Finite Group Databasebeta

← #25968904

Subgroups — #25968904

Order 11008.

2036 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583455C211yesmaximal, characteristic, complemented
2#532×D43C211yesmaximal, characteristic
3#19145794C212yesmaximal, complemented
4#19145788C212yesmaximal, complemented
5#19145787C211yesmaximal, characteristic, complemented
6#19145785C211yesmaximal, characteristic, complemented
7#19145781C211yesmaximal, characteristic, complemented
8#19145730C214yesmaximal, complemented
9#19145721C212yesmaximal, complemented
10#19145714C212yesmaximal, complemented
11#19145140C212yesmaximal, complemented
12#19144968C212yesmaximal, complemented
13#19144532C212yesmaximal, complemented
14#19144530C212yesmaximal, complemented
15#19144390C214yesmaximal, complemented
16#19143225C211yesmaximal, characteristic, complemented
17C43×#3234C211yesmaximal, characteristic, complemented
18C2×#41×D43—21no—
19#14583455—21no—
20#14583455—21no—
21#14583455—21no—
22#14583455—21no—
23#14583455C2212yes—
24#14583455C2212yes—
25#14583455C2212yescomplemented
26#14583455C2212yescomplemented
27#14583450C2211yescharacteristic
28#14583449C2211yescharacteristic
29#14583448—21no—
30#14583447C2211yescharacteristic
31#14583446—21no—
32#14583446C2212yes—
33#14583445—21no—
34#14583444—21no—
35#14583444C2212yes—
36C2×#13063324C2211yescharacteristic, complemented
37C2×#13063324C2211yescharacteristic, complemented
38C4⋊Q8×D43C2211yescharacteristic
39#127×D43C2211yescharacteristic
40C2×#13063317C2211yescharacteristic, complemented
41#124×D43—21no—
42C2×#13063303—21no—
43C2×#13063303—21no—
44#121×D43—21no—
45#121×D43C2212yes—
46C2×#13063290—21no—
47C2×#13063290—21no—
48C4×D4×D43—21no—
49C4×D4×D43C2212yes—
50C2×#13063283C2211yescharacteristic
51C2×#13063283C2211yescharacteristic
52C2×C42×D43C2211yescharacteristic
53#14583309C2212yescomplemented
54#14583308C2212yescomplemented
55#14583305C2212yescomplemented
56#14583303C2214yescomplemented
57#14583296C2214yescomplemented
58#14583265C2212yescomplemented
59#14583264C2212yescomplemented
60#14583263C2212yescomplemented
61#14583244C2214yescomplemented
62#14583244C2214yescomplemented
63#14583226C2214yescomplemented
64#14583225C2214yescomplemented
65#14583222C2214yescomplemented
66#14583221C2214yescomplemented
67#14583218C2212yescomplemented
68#14583217C2212yescomplemented
69#14583215C2212yescomplemented
70#14583213C2212yescomplemented
71#14583212C2212yescomplemented
72#14583210C2212yescomplemented
73#14583200C2214yescomplemented
74#14583199C2214yescomplemented
75#14583196C2214yescomplemented
76#14583188C2214yescomplemented
77#14583187C2214yescomplemented
78#14583178C2214yescomplemented
79#14583177C2214yescomplemented
80#14582956C2211yescharacteristic, complemented
81#14582954C2212yescomplemented
82#14582951C2212yescomplemented
83#14582949C2212yescomplemented
84#14582940C2214yes—
85#14582938C2214yes—
86#14582921C2212yes—
87#14582902C2214yes—
88#14582902C2214yes—
89#14582861C2212yes—
90#14582851C2212yes—
91C43×#532C2211yescharacteristic
92C2×#125×C43C2211yescharacteristic, complemented
93C43×#501C2212yescomplemented
94C43×#490C2212yescomplemented
95C43×#481C2212yescomplemented
96C43×#480C2212yescomplemented
97C43×#478C2214yescomplemented
98C43×#432C2211yescharacteristic, complemented
99C2×#10621902—21no—
100C2×#10621898—21no—
101C2×#10621898—22no—
102C2×#10621900—22no—
103C2×#10621900—21no—
104#41×D43—48no—
105C22×Dic86—21no—
106C22×Dic86—21no—
107C2×Q8×D43—21no—
108C2×D4×D43—22no—
109C2×D4×D43—21no—
110C2×D4×D43—21no—
111C2×D4×D43C2312yes—
112C22×C4×D43—22no—
113C22×C4×D43D411yescharacteristic
114C22×C4×D43D411yescharacteristic
115C22×C4×D43C2311yescharacteristic
116C2×#10621872C2314yes—
117#13063325C2311yescharacteristic
118#13063324—21no—
119#13063324—21no—
120#13063324—21no—
121#13063324—21no—
122#13063324—21no—
123#13063324C2312yes—
124#13063324C2312yes—
125#13063324C2312yes—
126#13063324C2312yes—
127#13063324C2312yes—
128#13063323—21no—
129#13063322C2311yescharacteristic
130#13063321—21no—
131#13063321—21no—
132#13063321C2312yes—
133#13063317—21no—
134#13063317—21no—
135#13063317C2312yes—
136#13063317C2312yes—
137#13063314—21no—
138#13063313—21no—
139#13063312—21no—
140#13063311—22no—
141#13063311—22no—
142#13063303—22no—
143#13063303—22no—
144#13063303—22no—
145#13063303—22no—
146#13063303—22no—
147#13063303—22no—
148#13063303—22no—
149#13063303—22no—
150#13063300—21no—
151#13063300C2312yes—
152#13063299—21no—
153#13063299C2312yes—
154#13063298—22no—
155#13063298—22no—
156#13063297—22no—
157#13063297—22no—
158#13063296—21no—
159#13063296C2312yes—
160#13063290—22no—
161#13063290—22no—
162#13063290—22no—
163#13063290—22no—
164#13063290—22no—
165#13063290—22no—
166#13063290—22no—
167#13063290—22no—
168C4×D172—21no—
169C4×D172C2312yes—
170D4×Dic43—21no—
171D4×Dic43C2312yes—
172#13063287—21no—
173#13063287C2312yes—
174C4×C22⋊D43—22no—
175C4×C22⋊D43—22no—
176(C22⋊D43)⋊C4—22no—
177(C22⋊D43)⋊C4—22no—
178#13063283—21no—
179#13063283—21no—
180#13063283—21no—
181#13063283—21no—
182#13063283C2312yes—
183#13063283C2312yes—
184#13063283C2312yes—
185#13063283C2312yes—
186C2×C4⋊Dic43C2311yescharacteristic
187C2×C4⋊Dic43C2311yescharacteristic
188C2×Dic43⋊C4—21no—
189C2×Dic43⋊C4—21no—
190C2×Dic43⋊C4—21no—
191C2×Dic43⋊C4—21no—
192C4⋊C4×D43—21no—
193C4⋊C4×D43C2312yes—
194C2×(C2×D43)⋊C4—21no—
195C2×(C2×D43)⋊C4—21no—
196C22⋊C4×D43—22no—
197C22⋊C4×D43—22no—
198C2×C4×Dic43—21no—
199C2×C4×Dic43—21no—
200C2×C4×Dic43D411yescharacteristic
201C2×C4×Dic43D411yescharacteristic
202C2×C4×Dic43C2311yescharacteristic
203C42×D43D411yescharacteristic
204C42×D43D411yescharacteristic
205C42×D43D411yescharacteristic
206C42×D43D411yescharacteristic
207C42×D43C2311yescharacteristic
208C42×D43C2311yescharacteristic
209C42×D43C2311yescharacteristic
210C42×D43C2311yescharacteristic
211#13063259C2314yes—
212#13063258C2314yes—
213#13063258C2314yes—
214#13063257C2314yes—
215#13063256C2314yes—
216#13063256C2314yes—
217C4⋊(C43⋊C8)C2312yes—
218Dic43⋊C8C2314yes—
219#13063247C2314yes—
220#13063247C2314yes—
221#13063246C2314yes—
222#13063246C2314yes—
223#13063245C2314yes—
224#13063245C2314yes—
225C22⋊(C43⋊C8)C2312yes—
226(C2×D43)⋊C8C2314yes—
227#13063236C2312yes—
228C8×Dic43C2314yes—
229C2×#41×C43—21no—
230C4⋊Q8×C43C2311yescharacteristic
231#127×C43C2311yescharacteristic
232#125×C43—21no—
233#125×C43—21no—
234#125×C43C2312yes—
235#125×C43C2312yes—
236#124×C43—21no—
237#121×C43—21no—
238#121×C43C2312yes—
239C4×D4×C43—21no—
240C4×D4×C43C2312yes—
241C2×C4⋊C4×C43—21no—
242C2×C4⋊C4×C43—21no—
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C42×C43C2311yescharacteristic
246#107×C43C2314yes—
247#106×C43C2314yes—
248C4⋊C8×C43C2312yes—
249#102×C43C2314yes—
250#102×C43C2314yes—
251C22⋊C8×C43C2312yes—
252#97×C43C2312yes—
253C23×D43—22no—
254C23×D43C2×D411yescharacteristic
255#41×C43—44no—
256C2×Q8×C43—21no—
257C2×D4×C43—21no—
258C2×D4×C43—21no—
259C2×D4×C43—22no—
260C2×D4×C43C2412yes—
261C22×C4×C43—22no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2×D411yescharacteristic
266C22×C4×C43C2411yescharacteristic
267C2×C22⋊D43—22no—
268C2×C22⋊D43—22no—
269C2×C22⋊D43—22no—
270C2×C22⋊D43—22no—
271C2×C22⋊D43—22no—
272C22×Dic43—22no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43C2×D411yescharacteristic
276C22×Dic43C2×D411yescharacteristic
277C22×Dic43C2×D411yescharacteristic
278#10621902—44no—
279Q8×D43—44no—
280#10621900—44no—
281#10621900—48no—
282D4×D43—28no—
283D4×D43—48no—
284D4×D43—44no—
285D4×D43—44no—
286#10621898—48no—
287#10621898—44no—
288C2×D172—21no—
289C2×D172—21no—
290C2×D172—22no—
291C2×D172C2412yes—
292C2×C4×D43—24no—
293C2×C4×D43—24no—
294C2×C4×D43—22no—
295C2×C4×D43—22no—
296C2×C4×D43—22no—
297C2×C4×D43—42no—
298C2×C4×D43—48no—
299C2×C4×D43C2×D411yescharacteristic
300C2×C4×D43C2×D411yescharacteristic
301C2×C4×D43C2×D411yescharacteristic
302C2×C4×D43C2×D411yescharacteristic
303C2×C4×D43C2×D411yescharacteristic
304C2×C4×D43C2×D411yescharacteristic
305C2×C4×D43C2×D411yescharacteristic
306C2×C4×D43C2×D411yescharacteristic
307C2×C4×D43C2×D411yescharacteristic
308C2×C4×D43C2×D411yescharacteristic
309C2×C4×D43C2411yescharacteristic
310C2×C4×D43C2411yescharacteristic
311C2×Dic86—21no—
312C2×Dic86—22no—
313C2×Dic86—22no—
314C2×Dic86—22no—
315C2×Dic86—22no—
316C2×Dic86—22no—
317C2×Dic86—44no—
318C2×Dic86—44no—
319C2×C8×C43C2414yes—
320C4⋊C4×C43—22no—
321C4⋊C4×C43—22no—
322C4⋊C4×C43—22no—
323C4⋊C4×C43—22no—
324C4⋊C4×C43—21no—
325C4⋊C4×C43—21no—
326C4⋊C4×C43—21no—
327C4⋊C4×C43C2412yes—
328C4⋊C4×C43C2412yes—
329C4⋊C4×C43C2412yes—
330C22⋊C4×C43—22no—
331C22⋊C4×C43—22no—
332C42×C43C2×D411yescharacteristic
333C42×C43C2×D411yescharacteristic
334C42×C43C2411yescharacteristic
335C42×C43C2411yescharacteristic
336C22⋊Dic43—22no—
337C22⋊Dic43—22no—
338(C2×D43)⋊C4—22no—
339(C2×D43)⋊C4—22no—
340(C2×D43)⋊C4—22no—
341(C2×D43)⋊C4—22no—
342(C2×D43)⋊C4—22no—
343(C2×D43)⋊C4—22no—
344(C2×D43)⋊C4—22no—
345(C2×D43)⋊C4—22no—
346C4⋊Dic43—21no—
347C4⋊Dic43—21no—
348C4⋊Dic43—21no—
349C4⋊Dic43C2412yes—
350C4⋊Dic43C2412yes—
351C4⋊Dic43C2412yes—
352Dic43⋊C4—22no—
353Dic43⋊C4—22no—
354Dic43⋊C4—22no—
355Dic43⋊C4—22no—
356Dic43⋊C4—22no—
357Dic43⋊C4—22no—
358Dic43⋊C4—22no—
359Dic43⋊C4—22no—
360Dic43⋊C4—22no—
361Dic43⋊C4—22no—
362C4×Dic43—22no—
363C4×Dic43—22no—
364C4×Dic43—22no—
365C4×Dic43—22no—
366C4×Dic43C2×D411yescharacteristic
367C4×Dic43C2×D411yescharacteristic
368C4×Dic43C2×D411yescharacteristic
369C4×Dic43C2×D411yescharacteristic
370C4×Dic43C2×D411yescharacteristic
371C4×Dic43C2×D411yescharacteristic
372C4×Dic43C2×D411yescharacteristic
373C4×Dic43C2×D411yescharacteristic
374C4×Dic43C2×D411yescharacteristic
375C4×Dic43C2×D411yescharacteristic
376C4×Dic43C2411yescharacteristic
377C4×Dic43C2411yescharacteristic
378C2×C43⋊C8C2414yes—
379#10621872—28no—
380C23×C43—22no—
381C23×C43C22×D411yescharacteristic
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—41no—
386C22×D43—44no—
387C22×D43—44no—
388C22×D43—44no—
389C22×D43C22×D411yescharacteristic
390C22×D43C22×D411yescharacteristic
391Q8×C43—42no—
392D4×C43—24no—
393D4×C43—42no—
394D4×C43—42no—
395D4×C43—44no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—41no—
402C2×C4×C43—44no—
403C2×C4×C43—42no—
404C2×C4×C43—42no—
405C2×C4×C43C22×D411yescharacteristic
406C2×C4×C43C22×D411yescharacteristic
407C2×C4×C43C22×D411yescharacteristic
408C2×C4×C43C22×D411yescharacteristic
409C2×C4×C43C22×D411yescharacteristic
410C2×C4×C43C2511yescharacteristic
411C22⋊D43—44no—
412C22⋊D43—44no—
413C22⋊D43—44no—
414C22⋊D43—44no—
415C22⋊D43—44no—
416C2×Dic43—22no—
417C2×Dic43—22no—
418C2×Dic43—22no—
419C2×Dic43—22no—
420C2×Dic43—22no—
421C2×Dic43—42no—
422C2×Dic43—42no—
423C2×Dic43—44no—
424C2×Dic43AGL(1,ℤ/8)14yes—
425C2×Dic43C22×D411yescharacteristic
426C2×Dic43C22×D411yescharacteristic
427C2×Dic43C22×D411yescharacteristic
428C2×Dic43C22×D411yescharacteristic
429C2×Dic43C22×D411yescharacteristic
430C2×Dic43C22×D411yescharacteristic
431D172—24no—
432D172—42no—
433D172—42no—
434D172—44no—
435C4×D43—22no—
436C4×D43—22no—
437C4×D43—22no—
438C4×D43—22no—
439C4×D43—22no—
440C4×D43—22no—
441C4×D43—22no—
442C4×D43—22no—
443C4×D43—22no—
444C4×D43—41no—
445C4×D43—41no—
446C4×D43—44no—
447C4×D43—44no—
448C4×D43—44no—
449C4×D432−1+414yes—
450Dic86—44no—
451Dic86—42no—
452Dic86—44no—
453Dic86—44no—
454Dic86—44no—
455Dic86—44no—
456C8×C43—24no—
457C43⋊C8—24no—
458#60864—431nomaximal, Sylow
459C22×C43—21no—
460C22×C43—21no—
461C22×C43—42no—
462C22×C43—42no—
463C22×C43—42no—
464C22×C43C2×AGL(1,ℤ/8)12yes—
465C22×C43C23×D411yescharacteristic
466C2×D43—21no—
467C2×D43—21no—
468C2×D43—21no—
469C2×D43—21no—
470C2×D43—21no—
471C2×D43—44no—
472C2×D43—42no—
473C2×D43—42no—
474C2×D43—42no—
475C2×D43—88no—
476C2×D43#53612yes—
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—21no—
480C4×C43—21no—
481C4×C43—21no—
482C4×C43—42no—
483C4×C43—42no—
484C4×C43—42no—
485C4×C43C2×2−1+412yes—
486Dic43—21no—
487Dic43—21no—
488Dic43—42no—
489Dic43—42no—
490Dic43—42no—
491Dic43#53612yes—
492Dic43C2×AGL(1,ℤ/8)12yes—
493Dic43C2×AGL(1,ℤ/8)12yes—
494Dic43#57512yes—
495C2×#533—431no—
496C2×#532—431no—
497#3235—432no—
498#3235—432no—
499#3234—431no—
500#3234—431no—
501#3234—431no—
502#3234D4311yescharacteristic, complemented
503#3228—434no—
504#3227—432no—
505#3226—432no—
506#3165—432no—
507#3138—432no—
508#3094—432no—
509#3094—432no—
510#3077—434no—
511#2920—431no—
512C2×C43—22no—
513C2×C43—82no—
514C2×C43C2×#53611yescharacteristic
515C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
516C2×C43C2×#57511yescharacteristic
517D43—22no—
518D43—41no—
519D43—82no—
520C22×#41—861no—
521#533—432no—
522#533—432no—
523#533—432no—
524#533—432no—
525#533—861no—
526#533—861no—
527#533—861no—
528#533—861no—
529#532—431no—
530#532—431no—
531#532—432no—
532#532—432no—
533#532—431no—
534#532—861no—
535#532—861no—
536#532—861no—
537#532—861no—
538#532C2×D4311yescharacteristic
539C2×C4⋊Q8—431no—
540C2×C4⋊Q8—431no—
541C2×C4⋊Q8—431no—
542C2×#127—431no—
543C2×#125—431no—
544C2×#125C2×D4311yescharacteristic, complemented
545C2×#124—861no—
546C2×C22⋊Q8—861no—
547C2×C22⋊Q8—861no—
548C2×#121—432no—
549C2×#121—861no—
550C2×C4×Q8—861no—
551C2×C4×Q8—861no—
552C2×C4×D4—432no—
553C2×C4×D4—861no—
554C2×#117—431no—
555C2×#117—431no—
556C22×C42—431no—
557#501—432no—
558#501—432no—
559#501—432no—
560#501C2×D4312yescomplemented
561#500—434no—
562#498—434no—
563#490—432no—
564#490—432no—
565#490—432no—
566#490C2×D4312yescomplemented
567#486—434no—
568#486—434no—
569#482—434no—
570#482—434no—
571#482—434no—
572#482—434no—
573#481—432no—
574#481—432no—
575#481—432no—
576#481C2×D4312yescomplemented
577#480—432no—
578#480—432no—
579#480—432no—
580#480C2×D4312yescomplemented
581#478—434no—
582#478—434no—
583#478—434no—
584#478C2×D4314yescomplemented
585#476—434no—
586#476—434no—
587#474—434no—
588#474—434no—
589#432—431no—
590#432—432no—
591#432C2×D4311yescharacteristic, complemented
592#431—432no—
593#431—432no—
594#428—434no—
595#428—434no—
596#423—432no—
597#418—434no—
598#418—434no—
599#407—432no—
600C4×M16—432no—
601C43#6086411yescharacteristic, complemented, Sylow
602C2×#41—21no—
603C2×#41—862no—
604C2×#41—862no—
605C2×#41—861no—
606C2×#41—861no—
607C2×#41—861no—
608C2×#41—1728no—
609C22×Q8—861no—
610C22×Q8—861no—
611C22×Q8—861no—
612C22×D4—432no—
613C22×D4—861no—
614C22×D4—861no—
615C22×D4—862no—
616C23×C4—431no—
617C23×C4—431no—
618C23×C4—431no—
619C23×C4—862no—
620C2×M16—434no—
621C4⋊Q8—432no—
622C4⋊Q8—432no—
623C4⋊Q8—432no—
624C4⋊Q8—432no—
625C4⋊Q8—432no—
626C4⋊Q8—431no—
627C4⋊Q8—861no—
628C4⋊Q8—861no—
629C4⋊Q8—861no—
630C4⋊Q8—861no—
631C4⋊Q8—861no—
632C4⋊Q8—861no—
633C4⋊Q8C22×D4311yescharacteristic
634#127—432no—
635#127—431no—
636#127—861no—
637#127—861no—
638#127C22×D4311yescharacteristic
639#125—21no—
640#125—21no—
641#125—432no—
642#125—432no—
643#125—861no—
644#125—861no—
645#125C22×D4312yes—
646#125C22×D4312yes—
647#124—21no—
648#124—862no—
649#124—862no—
650#124—861no—
651#124—861no—
652#124—861no—
653C22⋊Q8—862no—
654C22⋊Q8—862no—
655C22⋊Q8—862no—
656C22⋊Q8—862no—
657C22⋊Q8—862no—
658C22⋊Q8—862no—
659C22⋊Q8—862no—
660C22⋊Q8—862no—
661#121—21no—
662#121—432no—
663#121—432no—
664#121—432no—
665#121—862no—
666#121—862no—
667#121—861no—
668#121—862no—
669#121—861no—
670#121—862no—
671#121—861no—
672#121C22×D4312yes—
673C4×Q8—862no—
674C4×Q8—862no—
675C4×Q8—862no—
676C4×Q8—862no—
677C4×Q8—862no—
678C4×Q8—862no—
679C4×Q8—862no—
680C4×Q8—862no—
681C4×D4—21no—
682C4×D4—432no—
683C4×D4—432no—
684C4×D4—432no—
685C4×D4—862no—
686C4×D4—862no—
687C4×D4—861no—
688C4×D4—862no—
689C4×D4—862no—
690C4×D4—861no—
691C4×D4—861no—
692C4×D4C22×D4312yes—
693#117—432no—
694#117—432no—
695#117—432no—
696#117—432no—
697#117—861no—
698#117—861no—
699#117—861no—
700#117—861no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—431no—
704C2×C4⋊C4—431no—
705C2×C4⋊C4—432no—
706C2×C4⋊C4—861no—
707C2×C4⋊C4—861no—
708C2×C4⋊C4—861no—
709C2×C4⋊C4—861no—
710C2×C4⋊C4—861no—
711C2×C4⋊C4C22×D4311yescharacteristic
712C2×C4⋊C4C22×D4311yescharacteristic
713C2×C22⋊C4—862no—
714C2×C22⋊C4—862no—
715C2×C22⋊C4—861no—
716C2×C22⋊C4—861no—
717C2×C42—431no—
718C2×C42—431no—
719C2×C42—431no—
720C2×C42—431no—
721C2×C42—431no—
722C2×C42—431no—
723C2×C42—431no—
724C2×C42—431no—
725C2×C42—431no—
726C2×C42—431no—
727C2×C42—431no—
728C2×C42—861no—
729C2×C42—861no—
730C2×C42C22×D4311yescharacteristic
731#107—434no—
732#107—434no—
733#107—434no—
734#107C22×D4314yes—
735#106—434no—
736#106—434no—
737#106—434no—
738#106C22×D4314yes—
739C4⋊C8—434no—
740C4⋊C8—432no—
741C4⋊C8C22×D4312yes—
742#102—434no—
743#102—434no—
744#102—434no—
745#102—434no—
746#102—434no—
747#102—434no—
748#102C22×D4314yes—
749#102C22×D4314yes—
750C22⋊C8—432no—
751C22⋊C8—434no—
752C22⋊C8C22×D4312yes—
753#97—432no—
754#97C22×D4312yes—
755C4×C8—434no—
756C24—431no—
757C24—862no—
758#41—44no—
759#41—1724no—
760#41—1728no—
761#41—1728no—
762#41—1724no—
763#41—1724no—
764C2×Q8—21no—
765C2×Q8—862no—
766C2×Q8—862no—
767C2×Q8—862no—
768C2×Q8—862no—
769C2×Q8—862no—
770C2×Q8—861no—
771C2×Q8—1724no—
772C2×Q8—1724no—
773C2×Q8—1724no—
774C2×D4—22no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—432no—
778C2×D4—862no—
779C2×D4—868no—
780C2×D4—862no—
781C2×D4—862no—
782C2×D4—862no—
783C2×D4—862no—
784C2×D4—862no—
785C2×D4—861no—
786C2×D4—861no—
787C2×D4—1724no—
788C2×D4—1724no—
789C2×D4—1728no—
790C2×D4C23×D4312yes—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—431no—
795C22×C4—431no—
796C22×C4—431no—
797C22×C4—431no—
798C22×C4—431no—
799C22×C4—431no—
800C22×C4—431no—
801C22×C4—431no—
802C22×C4—431no—
803C22×C4—431no—
804C22×C4—431no—
805C22×C4—431no—
806C22×C4—431no—
807C22×C4—431no—
808C22×C4—431no—
809C22×C4—864no—
810C22×C4—864no—
811C22×C4—862no—
812C22×C4—862no—
813C22×C4—862no—
814C22×C4—861no—
815C22×C4—861no—
816C22×C4—862no—
817C22×C4—1722no—
818C22×C4—1728no—
819C22×C4D4×D4311yescharacteristic
820C22×C4D4×D4311yescharacteristic
821C22×C4C23×D4311yescharacteristic
822M16—868no—
823C2×C8—434no—
824C2×C8C23×D4314yes—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—432no—
833C4⋊C4—432no—
834C4⋊C4—432no—
835C4⋊C4—862no—
836C4⋊C4—862no—
837C4⋊C4—862no—
838C4⋊C4—862no—
839C4⋊C4—862no—
840C4⋊C4—862no—
841C4⋊C4—861no—
842C4⋊C4—861no—
843C4⋊C4—861no—
844C4⋊C4—862no—
845C4⋊C4—862no—
846C4⋊C4—862no—
847C4⋊C4—862no—
848C4⋊C4C23×D4312yes—
849C4⋊C4C23×D4312yes—
850C4⋊C4C23×D4312yes—
851C22⋊C4—22no—
852C22⋊C4—22no—
853C22⋊C4—862no—
854C22⋊C4—862no—
855C22⋊C4—862no—
856C22⋊C4—862no—
857C22⋊C4—862no—
858C22⋊C4—862no—
859C22⋊C4—862no—
860C22⋊C4—862no—
861C22⋊C4—862no—
862C22⋊C4—862no—
863C42—431no—
864C42—431no—
865C42—431no—
866C42—431no—
867C42—431no—
868C42—431no—
869C42—431no—
870C42—431no—
871C42—431no—
872C42—431no—
873C42—431no—
874C42—431no—
875C42—862no—
876C42—862no—
877C42—862no—
878C42—862no—
879C42D4×D4311yescharacteristic
880C42D4×D4311yescharacteristic
881C42C23×D4311yescharacteristic
882C42C23×D4311yescharacteristic
883C23—22no—
884C23—431no—
885C23—431no—
886C23—862no—
887C23—862no—
888C23—862no—
889C23—1721no—
890C23—1724no—
891C23—1724no—
892C23—1724no—
893C23C2×D4×D4311yescharacteristic
894Q8—42no—
895Q8—1722no—
896Q8—1724no—
897Q8—1724no—
898Q8—1724no—
899Q8—1724no—
900Q8—1724no—
901D4—24no—
902D4—42no—
903D4—42no—
904D4—44no—
905D4—864no—
906D4—1722no—
907D4—1722no—
908D4—1724no—
909D4—1724no—
910D4—1724no—
911D4—1724no—
912D4—1724no—
913D4—1724no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—41no—
920C2×C4—44no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—434no—
924C2×C4—431no—
925C2×C4—431no—
926C2×C4—431no—
927C2×C4—431no—
928C2×C4—434no—
929C2×C4—431no—
930C2×C4—431no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—862no—
934C2×C4—862no—
935C2×C4—862no—
936C2×C4—862no—
937C2×C4—862no—
938C2×C4—862no—
939C2×C4—862no—
940C2×C4—862no—
941C2×C4—862no—
942C2×C4—862no—
943C2×C4—862no—
944C2×C4—862no—
945C2×C4—1721no—
946C2×C4—1721no—
947C2×C4—1724no—
948C2×C4—1724no—
949C2×C4—1724no—
950C2×C4—1724no—
951C2×C4—1722no—
952C2×C4—1722no—
953C2×C4C2×D4×D4311yescharacteristic
954C2×C4C2×D4×D4311yescharacteristic
955C2×C4C2×D4×D4311yescharacteristic
956C2×C4C2×D4×D4311yescharacteristic
957C2×C4C2×D4×D4311yescharacteristic
958C2×C4C24×D4311yescharacteristic
959C8—24no—
960C8—864no—
961C22—21no—
962C22—21no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—432no—
967C22—861no—
968C22—861no—
969C22—861no—
970C22—861no—
971C22—861no—
972C22—3448no—
973C22—1724no—
974C22—1722no—
975C22—1722no—
976C22—1722no—
977C22AGL(1,ℤ/8)×D4312yes—
978C22C22×D4×D4311yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—432no—
988C4—432no—
989C4—432no—
990C4—432no—
991C4—861no—
992C4—861no—
993C4—1722no—
994C4—1722no—
995C4—1722no—
996C42−1+4×D4312yes—
997C2—22no—
998C2—82no—
999C2—862no—
1000C2—3442no—
1001C2—1721no—
1002C2#536×D4311yescharacteristic
1003C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1004C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3234C2
socleC22×C43C23×D4
prime radical#532×D43C2
hypercenter#3234D43
hypocenterC43#60864
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3234

Complements

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

NH ≅ G/Ntype
1. C2×#14583455C2semidirect
3. #19145794C2semidirect
4. #19145788C2semidirect
5. #19145787C2semidirect
6. #19145785C2semidirect
7. #19145781C2semidirect
8. #19145730C2semidirect
9. #19145721C2semidirect
10. #19145714C2semidirect
11. #19145140C2semidirect
12. #19144968C2semidirect
13. #19144532C2semidirect
14. #19144530C2semidirect
15. #19144390C2semidirect
16. #19143225C2semidirect
17. C43×#3234C2semidirect
25. #14583455C22semidirect
26. #14583455C22semidirect
36. C2×#13063324C22semidirect
37. C2×#13063324C22semidirect
40. C2×#13063317C22semidirect
53. #14583309C22semidirect
54. #14583308C22semidirect
55. #14583305C22semidirect
56. #14583303C22semidirect
57. #14583296C22semidirect
58. #14583265C22semidirect
59. #14583264C22semidirect
60. #14583263C22semidirect
61. #14583244C22semidirect
62. #14583244C22semidirect
63. #14583226C22semidirect
64. #14583225C22semidirect
65. #14583222C22semidirect
66. #14583221C22semidirect
67. #14583218C22semidirect
68. #14583217C22semidirect
69. #14583215C22semidirect
70. #14583213C22semidirect
71. #14583212C22semidirect
72. #14583210C22semidirect
73. #14583200C22semidirect
74. #14583199C22semidirect
75. #14583196C22semidirect
76. #14583188C22semidirect
77. #14583187C22semidirect
78. #14583178C22semidirect
79. #14583177C22semidirect
80. #14582956C22semidirect
81. #14582954C22semidirect
82. #14582951C22semidirect
83. #14582949C22semidirect
92. C2×#125×C43C22semidirect
93. C43×#501C22semidirect
94. C43×#490C22semidirect
95. C43×#481C22semidirect
96. C43×#480C22semidirect
97. C43×#478C22semidirect
98. C43×#432C22semidirect
502. #3234D43semidirect
544. C2×#125C2×D43semidirect
560. #501C2×D43semidirect
566. #490C2×D43semidirect
576. #481C2×D43semidirect
580. #480C2×D43semidirect
584. #478C2×D43semidirect
591. #432C2×D43semidirect
601. C43#60864semidirect

Maximal subgroups

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

subgroupindex
C2×#145834552
#532×D432
#191457942
#191457882
#191457872
#191457852
#191457812
#191457302
#191457212
#191457142
#191451402
#191449682
#191445322
#191445302
#191443902
#191432252
C43×#32342
#6086443