Finite Group Databasebeta

← #25254197

Subgroups — #25254197

Order 11008.

514 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147014C211yesmaximal, characteristic, complemented
2#19146939C211yesmaximal, characteristic, complemented
3#19136876C211yesmaximal, characteristic, complemented
4#19136784C211yesmaximal, characteristic, complemented
5#19136783C211yesmaximal, characteristic, complemented
6#19136779C211yesmaximal, characteristic, complemented
7#19136778C211yesmaximal, characteristic, complemented
8#19136740C211yesmaximal, characteristic, complemented
9#19136730C211yesmaximal, characteristic, complemented
10#19136695C211yesmaximal, characteristic, complemented
11D16×Dic43C211yesmaximal, characteristic, complemented
12#19136425C211yesmaximal, characteristic, complemented
13#19136383C211yesmaximal, characteristic, complemented
14#19136382C211yesmaximal, characteristic, complemented
15C43×#2218C211yesmaximal, characteristic, complemented
16#14583613—21no—
17#14583549—21no—
18C2×#13063264C2211yescharacteristic
19#14583303C2211yescharacteristic
20#14583303C2211yescharacteristic
21#14583222—21no—
22#14583220—21no—
23#14583211—21no—
24#14583210—21no—
25#14583187—21no—
26#14583177—21no—
27#14583132C2211yescharacteristic
28#14583132C2211yescharacteristic
29D8×Dic43C2211yescharacteristic
30D8×Dic43C2211yescharacteristic
31C8×C22⋊D43C2211yescharacteristic
32#14582937C2211yescharacteristic
33#14582936C2211yescharacteristic
34C2×#13063259C2211yescharacteristic
35#107×D43C2211yescharacteristic
36#14582727C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582726C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582726C2211yescharacteristic
41#14582725C2211yescharacteristic
42#14582725C2211yescharacteristic
43#14582724C2211yescharacteristic
44Dic43⋊C16C2211yescharacteristic
45#14582700C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×D16×C43C2211yescharacteristic
53C2×M32×C43C2211yescharacteristic
54C43×#466C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#367C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×#10621900—41no—
60C2×C8×D43C2311yescharacteristic
61#13063324—21no—
62#13063324—21no—
63#13063312—41no—
64#13063311—41no—
65#13063307—41no—
66#13063306—41no—
67#13063302—41no—
68#13063297—41no—
69#13063296—21no—
70#13063296—21no—
71D4×Dic43—21no—
72D4×Dic43—21no—
73C4×C22⋊D43D411yescharacteristic
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#13063246—21no—
94#13063246—21no—
95#13063246—21no—
96#13063246—21no—
97C22⋊(C43⋊C8)D411yescharacteristic
98(C2×D43)⋊C8D411yescharacteristic
99C8×Dic43C2311yescharacteristic
100C2×D8×C43C2311yescharacteristic
101C2×D8×C43C2311yescharacteristic
102C22×C8×C43C2311yescharacteristic
103#121×C43—21no—
104#121×C43—21no—
105D16×C43—22no—
106M32×C43—22no—
107C2×C16×C43C2311yescharacteristic
108C2×C16×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#102×C43—21no—
112#102×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—41no—
116C2×D4×C43—41no—
117C22×C4×C43C2×D411yescharacteristic
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43D811yescharacteristic
121C22×Dic43—41no—
122C22×Dic43—41no—
123C22×Dic43—41no—
124#10621900—84no—
125C2×C4×D43—41no—
126C2×C4×D43C2×D411yescharacteristic
127C2×Dic86—41no—
128C2×Dic86—41no—
129D8×C43—21no—
130D8×C43—21no—
131D8×C43—21no—
132D8×C43—21no—
133C2×C8×C43—21no—
134C2×C8×C43—21no—
135C2×C8×C43C2×D411yescharacteristic
136C2×C8×C43C2411yescharacteristic
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C22⋊C4×C43—41no—
140C22⋊C4×C43—41no—
141C22⋊Dic43—41no—
142C22⋊Dic43—41no—
143C22⋊Dic43—41no—
144C22⋊Dic43—41no—
145C22⋊Dic43—41no—
146C22⋊Dic43D811yescharacteristic
147(C2×D43)⋊C4—41no—
148(C2×D43)⋊C4D811yescharacteristic
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151C4⋊Dic43—21no—
152C4⋊Dic43—21no—
153C4⋊Dic43—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4D811yescharacteristic
158C4×Dic43—41no—
159C4×Dic43—41no—
160C4×Dic43C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162C2×C43⋊C8C2×D411yescharacteristic
163C8×D43—21no—
164C8×D43—21no—
165C16×C43—21no—
166C16×C43#4112yescomplemented
167C43⋊C16—21no—
168C43⋊C16—21no—
169C23×C43—41no—
170C23×C43—41no—
171C23×C43C2×D811yescharacteristic
172C22×D43C2×D811yescharacteristic
173D4×C43—41no—
174D4×C43—41no—
175D4×C43—41no—
176D4×C43—41no—
177D4×C43—82no—
178D4×C43—161no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43C2×D811yescharacteristic
184C2×C4×C43C22×D411yescharacteristic
185C22⋊D43—22no—
186C22⋊D43—82no—
187C22⋊D43—161no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—82no—
193C2×Dic43—82no—
194C2×Dic43—82no—
195C2×Dic43C2×D811yescharacteristic
196C2×Dic43C2×D811yescharacteristic
197C2×Dic43C2×D811yescharacteristic
198C4×D43—21no—
199C4×D43—21no—
200C4×D43—82no—
201Dic86—82no—
202Dic86—161no—
203C8×C43—21no—
204C8×C43C2×#4111yescharacteristic
205C8×C432−1+411yescharacteristic
206C43⋊C8—21no—
207C43⋊C8—21no—
208#33921—431nomaximal, Sylow
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—81no—
213C22×C43—81no—
214C22×C43—81no—
215C22×C43—81no—
216C22×C43—81no—
217C22×C43—81no—
218C22×C43C22×D811yescharacteristic
219C2×D43—21no—
220C2×D43—21no—
221C2×D43—21no—
222C4×C43—21no—
223C4×C43—81no—
224C4×C43—81no—
225C4×C43#54711yescharacteristic
226C4×C43#57811yescharacteristic
227Dic43—21no—
228Dic43—21no—
229Dic43—81no—
230Dic43—81no—
231Dic43—81no—
232Dic43—81no—
233Dic43#50912yes—
234#3341—431no—
235#3334—431no—
236#2254—431no—
237#2234—431no—
238#2234—431no—
239#2233—431no—
240#2233—431no—
241#2226—431no—
242#2224—431no—
243#2218—431no—
244#2218D4311yescharacteristic, complemented
245C4×D16—431no—
246#2169—431no—
247#2159—431no—
248#2159—431no—
249C2×C43—41no—
250C2×C43—161no—
251C2×C43—161no—
252C2×C43#333411yescharacteristic
253C2×C43C2×#50911yescharacteristic
254C2×C43#341611yescharacteristic
255D43—41no—
256#555—861no—
257#547—861no—
258C2×D16C2×D4311yescharacteristic
259C2×M32—431no—
260C2×M32C2×D4311yescharacteristic
261#500—431no—
262#500—431no—
263#482—861no—
264#482—861no—
265#480—861no—
266#480—861no—
267#476—861no—
268#474—861no—
269#466—431no—
270#466—431no—
271#466C2×D4311yescharacteristic
272#466C2×D4311yescharacteristic
273C4×D8—431no—
274C4×D8—431no—
275C8×D4—431no—
276#427—431no—
277#427—431no—
278C2×#107—431no—
279C2×#107—431no—
280#367—431no—
281#367—431no—
282#367—431no—
283#367—431no—
284#367—431no—
285#367C2×D4311yescharacteristic
286#366—431no—
287#366—431no—
288#366—431no—
289C4⋊C16—431no—
290#357—431no—
291#357—431no—
292#357—431no—
293#357—431no—
294#357C2×D4311yescharacteristic
295#357C2×D4311yescharacteristic
296C22⋊C16—431no—
297C22⋊C16—431no—
298C4×C16—431no—
299C43#3392111yescharacteristic, complemented, Sylow
300C2×#41—1721no—
301C2×D8C22×D4311yescharacteristic
302C2×D8C22×D4311yescharacteristic
303C22×C8—431no—
304C22×C8C22×D4311yescharacteristic
305C4⋊Q8—861no—
306C4⋊Q8—861no—
307#124—1721no—
308#124—1721no—
309#123—1721no—
310#123—1721no—
311C22⋊Q8—1721no—
312#121—21no—
313#121—21no—
314#121—861no—
315#121—861no—
316#121—1721no—
317C4×D4—431no—
318C4×D4—861no—
319C4×D4—861no—
320#117—861no—
321#117—861no—
322#117—1721no—
323C2×C4⋊C4—861no—
324C2×C4⋊C4—861no—
325D16—22no—
326M32—22no—
327M32—862no—
328C2×C16—431no—
329C2×C16—431no—
330C2×C16C22×D4311yescharacteristic
331C2×C16C22×D4311yescharacteristic
332#107—431no—
333#107—431no—
334#107—431no—
335#107—431no—
336#107—861no—
337#107—861no—
338#107—861no—
339#107—861no—
340#107C22×D4311yescharacteristic
341#107C22×D4311yescharacteristic
342#106—861no—
343#106—861no—
344C4⋊C8—431no—
345#102—21no—
346#102—21no—
347#102—861no—
348#102—861no—
349#102—861no—
350#102—861no—
351C22⋊C8—431no—
352C22⋊C8—431no—
353C4×C8—431no—
354#41—3444no—
355C2×Q8—1721no—
356C2×Q8—1721no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—431no—
362C2×D4—1721no—
363C2×D4—1721no—
364C22×C4—431no—
365C22×C4—1721no—
366C22×C4—1721no—
367C22×C4—1721no—
368C22×C4—1721no—
369C22×C4D4×D4311yescharacteristic
370D8—21no—
371D8—21no—
372D8—21no—
373D8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—431no—
377C2×C8—431no—
378C2×C8—861no—
379C2×C8—861no—
380C2×C8D4×D4311yescharacteristic
381C2×C8C23×D4311yescharacteristic
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—431no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C4⋊C4—861no—
388C4⋊C4—861no—
389C4⋊C4—1721no—
390C4⋊C4—1721no—
391C4⋊C4—1721no—
392C4⋊C4—1721no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—431no—
396C22⋊C4—431no—
397C22⋊C4—1721no—
398C22⋊C4—1721no—
399C22⋊C4—1721no—
400C22⋊C4—1721no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C42—431no—
404C42—1721no—
405C42—1721no—
406C16—21no—
407C16—861no—
408C16—861no—
409C16#1062190012yescomplemented
410C23—41no—
411C23—41no—
412C23—431no—
413C23D8×D4311yescharacteristic
414Q8—3442no—
415Q8—6881no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—82no—
421D4—161no—
422D4—862no—
423D4—3442no—
424D4—6881no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—431no—
430C2×C4—431no—
431C2×C4—431no—
432C2×C4—861no—
433C2×C4—861no—
434C2×C4—3442no—
435C2×C4—3442no—
436C2×C4—3442no—
437C2×C4—3442no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4D8×D4311yescharacteristic
443C2×C4C2×D4×D4311yescharacteristic
444C8—21no—
445C8—861no—
446C8—861no—
447C8C2×#1062190011yescharacteristic
448C8#1306337211yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—861no—
459C22—861no—
460C22—861no—
461C22C2×D8×D4311yescharacteristic
462C4—21no—
463C4—81no—
464C4—81no—
465C4—432no—
466C4—861no—
467C4—861no—
468C4—3441no—
469C4—3441no—
470C4—3441no—
471C4—3441no—
472C4#1458354911yescharacteristic
473C4#1458371311yescharacteristic
474C2—41no—
475C2—161no—
476C2—161no—
477C2—1721no—
478C2#1914693911yescharacteristic
479C2#509×D4311yescharacteristic
480C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2218C2
socleC22×C43C22×D8
hypercenter#2218D43
hypocenterC43#33921
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. #19147014C2semidirect
2. #19146939C2semidirect
3. #19136876C2semidirect
4. #19136784C2semidirect
5. #19136783C2semidirect
6. #19136779C2semidirect
7. #19136778C2semidirect
8. #19136740C2semidirect
9. #19136730C2semidirect
10. #19136695C2semidirect
11. D16×Dic43C2semidirect
12. #19136425C2semidirect
13. #19136383C2semidirect
14. #19136382C2semidirect
15. C43×#2218C2semidirect
166. C16×C43#41semidirect
244. #2218D43semidirect
299. C43#33921semidirect
409. C16#10621900semidirect

Maximal subgroups

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

subgroupindex
#191470142
#191469392
#191368762
#191367842
#191367832
#191367792
#191367782
#191367402
#191367302
#191366952
D16×Dic432
#191364252
#191363832
#191363822
C43×#22182
#3392143