Finite Group Databasebeta

← #25067555

Subgroups — #25067555

Order 11008.

672 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144601C211yesmaximal, characteristic
2#19143537C211yesmaximal, characteristic, complemented
3#19143331C211yesmaximal, characteristic
4#19133498C211yesmaximal, characteristic, complemented
5#19133497C211yesmaximal, characteristic, complemented
6#19133476C211yesmaximal, characteristic, complemented
7#19133455C211yesmaximal, characteristic, complemented
8#19133454C211yesmaximal, characteristic, complemented
9#19133406C211yesmaximal, characteristic, complemented
10#19133405C211yesmaximal, characteristic, complemented
11#19133368C211yesmaximal, characteristic, complemented
12#19133048C211yesmaximal, characteristic, complemented
13D4⋊C8×D43C211yesmaximal, characteristic
14#19132881C211yesmaximal, characteristic, complemented
15C43×#1588C211yesmaximal, characteristic, complemented
16C2×M16×D43—21no—
17#14583453C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583231C411yescharacteristic
20#14583228C411yescharacteristic
21#14583188C411yescharacteristic
22#14583187C411yescharacteristic
23#14583103C411yescharacteristic
24#14583102C411yescharacteristic
25#14583051C411yescharacteristic
26#14583048C411yescharacteristic
27#14583030C2211yescharacteristic, complemented
28#14583029—21no—
29#14583029C2211yescharacteristic, complemented
30#14583028—21no—
31#14583023C2211yescharacteristic, complemented
32C4×#10621873C2211yescharacteristic
33C4×#10621884C2211yescharacteristic
34C4×#10621883C2211yescharacteristic
35#14582977C2211yescharacteristic
36#14582973—21no—
37#14582968—21no—
38C8×D172C2211yescharacteristic
39#14582964C2211yescharacteristic
40#14582950C2211yescharacteristic
41#14582924—21no—
42#14582921C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44#14582861—21no—
45#14582853—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582651C2211yescharacteristic, complemented
51#14582631C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53#14582629C2211yescharacteristic, complemented
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic, complemented
58#14582620C2211yescharacteristic, complemented
59#14582620C2211yescharacteristic, complemented
60C8×Q8×C43C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#335C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C2×D4×D43C2×C411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621873C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621884C2×C411yescharacteristic
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×#10621872D411yescharacteristic
75C2×#10621872D411yescharacteristic
76M16×D43—44no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81#13063324C2×C411yescharacteristic
82#13063323C2×C411yescharacteristic
83#13063315—21no—
84#13063305C2×C411yescharacteristic
85#13063303—21no—
86#13063301C2×C411yescharacteristic
87C4×Dic86—21no—
88C4×Dic86C2311yescharacteristic
89C4×D172C2311yescharacteristic
90D4×Dic43C2×C411yescharacteristic
91#13063287C2×C411yescharacteristic
92C4×C22⋊D43—21no—
93(C22⋊D43)⋊C4—21no—
94#13063282—21no—
95C4⋊C4×D43C2×C411yescharacteristic
96C22⋊C4×D43—21no—
97C42×D43C2311yescharacteristic
98#13063257C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8C2×C411yescharacteristic
109Dic43⋊C8C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063249C2×C411yescharacteristic
112#13063248C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114#13063246C2×C411yescharacteristic
115#13063245C2×C411yescharacteristic
116C22⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8C2×C411yescharacteristic
120(C2×D43)⋊C8C2×C411yescharacteristic
121#13063236—21no—
122#13063235—21no—
123#13063235D411yescharacteristic
124#13063235D411yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43—21no—
130C2×SD16×C43C2×C411yescharacteristic
131C2×M16×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43C2×C411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×D4×C43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C22×Dic43—21no—
151D4×D43—22no—
152D4×D43—41no—
153C2×D172C22×C411yescharacteristic
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43C22×C411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86C22×C411yescharacteristic
164SD16×C43—41no—
165M16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43C22×C411yescharacteristic
175C4⋊C4×C43C22×C411yescharacteristic
176C22⋊C4×C43—21no—
177C42×C43—21no—
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180#10621884—22no—
181#10621883—41no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C22×C411yescharacteristic
188C4⋊Dic43C22×C411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195C4×Dic43—21no—
196C4×Dic43C22×C411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199#10621877—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207#10621873—22no—
208#10621872—22no—
209#10621872—22no—
210#10621872—42no—
211C8×D43—42no—
212C8×D43—42no—
213C8×D43—42no—
214C8×D43—42no—
215C23×C43—21no—
216C22×D43—21no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43—81no—
220C22×D43C4×D411yescharacteristic
221Q8×C43—21no—
222Q8×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—42no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—42no—
238C2×Dic43C4×D411yescharacteristic
239C2×Dic43C4×D411yescharacteristic
240C2×Dic43C4×D411yescharacteristic
241D172—21no—
242D172#13112yes—
243C4×D43—21no—
244C4×D43—21no—
245C4×D43—41no—
246C4×D43—42no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—42no—
250C4×D43AGL(1,ℤ/8)12yes—
251C4×D43#13712yes—
252Dic86—21no—
253Dic86—21no—
254Dic86—81no—
255C8×C43—22no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#18000—431nomaximal, Sylow
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43C2×C4×D411yescharacteristic
274C2×D43—21no—
275C2×D43—21no—
276C2×D43—22no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—84no—
280C2×D43#44012yes—
281C4×C43—21no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43C2×#13111yescharacteristic
286C4×C43#56811yescharacteristic
287C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C43C2×#13711yescharacteristic
289Dic43—21no—
290Dic43—21no—
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294Dic43#44012yes—
295#3101—431no—
296#2962—431no—
297D4×M16—431no—
298#1592—431no—
299#1592—431no—
300#1588—431no—
301#1588D4311yescharacteristic, complemented
302#1585—431no—
303#1585—431no—
304SD16⋊C8—431no—
305SD16⋊C8—431no—
306#1571—431no—
307#1493—431no—
308C2×D4⋊C8—431no—
309#1451—431no—
310C2×C43—81no—
311C2×C43#293311yescharacteristic
312C2×C43C2×#44011yescharacteristic
313C2×C43#295611yescharacteristic
314D43—22no—
315D43—42no—
316C22×M16—861no—
317#533—431no—
318C2×C4×D4—431no—
319#483—431no—
320#483—431no—
321#476—431no—
322#476—431no—
323#461—431no—
324#461—431no—
325#450—431no—
326#450—431no—
327#446—431no—
328#446—431no—
329#446—861no—
330#446—861no—
331C8×Q8—431no—
332C8×Q8C2×D4311yescharacteristic, complemented
333C4×SD16—431no—
334C4×SD16—431no—
335C4×SD16—431no—
336C4×SD16C2×D4311yescharacteristic
337#436—431no—
338#436C2×D4311yescharacteristic
339#435—861no—
340#435—861no—
341C8×D4—431no—
342C8×D4—431no—
343#431—431no—
344#424—861no—
345#423—431no—
346C2×C4⋊C8—431no—
347#407—861no—
348#405—861no—
349C4×M16—431no—
350C2×C4×C8—431no—
351#335—431no—
352#335—431no—
353#335—431no—
354#335C2×D4311yescharacteristic, complemented
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357Q8⋊C8—431no—
358Q8⋊C8C2×D4311yescharacteristic, complemented
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8C2×D4311yescharacteristic
363#322—431no—
364#322—431no—
365#322—431no—
366#322C2×D4311yescharacteristic, complemented
367C43#1800011yescharacteristic, complemented, Sylow
368C22×D4—431no—
369C23×C4—861no—
370C2×SD16—431no—
371C2×SD16—431no—
372C2×SD16—431no—
373C2×SD16C4×D4311yescharacteristic
374C2×M16—21no—
375C2×M16—431no—
376C2×M16—431no—
377C2×M16—861no—
378C2×M16—861no—
379C2×M16—1724no—
380C22×C8—861no—
381C22×C8—861no—
382C22×C8—861no—
383C22×C8—861no—
384C4⋊Q8—431no—
385C4⋊Q8—431no—
386#125—861no—
387C22⋊Q8—431no—
388C22⋊Q8—431no—
389C22⋊Q8—861no—
390C4×Q8—431no—
391C4×Q8—861no—
392C4×Q8C22×D4311yescharacteristic
393C4×D4—431no—
394C4×D4—431no—
395C4×D4—431no—
396C4×D4—861no—
397C4×D4—861no—
398C4×D4C22×D4311yescharacteristic
399#117—861no—
400C2×C4⋊C4—431no—
401C2×C22⋊C4—861no—
402C2×C42—431no—
403#106—431no—
404#106—431no—
405#106—431no—
406#106C4×D4311yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—431no—
420#103—431no—
421#103—431no—
422#103C4×D4311yescharacteristic
423#102—431no—
424#102—431no—
425#102—431no—
426#102C4×D4311yescharacteristic
427C22⋊C8—21no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—431no—
434#97—431no—
435#97—861no—
436#97—861no—
437C4×C8—21no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—861no—
442C4×C8—861no—
443C4×C8C22×D4311yescharacteristic
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446C24—861no—
447C2×Q8—431no—
448C2×Q8—861no—
449C2×Q8C2×C4×D4311yescharacteristic
450C2×D4—431no—
451C2×D4—861no—
452C2×D4—862no—
453C2×D4—1721no—
454C2×D4C2×C4×D4311yescharacteristic
455C22×C4—21no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—1722no—
464C22×C4—1722no—
465SD16—41no—
466SD16—862no—
467SD16—862no—
468SD16—1721no—
469M16—42no—
470M16—862no—
471M16—862no—
472M16—1722no—
473M16—1722no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—431no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—1722no—
485C2×C8—1722no—
486C2×C8—1722no—
487C2×C8—1722no—
488C2×C8C2×C4×D4311yescharacteristic
489C2×C8C2×C4×D4311yescharacteristic
490C2×C8D4×D4311yescharacteristic
491C2×C8D4×D4311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—431no—
494C4⋊C4—431no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4C2×C4×D4311yescharacteristic
503C4⋊C4C2×C4×D4311yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C42—21no—
511C42—431no—
512C42—431no—
513C42—431no—
514C42—861no—
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—431no—
518C23—861no—
519C23—3441no—
520C23—1722no—
521C23—1722no—
522Q8—21no—
523Q8—21no—
524Q8—861no—
525Q8—861no—
526Q8—3441no—
527D4—21no—
528D4—21no—
529D4—432no—
530D4—861no—
531D4—1722no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—431no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—431no—
541C2×C4—431no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—1721no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4C22×C4×D4311yescharacteristic
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C8—22no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—861no—
564C8—861no—
565C8—861no—
566C8—861no—
567C8—1721no—
568C8—1721no—
569C8—1721no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—432no—
574C22—861no—
575C22—861no—
576C22—862no—
577C22—3444no—
578C22—1721no—
579C22—1721no—
580C22C4×D4×D4311yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—432no—
586C4—861no—
587C4—861no—
588C4—1721no—
589C4—1721no—
590C4—1721no—
591C4#131×D4311yescharacteristic
592C4#1458366511yescharacteristic
593C4AGL(1,ℤ/8)×D4311yescharacteristic
594C4#137×D4311yescharacteristic
595C2—81no—
596C2—862no—
597C2—1722no—
598C2#1914331811yescharacteristic
599C2#440×D4311yescharacteristic
600C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1588C2
socleC22×C43C2×C4×D4
prime radicalC2×D4×D43C2×C4
cosocleC42×C43C24
hypercenter#1588D43
hypocenterC43#18000
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1588

Complements

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

NH ≅ G/Ntype
2. #19143537C2semidirect
4. #19133498C2semidirect
5. #19133497C2semidirect
6. #19133476C2semidirect
7. #19133455C2semidirect
8. #19133454C2semidirect
9. #19133406C2semidirect
10. #19133405C2semidirect
11. #19133368C2semidirect
12. #19133048C2semidirect
14. #19132881C2semidirect
15. C43×#1588C2semidirect
27. #14583030C22semidirect
29. #14583029C22semidirect
31. #14583023C22semidirect
48. #14582652C22semidirect
49. #14582651C22semidirect
50. #14582651C22semidirect
51. #14582631C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
53. #14582629C22semidirect
57. #14582621C22semidirect
58. #14582620C22semidirect
59. #14582620C22semidirect
60. C8×Q8×C43C22semidirect
63. C43×#335C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
301. #1588D43semidirect
332. C8×Q8C2×D43semidirect
354. #335C2×D43semidirect
358. Q8⋊C8C2×D43semidirect
366. #322C2×D43semidirect
367. C43#18000semidirect

Maximal subgroups

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

subgroupindex
#191446012
#191435372
#191433312
#191334982
#191334972
#191334762
#191334552
#191334542
#191334062
#191334052
#191333682
#191330482
D4⋊C8×D432
#191328812
C43×#15882
#1800043