22×C22⋊C4—861no—
493#485—434no—
494#485—434no—
495#482—434no—
496#482—434no—
497#478—434no—
498#478C2×D4314yescomplemented
499#476—432no—
500#476C2×D4312yescomplemented
501#474—432no—
502#474C2×D4312yescomplemented
503#463—434no—
504#463—434no—
505#461—432no—
506#461—432no—
507#459—432no—
508#459—432no—
509#450—434no—
510#450—434no—
511#447—434no—
512#447—434no—
513#442—434no—
514#442—434no—
515#440—434no—
516#440—434no—
517C4×SD16—434no—
518C4×SD16—434no—
519C4×D8—434no—
520C4×D8—434no—
521#433—434no—
522#433—434no—
523#428—432no—
524#428C2×D4312yescomplemented
525#423—431no—
526#423C2×D4311yescharacteristic, complemented
527#418—432no—
528#418C2×D4312yes—
529#417—432no—
530#417—432no—
531#407—432no—
532C4×M16—432no—
533C43#6056411yescharacteristic, complemented, Sylow
534C25—861no—
535C2×#41—432no—
536C22×D4—434no—
537C22×D4—431no—
538C22×D4—862no—
539C22×D4—861no—
540C22×D4—864no—
541C22×D4—864no—
542C22×D4C22×D4311yescharacteristic
543C23×C4—21no—
544C23×C4—431no—
545C23×C4—861no—
546C23×C4—861no—
547C23×C4—861no—
548AGL(1,ℤ/8)—868no—
549AGL(1,ℤ/8)—868no—
550C2×SD16—434no—
551C2×SD16—434no—
552C2×D8—434no—
553C2×D8—434no—
554C2×M16—432no—
555C2×M16C22×D4312yes—
556C4⋊Q8—431no—
557C4⋊Q8C22×D4311yescharacteristic, complemented
558C4⋊Q8C22×D4311yescharacteristic, complemented
559#127—431no—
560#126—862no—
561#126—862no—
562#126—862no—
563#126—862no—
564#125—862no—
565#125—862no—
566#125C22×D4312yescomplemented
567#124—432no—
568#124—862no—
569#124—862no—
570#123—862no—
571#123—862no—
572#123—862no—
573#123—862no—
574#123—862no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—432no—
578C22⋊Q8—432no—
579C22⋊Q8—862no—
580C22⋊Q8—862no—
581#121—432no—
582#121—432no—
583#121—862no—
584#121—862no—
585#121—861no—
586#121—861no—
587#120—862no—
588C4×Q8—21no—
589C4×Q8—21no—
590C4×Q8—432no—
591C4×Q8—432no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—434no—
595C4×D4—434no—
596C4×D4—432no—
597C4×D4—432no—
598C4×D4—432no—
599C4×D4—432no—
600C4×D4—862no—
601C4×D4—862no—
602C4×D4—862no—
603C4×D4—862no—
604C4×D4—864no—
605C4×D4—864no—
606C4×D4—862no—
607C4×D4—862no—
608C4×D4—864no—
609C4×D4—864no—
610C4×D4—861no—
611C4×D4—861no—
612C4×D4—861no—
613C4×D4—861no—
614C4×D4C22×D4312yes—
615C4×D4C22×D4312yes—
616#117—432no—
617#117—432no—
618#117—432no—
619#117—432no—
620#117—434no—
621#117—862no—
622#117—862no—
623#117C22×D4312yes—
624C2×C4⋊C4—431no—
625C2×C4⋊C4—431no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4C22×D4311yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—431no—
630C2×C22⋊C4—431no—
631C2×C22⋊C4—864no—
632C2×C22⋊C4—864no—
633C2×C22⋊C4—864no—
634C2×C22⋊C4—864no—
635C2×C22⋊C4—861no—
636C2×C22⋊C4—861no—
637C2×C22⋊C4—861no—
638C2×C22⋊C4—861no—
639C2×C42—431no—
640C2×C42—862no—
641C2×C42—861no—
642C2×C42C22×D4311yescharacteristic
643#107—434no—
644#107C22×D4314yescomplemented
645#106—434no—
646#106C22×D4314yescomplemented
647C4⋊C8—432no—
648C4⋊C8—432no—
649C4⋊C8C22×D4312yescomplemented
650C4⋊C8C22×D4312yescomplemented
651#103—434no—
652#103—434no—
653#102—434no—
654#102—434no—
655#102—434no—
656#102—434no—
657#102C22×D4314yes—
658#102C22×D4314yes—
659C22⋊C8—434no—
660C22⋊C8—434no—
661#97—434no—
662C4×C8—434no—
663C24—21no—
664C24—431no—
665C24—864no—
666C24—868no—
667C24—861no—
668C24—3442no—
669C24—3442no—
670#41—864no—
671#41—864no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—432no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—434no—
678C2×D4—432no—
679C2×D4—432no—
680C2×D4—862no—
681C2×D4—862no—
682C2×D4—864no—
683C2×D4—868no—
684C2×D4—8616no—
685C2×D4—868no—
686C2×D4—868no—
687C2×D4—862no—
688C2×D4—861no—
689C2×D4—861no—
690C2×D4—861no—
691C2×D4—862no—
692C2×D4#1062190214yes—
693C2×D4C23×D4312yes—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—82no—
698C22×C4—431no—
699C22×C4—431no—
700C22×C4—431no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—862no—
704C22×C4—862no—
705C22×C4—864no—
706C22×C4—864no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—861no—
710C22×C4—862no—
711C22×C4—862no—
712C22×C4—862no—
713C22×C4—3442no—
714C22×C4—3442no—
715C22×C4—3442no—
716C22×C4D4×D4311yescharacteristic
717C22×C4D4×D4311yescharacteristic
718C22×C4C23×D4311yescharacteristic
719SD16—868no—
720SD16—868no—
721D8—868no—
722D8—868no—
723M16—24no—
724M16—864no—
725C2×C8—434no—
726C2×C8C23×D4314yes—
727C4⋊C4—21no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—432no—
733C4⋊C4—432no—
734C4⋊C4—432no—
735C4⋊C4—432no—
736C4⋊C4—432no—
737C4⋊C4—862no—
738C4⋊C4—862no—
739C4⋊C4—862no—
740C4⋊C4—862no—
741C4⋊C4—861no—
742C4⋊C4—861no—
743C4⋊C4—861no—
744C4⋊C4C23×D4312yes—
745C4⋊C4C23×D4312yes—
746C4⋊C4C23×D4312yes—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—432no—
751C22⋊C4—432no—
752C22⋊C4—432no—
753C22⋊C4—432no—
754C22⋊C4—864no—
755C22⋊C4—862no—
756C22⋊C4—862no—
757C22⋊C4—862no—
758C22⋊C4—862no—
759C22⋊C4—864no—
760C22⋊C4—862no—
761C22⋊C4—862no—
762C22⋊C4—864no—
763C22⋊C4—862no—
764C22⋊C4—862no—
765C22⋊C4—862no—
766C22⋊C4—862no—
767C42—22no—
768C42—432no—
769C42—432no—
770C42—864no—
771C42—862no—
772C42—862no—
773C42D4×D4311yescharacteristic
774C42D4×D4311yescharacteristic
775C42C23×D4311yescharacteristic
776C42C23×D4311yescharacteristic
777C23—24no—
778C23—22no—
779C23—42no—
780C23—42no—
781C23—432no—
782C23—8616no—
783C23—862no—
784C23—864no—
785C23—862no—
786C23—862no—
787C23—3444no—
788C23—3444no—
789C23—34416no—
790C23—1721no—
791C23—1721no—
792C23—1722no—
793C23—1722no—
794C23C2×D4×D4311yescharacteristic
795Q8—81no—
796Q8—81no—
797Q8—862no—
798Q8—862no—
799D4—24no—
800D4—22no—
801D4—434no—
802D4—8616no—
803D4—864no—
804D4—862no—
805D4—862no—
806D4—862no—
807D4—3441no—
808D4—3441no—
809D4—3442no—
810D4—3442no—
811D4—1724no—
812D4C2×#1062190214yes—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—82no—
820C2×C4—82no—
821C2×C4—432no—
822C2×C4—432no—
823C2×C4—432no—
824C2×C4—862no—
825C2×C4—864no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4—862no—
830C2×C4—3442no—
831C2×C4—3442no—
832C2×C4—3444no—
833C2×C4—3442no—
834C2×C4—3442no—
835C2×C4—3444no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4—1722no—
839C2×C4—1724no—
840C2×C4C2×D4×D4311yescharacteristic
841C2×C4C2×D4×D4311yescharacteristic
842C2×C4C2×D4×D4311yescharacteristic
843C2×C4C2×D4×D4311yescharacteristic
844C2×C4C2×D4×D4311yescharacteristic
845C2×C4#41×D4312yes—
846C2×C4C2×#1062190212yes—
847C2×C4C24×D4311yescharacteristic
848C8—24no—
849C8—864no—
850C22—21no—
851C22—21no—
852C22—24no—
853C22—48no—
854C22—42no—
855C22—42no—
856C22—862no—
857C22—862no—
858C22—862no—
859C22—864no—
860C22—34416no—
861C22—1724no—
862C22—1728no—
863C22—1722no—
864C22—1722no—
865C22—1722no—
866C22—1722no—
867C22—1722no—
868C22#1458341212yes—
869C22C22×D4×D4311yescharacteristic
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—862no—
878C4—862no—
879C4—862no—
880C4—1722no—
881C4—1722no—
882C4#1458341212yes—
883C4C2×#41×D4311yescharacteristic
884C4C22×#1062190211yescharacteristic
885C2—22no—
886C2—44no—
887C2—3442no—
888C2—1722no—
889C2—1724no—
890C2C2×#1458341211yescharacteristic
891C2#1914937111yescharacteristic
892C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3077C2
socleC22×C43C23×D4
hypercenter#3077D43
hypocenterC43#60564
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #19147987C2semidirect
2. C2×#14583371C2semidirect
3. #19144849C2semidirect
4. #19144840C2semidirect
5. #19144786C2semidirect
6. #19144784C2semidirect
7. #19144529C2semidirect
8. #19144388C2semidirect
9. #19144061C2semidirect
10. #19144059C2semidirect
11. #19143824C2semidirect
12. #19143402C2semidirect
13. #19143399C2semidirect
14. #19143232C2semidirect
15. C43×#3077C2semidirect
19. #14583523C22semidirect
20. #14583523C22semidirect
21. #14583512C22semidirect
22. #14583505C22semidirect
27. #14583449C22semidirect
35. #14583367C22semidirect
45. #14583243C22semidirect
46. #14583242C22semidirect
47. #14583226C22semidirect
48. #14583225C22semidirect
49. #14583196C22semidirect
50. #14583186C22semidirect
51. #14583176C22semidirect
52. #14583115C22semidirect
53. #14583114C22semidirect
54. #14583105C22semidirect
55. #14583104C22semidirect
56. #14583095C22semidirect
57. #14583094C22semidirect
62. #14583010C22semidirect
63. #14583008C22semidirect
64. #14582998C22semidirect
65. #14582996C22semidirect
66. #14582990C22semidirect
67. #14582986C22semidirect
68. #14582981C22semidirect
69. #14582979C22semidirect
70. #14582959C22semidirect
71. #14582959C22semidirect
72. #14582942C22semidirect
73. #14582923C22semidirect
75. #14582901C22semidirect
76. #14582898C22semidirect
78. M16×Dic43C22semidirect
79. C43×#533C22semidirect
81. C43×#478C22semidirect
82. C43×#476C22semidirect
83. C43×#474C22semidirect
84. C43×#428C22semidirect
85. C43×#423C22semidirect
106. #13063325C23semidirect
107. #13063322C23semidirect
116. #13063313C23semidirect
133. #13063290C23semidirect
134. #13063290C23semidirect
147. #13063287C23semidirect
148. #13063287C23semidirect
178. #13063258C23semidirect
179. #13063256C23semidirect
180. C4⋊(C43⋊C8)C23semidirect
181. C4⋊(C43⋊C8)C23semidirect
182. #13063250C23semidirect
183. #13063248C23semidirect
184. #13063247C23semidirect
187. #13063245C23semidirect
190. #13063235C23semidirect
191. C8×Dic43C23semidirect
195. C4⋊Q8×C43C23semidirect
196. C4⋊Q8×C43C23semidirect
197. #125×C43C23semidirect
210. #107×C43C23semidirect
211. #106×C43C23semidirect
212. C4⋊C8×C43C23semidirect
213. C4⋊C8×C43C23semidirect
447. #3077D43semidirect
473. #533C2×D43semidirect
498. #478C2×D43semidirect
500. #476C2×D43semidirect
502. #474C2×D43semidirect
524. #428C2×D43semidirect
526. #423C2×D43semidirect
533. C43#60564semidirect
557. C4⋊Q8C22×D43semidirect
558. C4⋊Q8C22×D43semidirect
566. #125C22×D43semidirect
644. #107C22×D43semidirect
646. #106C22×D43semidirect
649. C4⋊C8C22×D43semidirect
650. C4⋊C8C22×D43semidirect

Maximal subgroups

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

subgroupindex
#191479872
C2×#145833712
#191448492
#191448402
#191447862
#191447842
#191445292
#191443882
#191440612
#191440592
#191438242
#191434022
#191433992
#191432322
C43×#30772
#6056443