Finite Group Databasebeta

← #25253494

Subgroups — #25253494

Order 11008.

546 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146964C211yesmaximal, characteristic, complemented
2#19136826C211yesmaximal, characteristic, complemented
3#19136800C211yesmaximal, characteristic, complemented
4#19136773C211yesmaximal, characteristic, complemented
5#19136759C211yesmaximal, characteristic, complemented
6#19136689C211yesmaximal, characteristic, complemented
7#19136684C211yesmaximal, characteristic, complemented
8#19136654C211yesmaximal, characteristic, complemented
9#19136535C211yesmaximal, characteristic, complemented
10#19136529C211yesmaximal, characteristic, complemented
11C4×#13063271C211yesmaximal, characteristic, complemented
12D4×C43⋊C16C211yesmaximal, characteristic, complemented
13#19136302C211yesmaximal, characteristic, complemented
14C2×#14582703C211yesmaximal, characteristic, complemented
15C43×#3285C211yesmaximal, characteristic
16#14583589—21no—
17C2×#13063271C2211yescharacteristic
18C2×#13063271C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20C22×C43⋊C16C2211yescharacteristic
21C22×C43⋊C16C2211yescharacteristic
22#14583301C2211yescharacteristic
23#14583241—21no—
24#14583230—21no—
25#14583207—21no—
26#14583140C2211yescharacteristic
27#14583140C2211yescharacteristic
28C4×Dic172C2211yescharacteristic
29#14582937C2211yescharacteristic
30C2×#13063259C2211yescharacteristic
31#14582726C2211yescharacteristic
32#14582724C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35#14582703C2211yescharacteristic
36#14582703C2211yescharacteristic
37#14582703C2211yescharacteristic
38#14582703C2211yescharacteristic
39#14582703C2211yescharacteristic
40#14582703C2211yescharacteristic
41#14582702C2211yescharacteristic
42#14582700C2211yescharacteristic
43#14582700C2211yescharacteristic
44#14582700C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C2×#135×C43C2211yescharacteristic
49C22×Q16×C43C2211yescharacteristic
50C43×#548—21no—
51C43×#495C2211yescharacteristic
52C43×#467C2211yescharacteristic
53C43×#466C2211yescharacteristic
54C43×#464—21no—
55C43×#452—21no—
56C43×#448—21no—
57C4×Q16×C43C2211yescharacteristic
58C8×D4×C43C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60#13063318—41no—
61#13063317—21no—
62#13063315—41no—
63#13063306—41no—
64#13063304—21no—
65#13063304—21no—
66C4×Dic86—21no—
67#13063284—21no—
68#13063281—41no—
69C2×C4⋊Dic43—21no—
70#13063271—22no—
71#13063271—41no—
72#13063269—41no—
73C2×C43⋊C16—41no—
74C2×C43⋊C16—41no—
75C2×C43⋊C16C2311yescharacteristic
76C2×C43⋊C16C2311yescharacteristic
77C2×C43⋊C16C2311yescharacteristic
78C2×C43⋊C16C2311yescharacteristic
79#13063259—21no—
80#13063259C2311yescharacteristic
81#13063259C2311yescharacteristic
82#13063259C2311yescharacteristic
83#13063257—21no—
84#13063257—21no—
85#13063250—21no—
86#13063250—21no—
87#13063250—21no—
88C2×#41×C43—21no—
89C22×Q8×C43—21no—
90#135×C43—22no—
91#135×C43—41no—
92C2×Q16×C43—22no—
93C2×Q16×C43—21no—
94C2×Q16×C43—41no—
95C2×Q16×C43C2311yescharacteristic
96C2×Q16×C43C2311yescharacteristic
97C2×SD16×C43—21no—
98C2×SD16×C43—21no—
99C2×D8×C43C2311yescharacteristic
100C22×C8×C43C2311yescharacteristic
101C22×C8×C43C2311yescharacteristic
102#124×C43—21no—
103#124×C43—41no—
104C22⋊Q8×C43—21no—
105C22⋊Q8×C43—41no—
106#121×C43—21no—
107#121×C43—41no—
108C4×Q8×C43—21no—
109C4×D4×C43—41no—
110C4×D4×C43D411yescharacteristic
111#107×C43C2311yescharacteristic
112C4⋊C8×C43D411yescharacteristic
113#103×C43—21no—
114#103×C43—21no—
115#102×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119#41×C43—42no—
120#41×C43—81no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—42no—
124C2×Q8×C43—41no—
125C2×Q8×C43—81no—
126C2×D4×C43—21no—
127C2×D4×C43—41no—
128C2×D4×C43—41no—
129C2×D4×C43D811yescharacteristic
130C22×C4×C43—41no—
131C22×C4×C43—41no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×Dic43—41no—
135C2×Dic86—21no—
136Q16×C43—21no—
137Q16×C43—21no—
138Q16×C43—21no—
139Q16×C43—42no—
140Q16×C43#4112yes—
141SD16×C43—42no—
142SD16×C43—81no—
143D8×C43—21no—
144D8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43C2×D411yescharacteristic
150C2×C8×C43C2×D411yescharacteristic
151C2×C8×C43C2×D411yescharacteristic
152C2×C8×C43C2411yescharacteristic
153C4⋊C4×C43—21no—
154C4⋊C4×C43—41no—
155C4⋊C4×C43—41no—
156C4⋊C4×C43D811yescharacteristic
157C22⋊C4×C43—41no—
158C22⋊C4×C43—41no—
159C22⋊C4×C43—41no—
160C22⋊C4×C43—41no—
161C22⋊C4×C43D811yescharacteristic
162C22⋊C4×C43D811yescharacteristic
163C42×C43—41no—
164C42×C43C2×D411yescharacteristic
165C22⋊Dic43—41no—
166C22⋊Dic43—41no—
167C22⋊Dic43—41no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—41no—
172Dic43⋊C4—41no—
173Dic43⋊C4—41no—
174Dic43⋊C4—41no—
175Dic43⋊C4—41no—
176Dic43⋊C4—41no—
177C4×Dic43—41no—
178C4×Dic43—41no—
179Dic172—21no—
180Dic172—21no—
181C43⋊C16—21no—
182C43⋊C16—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C23×C43—41no—
186C23×C43C2×D811yescharacteristic
187C23×C43C2×D811yescharacteristic
188Q8×C43—22no—
189Q8×C43—41no—
190Q8×C43—41no—
191Q8×C43—41no—
192Q8×C43—82no—
193D4×C43—22no—
194D4×C43—41no—
195D4×C43—41no—
196D4×C43—82no—
197D4×C43—82no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—82no—
206C2×C4×C43—82no—
207C2×C4×C43C2×D811yescharacteristic
208C2×C4×C43C2×D811yescharacteristic
209C2×C4×C43C2×D811yescharacteristic
210C2×C4×C43C2×D811yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—41no—
216C2×Dic43—82no—
217Dic86—41no—
218Dic86—41no—
219C8×C43—21no—
220C8×C43—21no—
221C8×C43—21no—
222C8×C43C2×#4111yescharacteristic
223C8×C43H(5,𝔽2)11yescharacteristic
224#33867—431nomaximal, Sylow
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43#50812yes—
234C22×C43C22×D811yescharacteristic
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—42no—
240C4×C43—81no—
241C4×C43—81no—
242C4×C43#54611yescharacteristic
243C4×C43#57711yescharacteristic
244Dic43—81no—
245Dic43—81no—
246Dic43—81no—
247Dic43—81no—
248#3336—431no—
249#3285D4311yescharacteristic
250#2242—431no—
251#2237—431no—
252#2232—431no—
253#2229—431no—
254#2217—431no—
255#2216—431no—
256#2211—431no—
257#2189—431no—
258#2188—431no—
259C4×Q32—431no—
260D4×C16—431no—
261#2138—431no—
262C2×#358—431no—
263C2×C43—22no—
264C2×C43—41no—
265C2×C43—161no—
266C2×C43#329411yescharacteristic
267C2×C43C2×#50811yescharacteristic
268C2×C43#341711yescharacteristic
269C2×#135C2×D4311yescharacteristic
270C22×Q16C2×D4311yescharacteristic
271#552—861no—
272#548—21no—
273C2×Q32—431no—
274C2×Q32—431no—
275C2×SD32—431no—
276C22×C16—431no—
277C22×C16—431no—
278#499—431no—
279#495C2×D4311yescharacteristic
280#485—861no—
281#483—861no—
282#479—861no—
283#467—431no—
284#467—431no—
285#467C2×D4311yescharacteristic
286#466C2×D4311yescharacteristic
287#464—21no—
288#452—21no—
289#448—21no—
290C4×Q16—431no—
291C4×Q16C2×D4311yescharacteristic
292C8×D4C2×D4311yescharacteristic
293#427—431no—
294C2×#107—431no—
295#367—431no—
296#366—431no—
297#366—431no—
298C4⋊C16—431no—
299#358—431no—
300#358—431no—
301#358—431no—
302#358—431no—
303#358—431no—
304#358—431no—
305#358—431no—
306#357—431no—
307#357—431no—
308#357—431no—
309C22⋊C16—431no—
310C22⋊C16—431no—
311C4×C16—431no—
312C43#3386711yescharacteristic, complemented, Sylow
313C2×#41—21no—
314C22×Q8—21no—
315#135—22no—
316#135—41no—
317C2×Q16—22no—
318C2×Q16—21no—
319C2×Q16—41no—
320C2×Q16—431no—
321C2×Q16C22×D4311yescharacteristic
322C2×Q16C22×D4311yescharacteristic
323C2×SD16—21no—
324C2×SD16—21no—
325C2×D8C22×D4311yescharacteristic
326C22×C8C22×D4311yescharacteristic
327C22×C8C22×D4311yescharacteristic
328#126—1721no—
329#125—861no—
330#125—1721no—
331#124—21no—
332#124—41no—
333#123—1721no—
334C22⋊Q8—21no—
335C22⋊Q8—41no—
336C22⋊Q8—861no—
337C22⋊Q8—861no—
338#121—21no—
339#121—41no—
340C4×Q8—21no—
341C4×Q8—861no—
342C4×D4—41no—
343C4×D4C22⋊D4311yescharacteristic
344#117—861no—
345#117—1721no—
346C2×C4⋊C4—861no—
347Q32—862no—
348Q32—1721no—
349SD32—1721no—
350C2×C16—431no—
351C2×C16—431no—
352C2×C16—431no—
353C2×C16—431no—
354C2×C16—1721no—
355C2×C16—1721no—
356#107—431no—
357#107—431no—
358#107—431no—
359#107—861no—
360#107C22×D4311yescharacteristic
361#106—861no—
362#106—861no—
363C4⋊C8C22⋊D4311yescharacteristic
364#103—21no—
365#103—21no—
366#103—861no—
367#103—861no—
368#103—861no—
369#102—21no—
370C22⋊C8C22⋊D4311yescharacteristic
371C22⋊C8C22⋊D4311yescharacteristic
372C4×C8C22×D4311yescharacteristic
373#41—42no—
374#41—81no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—42no—
378C2×Q8—41no—
379C2×Q8—81no—
380C2×Q8—861no—
381C2×D4—21no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4#1062188211yescharacteristic
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—1721no—
388C22×C4C2×C22⋊D4311yescharacteristic
389C22×C4C2×C22⋊D4311yescharacteristic
390Q16—21no—
391Q16—21no—
392Q16—21no—
393Q16—42no—
394Q16—861no—
395Q16—861no—
396Q16#1062190012yes—
397SD16—42no—
398SD16—81no—
399D8—21no—
400D8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8C2×C22⋊D4311yescharacteristic
406C2×C8C2×C22⋊D4311yescharacteristic
407C2×C8C2×C22⋊D4311yescharacteristic
408C2×C8C23×D4311yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—861no—
413C4⋊C4—861no—
414C4⋊C4—861no—
415C4⋊C4—1721no—
416C4⋊C4—1721no—
417C4⋊C4—1721no—
418C4⋊C4—1721no—
419C4⋊C4—1721no—
420C4⋊C4—1721no—
421C4⋊C4#1062188211yescharacteristic
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—1721no—
427C22⋊C4—1721no—
428C22⋊C4—1721no—
429C22⋊C4#1062188211yescharacteristic
430C22⋊C4#1062188211yescharacteristic
431C42—41no—
432C42—1721no—
433C42—1721no—
434C42C2×C22⋊D4311yescharacteristic
435C16—861no—
436C16—861no—
437C16—861no—
438C16—861no—
439C23—41no—
440C23C2×#1062188211yescharacteristic
441C23C2×#1062188211yescharacteristic
442Q8—22no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446Q8—82no—
447Q8—1721no—
448Q8—1721no—
449D4—22no—
450D4—41no—
451D4—41no—
452D4—82no—
453D4—82no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4—3442no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4—1721no—
467C2×C4—1721no—
468C2×C4C2×#1062188211yescharacteristic
469C2×C4C2×#1062188211yescharacteristic
470C2×C4C2×#1062188211yescharacteristic
471C2×C4C2×#1062188211yescharacteristic
472C2×C4C22×C22⋊D4311yescharacteristic
473C8—21no—
474C8—21no—
475C8—21no—
476C8C2×#1062190011yescharacteristic
477C8#1306337011yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22#1458332912yes—
487C22C22×#1062188211yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—81no—
494C4—81no—
495C4—3441no—
496C4—3441no—
497C4—3441no—
498C4—3441no—
499C4#1458354311yescharacteristic
500C4#1458371011yescharacteristic
501C2—22no—
502C2—41no—
503C2—161no—
504C2#1914640811yescharacteristic
505C2C2×#1458332911yescharacteristic
506C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
Fitting, prime radicalC43×#3285C2
socleC22×C43C22×D8
hypercenter#3285D43
hypocenterC43#33867
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3285

Complements

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

NH ≅ G/Ntype
1. #19146964C2semidirect
2. #19136826C2semidirect
3. #19136800C2semidirect
4. #19136773C2semidirect
5. #19136759C2semidirect
6. #19136689C2semidirect
7. #19136684C2semidirect
8. #19136654C2semidirect
9. #19136535C2semidirect
10. #19136529C2semidirect
11. C4×#13063271C2semidirect
12. D4×C43⋊C16C2semidirect
13. #19136302C2semidirect
14. C2×#14582703C2semidirect
312. C43#33867semidirect

Maximal subgroups

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

subgroupindex
#191469642
#191368262
#191368002
#191367732
#191367592
#191366892
#191366842
#191366542
#191365352
#191365292
C4×#130632712
D4×C43⋊C162
#191363022
C2×#145827032
C43×#32852
#3386743