Finite Group Databasebeta

← #25251767

Subgroups — #25251767

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#19145247C211yesmaximal, characteristic, complemented
2#19143447C211yesmaximal, characteristic
3#19136804C211yesmaximal, characteristic, complemented
4#19136800C211yesmaximal, characteristic, complemented
5#19136754C211yesmaximal, characteristic, complemented
6#19136750C211yesmaximal, characteristic, complemented
7#19136638C211yesmaximal, characteristic, complemented
8#19136638C211yesmaximal, characteristic, complemented
9#19136524C211yesmaximal, characteristic
10#19136460C211yesmaximal, characteristic, complemented
11#19136456C211yesmaximal, characteristic, complemented
12#19136450C211yesmaximal, characteristic, complemented
13SD32×Dic43C211yesmaximal, characteristic, complemented
14#19136399C211yesmaximal, characteristic, complemented
15C43×#2187C211yesmaximal, characteristic
16#14583509—21no—
17#14583374—21no—
18C2×#13063269C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20#14583300C2211yescharacteristic, complemented
21#14583277C2211yescharacteristic, complemented
22#14583266—21no—
23#14583155—21no—
24#14583140C2211yescharacteristic
25#14583011—21no—
26#14583011—21no—
27#14583003—21no—
28Q16×Dic43C2211yescharacteristic, complemented
29#14582993C2211yescharacteristic, complemented
30D8×Dic43C2211yescharacteristic
31D8×Dic43C2211yescharacteristic
32D8×Dic43C2211yescharacteristic
33D8×Dic43C2211yescharacteristic
34#14582937C2211yescharacteristic
35#14582904—21no—
36#14582854C2211yescharacteristic
37#14582727C2211yescharacteristic, complemented
38#14582726C2211yescharacteristic, complemented
39#14582725C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42Dic43⋊C16C2211yescharacteristic, complemented
43#14582704C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582703C2211yescharacteristic, complemented
46#14582703C2211yescharacteristic, complemented
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50#14582674C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C22×D8×C43C2211yescharacteristic
53C2×SD32×C43C2211yescharacteristic
54C2×SD32×C43C2211yescharacteristic
55C43×#467C2211yescharacteristic
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621885—21no—
61C2×#10621877D411yescharacteristic
62#13063323—21no—
63#13063318—41no—
64#13063318—41no—
65#13063316—21no—
66#13063316—41no—
67#13063315—41no—
68#13063304—21no—
69Q8×Dic43—21no—
70#13063290—21no—
71D4×Dic43—21no—
72D4×Dic43—21no—
73D4×Dic43—21no—
74D4×Dic43—21no—
75D4×Dic43—41no—
76D4×Dic43—41no—
77#13063284—21no—
78#13063284D411yescharacteristic
79C2×C22⋊Dic43—41no—
80C2×C22⋊Dic43—41no—
81#13063269—22no—
82#13063269—22no—
83C2×C43⋊C16C2311yescharacteristic
84C2×C43⋊C16C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063257—21no—
89#13063256—21no—
90#13063250—21no—
91#13063249—21no—
92#13063248—21no—
93#13063246—21no—
94#13063246—21no—
95#13063246—21no—
96#13063246—21no—
97#13063235D411yescharacteristic
98#13063235D411yescharacteristic
99C8×Dic43C2311yescharacteristic
100C8×Dic43C2311yescharacteristic
101C22×D4×C43—21no—
102C2×Q16×C43C2311yescharacteristic
103C2×D8×C43—22no—
104C2×D8×C43—22no—
105C2×D8×C43—21no—
106C2×D8×C43C2311yescharacteristic
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22⋊Q8×C43—21no—
110SD32×C43—22no—
111SD32×C43—22no—
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114#107×C43C2311yescharacteristic
115#103×C43—21no—
116C24×C43—41no—
117C2×Q8×C43—21no—
118C2×D4×C43—24no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—42no—
122C2×D4×C43—41no—
123C22×C4×C43C2×D411yescharacteristic
124C22×Dic43—41no—
125C22×Dic43—41no—
126C22×Dic43—41no—
127C22×Dic43—41no—
128C2×Dic86—21no—
129Q16×C43—21no—
130Q16×C43—21no—
131D8×C43—24no—
132D8×C43—21no—
133D8×C43—21no—
134D8×C43#4112yes—
135D8×C43#4112yes—
136C2×C8×C43—21no—
137C2×C8×C43—21no—
138C2×C8×C43C2×D411yescharacteristic
139C2×C8×C43C2411yescharacteristic
140C4⋊C4×C43—21no—
141C4⋊C4×C43—41no—
142C22⋊C4×C43—41no—
143C22⋊Dic43—41no—
144C22⋊Dic43—41no—
145C22⋊Dic43—41no—
146C22⋊Dic43—41no—
147C22⋊Dic43—41no—
148C22⋊Dic43—41no—
149C22⋊Dic43D811yescharacteristic
150C22⋊Dic43D811yescharacteristic
151#10621885—42no—
152C4⋊Dic43—21no—
153C4⋊Dic43—21no—
154C4⋊Dic43—21no—
155C4⋊Dic43—41no—
156C4⋊Dic43—41no—
157C4⋊Dic43D811yescharacteristic
158C4⋊Dic43D811yescharacteristic
159Dic43⋊C4—41no—
160Dic43⋊C4—41no—
161Dic43⋊C4—41no—
162Dic43⋊C4—41no—
163Dic43⋊C4—41no—
164C4×Dic43—41no—
165C4×Dic43—41no—
166C4×Dic43—41no—
167C4×Dic43C2×D411yescharacteristic
168C4×Dic43C2×D411yescharacteristic
169#10621877—41no—
170C2×C43⋊C8C2×D411yescharacteristic
171C2×C43⋊C8C2×D411yescharacteristic
172Dic172—21no—
173Dic172—21no—
174C16×C43—21no—
175C16×C43—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—44no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—161no—
182C23×C43—161no—
183C23×C43C2×D811yescharacteristic
184Q8×C43—41no—
185Q8×C43—41no—
186D4×C43—22no—
187D4×C43—22no—
188D4×C43—44no—
189D4×C43—41no—
190D4×C43—41no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43C2×D811yescharacteristic
196C2×C4×C43C22×D411yescharacteristic
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—161no—
202C2×Dic43—161no—
203C2×Dic43—161no—
204C2×Dic43—161no—
205C2×Dic43C2×D811yescharacteristic
206C2×Dic43C2×D811yescharacteristic
207C2×Dic43C2×D811yescharacteristic
208C2×Dic43C2×D811yescharacteristic
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—21no—
218C22×C43—21no—
219C22×C43—21no—
220C22×C43—42no—
221C22×C43—42no—
222C22×C43—81no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43—164no—
227C22×C43C22×D811yescharacteristic
228C4×C43—21no—
229C4×C43—81no—
230C4×C43—81no—
231C4×C43#52511yescharacteristic
232C4×C43#57511yescharacteristic
233Dic43—21no—
234Dic43—21no—
235Dic43—21no—
236Dic43—21no—
237Dic43—81no—
238Dic43—81no—
239Dic43—81no—
240Dic43—81no—
241#3177—431no—
242#2948—431no—
243#2237—431no—
244#2237—431no—
245#2228—431no—
246#2228—431no—
247#2208—431no—
248#2208—431no—
249#2187—431no—
250#2187D4311yescharacteristic
251#2175—431no—
252#2175—431no—
253C4×SD32—431no—
254C4×SD32—431no—
255#2164—431no—
256C2×C43—41no—
257C2×C43—82no—
258C2×C43—82no—
259C2×C43#310011yescharacteristic
260C2×C43#341611yescharacteristic
261C2×C43#341611yescharacteristic
262C22×D8C2×D4311yescharacteristic
263#541—861no—
264#518—861no—
265C2×SD32—431no—
266C2×SD32—431no—
267C2×SD32C2×D4311yescharacteristic
268C2×SD32C2×D4311yescharacteristic
269#499—431no—
270#494—431no—
271#491—861no—
272#470—861no—
273#467—431no—
274#467C2×D4311yescharacteristic
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×D8—431no—
284#427—431no—
285#418—861no—
286#405—431no—
287#367—431no—
288#367—431no—
289#366—431no—
290#366—431no—
291C4⋊C16—431no—
292C4⋊C16—431no—
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⋊C16C2×D4311yescharacteristic
303#346—431no—
304C4×C16—431no—
305C43#3368311yescharacteristic, complemented, Sylow
306C22×D4—21no—
307C2×Q16—431no—
308C2×Q16—861no—
309C2×Q16C22×D4311yescharacteristic
310C2×D8—22no—
311C2×D8—22no—
312C2×D8—21no—
313C2×D8C22×D4311yescharacteristic
314C2×D8C22×D4311yescharacteristic
315C2×M16—431no—
316C22×C8C22×D4311yescharacteristic
317C4⋊Q8—861no—
318#126—1721no—
319#126—1721no—
320#125—861no—
321#125—1721no—
322#125—1721no—
323C22⋊Q8—21no—
324C22⋊Q8—861no—
325C4×Q8—861no—
326C4×Q8—861no—
327C4×D4—861no—
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—22no—
338SD32—22no—
339SD32—862no—
340SD32—862no—
341C2×C16—431no—
342C2×C16—431no—
343C2×C16C22×D4311yescharacteristic
344C2×C16C22×D4311yescharacteristic
345#107—431no—
346#107—431no—
347#107—431no—
348#107C22×D4311yescharacteristic
349#106—861no—
350#106—861no—
351#103—21no—
352#103—861no—
353#103—861no—
354#103—861no—
355#102—861no—
356#102—861no—
357#102—861no—
358#102—861no—
359#97—431no—
360#97—431no—
361C4×C8—431no—
362C4×C8—431no—
363C24—41no—
364C2×Q8—21no—
365C2×Q8—861no—
366C2×D4—24no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—42no—
370C2×D4—41no—
371C22×C4—1721no—
372C22×C4—1721no—
373C22×C4—1721no—
374C22×C4—1721no—
375C22×C4D4×D4311yescharacteristic
376Q16—21no—
377Q16—21no—
378Q16—861no—
379Q16—861no—
380Q16—1722no—
381D8—24no—
382D8—21no—
383D8—21no—
384D8#1062190012yes—
385D8#1062190012yes—
386M16—1721no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—431no—
390C2×C8—431no—
391C2×C8D4×D4311yescharacteristic
392C2×C8C23×D4311yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—431no—
396C4⋊C4—431no—
397C4⋊C4—861no—
398C4⋊C4—861no—
399C4⋊C4—861no—
400C4⋊C4—1721no—
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—431no—
418C42—1721no—
419C42—1721no—
420C42—1721no—
421C16—21no—
422C16—21no—
423C16—861no—
424C16—861no—
425C23—44no—
426C23—41no—
427C23—41no—
428C23—161no—
429C23—161no—
430C23D8×D4311yescharacteristic
431Q8—41no—
432Q8—41no—
433Q8—1721no—
434Q8—1721no—
435D4—22no—
436D4—22no—
437D4—44no—
438D4—41no—
439D4—41no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—431no—
445C2×C4—431no—
446C2×C4—431no—
447C2×C4—431no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4—1721no—
452C2×C4—6881no—
453C2×C4—6881no—
454C2×C4—6881no—
455C2×C4—6881no—
456C2×C4D8×D4311yescharacteristic
457C2×C4C2×D4×D4311yescharacteristic
458C8—21no—
459C8—861no—
460C8—861no—
461C8C2×#1062190011yescharacteristic
462C8C2×#1062190011yescharacteristic
463C22—21no—
464C22—21no—
465C22—21no—
466C22—42no—
467C22—42no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—164no—
473C22C2×D8×D4311yescharacteristic
474C4—21no—
475C4—81no—
476C4—81no—
477C4—861no—
478C4—861no—
479C4—861no—
480C4—861no—
481C4—3441no—
482C4—3441no—
483C4—3441no—
484C4—3441no—
485C4#1458340511yescharacteristic
486C4#1458369511yescharacteristic
487C2—41no—
488C2—82no—
489C2—82no—
490C2#1914459011yescharacteristic
491C2#1914773711yescharacteristic
492C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2187C2
socleC22×C43C22×D8
prime radicalC22×D8×C43C22
hypercenter#2187D43
hypocenterC43#33683
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #19145247C2semidirect
3. #19136804C2semidirect
4. #19136800C2semidirect
5. #19136754C2semidirect
6. #19136750C2semidirect
7. #19136638C2semidirect
8. #19136638C2semidirect
10. #19136460C2semidirect
11. #19136456C2semidirect
12. #19136450C2semidirect
13. SD32×Dic43C2semidirect
14. #19136399C2semidirect
20. #14583300C22semidirect
21. #14583277C22semidirect
28. Q16×Dic43C22semidirect
29. #14582993C22semidirect
37. #14582727C22semidirect
38. #14582726C22semidirect
39. #14582725C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. Dic43⋊C16C22semidirect
43. #14582704C22semidirect
44. #14582704C22semidirect
45. #14582703C22semidirect
46. #14582703C22semidirect
50. #14582674C22semidirect
51. C16×Dic43C22semidirect
305. C43#33683semidirect

Maximal subgroups

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

subgroupindex
#191452472
#191434472
#191368042
#191368002
#191367542
#191367502
#191366382
#191365242
#191364602
#191364562
#191364502
SD32×Dic432
#191363992
C43×#21872
#3368343