Finite Group Databasebeta

← #25251665

Subgroups — #25251665

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145169C211yesmaximal, characteristic, complemented
2#135×Dic43C211yesmaximal, characteristic, complemented
3#19136787C211yesmaximal, characteristic, complemented
4#19136783C211yesmaximal, characteristic, complemented
5#19136735C211yesmaximal, characteristic, complemented
6#19136730C211yesmaximal, characteristic, complemented
7#19136633C211yesmaximal, characteristic, complemented
8#19136628C211yesmaximal, characteristic, complemented
9#19136518C211yesmaximal, characteristic, complemented
10#19136471C211yesmaximal, characteristic, complemented
11#19136468C211yesmaximal, characteristic, complemented
12#19136462C211yesmaximal, characteristic, complemented
13#19136460C211yesmaximal, characteristic, complemented
14#19136395C211yesmaximal, characteristic, complemented
15C43×#2186C211yesmaximal, characteristic, complemented
16#14583444—21no—
17#41×Dic43—21no—
18C2×#13063268C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20#14583303C2211yescharacteristic
21#14583274C2211yescharacteristic
22#14583244—21no—
23#14583135C2211yescharacteristic
24#14583133—21no—
25Q16×Dic43C2211yescharacteristic
26Q16×Dic43C2211yescharacteristic
27SD16×Dic43—21no—
28SD16×Dic43—21no—
29D8×Dic43C2211yescharacteristic
30D8×Dic43C2211yescharacteristic
31D8×Dic43C2211yescharacteristic
32#14582981C2211yescharacteristic
33#14582979—21no—
34#14582937C2211yescharacteristic
35#14582895—21no—
36C2×C8×Dic43C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582726C2211yescharacteristic
39#14582725C2211yescharacteristic
40#14582724C2211yescharacteristic
41Dic43⋊C16C2211yescharacteristic
42Dic43⋊C16C2211yescharacteristic
43#14582703C2211yescharacteristic
44#14582701C2211yescharacteristic
45#14582701C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50#14582674C2211yescharacteristic
51#14582674C2211yescharacteristic
52C2×#135×C43C2211yescharacteristic
53C2×SD32×C43C2211yescharacteristic
54C2×D16×C43C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic
59C2×#10621900—41no—
60C2×D344C2311yescharacteristic
61C2×#10621882—21no—
62C22×C43⋊C8D411yescharacteristic
63#13063324—21no—
64#13063321—21no—
65#13063311—41no—
66#13063299—21no—
67#13063297—41no—
68Q8×Dic43—21no—
69Q8×Dic43—21no—
70D4×Dic43—21no—
71D4×Dic43—21no—
72D4×Dic43—21no—
73D4×Dic43—41no—
74D4×Dic43—41no—
75#13063287—21no—
76(C22⋊D43)⋊C4—41no—
77#13063284—21no—
78#13063284—41no—
79C2×C4×Dic43—41no—
80C2×C4×Dic43D411yescharacteristic
81#13063268—22no—
82#13063266—22no—
83C2×C43⋊C16C2311yescharacteristic
84C2×C43⋊C16C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063258—21no—
89#13063257—21no—
90#13063249—21no—
91#13063249—21no—
92#13063247—21no—
93#13063246—21no—
94#13063246—21no—
95#13063246—21no—
96#13063245—21no—
97C8×Dic43D411yescharacteristic
98C8×Dic43D411yescharacteristic
99C8×Dic43C2311yescharacteristic
100C8×Dic43C2311yescharacteristic
101C2×#41×C43—21no—
102#135×C43—22no—
103#135×C43—22no—
104C2×Q16×C43C2311yescharacteristic
105C2×SD16×C43—21no—
106C2×D8×C43C2311yescharacteristic
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109#121×C43—21no—
110SD32×C43—22no—
111D16×C43—22no—
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114#107×C43C2311yescharacteristic
115#102×C43—21no—
116#41×C43—24no—
117#41×C43—42no—
118C2×Q8×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—41no—
122C2×D4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C22×Dic43—41no—
129C22×Dic43—41no—
130C22×Dic43—41no—
131C22×Dic43D811yescharacteristic
132C22×Dic43D811yescharacteristic
133#10621900—84no—
134C2×D172—21no—
135C2×C4×D43—41no—
136C2×Dic86—41no—
137Q16×C43—21no—
138Q16×C43#4112yescomplemented
139SD16×C43—24no—
140D8×C43—21no—
141D8×C43—21no—
142D8×C43—21no—
143D8×C43#4112yescomplemented
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43C2×D411yescharacteristic
147C2×C8×C43C2411yescharacteristic
148C4⋊C4×C43—21no—
149C22⋊C4×C43—41no—
150C22⋊Dic43—41no—
151C22⋊Dic43—41no—
152C22⋊Dic43—41no—
153C22⋊Dic43—41no—
154#10621882—42no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43—41no—
161C4⋊Dic43—41no—
162Dic43⋊C4—41no—
163C4×Dic43—41no—
164C4×Dic43—41no—
165C4×Dic43—41no—
166C4×Dic43D811yescharacteristic
167C4×Dic43D811yescharacteristic
168C4×Dic43C2×D411yescharacteristic
169C4×Dic43C2×D411yescharacteristic
170C2×C43⋊C8—41no—
171C2×C43⋊C8C2×D411yescharacteristic
172C2×C43⋊C8C2×D411yescharacteristic
173D344—21no—
174D344—21no—
175C16×C43—21no—
176C16×C43—21no—
177C43⋊C16—21no—
178C43⋊C16—21no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43C2×D811yescharacteristic
182C22×D43—41no—
183Q8×C43—22no—
184Q8×C43—41no—
185D4×C43—22no—
186D4×C43—44no—
187D4×C43—41no—
188D4×C43—41no—
189D4×C43—41no—
190D4×C43—82no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—44no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C22⋊D43—82no—
199C22⋊D43—82no—
200C22⋊D43—82no—
201C2×Dic43—22no—
202C2×Dic43—41no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—82no—
207C2×Dic43—82no—
208C2×Dic43—82no—
209C2×Dic43C2×D811yescharacteristic
210C2×Dic43C2×D811yescharacteristic
211C2×Dic43C2×D811yescharacteristic
212C2×Dic43C2×D811yescharacteristic
213D172—41no—
214D172—41no—
215C4×D43—82no—
216Dic86—82no—
217C8×C43—21no—
218C8×C43C2×#4111yescharacteristic
219C8×C43C2×#4111yescharacteristic
220C43⋊C8—21no—
221C43⋊C8—21no—
222#33675—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—42no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43—81no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43C22×D811yescharacteristic
233C2×D43—81no—
234C2×D43—81no—
235C2×D43—81no—
236C4×C43—21no—
237C4×C43—42no—
238C4×C43—81no—
239C4×C43#52511yescharacteristic
240C4×C43#57511yescharacteristic
241Dic43—21no—
242Dic43—21no—
243Dic43—21no—
244Dic43—81no—
245Dic43—81no—
246Dic43—81no—
247Dic43#50912yes—
248#3169—431no—
249C4×#135—431no—
250#2234—431no—
251#2234—431no—
252#2225—431no—
253#2224—431no—
254#2207—431no—
255#2206—431no—
256#2186—431no—
257#2186D4311yescharacteristic, complemented
258#2177—431no—
259#2177—431no—
260#2175—431no—
261#2175—431no—
262#2163—431no—
263C2×C43—41no—
264C2×C43—82no—
265C2×C43—161no—
266C2×C43#310011yescharacteristic
267C2×C43C2×#50911yescharacteristic
268C2×C43#341411yescharacteristic
269D43—161no—
270C2×#135C2×D4311yescharacteristic
271#532—861no—
272C4×#41—861no—
273C2×SD32—431no—
274C2×SD32C2×D4311yescharacteristic
275C2×D16—431no—
276C2×D16C2×D4311yescharacteristic
277#500—431no—
278#493—431no—
279#486—861no—
280#466—431no—
281#466—861no—
282#466C2×D4311yescharacteristic
283C4×Q16—431no—
284C4×Q16—431no—
285C4×SD16—861no—
286C4×SD16—861no—
287C4×D8—431no—
288C4×D8—431no—
289C4×D8—431no—
290C4×D8—431no—
291C4×D8—861no—
292#427—431no—
293#416—861no—
294C2×C4×C8—431no—
295#367—431no—
296#367—431no—
297#366—431no—
298#366—431no—
299C4⋊C16—431no—
300C4⋊C16—431no—
301#358—431no—
302#358C2×D4311yescharacteristic
303#357—431no—
304#357—431no—
305#357—431no—
306#357—431no—
307#357—431no—
308#357C2×D4311yescharacteristic
309C22⋊C16—431no—
310C22⋊C16C2×D4311yescharacteristic
311#346—431no—
312#346—431no—
313C43#3367511yescharacteristic, complemented, Sylow
314C2×#41—21no—
315C2×#41—1721no—
316#135—22no—
317#135—22no—
318C2×Q16C22×D4311yescharacteristic
319C2×SD16—21no—
320C2×D8—431no—
321C2×D8—861no—
322C2×D8C22×D4311yescharacteristic
323C2×D8C22×D4311yescharacteristic
324C22×C8—431no—
325C22×C8C22×D4311yescharacteristic
326C4⋊Q8—861no—
327#127—861no—
328#124—1721no—
329#121—21no—
330#121—861no—
331#121—1721no—
332C4×Q8—861no—
333C4×Q8—861no—
334C4×D4—861no—
335C4×D4—861no—
336C4×D4—861no—
337C4×D4—861no—
338C4×D4—1721no—
339C4×D4—1721no—
340C4×D4—1721no—
341#117—861no—
342#117—1721no—
343C2×C42—431no—
344C2×C42—1721no—
345SD32—22no—
346SD32—862no—
347D16—22no—
348D16—862no—
349C2×C16—431no—
350C2×C16—431no—
351C2×C16C22×D4311yescharacteristic
352C2×C16C22×D4311yescharacteristic
353#107—431no—
354#107—431no—
355#107—431no—
356#107—861no—
357#107C22×D4311yescharacteristic
358#106—861no—
359#103—861no—
360#103—861no—
361#102—21no—
362#102—861no—
363#102—861no—
364#102—861no—
365#102—861no—
366#102—861no—
367C4×C8—431no—
368C4×C8—431no—
369C4×C8—431no—
370C4×C8—431no—
371#41—24no—
372#41—42no—
373#41—3444no—
374C2×Q8—21no—
375C2×Q8—1721no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—861no—
381C2×D4—1721no—
382C2×D4—1721no—
383C2×D4—1721no—
384C22×C4—41no—
385C22×C4—431no—
386C22×C4—431no—
387C22×C4—1721no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4D4×D4311yescharacteristic
392Q16—21no—
393Q16#1062190012yescomplemented
394SD16—24no—
395D8—21no—
396D8—21no—
397D8—21no—
398D8—861no—
399D8—861no—
400D8—1722no—
401D8#1062190012yescomplemented
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—431no—
405C2×C8—431no—
406C2×C8—1721no—
407C2×C8D4×D4311yescharacteristic
408C2×C8C23×D4311yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—861no—
411C4⋊C4—861no—
412C4⋊C4—861no—
413C4⋊C4—1721no—
414C4⋊C4—1721no—
415C4⋊C4—1721no—
416C22⋊C4—41no—
417C22⋊C4—1721no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C22⋊C4—1721no—
422C22⋊C4—1721no—
423C42—431no—
424C42—431no—
425C42—431no—
426C42—431no—
427C42—1721no—
428C42—1721no—
429C42—1721no—
430C16—21no—
431C16—21no—
432C16—861no—
433C16—861no—
434C23—41no—
435C23—41no—
436C23—1721no—
437C23D8×D4311yescharacteristic
438Q8—22no—
439Q8—41no—
440Q8—3442no—
441D4—22no—
442D4—44no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—82no—
447D4—3442no—
448D4—3442no—
449D4—3442no—
450D4—1721no—
451D4—1721no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—44no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—431no—
458C2×C4—431no—
459C2×C4—431no—
460C2×C4—431no—
461C2×C4—862no—
462C2×C4—3442no—
463C2×C4—3442no—
464C2×C4—3442no—
465C2×C4—3442no—
466C2×C4—1721no—
467C2×C4—1721no—
468C2×C4—1721no—
469C2×C4—1721no—
470C2×C4D8×D4311yescharacteristic
471C2×C4C2×D4×D4311yescharacteristic
472C8—21no—
473C8—861no—
474C8—861no—
475C8C2×#1062190011yescharacteristic
476C8C2×#1062190011yescharacteristic
477C22—21no—
478C22—21no—
479C22—21no—
480C22—42no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—3441no—
487C22—3441no—
488C22—3441no—
489C22C2×D8×D4311yescharacteristic
490C4—21no—
491C4—42no—
492C4—81no—
493C4—432no—
494C4—861no—
495C4—861no—
496C4—861no—
497C4—3441no—
498C4—3441no—
499C4—3441no—
500C4#1458340511yescharacteristic
501C4#1458369511yescharacteristic
502C2—41no—
503C2—82no—
504C2—161no—
505C2—6881no—
506C2#1914459011yescharacteristic
507C2#509×D4311yescharacteristic
508C2#1914772811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2186C2
socleC22×C43C22×D8
hypercenter#2186D43
hypocenterC43#33675
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2186

Complements

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

NH ≅ G/Ntype
1. #19145169C2semidirect
2. #135×Dic43C2semidirect
3. #19136787C2semidirect
4. #19136783C2semidirect
5. #19136735C2semidirect
6. #19136730C2semidirect
7. #19136633C2semidirect
8. #19136628C2semidirect
9. #19136518C2semidirect
10. #19136471C2semidirect
11. #19136468C2semidirect
12. #19136462C2semidirect
13. #19136460C2semidirect
14. #19136395C2semidirect
15. C43×#2186C2semidirect
138. Q16×C43#41semidirect
143. D8×C43#41semidirect
257. #2186D43semidirect
313. C43#33675semidirect
393. Q16#10621900semidirect
401. D8#10621900semidirect

Maximal subgroups

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

subgroupindex
#191451692
#135×Dic432
#191367872
#191367832
#191367352
#191367302
#191366332
#191366282
#191365182
#191364712
#191364682
#191364622
#191364602
#191363952
C43×#21862
#3367543