Finite Group Databasebeta

← #25086831

Subgroups — #25086831

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147492C211yesmaximal, characteristic
2#19147460C211yesmaximal, characteristic
3#19146988C211yesmaximal, characteristic, complemented
4#19146472C211yesmaximal, characteristic, complemented
5#19134272C211yesmaximal, characteristic, complemented
6#19134124C211yesmaximal, characteristic, complemented
7#19134046C211yesmaximal, characteristic, complemented
8#19133994C211yesmaximal, characteristic, complemented
9#19133978C211yesmaximal, characteristic, complemented
10#19133812C211yesmaximal, characteristic, complemented
11#19133763C211yesmaximal, characteristic, complemented
12#19133731C211yesmaximal, characteristic, complemented
13#19133731C211yesmaximal, characteristic, complemented
14#19133447C211yesmaximal, characteristic, complemented
15C43×#1580C211yesmaximal, characteristic
16#14583606C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583606C2211yescharacteristic
19D4×Dic86C2211yescharacteristic
20#14583307—21no—
21#14583304C2211yescharacteristic
22#14583304C2211yescharacteristic
23#14583300—21no—
24#14583297C2211yescharacteristic
25#14583279C2211yescharacteristic
26#14583250C2211yescharacteristic
27#14583250C2211yescharacteristic
28#14583235—21no—
29#14583235—21no—
30#14583235—21no—
31#14583201—21no—
32#14583197—21no—
33#14583197—21no—
34#14583195C2211yescharacteristic
35#14583195C2211yescharacteristic
36#14583195C2211yescharacteristic
37#14583189C2211yescharacteristic
38#14583189C2211yescharacteristic
39#14583189C2211yescharacteristic
40#14583187—21no—
41#14583179C2211yescharacteristic
42#14583140—21no—
43#14583140—21no—
44#14583110C2211yescharacteristic
45#14583057—21no—
46#14583029C2211yescharacteristic
47C8×Dic86C2211yescharacteristic
48#14583011—21no—
49C4×Dic172C2211yescharacteristic
50D8×Dic43—21no—
51C2×#13063259—21no—
52C2×#13063250—21no—
53#14582652C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582631C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C22×Dic86—21no—
68C2×Dic172—21no—
69C2×Dic172—41no—
70C2×Dic172D411yescharacteristic
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063324—21no—
76#13063316—21no—
77#13063316—21no—
78#13063316—21no—
79#13063304—21no—
80#13063304—21no—
81#13063304—21no—
82#13063304—21no—
83#13063302—41no—
84#13063302—41no—
85#13063302—41no—
86#13063302—41no—
87C4×Dic86C2311yescharacteristic
88C4×Dic86C2311yescharacteristic
89D4×Dic43—21no—
90D4×Dic43—21no—
91D4×Dic43—21no—
92D4×Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96#13063259—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259D411yescharacteristic
104#13063258—21no—
105#13063257—21no—
106#13063257—21no—
107#13063256—21no—
108#13063256—21no—
109#13063256—21no—
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063250—41no—
121#13063250D411yescharacteristic
122#13063250D411yescharacteristic
123#13063246—21no—
124#13063246—21no—
125#13063246—21no—
126#13063246—21no—
127#13063235—21no—
128C8×Dic43—21no—
129C2×D8×C43D411yescharacteristic
130C22×C8×C43—21no—
131C22×C8×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43D411yescharacteristic
138#102×C43D411yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×D4×C43C2×D411yescharacteristic
145C2×D4×C43C2×D411yescharacteristic
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×Dic43—41no—
149C22×Dic43—41no—
150C22×Dic43—41no—
151C22×Dic43—41no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—42no—
157C2×Dic86—41no—
158C2×Dic86—81no—
159C2×Dic86C2×D411yescharacteristic
160C2×Dic86C2×D411yescharacteristic
161D8×C43Q1614yescomplemented
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—42no—
166C2×C8×C43—81no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C42×C43C2411yescharacteristic
176C22⋊Dic43—41no—
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179C22⋊Dic43—41no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4⋊Dic43—41no—
191C4⋊Dic43C2×D411yescharacteristic
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203Dic172—41no—
204Dic172—81no—
205Dic172—82no—
206C23×C43—21no—
207C23×C43—21no—
208D4×C43—21no—
209D4×C43—21no—
210D4×C43C2×Q1612yes—
211D4×C43C2×Q1612yes—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43H(5,𝔽2)11yescharacteristic
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—82no—
230C2×Dic43—161no—
231C2×Dic43—161no—
232C2×Dic43—161no—
233Dic86—21no—
234Dic86—21no—
235Dic86—21no—
236Dic86—21no—
237Dic86—41no—
238Dic86—41no—
239Dic86—82no—
240Dic86—81no—
241Dic86—81no—
242Dic86—81no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43C2×Q1612yes—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19814—431nomaximal, Sylow
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43D4211yescharacteristic
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43C22×Q1611yescharacteristic
264C4×C43#57511yescharacteristic
265C4×C43#57711yescharacteristic
266C4×C43#57811yescharacteristic
267Dic43—41no—
268Dic43—41no—
269Dic43—41no—
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273Dic43—81no—
274Dic43—81no—
275#3384—431no—
276#3380—431no—
277#3338—431no—
278#3299—431no—
279#1723—431no—
280#1696—431no—
281#1683—431no—
282#1675—431no—
283#1672—431no—
284#1644—431no—
285#1637—431no—
286#1632—431no—
287#1632—431no—
288#1584—431no—
289#1580D4311yescharacteristic
290C2×C43—42no—
291C2×C43—42no—
292C2×C43#326711yescharacteristic
293C2×C43D4×Q1611yescharacteristic
294C2×C43#328811yescharacteristic
295#554—431no—
296#554—431no—
297#554—431no—
298D4×Q8—431no—
299#501—861no—
300#500—431no—
301#500—431no—
302#499—861no—
303#498—431no—
304#494—431no—
305#487—431no—
306#487—431no—
307#484—861no—
308#484—861no—
309#484—861no—
310#478—861no—
311#478—861no—
312#478—861no—
313#477—431no—
314#477—431no—
315#477—431no—
316#476—431no—
317#476—431no—
318#476—431no—
319#476—861no—
320#474—431no—
321#467—861no—
322#467—861no—
323#462—431no—
324#451—861no—
325#446—431no—
326C8×Q8—431no—
327#442—861no—
328C4×Q16—431no—
329C4×D8—861no—
330C4×D8C2×D4311yescharacteristic
331C8×D4C2×D4311yescharacteristic
332C8×D4C2×D4311yescharacteristic
333C2×#107—861no—
334C2×#103—861no—
335#335—431no—
336#334C2×D4311yescharacteristic
337#333—431no—
338#333—431no—
339#333—431no—
340#332—431no—
341Q8⋊C8—431no—
342Q8⋊C8—431no—
343D4⋊C8C2×D4311yescharacteristic
344D4⋊C8C2×D4311yescharacteristic
345#322C2×D4311yescharacteristic
346C43#1981411yescharacteristic, complemented, Sylow
347C22×Q8—861no—
348C2×Q16—431no—
349C2×Q16—861no—
350C2×Q16—1721no—
351C2×D8D17211yescharacteristic
352C22×C8—21no—
353C22×C8—21no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8—861no—
359#125—861no—
360#125—861no—
361#125—861no—
362C22⋊Q8—861no—
363C22⋊Q8—861no—
364C22⋊Q8—861no—
365C22⋊Q8—861no—
366C22⋊Q8—1721no—
367C22⋊Q8—1721no—
368C22⋊Q8—1721no—
369C22⋊Q8—1721no—
370C4×Q8—431no—
371C4×Q8—431no—
372C4×D4—861no—
373C4×D4—861no—
374C4×D4—861no—
375C4×D4—861no—
376C4×D4C22×D4311yescharacteristic
377C4×D4C22×D4311yescharacteristic
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381#107—431no—
382#107—861no—
383#107—861no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107—861no—
388#107—861no—
389#107—861no—
390#107D17211yescharacteristic
391#106—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395#106—861no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—431no—
403#103—431no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—1721no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102D17211yescharacteristic
416#102D17211yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—21no—
419#97—861no—
420C4×C8—861no—
421C4×C8C22×D4311yescharacteristic
422C4×C8C22×D4311yescharacteristic
423C4×C8C22×D4311yescharacteristic
424C2×Q8—431no—
425C2×Q8—431no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—3441no—
431C2×Q8—1721no—
432C2×Q8—1722no—
433C2×D4C2×D17211yescharacteristic
434C2×D4C2×D17211yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—1721no—
438C22×C4—1721no—
439C22×C4—1721no—
440C22×C4—1721no—
441Q16—3441no—
442Q16—3442no—
443Q16—1721no—
444D8Dic17214yescomplemented
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8—81no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8C2×D17211yescharacteristic
453C2×C8C2×D17211yescharacteristic
454C2×C8D4×D4311yescharacteristic
455C2×C8D4×D4311yescharacteristic
456C4⋊C4—431no—
457C4⋊C4—431no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4C2×D17211yescharacteristic
476C4⋊C4C2×D17211yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—1721no—
480C22⋊C4—1721no—
481C22⋊C4—1721no—
482C22⋊C4—1721no—
483C42—861no—
484C42—861no—
485C42C23×D4311yescharacteristic
486C23—21no—
487C23—21no—
488Q8—861no—
489Q8—861no—
490Q8—861no—
491Q8—861no—
492Q8—3441no—
493Q8—3441no—
494Q8—3441no—
495Q8—3442no—
496Q8—1721no—
497Q8—1721no—
498D4—21no—
499D4—21no—
500D4C2×Dic17212yes—
501D4C2×Dic17212yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—3442no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—6881no—
518C2×C4—6881no—
519C2×C4—6881no—
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4C22×D17211yescharacteristic
522C2×C4#1306337111yescharacteristic
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—1721no—
530C8—1721no—
531C8C2×Dic17212yes—
532C22—22no—
533C22—22no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22D4×D17211yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—3441no—
543C4—3441no—
544C4—3441no—
545C4—3441no—
546C4—1721no—
547C4—1721no—
548C4—1721no—
549C4—1721no—
550C4C22×Dic17211yescharacteristic
551C4#1458369511yescharacteristic
552C4#1458370911yescharacteristic
553C4#1458371611yescharacteristic
554C2—42no—
555C2—42no—
556C2#1914612211yescharacteristic
557C2D4×Dic17211yescharacteristic
558C2#1914636211yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1580C2
socleC22×C43D42
prime radicalC2×D8×C43D4
hypercenter#1580D43
hypocenterC43#19814
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1580

Complements

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

NH ≅ G/Ntype
3. #19146988C2semidirect
4. #19146472C2semidirect
5. #19134272C2semidirect
6. #19134124C2semidirect
7. #19134046C2semidirect
8. #19133994C2semidirect
9. #19133978C2semidirect
10. #19133812C2semidirect
11. #19133763C2semidirect
12. #19133731C2semidirect
13. #19133731C2semidirect
14. #19133447C2semidirect
161. D8×C43Q16semidirect
346. C43#19814semidirect
444. D8Dic172semidirect

Maximal subgroups

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

subgroupindex
#191474922
#191474602
#191469882
#191464722
#191342722
#191341242
#191340462
#191339942
#191339782
#191338122
#191337632
#191337312
#191334472
C43×#15802
#1981443