Finite Group Databasebeta

← #25086861

Subgroups — #25086861

Order 11008.

564 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147503C211yesmaximal, characteristic
2#19147468C211yesmaximal, characteristic
3#19147274C211yesmaximal, characteristic, complemented
4#19146988C211yesmaximal, characteristic
5#19134272C211yesmaximal, characteristic, complemented
6#19134102C211yesmaximal, characteristic, complemented
7#19134046C211yesmaximal, characteristic
8#19134000C211yesmaximal, characteristic, complemented
9#19133999C211yesmaximal, characteristic, complemented
10#19133812C211yesmaximal, characteristic
11#19133756C211yesmaximal, characteristic, complemented
12#19133737C211yesmaximal, characteristic, complemented
13#19133731C211yesmaximal, characteristic
14#19133447C211yesmaximal, characteristic, complemented
15C43×SD16⋊C8C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17#14583628C2211yescharacteristic
18#14583606C2211yescharacteristic
19#14583606C2211yescharacteristic
20#14583306—21no—
21#14583304C2211yescharacteristic
22#14583304C2211yescharacteristic
23#14583299—21no—
24#14583297C2211yescharacteristic
25#14583279C2211yescharacteristic
26#14583250—21no—
27#14583250C2211yescharacteristic
28#14583250C2211yescharacteristic
29#14583235—21no—
30#14583235—21no—
31#14583208—21no—
32#14583204—21no—
33#14583201—21no—
34#14583195—21no—
35#14583195C2211yescharacteristic
36#14583195C2211yescharacteristic
37#14583195C2211yescharacteristic
38#14583194C2211yescharacteristic
39#14583194C2211yescharacteristic
40#14583189C2211yescharacteristic
41#14583179C2211yescharacteristic
42#14583177—21no—
43#14583140—21no—
44#14583110—21no—
45#14583110C2211yescharacteristic
46#14583029C2211yescharacteristic
47C8×Dic86C2211yescharacteristic
48#14583000—21no—
49C4×Dic172—21no—
50C4×Dic172C2211yescharacteristic
51SD16×Dic43—21no—
52C2×#13063259—21no—
53#14582652C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582631C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Dic172—21no—
68C2×Dic172—41no—
69C2×Dic172D411yescharacteristic
70#13063325—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—41no—
78#13063316—21no—
79#13063316—21no—
80#13063316—21no—
81#13063316—41no—
82#13063304—21no—
83#13063304—21no—
84#13063302—41no—
85#13063302—41no—
86Q8×Dic43—21no—
87Q8×Dic43—21no—
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×Dic86C2311yescharacteristic
91C4×Dic86C2311yescharacteristic
92D4×Dic43—21no—
93D4×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#13063258—21no—
106#13063258—21no—
107#13063257—21no—
108#13063257—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#13063249—21no—
124#13063249—21no—
125#13063246—21no—
126#13063246—21no—
127#13063235—21no—
128C8×Dic43—21no—
129C2×SD16×C43D411yescharacteristic
130C22×C8×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43D411yescharacteristic
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43C2×D411yescharacteristic
146C22×C4×C43—21no—
147C22×Dic43—41no—
148C22×Dic43—41no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—41no—
154C2×Dic86C2×D411yescharacteristic
155C2×Dic86C2×D411yescharacteristic
156SD16×C43Q1614yescomplemented
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—42no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43C2×D411yescharacteristic
167C4⋊C4×C43C2×D411yescharacteristic
168C22⋊C4×C43—21no—
169C42×C43—21no—
170C42×C43C2411yescharacteristic
171C22⋊Dic43—41no—
172C22⋊Dic43—41no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—41no—
182C4⋊Dic43—41no—
183C4⋊Dic43—41no—
184C4⋊Dic43—41no—
185C4⋊Dic43—41no—
186C4⋊Dic43C2×D411yescharacteristic
187C4⋊Dic43C2×D411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200Dic172—41no—
201Dic172—42no—
202Dic172—82no—
203C23×C43—21no—
204Q8×C43—21no—
205Q8×C43C2×Q1612yes—
206D4×C43—21no—
207D4×C43C2×Q1612yes—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43H(5,𝔽2)11yescharacteristic
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—161no—
225C2×Dic43—161no—
226Dic86—21no—
227Dic86—21no—
228Dic86—21no—
229Dic86—21no—
230Dic86—41no—
231Dic86—41no—
232Dic86—81no—
233Dic86—81no—
234Dic86—81no—
235Dic86—161no—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—41no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43C2×Q1612yes—
243C43⋊C8—41no—
244C43⋊C8—41no—
245#19816—431nomaximal, Sylow
246C22×C43—22no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43D4211yescharacteristic
250C4×C43—22no—
251C4×C43—21no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43C22×Q1611yescharacteristic
255C4×C43#57511yescharacteristic
256C4×C43#57811yescharacteristic
257C4×C43#57811yescharacteristic
258Dic43—41no—
259Dic43—41no—
260Dic43—41no—
261Dic43—41no—
262Dic43—81no—
263Dic43—81no—
264Dic43—81no—
265Dic43—81no—
266#3385—431no—
267#3381—431no—
268#3363—431no—
269#3338—431no—
270#1723—431no—
271#1692—431no—
272#1683—431no—
273#1676—431no—
274#1676—431no—
275#1644—431no—
276#1636—431no—
277#1633—431no—
278#1632—431no—
279#1584—431no—
280SD16⋊C8D4311yescharacteristic
281C2×C43—42no—
282C2×C43#326911yescharacteristic
283C2×C43D4×Q1611yescharacteristic
284C2×C43#328811yescharacteristic
285Q82—431no—
286#557—431no—
287#554—431no—
288#554—431no—
289#501—861no—
290#500—431no—
291#500—431no—
292#499—861no—
293#498—431no—
294#494—431no—
295#487—431no—
296#487—431no—
297#487—861no—
298#484—861no—
299#484—861no—
300#479—861no—
301#479—861no—
302#478—861no—
303#477—431no—
304#477—431no—
305#477—431no—
306#477—431no—
307#477—431no—
308#477—861no—
309#476—431no—
310#474—431no—
311#474—861no—
312#467—861no—
313#462—431no—
314#462—861no—
315#446—431no—
316C8×Q8—431no—
317C8×Q8C2×D4311yescharacteristic
318#440—861no—
319C4×Q16—431no—
320C4×Q16—861no—
321C4×SD16—861no—
322C4×SD16C2×D4311yescharacteristic
323C8×D4C2×D4311yescharacteristic
324C2×#107—861no—
325#335—431no—
326#335C2×D4311yescharacteristic
327#333—431no—
328#333—431no—
329#333—431no—
330#332—431no—
331Q8⋊C8—431no—
332Q8⋊C8—431no—
333Q8⋊C8C2×D4311yescharacteristic
334D4⋊C8C2×D4311yescharacteristic
335#322C2×D4311yescharacteristic
336C43#1981611yescharacteristic, complemented, Sylow
337C2×Q16—431no—
338C2×Q16—861no—
339C2×Q16—1721no—
340C2×SD16D17211yescharacteristic
341C22×C8—21no—
342C4⋊Q8—431no—
343C4⋊Q8—431no—
344C4⋊Q8—431no—
345C4⋊Q8—431no—
346C4⋊Q8—861no—
347C4⋊Q8—861no—
348C4⋊Q8—861no—
349C4⋊Q8—1721no—
350#125—861no—
351#125—861no—
352#125—861no—
353#125—1721no—
354C22⋊Q8—861no—
355C22⋊Q8—861no—
356C22⋊Q8—1721no—
357C22⋊Q8—1721no—
358C4×Q8—431no—
359C4×Q8—431no—
360C4×Q8—861no—
361C4×Q8—861no—
362C4×Q8—861no—
363C4×Q8—861no—
364C4×Q8C22×D4311yescharacteristic
365C4×D4—861no—
366C4×D4—861no—
367C4×D4C22×D4311yescharacteristic
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370#107—431no—
371#107—861no—
372#107—861no—
373#107—861no—
374#107—861no—
375#107—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107—861no—
381#106—861no—
382#106—861no—
383#106—861no—
384#106D17211yescharacteristic
385C4⋊C8—21no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8C22×D4311yescharacteristic
391C4⋊C8C22×D4311yescharacteristic
392#103—431no—
393#103—431no—
394#103—861no—
395#103—861no—
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—1721no—
403#103D17211yescharacteristic
404#102—861no—
405#102—861no—
406#102D17211yescharacteristic
407C22⋊C8—21no—
408#97—861no—
409C4×C8—21no—
410C4×C8—861no—
411C4×C8C22×D4311yescharacteristic
412C4×C8C22×D4311yescharacteristic
413C4×C8C22×D4311yescharacteristic
414C2×Q8—431no—
415C2×Q8—431no—
416C2×Q8—861no—
417C2×Q8—861no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8—1721no—
421C2×Q8C2×D17211yescharacteristic
422C2×D4C2×D17211yescharacteristic
423C22×C4—21no—
424C22×C4—1721no—
425C22×C4—1721no—
426Q16—3442no—
427Q16—1721no—
428Q16—1722no—
429SD16Dic17214yescomplemented
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—42no—
434C2×C8—861no—
435C2×C8—861no—
436C2×C8C2×D17211yescharacteristic
437C2×C8C2×D17211yescharacteristic
438C2×C8D4×D4311yescharacteristic
439C2×C8D4×D4311yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—431no—
442C4⋊C4—431no—
443C4⋊C4—861no—
444C4⋊C4—861no—
445C4⋊C4—861no—
446C4⋊C4—861no—
447C4⋊C4—861no—
448C4⋊C4—861no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—1721no—
454C4⋊C4—1721no—
455C4⋊C4—1721no—
456C4⋊C4—1721no—
457C4⋊C4—1721no—
458C4⋊C4—1721no—
459C4⋊C4—1721no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4C2×D17211yescharacteristic
463C4⋊C4C2×D17211yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—1721no—
466C22⋊C4—1721no—
467C42—21no—
468C42—861no—
469C42—861no—
470C42—1721no—
471C42—1721no—
472C42C23×D4311yescharacteristic
473C23—21no—
474Q8—21no—
475Q8—861no—
476Q8—861no—
477Q8—861no—
478Q8—861no—
479Q8—3441no—
480Q8—3441no—
481Q8—3441no—
482Q8—1721no—
483Q8—1721no—
484Q8—6881no—
485Q8C2×Dic17212yes—
486D4—21no—
487D4C2×Dic17212yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—861no—
496C2×C4—861no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4—1721no—
500C2×C4—1721no—
501C2×C4—6881no—
502C2×C4—6881no—
503C2×C4C2×D4×D4311yescharacteristic
504C2×C4C22×D17211yescharacteristic
505C2×C4#1306337111yescharacteristic
506C8—21no—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—1721no—
513C8—1721no—
514C8C2×Dic17212yes—
515C22—22no—
516C22—41no—
517C22—41no—
518C22D4×D17211yescharacteristic
519C4—22no—
520C4—21no—
521C4—41no—
522C4—41no—
523C4—3441no—
524C4—3441no—
525C4—3441no—
526C4—3441no—
527C4—1721no—
528C4—1721no—
529C4—1721no—
530C4—1721no—
531C4C22×Dic17211yescharacteristic
532C4#1458369511yescharacteristic
533C4#1458371511yescharacteristic
534C4#1458371611yescharacteristic
535C2—42no—
536C2#1914615211yescharacteristic
537C2D4×Dic17211yescharacteristic
538C2#1914636211yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×SD16⋊C8C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenterSD16⋊C8D43
hypocenterC43#19816
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
3. #19147274C2semidirect
5. #19134272C2semidirect
6. #19134102C2semidirect
8. #19134000C2semidirect
9. #19133999C2semidirect
11. #19133756C2semidirect
12. #19133737C2semidirect
14. #19133447C2semidirect
156. SD16×C43Q16semidirect
336. C43#19816semidirect
429. SD16Dic172semidirect

Maximal subgroups

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

subgroupindex
#191475032
#191474682
#191472742
#191469882
#191342722
#191341022
#191340462
#191340002
#191339992
#191338122
#191337562
#191337372
#191337312
#191334472
C43×SD16⋊C82
#1981643