Finite Group Databasebeta

← #25063540

Subgroups — #25063540

Order 11008.

994 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148186C211yesmaximal, characteristic
2#19143557C211yesmaximal, characteristic, complemented
3#19143160C211yesmaximal, characteristic, complemented
4#19133060C211yesmaximal, characteristic, complemented
5#19133059C211yesmaximal, characteristic, complemented
6#19133044C211yesmaximal, characteristic, complemented
7#19133035C211yesmaximal, characteristic, complemented
8#19133031C211yesmaximal, characteristic, complemented
9#19133022C211yesmaximal, characteristic, complemented
10#19133007C211yesmaximal, characteristic, complemented
11#19132992C211yesmaximal, characteristic, complemented
12#19132980C211yesmaximal, characteristic, complemented
13#19132979C211yesmaximal, characteristic, complemented
14Q8⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1483C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17#14583633—21no—
18#14583631C411yescharacteristic
19#14583626C411yescharacteristic
20#14583620C411yescharacteristic
21#14583616—21no—
22#14583602C411yescharacteristic
23#14583600—21no—
24#14583596C411yescharacteristic
25#14583594—21no—
26#14583567C411yescharacteristic
27#14583559C411yescharacteristic
28#14583557C411yescharacteristic
29#14583446—21no—
30#14583446C2211yescharacteristic
31#14583436C2211yescharacteristic
32#14583429—21no—
33#14583427—21no—
34C4×#10621898C2211yescharacteristic
35C4×#10621898C2211yescharacteristic
36#14583367—21no—
37C4×#10621900C2211yescharacteristic
38C4×Q8×D43C2211yescharacteristic
39#14583027—21no—
40#14582975—21no—
41#14582972—21no—
42#14582968—21no—
43#14582952C2211yescharacteristic
44#14582950C2211yescharacteristic
45#14582950C2211yescharacteristic
46#14582925—21no—
47#14582924—21no—
48#14582924—21no—
49#14582923C2211yescharacteristic
50#14582921C2211yescharacteristic
51#14582921C2211yescharacteristic
52C4⋊C8×D43C2211yescharacteristic
53C4⋊C8×D43C2211yescharacteristic
54C4×#10621872C2211yescharacteristic
55C4×C8×D43C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58Q8⋊(C43⋊C8)C2211yescharacteristic
59Q8⋊(C43⋊C8)C2211yescharacteristic
60#14582629C2211yescharacteristic
61#14582629C2211yescharacteristic
62#14582628C2211yescharacteristic
63#14582628C2211yescharacteristic
64D4⋊(C43⋊C8)C2211yescharacteristic
65D4⋊(C43⋊C8)C2211yescharacteristic
66#14582626C2211yescharacteristic
67#14582626C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C2×C4⋊C8×C43C2211yescharacteristic
70C4×M16×C43C2211yescharacteristic
71C43×Q8⋊C8C2211yescharacteristic
72C43×Q8⋊C8C2211yescharacteristic
73C43×D4⋊C8C2211yescharacteristic
74C43×D4⋊C8C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621898C2×C411yescharacteristic
77C2×#10621898D411yescharacteristic
78C2×#10621900C2×C411yescharacteristic
79C2×Q8×D43C2×C411yescharacteristic
80#13063331—44no—
81C2×#10621877—21no—
82C2×#10621872—21no—
83C2×#10621872—21no—
84C2×#10621872—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87C2×C8×D43—21no—
88#13063324—21no—
89#13063324C2×C411yescharacteristic
90#13063321—21no—
91#13063321C2×C411yescharacteristic
92#13063320—21no—
93#13063320—21no—
94#13063320—21no—
95#13063318—21no—
96#13063318—21no—
97#13063316C2×C411yescharacteristic
98#13063315—21no—
99#13063315—21no—
100#13063314C2×C411yescharacteristic
101#13063311—21no—
102#13063311—21no—
103#13063311—21no—
104#13063311—21no—
105#13063311—21no—
106#13063310—21no—
107#13063310—21no—
108#13063309—21no—
109#13063307—21no—
110#13063306—21no—
111#13063303—21no—
112#13063302—21no—
113#13063301C2×C411yescharacteristic
114#13063300—21no—
115#13063300C2×C411yescharacteristic
116#13063300C2×C411yescharacteristic
117#13063298—21no—
118#13063298—21no—
119#13063298—21no—
120#13063298—21no—
121#13063297—21no—
122#13063296—21no—
123#13063296C2×C411yescharacteristic
124Q8×Dic43C2×C411yescharacteristic
125C4×Dic86—21no—
126C4×Dic86C2×C411yescharacteristic
127C4×Dic86C2×C411yescharacteristic
128C4×Dic86D411yescharacteristic
129C4×Dic86C2311yescharacteristic
130#13063290—21no—
131#13063290—21no—
132#13063290—21no—
133#13063290C2×C411yescharacteristic
134#13063290C2×C411yescharacteristic
135C4×D172—21no—
136C4×D172C2×C411yescharacteristic
137C4×D172C2×C411yescharacteristic
138C4×D172D411yescharacteristic
139C4×D172C2311yescharacteristic
140D4×Dic43C2×C411yescharacteristic
141#13063287—21no—
142#13063287—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43C2×C411yescharacteristic
148C4×C22⋊D43C2×C411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150C4×C22⋊D43D411yescharacteristic
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155(C22⋊D43)⋊C4—21no—
156#13063284C2×C411yescharacteristic
157#13063284D411yescharacteristic
158#13063283C2×C411yescharacteristic
159#13063282—21no—
160#13063282—21no—
161#13063282D411yescharacteristic
162#13063282D411yescharacteristic
163#13063281—21no—
164C4⋊C4×D43—21no—
165C4⋊C4×D43C2×C411yescharacteristic
166C2×C4×Dic43—21no—
167C42×D43—21no—
168C42×D43—21no—
169C42×D43C2311yescharacteristic
170C42×D43C2311yescharacteristic
171C4⋊(C43⋊C8)—21no—
172C4⋊(C43⋊C8)—21no—
173C4⋊(C43⋊C8)C2311yescharacteristic
174C4⋊(C43⋊C8)C2311yescharacteristic
175Dic43⋊C8—21no—
176Dic43⋊C8—21no—
177Dic43⋊C8—21no—
178Dic43⋊C8—21no—
179Dic43⋊C8—21no—
180Dic43⋊C8—21no—
181C22⋊(C43⋊C8)—21no—
182(C2×D43)⋊C8—21no—
183(C2×D43)⋊C8—21no—
184#13063235—21no—
185C4×C43⋊C8C2311yescharacteristic
186C4×C43⋊C8C2311yescharacteristic
187C8×Dic43—21no—
188C2×M16×C43—21no—
189C22×C8×C43—21no—
190#126×C43—21no—
191#125×C43C2×C411yescharacteristic
192#124×C43C2×C411yescharacteristic
193#123×C43—21no—
194C22⋊Q8×C43C2×C411yescharacteristic
195#121×C43C2×C411yescharacteristic
196C4×Q8×C43C2311yescharacteristic
197C4×D4×C43—21no—
198C4×D4×C43C2311yescharacteristic
199#117×C43—21no—
200C2×C42×C43C2311yescharacteristic
201C4⋊C8×C43—21no—
202C4⋊C8×C43C2311yescharacteristic
203C4⋊C8×C43C2311yescharacteristic
204#97×C43—21no—
205C4×C8×C43C2311yescharacteristic
206C4×C8×C43C2311yescharacteristic
207C2×Q8×C43C22×C411yescharacteristic
208C2×D4×C43—21no—
209C2×D4×C43C22×C411yescharacteristic
210C22×C4×C43—21no—
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C2×C22⋊D43—21no—
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43C22⋊C411yescharacteristic
220C2×C22⋊D43C22⋊C411yescharacteristic
221C22×Dic43—21no—
222C22×Dic43—21no—
223Q8×D43—22no—
224Q8×D43—41no—
225#10621900—22no—
226#10621900—41no—
227#10621898—22no—
228#10621898—22no—
229#10621898—22no—
230#10621898—41no—
231#10621898—42no—
232#10621898—42no—
233C2×D172—21no—
234C2×D172—21no—
235C2×D172C22⋊C411yescharacteristic
236C2×D172C22×C411yescharacteristic
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43C22×C411yescharacteristic
243C2×C4×D43C22×C411yescharacteristic
244C2×C4×D43C2×D411yescharacteristic
245C2×C4×D43C2×D411yescharacteristic
246C2×C4×D43C2×D411yescharacteristic
247C2×C4×D43C2×D411yescharacteristic
248C2×Dic86—21no—
249C2×Dic86—21no—
250C2×Dic86C22⋊C411yescharacteristic
251C2×Dic86C22×C411yescharacteristic
252M16×C43—42no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—42no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43C22×C411yescharacteristic
263C4⋊C4×C43C22×C411yescharacteristic
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—21no—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C42×C43—21no—
270C42×C43C22×C411yescharacteristic
271C42×C43C2×D411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2411yescharacteristic
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43—21no—
277C22⋊Dic43C22⋊C411yescharacteristic
278C22⋊Dic43C22⋊C411yescharacteristic
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4C22⋊C411yescharacteristic
288(C2×D43)⋊C4C22⋊C411yescharacteristic
289(C2×D43)⋊C4C22⋊C411yescharacteristic
290(C2×D43)⋊C4C22⋊C411yescharacteristic
291C4⋊Dic43—21no—
292C4⋊Dic43—21no—
293C4⋊Dic43C22⋊C411yescharacteristic
294C4⋊Dic43C22⋊C411yescharacteristic
295C4⋊Dic43C22×C411yescharacteristic
296C4⋊Dic43C22×C411yescharacteristic
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4C22⋊C411yescharacteristic
306Dic43⋊C4C22⋊C411yescharacteristic
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43C22×C411yescharacteristic
317C4×Dic43C22×C411yescharacteristic
318C4×Dic43C2×D411yescharacteristic
319C4×Dic43C2×D411yescharacteristic
320C4×Dic43C2×D411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322#10621877—42no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327#10621872—42no—
328#10621872—42no—
329#10621872—42no—
330C8×D43—42no—
331C8×D43—42no—
332C8×D43—42no—
333C23×C43—21no—
334C23×C43C2×C22⋊C411yescharacteristic
335C22×D43—21no—
336C22×D43C2×C22⋊C411yescharacteristic
337C22×D43C2×C22⋊C411yescharacteristic
338Q8×C43—21no—
339Q8×C43—21no—
340D4×C43—21no—
341D4×C43—21no—
342D4×C43—81no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43C2×C22⋊C411yescharacteristic
354C2×C4×C43C2×C22⋊C411yescharacteristic
355C2×C4×C43C2×C22⋊C411yescharacteristic
356C2×C4×C43C23×C411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C22⋊D43—22no—
360C22⋊D43—22no—
361C22⋊D43—42no—
362C22⋊D43—42no—
363C22⋊D43—42no—
364C22⋊D43—42no—
365C22⋊D43—81no—
366C2×Dic43—21no—
367C2×Dic43—21no—
368C2×Dic43—21no—
369C2×Dic43—42no—
370C2×Dic43—81no—
371C2×Dic43C2×C22⋊C411yescharacteristic
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377D172—22no—
378D172—21no—
379D172—21no—
380D172—42no—
381D172—81no—
382C4×D43—21no—
383C4×D43—21no—
384C4×D43—21no—
385C4×D43—21no—
386C4×D43—21no—
387C4×D43—21no—
388C4×D43—41no—
389C4×D43—41no—
390C4×D43—42no—
391C4×D43—42no—
392C4×D43—41no—
393C4×D43—41no—
394C4×D43—81no—
395C4×D43—81no—
396C4×D43AGL(1,ℤ/8)12yes—
397C4×D43#13712yes—
398Dic86—21no—
399Dic86—22no—
400Dic86—42no—
401Dic86—42no—
402Dic86#13112yescomplemented
403C8×C43—22no—
404C8×C43—41no—
405C8×C43—41no—
406C8×C43—41no—
407C43⋊C8—41no—
408C43⋊C8—41no—
409C43⋊C8—41no—
410C43⋊C8—41no—
411#17515—431nomaximal, Sylow
412C22×C43—21no—
413C22×C43—21no—
414C22×C43—21no—
415C22×C43—41no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43C22×C22⋊C411yescharacteristic
419C2×D43—21no—
420C2×D43—21no—
421C2×D43—21no—
422C2×D43—21no—
423C2×D43—21no—
424C2×D43—41no—
425C2×D43—41no—
426C2×D43—41no—
427C2×D43#41712yes—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—21no—
432C4×C43—41no—
433C4×C43—41no—
434C4×C43—41no—
435C4×C43C2×#13111yescharacteristic
436C4×C43#56811yescharacteristic
437C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
438C4×C43C2×#13711yescharacteristic
439Dic43—22no—
440Dic43—21no—
441Dic43—21no—
442Dic43—21no—
443Dic43—21no—
444Dic43—21no—
445Dic43—41no—
446Dic43—41no—
447Dic43#41712yes—
448#3480—431no—
449#2965—431no—
450#2906—431no—
451#1495—431no—
452#1495—431no—
453#1492—431no—
454#1489—431no—
455#1489—431no—
456#1487—431no—
457#1483—431no—
458#1483D4311yescharacteristic, complemented
459#1480—431no—
460#1477—431no—
461#1477—431no—
462C2×Q8⋊C8—431no—
463C2×C43—41no—
464C2×C43—81no—
465C2×C43#288011yescharacteristic
466C2×C43C2×#41711yescharacteristic
467C2×C43#290111yescharacteristic
468D43—22no—
469D43—41no—
470D43—81no—
471C2×#131—861no—
472#559—431no—
473#559—861no—
474#557—431no—
475#556—431no—
476#556—861no—
477#553—431no—
478#553—431no—
479#553—861no—
480#553—861no—
481#550—431no—
482#548—431no—
483#548—431no—
484#532—431no—
485#532—861no—
486#529—431no—
487#529—861no—
488#529—861no—
489#529C2×D4311yescharacteristic
490C4×#41—431no—
491C4×#41—431no—
492C4×#41—431no—
493C4×#41—861no—
494C2×C4×Q8—431no—
495#446—861no—
496#436—861no—
497#435—861no—
498#435—861no—
499#431—431no—
500#431—431no—
501#431—431no—
502#424—861no—
503#424—861no—
504#424—861no—
505#423—431no—
506#423—431no—
507#423—431no—
508C2×C4⋊C8—431no—
509C2×C4⋊C8—431no—
510C2×C4⋊C8C2×D4311yescharacteristic
511C4×M16—431no—
512C4×M16C2×D4311yescharacteristic
513C2×C4×C8—431no—
514Q8⋊C8—431no—
515Q8⋊C8—431no—
516Q8⋊C8—431no—
517Q8⋊C8—431no—
518Q8⋊C8—431no—
519Q8⋊C8—431no—
520Q8⋊C8C2×D4311yescharacteristic
521Q8⋊C8C2×D4311yescharacteristic
522D4⋊C8—431no—
523D4⋊C8—431no—
524D4⋊C8—431no—
525D4⋊C8—431no—
526D4⋊C8—431no—
527D4⋊C8—431no—
528D4⋊C8C2×D4311yescharacteristic
529D4⋊C8C2×D4311yescharacteristic
530C43#1751511yescharacteristic, complemented, Sylow
531C2×#41—431no—
532C2×#41—431no—
533C2×#41—431no—
534C2×#41—861no—
535C22×Q8—431no—
536#131—1724no—
537C2×M16—21no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—861no—
541C2×M16—861no—
542C22×C8—21no—
543C22×C8—861no—
544C22×C8—861no—
545C22×C8—861no—
546C4⋊Q8—431no—
547C4⋊Q8—861no—
548#127—431no—
549#127—861no—
550#126—21no—
551#126—861no—
552#126—861no—
553#126—861no—
554#126—861no—
555#126—861no—
556#125—431no—
557#125—861no—
558#125—861no—
559#125C4×D4311yescharacteristic
560#124—431no—
561#124—861no—
562#124—861no—
563#124—861no—
564#124—861no—
565#124—861no—
566#124C4×D4311yescharacteristic
567#123—21no—
568#123—861no—
569#123—861no—
570#123—861no—
571#123—861no—
572#123—861no—
573C22⋊Q8—431no—
574C22⋊Q8—861no—
575C22⋊Q8—861no—
576C22⋊Q8C4×D4311yescharacteristic
577#121—431no—
578#121—431no—
579#121—431no—
580#121—861no—
581#121—861no—
582#121—861no—
583#121—861no—
584#121—861no—
585#121—861no—
586#121—861no—
587#121C4×D4311yescharacteristic
588C4×Q8—431no—
589C4×Q8—431no—
590C4×Q8—431no—
591C4×Q8—431no—
592C4×Q8—431no—
593C4×Q8—431no—
594C4×Q8—431no—
595C4×Q8—861no—
596C4×Q8—861no—
597C4×Q8—861no—
598C4×Q8—861no—
599C4×Q8C22×D4311yescharacteristic
600C4×D4—21no—
601C4×D4—431no—
602C4×D4—431no—
603C4×D4—431no—
604C4×D4—431no—
605C4×D4—431no—
606C4×D4—431no—
607C4×D4—431no—
608C4×D4—431no—
609C4×D4—431no—
610C4×D4—861no—
611C4×D4—861no—
612C4×D4—861no—
613C4×D4—861no—
614C4×D4—861no—
615C4×D4—861no—
616C4×D4—861no—
617C4×D4—861no—
618C4×D4—861no—
619C4×D4—861no—
620C4×D4—861no—
621C4×D4—861no—
622C4×D4C22×D4311yescharacteristic
623#117—21no—
624#117—431no—
625#117—431no—
626#117—431no—
627#117—431no—
628#117—431no—
629#117—861no—
630#117—861no—
631#117—861no—
632C2×C4⋊C4—431no—
633C2×C4⋊C4—861no—
634C2×C42—431no—
635C2×C42—431no—
636C2×C42—861no—
637C2×C42—861no—
638C2×C42—861no—
639C2×C42C22×D4311yescharacteristic
640C4⋊C8—21no—
641C4⋊C8—431no—
642C4⋊C8—431no—
643C4⋊C8—861no—
644C4⋊C8—861no—
645C4⋊C8—861no—
646C4⋊C8—861no—
647C4⋊C8—861no—
648C4⋊C8—861no—
649C4⋊C8—861no—
650C4⋊C8—861no—
651C4⋊C8C22×D4311yescharacteristic
652C4⋊C8C22×D4311yescharacteristic
653C22⋊C8—861no—
654C22⋊C8—861no—
655C22⋊C8—861no—
656#97—21no—
657#97—861no—
658C4×C8—431no—
659C4×C8—431no—
660C4×C8—861no—
661C4×C8C22×D4311yescharacteristic
662C4×C8C22×D4311yescharacteristic
663#41—862no—
664#41—862no—
665#41—862no—
666#41—862no—
667#41—1721no—
668#41—1722no—
669#41—1722no—
670#41—1721no—
671C2×Q8—431no—
672C2×Q8—431no—
673C2×Q8—861no—
674C2×Q8—861no—
675C2×Q8—862no—
676C2×Q8—1721no—
677C2×Q8C2×C4×D4311yescharacteristic
678C2×D4—21no—
679C2×D4—431no—
680C2×D4—431no—
681C2×D4—431no—
682C2×D4—431no—
683C2×D4—861no—
684C2×D4—861no—
685C2×D4—861no—
686C2×D4—861no—
687C2×D4—861no—
688C2×D4—861no—
689C2×D4—861no—
690C2×D4C2×C4×D4311yescharacteristic
691C22×C4—21no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—431no—
695C22×C4—431no—
696C22×C4—431no—
697C22×C4—431no—
698C22×C4—861no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4C2×C4×D4311yescharacteristic
706C22×C4D4×D4311yescharacteristic
707C22×C4D4×D4311yescharacteristic
708M16—42no—
709M16—1722no—
710M16—1722no—
711M16—1722no—
712M16—1722no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—42no—
718C2×C8—861no—
719C2×C8—861no—
720C2×C8—861no—
721C2×C8—861no—
722C2×C8—1722no—
723C2×C8—1722no—
724C2×C8—1722no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—431no—
730C4⋊C4—431no—
731C4⋊C4—431no—
732C4⋊C4—431no—
733C4⋊C4—431no—
734C4⋊C4—431no—
735C4⋊C4—431no—
736C4⋊C4—431no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4—861no—
742C4⋊C4—861no—
743C4⋊C4—861no—
744C4⋊C4—861no—
745C4⋊C4—861no—
746C4⋊C4—861no—
747C4⋊C4C2×C4×D4311yescharacteristic
748C4⋊C4C2×C4×D4311yescharacteristic
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—431no—
755C22⋊C4—431no—
756C22⋊C4—431no—
757C22⋊C4—431no—
758C22⋊C4—431no—
759C22⋊C4—431no—
760C22⋊C4—861no—
761C22⋊C4—861no—
762C22⋊C4—861no—
763C22⋊C4—861no—
764C22⋊C4—861no—
765C22⋊C4—861no—
766C22⋊C4—861no—
767C22⋊C4—861no—
768C22⋊C4—861no—
769C22⋊C4—861no—
770C22⋊C4—861no—
771C42—21no—
772C42—431no—
773C42—431no—
774C42—431no—
775C42—431no—
776C42—431no—
777C42—431no—
778C42—861no—
779C42—861no—
780C42—861no—
781C42—861no—
782C42—861no—
783C42—861no—
784C42—861no—
785C42C2×C4×D4311yescharacteristic
786C42D4×D4311yescharacteristic
787C42D4×D4311yescharacteristic
788C42C23×D4311yescharacteristic
789C23—21no—
790C23—431no—
791C23—431no—
792C23—861no—
793C23C22⋊C4×D4311yescharacteristic
794Q8—21no—
795Q8—21no—
796Q8—432no—
797Q8—862no—
798Q8—861no—
799Q8—1722no—
800Q8—1722no—
801D4—21no—
802D4—21no—
803D4—81no—
804D4—862no—
805D4—862no—
806D4—862no—
807D4—861no—
808D4—861no—
809D4—3441no—
810D4—3441no—
811D4—1722no—
812D4—1722no—
813D4—1722no—
814D4—1722no—
815D4—1722no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—431no—
827C2×C4—432no—
828C2×C4—432no—
829C2×C4—431no—
830C2×C4—431no—
831C2×C4—431no—
832C2×C4—431no—
833C2×C4—431no—
834C2×C4—861no—
835C2×C4—861no—
836C2×C4—861no—
837C2×C4—861no—
838C2×C4—861no—
839C2×C4—861no—
840C2×C4—861no—
841C2×C4—861no—
842C2×C4—861no—
843C2×C4—3441no—
844C2×C4—3441no—
845C2×C4—3441no—
846C2×C4—1721no—
847C2×C4—1721no—
848C2×C4—1722no—
849C2×C4—1722no—
850C2×C4—1722no—
851C2×C4—1721no—
852C2×C4—1721no—
853C2×C4C22⋊C4×D4311yescharacteristic
854C2×C4C22⋊C4×D4311yescharacteristic
855C2×C4C22⋊C4×D4311yescharacteristic
856C2×C4C22×C4×D4311yescharacteristic
857C2×C4C2×D4×D4311yescharacteristic
858C2×C4C2×D4×D4311yescharacteristic
859C8—22no—
860C8—41no—
861C8—41no—
862C8—41no—
863C8—1721no—
864C8—1721no—
865C8—1721no—
866C8—1721no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—432no—
874C22—861no—
875C22—861no—
876C22—861no—
877C22—861no—
878C22—861no—
879C22—1721no—
880C22—1721no—
881C22—1721no—
882C22C2×C22⋊C4×D4311yescharacteristic
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—432no—
891C4—861no—
892C4—861no—
893C4—862no—
894C4—861no—
895C4—861no—
896C4—861no—
897C4—1721no—
898C4—1721no—
899C4#131×D4311yescharacteristic
900C4#1458366411yescharacteristic
901C4AGL(1,ℤ/8)×D4311yescharacteristic
902C4#137×D4311yescharacteristic
903C2—41no—
904C2—81no—
905C2—862no—
906C2—3441no—
907C2—1721no—
908C2#1914304311yescharacteristic
909C2#417×D4311yescharacteristic
910C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1483C2
socleC22×C43C22×C22⋊C4
prime radical#19148186C2
cosocleC42×C43C24
hypercenter#1483D43
hypocenterC43#17515
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
2. #19143557C2semidirect
3. #19143160C2semidirect
4. #19133060C2semidirect
5. #19133059C2semidirect
6. #19133044C2semidirect
7. #19133035C2semidirect
8. #19133031C2semidirect
9. #19133022C2semidirect
10. #19133007C2semidirect
11. #19132992C2semidirect
12. #19132980C2semidirect
13. #19132979C2semidirect
14. Q8⋊C8×D43C2semidirect
15. C43×#1483C2semidirect
402. Dic86#131semidirect
458. #1483D43semidirect
530. C43#17515semidirect

Maximal subgroups

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

subgroupindex
#191481862
#191435572
#191431602
#191330602
#191330592
#191330442
#191330352
#191330312
#191330222
#191330072
#191329922
#191329802
#191329792
Q8⋊C8×D432
C43×#14832
#1751543