Finite Group Databasebeta

← #25249963

Subgroups — #25249963

Order 11008.

682 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD32×D43C211yesmaximal, characteristic
2#19143458C211yesmaximal, characteristic, complemented
3#19143442C211yesmaximal, characteristic
4#19136461C211yesmaximal, characteristic, complemented
5#19136460C211yesmaximal, characteristic, complemented
6#19136458C211yesmaximal, characteristic, complemented
7#19136450C211yesmaximal, characteristic, complemented
8C4×#13063268C211yesmaximal, characteristic, complemented
9C4×#13063269C211yesmaximal, characteristic, complemented
10#19136444C211yesmaximal, characteristic, complemented
11#19136376C211yesmaximal, characteristic, complemented
12#19136313C211yesmaximal, characteristic, complemented
13#19136309C211yesmaximal, characteristic
14#19136193C211yesmaximal, characteristic, complemented
15C43×#2175C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583375—21no—
19#14583371—21no—
20C2×#13063270C2211yescharacteristic
21C2×#13063269C2211yescharacteristic
22C2×#13063268C2211yescharacteristic
23SD32×D43C418yescomplemented
24C2×#13063264C2211yescharacteristic
25C2×C16×D43C2211yescharacteristic
26#14583009—21no—
27#14583008—21no—
28#14583004—21no—
29#14583003—21no—
30C4×Dic172C2211yescharacteristic, complemented
31Q16×Dic43C2211yescharacteristic, complemented
32#14582993C2211yescharacteristic, complemented
33C4×D344C2211yescharacteristic
34D8×Dic43C2211yescharacteristic
35#14582981C2211yescharacteristic
36#14582936C2211yescharacteristic
37#14582936C2211yescharacteristic
38#14582906—21no—
39#14582902—21no—
40#14582853C2211yescharacteristic
41#14582726C2211yescharacteristic, complemented
42#14582726C2211yescharacteristic, complemented
43#14582725C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582703C2211yescharacteristic, complemented
46#14582702C2211yescharacteristic, complemented
47#14582701C2211yescharacteristic
48#14582700C2211yescharacteristic
49#14582699C2211yescharacteristic
50#14582674C2211yescharacteristic, complemented
51C4×C43⋊C16C2211yescharacteristic, complemented
52C16×Dic43C2211yescharacteristic, complemented
53C2×SD32×C43C2211yescharacteristic
54C4×Q16×C43C2211yescharacteristic, complemented
55C4×D8×C43C2211yescharacteristic
56C43×#366C2211yescharacteristic, complemented
57C43×#358C2211yescharacteristic, complemented
58C43×#357C2211yescharacteristic
59C43×#346C2211yescharacteristic, complemented
60C2×Q8×D43—21no—
61C2×D4×D43—21no—
62C2×Dic172C2311yescharacteristic
63C2×#10621885—21no—
64Q16×D43—22no—
65Q16×D43C2×C414yescomplemented
66C2×D344C2311yescharacteristic
67C2×#10621882—21no—
68D8×D43—22no—
69D8×D43C2×C414yes—
70C2×#10621872D411yescharacteristic
71C2×C8×D43C2311yescharacteristic
72Q8×Dic43—21no—
73C4×Dic86—21no—
74C4×Dic86—41no—
75#13063290—21no—
76#13063290—41no—
77C4×D172—21no—
78D4×Dic43—21no—
79#13063287—21no—
80C4×C22⋊D43—41no—
81(C22⋊D43)⋊C4—41no—
82#13063283—21no—
83#13063283—21no—
84#13063283—41no—
85#13063282—41no—
86#13063282D411yescharacteristic
87C2×(C2×D43)⋊C4—41no—
88C22⋊C4×D43—41no—
89#13063270C2×C414yescomplemented
90#13063269C2×C414yescomplemented
91#13063268C2×C414yescomplemented
92#13063264—22no—
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C16×D43C2×C414yescomplemented
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063256—21no—
99#13063256—21no—
100#13063250—21no—
101#13063249—21no—
102#13063248—21no—
103#13063247—21no—
104#13063246—21no—
105#13063245—21no—
106#13063236D411yescharacteristic
107#13063235D411yescharacteristic
108C8×Dic43C2311yescharacteristic
109C2×Q16×C43C2311yescharacteristic
110C2×D8×C43C2311yescharacteristic
111C4×Q8×C43—21no—
112C4×D4×C43—21no—
113SD32×C43C2×C414yescomplemented
114C2×C16×C43C2311yescharacteristic
115C2×C16×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#107×C43C2311yescharacteristic
118#103×C43—21no—
119#102×C43—21no—
120C4×C8×C43C2311yescharacteristic
121C23×D43—41no—
122C2×Q8×C43—21no—
123C2×D4×C43—21no—
124C22×C4×C43—41no—
125C2×C22⋊D43—41no—
126C22×Dic43—41no—
127Q8×D43—24no—
128Q8×D43—42no—
129D4×D43—24no—
130D4×D43—42no—
131C2×D172—21no—
132C2×C4×D43—41no—
133C2×C4×D43—41no—
134C2×C4×D43—41no—
135C2×C4×D43C2×D411yescharacteristic
136C2×Dic86—21no—
137C2×Dic86—41no—
138Q16×C43—21no—
139Q16×C43C22×C412yes—
140D8×C43—21no—
141D8×C43C22×C412yes—
142C2×C8×C43C2×D411yescharacteristic
143C2×C8×C43C2411yescharacteristic
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C42×C43—41no—
149C42×C43C2×D411yescharacteristic
150C22⋊Dic43—41no—
151#10621885—24no—
152#10621882—24no—
153(C2×D43)⋊C4—41no—
154(C2×D43)⋊C4—41no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4D811yescharacteristic
158(C2×D43)⋊C4D811yescharacteristic
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43—41no—
162Dic43⋊C4—41no—
163Dic43⋊C4—41no—
164Dic43⋊C4D811yescharacteristic
165Dic43⋊C4D811yescharacteristic
166C4×Dic43—41no—
167C4×Dic43—41no—
168C4×Dic43—41no—
169C4×Dic43—41no—
170C4×Dic43—41no—
171C4×Dic43C2×D411yescharacteristic
172C2×C43⋊C8C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174Dic172—21no—
175Dic172C22×C412yes—
176D344—21no—
177D344C22×C412yes—
178#10621872—22no—
179C8×D43C22×C412yes—
180C8×D43#4112yes—
181C16×C43—21no—
182C16×C43C22×C412yes—
183C43⋊C16—21no—
184C43⋊C16C22×C412yes—
185C23×C43—41no—
186C22×D43—41no—
187C22×D43—44no—
188C22×D43—161no—
189C22×D43—161no—
190C22×D43C2×D811yescharacteristic
191Q8×C43—22no—
192Q8×C43—41no—
193D4×C43—22no—
194D4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—161no—
199C2×C4×C43C2×D811yescharacteristic
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C22⋊D43—44no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—161no—
207C2×Dic43C2×D811yescharacteristic
208C2×Dic43C2×D811yescharacteristic
209C2×Dic43C2×D811yescharacteristic
210D172—22no—
211D172—41no—
212C4×D43—44no—
213C4×D43—161no—
214C4×D43—161no—
215C4×D43C4×D412yes—
216C4×D43#13512yes—
217Dic86—22no—
218Dic86—41no—
219Dic86—44no—
220C8×C43—21no—
221C8×C43C23×C411yescharacteristic
222C8×C43C2×#4111yescharacteristic
223C43⋊C8—21no—
224C43⋊C8C4×D412yes—
225#33457—431nomaximal, Sylow
226C22×C43—42no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43C22×D811yescharacteristic
230C2×D43—21no—
231C2×D43—21no—
232C2×D43—42no—
233C2×D43—81no—
234C2×D43—81no—
235C2×D43—164no—
236C2×D43C4×D812yes—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—42no—
240C4×C43—81no—
241C4×C43—81no—
242C4×C43C2×C4×D411yescharacteristic
243C4×C43C2×#13511yescharacteristic
244Dic43—21no—
245Dic43—21no—
246Dic43—42no—
247Dic43—81no—
248Dic43—81no—
249Dic43C4×D812yes—
250C22×SD32—431no—
251#2950—431no—
252#2948—431no—
253#2175—431no—
254#2175—431no—
255#2175—431no—
256#2175D4311yescharacteristic, complemented
257C4×SD32—431no—
258C4×SD32—431no—
259C4×SD32—431no—
260C4×SD32—431no—
261#2158—431no—
262#2141—431no—
263#2140—431no—
264#2108—431no—
265C2×C43—82no—
266C2×C43C2×C4×D811yescharacteristic
267C2×C43#341611yescharacteristic
268C2×C43#341611yescharacteristic
269D43—22no—
270D43—82no—
271C22×Q16—431no—
272C22×D8—431no—
273#519—861no—
274#518—861no—
275C2×SD32—431no—
276C2×SD32—431no—
277C2×SD32—438no—
278C2×SD32—431no—
279C2×SD32C2×D4311yescharacteristic
280C2×M32—431no—
281C22×C16—431no—
282#442—861no—
283#442—861no—
284#441—861no—
285#441—861no—
286C4×Q16—431no—
287C4×Q16—431no—
288C4×Q16—431no—
289C4×Q16C2×D4311yescharacteristic, complemented
290C4×D8—431no—
291C4×D8—431no—
292C4×D8—431no—
293C4×D8C2×D4311yescharacteristic
294#427—431no—
295#427—431no—
296#419—861no—
297#418—861no—
298#405—431no—
299#367—431no—
300#367—431no—
301#366—431no—
302#366C2×D4311yescharacteristic, complemented
303#358—431no—
304#358—431no—
305#358—431no—
306#358C2×D4311yescharacteristic, complemented
307#357—431no—
308#357—431no—
309#357—431no—
310#357C2×D4311yescharacteristic
311#346—431no—
312#346C2×D4311yescharacteristic, complemented
313C4×C16—431no—
314C4×C16—431no—
315C43#3345711yescharacteristic, complemented, Sylow
316C22×Q8—861no—
317C22×D4—861no—
318C2×Q16—434no—
319C2×Q16—431no—
320C2×Q16—862no—
321C2×Q16—861no—
322C2×Q16C22×D4311yescharacteristic
323C2×D8—434no—
324C2×D8—431no—
325C2×D8—862no—
326C2×D8—861no—
327C2×D8C22×D4311yescharacteristic
328C2×M16—431no—
329C22×C8—431no—
330C4×Q8—21no—
331C4×Q8—861no—
332C4×Q8—861no—
333C4×Q8—861no—
334C4×Q8—1721no—
335C4×Q8—1721no—
336C4×D4—21no—
337C4×D4—861no—
338C4×D4—861no—
339C4×D4—861no—
340C4×D4—1721no—
341C4×D4—1721no—
342#117—431no—
343#117—861no—
344#117—861no—
345#117—1721no—
346#117—1721no—
347C2×C22⋊C4—1721no—
348C2×C22⋊C4—1721no—
349SD32—434no—
350SD32—434no—
351SD32—434no—
352SD32C4×D4314yescomplemented
353M32—862no—
354C2×C16—431no—
355C2×C16—434no—
356C2×C16—431no—
357C2×C16C22×D4311yescharacteristic
358C2×C16C22×D4311yescharacteristic
359#107—431no—
360#107—431no—
361#107C22×D4311yescharacteristic
362#107C22×D4311yescharacteristic
363#106—861no—
364#106—861no—
365#103—21no—
366#103—861no—
367#103—861no—
368#103—861no—
369#102—21no—
370#102—861no—
371#102—861no—
372#102—861no—
373#97—431no—
374#97—431no—
375C4×C8—431no—
376C4×C8C22×D4311yescharacteristic
377C24—1721no—
378C2×Q8—21no—
379C2×Q8—864no—
380C2×Q8—861no—
381C2×Q8—1721no—
382C2×Q8—1722no—
383C2×D4—21no—
384C2×D4—864no—
385C2×D4—861no—
386C2×D4—1722no—
387C2×D4—1721no—
388C22×C4—41no—
389C22×C4—431no—
390C22×C4—1721no—
391C22×C4—1721no—
392C22×C4—1721no—
393C22×C4—1721no—
394Q16—21no—
395Q16—432no—
396Q16—864no—
397Q16—861no—
398Q16C2×C4×D4312yes—
399D8—21no—
400D8—432no—
401D8—864no—
402D8—861no—
403D8C2×C4×D4312yes—
404M16—862no—
405C2×C8—431no—
406C2×C8—432no—
407C2×C8—432no—
408C2×C8—431no—
409C2×C8D4×D4311yescharacteristic
410C2×C8C23×D4311yescharacteristic
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—41no—
414C4⋊C4—431no—
415C4⋊C4—431no—
416C4⋊C4—861no—
417C4⋊C4—861no—
418C4⋊C4—1721no—
419C4⋊C4—1721no—
420C4⋊C4—1721no—
421C22⋊C4—41no—
422C22⋊C4—431no—
423C22⋊C4—431no—
424C22⋊C4—1721no—
425C22⋊C4—1721no—
426C22⋊C4—1721no—
427C22⋊C4—1721no—
428C22⋊C4—1721no—
429C42—41no—
430C42—431no—
431C42—1721no—
432C42—1721no—
433C42—1721no—
434C42—1721no—
435C42—1721no—
436C42D4×D4311yescharacteristic
437C16—21no—
438C16—432no—
439C16—861no—
440C16C2×C4×D4312yes—
441C23—41no—
442C23—431no—
443C23—1724no—
444C23—1721no—
445C23—6881no—
446C23—6881no—
447Q8—22no—
448Q8—41no—
449Q8—862no—
450Q8—1724no—
451Q8—1721no—
452D4—22no—
453D4—41no—
454D4—862no—
455D4—1724no—
456D4—1721no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—161no—
461C2×C4—431no—
462C2×C4—432no—
463C2×C4—432no—
464C2×C4—431no—
465C2×C4—431no—
466C2×C4—1724no—
467C2×C4—1721no—
468C2×C4—1721no—
469C2×C4—1721no—
470C2×C4—6881no—
471C2×C4—6881no—
472C2×C4—6881no—
473C2×C4D8×D4311yescharacteristic
474C2×C4D8×D4311yescharacteristic
475C2×C4C2×D4×D4311yescharacteristic
476C8—21no—
477C8—432no—
478C8—861no—
479C8C22×C4×D4311yescharacteristic
480C8#41×D4311yescharacteristic
481C22—42no—
482C22—81no—
483C22—81no—
484C22—432no—
485C22—861no—
486C22—861no—
487C22—3441no—
488C22—3441no—
489C22—1722no—
490C22—6884no—
491C22C2×D8×D4311yescharacteristic
492C4—21no—
493C4—21no—
494C4—42no—
495C4—81no—
496C4—81no—
497C4—432no—
498C4—861no—
499C4—861no—
500C4—3441no—
501C4—3441no—
502C4—1722no—
503C4C4×D4×D4311yescharacteristic
504C4#135×D4311yescharacteristic
505C2—82no—
506C2—862no—
507C2—3442no—
508C2C4×D8×D4311yescharacteristic
509C2#1914774011yescharacteristic
510C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2175C2
socleC22×C43C22×D8
prime radicalC2×D8×D43C22
cosocleC2×C8×C43C24
hypercenter#2175D43
hypocenterC43#33457
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
2. #19143458C2semidirect
4. #19136461C2semidirect
5. #19136460C2semidirect
6. #19136458C2semidirect
7. #19136450C2semidirect
8. C4×#13063268C2semidirect
9. C4×#13063269C2semidirect
10. #19136444C2semidirect
11. #19136376C2semidirect
12. #19136313C2semidirect
14. #19136193C2semidirect
15. C43×#2175C2semidirect
23. SD32×D43C4semidirect
30. C4×Dic172C22semidirect
31. Q16×Dic43C22semidirect
32. #14582993C22semidirect
41. #14582726C22semidirect
42. #14582726C22semidirect
43. #14582725C22semidirect
44. #14582704C22semidirect
45. #14582703C22semidirect
46. #14582702C22semidirect
50. #14582674C22semidirect
51. C4×C43⋊C16C22semidirect
52. C16×Dic43C22semidirect
54. C4×Q16×C43C22semidirect
56. C43×#366C22semidirect
57. C43×#358C22semidirect
59. C43×#346C22semidirect
65. Q16×D43C2×C4semidirect
89. #13063270C2×C4semidirect
90. #13063269C2×C4semidirect
91. #13063268C2×C4semidirect
95. C16×D43C2×C4semidirect
113. SD32×C43C2×C4semidirect
256. #2175D43semidirect
289. C4×Q16C2×D43semidirect
302. #366C2×D43semidirect
306. #358C2×D43semidirect
312. #346C2×D43semidirect
315. C43#33457semidirect
352. SD32C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D432
#191434582
#191434422
#191364612
#191364602
#191364582
#191364502
C4×#130632682
C4×#130632692
#191364442
#191363762
#191363132
#191363092
#191361932
C43×#21752
#3345743