Finite Group Databasebeta

← #24989057

Subgroups — #24989057

Order 11008.

808 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135528C211yesmaximal, characteristic, complemented
2#19135515C211yesmaximal, characteristic, complemented
3#19133290C211yesmaximal, characteristic, complemented
4#19133193C211yesmaximal, characteristic, complemented
5#19133120C211yesmaximal, characteristic, complemented
6#19133008C211yesmaximal, characteristic, complemented
7C43×#3558C211yesmaximal, characteristic
8#14582956C2211yescharacteristic, complemented
9C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
10C2×#13063252—22no—
11C2×#13063249—21no—
12C2×#13063246—21no—
13C4×#10621877C2211yescharacteristic, complemented
14C4×C4⋊Dic43C2211yescharacteristic, complemented
15#14582648—21no—
16#14582643—21no—
17#14582639—22no—
18#14582636—21no—
19#14582633—21no—
20Q8⋊(C43⋊C8)—21no—
21D4⋊(C43⋊C8)—21no—
22C43×#562C412yescomplemented
23C43×H(3,𝔽4)C412yescomplemented
24C43×#559—21no—
25C43×#548—21no—
26C43×#546—22no—
27C43×#546—21no—
28D42×C43—21no—
29C43×#542—21no—
30C43×#538—22no—
31C43×#538—21no—
32C43×#535—21no—
33C43×#534—21no—
34C43×#532C2211yescharacteristic
35C43×#529C2211yescharacteristic
36C2×#124×C43C2211yescharacteristic
37C2×#10621877—21no—
38C22×C43⋊C8—21no—
39C2×C4⋊Dic43—21no—
40C2×C4×Dic43—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44#13063252—44no—
45#13063249—42no—
46#13063246—42no—
47C22⋊(C43⋊C8)—21no—
48#13063236—21no—
49#13063236—21no—
50C4×C43⋊C8—21no—
51C43⋊#95—21no—
52C2×#41×C43—21no—
53C2×#41×C43D412yes—
54C22×Q8×C43D411yescharacteristic
55C22×D4×C43—22no—
56C22×D4×C43—21no—
57C22×D4×C43D411yescharacteristic
58C4⋊Q8×C43D411yescharacteristic
59#127×C43—21no—
60#127×C43D411yescharacteristic
61#126×C43—22no—
62#126×C43—21no—
63#125×C43C2×C411yescharacteristic
64#124×C43—21no—
65#124×C43—22no—
66#124×C43—22no—
67#124×C43—22no—
68#124×C43—21no—
69#124×C43—21no—
70#124×C43C2×C412yes—
71#124×C43C2×C411yescharacteristic
72#124×C43C2×C412yes—
73#124×C43D412yes—
74#123×C43—22no—
75#123×C43—22no—
76#123×C43—21no—
77#123×C43—22no—
78#123×C43—22no—
79C22⋊Q8×C43—21no—
80C22⋊Q8×C43—22no—
81C22⋊Q8×C43—22no—
82C22⋊Q8×C43D411yescharacteristic
83#121×C43—22no—
84#121×C43—22no—
85#121×C43—22no—
86#121×C43—21no—
87#121×C43—22no—
88#121×C43—22no—
89#121×C43—21no—
90#121×C43—21no—
91#121×C43D411yescharacteristic
92#120×C43—22no—
93#120×C43—22no—
94#120×C43—22no—
95#120×C43—22no—
96#120×C43—22no—
97C4×Q8×C43—21no—
98C4×Q8×C43D411yescharacteristic
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43D411yescharacteristic
106#117×C43—21no—
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C42×C43C2311yescharacteristic
111C24×C43—22no—
112C24×C43—21no—
113#41×C43—42no—
114#41×C43—42no—
115#41×C43—81no—
116#41×C43—81no—
117C2×Q8×C43—21no—
118C2×Q8×C43—41no—
119C2×Q8×C43—41no—
120C2×Q8×C43C22⋊C411yescharacteristic
121C2×Q8×C43C22⋊C412yes—
122C2×Q8×C43C22⋊C412yes—
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—22no—
132C2×D4×C43—21no—
133C2×D4×C43—41no—
134C2×D4×C43—41no—
135C2×D4×C43—82no—
136C2×D4×C43—82no—
137C2×D4×C43—81no—
138C2×D4×C43—81no—
139C2×D4×C43C22⋊C411yescharacteristic
140C2×D4×C43C22⋊C412yes—
141C2×D4×C43C22⋊C412yes—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—21no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×Dic43—41no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43C22⋊C411yescharacteristic
160C4⋊C4×C43C22⋊C411yescharacteristic
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—21no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C42×C43—22no—
178C42×C43—21no—
179C42×C43C22×C411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C4⋊Dic43—22no—
184C4⋊Dic43—41no—
185C4×Dic43—42no—
186#10621877—22no—
187#10621877—41no—
188C2×C43⋊C8—41no—
189C2×C43⋊C8—41no—
190C2×C43⋊C8—41no—
191C2×C43⋊C8—41no—
192C2×C43⋊C8—41no—
193C23×C43—22no—
194C23×C43—21no—
195C23×C43—22no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—81no—
199C23×C43—81no—
200C23×C43—82no—
201C23×C43—82no—
202C23×C43—82no—
203C23×C43#12011yescharacteristic
204Q8×C43—42no—
205Q8×C43—41no—
206Q8×C43—42no—
207Q8×C43—41no—
208Q8×C43—41no—
209D4×C43—42no—
210D4×C43—41no—
211D4×C43—42no—
212D4×C43—41no—
213D4×C43—42no—
214D4×C43—41no—
215D4×C43—42no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—81no—
221D4×C43—82no—
222D4×C43—82no—
223D4×C43—82no—
224D4×C43—82no—
225D4×C43—82no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43—81no—
240C2×C4×C43—82no—
241C2×C4×C43—82no—
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43#12011yescharacteristic
247C2×C4×C43#12011yescharacteristic
248C2×Dic43—42no—
249C2×Dic43—81no—
250C2×Dic43—81no—
251C43⋊C8—42no—
252C43⋊C8—81no—
253C43⋊C8—81no—
254#8510—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—42no—
258C22×C43—41no—
259C22×C43—42no—
260C22×C43—41no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—41no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—161no—
267C22×C43—161no—
268C22×C43—164no—
269C22×C43#37911yescharacteristic
270C22×C43#45311yescharacteristic
271C22×C43#45511yescharacteristic
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—42no—
280C4×C43—42no—
281C4×C43—41no—
282C4×C43#45311yescharacteristic
283C4×C43#45511yescharacteristic
284Dic43—82no—
285#3558D4311yescharacteristic
286#1983—431no—
287#1980—431no—
288#1551—431no—
289#1527—431no—
290#1509—431no—
291#1483—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—82no—
295C2×C43—82no—
296C2×C43—81no—
297C2×C43#179211yescharacteristic
298C2×C43#179211yescharacteristic
299C2×C43#179411yescharacteristic
300#562Dic4312yescomplemented
301H(3,𝔽4)Dic4312yescomplemented
302#559—21no—
303#548—21no—
304#546—22no—
305#546—21no—
306D42—21no—
307#542—21no—
308#538—22no—
309#538—21no—
310#535—21no—
311#534—21no—
312#532C2×D4311yescharacteristic
313#529C2×D4311yescharacteristic
314C2×#124C2×D4311yescharacteristic
315#432—431no—
316C2×C4⋊C8—431no—
317C2×#104—862no—
318C2×#103—861no—
319C2×#102—861no—
320C4×M16—431no—
321C4×C4⋊C4—431no—
322#333—861no—
323#331—861no—
324#329—862no—
325#328—861no—
326#327—861no—
327Q8⋊C8—861no—
328D4⋊C8—861no—
329C43#851011yescharacteristic, complemented, Sylow
330C2×#41—21no—
331C2×#41C22⋊D4312yes—
332C22×Q8C22⋊D4311yescharacteristic
333C22×D4—22no—
334C22×D4—21no—
335C22×D4C22⋊D4311yescharacteristic
336C2×M16—861no—
337C22×C8—861no—
338C4⋊Q8C22⋊D4311yescharacteristic
339#127—21no—
340#127C22⋊D4311yescharacteristic
341#126—22no—
342#126—21no—
343#125C2×Dic4311yescharacteristic
344#124—21no—
345#124—22no—
346#124—22no—
347#124—22no—
348#124—21no—
349#124—21no—
350#124C2×Dic4312yes—
351#124C2×Dic4311yescharacteristic
352#124C2×Dic4312yes—
353#124C22⋊D4312yes—
354#123—22no—
355#123—22no—
356#123—21no—
357#123—22no—
358#123—22no—
359C22⋊Q8—21no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8C22⋊D4311yescharacteristic
363#121—22no—
364#121—22no—
365#121—22no—
366#121—21no—
367#121—22no—
368#121—22no—
369#121—21no—
370#121—21no—
371#121C22⋊D4311yescharacteristic
372#120—22no—
373#120—22no—
374#120—22no—
375#120—22no—
376#120—22no—
377C4×Q8—21no—
378C4×Q8C22⋊D4311yescharacteristic
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C22⋊D4311yescharacteristic
386#117—21no—
387C2×C4⋊C4—861no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396#104—1724no—
397#103—1722no—
398#102—1722no—
399C22⋊C8—861no—
400#97—861no—
401#97—861no—
402C4×C8—861no—
403#95—861no—
404C24—22no—
405C24—21no—
406#41—42no—
407#41—42no—
408#41—81no—
409#41—81no—
410C2×Q8—21no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8C22⋊Dic4311yescharacteristic
414C2×Q8C22⋊Dic4312yes—
415C2×Q8C22⋊Dic4312yes—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—81no—
429C2×D4—81no—
430C2×D4—82no—
431C2×D4—82no—
432C2×D4C22⋊Dic4311yescharacteristic
433C2×D4C22⋊Dic4312yes—
434C2×D4C22⋊Dic4312yes—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—1721no—
441C22×C4C2×C22⋊D4311yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C2×C22⋊D4311yescharacteristic
444M16—862no—
445M16—1721no—
446C2×C8—1721no—
447C2×C8—1721no—
448C2×C8—1721no—
449C2×C8—1721no—
450C2×C8—1721no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—862no—
460C4⋊C4—1721no—
461C4⋊C4C22⋊Dic4311yescharacteristic
462C4⋊C4C22⋊Dic4311yescharacteristic
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—21no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—21no—
477C22⋊C4—22no—
478C22⋊C4—21no—
479C42—22no—
480C42—21no—
481C42—1722no—
482C42C22×Dic4311yescharacteristic
483C42C2×C22⋊D4311yescharacteristic
484C42C2×C22⋊D4311yescharacteristic
485C42C2×C22⋊D4311yescharacteristic
486C23—21no—
487C23—22no—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—81no—
492C23—81no—
493C23—82no—
494C23—82no—
495C23—82no—
496C23#1306329411yescharacteristic
497Q8—42no—
498Q8—42no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502D4—42no—
503D4—42no—
504D4—41no—
505D4—41no—
506D4—42no—
507D4—41no—
508D4—42no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—81no—
514D4—82no—
515D4—82no—
516D4—82no—
517D4—82no—
518D4—82no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—81no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—3441no—
536C2×C4—3441no—
537C2×C4—1722no—
538C2×C4C2×C22⋊Dic4311yescharacteristic
539C2×C4C2×C22⋊Dic4311yescharacteristic
540C2×C4C2×C22⋊Dic4311yescharacteristic
541C2×C4#1306329411yescharacteristic
542C2×C4#1306329411yescharacteristic
543C2×C4#1306329411yescharacteristic
544C8—3441no—
545C8—3441no—
546C8—1722no—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—41no—
555C22—41no—
556C22—42no—
557C22—42no—
558C22—161no—
559C22—161no—
560C22—164no—
561C22#1458275511yescharacteristic
562C22#1458306711yescharacteristic
563C22#1458307711yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—42no—
572C4—42no—
573C4—41no—
574C4—3442no—
575C4#1458306711yescharacteristic
576C4#1458307711yescharacteristic
577C2—21no—
578C2—21no—
579C2—81no—
580C2—82no—
581C2—82no—
582C2#1913454911yescharacteristic
583C2#1913454911yescharacteristic
584C2#1913455911yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3558C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3558D43
hypocenterC43#8510
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3558

Complements

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

NH ≅ G/Ntype
1. #19135528C2semidirect
2. #19135515C2semidirect
3. #19133290C2semidirect
4. #19133193C2semidirect
5. #19133120C2semidirect
6. #19133008C2semidirect
8. #14582956C22semidirect
9. C2×C4⋊(C43⋊C8)C22semidirect
13. C4×#10621877C22semidirect
14. C4×C4⋊Dic43C22semidirect
22. C43×#562C4semidirect
23. C43×H(3,𝔽4)C4semidirect
300. #562Dic43semidirect
301. H(3,𝔽4)Dic43semidirect
329. C43#8510semidirect

Maximal subgroups

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

subgroupindex
#191355282
#191355152
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