Finite Group Databasebeta

← #25251775

Subgroups — #25251775

Order 11008.

556 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145255C211yesmaximal, characteristic, complemented
2#19143442C211yesmaximal, characteristic
3#19136806C211yesmaximal, characteristic, complemented
4#19136805C211yesmaximal, characteristic, complemented
5#19136749C211yesmaximal, characteristic, complemented
6#19136641C211yesmaximal, characteristic, complemented
7#19136640C211yesmaximal, characteristic, complemented
8#19136525C211yesmaximal, characteristic
9#19136525C211yesmaximal, characteristic
10#19136458C211yesmaximal, characteristic, complemented
11#19136456C211yesmaximal, characteristic, complemented
12#19136450C211yesmaximal, characteristic, complemented
13#19136446C211yesmaximal, characteristic, complemented
14#19136401C211yesmaximal, characteristic, complemented
15C43×#2228C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17#14583512—21no—
18#14583371—21no—
19C2×#13063270C2211yescharacteristic
20C2×#13063270C2211yescharacteristic
21C2×#13063269C2211yescharacteristic
22C2×#13063269C2211yescharacteristic
23#14583279C2211yescharacteristic, complemented
24#14583269—21no—
25#14583158—21no—
26#14583141C2211yescharacteristic
27#14583141C2211yescharacteristic
28#14583009—21no—
29#14583008—21no—
30#14583005—21no—
31#14582993C2211yescharacteristic, complemented
32#14582993C2211yescharacteristic, complemented
33C4×D344C2211yescharacteristic
34D8×Dic43C2211yescharacteristic
35#14582981C2211yescharacteristic
36#14582936C2211yescharacteristic
37#14582902—21no—
38#14582853C2211yescharacteristic
39#14582726C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41C4⋊(C43⋊C16)C2211yescharacteristic, complemented
42#14582704C2211yescharacteristic, complemented
43#14582704C2211yescharacteristic, complemented
44#14582702C2211yescharacteristic, complemented
45#14582702C2211yescharacteristic, complemented
46#14582699C2211yescharacteristic
47#14582699C2211yescharacteristic
48(C2×D43)⋊C16C2211yescharacteristic
49(C2×D43)⋊C16C2211yescharacteristic
50#14582674C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C43×#499C2211yescharacteristic, complemented
53C4×D8×C43C2211yescharacteristic
54C43×#367C2211yescharacteristic, complemented
55C43×#366C2211yescharacteristic, complemented
56C43×C4⋊C16C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×D4×D43—21no—
60C2×Dic172—21no—
61C2×Dic172C2311yescharacteristic
62C2×Dic172C2311yescharacteristic
63C2×D344C2311yescharacteristic
64C2×#10621882—21no—
65D8×D43—22no—
66D8×D43—22no—
67C2×#10621872D411yescharacteristic
68C2×C8×D43C2311yescharacteristic
69#13063325—21no—
70#13063320—41no—
71#13063320—41no—
72#13063316—41no—
73#13063316—41no—
74#13063305—21no—
75#13063305—21no—
76#13063290—21no—
77#13063290—21no—
78C4×D172—21no—
79D4×Dic43—21no—
80#13063287—21no—
81C4×C22⋊D43—41no—
82(C22⋊D43)⋊C4—41no—
83#13063283—21no—
84#13063282D411yescharacteristic
85C2×(C2×D43)⋊C4—41no—
86C22⋊C4×D43—41no—
87#13063270—22no—
88#13063270—22no—
89#13063269—22no—
90#13063269—22no—
91C2×C43⋊C16C2311yescharacteristic
92C2×C43⋊C16C2311yescharacteristic
93#13063259C2311yescharacteristic
94#13063256—21no—
95#13063248—21no—
96#13063248—21no—
97#13063248—21no—
98#13063248—21no—
99#13063247—21no—
100#13063246—21no—
101#13063245—21no—
102#13063236D411yescharacteristic
103#13063235D411yescharacteristic
104C8×Dic43C2311yescharacteristic
105C2×D8×C43C2311yescharacteristic
106#125×C43—21no—
107C4×D4×C43—21no—
108C2×C16×C43C2311yescharacteristic
109C2×C16×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#106×C43—21no—
114#102×C43—21no—
115C4×C8×C43C2311yescharacteristic
116C23×D43—41no—
117C2×D4×C43—21no—
118C22×C4×C43—41no—
119C2×C22⋊D43—41no—
120C22×Dic43—41no—
121D4×D43—24no—
122D4×D43—42no—
123C2×D172—21no—
124C2×C4×D43—41no—
125C2×C4×D43—41no—
126C2×C4×D43C2×D411yescharacteristic
127C2×Dic86—21no—
128C2×Dic86—21no—
129D8×C43—21no—
130D8×C43#4112yes—
131C2×C8×C43C2×D411yescharacteristic
132C2×C8×C43C2411yescharacteristic
133C4⋊C4×C43—21no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43—41no—
138C22⋊C4×C43—41no—
139C42×C43C2×D411yescharacteristic
140C22⋊Dic43—41no—
141#10621882—24no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4—41no—
146(C2×D43)⋊C4—41no—
147(C2×D43)⋊C4D811yescharacteristic
148(C2×D43)⋊C4D811yescharacteristic
149C4⋊Dic43—21no—
150C4⋊Dic43—41no—
151C4⋊Dic43—41no—
152C4⋊Dic43—41no—
153C4⋊Dic43—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4—41no—
156Dic43⋊C4D811yescharacteristic
157Dic43⋊C4D811yescharacteristic
158C4×Dic43—41no—
159C4×Dic43—41no—
160C4×Dic43—41no—
161C4×Dic43C2×D411yescharacteristic
162C2×C43⋊C8C2×D411yescharacteristic
163C2×C43⋊C8C2×D411yescharacteristic
164Dic172—21no—
165Dic172—21no—
166Dic172—21no—
167Dic172—21no—
168Dic172—42no—
169D344—21no—
170D344#4112yes—
171#10621872—41no—
172C8×D43—21no—
173C8×D43—21no—
174C16×C43—21no—
175C16×C43—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—41no—
179C22×D43—44no—
180C22×D43—41no—
181C22×D43—161no—
182C22×D43—161no—
183C22×D43C2×D811yescharacteristic
184D4×C43—22no—
185D4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—161no—
190C2×C4×C43C2×D811yescharacteristic
191C2×C4×C43C2×D811yescharacteristic
192C2×C4×C43C22×D411yescharacteristic
193C22⋊D43—44no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—161no—
198C2×Dic43C2×D811yescharacteristic
199C2×Dic43C2×D811yescharacteristic
200C2×Dic43C2×D811yescharacteristic
201D172—22no—
202D172—41no—
203C4×D43—21no—
204C4×D43—21no—
205C4×D43—161no—
206C4×D43—161no—
207Dic86—41no—
208Dic86—41no—
209Dic86—41no—
210Dic86—41no—
211C8×C43—21no—
212C8×C43C2×#4111yescharacteristic
213C8×C43C2×#4111yescharacteristic
214C43⋊C8—21no—
215C43⋊C8—21no—
216#33683—431nomaximal, Sylow
217C22×C43—42no—
218C22×C43—81no—
219C22×C43—81no—
220C22×C43C22×D811yescharacteristic
221C2×D43—21no—
222C2×D43—21no—
223C2×D43—21no—
224C2×D43—42no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—164no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—81no—
231C4×C43—81no—
232C4×C43—81no—
233C4×C43#52511yescharacteristic
234C4×C43#57511yescharacteristic
235Dic43—21no—
236Dic43—21no—
237Dic43—21no—
238Dic43—81no—
239Dic43—81no—
240Dic43—81no—
241#3177—431no—
242#2948—431no—
243#2237—431no—
244#2237—431no—
245#2228—431no—
246#2228D4311yescharacteristic, complemented
247#2208—431no—
248#2208—431no—
249#2187—431no—
250#2187—431no—
251#2175—431no—
252#2175—431no—
253C4×SD32—431no—
254C4×SD32—431no—
255#2164—431no—
256C2×C43—82no—
257C2×C43#310011yescharacteristic
258C2×C43#341611yescharacteristic
259C2×C43#341611yescharacteristic
260D43—41no—
261D43—82no—
262C22×D8—431no—
263#541—861no—
264#518—861no—
265C2×SD32—431no—
266C2×SD32—431no—
267C2×SD32—431no—
268C2×SD32—431no—
269#499C2×D4311yescharacteristic, complemented
270#494—431no—
271#491—861no—
272#470—861no—
273#467—431no—
274#467—431no—
275#442—861no—
276#442—861no—
277#441—861no—
278C4×Q16—431no—
279C4×Q16—431no—
280C4×D8—431no—
281C4×D8—431no—
282C4×D8—431no—
283C4×D8C2×D4311yescharacteristic
284#427—431no—
285#418—861no—
286#405—431no—
287#367—431no—
288#367C2×D4311yescharacteristic, complemented
289#366—431no—
290#366C2×D4311yescharacteristic, complemented
291C4⋊C16—431no—
292C4⋊C16C2×D4311yescharacteristic, complemented
293#358—431no—
294#358—431no—
295#358—431no—
296#358—431no—
297#357—431no—
298#357—431no—
299#357C2×D4311yescharacteristic
300#357C2×D4311yescharacteristic
301C22⋊C16—431no—
302C22⋊C16—431no—
303#346—431no—
304C4×C16—431no—
305C43#3368311yescharacteristic, complemented, Sylow
306C22×D4—861no—
307C2×Q16—431no—
308C2×Q16—431no—
309C2×Q16—861no—
310C2×D8—431no—
311C2×D8—861no—
312C2×D8—862no—
313C2×D8—862no—
314C2×D8C22×D4311yescharacteristic
315C2×M16—431no—
316C22×C8—431no—
317C4⋊Q8—861no—
318#126—1721no—
319#126—1721no—
320#125—21no—
321#125—1721no—
322#125—1721no—
323C22⋊Q8—861no—
324C22⋊Q8—861no—
325C4×Q8—861no—
326C4×Q8—861no—
327C4×D4—21no—
328C4×D4—861no—
329C4×D4—861no—
330C4×D4—861no—
331C4×D4—1721no—
332C4×D4—1721no—
333#117—431no—
334#117—861no—
335C2×C22⋊C4—1721no—
336C2×C22⋊C4—1721no—
337SD32—862no—
338SD32—862no—
339SD32—862no—
340SD32—862no—
341C2×C16—431no—
342C2×C16—431no—
343C2×C16C22×D4311yescharacteristic
344C2×C16C22×D4311yescharacteristic
345#107—431no—
346#107C22×D4311yescharacteristic
347#107C22×D4311yescharacteristic
348#107C22×D4311yescharacteristic
349#106—21no—
350#106—861no—
351#103—861no—
352#103—861no—
353#103—861no—
354#103—861no—
355#102—21no—
356#102—861no—
357#102—861no—
358#102—861no—
359#97—431no—
360#97—431no—
361C4×C8—431no—
362C4×C8C22×D4311yescharacteristic
363C24—1721no—
364C2×Q8—861no—
365C2×Q8—861no—
366C2×D4—21no—
367C2×D4—864no—
368C2×D4—861no—
369C2×D4—1721no—
370C2×D4—1722no—
371C22×C4—41no—
372C22×C4—431no—
373C22×C4—1721no—
374C22×C4—1721no—
375C22×C4—1721no—
376Q16—861no—
377Q16—861no—
378Q16—861no—
379Q16—861no—
380Q16—1722no—
381D8—21no—
382D8—432no—
383D8—864no—
384D8—861no—
385D8#1062190212yes—
386M16—1721no—
387C2×C8—431no—
388C2×C8—431no—
389C2×C8—861no—
390C2×C8—861no—
391C2×C8D4×D4311yescharacteristic
392C2×C8C23×D4311yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—431no—
399C4⋊C4—431no—
400C4⋊C4—861no—
401C4⋊C4—1721no—
402C4⋊C4—1721no—
403C4⋊C4—1721no—
404C4⋊C4—1721no—
405C4⋊C4—1721no—
406C4⋊C4—1721no—
407C22⋊C4—41no—
408C22⋊C4—431no—
409C22⋊C4—431no—
410C22⋊C4—1721no—
411C22⋊C4—1721no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C42—431no—
417C42—1721no—
418C42—1721no—
419C42—1721no—
420C42D4×D4311yescharacteristic
421C16—21no—
422C16—21no—
423C16—861no—
424C16—861no—
425C23—41no—
426C23—431no—
427C23—1724no—
428C23—1721no—
429C23—6881no—
430C23—6881no—
431Q8—1721no—
432Q8—1721no—
433Q8—1721no—
434Q8—1721no—
435D4—22no—
436D4—41no—
437D4—862no—
438D4—1724no—
439D4—1721no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—161no—
444C2×C4—431no—
445C2×C4—431no—
446C2×C4—431no—
447C2×C4—861no—
448C2×C4—861no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4—1721no—
452C2×C4—6881no—
453C2×C4—6881no—
454C2×C4—6881no—
455C2×C4D8×D4311yescharacteristic
456C2×C4D8×D4311yescharacteristic
457C2×C4C2×D4×D4311yescharacteristic
458C8—21no—
459C8—861no—
460C8—861no—
461C8#41×D4311yescharacteristic
462C8C2×#1062190211yescharacteristic
463C22—42no—
464C22—81no—
465C22—81no—
466C22—861no—
467C22—861no—
468C22—861no—
469C22—3441no—
470C22—3441no—
471C22—1722no—
472C22—6884no—
473C22C2×D8×D4311yescharacteristic
474C4—21no—
475C4—21no—
476C4—81no—
477C4—81no—
478C4—81no—
479C4—861no—
480C4—861no—
481C4—861no—
482C4—3441no—
483C4—3441no—
484C4—3441no—
485C4#1458341211yescharacteristic
486C4#1458369811yescharacteristic
487C2—82no—
488C2—3442no—
489C2—1721no—
490C2#1914459711yescharacteristic
491C2#1914773811yescharacteristic
492C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2228C2
socleC22×C43C22×D8
prime radicalC2×D8×D43C22
hypercenter#2228D43
hypocenterC43#33683
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #19145255C2semidirect
3. #19136806C2semidirect
4. #19136805C2semidirect
5. #19136749C2semidirect
6. #19136641C2semidirect
7. #19136640C2semidirect
10. #19136458C2semidirect
11. #19136456C2semidirect
12. #19136450C2semidirect
13. #19136446C2semidirect
14. #19136401C2semidirect
15. C43×#2228C2semidirect
23. #14583279C22semidirect
31. #14582993C22semidirect
32. #14582993C22semidirect
39. #14582726C22semidirect
40. #14582724C22semidirect
41. C4⋊(C43⋊C16)C22semidirect
42. #14582704C22semidirect
43. #14582704C22semidirect
44. #14582702C22semidirect
45. #14582702C22semidirect
50. #14582674C22semidirect
51. C16×Dic43C22semidirect
52. C43×#499C22semidirect
54. C43×#367C22semidirect
55. C43×#366C22semidirect
56. C43×C4⋊C16C22semidirect
246. #2228D43semidirect
269. #499C2×D43semidirect
288. #367C2×D43semidirect
290. #366C2×D43semidirect
292. C4⋊C16C2×D43semidirect
305. C43#33683semidirect

Maximal subgroups

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

subgroupindex
#191452552
#191434422
#191368062
#191368052
#191367492
#191366412
#191366402
#191365252
#191364582
#191364562
#191364502
#191364462
#191364012
C43×#22282
#3368343