Finite Group Databasebeta

← #25253488

Subgroups — #25253488

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#19146338C211yesmaximal, characteristic
2#19136829C211yesmaximal, characteristic, complemented
3#19136803C211yesmaximal, characteristic, complemented
4#19136775C211yesmaximal, characteristic, complemented
5#19136756C211yesmaximal, characteristic, complemented
6#19136693C211yesmaximal, characteristic, complemented
7#19136684C211yesmaximal, characteristic, complemented
8#19136657C211yesmaximal, characteristic, complemented
9#19136533C211yesmaximal, characteristic, complemented
10#19136528C211yesmaximal, characteristic, complemented
11C4×#13063271C211yesmaximal, characteristic, complemented
12D4×C43⋊C16C211yesmaximal, characteristic, complemented
13#19136300C211yesmaximal, characteristic, complemented
14C2×#14582702C211yesmaximal, characteristic, complemented
15C43×#3336C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18#14583558—21no—
19C2×#13063271C2211yescharacteristic
20C2×#13063271C2211yescharacteristic
21C2×#13063268C2211yescharacteristic
22C22×C43⋊C16C2211yescharacteristic
23C22×C43⋊C16C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583140C2211yescharacteristic
26#14583135C2211yescharacteristic
27#14583122—21no—
28#14583063—21no—
29#14583040—21no—
30C4×Dic172C2211yescharacteristic
31#14582726C2211yescharacteristic
32#14582724C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35#14582703C2211yescharacteristic
36#14582702C2211yescharacteristic
37#14582702C2211yescharacteristic
38#14582702C2211yescharacteristic
39#14582702C2211yescharacteristic
40#14582702C2211yescharacteristic
41#14582702C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44#14582699C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C43×#552—21no—
49C43×#499C2211yescharacteristic
50C43×#485—21no—
51C43×#483—21no—
52C43×#479—21no—
53C43×#467C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C4×Q16×C43C2211yescharacteristic
56C8×D4×C43C2211yescharacteristic
57C43×#427C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic
59C2×#10621898—21no—
60C22×Dic86—21no—
61#13063347—22no—
62#13063347—41no—
63C2×Dic172—22no—
64C2×Dic172—21no—
65C2×Dic172—41no—
66C2×Dic172C2311yescharacteristic
67C2×Dic172C2311yescharacteristic
68C2×#10621873—21no—
69C2×#10621873—21no—
70C2×D344C2311yescharacteristic
71#13063313—21no—
72#13063311—41no—
73#13063304—21no—
74#13063303—41no—
75#13063299—21no—
76#13063297—41no—
77C4×Dic86—21no—
78(C22⋊D43)⋊C4—41no—
79#13063271—22no—
80#13063271—41no—
81#13063268—41no—
82C2×C43⋊C16—41no—
83C2×C43⋊C16—41no—
84C2×C43⋊C16C2311yescharacteristic
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063250—21no—
90#13063250—21no—
91#13063247—21no—
92C2×Q16×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95#126×C43—41no—
96#125×C43—21no—
97#125×C43—41no—
98#123×C43—41no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—21no—
101C4×Q8×C43—21no—
102C4×D4×C43D411yescharacteristic
103#117×C43—21no—
104#117×C43—41no—
105C2×C4⋊C4×C43—21no—
106#107×C43—21no—
107#107×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#106×C43—21no—
111#106×C43—21no—
112C4⋊C8×C43D411yescharacteristic
113#103×C43—21no—
114#103×C43—21no—
115#103×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C2×Q8×C43—21no—
120C2×D4×C43D811yescharacteristic
121C22×C4×C43—41no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C2×C22⋊D43—41no—
125C2×C22⋊D43—41no—
126C22×Dic43—41no—
127#10621898—42no—
128#10621898—81no—
129C2×D172—21no—
130C2×C4×D43—41no—
131C2×Dic86—21no—
132C2×Dic86—21no—
133C2×Dic86—42no—
134C2×Dic86—41no—
135C2×Dic86—81no—
136Q16×C43—21no—
137Q16×C43—21no—
138C2×C8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43C2×D411yescharacteristic
143C2×C8×C43C2×D411yescharacteristic
144C2×C8×C43C2×D411yescharacteristic
145C2×C8×C43C2411yescharacteristic
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—41no—
150C4⋊C4×C43—41no—
151C4⋊C4×C43—41no—
152C4⋊C4×C43—41no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43—41no—
155C4⋊C4×C43D811yescharacteristic
156C22⋊C4×C43—41no—
157C22⋊C4×C43—41no—
158C22⋊C4×C43—41no—
159C22⋊C4×C43D811yescharacteristic
160C22⋊C4×C43D811yescharacteristic
161C42×C43—41no—
162C42×C43—41no—
163C42×C43C2×D411yescharacteristic
164C22⋊Dic43—41no—
165(C2×D43)⋊C4—41no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—41no—
168C4⋊Dic43—21no—
169Dic43⋊C4—41no—
170Dic43⋊C4—41no—
171C4×Dic43—41no—
172Dic172—21no—
173Dic172—21no—
174Dic172—21no—
175Dic172—42no—
176Dic172#4112yes—
177D344—21no—
178D344—21no—
179#10621873—42no—
180#10621873—81no—
181C43⋊C16—21no—
182C43⋊C16—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C23×C43C2×D811yescharacteristic
186C23×C43C2×D811yescharacteristic
187C22×D43—41no—
188Q8×C43—41no—
189Q8×C43—41no—
190D4×C43—22no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—82no—
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C2×D811yescharacteristic
203C2×C4×C43C2×D811yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C22⋊D43—82no—
206C22⋊D43—82no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—82no—
211D172—41no—
212D172—41no—
213C4×D43—82no—
214Dic86—22no—
215Dic86—41no—
216Dic86—41no—
217Dic86—41no—
218Dic86—82no—
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#50812yes—
231C22×C43C22×D811yescharacteristic
232C2×D43—81no—
233C2×D43—81no—
234C2×D43—81no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—81no—
240C4×C43—81no—
241C4×C43—81no—
242C4×C43—81no—
243C4×C43#54611yescharacteristic
244C4×C43#57711yescharacteristic
245Dic43—42no—
246Dic43—81no—
247Dic43—81no—
248#3336D4311yescharacteristic, complemented
249#3285—431no—
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#329411yescharacteristic
266C2×C43C2×#50811yescharacteristic
267C2×C43#341711yescharacteristic
268D43—161no—
269C2×#135—431no—
270C22×Q16—431no—
271#552—21no—
272#548—861no—
273C2×Q32—431no—
274C2×Q32—431no—
275C2×SD32—431no—
276C22×C16—431no—
277C22×C16—431no—
278#499C2×D4311yescharacteristic
279#495—431no—
280#485—21no—
281#483—21no—
282#479—21no—
283#467—431no—
284#467C2×D4311yescharacteristic
285#467C2×D4311yescharacteristic
286#466—431no—
287#464—861no—
288#452—861no—
289#448—861no—
290C4×Q16—431no—
291C4×Q16C2×D4311yescharacteristic
292C8×D4C2×D4311yescharacteristic
293#427C2×D4311yescharacteristic
294C2×#107C2×D4311yescharacteristic
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—861no—
314C22×Q8—861no—
315#135—862no—
316#135—1721no—
317C2×Q16—431no—
318C2×Q16—431no—
319C2×Q16—862no—
320C2×Q16—861no—
321C2×Q16—1721no—
322C2×Q16C22×D4311yescharacteristic
323C2×SD16—861no—
324C2×SD16—861no—
325C2×D8—431no—
326C22×C8C22×D4311yescharacteristic
327C22×C8C22×D4311yescharacteristic
328#126—41no—
329#125—21no—
330#125—41no—
331#124—861no—
332#124—1721no—
333#123—41no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—861no—
337C22⋊Q8—1721no—
338#121—861no—
339#121—1721no—
340C4×Q8—21no—
341C4×Q8—861no—
342C4×D4—1721no—
343C4×D4C22⋊D4311yescharacteristic
344#117—21no—
345#117—41no—
346C2×C4⋊C4—21no—
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—21no—
357#107—431no—
358#107C22×D4311yescharacteristic
359#107C22×D4311yescharacteristic
360#107C22×D4311yescharacteristic
361#106—21no—
362#106—21no—
363C4⋊C8C22⋊D4311yescharacteristic
364#103—21no—
365#103—21no—
366#103—21no—
367#103—861no—
368#103—861no—
369#102—861no—
370C22⋊C8C22⋊D4311yescharacteristic
371C22⋊C8C22⋊D4311yescharacteristic
372C4×C8C22×D4311yescharacteristic
373#41—3441no—
374#41—1722no—
375C2×Q8—21no—
376C2×Q8—861no—
377C2×Q8—861no—
378C2×Q8—3441no—
379C2×Q8—1722no—
380C2×Q8—1721no—
381C2×D4—861no—
382C2×D4—1721no—
383C2×D4—1721no—
384C2×D4#1062188211yescharacteristic
385C22×C4—41no—
386C22×C4—1721no—
387C22×C4—1721no—
388C22×C4C2×C22⋊D4311yescharacteristic
389C22×C4C2×C22⋊D4311yescharacteristic
390Q16—21no—
391Q16—21no—
392Q16—432no—
393Q16—861no—
394Q16—861no—
395Q16—861no—
396Q16—1722no—
397SD16—3441no—
398SD16—1722no—
399D8—861no—
400D8—861no—
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—21no—
411C4⋊C4—21no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—861no—
419C4⋊C4—1721no—
420C4⋊C4—1721no—
421C4⋊C4#1062188211yescharacteristic
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—1721no—
426C22⋊C4—1721no—
427C22⋊C4—1721no—
428C22⋊C4—1721no—
429C22⋊C4#1062188211yescharacteristic
430C22⋊C4#1062188211yescharacteristic
431C42—41no—
432C42—41no—
433C42—1721no—
434C42C2×C22⋊D4311yescharacteristic
435C16—861no—
436C16—861no—
437C16—861no—
438C16—861no—
439C23—1721no—
440C23C2×#1062188211yescharacteristic
441C23C2×#1062188211yescharacteristic
442Q8—41no—
443Q8—41no—
444Q8—862no—
445Q8—3442no—
446Q8—1721no—
447Q8—1721no—
448Q8—1721no—
449D4—22no—
450D4—3442no—
451D4—3442no—
452D4—1721no—
453D4—1721no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—82no—
463C2×C4—3442no—
464C2×C4—3442no—
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—
476C8#41×D4311yescharacteristic
477C8#1306337111yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—3441no—
484C22—3441no—
485C22—3441no—
486C22#1458332912yes—
487C22C22×#1062188211yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—3441no—
497C4—3441no—
498C4—1722no—
499C4#1458353711yescharacteristic
500C4#1458370711yescharacteristic
501C2—22no—
502C2—41no—
503C2—6881no—
504C2#1914640211yescharacteristic
505C2C2×#1458332911yescharacteristic
506C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3336C2
socleC22×C43C22×D8
prime radical#19146338C2
hypercenter#3336D43
hypocenterC43#33867
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3336

Complements

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

NH ≅ G/Ntype
2. #19136829C2semidirect
3. #19136803C2semidirect
4. #19136775C2semidirect
5. #19136756C2semidirect
6. #19136693C2semidirect
7. #19136684C2semidirect
8. #19136657C2semidirect
9. #19136533C2semidirect
10. #19136528C2semidirect
11. C4×#13063271C2semidirect
12. D4×C43⋊C16C2semidirect
13. #19136300C2semidirect
14. C2×#14582702C2semidirect
15. C43×#3336C2semidirect
248. #3336D43semidirect
312. C43#33867semidirect

Maximal subgroups

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

subgroupindex
#191463382
#191368292
#191368032
#191367752
#191367562
#191366932
#191366842
#191366572
#191365332
#191365282
C4×#130632712
D4×C43⋊C162
#191363002
C2×#145827022
C43×#33362
#3386743