Finite Group Databasebeta

← #25254228

Subgroups — #25254228

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147014C211yesmaximal, characteristic
2#19146984C211yesmaximal, characteristic, complemented
3#19136869C211yesmaximal, characteristic, complemented
4#19136801C211yesmaximal, characteristic, complemented
5#19136800C211yesmaximal, characteristic, complemented
6#19136774C211yesmaximal, characteristic, complemented
7#19136773C211yesmaximal, characteristic, complemented
8#19136745C211yesmaximal, characteristic, complemented
9#19136740C211yesmaximal, characteristic, complemented
10#19136705C211yesmaximal, characteristic, complemented
11SD32×Dic43C211yesmaximal, characteristic, complemented
12#19136425C211yesmaximal, characteristic, complemented
13#19136383C211yesmaximal, characteristic, complemented
14#19136380C211yesmaximal, characteristic, complemented
15C43×#2220C211yesmaximal, characteristic, complemented
16#14583613—21no—
17#14583607—21no—
18C2×#13063264C2211yescharacteristic
19#14583303C2211yescharacteristic
20#14583303C2211yescharacteristic
21#14583233—21no—
22#14583232—21no—
23#14583222—21no—
24#14583220—21no—
25#14583192—21no—
26#14583187—21no—
27#14583137C2211yescharacteristic
28#14583132C2211yescharacteristic
29Q16×Dic43C2211yescharacteristic
30D8×Dic43C2211yescharacteristic
31C8×C22⋊D43C2211yescharacteristic
32#14582937C2211yescharacteristic
33#14582936C2211yescharacteristic
34C2×#13063259C2211yescharacteristic
35#107×D43C2211yescharacteristic
36#14582727C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582726C2211yescharacteristic
39#14582725C2211yescharacteristic
40#14582725C2211yescharacteristic
41#14582724C2211yescharacteristic
42#14582724C2211yescharacteristic
43#14582724C2211yescharacteristic
44Dic43⋊C16C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582703C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×SD32×C43C2211yescharacteristic
53C2×M32×C43C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#366C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×C8×D43C2311yescharacteristic
60#13063324—21no—
61#13063324—21no—
62#13063315—41no—
63#13063312—41no—
64#13063311—41no—
65#13063305—41no—
66#13063302—41no—
67#13063301—21no—
68#13063297—41no—
69#13063296—21no—
70Q8×Dic43—21no—
71D4×Dic43—21no—
72C4×C22⋊D43D411yescharacteristic
73(C22⋊D43)⋊C4—41no—
74#13063284—21no—
75#13063283—21no—
76#13063281—41no—
77C2×C4⋊Dic43—21no—
78C4⋊C4×D43—21no—
79#13063264—22no—
80C2×C43⋊C16C2311yescharacteristic
81C2×C43⋊C16C2311yescharacteristic
82#13063259—21no—
83#13063259C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063257—21no—
91#13063256—21no—
92Dic43⋊C8D411yescharacteristic
93#13063249—21no—
94#13063249—21no—
95#13063246—21no—
96#13063246—21no—
97C22⋊(C43⋊C8)D411yescharacteristic
98(C2×D43)⋊C8D411yescharacteristic
99C8×Dic43C2311yescharacteristic
100C2×Q16×C43C2311yescharacteristic
101C2×D8×C43C2311yescharacteristic
102C22×C8×C43C2311yescharacteristic
103C22⋊Q8×C43—21no—
104#121×C43—21no—
105SD32×C43—22no—
106M32×C43—22no—
107C2×C16×C43C2311yescharacteristic
108C2×C16×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#103×C43—21no—
112#102×C43—21no—
113C2×Q8×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—41no—
116C22×C4×C43C2×D411yescharacteristic
117C2×C22⋊D43—41no—
118C2×C22⋊D43D811yescharacteristic
119C22×Dic43—41no—
120C22×Dic43—41no—
121C2×C4×D43—41no—
122C2×C4×D43C2×D411yescharacteristic
123C2×Dic86—41no—
124C2×Dic86—41no—
125Q16×C43—21no—
126Q16×C43—21no—
127D8×C43—21no—
128D8×C43—21no—
129C2×C8×C43—21no—
130C2×C8×C43—21no—
131C2×C8×C43C2×D411yescharacteristic
132C2×C8×C43C2411yescharacteristic
133C4⋊C4×C43—21no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—41no—
136C22⋊C4×C43—41no—
137C22⋊C4×C43—41no—
138C22⋊Dic43—41no—
139C22⋊Dic43—41no—
140C22⋊Dic43—41no—
141C22⋊Dic43D811yescharacteristic
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4D811yescharacteristic
145C4⋊Dic43—21no—
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—41no—
150C4⋊Dic43—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4D811yescharacteristic
156C4×Dic43—41no—
157C4×Dic43—41no—
158C4×Dic43—41no—
159C4×Dic43C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162C8×D43—21no—
163C8×D43—21no—
164C16×C43—21no—
165C16×C43#4112yes—
166C43⋊C16—21no—
167C43⋊C16—21no—
168C23×C43—41no—
169C23×C43C2×D811yescharacteristic
170C22×D43C2×D811yescharacteristic
171Q8×C43—41no—
172Q8×C43—41no—
173D4×C43—41no—
174D4×C43—41no—
175D4×C43—161no—
176C2×C4×C43—21no—
177C2×C4×C43—21no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C22⋊D43—22no—
184C22⋊D43—161no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—82no—
190C2×Dic43—161no—
191C2×Dic43C2×D811yescharacteristic
192C2×Dic43C2×D811yescharacteristic
193C2×Dic43C2×D811yescharacteristic
194C4×D43—21no—
195C4×D43—21no—
196C4×D43—161no—
197Dic86—161no—
198Dic86—161no—
199C8×C43—21no—
200C8×C43C2×#4111yescharacteristic
201C8×C432−1+411yescharacteristic
202C43⋊C8—21no—
203C43⋊C8—21no—
204#33924—431nomaximal, Sylow
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—81no—
209C22×C43—81no—
210C22×C43—81no—
211C22×C43C22×D811yescharacteristic
212C2×D43—21no—
213C2×D43—21no—
214C2×D43—21no—
215C4×C43—21no—
216C4×C43—81no—
217C4×C43—81no—
218C4×C43—81no—
219C4×C43#54711yescharacteristic
220C4×C43#57811yescharacteristic
221Dic43—21no—
222Dic43—21no—
223Dic43—81no—
224Dic43—81no—
225Dic43—81no—
226Dic43—81no—
227Dic43#51012yes—
228#3341—431no—
229#3338—431no—
230#2252—431no—
231#2237—431no—
232#2237—431no—
233#2232—431no—
234#2232—431no—
235#2227—431no—
236#2226—431no—
237#2220—431no—
238#2220D4311yescharacteristic, complemented
239C4×SD32—431no—
240#2169—431no—
241#2159—431no—
242#2159—431no—
243C2×C43—41no—
244C2×C43—161no—
245C2×C43#333411yescharacteristic
246C2×C43C2×#51011yescharacteristic
247C2×C43#341511yescharacteristic
248D43—41no—
249#555—861no—
250#554—861no—
251C2×SD32C2×D4311yescharacteristic
252C2×M32—431no—
253C2×M32C2×D4311yescharacteristic
254#500—431no—
255#500—431no—
256#484—861no—
257#484—861no—
258#482—861no—
259#482—861no—
260#477—861no—
261#476—861no—
262#467—431no—
263#467C2×D4311yescharacteristic
264#466—431no—
265#466C2×D4311yescharacteristic
266C4×Q16—431no—
267C4×D8—431no—
268C8×D4—431no—
269#427—431no—
270#427—431no—
271C2×#107—431no—
272C2×#107—431no—
273#367—431no—
274#367—431no—
275#367—431no—
276#366—431no—
277#366—431no—
278#366—431no—
279#366—431no—
280#366—431no—
281#366C2×D4311yescharacteristic
282C4⋊C16—431no—
283#358—431no—
284#358—431no—
285#358C2×D4311yescharacteristic
286#357—431no—
287#357—431no—
288#357C2×D4311yescharacteristic
289C22⋊C16—431no—
290C22⋊C16—431no—
291C4×C16—431no—
292C43#3392411yescharacteristic, complemented, Sylow
293C2×Q16C22×D4311yescharacteristic
294C2×D8C22×D4311yescharacteristic
295C22×C8—431no—
296C22×C8C22×D4311yescharacteristic
297C4⋊Q8—861no—
298C4⋊Q8—861no—
299#125—1721no—
300#124—1721no—
301#124—1721no—
302C22⋊Q8—21no—
303C22⋊Q8—861no—
304C22⋊Q8—1721no—
305C22⋊Q8—1721no—
306#121—21no—
307#121—861no—
308#121—1721no—
309C4×Q8—861no—
310C4×D4—431no—
311C4×D4—861no—
312C4×D4—1721no—
313#117—861no—
314#117—861no—
315#117—1721no—
316C2×C4⋊C4—861no—
317C2×C4⋊C4—861no—
318SD32—22no—
319M32—22no—
320M32—862no—
321C2×C16—431no—
322C2×C16—431no—
323C2×C16C22×D4311yescharacteristic
324C2×C16C22×D4311yescharacteristic
325#107—431no—
326#107—431no—
327#107—431no—
328#107—431no—
329#107—861no—
330#107—861no—
331#107—861no—
332#107—861no—
333#107C22×D4311yescharacteristic
334#107C22×D4311yescharacteristic
335#106—861no—
336#106—861no—
337C4⋊C8—431no—
338#103—21no—
339#103—861no—
340#103—861no—
341#102—21no—
342#102—861no—
343#102—861no—
344C22⋊C8—431no—
345C22⋊C8—431no—
346C4×C8—431no—
347C2×Q8—21no—
348C2×Q8—1721no—
349C2×Q8—1721no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—431no—
353C2×D4—1721no—
354C22×C4—431no—
355C22×C4—1721no—
356C22×C4—1721no—
357C22×C4—1721no—
358C22×C4D4×D4311yescharacteristic
359Q16—21no—
360Q16—21no—
361D8—21no—
362D8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—431no—
366C2×C8—431no—
367C2×C8—861no—
368C2×C8—861no—
369C2×C8D4×D4311yescharacteristic
370C2×C8C23×D4311yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—431no—
375C4⋊C4—861no—
376C4⋊C4—861no—
377C4⋊C4—861no—
378C4⋊C4—861no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C4⋊C4—1721no—
384C4⋊C4—1721no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—431no—
388C22⋊C4—431no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C42—431no—
395C42—1721no—
396C42—1721no—
397C42—1721no—
398C16—21no—
399C16—861no—
400C16—861no—
401C16#1062190012yes—
402C23—41no—
403C23—431no—
404C23D8×D4311yescharacteristic
405Q8—41no—
406Q8—41no—
407Q8—6881no—
408Q8—6881no—
409D4—41no—
410D4—41no—
411D4—161no—
412D4—862no—
413D4—6881no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—431no—
420C2×C4—431no—
421C2×C4—431no—
422C2×C4—861no—
423C2×C4—861no—
424C2×C4—3442no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4—1721no—
428C2×C4—1721no—
429C2×C4—6881no—
430C2×C4—6881no—
431C2×C4D8×D4311yescharacteristic
432C2×C4C2×D4×D4311yescharacteristic
433C8—21no—
434C8—861no—
435C8—861no—
436C8C2×#1062190011yescharacteristic
437C8#1306337211yescharacteristic
438C22—21no—
439C22—21no—
440C22—21no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—861no—
445C22—861no—
446C22—861no—
447C22C2×D8×D4311yescharacteristic
448C4—21no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—432no—
453C4—861no—
454C4—861no—
455C4—3441no—
456C4—3441no—
457C4—3441no—
458C4—3441no—
459C4#1458354911yescharacteristic
460C4#1458371311yescharacteristic
461C2—41no—
462C2—161no—
463C2—1721no—
464C2#1914693911yescharacteristic
465C2#510×D4311yescharacteristic
466C2#1914773511yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2220C2
socleC22×C43C22×D8
prime radical#19147014C2
hypercenter#2220D43
hypocenterC43#33924
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2220

Complements

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

NH ≅ G/Ntype
2. #19146984C2semidirect
3. #19136869C2semidirect
4. #19136801C2semidirect
5. #19136800C2semidirect
6. #19136774C2semidirect
7. #19136773C2semidirect
8. #19136745C2semidirect
9. #19136740C2semidirect
10. #19136705C2semidirect
11. SD32×Dic43C2semidirect
12. #19136425C2semidirect
13. #19136383C2semidirect
14. #19136380C2semidirect
15. C43×#2220C2semidirect
238. #2220D43semidirect
292. C43#33924semidirect

Maximal subgroups

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

subgroupindex
#191470142
#191469842
#191368692
#191368012
#191368002
#191367742
#191367732
#191367452
#191367402
#191367052
SD32×Dic432
#191364252
#191363832
#191363802
C43×#22202
#3392443