Finite Group Databasebeta

← #25082117

Subgroups — #25082117

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145732C211yesmaximal, characteristic, complemented
2#19144754C211yesmaximal, characteristic, complemented
3#19144657C211yesmaximal, characteristic
4#19143702C211yesmaximal, characteristic, complemented
5#19134042C211yesmaximal, characteristic, complemented
6#19134034C211yesmaximal, characteristic, complemented
7#19134012C211yesmaximal, characteristic, complemented
8#19134004C211yesmaximal, characteristic, complemented
9#19133998C211yesmaximal, characteristic, complemented
10#19133992C211yesmaximal, characteristic, complemented
11#19133974C211yesmaximal, characteristic, complemented
12#19133372C211yesmaximal, characteristic, complemented
13#19133289C211yesmaximal, characteristic, complemented
14#19133251C211yesmaximal, characteristic, complemented
15C43×#1671C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583450C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583239—21no—
23#14583225—21no—
24#14583225—21no—
25#14583225—21no—
26#14583198—21no—
27#14583198—21no—
28#14583195C2211yescharacteristic
29#14583191C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583106C2211yescharacteristic
32#14583100C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583058—21no—
35#14583045—21no—
36C8×Dic86C2211yescharacteristic
37#14583023C2211yescharacteristic
38#14583003—21no—
39#14583000—21no—
40#14582986—21no—
41#14582979—21no—
42D4×C43⋊C8C2211yescharacteristic
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582949—21no—
49C2×Dic43⋊C8—21no—
50C4⋊C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621902—21no—
68C2×#10621900D411yescharacteristic
69C2×#10621885—21no—
70C2×#10621873—21no—
71C2×#10621882—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063322C2311yescharacteristic
76#13063316—21no—
77#13063314—21no—
78#13063305—21no—
79#13063301—21no—
80#13063300—21no—
81#13063300—21no—
82Q8×Dic43—21no—
83C4×Dic86C2311yescharacteristic
84#13063290—21no—
85#13063290D411yescharacteristic
86D4×Dic43D411yescharacteristic
87#13063287—21no—
88#13063287—21no—
89C4×C22⋊D43—21no—
90(C22⋊D43)⋊C4—21no—
91#13063283—21no—
92#13063283D411yescharacteristic
93#13063281—21no—
94C2×C4×Dic43—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8D411yescharacteristic
108Dic43⋊C8D411yescharacteristic
109#13063250—21no—
110#13063249—21no—
111#13063248—21no—
112#13063247—21no—
113#13063247—21no—
114#13063247—21no—
115#13063246—21no—
116#13063245—21no—
117#13063245—21no—
118#13063245—21no—
119C22⋊(C43⋊C8)—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8D411yescharacteristic
123(C2×D43)⋊C8D411yescharacteristic
124#13063235—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C22×C8×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151#10621902—82no—
152#10621900—22no—
153#10621900—22no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—41no—
158C2×C4×D43—41no—
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164SD16×C43—42no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C42×C43C2411yescharacteristic
178C22⋊Dic43—21no—
179#10621885—42no—
180#10621882—42no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184(C2×D43)⋊C4—41no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—41no—
188C4⋊Dic43C2×D411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—41no—
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621873—42no—
206C8×D43—81no—
207C23×C43—21no—
208C22×D43—41no—
209C22×D43#12111yescharacteristic
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213D4×C43—21no—
214D4×C43#13512yes—
215C2×C4×C43—21no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C22⋊D43—24no—
224C2×Dic43—24no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—41no—
228C2×Dic43—81no—
229C2×Dic43#12111yescharacteristic
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232D172—41no—
233D172—41no—
234D172—41no—
235D172—41no—
236D172—81no—
237D172—82no—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—21no—
242C4×D43—41no—
243C4×D43—82no—
244Dic86—21no—
245Dic86—81no—
246Dic86#13512yes—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19419—431nomaximal, Sylow
258C22×C43—22no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43C2×#12111yescharacteristic
262C2×D43—21no—
263C2×D43—21no—
264C2×D43—21no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43C2×#13511yescharacteristic
273C4×C43C2×#13511yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57811yescharacteristic
276Dic43—21no—
277Dic43—22no—
278Dic43—21no—
279Dic43—21no—
280Dic43—41no—
281Dic43—81no—
282#3228—431no—
283#3116—431no—
284#3106—431no—
285#2988—431no—
286#1682—431no—
287#1681—431no—
288#1678—431no—
289#1677—431no—
290#1676—431no—
291#1675—431no—
292#1672—431no—
293#1671D4311yescharacteristic, complemented
294#1572—431no—
295#1551—431no—
296#1542—431no—
297C2×C43—42no—
298C2×C43#304611yescharacteristic
299C2×C43#305011yescharacteristic
300C2×C43#306811yescharacteristic
301D43—41no—
302D43—161no—
303#533—431no—
304#532—431no—
305C4×#41—431no—
306#500—431no—
307#498C2×D4311yescharacteristic
308#486—431no—
309#486—431no—
310#485—861no—
311#482—861no—
312#482—861no—
313#482—861no—
314#478—861no—
315#478—861no—
316#477—431no—
317#477—431no—
318#476—431no—
319#476C2×D4311yescharacteristic
320#462—431no—
321#461C2×D4311yescharacteristic
322#460—431no—
323#459—431no—
324#452—861no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8—431no—
328#441—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332C8×D4—431no—
333C8×D4—861no—
334C8×D4—861no—
335C8×D4C2×D4311yescharacteristic
336#432—431no—
337#431—431no—
338#431—431no—
339#431—861no—
340C2×C4⋊C8—431no—
341C2×C4⋊C8—861no—
342#335—431no—
343#335—431no—
344#334—431no—
345#334C2×D4311yescharacteristic
346#333—431no—
347#333—431no—
348#333—431no—
349#333C2×D4311yescharacteristic
350#332—431no—
351#332C2×D4311yescharacteristic
352#331—431no—
353#331—431no—
354C43#1941911yescharacteristic, complemented, Sylow
355C2×#41—431no—
356C2×#41—861no—
357C2×Q16—861no—
358C2×SD16—21no—
359C2×SD16—861no—
360C2×D8—861no—
361C22×C8—21no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8C22×D4311yescharacteristic
366C4⋊Q8C22×D4311yescharacteristic
367#127—431no—
368#125—861no—
369#124—861no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—861no—
373#121—861no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×D4—431no—
379C4×D4—861no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4—861no—
383C4×D4C22×D4311yescharacteristic
384#117—431no—
385#117—861no—
386#117—861no—
387C2×C42—431no—
388C2×C42—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408#103—21no—
409#103—861no—
410#103—861no—
411#103—861no—
412#102—21no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—21no—
421C22⋊C8—431no—
422C22⋊C8—431no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—861no—
427C4×C8—431no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8C22×D4311yescharacteristic
432#41—862no—
433#41—862no—
434#41—3442no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—431no—
438C2×Q8—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—1721no—
444C2×D4D4×D4311yescharacteristic
445C22×C4—21no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—1721no—
452Q16—1722no—
453SD16—42no—
454SD16—1722no—
455D8—1722no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—3441no—
466C2×C8—3441no—
467C2×C8D4×D4311yescharacteristic
468C2×C8D4×D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—431no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4D4×D4311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—431no—
488C42—431no—
489C42—431no—
490C42—861no—
491C42—861no—
492C42—861no—
493C42—1721no—
494C42C23×D4311yescharacteristic
495C23—21no—
496C23—431no—
497C23—1721no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—432no—
502Q8—861no—
503Q8—3441no—
504D4—21no—
505D4—864no—
506D4—3441no—
507D4—3442no—
508D4—1721no—
509D4—1721no—
510D4—1721no—
511D4—1721no—
512D4#1306334612yes—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—431no—
519C2×C4—431no—
520C2×C4—431no—
521C2×C4—864no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—3442no—
529C2×C4—3441no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4#41×D4311yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—861no—
541C8—861no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C22—22no—
546C22—41no—
547C22—41no—
548C22—861no—
549C22—861no—
550C22—861no—
551C22—3441no—
552C22—3441no—
553C22—3441no—
554C22#121×D4311yescharacteristic
555C4—21no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—861no—
560C4—861no—
561C4—861no—
562C4—862no—
563C4—3441no—
564C4—1721no—
565C4#135×D4311yescharacteristic
566C4C2×#1306334611yescharacteristic
567C4#1458370511yescharacteristic
568C4#1458371511yescharacteristic
569C2—42no—
570C2—1721no—
571C2—6881no—
572C2#1914414011yescharacteristic
573C2#1914417111yescharacteristic
574C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1671C2
socleC22×C43C2×#121
prime radical#19144657C2
hypercenter#1671D43
hypocenterC43#19419
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1671

Complements

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

NH ≅ G/Ntype
1. #19145732C2semidirect
2. #19144754C2semidirect
4. #19143702C2semidirect
5. #19134042C2semidirect
6. #19134034C2semidirect
7. #19134012C2semidirect
8. #19134004C2semidirect
9. #19133998C2semidirect
10. #19133992C2semidirect
11. #19133974C2semidirect
12. #19133372C2semidirect
13. #19133289C2semidirect
14. #19133251C2semidirect
15. C43×#1671C2semidirect
293. #1671D43semidirect
354. C43#19419semidirect

Maximal subgroups

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

subgroupindex
#191457322
#191447542
#191446572
#191437022
#191340422
#191340342
#191340122
#191340042
#191339982
#191339922
#191339742
#191333722
#191332892
#191332512
C43×#16712
#1941943