Finite Group Databasebeta

← #25251527

Subgroups — #25251527

Order 11008.

610 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145178C211yesmaximal, characteristic, complemented
2C4×D8×D43C211yesmaximal, characteristic
3#19136794C211yesmaximal, characteristic, complemented
4#19136791C211yesmaximal, characteristic, complemented
5#19136741C211yesmaximal, characteristic, complemented
6#19136740C211yesmaximal, characteristic, complemented
7#19136639C211yesmaximal, characteristic, complemented
8#19136638C211yesmaximal, characteristic, complemented
9#19136525C211yesmaximal, characteristic
10#19136522C211yesmaximal, characteristic
11C4×#13063270C211yesmaximal, characteristic, complemented
12C4×#13063268C211yesmaximal, characteristic, complemented
13C4×#13063269C211yesmaximal, characteristic, complemented
14#19136392C211yesmaximal, characteristic, complemented
15C4×SD32×C43C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17#14583453—21no—
18C4×D4×D43—21no—
19C2×#13063270C2211yescharacteristic
20C2×#13063269C2211yescharacteristic
21C2×#13063268C2211yescharacteristic
22#14583303C2211yescharacteristic, complemented
23#14583277C2211yescharacteristic, complemented
24#14583248—21no—
25#14583141C2211yescharacteristic
26#14583139—21no—
27#14583137C2211yescharacteristic
28C4×Dic172C2211yescharacteristic, complemented
29C4×#10621885—21no—
30C4×D344C2211yescharacteristic
31D8×Dic43C2211yescharacteristic
32#14582981C2211yescharacteristic
33C4×#10621882—21no—
34#14582979—21no—
35#107×D43C2211yescharacteristic
36#102×D43—21no—
37C4×C8×D43C2211yescharacteristic
38#14582727C2211yescharacteristic, complemented
39#14582726C2211yescharacteristic, complemented
40#14582726C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42Dic43⋊C16C2211yescharacteristic, complemented
43#14582704C2211yescharacteristic, complemented
44#14582703C2211yescharacteristic, complemented
45#14582702C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582699C2211yescharacteristic
49(C2×D43)⋊C16C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C4×C43⋊C16C2211yescharacteristic, complemented
52C2×SD32×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic, complemented
54C4×D8×C43C2211yescharacteristic
55C43×#367C2211yescharacteristic, complemented
56C43×#358C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic
58C4×C16×C43C2211yescharacteristic, complemented
59C2×D4×D43—21no—
60C22×C4×D43—41no—
61C2×Dic172C2311yescharacteristic
62C2×#10621885—21no—
63C2×D344C2311yescharacteristic
64C2×#10621882—21no—
65D8×D43—22no—
66D8×D43—22no—
67C2×C8×D43D411yescharacteristic
68C2×C8×D43C2311yescharacteristic
69#13063324—21no—
70#13063323—21no—
71#13063315—41no—
72#13063305—21no—
73#13063303—41no—
74#13063301—21no—
75C4×Dic86—21no—
76C4×Dic86—41no—
77C4×D172—21no—
78D4×Dic43—21no—
79#13063287—21no—
80C4×C22⋊D43—41no—
81(C22⋊D43)⋊C4—41no—
82#13063282—41no—
83C4⋊C4×D43—21no—
84C22⋊C4×D43—41no—
85C42×D43D411yescharacteristic
86#13063270—22no—
87#13063269—22no—
88#13063268—22no—
89C2×C43⋊C16C2311yescharacteristic
90C2×C43⋊C16C2311yescharacteristic
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95#13063250—21no—
96#13063249—21no—
97#13063248—21no—
98#13063247—21no—
99#13063246—21no—
100#13063245—21no—
101C4×C43⋊C8D411yescharacteristic
102C8×Dic43D411yescharacteristic
103C8×Dic43C2311yescharacteristic
104C2×Q16×C43C2311yescharacteristic
105C2×D8×C43C2311yescharacteristic
106C4×Q8×C43—21no—
107C4×D4×C43—21no—
108SD32×C43—22no—
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#103×C43—21no—
114#102×C43—21no—
115C4×C8×C43C2311yescharacteristic
116C23×D43—41no—
117C2×Q8×C43—21no—
118C2×D4×C43—21no—
119C22×C4×C43—41no—
120C2×C22⋊D43—41no—
121C22×Dic43—41no—
122D4×D43—24no—
123D4×D43—42no—
124C2×D172—21no—
125C2×C4×D43—41no—
126C2×C4×D43—41no—
127C2×C4×D43—41no—
128C2×C4×D43—84no—
129C2×C4×D43D811yescharacteristic
130C2×C4×D43D811yescharacteristic
131C2×C4×D43C2×D411yescharacteristic
132C2×Dic86—21no—
133C2×Dic86—41no—
134Q16×C43—21no—
135Q16×C43—21no—
136D8×C43—21no—
137D8×C43#4112yes—
138C2×C8×C43C2×D411yescharacteristic
139C2×C8×C43C2411yescharacteristic
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—41no—
143C22⋊C4×C43—41no—
144C42×C43—41no—
145C42×C43C2×D411yescharacteristic
146C22⋊Dic43—41no—
147#10621885—42no—
148#10621882—24no—
149(C2×D43)⋊C4—41no—
150(C2×D43)⋊C4—41no—
151(C2×D43)⋊C4—41no—
152(C2×D43)⋊C4—41no—
153C4⋊Dic43—21no—
154C4⋊Dic43—21no—
155C4⋊Dic43—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4—41no—
158Dic43⋊C4—41no—
159Dic43⋊C4—41no—
160Dic43⋊C4—41no—
161Dic43⋊C4—41no—
162C4×Dic43—41no—
163C4×Dic43D811yescharacteristic
164C4×Dic43D811yescharacteristic
165C4×Dic43C2×D411yescharacteristic
166C2×C43⋊C8C2×D411yescharacteristic
167C2×C43⋊C8C2×D411yescharacteristic
168Dic172—21no—
169Dic172—21no—
170D344—21no—
171D344#4112yes—
172C8×D43—21no—
173C8×D43—21no—
174C8×D43—41no—
175C16×C43—21no—
176C16×C43—21no—
177C43⋊C16—21no—
178C43⋊C16—21no—
179C23×C43—41no—
180C22×D43—44no—
181C22×D43—41no—
182C22×D43—82no—
183C22×D43—82no—
184C22×D43C2×D811yescharacteristic
185Q8×C43—41no—
186Q8×C43—41no—
187D4×C43—22no—
188D4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—82no—
193C2×C4×C43C2×D811yescharacteristic
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C22⋊D43—44no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—82no—
201C2×Dic43C2×D811yescharacteristic
202C2×Dic43C2×D811yescharacteristic
203C2×Dic43C2×D811yescharacteristic
204D172—22no—
205D172—41no—
206C4×D43—21no—
207C4×D43—21no—
208C4×D43—41no—
209C4×D43—82no—
210C4×D43—82no—
211C4×D43—82no—
212C4×D43SD3214yescomplemented
213Dic86—41no—
214Dic86—41no—
215Dic86—82no—
216C8×C43—21no—
217C8×C43C2×#4111yescharacteristic
218C8×C43C2×#4111yescharacteristic
219C43⋊C8—21no—
220C43⋊C8—21no—
221#33661—431nomaximal, Sylow
222C22×C43—42no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43C22×D811yescharacteristic
226C2×D43—21no—
227C2×D43—21no—
228C2×D43—42no—
229C2×D43—88no—
230C2×D43—81no—
231C2×D43—81no—
232C2×D43C2×SD3212yes—
233C4×C43—21no—
234C4×C43—81no—
235C4×C43—81no—
236C4×C43—81no—
237C4×C43C2×SD3212yes—
238C4×C43#52511yescharacteristic
239C4×C43#57511yescharacteristic
240Dic43—21no—
241Dic43—21no—
242Dic43—81no—
243Dic43—81no—
244Dic43—81no—
245Dic43C2×SD3212yes—
246#3170—431no—
247C2×C4×D8—431no—
248#2235—431no—
249#2235—431no—
250#2226—431no—
251#2226—431no—
252#2208—431no—
253#2208—431no—
254#2187—431no—
255#2187—431no—
256C4×SD32—431no—
257C4×SD32—431no—
258C4×SD32—431no—
259C4×SD32D4311yescharacteristic, complemented
260#2162—431no—
261C2×C43—82no—
262C2×C43#310011yescharacteristic
263C2×C43C22×SD3211yescharacteristic
264C2×C43#341411yescharacteristic
265D43—22no—
266D43—82no—
267C22×D8—431no—
268#533—861no—
269C2×C4×D4—861no—
270C2×SD32—431no—
271C2×SD32—431no—
272C2×SD32—431no—
273C2×SD32C2×D4311yescharacteristic
274#500—431no—
275#494—431no—
276#487—861no—
277#467—431no—
278#467—431no—
279#467—861no—
280C4×Q16—431no—
281C4×Q16—861no—
282C4×Q16C2×D4311yescharacteristic, complemented
283C4×D8—431no—
284C4×D8—431no—
285C4×D8—431no—
286C4×D8—861no—
287C4×D8—861no—
288C4×D8C2×D4311yescharacteristic
289C2×#107—431no—
290C2×#102—861no—
291C2×C4×C8—431no—
292#367—431no—
293#367—431no—
294#367—431no—
295#367C2×D4311yescharacteristic, complemented
296C4⋊C16—431no—
297C4⋊C16—431no—
298#358—431no—
299#358—431no—
300#358—431no—
301#358C2×D4311yescharacteristic, complemented
302#357—431no—
303#357—431no—
304#357—431no—
305#357C2×D4311yescharacteristic
306C22⋊C16—431no—
307C22⋊C16—431no—
308C4×C16—431no—
309C4×C16C2×D4311yescharacteristic, complemented
310C43#3366111yescharacteristic, complemented, Sylow
311C22×D4—861no—
312C23×C4—1721no—
313C2×Q16—431no—
314C2×Q16—861no—
315C2×Q16C22×D4311yescharacteristic
316C2×D8—431no—
317C2×D8—861no—
318C2×D8—862no—
319C2×D8—862no—
320C2×D8C22×D4311yescharacteristic
321C22×C8—431no—
322C22×C8—431no—
323C4⋊Q8—861no—
324C4⋊Q8—861no—
325#125—1721no—
326C22⋊Q8—861no—
327C22⋊Q8—861no—
328C22⋊Q8—1721no—
329C4×Q8—21no—
330C4×Q8—861no—
331C4×Q8—1721no—
332C4×D4—21no—
333C4×D4—861no—
334C4×D4—861no—
335C4×D4—861no—
336C4×D4—1721no—
337C4×D4—1721no—
338#117—1721no—
339C2×C4⋊C4—861no—
340C2×C22⋊C4—1721no—
341C2×C42—431no—
342SD32—22no—
343SD32—862no—
344SD32—862no—
345SD32—862no—
346C2×C16—431no—
347C2×C16—431no—
348C2×C16C22×D4311yescharacteristic
349C2×C16C22×D4311yescharacteristic
350#107—431no—
351#107—431no—
352#107—861no—
353#107—861no—
354#107C22×D4311yescharacteristic
355#107C22×D4311yescharacteristic
356#103—21no—
357#103—861no—
358#103—861no—
359#103—861no—
360#102—21no—
361#102—861no—
362#102—861no—
363#102—861no—
364C4×C8—431no—
365C4×C8—431no—
366C4×C8—431no—
367C4×C8C22×D4311yescharacteristic
368C24—1721no—
369C2×Q8—21no—
370C2×Q8—861no—
371C2×Q8—1721no—
372C2×D4—21no—
373C2×D4—864no—
374C2×D4—861no—
375C2×D4—1721no—
376C2×D4—1722no—
377C22×C4—41no—
378C22×C4—431no—
379C22×C4—431no—
380C22×C4—431no—
381C22×C4—3444no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4—1721no—
385C22×C4—1721no—
386Q16—21no—
387Q16—21no—
388Q16—861no—
389Q16—861no—
390Q16—1722no—
391D8—21no—
392D8—432no—
393D8—864no—
394D8—861no—
395D8#1062189812yes—
396C2×C8—431no—
397C2×C8—431no—
398C2×C8—861no—
399C2×C8—861no—
400C2×C8—1721no—
401C2×C8D4×D4311yescharacteristic
402C2×C8C23×D4311yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—861no—
407C4⋊C4—861no—
408C4⋊C4—1721no—
409C4⋊C4—1721no—
410C4⋊C4—1721no—
411C4⋊C4—1721no—
412C4⋊C4—1721no—
413C4⋊C4—1721no—
414C4⋊C4—1721no—
415C22⋊C4—41no—
416C22⋊C4—1721no—
417C22⋊C4—1721no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C42—41no—
422C42—431no—
423C42—431no—
424C42—431no—
425C42—1721no—
426C42D4×D4311yescharacteristic
427C16—21no—
428C16—21no—
429C16—861no—
430C16—861no—
431C23—41no—
432C23—431no—
433C23—3442no—
434C23—3442no—
435C23—1724no—
436C23—1721no—
437Q8—41no—
438Q8—41no—
439Q8—3442no—
440Q8—1721no—
441Q8—1721no—
442D4—22no—
443D4—41no—
444D4—862no—
445D4—1724no—
446D4—1721no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—82no—
451C2×C4—431no—
452C2×C4—434no—
453C2×C4—431no—
454C2×C4—431no—
455C2×C4—861no—
456C2×C4—861no—
457C2×C4—3442no—
458C2×C4—3442no—
459C2×C4—3442no—
460C2×C4—3442no—
461C2×C4—1721no—
462C2×C4—1721no—
463C2×C4—1721no—
464C2×C4—1721no—
465C2×C4D8×D4311yescharacteristic
466C2×C4D8×D4311yescharacteristic
467C2×C4C2×D4×D4311yescharacteristic
468C8—21no—
469C8—861no—
470C8—861no—
471C8#41×D4311yescharacteristic
472C8C2×#1062189811yescharacteristic
473C22—42no—
474C22—81no—
475C22—81no—
476C22—432no—
477C22—861no—
478C22—861no—
479C22—3448no—
480C22—3441no—
481C22—3441no—
482C22—1722no—
483C22C2×D8×D4311yescharacteristic
484C4—21no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—432no—
489C4—861no—
490C4—861no—
491C4—3441no—
492C4—3441no—
493C4—3441no—
494C4SD32×D4312yes—
495C4#1458340811yescharacteristic
496C4#1458369611yescharacteristic
497C2—82no—
498C2—862no—
499C2—3442no—
500C2#1914459311yescharacteristic
501C2C2×SD32×D4311yescharacteristic
502C2#1914772811yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC4×SD32×C43C2
socleC22×C43C22×D8
prime radicalC2×D8×D43C22
hypercenterC4×SD32D43
hypocenterC43#33661
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #19145178C2semidirect
3. #19136794C2semidirect
4. #19136791C2semidirect
5. #19136741C2semidirect
6. #19136740C2semidirect
7. #19136639C2semidirect
8. #19136638C2semidirect
11. C4×#13063270C2semidirect
12. C4×#13063268C2semidirect
13. C4×#13063269C2semidirect
14. #19136392C2semidirect
15. C4×SD32×C43C2semidirect
22. #14583303C22semidirect
23. #14583277C22semidirect
28. C4×Dic172C22semidirect
38. #14582727C22semidirect
39. #14582726C22semidirect
40. #14582726C22semidirect
41. Dic43⋊C16C22semidirect
42. Dic43⋊C16C22semidirect
43. #14582704C22semidirect
44. #14582703C22semidirect
45. #14582702C22semidirect
51. C4×C43⋊C16C22semidirect
53. C4×Q16×C43C22semidirect
55. C43×#367C22semidirect
56. C43×#358C22semidirect
58. C4×C16×C43C22semidirect
212. C4×D43SD32semidirect
259. C4×SD32D43semidirect
282. C4×Q16C2×D43semidirect
295. #367C2×D43semidirect
301. #358C2×D43semidirect
309. C4×C16C2×D43semidirect
310. C43#33661semidirect

Maximal subgroups

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

subgroupindex
#191451782
C4×D8×D432
#191367942
#191367912
#191367412
#191367402
#191366392
#191366382
#191365252
#191365222
C4×#130632702
C4×#130632682
C4×#130632692
#191363922
C4×SD32×C432
#3366143