Finite Group Databasebeta

← #25081982

Subgroups — #25081982

Order 11008.

576 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145755C211yesmaximal, characteristic
2#19144724C211yesmaximal, characteristic
3#19144633C211yesmaximal, characteristic
4#19143674C211yesmaximal, characteristic
5#19134054C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134028C211yesmaximal, characteristic, complemented
8#19134027C211yesmaximal, characteristic, complemented
9#19133986C211yesmaximal, characteristic, complemented
10#19133976C211yesmaximal, characteristic, complemented
11#19133975C211yesmaximal, characteristic, complemented
12#19133374C211yesmaximal, characteristic
13#19133302C211yesmaximal, characteristic
14#19133258C211yesmaximal, characteristic
15C43×#1674C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583242—21no—
23#14583242—21no—
24#14583233—21no—
25#14583228—21no—
26#14583205—21no—
27#14583205—21no—
28#14583195C2211yescharacteristic
29#14583194C2211yescharacteristic
30#14583185C2211yescharacteristic
31#14583184C2211yescharacteristic
32#14583106C2211yescharacteristic
33#14583106C2211yescharacteristic
34#14583053—21no—
35#14583053—21no—
36Q8×C43⋊C8C2211yescharacteristic
37C8×Dic86—21no—
38C8×Dic86C2211yescharacteristic
39#14583023—21no—
40#14583023C2211yescharacteristic
41#14583006—21no—
42#14583003—21no—
43Q16×Dic43—21no—
44#14582991—21no—
45#14582955C2211yescharacteristic
46#14582951—21no—
47#14582951C2211yescharacteristic
48#14582951C2211yescharacteristic
49#14582950—21no—
50#14582950C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#500C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621885—21no—
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063316—21no—
73#13063316—21no—
74#13063305—21no—
75#13063305—21no—
76#13063301—21no—
77#13063301—21no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80Q8×Dic43D411yescharacteristic
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290—21no—
85#13063290—21no—
86#13063290D411yescharacteristic
87#13063283—21no—
88#13063283—21no—
89C4⋊C4×D43—21no—
90C4⋊C4×D43D411yescharacteristic
91C42×D43—21no—
92C42×D43C2311yescharacteristic
93#13063259—21no—
94#13063258—21no—
95#13063257—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063249—21no—
113#13063249—21no—
114#13063249—21no—
115#13063248—21no—
116#13063248—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8D411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×Q16×C43—21no—
130C2×Q16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#107×C43—21no—
135#107×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147Q8×D43—22no—
148Q8×D43—22no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43C2×D411yescharacteristic
152C2×C4×D43C2×D411yescharacteristic
153C2×C4×D43#4111yescharacteristic
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C2×D411yescharacteristic
158Q16×C43—42no—
159Q16×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C2×D411yescharacteristic
171C42×C43—21no—
172C42×C43C2411yescharacteristic
173#10621885—42no—
174#10621885—42no—
175(C2×D43)⋊C4—41no—
176(C2×D43)⋊C4—41no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—41no—
183C4⋊Dic43—41no—
184C4⋊Dic43C2×D411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—41no—
194C4×Dic43—41no—
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C22×D43#12111yescharacteristic
204Q8×C43—21no—
205Q8×C43—41no—
206Q8×C43—41no—
207Q8×C43—41no—
208Q8×C43—41no—
209Q8×C43#13512yes—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C2×#4111yescharacteristic
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43#12111yescharacteristic
222C2×Dic43#12111yescharacteristic
223C2×Dic43#12111yescharacteristic
224C4×D43—24no—
225C4×D43—21no—
226C4×D43—21no—
227C4×D43—21no—
228C4×D43—21no—
229C4×D43—41no—
230C4×D43—81no—
231Dic86—24no—
232Dic86—21no—
233Dic86—41no—
234Dic86—41no—
235Dic86—81no—
236Dic86#13512yes—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—41no—
240C8×C43—41no—
241C8×C43—41no—
242C43⋊C8—21no—
243C43⋊C8—21no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247#19407—431nomaximal, Sylow
248C22×C43C2×#12111yescharacteristic
249C2×D43—21no—
250C2×D43—21no—
251C2×D43—21no—
252C4×C43—22no—
253C4×C43—21no—
254C4×C43—41no—
255C4×C43—81no—
256C4×C43—81no—
257C4×C43C2×#13511yescharacteristic
258C4×C43C2×#13511yescharacteristic
259C4×C43#57811yescharacteristic
260C4×C43#57811yescharacteristic
261Dic43—21no—
262Dic43—21no—
263Dic43—22no—
264Dic43—21no—
265Dic43—41no—
266Dic43—81no—
267Dic43—81no—
268#3231—431no—
269#3113—431no—
270#3104—431no—
271#2982—431no—
272#1684—431no—
273#1684—431no—
274#1680—431no—
275#1680—431no—
276#1674—431no—
277#1674D4311yescharacteristic, complemented
278#1672—431no—
279#1672—431no—
280#1572—431no—
281#1554—431no—
282#1544—431no—
283C2×C43#304411yescharacteristic
284C2×C43#305011yescharacteristic
285C2×C43#306911yescharacteristic
286D43—41no—
287#533—431no—
288#533—431no—
289C2×C4×Q8—431no—
290#500C2×D4311yescharacteristic
291#498—431no—
292#487—431no—
293#487—431no—
294#485—861no—
295#485—861no—
296#484—861no—
297#483—861no—
298#479—861no—
299#479—861no—
300#477—431no—
301#477—431no—
302#475—431no—
303#475—431no—
304#462—431no—
305#462—431no—
306#462C2×D4311yescharacteristic
307#462C2×D4311yescharacteristic
308#451—861no—
309#451—861no—
310C8×Q8—431no—
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—861no—
314C8×Q8—861no—
315C8×Q8C2×D4311yescharacteristic
316#441—861no—
317#441—861no—
318C4×Q16—861no—
319C4×Q16—861no—
320#432—431no—
321#431—431no—
322#431—431no—
323#431—431no—
324#431—861no—
325#431—861no—
326#335—431no—
327#335C2×D4311yescharacteristic
328#334—431no—
329#334—431no—
330#333—431no—
331#333—431no—
332#332—431no—
333#332—431no—
334#332—431no—
335#332—431no—
336#332C2×D4311yescharacteristic
337#332C2×D4311yescharacteristic
338C43#1940711yescharacteristic, complemented, Sylow
339C22×Q8—431no—
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16—861no—
343C2×Q16—861no—
344C4⋊Q8—431no—
345C4⋊Q8—431no—
346C4⋊Q8C22×D4311yescharacteristic
347C4⋊Q8C22×D4311yescharacteristic
348#125—861no—
349#125—861no—
350C22⋊Q8—861no—
351C22⋊Q8—861no—
352C22⋊Q8—861no—
353C22⋊Q8—861no—
354C4×Q8—431no—
355C4×Q8—431no—
356C4×Q8—431no—
357C4×Q8—861no—
358C4×Q8—861no—
359C4×Q8—861no—
360C4×Q8—861no—
361C4×Q8—861no—
362C4×Q8—861no—
363C4×Q8C22×D4311yescharacteristic
364#117—861no—
365#117—861no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—861no—
368C2×C42—431no—
369C2×C42—861no—
370#107—21no—
371#107—21no—
372#107—861no—
373#107—861no—
374#106—861no—
375#106—861no—
376#106—861no—
377#106—861no—
378C4⋊C8—21no—
379C4⋊C8—431no—
380C4⋊C8—431no—
381C4⋊C8—431no—
382C4⋊C8—431no—
383C4⋊C8—431no—
384C4⋊C8—861no—
385C4⋊C8—861no—
386C4⋊C8—861no—
387C4⋊C8C22×D4311yescharacteristic
388C4⋊C8C22×D4311yescharacteristic
389C4⋊C8C22×D4311yescharacteristic
390#103—21no—
391#103—21no—
392#103—861no—
393#103—861no—
394#103—861no—
395#103—861no—
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402C22⋊C8—431no—
403C22⋊C8—431no—
404C22⋊C8—861no—
405C22⋊C8—861no—
406C22⋊C8—861no—
407#97—861no—
408C4×C8—21no—
409C4×C8—431no—
410C4×C8—861no—
411C4×C8—861no—
412C4×C8—861no—
413C4×C8—861no—
414C4×C8—861no—
415C4×C8C22×D4311yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—431no—
419C2×Q8—861no—
420C2×Q8—862no—
421C2×Q8—862no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8D4×D4311yescharacteristic
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—861no—
429C22×C4—861no—
430Q16—42no—
431Q16—42no—
432Q16—1722no—
433Q16—1722no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—431no—
438C2×C8—431no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8D4×D4311yescharacteristic
443C2×C8D4×D4311yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—431no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—1721no—
459C4⋊C4—1721no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4D4×D4311yescharacteristic
463C22⋊C4—1721no—
464C22⋊C4—1721no—
465C42—21no—
466C42—431no—
467C42—431no—
468C42—431no—
469C42—861no—
470C42—861no—
471C42—861no—
472C42—1721no—
473C42—1721no—
474C42C23×D4311yescharacteristic
475C23—431no—
476Q8—21no—
477Q8—41no—
478Q8—41no—
479Q8—41no—
480Q8—41no—
481Q8—432no—
482Q8—864no—
483Q8—861no—
484Q8—3441no—
485Q8—1721no—
486Q8—1721no—
487Q8#1306334412yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—431no—
493C2×C4—431no—
494C2×C4—431no—
495C2×C4—864no—
496C2×C4—861no—
497C2×C4—861no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—3441no—
503C2×C4—1721no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4C2×D4×D4311yescharacteristic
507C2×C4C2×D4×D4311yescharacteristic
508C2×C4#41×D4311yescharacteristic
509C8—21no—
510C8—21no—
511C8—41no—
512C8—41no—
513C8—41no—
514C8—861no—
515C8—861no—
516C8—1721no—
517C8—1721no—
518C8—1721no—
519C22—861no—
520C22—861no—
521C22—861no—
522C22#121×D4311yescharacteristic
523C4—21no—
524C4—22no—
525C4—41no—
526C4—81no—
527C4—81no—
528C4—861no—
529C4—861no—
530C4—861no—
531C4—862no—
532C4—3441no—
533C4—3441no—
534C4—1721no—
535C4#135×D4311yescharacteristic
536C4C2×#1306334411yescharacteristic
537C4#1458371211yescharacteristic
538C4#1458371511yescharacteristic
539C2—1721no—
540C2#1914412011yescharacteristic
541C2#1914417411yescharacteristic
542C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1674C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1674D43
hypocenterC43#19407
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1674

Complements

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

NH ≅ G/Ntype
5. #19134054C2semidirect
6. #19134053C2semidirect
7. #19134028C2semidirect
8. #19134027C2semidirect
9. #19133986C2semidirect
10. #19133976C2semidirect
11. #19133975C2semidirect
15. C43×#1674C2semidirect
277. #1674D43semidirect
338. C43#19407semidirect

Maximal subgroups

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

subgroupindex
#191457552
#191447242
#191446332
#191436742
#191340542
#191340532
#191340282
#191340272
#191339862
#191339762
#191339752
#191333742
#191333022
#191332582
C43×#16742
#1940743