Finite Group Databasebeta

← #25066503

Subgroups — #25066503

Order 11008.

634 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144613C211yesmaximal, characteristic
2#19143570C211yesmaximal, characteristic, complemented
3#19133445C211yesmaximal, characteristic, complemented
4#19133438C211yesmaximal, characteristic, complemented
5#19133431C211yesmaximal, characteristic, complemented
6#19133424C211yesmaximal, characteristic, complemented
7C8×#10621885C211yesmaximal, characteristic, complemented
8C8×#10621884C211yesmaximal, characteristic, complemented
9C8×#10621883C211yesmaximal, characteristic, complemented
10C8×#10621882C211yesmaximal, characteristic, complemented
11#19133373C211yesmaximal, characteristic, complemented
12#19133029C211yesmaximal, characteristic, complemented
13#19133001C211yesmaximal, characteristic, complemented
14#19132878C211yesmaximal, characteristic, complemented
15C8×#41×C43C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583240C411yescharacteristic
18#14583223C411yescharacteristic
19#14583206C411yescharacteristic
20#14583199C411yescharacteristic
21#14583121C411yescharacteristic
22#14583114C411yescharacteristic
23#14583061C411yescharacteristic
24#14583044C411yescharacteristic
25#14583029C2211yescharacteristic
26C8×Dic86C2211yescharacteristic
27C4×#10621885C2211yescharacteristic
28C4×#10621884C2211yescharacteristic
29C4×#10621883C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582970—21no—
33C8×D172C2211yescharacteristic
34C8×C22⋊D43—21no—
35#14582958—21no—
36#14582956C2211yescharacteristic
37#14582952C2211yescharacteristic
38#14582952C2211yescharacteristic
39#14582853—21no—
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46#14582629C2211yescharacteristic
47#14582629C2211yescharacteristic
48D4⋊(C43⋊C8)C2211yescharacteristic
49D4⋊(C43⋊C8)C2211yescharacteristic
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582620C2211yescharacteristic
53#14582620C2211yescharacteristic
54C8×C43⋊C8C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C8×D4×C43—21no—
60C8×D4×C43—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#431—21no—
64C43×#431C2211yescharacteristic
65C2×C4×C8×C43—21no—
66C2×C4×C8×C43C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621872—21no—
72C2×C8×D43—21no—
73#13063319—21no—
74#13063317C2×C411yescharacteristic
75#13063313C2×C411yescharacteristic
76#13063308—21no—
77#13063304C2×C411yescharacteristic
78#13063299C2×C411yescharacteristic
79C4×Dic86C2311yescharacteristic
80C4×D172C2311yescharacteristic
81C4×C22⋊D43—21no—
82#13063282—21no—
83#13063258C2×C411yescharacteristic
84#13063258C2×C411yescharacteristic
85#13063256C2×C411yescharacteristic
86#13063256C2×C411yescharacteristic
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)C2×C411yescharacteristic
89C4⋊(C43⋊C8)C2×C411yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92Dic43⋊C8—21no—
93Dic43⋊C8—21no—
94#13063249C2×C411yescharacteristic
95#13063249C2×C411yescharacteristic
96#13063248C2×C411yescharacteristic
97#13063248C2×C411yescharacteristic
98#13063246C2×C411yescharacteristic
99#13063246C2×C411yescharacteristic
100#13063245C2×C411yescharacteristic
101#13063245C2×C411yescharacteristic
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)C2×C411yescharacteristic
105C22⋊(C43⋊C8)C2×C411yescharacteristic
106(C2×D43)⋊C8—21no—
107(C2×D43)⋊C8—21no—
108#13063236—21no—
109#13063235—21no—
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43C2×C411yescharacteristic
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43D411yescharacteristic
119C22×C8×C43D411yescharacteristic
120C4×Q8×C43C2×C411yescharacteristic
121C4×Q8×C43C2311yescharacteristic
122C4×D4×C43—21no—
123C4×D4×C43—21no—
124C4×D4×C43C2×C411yescharacteristic
125C4×D4×C43C2311yescharacteristic
126#117×C43—21no—
127#117×C43C2×C411yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C4×C8×C43—21no—
138C4×C8×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43D411yescharacteristic
141C4×C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—21no—
156C2×D172C22×C411yescharacteristic
157C2×C4×D43—21no—
158C2×Dic86C22×C411yescharacteristic
159C2×C8×C43—22no—
160C2×C8×C43—22no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—42no—
164C2×C8×C43—42no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C22×C411yescharacteristic
172C4⋊C4×C43C22×C411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43C22×C411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43#4111yescharacteristic
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184#10621885—22no—
185#10621884—22no—
186#10621883—22no—
187#10621882—22no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43C22×C411yescharacteristic
193C4⋊Dic43C22×C411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198C4×Dic43—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207#10621872—42no—
208C8×D43—42no—
209C23×C43—21no—
210C23×C43C4×D411yescharacteristic
211C22×D43—21no—
212Q8×C43—21no—
213Q8×C43#13112yes—
214D4×C43—24no—
215D4×C43—21no—
216D4×C43#13112yes—
217C2×C4×C43—24no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43C4×D411yescharacteristic
230C2×C4×C43C4×D411yescharacteristic
231C2×C4×C43C4×D411yescharacteristic
232C2×C4×C43C23×C411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—42no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239D172—21no—
240D172—21no—
241C4×D43—41no—
242C4×D43—41no—
243Dic86—21no—
244Dic86—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43#13512yes—
250C8×C43#13512yes—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#17904—431nomaximal, Sylow
260C22×C43—22no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43C2×C4×D411yescharacteristic
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C4×C43—21no—
271C4×C43—22no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43C2×#13111yescharacteristic
278C4×C43C2×#13111yescharacteristic
279C4×C43C2×#13511yescharacteristic
280C4×C43C2×#13511yescharacteristic
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284#3102—431no—
285#2966—431no—
286C8×#41D4311yescharacteristic, complemented
287#1584—431no—
288#1583—431no—
289#1582—431no—
290#1581—431no—
291C8×Q16—431no—
292C8×SD16—431no—
293C8×SD16—431no—
294C8×D8—431no—
295#1572—431no—
296#1488—431no—
297#1482—431no—
298#1450—431no—
299C2×C43—41no—
300C2×C43—42no—
301C2×C43#292911yescharacteristic
302C2×C43C4×#13511yescharacteristic
303C2×C43#295511yescharacteristic
304D43—81no—
305#529—431no—
306C4×#41C2×D4311yescharacteristic
307#485—431no—
308#482—431no—
309#479—431no—
310#478—431no—
311#464—431no—
312#463—431no—
313#452—431no—
314#449—431no—
315#446—431no—
316C8×Q8—431no—
317C8×Q8C2×D4311yescharacteristic
318C8×Q8C2×D4311yescharacteristic
319C4×Q16—431no—
320C4×SD16—431no—
321C4×SD16—431no—
322C4×D8—431no—
323#436—431no—
324#435—861no—
325C8×D4—21no—
326C8×D4—21no—
327C8×D4—431no—
328C8×D4—861no—
329C8×D4C2×D4311yescharacteristic
330C8×D4C2×D4311yescharacteristic
331#433—861no—
332#432—431no—
333#431—21no—
334#431—431no—
335#431—431no—
336#431C2×D4311yescharacteristic
337#405—861no—
338C2×C4×C8—21no—
339C2×C4×C8C2×D4311yescharacteristic
340#335—431no—
341#335—431no—
342#334—431no—
343#334—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8—431no—
350D4⋊C8—431no—
351D4⋊C8—431no—
352#322—431no—
353#322—431no—
354C82—431no—
355C82—431no—
356C43#1790411yescharacteristic, complemented, Sylow
357C2×#41C4×D4311yescharacteristic
358C2×Q16—431no—
359C2×SD16—431no—
360C2×SD16—431no—
361C2×D8—431no—
362C2×M16—861no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—861no—
366C22×C8C22⋊D4311yescharacteristic
367C22×C8C22⋊D4311yescharacteristic
368#126—861no—
369#125—431no—
370#124—431no—
371#123—861no—
372C22⋊Q8—431no—
373#121—431no—
374C4×Q8—431no—
375C4×Q8C4×D4311yescharacteristic
376C4×Q8C22×D4311yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—431no—
380C4×D4—861no—
381C4×D4C4×D4311yescharacteristic
382C4×D4C22×D4311yescharacteristic
383#117—21no—
384#117—861no—
385#117C4×D4311yescharacteristic
386C2×C42—21no—
387C2×C42C22×D4311yescharacteristic
388#107—431no—
389#107—431no—
390#106—431no—
391#106—431no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8C22×D4311yescharacteristic
402C4⋊C8C22×D4311yescharacteristic
403#103—431no—
404#103—431no—
405#103—431no—
406#103—431no—
407#102—431no—
408#102—431no—
409#102—431no—
410#102—431no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—431no—
415C22⋊C8—431no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420#97—861no—
421#97—861no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8—21no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8C22⋊D4311yescharacteristic
431C4×C8C22⋊D4311yescharacteristic
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434#41—22no—
435#41—22no—
436C2×Q8—431no—
437C2×Q8C2×C4×D4311yescharacteristic
438C2×D4—21no—
439C2×D4—431no—
440C2×D4—861no—
441C2×D4C2×C4×D4311yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—861no—
446C22×C4C2×C4×D4311yescharacteristic
447C22×C4#1062189811yescharacteristic
448C22×C4C2×C22⋊D4311yescharacteristic
449Q16—862no—
450SD16—862no—
451SD16—862no—
452D8—862no—
453M16—1722no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—42no—
459C2×C8—42no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C2×C8C2×C22⋊D4311yescharacteristic
470C2×C8C2×C22⋊D4311yescharacteristic
471C2×C8C2×C22⋊D4311yescharacteristic
472C2×C8C2×C22⋊D4311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—431no—
476C4⋊C4—431no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4C2×C4×D4311yescharacteristic
482C4⋊C4C2×C4×D4311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—861no—
495C42C2×C4×D4311yescharacteristic
496C42#1062189811yescharacteristic
497C42C2×C22⋊D4311yescharacteristic
498C42C23×D4311yescharacteristic
499C23—21no—
500C23—861no—
501C23C4×C22⋊D4311yescharacteristic
502Q8—21no—
503Q8—861no—
504Q8—861no—
505Q8#1306333112yes—
506D4—24no—
507D4—21no—
508D4—861no—
509D4—861no—
510D4—1722no—
511D4#1306333112yes—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4C4×C22⋊D4311yescharacteristic
530C2×C4C4×C22⋊D4311yescharacteristic
531C2×C4C4×C22⋊D4311yescharacteristic
532C2×C4C22×C4×D4311yescharacteristic
533C2×C4C22×C22⋊D4311yescharacteristic
534C2×C4C2×#1062189811yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—861no—
540C8—861no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8—1721no—
547C8#1306334512yes—
548C8#1306334512yes—
549C22—21no—
550C22—21no—
551C22—22no—
552C22—21no—
553C22—41no—
554C22—41no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22C2×C4×C22⋊D4311yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—22no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—1721no—
567C4—1721no—
568C4—1721no—
569C4C2×#1306333111yescharacteristic
570C4C2×#1306333111yescharacteristic
571C4C2×#1306334511yescharacteristic
572C4C2×#1306334511yescharacteristic
573C2—41no—
574C2—42no—
575C2—3441no—
576C2#1914328911yescharacteristic
577C2C4×#1306334511yescharacteristic
578C2#1914349611yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×#41×C43C2
socleC22×C43C2×C4×D4
prime radical#14583044C4
cosocleC42×C43C24
hypercenterC8×#41D43
hypocenterC43#17904
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
2. #19143570C2semidirect
3. #19133445C2semidirect
4. #19133438C2semidirect
5. #19133431C2semidirect
6. #19133424C2semidirect
7. C8×#10621885C2semidirect
8. C8×#10621884C2semidirect
9. C8×#10621883C2semidirect
10. C8×#10621882C2semidirect
11. #19133373C2semidirect
12. #19133029C2semidirect
13. #19133001C2semidirect
14. #19132878C2semidirect
15. C8×#41×C43C2semidirect
286. C8×#41D43semidirect
356. C43#17904semidirect

Maximal subgroups

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

subgroupindex
#191446132
#191435702
#191334452
#191334382
#191334312
#191334242
C8×#106218852
C8×#106218842
C8×#106218832
C8×#106218822
#191333732
#191330292
#191330012
#191328782
C8×#41×C432
#1790443