Finite Group Databasebeta

← #25251422

Subgroups — #25251422

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#466×D43C211yesmaximal, characteristic
2#427×D43C211yesmaximal, characteristic, complemented
3#19136787C211yesmaximal, characteristic, complemented
4#19136786C211yesmaximal, characteristic, complemented
5#19136783C211yesmaximal, characteristic, complemented
6#19136782C211yesmaximal, characteristic, complemented
7#19136779C211yesmaximal, characteristic, complemented
8#19136777C211yesmaximal, characteristic, complemented
9#19136774C211yesmaximal, characteristic, complemented
10#19136382C211yesmaximal, characteristic, complemented
11#19136380C211yesmaximal, characteristic, complemented
12#19136309C211yesmaximal, characteristic, complemented
13#19136309C211yesmaximal, characteristic, complemented
14#19136204C211yesmaximal, characteristic, complemented
15C43×#2234C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#121×D43—21no—
19#117×D43—21no—
20C2×#13063264C2211yescharacteristic
21C2×#13063264C2211yescharacteristic
22#14583136C2211yescharacteristic
23#14583135C2211yescharacteristic
24#14583134—21no—
25#14583133—21no—
26#14583132C2211yescharacteristic
27#14582937C2211yescharacteristic, complemented
28#14582936C2211yescharacteristic
29#14582936C2211yescharacteristic
30#14582935—21no—
31#14582934—21no—
32#107×D43C2211yescharacteristic
33#107×D43C2211yescharacteristic, complemented
34#107×D43C2211yescharacteristic, complemented
35#106×D43—21no—
36#102×D43—21no—
37#14582727C2211yescharacteristic, complemented
38#14582726C2211yescharacteristic, complemented
39#14582726C2211yescharacteristic, complemented
40#14582725C2211yescharacteristic, complemented
41#14582724C2211yescharacteristic, complemented
42#14582724C2211yescharacteristic, complemented
43#14582701C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic, complemented
46#14582700C2211yescharacteristic, complemented
47#14582699C2211yescharacteristic, complemented
48#14582699C2211yescharacteristic, complemented
49C22⋊(C43⋊C16)C2211yescharacteristic, complemented
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51(C2×D43)⋊C16C2211yescharacteristic, complemented
52C43×#466C2211yescharacteristic
53C43×#427C2211yescharacteristic, complemented
54C43×#367C2211yescharacteristic, complemented
55C43×#366C2211yescharacteristic, complemented
56C43×#357C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic, complemented
58C43×C22⋊C16C2211yescharacteristic, complemented
59C2×D4×D43—21no—
60C2×D4×D43—41no—
61C22×C4×D43D411yescharacteristic
62C2×D344C2311yescharacteristic
63C2×#10621882—21no—
64D8×D43—22no—
65D8×D43—22no—
66C22×C43⋊C8D411yescharacteristic
67C2×C8×D43—22no—
68C2×C8×D43—22no—
69C2×C8×D43D411yescharacteristic
70C2×C8×D43D411yescharacteristic
71C2×C8×D43C2311yescharacteristic
72C2×C8×D43C2311yescharacteristic
73#13063300—21no—
74#13063299—21no—
75#13063298—41no—
76#13063297—41no—
77#13063296—21no—
78#13063284—21no—
79#13063283—21no—
80#13063283—21no—
81#13063282—41no—
82#13063281—41no—
83C4⋊C4×D43—21no—
84C4⋊C4×D43—21no—
85C4⋊C4×D43—21no—
86C22⋊C4×D43—41no—
87C22⋊C4×D43—41no—
88C42×D43—41no—
89#13063264—22no—
90#13063264—22no—
91C2×C43⋊C16C2311yescharacteristic
92C2×C43⋊C16C2311yescharacteristic
93#13063259C2311yescharacteristic
94#13063259C2311yescharacteristic
95#13063259C2311yescharacteristic
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102#13063247—21no—
103#13063246—21no—
104#13063245—21no—
105C2×D8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107#121×C43—21no—
108#117×C43—21no—
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#107×C43C2311yescharacteristic
114#106×C43—21no—
115#102×C43—21no—
116C23×D43—41no—
117C23×D43D811yescharacteristic
118C2×D4×C43—21no—
119C2×D4×C43—41no—
120C22×C4×C43C2×D411yescharacteristic
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C2×C22⋊D43—41no—
124C22×Dic43D811yescharacteristic
125D4×D43—42no—
126D4×D43—42no—
127D4×D43—84no—
128C2×D172—21no—
129C2×D172—41no—
130C2×C4×D43—22no—
131C2×C4×D43—22no—
132C2×C4×D43—41no—
133C2×C4×D43—41no—
134C2×C4×D43—41no—
135C2×C4×D43D811yescharacteristic
136C2×C4×D43D811yescharacteristic
137C2×C4×D43C2×D411yescharacteristic
138C2×C4×D43C2×D411yescharacteristic
139D8×C43—21no—
140D8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43C2×D411yescharacteristic
144C2×C8×C43C2411yescharacteristic
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C42×C43—41no—
151C22⋊Dic43—41no—
152C22⋊Dic43—41no—
153#10621882—42no—
154(C2×D43)⋊C4—41no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161Dic43⋊C4—41no—
162Dic43⋊C4—41no—
163Dic43⋊C4—41no—
164C4×Dic43—41no—
165C4×Dic43—41no—
166C4×Dic43—41no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8C2×D411yescharacteristic
169C2×C43⋊C8C2×D411yescharacteristic
170D344—21no—
171D344—21no—
172C8×D43—22no—
173C8×D43—21no—
174C8×D43—21no—
175C8×D43—22no—
176C8×D43#4112yes—
177C8×D43#4112yes—
178C16×C43—21no—
179C16×C43—21no—
180C43⋊C16—21no—
181C43⋊C16—21no—
182C23×C43—41no—
183C23×C43C2×D811yescharacteristic
184C22×D43—22no—
185C22×D43—22no—
186C22×D43—41no—
187C22×D43—41no—
188C22×D43—82no—
189C22×D43—82no—
190C22×D43—82no—
191C22×D43C2×D811yescharacteristic
192C22×D43C2×D811yescharacteristic
193D4×C43—41no—
194D4×C43—41no—
195D4×C43—82no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C22⋊D43—82no—
204C22⋊D43—82no—
205C22⋊D43—82no—
206C2×Dic43—22no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43C2×D811yescharacteristic
211C2×Dic43C2×D811yescharacteristic
212D172—41no—
213D172—41no—
214D172—82no—
215C4×D43—22no—
216C4×D43—21no—
217C4×D43—21no—
218C4×D43—22no—
219C4×D43—82no—
220C4×D43—82no—
221C4×D43—82no—
222C4×D43#12312yes—
223C4×D43#13712yes—
224C8×C43—21no—
225C8×C43C2×#4111yescharacteristic
226C8×C43C2×#4111yescharacteristic
227C43⋊C8—21no—
228C43⋊C8#12312yes—
229#33648—431nomaximal, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43C22×D811yescharacteristic
237C2×D43—21no—
238C2×D43—21no—
239C2×D43—21no—
240C2×D43—21no—
241C2×D43—44no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—81no—
245C2×D43—164no—
246C2×D43#48012yes—
247C2×D43#50912yes—
248C4×C43—21no—
249C4×C43—81no—
250C4×C43—81no—
251C4×C43—81no—
252C4×C43C2×#12311yescharacteristic
253C4×C43C2×#13711yescharacteristic
254Dic43—21no—
255Dic43—81no—
256Dic43—81no—
257Dic43—81no—
258Dic43#48012yes—
259C2×#466—431no—
260C2×#427—431no—
261#2234—431no—
262#2234—431no—
263#2234—431no—
264#2234D4311yescharacteristic, complemented
265#2233—431no—
266#2233—431no—
267#2232—431no—
268#2232—431no—
269#2159—431no—
270#2159—431no—
271#2140—431no—
272#2140—431no—
273#2112—431no—
274C2×C43—41no—
275C2×C43—161no—
276C2×C43C2×#48011yescharacteristic
277C2×C43C2×#50911yescharacteristic
278C2×C43#341411yescharacteristic
279D43—22no—
280D43—22no—
281D43—161no—
282C22×D8—431no—
283C23×C8—431no—
284C2×#121—861no—
285C2×#117—861no—
286C2×M32—431no—
287C2×M32—431no—
288#466—431no—
289#466—431no—
290#466—431no—
291#466—861no—
292#466—861no—
293#466C2×D4311yescharacteristic
294#427—431no—
295#427—431no—
296#427—431no—
297#427—861no—
298#427—861no—
299#427C2×D4311yescharacteristic, complemented
300C2×#107—431no—
301C2×#107—431no—
302C2×#107—431no—
303C2×#106—861no—
304C2×#102—861no—
305#367—431no—
306#367—431no—
307#367—431no—
308#367C2×D4311yescharacteristic, complemented
309#366—431no—
310#366—431no—
311#366—431no—
312#366C2×D4311yescharacteristic, complemented
313#357—431no—
314#357—431no—
315#357—431no—
316#357—431no—
317#357—431no—
318#357—431no—
319#357C2×D4311yescharacteristic, complemented
320#357C2×D4311yescharacteristic, complemented
321C22⋊C16—431no—
322C22⋊C16—431no—
323C22⋊C16—431no—
324C22⋊C16C2×D4311yescharacteristic, complemented
325C43#3364811yescharacteristic, complemented, Sylow
326C22×D4—861no—
327C22×D4—1721no—
328C23×C4—431no—
329C2×D8—431no—
330C2×D8—862no—
331C2×D8—862no—
332C2×D8—861no—
333C2×D8C22×D4311yescharacteristic
334C22×C8—431no—
335C22×C8—431no—
336C22×C8—431no—
337C22×C8—431no—
338C22×C8—431no—
339C22×C8—862no—
340C22×C8—862no—
341C22×C8C22×D4311yescharacteristic
342#121—21no—
343#121—861no—
344#121—861no—
345#121—861no—
346#121—1721no—
347#121—1721no—
348#117—21no—
349#117—861no—
350#117—861no—
351#117—861no—
352#117—1721no—
353#117—1721no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—861no—
357C2×C22⋊C4—1721no—
358C2×C22⋊C4—1721no—
359C2×C42—1721no—
360M32—862no—
361M32—862no—
362C2×C16—431no—
363C2×C16—431no—
364C2×C16C22×D4311yescharacteristic
365C2×C16C22×D4311yescharacteristic
366#107—431no—
367#107—431no—
368#107—431no—
369#107—861no—
370#107—861no—
371#107—861no—
372#107C22×D4311yescharacteristic
373#107C22×D4311yescharacteristic
374#107C22×D4311yescharacteristic
375#106—21no—
376#106—861no—
377#106—861no—
378#106—861no—
379#102—21no—
380#102—861no—
381#102—861no—
382#102—861no—
383C24—431no—
384C24—1721no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—861no—
388C2×D4—3444no—
389C2×D4—1721no—
390C2×D4—1722no—
391C2×D4—1722no—
392C2×D4—1721no—
393C2×D4—1721no—
394C2×D4—1721no—
395C22×C4—431no—
396C22×C4—431no—
397C22×C4—431no—
398C22×C4—431no—
399C22×C4—431no—
400C22×C4—862no—
401C22×C4—862no—
402C22×C4—1721no—
403C22×C4—1721no—
404C22×C4—1721no—
405C22×C4D4×D4311yescharacteristic
406D8—21no—
407D8—21no—
408D8—861no—
409D8—861no—
410D8—1722no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—431no—
414C2×C8—432no—
415C2×C8—432no—
416C2×C8—431no—
417C2×C8—862no—
418C2×C8—862no—
419C2×C8—862no—
420C2×C8—861no—
421C2×C8—861no—
422C2×C8D4×D4311yescharacteristic
423C2×C8C23×D4311yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—1721no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C22⋊C4—1721no—
440C22⋊C4—1721no—
441C42—41no—
442C42—1721no—
443C42—1721no—
444C42—1721no—
445C16—21no—
446C16—21no—
447C16—861no—
448C16—861no—
449C23—41no—
450C23—431no—
451C23—431no—
452C23—862no—
453C23—862no—
454C23—3442no—
455C23—3442no—
456C23—3442no—
457C23—1721no—
458C23—1721no—
459C23D8×D4311yescharacteristic
460D4—41no—
461D4—41no—
462D4—82no—
463D4—3442no—
464D4—3442no—
465D4—3442no—
466D4—3442no—
467D4—1721no—
468D4—1721no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—431no—
475C2×C4—432no—
476C2×C4—432no—
477C2×C4—431no—
478C2×C4—862no—
479C2×C4—862no—
480C2×C4—862no—
481C2×C4—861no—
482C2×C4—861no—
483C2×C4—3442no—
484C2×C4—3442no—
485C2×C4—3442no—
486C2×C4—1721no—
487C2×C4—1721no—
488C2×C4—1721no—
489C2×C4D8×D4311yescharacteristic
490C2×C4C2×D4×D4311yescharacteristic
491C8—21no—
492C8—432no—
493C8—861no—
494C8#41×D4311yescharacteristic
495C8#41×D4311yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—432no—
503C22—432no—
504C22—861no—
505C22—861no—
506C22—861no—
507C22—861no—
508C22—3441no—
509C22—3441no—
510C22—3441no—
511C22—1724no—
512C22—6884no—
513C22C2×D8×D4311yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—432no—
519C4—861no—
520C4—3441no—
521C4—3441no—
522C4—3441no—
523C4#123×D4311yescharacteristic
524C4#137×D4311yescharacteristic
525C2—41no—
526C2—161no—
527C2—862no—
528C2—862no—
529C2—6881no—
530C2#480×D4311yescharacteristic
531C2#509×D4311yescharacteristic
532C2#1914772811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2234C2
socleC22×C43C22×D8
prime radical#466×D43C2
hypercenter#2234D43
hypocenterC43#33648
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
2. #427×D43C2semidirect
3. #19136787C2semidirect
4. #19136786C2semidirect
5. #19136783C2semidirect
6. #19136782C2semidirect
7. #19136779C2semidirect
8. #19136777C2semidirect
9. #19136774C2semidirect
10. #19136382C2semidirect
11. #19136380C2semidirect
12. #19136309C2semidirect
13. #19136309C2semidirect
14. #19136204C2semidirect
15. C43×#2234C2semidirect
27. #14582937C22semidirect
33. #107×D43C22semidirect
34. #107×D43C22semidirect
37. #14582727C22semidirect
38. #14582726C22semidirect
39. #14582726C22semidirect
40. #14582725C22semidirect
41. #14582724C22semidirect
42. #14582724C22semidirect
43. #14582701C22semidirect
44. #14582701C22semidirect
45. #14582700C22semidirect
46. #14582700C22semidirect
47. #14582699C22semidirect
48. #14582699C22semidirect
49. C22⋊(C43⋊C16)C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. (C2×D43)⋊C16C22semidirect
53. C43×#427C22semidirect
54. C43×#367C22semidirect
55. C43×#366C22semidirect
56. C43×#357C22semidirect
57. C43×#357C22semidirect
58. C43×C22⋊C16C22semidirect
264. #2234D43semidirect
299. #427C2×D43semidirect
308. #367C2×D43semidirect
312. #366C2×D43semidirect
319. #357C2×D43semidirect
320. #357C2×D43semidirect
324. C22⋊C16C2×D43semidirect
325. C43#33648semidirect

Maximal subgroups

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

subgroupindex
#466×D432
#427×D432
#191367872
#191367862
#191367832
#191367822
#191367792
#191367772
#191367742
#191363822
#191363802
#191363092
#191362042
C43×#22342
#3364843