Finite Group Databasebeta

← #25093900

Subgroups — #25093900

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147646C211yesmaximal, characteristic
2#19147644C211yesmaximal, characteristic
3#19147523C211yesmaximal, characteristic, complemented
4#19134183C211yesmaximal, characteristic
5#19134103C211yesmaximal, characteristic, complemented
6#19134098C211yesmaximal, characteristic, complemented
7#19134069C211yesmaximal, characteristic
8#19134067C211yesmaximal, characteristic
9#19133872C211yesmaximal, characteristic, complemented
10#19133871C211yesmaximal, characteristic, complemented
11#19133715C211yesmaximal, characteristic
12#19133673C211yesmaximal, characteristic
13#19133492C211yesmaximal, characteristic, complemented
14#19133490C211yesmaximal, characteristic, complemented
15C43×#3387C211yesmaximal, characteristic, complemented
16#14583634C2211yescharacteristic
17#14583627C2211yescharacteristic
18#14583305—21no—
19#14583295C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583292—21no—
22#14583291—21no—
23#14583273C2211yescharacteristic
24#14583273C2211yescharacteristic
25#14583272C2211yescharacteristic
26#14583206—21no—
27#14583191C2211yescharacteristic
28#14583184C2211yescharacteristic
29#14583181—21no—
30#14583124—21no—
31#14583121—21no—
32#14583109C2211yescharacteristic
33#14583106C2211yescharacteristic
34#14583103—21no—
35#14583101—21no—
36#14583099C2211yescharacteristic
37#14583099C2211yescharacteristic
38#14583030C2211yescharacteristic
39#14583030C2211yescharacteristic
40#14583029C2211yescharacteristic
41#14583004—21no—
42#14582998—21no—
43#14582997—21no—
44C4×#10621885C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582629C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57C43×#557C2211yescharacteristic
58C43×#501—21no—
59C43×#498C2211yescharacteristic
60C43×#479—21no—
61C43×#477C2211yescharacteristic
62C43×#475—21no—
63C43×#475C2211yescharacteristic
64C43×#446C2211yescharacteristic
65C43×#441—21no—
66C4×Q16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885D411yescharacteristic
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884—41no—
77#13063325C2311yescharacteristic
78#13063323—21no—
79#13063322C2311yescharacteristic
80#13063317—21no—
81#13063315—41no—
82#13063314—21no—
83#13063313—21no—
84#13063310—41no—
85C4×Dic86—21no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88C4×D172—21no—
89#13063287—21no—
90#13063258—21no—
91#13063258D411yescharacteristic
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—41no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249D411yescharacteristic
105#13063248—21no—
106#13063248—21no—
107#13063248D411yescharacteristic
108#13063245—21no—
109#13063245—21no—
110#13063236—21no—
111#13063236—21no—
112#13063235—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43D411yescharacteristic
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—41no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123#125×C43—41no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131#107×C43—21no—
132#107×C43D411yescharacteristic
133#106×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×C4×D43—41no—
154C2×Dic86—21no—
155C2×Dic86C2×D411yescharacteristic
156Q16×C43—22no—
157C2×C8×C43—21no—
158C2×C8×C43C2×D411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—41no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—41no—
179C42×C43—41no—
180C42×C43C2411yescharacteristic
181#10621885—22no—
182#10621885—81no—
183#10621885—81no—
184#10621884—42no—
185#10621884—81no—
186#10621884—82no—
187#10621884—81no—
188#10621884—81no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199C4×Dic43—21no—
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207#10621873—42no—
208#10621873—81no—
209C22×D43—41no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—81no—
219Q8×C43—161no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—41no—
234D172—41no—
235D172—41no—
236D172—41no—
237D172—41no—
238D172—81no—
239C4×D43—161no—
240Dic86—21no—
241Dic86—21no—
242Dic86—41no—
243Dic86—41no—
244C8×C43—21no—
245C8×C43—41no—
246C8×C43#13712yes—
247C43⋊C8—22no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8#13712yes—
253#20323—431nomaximal, Sylow
254C22×C43D4211yescharacteristic
255C2×D43—81no—
256C2×D43—81no—
257C2×D43—81no—
258C4×C43—21no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43C2×#13711yescharacteristic
268C4×C43C2×#13711yescharacteristic
269C4×C43#57711yescharacteristic
270C4×C43#57711yescharacteristic
271Dic43—41no—
272Dic43—41no—
273Dic43—81no—
274#3400—431no—
275#3400—431no—
276#3387—431no—
277#3387D4311yescharacteristic, complemented
278#1705—431no—
279#1692—431no—
280#1692—431no—
281#1686—431no—
282#1686—431no—
283#1653—431no—
284#1653—431no—
285#1630—431no—
286#1623—431no—
287#1591—431no—
288#1591—431no—
289C2×C43#327811yescharacteristic
290C2×C43#327811yescharacteristic
291C2×C43#329111yescharacteristic
292D43—161no—
293#559—431no—
294Q82C2×D4311yescharacteristic
295#557—431no—
296#557C2×D4311yescharacteristic
297#501—21no—
298#501—861no—
299#498—431no—
300#498—431no—
301#498C2×D4311yescharacteristic
302#497—861no—
303#497—861no—
304#492—431no—
305#492—431no—
306#492—431no—
307#479—21no—
308#479—861no—
309#477—431no—
310#477C2×D4311yescharacteristic
311#475—21no—
312#475—431no—
313#475—861no—
314#475C2×D4311yescharacteristic
315#464—861no—
316#464—861no—
317#462—431no—
318#462—431no—
319#461—861no—
320#461—861no—
321#460—431no—
322#460—431no—
323#446—431no—
324#446—431no—
325#446—431no—
326#446C2×D4311yescharacteristic
327#441—21no—
328#441—861no—
329#440—861no—
330#440—861no—
331C4×Q16—431no—
332C4×Q16C2×D4311yescharacteristic
333#335—431no—
334#335—431no—
335#333—431no—
336#332—431no—
337#332—431no—
338#331—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342Q8⋊C8—431no—
343C82—431no—
344C43#2032311yescharacteristic, complemented, Sylow
345C2×Q16—431no—
346C2×Q16—861no—
347C2×Q16—861no—
348C2×Q16C22⋊D4311yescharacteristic
349C2×SD16—861no—
350C2×SD16—861no—
351C2×SD16—861no—
352C2×SD16—861no—
353C2×SD16—861no—
354C2×SD16—861no—
355C2×SD16—1721no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—41no—
360C4⋊Q8—431no—
361C4⋊Q8—861no—
362C4⋊Q8C22×D4311yescharacteristic
363C4⋊Q8C22×D4311yescharacteristic
364#127—431no—
365#125—21no—
366#125—41no—
367#125—861no—
368#125—1721no—
369#124—861no—
370#124—861no—
371#123—1721no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—431no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8C22×D4311yescharacteristic
380C4×Q8C22×D4311yescharacteristic
381C4×Q8C22×D4311yescharacteristic
382C4×D4—861no—
383C4×D4—861no—
384#107—21no—
385#107—431no—
386#107—861no—
387#107C22⋊D4311yescharacteristic
388#106—21no—
389#106—21no—
390#106—21no—
391#106—861no—
392#106—861no—
393#106—861no—
394#106—1721no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403#103—21no—
404#103—21no—
405#103—431no—
406#103—431no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103C22⋊D4311yescharacteristic
412#103C22⋊D4311yescharacteristic
413#102—861no—
414#102—861no—
415#97—21no—
416#97—861no—
417#97—861no—
418#97—861no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8C22×D4311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—41no—
425C2×Q8—431no—
426C2×Q8—861no—
427C2×Q8D4×D4311yescharacteristic
428C2×Q8C2×C22⋊D4311yescharacteristic
429C2×Q8C2×C22⋊D4311yescharacteristic
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C22×C4—1721no—
434Q16—22no—
435Q16—862no—
436Q16—3441no—
437Q16—3441no—
438SD16—3441no—
439SD16—3442no—
440SD16—3441no—
441SD16—3441no—
442SD16—3441no—
443SD16—1722no—
444SD16—1722no—
445C2×C8—21no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8C2×C22⋊D4311yescharacteristic
453C2×C8C2×C22⋊D4311yescharacteristic
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—431no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4D4×D4311yescharacteristic
474C4⋊C4C2×C22⋊D4311yescharacteristic
475C4⋊C4C2×C22⋊D4311yescharacteristic
476C22⋊C4—1721no—
477C22⋊C4—1721no—
478C22⋊C4—1721no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42—861no—
485C42—1721no—
486C42C23×D4311yescharacteristic
487C23—1721no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—81no—
497Q8—161no—
498Q8—861no—
499Q8—861no—
500Q8—1721no—
501Q8—1721no—
502D4—3441no—
503D4—1721no—
504D4—1721no—
505D4—1721no—
506D4—1721no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—1721no—
518C2×C4—6881no—
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C22×C22⋊D4311yescharacteristic
521C2×C4#1306337011yescharacteristic
522C8—21no—
523C8—41no—
524C8—432no—
525C8—862no—
526C8—861no—
527C8—1721no—
528C8—1721no—
529C8—1721no—
530C8#1306335612yes—
531C22—3441no—
532C22—3441no—
533C22—3441no—
534C22D4×C22⋊D4311yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—3441no—
545C4—1721no—
546C4—1721no—
547C4#137×D4311yescharacteristic
548C4C2×#1306335611yescharacteristic
549C4#1458370711yescharacteristic
550C4#1458370811yescharacteristic
551C2—6881no—
552C2#1914625511yescharacteristic
553C2#1914625711yescharacteristic
554C2#1914638611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3387C2
socleC22×C43D42
prime radical#13063322C23
hypercenter#3387D43
hypocenterC43#20323
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3387

Complements

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

NH ≅ G/Ntype
3. #19147523C2semidirect
5. #19134103C2semidirect
6. #19134098C2semidirect
9. #19133872C2semidirect
10. #19133871C2semidirect
13. #19133492C2semidirect
14. #19133490C2semidirect
15. C43×#3387C2semidirect
277. #3387D43semidirect
344. C43#20323semidirect

Maximal subgroups

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

subgroupindex
#191476462
#191476442
#191475232
#191341832
#191341032
#191340982
#191340692
#191340672
#191338722
#191338712
#191337152
#191336732
#191334922
#191334902
C43×#33872
#2032343