Finite Group Databasebeta

← #25252145

Subgroups — #25252145

Order 11008.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145166C211yesmaximal, characteristic, complemented
2#19145160C211yesmaximal, characteristic, complemented
3#19136873C211yesmaximal, characteristic, complemented
4#19136855C211yesmaximal, characteristic, complemented
5#19136828C211yesmaximal, characteristic, complemented
6#19136825C211yesmaximal, characteristic, complemented
7#19136691C211yesmaximal, characteristic, complemented
8#19136684C211yesmaximal, characteristic, complemented
9#19136679C211yesmaximal, characteristic
10#19136451C211yesmaximal, characteristic, complemented
11SD32×Dic43C211yesmaximal, characteristic, complemented
12#19136446C211yesmaximal, characteristic, complemented
13#19136439C211yesmaximal, characteristic, complemented
14C2×C16×Dic43C211yesmaximal, characteristic, complemented
15C43×#2217C211yesmaximal, characteristic, complemented
16#14583435—21no—
17#14583430—21no—
18C2×#13063271C2211yescharacteristic
19C2×#13063270C2211yescharacteristic
20C2×#13063266C2211yescharacteristic
21C22×C43⋊C16C2211yescharacteristic
22#14583300C2211yescharacteristic
23#14583300C2211yescharacteristic
24#14583284C2211yescharacteristic
25#14583282C2211yescharacteristic
26#14583255—21no—
27#14583252—21no—
28#14583140C2211yescharacteristic
29#14583135C2211yescharacteristic
30#14583130—21no—
31#14583126—21no—
32Q16×Dic43C2211yescharacteristic
33#14582993C2211yescharacteristic
34#14582990—21no—
35#14582984—21no—
36D8×Dic43C2211yescharacteristic
37#14582981C2211yescharacteristic
38C2×C8×Dic43C2211yescharacteristic
39#14582727C2211yescharacteristic
40#14582724C2211yescharacteristic
41#14582724C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582703C2211yescharacteristic
44#14582702C2211yescharacteristic
45#14582701C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582699C2211yescharacteristic
48C16×Dic43C2211yescharacteristic
49C16×Dic43C2211yescharacteristic
50C16×Dic43C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×SD32×C43C2211yescharacteristic
53C22×C16×C43C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#367C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621883—21no—
61C2×#10621884—21no—
62C2×D344C2311yescharacteristic
63C22×C43⋊C8D411yescharacteristic
64#13063320—41no—
65#13063318—41no—
66#13063316—21no—
67#13063316—21no—
68#13063314—21no—
69#13063312—21no—
70#13063309—41no—
71#13063306—41no—
72#13063304—21no—
73#13063299—21no—
74Q8×Dic43—21no—
75#13063290—21no—
76D4×Dic43—21no—
77D4×Dic43—41no—
78#13063287—21no—
79(C22⋊D43)⋊C4—41no—
80#13063283—41no—
81#13063281—41no—
82C2×C4×Dic43D411yescharacteristic
83#13063271—22no—
84#13063270—22no—
85#13063266—22no—
86C2×C43⋊C16—22no—
87C2×C43⋊C16C2311yescharacteristic
88C2×C43⋊C16C2311yescharacteristic
89#13063259C2311yescharacteristic
90#13063259C2311yescharacteristic
91#13063256—21no—
92#13063256—21no—
93#13063250—21no—
94#13063249—21no—
95#13063248—21no—
96#13063247—21no—
97#13063246—21no—
98#13063245—21no—
99C8×Dic43D411yescharacteristic
100C8×Dic43D411yescharacteristic
101C8×Dic43C2311yescharacteristic
102C8×Dic43C2311yescharacteristic
103C2×Q16×C43C2311yescharacteristic
104C2×D8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22⋊Q8×C43—21no—
107#121×C43—21no—
108SD32×C43—22no—
109C2×C16×C43—22no—
110C2×C16×C43C2311yescharacteristic
111C2×C16×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#107×C43C2311yescharacteristic
114#103×C43—21no—
115#102×C43—21no—
116C2×Q8×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—41no—
119C22×C4×C43C2×D411yescharacteristic
120C2×C22⋊D43—41no—
121C22×Dic43—41no—
122C22×Dic43D811yescharacteristic
123C22×Dic43D811yescharacteristic
124C2×D172—21no—
125C2×C4×D43—41no—
126C2×Dic86—21no—
127Q16×C43—21no—
128Q16×C43—21no—
129D8×C43—21no—
130D8×C43—21no—
131C2×C8×C43—21no—
132C2×C8×C43—21no—
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2411yescharacteristic
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—41no—
138C22⋊C4×C43—41no—
139C22⋊C4×C43—41no—
140C22⋊Dic43—41no—
141C22⋊Dic43—41no—
142C22⋊Dic43—41no—
143C22⋊Dic43—41no—
144#10621884—42no—
145#10621883—42no—
146(C2×D43)⋊C4—41no—
147(C2×D43)⋊C4—41no—
148(C2×D43)⋊C4—41no—
149(C2×D43)⋊C4—41no—
150C4⋊Dic43—21no—
151C4⋊Dic43—21no—
152C4⋊Dic43—41no—
153C4⋊Dic43—41no—
154C4⋊Dic43—41no—
155Dic43⋊C4—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4—41no—
158Dic43⋊C4—41no—
159C4×Dic43—41no—
160C4×Dic43—41no—
161C4×Dic43D811yescharacteristic
162C4×Dic43D811yescharacteristic
163C4×Dic43C2×D411yescharacteristic
164C4×Dic43C2×D411yescharacteristic
165C2×C43⋊C8—22no—
166C2×C43⋊C8C2×D411yescharacteristic
167C2×C43⋊C8C2×D411yescharacteristic
168Dic172—21no—
169Dic172—21no—
170D344—21no—
171D344—21no—
172C16×C43—21no—
173C16×C43#4112yes—
174C43⋊C16—21no—
175C43⋊C16#4112yes—
176C23×C43—41no—
177C23×C43C2×D811yescharacteristic
178C22×D43—41no—
179Q8×C43—41no—
180Q8×C43—41no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—82no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43C2×D811yescharacteristic
190C2×C4×C43C22×D411yescharacteristic
191C22⋊D43—82no—
192C2×Dic43—22no—
193C2×Dic43—22no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—82no—
198C2×Dic43C2×D811yescharacteristic
199C2×Dic43C2×D811yescharacteristic
200C2×Dic43C2×D811yescharacteristic
201C2×Dic43C2×D811yescharacteristic
202D172—41no—
203D172—41no—
204C4×D43—82no—
205Dic86—41no—
206Dic86—41no—
207C8×C43—21no—
208C8×C43C2×#4111yescharacteristic
209C8×C43C2×#4111yescharacteristic
210C43⋊C8—21no—
211C43⋊C8#13512yes—
212#33735—431nomaximal, Sylow
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—81no—
216C22×C43—81no—
217C22×C43—81no—
218C22×C43#50812yes—
219C22×C43C22×D811yescharacteristic
220C2×D43—81no—
221C2×D43—81no—
222C2×D43—81no—
223C4×C43—21no—
224C4×C43—81no—
225C4×C43—81no—
226C4×C43—81no—
227C4×C43#53211yescharacteristic
228C4×C43C2×#13511yescharacteristic
229Dic43—21no—
230Dic43—21no—
231Dic43—21no—
232Dic43—81no—
233Dic43—81no—
234Dic43—81no—
235Dic43#50812yes—
236#3168—431no—
237#3168—431no—
238#2253—431no—
239#2249—431no—
240#2242—431no—
241#2242—431no—
242#2217—431no—
243#2217D4311yescharacteristic, complemented
244#2216—431no—
245#2215—431no—
246C4×Q32—431no—
247C4×SD32—431no—
248C4×SD32—431no—
249C4×D16—431no—
250C2×C4×C16—431no—
251C2×C43—22no—
252C2×C43—161no—
253C2×C43#316911yescharacteristic
254C2×C43C2×#50811yescharacteristic
255C2×C43C2×#50811yescharacteristic
256D43—161no—
257#529—861no—
258#529—861no—
259C2×Q32—431no—
260C2×SD32—431no—
261C2×SD32C2×D4311yescharacteristic
262C2×D16—431no—
263C22×C16—431no—
264C22×C16C2×D4311yescharacteristic
265#499—431no—
266#499—431no—
267#495—431no—
268#495—431no—
269#488—861no—
270#488—861no—
271#467—431no—
272#467C2×D4311yescharacteristic
273#466—431no—
274#466C2×D4311yescharacteristic
275#465—861no—
276#465—861no—
277C4×Q16—431no—
278C4×Q16—431no—
279C4×SD16—861no—
280C4×SD16—861no—
281C4×D8—431no—
282C4×D8—431no—
283C2×C4×C8—431no—
284#367—431no—
285#367C2×D4311yescharacteristic
286#366—431no—
287#366—431no—
288#358—431no—
289#358—431no—
290#358—431no—
291#358C2×D4311yescharacteristic
292#357—431no—
293#357—431no—
294#357—431no—
295#357C2×D4311yescharacteristic
296C4×C16—431no—
297C4×C16—431no—
298C4×C16—431no—
299C4×C16—431no—
300C43#3373511yescharacteristic, complemented, Sylow
301C2×Q16—431no—
302C2×Q16C22×D4311yescharacteristic
303C2×SD16—861no—
304C2×SD16—861no—
305C2×D8—431no—
306C2×D8C22×D4311yescharacteristic
307C22×C8—431no—
308C22×C8C22×D4311yescharacteristic
309#126—1721no—
310#126—1721no—
311#125—861no—
312#125—861no—
313#124—861no—
314#124—861no—
315#123—1721no—
316#123—1721no—
317C22⋊Q8—21no—
318C22⋊Q8—861no—
319#121—21no—
320#121—861no—
321C4×Q8—861no—
322C4×Q8—861no—
323C4×D4—861no—
324C4×D4—861no—
325C4×D4—1721no—
326C4×D4—1721no—
327#117—1721no—
328#117—1721no—
329C2×C42—431no—
330Q32—862no—
331SD32—22no—
332SD32—862no—
333D16—862no—
334C2×C16—22no—
335C2×C16—431no—
336C2×C16—431no—
337C2×C16—862no—
338C2×C16C22×D4311yescharacteristic
339C2×C16C22×D4311yescharacteristic
340#107—431no—
341#107—431no—
342#107C22×D4311yescharacteristic
343#107C22×D4311yescharacteristic
344#106—861no—
345#106—861no—
346#103—21no—
347#103—861no—
348#103—861no—
349#103—861no—
350#102—21no—
351#102—861no—
352#102—861no—
353#102—861no—
354C4×C8—431no—
355C4×C8—431no—
356C4×C8—431no—
357C4×C8—431no—
358C2×Q8—21no—
359C2×Q8—861no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—861no—
363C2×D4—1721no—
364C22×C4—431no—
365C22×C4—431no—
366C22×C4—1721no—
367C22×C4—1721no—
368C22×C4D4×D4311yescharacteristic
369Q16—21no—
370Q16—21no—
371Q16—861no—
372Q16—861no—
373SD16—1722no—
374SD16—1722no—
375D8—21no—
376D8—21no—
377D8—861no—
378D8—861no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—431no—
382C2×C8—431no—
383C2×C8—862no—
384C2×C8D4×D4311yescharacteristic
385C2×C8C23×D4311yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—861no—
390C4⋊C4—861no—
391C4⋊C4—1721no—
392C4⋊C4—1721no—
393C4⋊C4—1721no—
394C4⋊C4—1721no—
395C4⋊C4—1721no—
396C4⋊C4—1721no—
397C4⋊C4—1721no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—1721no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C22⋊C4—1721no—
404C22⋊C4—1721no—
405C22⋊C4—1721no—
406C22⋊C4—1721no—
407C22⋊C4—1721no—
408C42—431no—
409C42—431no—
410C42—431no—
411C42—431no—
412C42—1721no—
413C42—1721no—
414C16—21no—
415C16—432no—
416C16—861no—
417C16#1062190012yes—
418C23—41no—
419C23—1721no—
420C23D8×D4311yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—1721no—
424Q8—1721no—
425D4—41no—
426D4—41no—
427D4—82no—
428D4—3442no—
429D4—1721no—
430D4—1721no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—431no—
437C2×C4—431no—
438C2×C4—431no—
439C2×C4—431no—
440C2×C4—862no—
441C2×C4—862no—
442C2×C4—3442no—
443C2×C4—3442no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4D8×D4311yescharacteristic
448C2×C4C2×D4×D4311yescharacteristic
449C8—21no—
450C8—432no—
451C8—861no—
452C8#41×D4311yescharacteristic
453C8C2×#1062190011yescharacteristic
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—3441no—
460C22—3441no—
461C22—3441no—
462C22#1458333012yes—
463C22C2×D8×D4311yescharacteristic
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—432no—
469C4—861no—
470C4—861no—
471C4—861no—
472C4—3441no—
473C4—3441no—
474C4—3441no—
475C4#1458344411yescharacteristic
476C4#135×D4311yescharacteristic
477C2—22no—
478C2—161no—
479C2—6881no—
480C2#1914516911yescharacteristic
481C2#508×D4311yescharacteristic
482C2C2×#1458333011yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2217C2
socleC22×C43C22×D8
prime radical#19136679C2
hypercenter#2217D43
hypocenterC43#33735
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #19145166C2semidirect
2. #19145160C2semidirect
3. #19136873C2semidirect
4. #19136855C2semidirect
5. #19136828C2semidirect
6. #19136825C2semidirect
7. #19136691C2semidirect
8. #19136684C2semidirect
10. #19136451C2semidirect
11. SD32×Dic43C2semidirect
12. #19136446C2semidirect
13. #19136439C2semidirect
14. C2×C16×Dic43C2semidirect
15. C43×#2217C2semidirect
243. #2217D43semidirect
300. C43#33735semidirect

Maximal subgroups

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

subgroupindex
#191451662
#191451602
#191368732
#191368552
#191368282
#191368252
#191366912
#191366842
#191366792
#191364512
SD32×Dic432
#191364462
#191364392
C2×C16×Dic432
C43×#22172
#3373543