Finite Group Databasebeta

← #25063250

Subgroups — #25063250

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D43C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic, complemented
3#431×D43C211yesmaximal, characteristic, complemented
4#19133061C211yesmaximal, characteristic, complemented
5#19133060C211yesmaximal, characteristic, complemented
6#19133058C211yesmaximal, characteristic, complemented
7#19133054C212yesmaximal, complemented
8#19133052C212yesmaximal, complemented
9#19132988C212yesmaximal, complemented
10#19132984C212yesmaximal, complemented
11C43×#1495C211yesmaximal, 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#14582955—21no—
35#14582955C2212yescomplemented
36#14582952C2211yescharacteristic, complemented
37#14582951—21no—
38#14582951—21no—
39#14582951C2212yes—
40#14582950C2212yes—
41#14582949—21no—
42#14582923C2211yescharacteristic, complemented
43C4⋊C8×D43—21no—
44#14582862—21no—
45C22⋊C8×D43—21no—
46M16×Dic43—21no—
47C4×C8×D43C2212yescomplemented
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C43×#529C2211yescharacteristic
55C43×#431C2211yescharacteristic, complemented
56C43×#423C2211yescharacteristic, 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—
67C2×C8×D43—22no—
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)—21no—
151C4⋊(C43⋊C8)C2312yes—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)—21no—
154(C2×D43)⋊C8—22no—
155(C2×D43)⋊C8—22no—
156(C2×D43)⋊C8—22no—
157#13063235—22no—
158C4×C43⋊C8C2312yes—
159C8×Dic43—22no—
160C8×Dic43—22no—
161C2×M16×C43—21no—
162#126×C43—21no—
163#125×C43C2×C411yescharacteristic
164#124×C43C2×C411yescharacteristic
165#123×C43—21no—
166C22⋊Q8×C43C2×C411yescharacteristic
167#121×C43C2×C411yescharacteristic
168C4×Q8×C43C2311yescharacteristic
169C4×D4×C43—21no—
170C4×D4×C43C2311yescharacteristic
171#117×C43—21no—
172C2×C42×C43C2311yescharacteristic
173C4⋊C8×C43—21no—
174C4⋊C8×C43—21no—
175C4⋊C8×C43C2312yes—
176C22⋊C8×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—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C22×C411yescharacteristic
232C4⋊C4×C43C22×C411yescharacteristic
233C22⋊C4×C43—21no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C42×C43—21no—
239C42×C43C22×C411yescharacteristic
240C42×C43C2×D411yescharacteristic
241C42×C43C2×D411yescharacteristic
242C42×C43C2411yescharacteristic
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248(C2×D43)⋊C4—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—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C22×C411yescharacteristic
263C4⋊Dic43C22×C411yescharacteristic
264Dic43⋊C4—21no—
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—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22×C411yescharacteristic
284C4×Dic43C22×C411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289#10621877—42no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8—22no—
292C8×D43—44no—
293C23×C43—21no—
294C23×C43C2×C22⋊C411yescharacteristic
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—21no—
298C22×D43—41no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43C2×C22⋊C411yescharacteristic
303C22×D43C2×C22⋊C411yescharacteristic
304Q8×C43—22no—
305D4×C43—22no—
306D4×C43—42no—
307C2×C4×C43—22no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43C2×C22⋊C411yescharacteristic
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C23×C411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C22⋊D43—42no—
323C22⋊D43—42no—
324C22⋊D43—42no—
325C2×Dic43—22no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—42no—
332C2×Dic43C2×C22⋊C411yescharacteristic
333C2×Dic43C2×C22⋊C411yescharacteristic
334C2×Dic43C2×C22⋊C411yescharacteristic
335C2×Dic43C2×C22⋊C411yescharacteristic
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338D172—22no—
339D172—42no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—21no—
345C4×D43—21no—
346C4×D43—21no—
347C4×D43—21no—
348C4×D43—22no—
349C4×D43—41no—
350C4×D43—41no—
351C4×D43—41no—
352C4×D43—41no—
353C4×D43—42no—
354C4×D43—42no—
355C4×D43—42no—
356C4×D43—42no—
357C4×D43—41no—
358C4×D43—41no—
359C4×D43#13114yes—
360Dic86—22no—
361Dic86—42no—
362C8×C43—42no—
363C8×C43—42no—
364C43⋊C8—42no—
365C43⋊C8—42no—
366#17480—431nomaximal, Sylow
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43C22×C22⋊C411yescharacteristic
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—44no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—84no—
383C2×D43#40812yes—
384C2×D43#42112yes—
385C4×C43—21no—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43C2×#13112yes—
393C4×C43#57511yescharacteristic
394C4×C43#57511yescharacteristic
395Dic43—21no—
396Dic43—21no—
397Dic43—21no—
398Dic43—21no—
399Dic43—21no—
400Dic43—41no—
401Dic43—41no—
402Dic43—41no—
403Dic43#40812yes—
404C2×#529—431no—
405#2920—431no—
406C2×#431—431no—
407#1495—431no—
408#1495—431no—
409#1495—431no—
410#1495D4311yescharacteristic, complemented
411#1494—432no—
412#1494—432no—
413#1479—432no—
414#1478—432no—
415C2×C43—41no—
416C2×C43—81no—
417C2×C43C2×#40811yescharacteristic
418C2×C43#289611yescharacteristic
419C2×C43C2×#42111yescharacteristic
420D43—22no—
421D43—22no—
422D43—81no—
423#529—431no—
424#529—431no—
425#529—431no—
426#529—431no—
427#529—431no—
428#529—431no—
429#529—431no—
430#529—861no—
431#529—861no—
432#529—861no—
433#529—861no—
434#529C2×D4311yescharacteristic
435C2×#126—861no—
436C2×#125—431no—
437C2×#124—431no—
438C2×#123—861no—
439C2×C22⋊Q8—431no—
440C2×#121—431no—
441C2×C4×Q8—431no—
442C2×C4×D4—431no—
443C2×C4×D4—861no—
444C2×#117—861no—
445C22×C42—431no—
446#432—432no—
447#432—861no—
448#431—431no—
449#431—432no—
450#431—432no—
451#431—861no—
452#431—861no—
453#431—861no—
454#431C2×D4311yescharacteristic, complemented
455#423—431no—
456#423C2×D4311yescharacteristic, complemented
457C2×C4⋊C8—861no—
458#407—861no—
459C2×C22⋊C8—861no—
460C4×M16—861no—
461C2×C4×C8—432no—
462Q8⋊C8—432no—
463Q8⋊C8—432no—
464Q8⋊C8—432no—
465Q8⋊C8C2×D4312yescomplemented
466D4⋊C8—432no—
467D4⋊C8—432no—
468D4⋊C8—432no—
469D4⋊C8C2×D4312yescomplemented
470C43#1748011yescharacteristic, complemented, Sylow
471C22×Q8—431no—
472C22×D4—431no—
473C22×D4—861no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—861no—
478C2×M16—21no—
479C2×M16—861no—
480C22×C8—862no—
481#126—21no—
482#126—861no—
483#126—861no—
484#126—861no—
485#126—861no—
486#126—861no—
487#126—861no—
488#126—861no—
489#125—431no—
490#125—431no—
491#125—431no—
492#125—861no—
493#125—861no—
494#125C4×D4311yescharacteristic
495#124—431no—
496#124—431no—
497#124—431no—
498#124—861no—
499#124—861no—
500#124C4×D4311yescharacteristic
501#123—21no—
502#123—861no—
503#123—861no—
504#123—861no—
505#123—861no—
506#123—861no—
507#123—861no—
508#123—861no—
509C22⋊Q8—431no—
510C22⋊Q8—431no—
511C22⋊Q8—431no—
512C22⋊Q8—861no—
513C22⋊Q8—861no—
514C22⋊Q8C4×D4311yescharacteristic
515#121—431no—
516#121—431no—
517#121—431no—
518#121—861no—
519#121—861no—
520#121C4×D4311yescharacteristic
521C4×Q8—431no—
522C4×Q8—431no—
523C4×Q8—431no—
524C4×Q8—861no—
525C4×Q8—861no—
526C4×Q8C22×D4311yescharacteristic
527C4×D4—21no—
528C4×D4—431no—
529C4×D4—431no—
530C4×D4—431no—
531C4×D4—861no—
532C4×D4—861no—
533C4×D4—861no—
534C4×D4—861no—
535C4×D4—861no—
536C4×D4—861no—
537C4×D4—861no—
538C4×D4—861no—
539C4×D4—861no—
540C4×D4C22×D4311yescharacteristic
541#117—21no—
542#117—861no—
543#117—861no—
544#117—861no—
545#117—861no—
546#117—861no—
547#117—861no—
548#117—861no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C42—431no—
561C2×C42—431no—
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—861no—
572C2×C42C22×D4311yescharacteristic
573C4⋊C8—21no—
574C4⋊C8—21no—
575C4⋊C8—432no—
576C4⋊C8—862no—
577C4⋊C8—861no—
578C4⋊C8—861no—
579C4⋊C8C22×D4312yes—
580C22⋊C8—21no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—862no—
584C22⋊C8—861no—
585#97—862no—
586C4×C8—432no—
587C4×C8—862no—
588C4×C8—862no—
589C4×C8C22×D4312yes—
590C24—431no—
591C24—861no—
592C2×Q8—431no—
593C2×Q8—861no—
594C2×Q8—864no—
595C2×Q8C2×C4×D4311yescharacteristic
596C2×D4—21no—
597C2×D4—431no—
598C2×D4—861no—
599C2×D4—864no—
600C2×D4—861no—
601C2×D4—861no—
602C2×D4—861no—
603C2×D4—1724no—
604C2×D4C2×C4×D4311yescharacteristic
605C22×C4—21no—
606C22×C4—431no—
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—864no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—1721no—
629C22×C4—1721no—
630C22×C4—1722no—
631C22×C4—1722no—
632C22×C4—1722no—
633C22×C4C2×C4×D4311yescharacteristic
634C22×C4D4×D4311yescharacteristic
635C22×C4D4×D4311yescharacteristic
636M16—42no—
637M16—1722no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—862no—
641C2×C8—862no—
642C2×C8—1724no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—431no—
648C4⋊C4—431no—
649C4⋊C4—861no—
650C4⋊C4—861no—
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⋊C4C2×C4×D4311yescharacteristic
664C4⋊C4C2×C4×D4311yescharacteristic
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—861no—
671C22⋊C4—861no—
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—
685C42—21no—
686C42—431no—
687C42—431no—
688C42—431no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—861no—
699C42—861no—
700C42—861no—
701C42C2×C4×D4311yescharacteristic
702C42D4×D4311yescharacteristic
703C42D4×D4311yescharacteristic
704C42C23×D4311yescharacteristic
705C23—21no—
706C23—431no—
707C23—431no—
708C23—862no—
709C23—862no—
710C23—861no—
711C23—1721no—
712C23—1722no—
713C23—1722no—
714C23—1722no—
715C23C22⋊C4×D4311yescharacteristic
716Q8—22no—
717Q8—862no—
718Q8—1722no—
719D4—22no—
720D4—42no—
721D4—862no—
722D4—1722no—
723D4—1722no—
724D4—1722no—
725D4—1722no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—431no—
736C2×C4—434no—
737C2×C4—431no—
738C2×C4—431no—
739C2×C4—431no—
740C2×C4—431no—
741C2×C4—431no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1721no—
764C2×C4—1721no—
765C2×C4—1722no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4C22⋊C4×D4311yescharacteristic
769C2×C4C22⋊C4×D4311yescharacteristic
770C2×C4C22⋊C4×D4311yescharacteristic
771C2×C4C22×C4×D4311yescharacteristic
772C2×C4C2×D4×D4311yescharacteristic
773C2×C4C2×D4×D4311yescharacteristic
774C8—42no—
775C8—42no—
776C8—1722no—
777C8—1722no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—432no—
785C22—432no—
786C22—861no—
787C22—861no—
788C22—861no—
789C22—861no—
790C22—3444no—
791C22—1724no—
792C22—1721no—
793C22—1721no—
794C22—1721no—
795C22C2×C22⋊C4×D4311yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—432no—
804C4—861no—
805C4—861no—
806C4—861no—
807C4—861no—
808C4—861no—
809C4—1721no—
810C4—1721no—
811C4—1721no—
812C4#131×D4312yes—
813C4#1458369511yescharacteristic
814C4#1458369811yescharacteristic
815C2—41no—
816C2—81no—
817C2—862no—
818C2—862no—
819C2—3441no—
820C2#408×D4311yescharacteristic
821C2#1914311111yescharacteristic
822C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1495C2
socleC22×C43C22×C22⋊C4
prime radical#121×D43C4
cosocleC42×C43C24
hypercenter#1495D43
hypocenterC43#17480
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #19143227C2semidirect
3. #431×D43C2semidirect
4. #19133061C2semidirect
5. #19133060C2semidirect
6. #19133058C2semidirect
7. #19133054C2semidirect
8. #19133052C2semidirect
9. #19132988C2semidirect
10. #19132984C2semidirect
11. C43×#1495C2semidirect
35. #14582955C22semidirect
36. #14582952C22semidirect
42. #14582923C22semidirect
47. C4×C8×D43C22semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
55. C43×#431C22semidirect
56. C43×#423C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
410. #1495D43semidirect
454. #431C2×D43semidirect
456. #423C2×D43semidirect
465. Q8⋊C8C2×D43semidirect
469. D4⋊C8C2×D43semidirect
470. C43#17480semidirect

Maximal subgroups

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

subgroupindex
#529×D432
#191432272
#431×D432
#191330612
#191330602
#191330582
#191330542
#191330522
#191329882
#191329842
C43×#14952
#1748043