Finite Group Databasebeta

← #25063147

Subgroups — #25063147

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D43C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3#431×D43C211yesmaximal, characteristic, complemented
4#19133007C212yesmaximal, complemented
5#19133005C212yesmaximal, complemented
6#19133004C211yesmaximal, characteristic, complemented
7#19133003C211yesmaximal, characteristic, complemented
8#19133001C211yesmaximal, characteristic, complemented
9#19132988C212yesmaximal, complemented
10#19132984C212yesmaximal, complemented
11C43×#1482C211yesmaximal, 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#14582953—21no—
36#14582952C2211yescharacteristic, complemented
37#14582952C2211yescharacteristic, complemented
38#14582951C2212yes—
39#14582950—21no—
40#14582950C2212yes—
41#14582949—21no—
42#14582921—21no—
43C4⋊C8×D43C2212yescomplemented
44#14582861—21no—
45C22⋊C8×D43—21no—
46C4×#10621872C2212yescomplemented
47C4×C8×D43—21no—
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C43×#529C2211yescharacteristic
55C43×#431C2211yescharacteristic, complemented
56C43×#431C2211yescharacteristic, 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×#10621872—22no—
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)C2312yes—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)—21no—
154C22⋊(C43⋊C8)—21no—
155(C2×D43)⋊C8—22no—
156(C2×D43)⋊C8—22no—
157#13063235—22no—
158C4×C43⋊C8—21no—
159C4×C43⋊C8C2312yes—
160C8×Dic43—22no—
161#126×C43—21no—
162#125×C43C2×C411yescharacteristic
163#124×C43C2×C411yescharacteristic
164#123×C43—21no—
165C22⋊Q8×C43C2×C411yescharacteristic
166#121×C43C2×C411yescharacteristic
167C4×Q8×C43C2311yescharacteristic
168C4×D4×C43—21no—
169C4×D4×C43C2311yescharacteristic
170#117×C43—21no—
171C2×C42×C43C2311yescharacteristic
172C4⋊C8×C43—21no—
173C4⋊C8×C43C2312yes—
174C22⋊C8×C43—21no—
175C22⋊C8×C43—21no—
176C4×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—42no—
207C2×C4×D43—44no—
208C2×C4×D43C22⋊C411yescharacteristic
209C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
217C2×C4×D43C2×D411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×Dic86—21no—
221C2×Dic86C22×C411yescharacteristic
222C2×C8×C43—22no—
223C2×C8×C43—22no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43C22×C411yescharacteristic
229C4⋊C4×C43C22×C411yescharacteristic
230C22⋊C4×C43—21no—
231C22⋊C4×C43—21no—
232C22⋊C4×C43—21no—
233C22⋊C4×C43—21no—
234C22⋊C4×C43—21no—
235C42×C43—21no—
236C42×C43C22×C411yescharacteristic
237C42×C43C2×D411yescharacteristic
238C42×C43C2×D411yescharacteristic
239C42×C43C2411yescharacteristic
240C22⋊Dic43—21no—
241C22⋊Dic43—21no—
242C22⋊Dic43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245(C2×D43)⋊C4—21no—
246(C2×D43)⋊C4—21no—
247(C2×D43)⋊C4—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—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43C22×C411yescharacteristic
260C4⋊Dic43C22×C411yescharacteristic
261Dic43⋊C4—21no—
262Dic43⋊C4—21no—
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271C4×Dic43—21no—
272C4×Dic43—21no—
273C4×Dic43—21no—
274C4×Dic43C22⋊C411yescharacteristic
275C4×Dic43C22⋊C411yescharacteristic
276C4×Dic43C22⋊C411yescharacteristic
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22×C411yescharacteristic
281C4×Dic43C22×C411yescharacteristic
282C4×Dic43C2×D411yescharacteristic
283C4×Dic43C2×D411yescharacteristic
284C4×Dic43C2×D411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C2×C43⋊C8—22no—
287C2×C43⋊C8—22no—
288#10621872—44no—
289C8×D43—44no—
290C23×C43—21no—
291C23×C43C2×C22⋊C411yescharacteristic
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—21no—
295C22×D43—41no—
296C22×D43—42no—
297C22×D43—42no—
298C22×D43—42no—
299C22×D43C2×C22⋊C411yescharacteristic
300C22×D43C2×C22⋊C411yescharacteristic
301Q8×C43—22no—
302D4×C43—22no—
303D4×C43—42no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—41no—
310C2×C4×C43—42no—
311C2×C4×C43C2×C22⋊C411yescharacteristic
312C2×C4×C43C2×C22⋊C411yescharacteristic
313C2×C4×C43C2×C22⋊C411yescharacteristic
314C2×C4×C43C23×C411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C22⋊D43—42no—
318C22⋊D43—42no—
319C22⋊D43—42no—
320C2×Dic43—22no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—42no—
327C2×Dic43C2×C22⋊C411yescharacteristic
328C2×Dic43C2×C22⋊C411yescharacteristic
329C2×Dic43C2×C22⋊C411yescharacteristic
330C2×Dic43C2×C22⋊C411yescharacteristic
331C2×Dic43C2×C22⋊C411yescharacteristic
332C2×Dic43C2×C22⋊C411yescharacteristic
333D172—22no—
334D172—42no—
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—41no—
343C4×D43—41no—
344C4×D43—41no—
345C4×D43—41no—
346C4×D43—42no—
347C4×D43—42no—
348C4×D43—42no—
349C4×D43—42no—
350C4×D43—42no—
351C4×D43#13114yes—
352Dic86—22no—
353Dic86—42no—
354C8×C43—42no—
355C8×C43—42no—
356C43⋊C8—42no—
357C43⋊C8—42no—
358#17465—431nomaximal, Sylow
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—21no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43C22×C22⋊C411yescharacteristic
366C2×D43—21no—
367C2×D43—21no—
368C2×D43—21no—
369C2×D43—21no—
370C2×D43—44no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—84no—
375C2×D43#40812yes—
376C2×D43#42112yes—
377C4×C43—21no—
378C4×C43—21no—
379C4×C43—21no—
380C4×C43—21no—
381C4×C43—41no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43C2×#13112yes—
385C4×C43#57512yes—
386Dic43—21no—
387Dic43—21no—
388Dic43—21no—
389Dic43—21no—
390Dic43—21no—
391Dic43—41no—
392Dic43—41no—
393Dic43—41no—
394Dic43#40812yes—
395C2×#529—431no—
396#2920—431no—
397C2×#431—431no—
398#1483—432no—
399#1483—432no—
400#1482—431no—
401#1482—431no—
402#1482—431no—
403#1482D4311yescharacteristic, complemented
404#1479—432no—
405#1478—432no—
406C2×C43—41no—
407C2×C43—81no—
408C2×C43C2×#40811yescharacteristic
409C2×C43#289611yescharacteristic
410C2×C43C2×#42111yescharacteristic
411D43—22no—
412D43—22no—
413D43—81no—
414#529—431no—
415#529—431no—
416#529—431no—
417#529—431no—
418#529—431no—
419#529—431no—
420#529—431no—
421#529—861no—
422#529—861no—
423#529—861no—
424#529—861no—
425#529C2×D4311yescharacteristic
426C2×#126—861no—
427C2×#125—431no—
428C2×#124—431no—
429C2×#123—861no—
430C2×C22⋊Q8—431no—
431C2×#121—431no—
432C2×C4×Q8—431no—
433C2×C4×D4—431no—
434C2×C4×D4—861no—
435C2×#117—861no—
436C22×C42—431no—
437#432—861no—
438#432—861no—
439#431—431no—
440#431—432no—
441#431—431no—
442#431—432no—
443#431—861no—
444#431—861no—
445#431C2×D4311yescharacteristic, complemented
446#431C2×D4311yescharacteristic, complemented
447#423—861no—
448C2×C4⋊C8—432no—
449#407—861no—
450C2×C22⋊C8—861no—
451C4×M16—432no—
452C2×C4×C8—861no—
453Q8⋊C8—432no—
454Q8⋊C8—432no—
455Q8⋊C8—432no—
456Q8⋊C8C2×D4312yescomplemented
457D4⋊C8—432no—
458D4⋊C8—432no—
459D4⋊C8—432no—
460D4⋊C8C2×D4312yescomplemented
461C43#1746511yescharacteristic, complemented, Sylow
462C22×Q8—431no—
463C22×D4—431no—
464C22×D4—861no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—861no—
469C2×M16—862no—
470C22×C8—862no—
471#126—21no—
472#126—861no—
473#126—861no—
474#126—861no—
475#126—861no—
476#126—861no—
477#126—861no—
478#126—861no—
479#125—431no—
480#125—431no—
481#125—431no—
482#125—861no—
483#125—861no—
484#125C4×D4311yescharacteristic
485#124—431no—
486#124—431no—
487#124—431no—
488#124—861no—
489#124—861no—
490#124C4×D4311yescharacteristic
491#123—21no—
492#123—861no—
493#123—861no—
494#123—861no—
495#123—861no—
496#123—861no—
497#123—861no—
498#123—861no—
499C22⋊Q8—431no—
500C22⋊Q8—431no—
501C22⋊Q8—431no—
502C22⋊Q8—861no—
503C22⋊Q8—861no—
504C22⋊Q8C4×D4311yescharacteristic
505#121—431no—
506#121—431no—
507#121—431no—
508#121—861no—
509#121—861no—
510#121C4×D4311yescharacteristic
511C4×Q8—431no—
512C4×Q8—431no—
513C4×Q8—431no—
514C4×Q8—861no—
515C4×Q8—861no—
516C4×Q8C22×D4311yescharacteristic
517C4×D4—21no—
518C4×D4—431no—
519C4×D4—431no—
520C4×D4—431no—
521C4×D4—861no—
522C4×D4—861no—
523C4×D4—861no—
524C4×D4—861no—
525C4×D4—861no—
526C4×D4—861no—
527C4×D4—861no—
528C4×D4—861no—
529C4×D4—861no—
530C4×D4C22×D4311yescharacteristic
531#117—21no—
532#117—861no—
533#117—861no—
534#117—861no—
535#117—861no—
536#117—861no—
537#117—861no—
538#117—861no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C42—431no—
551C2×C42—431no—
552C2×C42—431no—
553C2×C42—431no—
554C2×C42—431no—
555C2×C42—431no—
556C2×C42—431no—
557C2×C42—431no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—431no—
561C2×C42—861no—
562C2×C42C22×D4311yescharacteristic
563C4⋊C8—21no—
564C4⋊C8—432no—
565C4⋊C8—862no—
566C4⋊C8—862no—
567C4⋊C8—861no—
568C4⋊C8C22×D4312yes—
569C22⋊C8—21no—
570C22⋊C8—21no—
571C22⋊C8—862no—
572C22⋊C8—862no—
573C22⋊C8—861no—
574C22⋊C8—861no—
575#97—862no—
576C4×C8—21no—
577C4×C8—432no—
578C4×C8—862no—
579C4×C8—861no—
580C4×C8C22×D4312yes—
581C24—431no—
582C24—861no—
583C2×Q8—431no—
584C2×Q8—861no—
585C2×Q8—864no—
586C2×Q8C2×C4×D4311yescharacteristic
587C2×D4—21no—
588C2×D4—431no—
589C2×D4—861no—
590C2×D4—864no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—1724no—
595C2×D4C2×C4×D4311yescharacteristic
596C22×C4—21no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—864no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—1722no—
620C22×C4—1722no—
621C22×C4—1724no—
622C22×C4C2×C4×D4311yescharacteristic
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625M16—1724no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—862no—
629C2×C8—862no—
630C2×C8—1724no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—431no—
636C4⋊C4—431no—
637C4⋊C4—861no—
638C4⋊C4—861no—
639C4⋊C4—861no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4C2×C4×D4311yescharacteristic
652C4⋊C4C2×C4×D4311yescharacteristic
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—861no—
659C22⋊C4—861no—
660C22⋊C4—861no—
661C22⋊C4—861no—
662C22⋊C4—861no—
663C22⋊C4—861no—
664C22⋊C4—861no—
665C22⋊C4—861no—
666C22⋊C4—861no—
667C22⋊C4—861no—
668C22⋊C4—861no—
669C22⋊C4—861no—
670C22⋊C4—861no—
671C22⋊C4—861no—
672C22⋊C4—861no—
673C42—21no—
674C42—431no—
675C42—431no—
676C42—431no—
677C42—431no—
678C42—431no—
679C42—431no—
680C42—431no—
681C42—431no—
682C42—431no—
683C42—431no—
684C42—431no—
685C42—431no—
686C42—861no—
687C42—861no—
688C42—861no—
689C42C2×C4×D4311yescharacteristic
690C42D4×D4311yescharacteristic
691C42D4×D4311yescharacteristic
692C42C23×D4311yescharacteristic
693C23—21no—
694C23—431no—
695C23—431no—
696C23—862no—
697C23—862no—
698C23—861no—
699C23—1721no—
700C23—1722no—
701C23—1722no—
702C23—1722no—
703C23C22⋊C4×D4311yescharacteristic
704Q8—22no—
705Q8—862no—
706Q8—1722no—
707D4—22no—
708D4—42no—
709D4—862no—
710D4—1722no—
711D4—1722no—
712D4—1722no—
713D4—1722no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—431no—
722C2×C4—434no—
723C2×C4—431no—
724C2×C4—431no—
725C2×C4—431no—
726C2×C4—431no—
727C2×C4—431no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1722no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1722no—
750C2×C4—1722no—
751C2×C4C22⋊C4×D4311yescharacteristic
752C2×C4C22⋊C4×D4311yescharacteristic
753C2×C4C22⋊C4×D4311yescharacteristic
754C2×C4C22×C4×D4311yescharacteristic
755C2×C4C2×D4×D4311yescharacteristic
756C2×C4C2×D4×D4311yescharacteristic
757C8—42no—
758C8—42no—
759C8—1722no—
760C8—1722no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—432no—
768C22—432no—
769C22—861no—
770C22—861no—
771C22—861no—
772C22—861no—
773C22—3444no—
774C22—1724no—
775C22—1721no—
776C22—1721no—
777C22—1721no—
778C22C2×C22⋊C4×D4311yescharacteristic
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—432no—
787C4—861no—
788C4—861no—
789C4—861no—
790C4—861no—
791C4—861no—
792C4—1721no—
793C4—1721no—
794C4—1721no—
795C4#131×D4312yes—
796C4#1458369612yes—
797C2—41no—
798C2—81no—
799C2—862no—
800C2—862no—
801C2—3441no—
802C2#408×D4311yescharacteristic
803C2#1914311011yescharacteristic
804C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1482C2
socleC22×C43C22×C22⋊C4
prime radical#121×D43C4
cosocleC42×C43C24
hypercenter#1482D43
hypocenterC43#17465
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. #431×D43C2semidirect
4. #19133007C2semidirect
5. #19133005C2semidirect
6. #19133004C2semidirect
7. #19133003C2semidirect
8. #19133001C2semidirect
9. #19132988C2semidirect
10. #19132984C2semidirect
11. C43×#1482C2semidirect
36. #14582952C22semidirect
37. #14582952C22semidirect
43. C4⋊C8×D43C22semidirect
46. C4×#10621872C22semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
55. C43×#431C22semidirect
56. C43×#431C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
403. #1482D43semidirect
445. #431C2×D43semidirect
446. #431C2×D43semidirect
456. Q8⋊C8C2×D43semidirect
460. D4⋊C8C2×D43semidirect
461. C43#17465semidirect

Maximal subgroups

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

subgroupindex
#529×D432
#191432232
#431×D432
#191330072
#191330052
#191330042
#191330032
#191330012
#191329882
#191329842
C43×#14822
#1746543