Finite Group Databasebeta

← #25066263

Subgroups — #25066263

Order 11008.

726 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143633C211yesmaximal, characteristic, complemented
2#19143616C211yesmaximal, characteristic, complemented
3C4×D8×D43C211yesmaximal, characteristic
4#19133462C211yesmaximal, characteristic, complemented
5#19133459C211yesmaximal, characteristic, complemented
6#19133457C211yesmaximal, characteristic, complemented
7#19133456C211yesmaximal, characteristic, complemented
8#19133426C211yesmaximal, characteristic, complemented
9#19133425C211yesmaximal, characteristic, complemented
10#19133423C211yesmaximal, characteristic, complemented
11#19133342C211yesmaximal, characteristic, complemented
12#19132984C211yesmaximal, characteristic, complemented
13#19132984C211yesmaximal, characteristic, complemented
14#19132886C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16C2×D8×D43C411yescharacteristic
17C4×D4×D43C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19C4×D344C2211yescharacteristic
20D8×Dic43C411yescharacteristic
21#14582981C411yescharacteristic
22C4×#10621882C2211yescharacteristic
23C4×#10621882C2211yescharacteristic
24#14582979C411yescharacteristic
25#14582979C411yescharacteristic
26#14582978C2211yescharacteristic, complemented
27#14582977C2211yescharacteristic, complemented
28#14582976C2211yescharacteristic, complemented
29#14582975—21no—
30#14582974—21no—
31C8×D172C2211yescharacteristic, complemented
32D4×C43⋊C8C2211yescharacteristic, complemented
33#14582964C2211yescharacteristic, complemented
34C8×C22⋊D43—21no—
35(C22⋊D43)⋊C8—21no—
36#14582951C2211yescharacteristic
37#14582951C2211yescharacteristic
38#14582950C2211yescharacteristic
39#14582950C2211yescharacteristic
40#107×D43C411yescharacteristic
41#102×D43C411yescharacteristic
42#102×D43C411yescharacteristic
43#14582862—21no—
44#14582861—21no—
45C2×(C2×D43)⋊C8—21no—
46C22⋊C8×D43—21no—
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic, complemented
49#14582649C2211yescharacteristic, complemented
50#14582649C2211yescharacteristic, complemented
51#14582628C2211yescharacteristic, complemented
52#14582628C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582626C2211yescharacteristic, complemented
56#14582626C2211yescharacteristic, complemented
57#14582621C2211yescharacteristic, complemented
58#14582621C2211yescharacteristic, complemented
59#14582620C2211yescharacteristic, complemented
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic, complemented
62C8×D4×C43C2211yescharacteristic, complemented
63C43×#335C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×D4×D43C2×C411yescharacteristic
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C2×D344C2×C411yescharacteristic
72C2×#10621882C2×C411yescharacteristic
73C2×#10621882C2×C411yescharacteristic
74D8×D43—24no—
75C2×#10621877—21no—
76C2×#10621872—21no—
77C2×#10621872—21no—
78C22×C43⋊C8—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81C2×C8×D43C2×C411yescharacteristic
82C2×C8×D43C2×C411yescharacteristic
83C4×D172C2311yescharacteristic
84C4×D172C2311yescharacteristic
85D4×Dic43C2×C411yescharacteristic
86D4×Dic43C2×C411yescharacteristic
87#13063287C2×C411yescharacteristic
88#13063287C2×C411yescharacteristic
89C4×C22⋊D43—21no—
90C4×C22⋊D43—21no—
91(C22⋊D43)⋊C4—21no—
92(C22⋊D43)⋊C4—21no—
93C4⋊C4×D43C2×C411yescharacteristic
94C4⋊C4×D43C2×C411yescharacteristic
95C22⋊C4×D43—21no—
96C22⋊C4×D43—21no—
97C42×D43C2311yescharacteristic
98#13063259C2×C411yescharacteristic
99#13063258C2×C411yescharacteristic
100#13063258C2×C411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8D411yescharacteristic
105Dic43⋊C8D411yescharacteristic
106#13063247C2×C411yescharacteristic
107#13063247C2×C411yescharacteristic
108#13063246C2×C411yescharacteristic
109#13063246C2×C411yescharacteristic
110#13063245C2×C411yescharacteristic
111#13063245C2×C411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8D411yescharacteristic
122(C2×D43)⋊C8D411yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43C2×C411yescharacteristic
129C8×Dic43C2×C411yescharacteristic
130C2×D8×C43C2×C411yescharacteristic
131C2×M16×C43—21no—
132C22×C8×C43—21no—
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43C2×C411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#102×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C23×D43—21no—
147C2×D4×C43C22×C411yescharacteristic
148C2×D4×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155D4×D43—22no—
156D4×D43—22no—
157D4×D43—22no—
158D4×D43M1614yescomplemented
159C2×D172C22×C411yescharacteristic
160C2×D172C22×C411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
171C2×C4×D43C22×C411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43#4111yescharacteristic
174D8×C43—22no—
175M16×C43—81no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—81no—
180C2×C8×C43C22×C411yescharacteristic
181C2×C8×C43C22×C411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43C22×C411yescharacteristic
185C4⋊C4×C43C22×C411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C42×C43C2411yescharacteristic
189C22⋊Dic43—21no—
190C22⋊Dic43—21no—
191#10621882—22no—
192#10621882—22no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197C4⋊Dic43C22×C411yescharacteristic
198C4⋊Dic43C22×C411yescharacteristic
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201C4×Dic43C22×C411yescharacteristic
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43#4111yescharacteristic
204#10621877—81no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—81no—
209C2×C43⋊C8C22×C411yescharacteristic
210C2×C43⋊C8C22×C411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213D344—22no—
214#10621872—81no—
215#10621872—81no—
216C8×D43—22no—
217C8×D43—22no—
218C8×D43—81no—
219C8×D43—81no—
220C23×C43—21no—
221C23×C43—21no—
222C22×D43—21no—
223C22×D43—24no—
224C22×D43—21no—
225C22×D43—42no—
226C22×D43—81no—
227C22×D43—81no—
228C22×D43—81no—
229C22×D43—81no—
230C22×D43C4×D411yescharacteristic
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43C2×M1612yes—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43C23×C411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C22⋊D43—24no—
245C22⋊D43—42no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—81no—
249C2×Dic43—81no—
250C2×Dic43C4×D411yescharacteristic
251C2×Dic43C4×D411yescharacteristic
252C2×Dic43C4×D411yescharacteristic
253D172—21no—
254D172—21no—
255D172—21no—
256D172C2×M1612yes—
257C4×D43—21no—
258C4×D43—21no—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—81no—
265C4×D43—81no—
266C4×D43—81no—
267C4×D43—81no—
268C4×D43C2×M1612yes—
269C4×D43#13112yes—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—21no—
273C8×C43—21no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—21no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#17877—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43C2×C4×D411yescharacteristic
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—22no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—84no—
301C2×D43—84no—
302C2×D43#43512yes—
303C4×C43—21no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43C22×M1611yescharacteristic
307C4×C43C2×#13111yescharacteristic
308C4×C43#57611yescharacteristic
309C4×C43#57611yescharacteristic
310Dic43—21no—
311Dic43—21no—
312Dic43—41no—
313Dic43—41no—
314Dic43#43512yes—
315#2975—431no—
316#2972—431no—
317C2×C4×D8—431no—
318#1586—431no—
319#1586—431no—
320#1586—431no—
321#1586—431no—
322#1581—431no—
323#1581—431no—
324#1581—431no—
325#1581D4311yescharacteristic, complemented
326#1564—431no—
327#1478—431no—
328#1478—431no—
329#1452—431no—
330C2×C43—42no—
331C2×C43—81no—
332C2×C43C2×#43511yescharacteristic
333C2×C43#294811yescharacteristic
334C2×C43#295711yescharacteristic
335D43—22no—
336D43—42no—
337D43—81no—
338C22×D8—431no—
339C2×C4×D4—431no—
340C2×C4×D4—431no—
341C4×D8—431no—
342C4×D8—431no—
343C4×D8—431no—
344C4×D8—431no—
345C4×D8—431no—
346C4×D8—431no—
347C4×D8—431no—
348C4×D8C2×D4311yescharacteristic
349#436—431no—
350#436—431no—
351#436—431no—
352#436—861no—
353#436—861no—
354#436C2×D4311yescharacteristic, complemented
355C8×D4—431no—
356C8×D4—431no—
357C8×D4—431no—
358C8×D4—861no—
359C8×D4—861no—
360C8×D4C2×D4311yescharacteristic, complemented
361#431—431no—
362#431—431no—
363#431—431no—
364#431—431no—
365C2×#107—431no—
366C2×#102—431no—
367C2×#102—431no—
368#407—861no—
369#407—861no—
370C2×C22⋊C8—861no—
371C2×C22⋊C8—861no—
372C2×C4×C8—431no—
373#335—431no—
374#335C2×D4311yescharacteristic, complemented
375#334—431no—
376#334—431no—
377D4⋊C8—431no—
378D4⋊C8—431no—
379D4⋊C8—431no—
380D4⋊C8—431no—
381D4⋊C8—431no—
382D4⋊C8—431no—
383D4⋊C8C2×D4311yescharacteristic, complemented
384D4⋊C8C2×D4311yescharacteristic, complemented
385#322—431no—
386#322—431no—
387#322—431no—
388#322C2×D4311yescharacteristic, complemented
389C43#1787711yescharacteristic, complemented, Sylow
390C22×D4—431no—
391C22×D4—431no—
392C23×C4—861no—
393C23×C4—861no—
394C2×D8—431no—
395C2×D8—431no—
396C2×D8—431no—
397C2×D8—864no—
398C2×D8C4×D4311yescharacteristic
399C2×M16—21no—
400C2×M16—861no—
401C2×M16—861no—
402C2×M16—861no—
403C22×C8—21no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8—861no—
407C22×C8—861no—
408C22×C8—861no—
409C4×D4—431no—
410C4×D4—431no—
411C4×D4—431no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—431no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4—861no—
419C4×D4C22×D4311yescharacteristic
420C4×D4C22×D4311yescharacteristic
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C42—431no—
426#107—431no—
427#107—431no—
428#107—431no—
429#107C4×D4311yescharacteristic
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—431no—
434C4⋊C8—861no—
435C4⋊C8C22×D4311yescharacteristic
436C4⋊C8C22×D4311yescharacteristic
437#102—431no—
438#102—431no—
439#102—431no—
440#102—431no—
441#102—431no—
442#102—431no—
443#102C4×D4311yescharacteristic
444#102C4×D4311yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—431no—
448C22⋊C8—431no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456C22⋊C8—861no—
457C22⋊C8—861no—
458C4×C8—431no—
459C4×C8—431no—
460C4×C8—431no—
461C4×C8—431no—
462C4×C8—431no—
463C4×C8—861no—
464C4×C8—861no—
465C4×C8C22×D4311yescharacteristic
466C4×C8C22×D4311yescharacteristic
467C4×C8C22×D4311yescharacteristic
468C24—861no—
469C24—861no—
470C2×D4—434no—
471C2×D4—431no—
472C2×D4—431no—
473C2×D4—862no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4C2×C4×D4311yescharacteristic
479C2×D4C2×C4×D4311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—3441no—
494C22×C4—3441no—
495C22×C4—3441no—
496C22×C4—3441no—
497D8—22no—
498D8—862no—
499D8—862no—
500D8—862no—
501M16—81no—
502M16—3441no—
503M16—3441no—
504M16—3441no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—81no—
509C2×C8—431no—
510C2×C8—431no—
511C2×C8—431no—
512C2×C8—431no—
513C2×C8—862no—
514C2×C8—862no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—3441no—
519C2×C8—3441no—
520C2×C8—3441no—
521C2×C8C2×C4×D4311yescharacteristic
522C2×C8C2×C4×D4311yescharacteristic
523C2×C8D4×D4311yescharacteristic
524C2×C8D4×D4311yescharacteristic
525C4⋊C4—431no—
526C4⋊C4—431no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4C2×C4×D4311yescharacteristic
530C4⋊C4C2×C4×D4311yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—861no—
534C22⋊C4—861no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C22⋊C4—861no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42C23×D4311yescharacteristic
543C23—21no—
544C23—21no—
545C23—431no—
546C23—864no—
547C23—861no—
548C23—861no—
549C23—3441no—
550C23—3441no—
551C23—3441no—
552C23—3441no—
553C23—1722no—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—432no—
558D4—864no—
559D4—861no—
560D4—861no—
561D4—861no—
562D4—1722no—
563D4M16×D4312yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—431no—
571C2×C4—432no—
572C2×C4—432no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—3441no—
580C2×C4—3441no—
581C2×C4—3441no—
582C2×C4—3441no—
583C2×C4—3441no—
584C2×C4—3441no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4C22×C4×D4311yescharacteristic
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—861no—
601C8—861no—
602C8—861no—
603C8—861no—
604C8—1721no—
605C8—1721no—
606C8—1721no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—432no—
614C22—861no—
615C22—861no—
616C22—862no—
617C22—3444no—
618C22—3444no—
619C22—1721no—
620C22—1721no—
621C22—1721no—
622C22—1721no—
623C22—1721no—
624C22C4×D4×D4311yescharacteristic
625C4—21no—
626C4—41no—
627C4—41no—
628C4—432no—
629C4—861no—
630C4—861no—
631C4—1721no—
632C4—1721no—
633C4C2×M16×D4311yescharacteristic
634C4#131×D4311yescharacteristic
635C4#1458370011yescharacteristic
636C4#1458370111yescharacteristic
637C2—42no—
638C2—81no—
639C2—862no—
640C2—3441no—
641C2—1722no—
642C2#435×D4311yescharacteristic
643C2#1914344211yescharacteristic
644C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1581C2
socleC22×C43C2×C4×D4
prime radicalC2×D8×D43C4
cosocleC42×C43C24
hypercenter#1581D43
hypocenterC43#17877
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
1. #19143633C2semidirect
2. #19143616C2semidirect
4. #19133462C2semidirect
5. #19133459C2semidirect
6. #19133457C2semidirect
7. #19133456C2semidirect
8. #19133426C2semidirect
9. #19133425C2semidirect
10. #19133423C2semidirect
11. #19133342C2semidirect
12. #19132984C2semidirect
13. #19132984C2semidirect
14. #19132886C2semidirect
15. C43×#1581C2semidirect
26. #14582978C22semidirect
27. #14582977C22semidirect
28. #14582976C22semidirect
31. C8×D172C22semidirect
32. D4×C43⋊C8C22semidirect
33. #14582964C22semidirect
48. #14582652C22semidirect
49. #14582649C22semidirect
50. #14582649C22semidirect
51. #14582628C22semidirect
52. #14582628C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. #14582626C22semidirect
56. #14582626C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. #14582620C22semidirect
61. C43×#436C22semidirect
62. C8×D4×C43C22semidirect
63. C43×#335C22semidirect
64. C43×D4⋊C8C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
158. D4×D43M16semidirect
325. #1581D43semidirect
354. #436C2×D43semidirect
360. C8×D4C2×D43semidirect
374. #335C2×D43semidirect
383. D4⋊C8C2×D43semidirect
384. D4⋊C8C2×D43semidirect
388. #322C2×D43semidirect
389. C43#17877semidirect

Maximal subgroups

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

subgroupindex
#191436332
#191436162
C4×D8×D432
#191334622
#191334592
#191334572
#191334562
#191334262
#191334252
#191334232
#191333422
#191329842
#191328862
C43×#15812
#1787743