Finite Group Databasebeta

← #25063048

Subgroups — #25063048

Order 11008.

1246 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D43C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic, complemented
3#19143226C211yesmaximal, characteristic, complemented
4#19133035C211yesmaximal, characteristic, complemented
5#19133034C211yesmaximal, characteristic, complemented
6#19133032C211yesmaximal, characteristic, complemented
7#19133028C212yesmaximal, complemented
8#19133026C212yesmaximal, complemented
9#19132988C212yesmaximal, complemented
10#19132984C212yesmaximal, complemented
11C43×#1489C211yesmaximal, characteristic, complemented
12C2×#41×D43C411yescharacteristic
13#41×Dic43C411yescharacteristic
14C4×#10621902C411yescharacteristic
15C4×#10621902C2211yescharacteristic
16C4×#10621898—21no—
17C4×#10621898C2211yescharacteristic
18#14583367—21no—
19#14583367C411yescharacteristic
20C4×#10621900—21no—
21C4×#10621900—21no—
22C4×#10621900C411yescharacteristic
23C4×#10621900C2211yescharacteristic
24C4×Q8×D43C411yescharacteristic
25C4×Q8×D43C2211yescharacteristic
26C4×D4×D43—21no—
27C4×D4×D43—21no—
28C4×D4×D43C411yescharacteristic
29C4×D4×D43C2211yescharacteristic
30#117×D43—21no—
31#117×D43C411yescharacteristic
32C2×C42×D43—21no—
33C2×C42×D43C2211yescharacteristic
34#14582955—21no—
35#14582955C2212yescomplemented
36#14582954—21no—
37#14582954—21no—
38#14582951—21no—
39#14582951C2212yes—
40#14582950C2212yes—
41#14582950C2212yescomplemented
42#14582923C2211yescharacteristic, complemented
43#14582922—21no—
44#14582862—21no—
45#14582862—21no—
46C4×#10621877C2211yescharacteristic, complemented
47M16×Dic43—21no—
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C4×#41×C43C2211yescharacteristic
55C43×#423C2211yescharacteristic, complemented
56C4×M16×C43C2211yescharacteristic, complemented
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×#10621902C2×C411yescharacteristic
60C2×#10621898—21no—
61C2×#10621898C2×C411yescharacteristic
62C2×#10621900—21no—
63C2×#10621900C2×C411yescharacteristic
64#41×D43—24no—
65#41×D43—24no—
66C2×Q8×D43C2×C411yescharacteristic
67C2×D4×D43—21no—
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2×C411yescharacteristic
73C22×C4×D43D411yescharacteristic
74C22×C4×D43D411yescharacteristic
75C2×#10621877—21no—
76C2×#10621877—21no—
77Q8×Dic43C2×C411yescharacteristic
78Q8×Dic43C2×C411yescharacteristic
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×Dic86C2×C411yescharacteristic
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290—21no—
85#13063290C2×C411yescharacteristic
86#13063290C2×C411yescharacteristic
87C4×D172—21no—
88C4×D172—21no—
89C4×D172C2×C411yescharacteristic
90C4×D172C2311yescharacteristic
91D4×Dic43—21no—
92D4×Dic43—21no—
93D4×Dic43C2×C411yescharacteristic
94D4×Dic43C2×C411yescharacteristic
95#13063287—21no—
96#13063287—21no—
97#13063287C2×C411yescharacteristic
98#13063287C2×C411yescharacteristic
99C4×C22⋊D43—21no—
100C4×C22⋊D43—21no—
101C4×C22⋊D43—21no—
102C4×C22⋊D43—21no—
103C4×C22⋊D43—21no—
104C4×C22⋊D43—21no—
105(C22⋊D43)⋊C4—21no—
106(C22⋊D43)⋊C4—21no—
107(C22⋊D43)⋊C4—21no—
108(C22⋊D43)⋊C4—21no—
109(C22⋊D43)⋊C4—21no—
110(C22⋊D43)⋊C4—21no—
111#13063284—21no—
112#13063284C2×C411yescharacteristic
113#13063283—21no—
114#13063283—21no—
115#13063283C2×C411yescharacteristic
116#13063283C2×C411yescharacteristic
117#13063282—21no—
118#13063282—21no—
119#13063282—21no—
120#13063281—21no—
121#13063281—21no—
122#13063281—21no—
123C4⋊C4×D43—21no—
124C4⋊C4×D43—21no—
125C4⋊C4×D43C2×C411yescharacteristic
126C4⋊C4×D43C2×C411yescharacteristic
127C22⋊C4×D43—21no—
128C22⋊C4×D43—21no—
129C22⋊C4×D43—21no—
130C2×C4×Dic43—21no—
131C2×C4×Dic43—21no—
132C2×C4×Dic43—21no—
133C2×C4×Dic43C2×C411yescharacteristic
134C2×C4×Dic43D411yescharacteristic
135C2×C4×Dic43D411yescharacteristic
136C42×D43—21no—
137C42×D43—21no—
138C42×D43—21no—
139C42×D43—21no—
140C42×D43—21no—
141C42×D43—21no—
142C42×D43—21no—
143C42×D43C2×C411yescharacteristic
144C42×D43C2×C411yescharacteristic
145C42×D43D411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43D411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43C2311yescharacteristic
150C42×D43C2311yescharacteristic
151C4⋊(C43⋊C8)—21no—
152C4⋊(C43⋊C8)C2312yes—
153Dic43⋊C8—22no—
154Dic43⋊C8—22no—
155(C2×D43)⋊C8—22no—
156(C2×D43)⋊C8—22no—
157(C2×D43)⋊C8—22no—
158(C2×D43)⋊C8—22no—
159#13063236—21no—
160#13063235—22no—
161C4×C43⋊C8C2312yes—
162C8×Dic43—22no—
163C2×#41×C43C2×C411yescharacteristic
164C2×M16×C43—21no—
165C2×M16×C43—21no—
166C4×Q8×C43C2×C411yescharacteristic
167C4×Q8×C43C2311yescharacteristic
168C4×D4×C43—21no—
169C4×D4×C43—21no—
170C4×D4×C43C2×C411yescharacteristic
171C4×D4×C43C2311yescharacteristic
172#117×C43—21no—
173#117×C43C2×C411yescharacteristic
174C2×C42×C43—21no—
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43—21no—
177C4⋊C8×C43C2312yes—
178#97×C43—21no—
179C4×C8×C43C2312yes—
180C23×D43—21no—
181C23×D43C22⋊C411yescharacteristic
182#41×C43—22no—
183#41×C43—22no—
184C2×Q8×C43C22×C411yescharacteristic
185C2×D4×C43—21no—
186C2×D4×C43C22×C411yescharacteristic
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43C22×C411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C2×C22⋊D43—21no—
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43C22⋊C411yescharacteristic
200C22×Dic43C22⋊C411yescharacteristic
201C22×Dic43C22⋊C411yescharacteristic
202#10621902—22no—
203#10621902—22no—
204Q8×D43—22no—
205Q8×D43M1614yescomplemented
206#10621900—28no—
207#10621900—22no—
208#10621900—22no—
209D4×D43—28no—
210D4×D43—22no—
211D4×D43M1614yescomplemented
212#10621898—28no—
213#10621898—22no—
214#10621898—22no—
215C2×D172—21no—
216C2×D172C22×C411yescharacteristic
217C2×C4×D43—28no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—41no—
230C2×C4×D43—41no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—42no—
234C2×C4×D43—44no—
235C2×C4×D43C22⋊C411yescharacteristic
236C2×C4×D43C22⋊C411yescharacteristic
237C2×C4×D43C22⋊C411yescharacteristic
238C2×C4×D43C22⋊C411yescharacteristic
239C2×C4×D43C22⋊C411yescharacteristic
240C2×C4×D43C22⋊C411yescharacteristic
241C2×C4×D43C22×C411yescharacteristic
242C2×C4×D43C22×C411yescharacteristic
243C2×C4×D43C2×D411yescharacteristic
244C2×C4×D43C2×D411yescharacteristic
245C2×C4×D43C2×D411yescharacteristic
246C2×C4×D43C2×D411yescharacteristic
247C2×Dic86—21no—
248C2×Dic86C22×C411yescharacteristic
249M16×C43—42no—
250M16×C43—42no—
251C2×C8×C43—22no—
252C2×C8×C43—22no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43C22×C411yescharacteristic
256C4⋊C4×C43C22×C411yescharacteristic
257C22⋊C4×C43—21no—
258C22⋊C4×C43—21no—
259C22⋊C4×C43—21no—
260C42×C43—21no—
261C42×C43—21no—
262C42×C43—21no—
263C42×C43C22×C411yescharacteristic
264C42×C43C2×D411yescharacteristic
265C42×C43C2×D411yescharacteristic
266C42×C43C2411yescharacteristic
267C22⋊Dic43—21no—
268C22⋊Dic43—21no—
269C22⋊Dic43—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4—21no—
275(C2×D43)⋊C4—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43C22×C411yescharacteristic
279C4⋊Dic43C22×C411yescharacteristic
280Dic43⋊C4—21no—
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
283Dic43⋊C4—21no—
284Dic43⋊C4—21no—
285Dic43⋊C4—21no—
286C4×Dic43—21no—
287C4×Dic43—21no—
288C4×Dic43—21no—
289C4×Dic43—21no—
290C4×Dic43—21no—
291C4×Dic43—21no—
292C4×Dic43—21no—
293C4×Dic43—21no—
294C4×Dic43—21no—
295C4×Dic43C22⋊C411yescharacteristic
296C4×Dic43C22⋊C411yescharacteristic
297C4×Dic43C22⋊C411yescharacteristic
298C4×Dic43C22⋊C411yescharacteristic
299C4×Dic43C22⋊C411yescharacteristic
300C4×Dic43C22⋊C411yescharacteristic
301C4×Dic43C22×C411yescharacteristic
302C4×Dic43C22×C411yescharacteristic
303C4×Dic43C2×D411yescharacteristic
304C4×Dic43C2×D411yescharacteristic
305C4×Dic43C2×D411yescharacteristic
306C4×Dic43C2×D411yescharacteristic
307#10621877—42no—
308#10621877—42no—
309C2×C43⋊C8—22no—
310C2×C43⋊C8—22no—
311C23×C43—21no—
312C23×C43C2×C22⋊C411yescharacteristic
313C22×D43—21no—
314C22×D43—22no—
315C22×D43—24no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43—42no—
319C22×D43—42no—
320C22×D43C2×C22⋊C411yescharacteristic
321C22×D43C2×C22⋊C411yescharacteristic
322Q8×C43—21no—
323Q8×C43C2×M1612yes—
324D4×C43—24no—
325D4×C43—21no—
326D4×C43C2×M1612yes—
327C2×C4×C43—24no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—42no—
339C2×C4×C43C2×C22⋊C411yescharacteristic
340C2×C4×C43C2×C22⋊C411yescharacteristic
341C2×C4×C43C2×C22⋊C411yescharacteristic
342C2×C4×C43C23×C411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C22⋊D43—24no—
346C22⋊D43—24no—
347C22⋊D43—24no—
348C2×Dic43—24no—
349C2×Dic43—21no—
350C2×Dic43—22no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—42no—
356C2×Dic43—42no—
357C2×Dic43C2×C22⋊C411yescharacteristic
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362C2×Dic43C2×C22⋊C411yescharacteristic
363D172—24no—
364D172—21no—
365D172C2×M1612yes—
366C4×D43—24no—
367C4×D43—24no—
368C4×D43—22no—
369C4×D43—24no—
370C4×D43—21no—
371C4×D43—21no—
372C4×D43—21no—
373C4×D43—21no—
374C4×D43—21no—
375C4×D43—21no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—41no—
380C4×D43—41no—
381C4×D43—41no—
382C4×D43—41no—
383C4×D43—42no—
384C4×D43—42no—
385C4×D43—42no—
386C4×D43—42no—
387C4×D43—41no—
388C4×D43—41no—
389C4×D43—42no—
390C4×D43C2×M1612yes—
391C4×D43C2×M1612yes—
392Dic86—21no—
393Dic86—24no—
394Dic86C2×M1612yes—
395C8×C43—42no—
396C8×C43—42no—
397C43⋊C8—42no—
398C43⋊C8—42no—
399#17450—431nomaximal, Sylow
400C22×C43—22no—
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43C22×C22⋊C411yescharacteristic
407C2×D43—21no—
408C2×D43—21no—
409C2×D43—22no—
410C2×D43—21no—
411C2×D43—21no—
412C2×D43—21no—
413C2×D43—44no—
414C2×D43—48no—
415C2×D43—41no—
416C2×D43—41no—
417C2×D43#40712yes—
418C4×C43—22no—
419C4×C43—21no—
420C4×C43—21no—
421C4×C43—21no—
422C4×C43—41no—
423C4×C43—41no—
424C4×C43#42112yes—
425C4×C43C22×M1611yescharacteristic
426C4×C43C22×M1611yescharacteristic
427C4×C43#57511yescharacteristic
428C4×C43#57511yescharacteristic
429Dic43—22no—
430Dic43—21no—
431Dic43—21no—
432Dic43—21no—
433Dic43—21no—
434Dic43—21no—
435Dic43—41no—
436Dic43—41no—
437Dic43#40712yes—
438C2×C4×#41—431no—
439#2920—431no—
440#2920—431no—
441#1489—431no—
442#1489—431no—
443#1489—431no—
444#1489D4311yescharacteristic, complemented
445#1488—432no—
446#1488—432no—
447#1479—432no—
448#1478—432no—
449C2×C43—41no—
450C2×C43—42no—
451C2×C43C2×#40711yescharacteristic
452C2×C43#289611yescharacteristic
453C2×C43C2×#42111yescharacteristic
454D43—22no—
455D43—41no—
456D43—42no—
457C22×#41—431no—
458C4×#41—431no—
459C4×#41—431no—
460C4×#41—431no—
461C4×#41—431no—
462C4×#41—431no—
463C4×#41—431no—
464C4×#41—431no—
465C4×#41—861no—
466C4×#41—861no—
467C4×#41—861no—
468C4×#41—861no—
469C4×#41C2×D4311yescharacteristic
470C2×C4×Q8—431no—
471C2×C4×Q8—431no—
472C2×C4×D4—431no—
473C2×C4×D4—431no—
474C2×C4×D4—861no—
475C2×C4×D4—861no—
476C2×#117—431no—
477C2×#117—861no—
478C22×C42—431no—
479C22×C42—861no—
480#432—432no—
481#432—861no—
482#432—861no—
483#432—861no—
484#431—432no—
485#431—432no—
486#431—432no—
487#431—861no—
488#423—431no—
489#423—861no—
490#423C2×D4311yescharacteristic, complemented
491#407—861no—
492#407—861no—
493C4×M16—431no—
494C4×M16—861no—
495C4×M16C2×D4311yescharacteristic, complemented
496Q8⋊C8—432no—
497Q8⋊C8—432no—
498Q8⋊C8—432no—
499Q8⋊C8C2×D4312yescomplemented
500D4⋊C8—432no—
501D4⋊C8—432no—
502D4⋊C8—432no—
503D4⋊C8C2×D4312yescomplemented
504C43#1745011yescharacteristic, complemented, Sylow
505C2×#41—431no—
506C2×#41—431no—
507C2×#41—431no—
508C2×#41—861no—
509C2×#41—861no—
510C2×#41—864no—
511C2×#41—864no—
512C2×#41C4×D4311yescharacteristic
513C22×Q8—431no—
514C22×D4—431no—
515C22×D4—861no—
516C23×C4—431no—
517C23×C4—431no—
518C23×C4—431no—
519C23×C4—861no—
520C23×C4—861no—
521C23×C4—861no—
522C2×M16—21no—
523C2×M16—21no—
524C2×M16—861no—
525C2×M16—861no—
526C4×Q8—431no—
527C4×Q8—431no—
528C4×Q8—431no—
529C4×Q8—431no—
530C4×Q8—431no—
531C4×Q8—431no—
532C4×Q8—861no—
533C4×Q8—861no—
534C4×Q8—861no—
535C4×Q8—861no—
536C4×Q8C4×D4311yescharacteristic
537C4×Q8C22×D4311yescharacteristic
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—431no—
541C4×D4—431no—
542C4×D4—431no—
543C4×D4—431no—
544C4×D4—431no—
545C4×D4—431no—
546C4×D4—861no—
547C4×D4—861no—
548C4×D4—861no—
549C4×D4—861no—
550C4×D4—861no—
551C4×D4—861no—
552C4×D4—861no—
553C4×D4—861no—
554C4×D4—861no—
555C4×D4—861no—
556C4×D4—861no—
557C4×D4—861no—
558C4×D4—861no—
559C4×D4—861no—
560C4×D4—861no—
561C4×D4—861no—
562C4×D4—861no—
563C4×D4—861no—
564C4×D4C4×D4311yescharacteristic
565C4×D4C22×D4311yescharacteristic
566#117—21no—
567#117—431no—
568#117—431no—
569#117—431no—
570#117—861no—
571#117—861no—
572#117—861no—
573#117—861no—
574#117—861no—
575#117—861no—
576#117—861no—
577#117—861no—
578#117—861no—
579#117C4×D4311yescharacteristic
580C2×C4⋊C4—431no—
581C2×C4⋊C4—431no—
582C2×C4⋊C4—861no—
583C2×C4⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C42—21no—
588C2×C42—431no—
589C2×C42—431no—
590C2×C42—431no—
591C2×C42—431no—
592C2×C42—431no—
593C2×C42—431no—
594C2×C42—431no—
595C2×C42—431no—
596C2×C42—431no—
597C2×C42—431no—
598C2×C42—431no—
599C2×C42—861no—
600C2×C42—861no—
601C2×C42—861no—
602C2×C42—861no—
603C2×C42—861no—
604C2×C42—861no—
605C2×C42—861no—
606C2×C42—861no—
607C2×C42—861no—
608C2×C42—861no—
609C2×C42C22×D4311yescharacteristic
610C4⋊C8—21no—
611C4⋊C8—432no—
612C4⋊C8—862no—
613C4⋊C8—862no—
614C4⋊C8—861no—
615C4⋊C8C22×D4312yes—
616C22⋊C8—862no—
617C22⋊C8—862no—
618C22⋊C8—862no—
619C22⋊C8—862no—
620#97—21no—
621#97—862no—
622#97—861no—
623C4×C8—432no—
624C4×C8—862no—
625C4×C8C22×D4312yes—
626C24—431no—
627C24—861no—
628#41—22no—
629#41—22no—
630#41—862no—
631#41—862no—
632#41—868no—
633#41—862no—
634#41—868no—
635#41—862no—
636#41—862no—
637#41—862no—
638C2×Q8—434no—
639C2×Q8—431no—
640C2×Q8—861no—
641C2×Q8—862no—
642C2×Q8C2×C4×D4311yescharacteristic
643C2×D4—21no—
644C2×D4—434no—
645C2×D4—431no—
646C2×D4—861no—
647C2×D4—862no—
648C2×D4—861no—
649C2×D4—868no—
650C2×D4—861no—
651C2×D4—861no—
652C2×D4C2×C4×D4311yescharacteristic
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—861no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—868no—
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—1722no—
687C22×C4—1721no—
688C22×C4—1721no—
689C22×C4—1724no—
690C22×C4—1722no—
691C22×C4—1722no—
692C22×C4C2×C4×D4311yescharacteristic
693C22×C4D4×D4311yescharacteristic
694C22×C4D4×D4311yescharacteristic
695M16—42no—
696M16—42no—
697M16—1722no—
698M16—1722no—
699C2×C8—22no—
700C2×C8—22no—
701C2×C8—862no—
702C2×C8—862no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—431no—
706C4⋊C4—431no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4C2×C4×D4311yescharacteristic
716C4⋊C4C2×C4×D4311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—431no—
733C42—431no—
734C42—431no—
735C42—431no—
736C42—431no—
737C42—431no—
738C42—431no—
739C42—431no—
740C42—431no—
741C42—431no—
742C42—431no—
743C42—431no—
744C42—861no—
745C42—861no—
746C42—861no—
747C42—861no—
748C42—861no—
749C42—861no—
750C42—861no—
751C42—861no—
752C42—861no—
753C42C2×C4×D4311yescharacteristic
754C42D4×D4311yescharacteristic
755C42D4×D4311yescharacteristic
756C42C23×D4311yescharacteristic
757C23—21no—
758C23—431no—
759C23—431no—
760C23—864no—
761C23—862no—
762C23—861no—
763C23—1721no—
764C23—1721no—
765C23—1722no—
766C23—1722no—
767C23C22⋊C4×D4311yescharacteristic
768Q8—21no—
769Q8—432no—
770Q8—864no—
771Q8—861no—
772Q8M16×D4312yes—
773D4—24no—
774D4—21no—
775D4—432no—
776D4—864no—
777D4—864no—
778D4—864no—
779D4—864no—
780D4—861no—
781D4M16×D4312yes—
782C2×C4—24no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—431no—
795C2×C4—432no—
796C2×C4—432no—
797C2×C4—431no—
798C2×C4—431no—
799C2×C4—431no—
800C2×C4—431no—
801C2×C4—431no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—864no—
805C2×C4—864no—
806C2×C4—864no—
807C2×C4—862no—
808C2×C4—864no—
809C2×C4—861no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—862no—
813C2×C4—862no—
814C2×C4—861no—
815C2×C4—861no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—861no—
820C2×C4—1721no—
821C2×C4—1721no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1722no—
825C2×C4—1722no—
826C2×C4—1722no—
827C2×C4—1722no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4—1722no—
833C2×C4—1721no—
834C2×C4—1721no—
835C2×C4C22⋊C4×D4311yescharacteristic
836C2×C4C22⋊C4×D4311yescharacteristic
837C2×C4C22⋊C4×D4311yescharacteristic
838C2×C4C22×C4×D4311yescharacteristic
839C2×C4C2×D4×D4311yescharacteristic
840C2×C4C2×D4×D4311yescharacteristic
841C8—42no—
842C8—42no—
843C8—1722no—
844C8—1722no—
845C22—21no—
846C22—22no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—432no—
852C22—861no—
853C22—861no—
854C22—862no—
855C22—861no—
856C22—861no—
857C22—861no—
858C22—1724no—
859C22—1728no—
860C22—1721no—
861C22—1721no—
862C22C2×C22⋊C4×D4311yescharacteristic
863C4—21no—
864C4—22no—
865C4—21no—
866C4—21no—
867C4—41no—
868C4—41no—
869C4—432no—
870C4—861no—
871C4—862no—
872C4—861no—
873C4—861no—
874C4—861no—
875C4—861no—
876C4—1721no—
877C4—1721no—
878C4#1458291412yes—
879C4C2×M16×D4311yescharacteristic
880C4C2×M16×D4311yescharacteristic
881C4#1458369511yescharacteristic
882C4#1458369811yescharacteristic
883C2—41no—
884C2—42no—
885C2—862no—
886C2—1721no—
887C2—1722no—
888C2#407×D4311yescharacteristic
889C2#1914311111yescharacteristic
890C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1489C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#41×D43C4
cosocleC42×C43C24
hypercenter#1489D43
hypocenterC43#17450
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #19143227C2semidirect
3. #19143226C2semidirect
4. #19133035C2semidirect
5. #19133034C2semidirect
6. #19133032C2semidirect
7. #19133028C2semidirect
8. #19133026C2semidirect
9. #19132988C2semidirect
10. #19132984C2semidirect
11. C43×#1489C2semidirect
35. #14582955C22semidirect
41. #14582950C22semidirect
42. #14582923C22semidirect
46. C4×#10621877C22semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
55. C43×#423C22semidirect
56. C4×M16×C43C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
205. Q8×D43M16semidirect
211. D4×D43M16semidirect
444. #1489D43semidirect
490. #423C2×D43semidirect
495. C4×M16C2×D43semidirect
499. Q8⋊C8C2×D43semidirect
503. D4⋊C8C2×D43semidirect
504. C43#17450semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D432
#191432272
#191432262
#191330352
#191330342
#191330322
#191330282
#191330262
#191329882
#191329842
C43×#14892
#1745043