Finite Group Databasebeta

← #25063149

Subgroups — #25063149

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D43C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3C2×#14582951C211yesmaximal, characteristic, complemented
4#19133009C211yesmaximal, characteristic, complemented
5#19133008C211yesmaximal, characteristic, complemented
6#19133006C211yesmaximal, characteristic, complemented
7#19133002C212yesmaximal, complemented
8#19133000C212yesmaximal, complemented
9#19132988C212yesmaximal, complemented
10#19132984C212yesmaximal, complemented
11C43×#1483C211yesmaximal, characteristic, complemented
12#14583436C2211yescharacteristic
13#14583435C411yescharacteristic
14#14583434C411yescharacteristic
15#14583433C2211yescharacteristic
16#14583432—21no—
17#14583431C2211yescharacteristic
18#14583430C411yescharacteristic
19#14583429—21no—
20#14583428C411yescharacteristic
21#14583427—21no—
22#14583426—21no—
23#126×D43—21no—
24#125×D43C411yescharacteristic
25#124×D43C411yescharacteristic
26#123×D43—21no—
27C22⋊Q8×D43C411yescharacteristic
28#121×D43C411yescharacteristic
29C4×Q8×D43C2211yescharacteristic
30C4×D4×D43—21no—
31C4×D4×D43C2211yescharacteristic
32#117×D43—21no—
33C2×C42×D43C2211yescharacteristic
34#14582954—21no—
35#14582954—21no—
36#14582951—21no—
37#14582951—21no—
38#14582951C2212yes—
39#14582951C2212yescomplemented
40#14582950C2212yes—
41#14582950C2212yescomplemented
42#14582922—21no—
43C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
44#14582862—21no—
45C2×(C2×D43)⋊C8—21no—
46C4×#10621877C2211yescharacteristic, complemented
47C2×C8×Dic43—21no—
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C43×#529C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic, complemented
56C4×M16×C43C2211yescharacteristic, complemented
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×Q8×D43C2×C411yescharacteristic
60C2×D4×D43—21no—
61C2×D4×D43C2×C411yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43C2×C411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C2×#10621877—21no—
67C22×C43⋊C8—21no—
68#13063320—21no—
69#13063320—21no—
70#13063320—21no—
71#13063319—21no—
72#13063318—21no—
73#13063318—21no—
74#13063318—21no—
75#13063317C2×C411yescharacteristic
76#13063316C2×C411yescharacteristic
77#13063316C2×C411yescharacteristic
78#13063315—21no—
79#13063315—21no—
80#13063314C2×C411yescharacteristic
81#13063313C2×C411yescharacteristic
82#13063312C2×C411yescharacteristic
83#13063311—21no—
84#13063311—21no—
85#13063310—21no—
86#13063310—21no—
87#13063309—21no—
88#13063308—21no—
89#13063307—21no—
90#13063307—21no—
91#13063306—21no—
92#13063305C2×C411yescharacteristic
93#13063304C2×C411yescharacteristic
94#13063303—21no—
95#13063302—21no—
96#13063301C2×C411yescharacteristic
97#13063300C2×C411yescharacteristic
98#13063299C2×C411yescharacteristic
99#13063298—21no—
100#13063297—21no—
101#13063296C2×C411yescharacteristic
102Q8×Dic43C2×C411yescharacteristic
103C4×Dic86—21no—
104C4×Dic86C2311yescharacteristic
105#13063290—21no—
106#13063290C2×C411yescharacteristic
107C4×D172—21no—
108C4×D172C2311yescharacteristic
109D4×Dic43—21no—
110D4×Dic43C2×C411yescharacteristic
111#13063287—21no—
112#13063287C2×C411yescharacteristic
113C4×C22⋊D43—21no—
114C4×C22⋊D43—21no—
115C4×C22⋊D43—21no—
116(C22⋊D43)⋊C4—21no—
117(C22⋊D43)⋊C4—21no—
118(C22⋊D43)⋊C4—21no—
119#13063284—21no—
120#13063283—21no—
121#13063283—21no—
122#13063282—21no—
123#13063282—21no—
124#13063281—21no—
125#13063281—21no—
126C4⋊C4×D43—21no—
127C4⋊C4×D43—21no—
128C4⋊C4×D43—21no—
129C4⋊C4×D43—21no—
130C4⋊C4×D43C2×C411yescharacteristic
131C4⋊C4×D43C2×C411yescharacteristic
132C22⋊C4×D43—21no—
133C22⋊C4×D43—21no—
134C22⋊C4×D43—21no—
135C22⋊C4×D43—21no—
136C22⋊C4×D43—21no—
137C2×C4×Dic43C2×C411yescharacteristic
138C2×C4×Dic43D411yescharacteristic
139C2×C4×Dic43D411yescharacteristic
140C42×D43—21no—
141C42×D43C2×C411yescharacteristic
142C42×D43C2×C411yescharacteristic
143C42×D43D411yescharacteristic
144C42×D43D411yescharacteristic
145C42×D43D411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43C2311yescharacteristic
148C42×D43C2311yescharacteristic
149C4⋊(C43⋊C8)—21no—
150C4⋊(C43⋊C8)C2312yes—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153(C2×D43)⋊C8—22no—
154(C2×D43)⋊C8—22no—
155(C2×D43)⋊C8—22no—
156(C2×D43)⋊C8—22no—
157#13063236—21no—
158C4×C43⋊C8C2312yes—
159C8×Dic43—22no—
160C8×Dic43—22no—
161C2×M16×C43—21no—
162C22×C8×C43—21no—
163#126×C43—21no—
164#125×C43C2×C411yescharacteristic
165#124×C43C2×C411yescharacteristic
166#123×C43—21no—
167C22⋊Q8×C43C2×C411yescharacteristic
168#121×C43C2×C411yescharacteristic
169C4×Q8×C43C2311yescharacteristic
170C4×D4×C43—21no—
171C4×D4×C43C2311yescharacteristic
172#117×C43—21no—
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43—21no—
175C4⋊C8×C43C2312yes—
176#97×C43—21no—
177C4×C8×C43C2312yes—
178C23×D43—21no—
179C23×D43C22⋊C411yescharacteristic
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C22×Dic43—21no—
191C22×Dic43C22⋊C411yescharacteristic
192C22×Dic43C22⋊C411yescharacteristic
193C22×Dic43C22⋊C411yescharacteristic
194Q8×D43—24no—
195D4×D43—24no—
196D4×D43—44no—
197C2×D172—21no—
198C2×D172C22×C411yescharacteristic
199C2×C4×D43—24no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—42no—
206C2×C4×D43—41no—
207C2×C4×D43—41no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43C22⋊C411yescharacteristic
211C2×C4×D43C22⋊C411yescharacteristic
212C2×C4×D43C22⋊C411yescharacteristic
213C2×C4×D43C22⋊C411yescharacteristic
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22⋊C411yescharacteristic
216C2×C4×D43C22×C411yescharacteristic
217C2×C4×D43C22×C411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×Dic86—21no—
223C2×Dic86C22×C411yescharacteristic
224M16×C43—42no—
225C2×C8×C43—22no—
226C2×C8×C43—22no—
227C2×C8×C43—42no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43C22×C411yescharacteristic
233C4⋊C4×C43C22×C411yescharacteristic
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C42×C43—21no—
240C42×C43C22×C411yescharacteristic
241C42×C43C2×D411yescharacteristic
242C42×C43C2×D411yescharacteristic
243C42×C43C2411yescharacteristic
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43C22×C411yescharacteristic
264C4⋊Dic43C22×C411yescharacteristic
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22×C411yescharacteristic
285C4×Dic43C22×C411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290#10621877—42no—
291C2×C43⋊C8—22no—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—42no—
294C23×C43—21no—
295C23×C43C2×C22⋊C411yescharacteristic
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—21no—
299C22×D43—41no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43—42no—
303C22×D43C2×C22⋊C411yescharacteristic
304C22×D43C2×C22⋊C411yescharacteristic
305Q8×C43—22no—
306D4×C43—22no—
307D4×C43—42no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C23×C411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C22⋊D43—42no—
324C22⋊D43—42no—
325C22⋊D43—42no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—41no—
332C2×Dic43—42no—
333C2×Dic43C2×C22⋊C411yescharacteristic
334C2×Dic43C2×C22⋊C411yescharacteristic
335C2×Dic43C2×C22⋊C411yescharacteristic
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338C2×Dic43C2×C22⋊C411yescharacteristic
339D172—22no—
340D172—42no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—21no—
344C4×D43—21no—
345C4×D43—21no—
346C4×D43—21no—
347C4×D43—22no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—41no—
351C4×D43—41no—
352C4×D43—41no—
353C4×D43—41no—
354C4×D43—42no—
355C4×D43—42no—
356C4×D43—42no—
357C4×D43—42no—
358C4×D43—41no—
359C4×D43—41no—
360C4×D43#13114yes—
361Dic86—22no—
362Dic86—42no—
363C8×C43—42no—
364C8×C43—42no—
365C43⋊C8—42no—
366C43⋊C8—42no—
367#17465—431nomaximal, Sylow
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43#42112yes—
374C22×C43C22×C22⋊C411yescharacteristic
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—21no—
380C2×D43—44no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—84no—
385C2×D43#40812yes—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43—41no—
393C4×C43C2×#13112yes—
394C4×C43#57511yescharacteristic
395C4×C43#57511yescharacteristic
396Dic43—21no—
397Dic43—21no—
398Dic43—21no—
399Dic43—21no—
400Dic43—21no—
401Dic43—41no—
402Dic43—41no—
403Dic43—41no—
404Dic43#40812yes—
405C2×#529—431no—
406#2920—431no—
407C2×#431—431no—
408#1483—431no—
409#1483—431no—
410#1483—431no—
411#1483D4311yescharacteristic, complemented
412#1482—432no—
413#1482—432no—
414#1479—432no—
415#1478—432no—
416C2×C43—22no—
417C2×C43—81no—
418C2×C43C2×#40811yescharacteristic
419C2×C43#289611yescharacteristic
420C2×C43C2×#42111yescharacteristic
421D43—22no—
422D43—41no—
423D43—81no—
424#529—431no—
425#529—431no—
426#529—431no—
427#529—431no—
428#529—431no—
429#529—431no—
430#529—431no—
431#529—861no—
432#529—861no—
433#529—861no—
434#529—861no—
435#529C2×D4311yescharacteristic
436C2×#126—861no—
437C2×#125—431no—
438C2×#124—431no—
439C2×#123—861no—
440C2×C22⋊Q8—431no—
441C2×#121—431no—
442C2×C4×Q8—431no—
443C2×C4×D4—431no—
444C2×C4×D4—861no—
445C2×#117—861no—
446C22×C42—431no—
447#432—861no—
448#432—861no—
449#431—432no—
450#431—432no—
451#431—432no—
452#431—432no—
453#431—861no—
454#431—861no—
455#423—861no—
456C2×C4⋊C8—431no—
457C2×C4⋊C8C2×D4311yescharacteristic, complemented
458#407—861no—
459C2×C22⋊C8—861no—
460C4×M16—431no—
461C4×M16C2×D4311yescharacteristic, complemented
462C2×C4×C8—861no—
463Q8⋊C8—432no—
464Q8⋊C8—432no—
465Q8⋊C8—432no—
466Q8⋊C8C2×D4312yescomplemented
467D4⋊C8—432no—
468D4⋊C8—432no—
469D4⋊C8—432no—
470D4⋊C8C2×D4312yescomplemented
471C43#1746511yescharacteristic, complemented, Sylow
472C22×Q8—431no—
473C22×D4—431no—
474C22×D4—861no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—861no—
479C2×M16—21no—
480C2×M16—861no—
481C22×C8—21no—
482C22×C8—861no—
483#126—21no—
484#126—861no—
485#126—861no—
486#126—861no—
487#126—861no—
488#126—861no—
489#126—861no—
490#126—861no—
491#125—431no—
492#125—431no—
493#125—431no—
494#125—861no—
495#125—861no—
496#125C4×D4311yescharacteristic
497#124—431no—
498#124—431no—
499#124—431no—
500#124—861no—
501#124—861no—
502#124C4×D4311yescharacteristic
503#123—21no—
504#123—861no—
505#123—861no—
506#123—861no—
507#123—861no—
508#123—861no—
509#123—861no—
510#123—861no—
511C22⋊Q8—431no—
512C22⋊Q8—431no—
513C22⋊Q8—431no—
514C22⋊Q8—861no—
515C22⋊Q8—861no—
516C22⋊Q8C4×D4311yescharacteristic
517#121—431no—
518#121—431no—
519#121—431no—
520#121—861no—
521#121—861no—
522#121C4×D4311yescharacteristic
523C4×Q8—431no—
524C4×Q8—431no—
525C4×Q8—431no—
526C4×Q8—861no—
527C4×Q8—861no—
528C4×Q8C22×D4311yescharacteristic
529C4×D4—21no—
530C4×D4—431no—
531C4×D4—431no—
532C4×D4—431no—
533C4×D4—861no—
534C4×D4—861no—
535C4×D4—861no—
536C4×D4—861no—
537C4×D4—861no—
538C4×D4—861no—
539C4×D4—861no—
540C4×D4—861no—
541C4×D4—861no—
542C4×D4C22×D4311yescharacteristic
543#117—21no—
544#117—861no—
545#117—861no—
546#117—861no—
547#117—861no—
548#117—861no—
549#117—861no—
550#117—861no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—861no—
574C2×C42C22×D4311yescharacteristic
575C4⋊C8—21no—
576C4⋊C8—432no—
577C4⋊C8—862no—
578C4⋊C8—862no—
579C4⋊C8—861no—
580C4⋊C8C22×D4312yes—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—862no—
584C22⋊C8—862no—
585#97—21no—
586#97—861no—
587C4×C8—432no—
588C4×C8—862no—
589C4×C8—862no—
590C4×C8C22×D4312yes—
591C24—431no—
592C24—861no—
593C2×Q8—431no—
594C2×Q8—861no—
595C2×Q8—864no—
596C2×Q8C2×C4×D4311yescharacteristic
597C2×D4—21no—
598C2×D4—431no—
599C2×D4—861no—
600C2×D4—864no—
601C2×D4—861no—
602C2×D4—861no—
603C2×D4—861no—
604C2×D4—1724no—
605C2×D4C2×C4×D4311yescharacteristic
606C22×C4—21no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—864no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—1721no—
630C22×C4—1721no—
631C22×C4—1722no—
632C22×C4—1722no—
633C22×C4—1722no—
634C22×C4C2×C4×D4311yescharacteristic
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637M16—42no—
638M16—1722no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—42no—
642C2×C8—862no—
643C2×C8—862no—
644C2×C8—1722no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—431no—
650C4⋊C4—431no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4C2×C4×D4311yescharacteristic
666C4⋊C4C2×C4×D4311yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—861no—
673C22⋊C4—861no—
674C22⋊C4—861no—
675C22⋊C4—861no—
676C22⋊C4—861no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—861no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C22⋊C4—861no—
687C42—21no—
688C42—431no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—861no—
701C42—861no—
702C42—861no—
703C42C2×C4×D4311yescharacteristic
704C42D4×D4311yescharacteristic
705C42D4×D4311yescharacteristic
706C42C23×D4311yescharacteristic
707C23—21no—
708C23—431no—
709C23—431no—
710C23—862no—
711C23—862no—
712C23—861no—
713C23—1721no—
714C23—1722no—
715C23—1722no—
716C23—1722no—
717C23C22⋊C4×D4311yescharacteristic
718Q8—22no—
719Q8—862no—
720Q8—1722no—
721D4—22no—
722D4—42no—
723D4—862no—
724D4—1722no—
725D4—1722no—
726D4—1722no—
727D4—1722no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—431no—
738C2×C4—434no—
739C2×C4—431no—
740C2×C4—431no—
741C2×C4—431no—
742C2×C4—431no—
743C2×C4—431no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—861no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1721no—
767C2×C4—1722no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4C22⋊C4×D4311yescharacteristic
771C2×C4C22⋊C4×D4311yescharacteristic
772C2×C4C22⋊C4×D4311yescharacteristic
773C2×C4C22×C4×D4311yescharacteristic
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C2×D4×D4311yescharacteristic
776C8—42no—
777C8—42no—
778C8—1722no—
779C8—1722no—
780C22—21no—
781C22—21no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—432no—
786C22—861no—
787C22—861no—
788C22—861no—
789C22—861no—
790C22—861no—
791C22—3444no—
792C22—1724no—
793C22—1721no—
794C22—1721no—
795C22—1721no—
796C22#1458291412yes—
797C22C2×C22⋊C4×D4311yescharacteristic
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—432no—
806C4—861no—
807C4—861no—
808C4—861no—
809C4—861no—
810C4—861no—
811C4—1721no—
812C4—1721no—
813C4—1721no—
814C4#131×D4312yes—
815C4#1458369511yescharacteristic
816C4#1458369811yescharacteristic
817C2—22no—
818C2—81no—
819C2—862no—
820C2—3441no—
821C2—1721no—
822C2#408×D4311yescharacteristic
823C2#1914311111yescharacteristic
824C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1483C2
socleC22×C43C22×C22⋊C4
prime radical#121×D43C4
cosocleC42×C43C24
hypercenter#1483D43
hypocenterC43#17465
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. #19143226C2semidirect
3. C2×#14582951C2semidirect
4. #19133009C2semidirect
5. #19133008C2semidirect
6. #19133006C2semidirect
7. #19133002C2semidirect
8. #19133000C2semidirect
9. #19132988C2semidirect
10. #19132984C2semidirect
11. C43×#1483C2semidirect
39. #14582951C22semidirect
41. #14582950C22semidirect
43. C2×C4⋊(C43⋊C8)C22semidirect
46. C4×#10621877C22semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
55. C2×C4⋊C8×C43C22semidirect
56. C4×M16×C43C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
411. #1483D43semidirect
457. C2×C4⋊C8C2×D43semidirect
461. C4×M16C2×D43semidirect
466. Q8⋊C8C2×D43semidirect
470. D4⋊C8C2×D43semidirect
471. C43#17465semidirect

Maximal subgroups

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

subgroupindex
#529×D432
#191432262
C2×#145829512
#191330092
#191330082
#191330062
#191330022
#191330002
#191329882
#191329842
C43×#14832
#1746543