Finite Group Databasebeta

← #25254331

Subgroups — #25254331

Order 11008.

518 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#19147568C211yesmaximal, characteristic
2#19147486C211yesmaximal, characteristic, complemented
3#19136836C211yesmaximal, characteristic, complemented
4#19136835C211yesmaximal, characteristic, complemented
5#19136817C211yesmaximal, characteristic, complemented
6#19136754C211yesmaximal, characteristic, complemented
7#19136753C211yesmaximal, characteristic, complemented
8#19136730C211yesmaximal, characteristic, complemented
9#19136633C211yesmaximal, characteristic, complemented
10#19136633C211yesmaximal, characteristic, complemented
11#19136502C211yesmaximal, characteristic, complemented
12#19136460C211yesmaximal, characteristic, complemented
13#19136457C211yesmaximal, characteristic, complemented
14SD32×Dic43C211yesmaximal, characteristic, complemented
15C43×#2207C211yesmaximal, characteristic, complemented
16#14583625—21no—
17#14583569—21no—
18C2×#13063268C2211yescharacteristic
19#14583303C2211yescharacteristic
20#14583301C2211yescharacteristic
21#14583300C2211yescharacteristic
22#14583274C2211yescharacteristic
23#14583274C2211yescharacteristic
24#14583206—21no—
25#14583204—21no—
26#14583182—21no—
27#14583092—21no—
28#14583092—21no—
29#14583091—21no—
30C8×Dic86C2211yescharacteristic
31Q16×Dic43C2211yescharacteristic
32Q16×Dic43C2211yescharacteristic
33C4×D344C2211yescharacteristic
34D8×Dic43C2211yescharacteristic
35D8×Dic43C2211yescharacteristic
36#14582727C2211yescharacteristic
37#14582725C2211yescharacteristic
38#14582724C2211yescharacteristic
39Dic43⋊C16C2211yescharacteristic
40Dic43⋊C16C2211yescharacteristic
41#14582703C2211yescharacteristic
42#14582701C2211yescharacteristic
43#14582701C2211yescharacteristic
44#14582700C2211yescharacteristic
45#14582700C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582699C2211yescharacteristic
49#14582675C2211yescharacteristic
50#14582674C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×SD32×C43C2211yescharacteristic
53C2×SD32×C43C2211yescharacteristic
54C43×#493C2211yescharacteristic
55C4×Q16×C43C2211yescharacteristic
56C43×C4⋊C16C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×#10621900—41no—
60C2×D344C2311yescharacteristic
61C2×#10621882—21no—
62C2×#10621882—21no—
63#13063324—21no—
64#13063324—41no—
65#13063321—21no—
66#13063321—21no—
67#13063317—21no—
68#13063317—41no—
69#13063316—21no—
70#13063316—41no—
71#13063297—41no—
72#13063297—41no—
73#13063296—41no—
74Q8×Dic43—21no—
75Q8×Dic43—21no—
76C4×Dic86—41no—
77C4×Dic86D411yescharacteristic
78C4×D172—21no—
79D4×Dic43—21no—
80D4×Dic43—21no—
81#13063268—22no—
82C2×C43⋊C16C2311yescharacteristic
83C2×C43⋊C16C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063258—21no—
88#13063257—21no—
89#13063256—21no—
90C4⋊(C43⋊C8)D411yescharacteristic
91Dic43⋊C8D411yescharacteristic
92Dic43⋊C8D411yescharacteristic
93#13063249—21no—
94#13063249—21no—
95#13063247—21no—
96#13063246—21no—
97#13063246—21no—
98C8×Dic43C2311yescharacteristic
99C8×Dic43C2311yescharacteristic
100C2×Q16×C43C2311yescharacteristic
101C2×D8×C43—21no—
102C2×D8×C43C2311yescharacteristic
103C2×D8×C43C2311yescharacteristic
104#127×C43—21no—
105C4×Q8×C43—21no—
106SD32×C43—22no—
107SD32×C43—22no—
108C2×C16×C43C2311yescharacteristic
109C2×C16×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#103×C43—21no—
112C4×C8×C43C2311yescharacteristic
113C2×Q8×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—41no—
117C2×D4×C43—41no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121C2×C22⋊D43—41no—
122C22×Dic43—41no—
123C22×Dic43—41no—
124#10621900—84no—
125C2×D172—21no—
126C2×C4×D43—41no—
127C2×Dic86—41no—
128C2×Dic86D811yescharacteristic
129Q16×C43—21no—
130Q16×C43#4112yescomplemented
131D8×C43—21no—
132D8×C43—21no—
133D8×C43—21no—
134D8×C43—21no—
135D8×C43—81no—
136C2×C8×C43C2×D411yescharacteristic
137C2×C8×C43C2411yescharacteristic
138C4⋊C4×C43—21no—
139C4⋊C4×C43—41no—
140C42×C43—41no—
141C42×C43C2×D411yescharacteristic
142C22⋊Dic43—41no—
143C22⋊Dic43—41no—
144#10621882—81no—
145#10621882—81no—
146(C2×D43)⋊C4—41no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C4⋊Dic43—41no—
151C4⋊Dic43—41no—
152C4⋊Dic43—41no—
153C4⋊Dic43D811yescharacteristic
154Dic43⋊C4—41no—
155Dic43⋊C4—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4—41no—
158Dic43⋊C4D811yescharacteristic
159Dic43⋊C4D811yescharacteristic
160C4×Dic43—41no—
161C4×Dic43—41no—
162C4×Dic43C2×D411yescharacteristic
163C4×Dic43C2×D411yescharacteristic
164C2×C43⋊C8C2×D411yescharacteristic
165C2×C43⋊C8C2×D411yescharacteristic
166D344—21no—
167D344—21no—
168C16×C43—21no—
169C16×C43—21no—
170C43⋊C16—21no—
171C43⋊C16—21no—
172C23×C43—41no—
173C23×C43—41no—
174C22×D43—41no—
175Q8×C43—22no—
176Q8×C43—41no—
177D4×C43—41no—
178D4×C43—41no—
179D4×C43—41no—
180D4×C43—41no—
181D4×C43—82no—
182D4×C43—161no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43C2×D811yescharacteristic
186C2×C4×C43C2×D811yescharacteristic
187C2×C4×C43C22×D411yescharacteristic
188C22⋊D43—82no—
189C22⋊D43—82no—
190C22⋊D43—161no—
191C22⋊D43—161no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—82no—
196C2×Dic43—82no—
197C2×Dic43C2×D811yescharacteristic
198C2×Dic43C2×D811yescharacteristic
199C2×Dic43C2×D811yescharacteristic
200C2×Dic43C2×D811yescharacteristic
201D172—41no—
202D172—41no—
203C4×D43—82no—
204Dic86—22no—
205Dic86—82no—
206C8×C43—21no—
207C8×C43C2×#4111yescharacteristic
208C8×C432−1+411yescharacteristic
209C43⋊C8—21no—
210C43⋊C8—21no—
211#33935—431nomaximal, Sylow
212C22×C43—81no—
213C22×C43—81no—
214C22×C43—81no—
215C22×C43—81no—
216C22×C43—81no—
217C22×C43—81no—
218C22×C43C22×D811yescharacteristic
219C2×D43—81no—
220C2×D43—81no—
221C2×D43—81no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—42no—
225C4×C43—81no—
226C4×C43#54811yescharacteristic
227C4×C43#57711yescharacteristic
228Dic43—21no—
229Dic43—21no—
230Dic43—21no—
231Dic43—81no—
232Dic43—81no—
233Dic43—81no—
234Dic43#50912yes—
235#3391—431no—
236#3383—431no—
237#2244—431no—
238#2244—431no—
239#2240—431no—
240#2228—431no—
241#2228—431no—
242#2224—431no—
243#2207—431no—
244#2207—431no—
245#2207D4311yescharacteristic, complemented
246#2183—431no—
247#2175—431no—
248#2175—431no—
249C4×SD32—431no—
250C2×C43—161no—
251C2×C43—161no—
252C2×C43#335811yescharacteristic
253C2×C43C2×#50911yescharacteristic
254C2×C43#341611yescharacteristic
255D43—161no—
256#557—861no—
257#550—861no—
258C2×SD32—431no—
259C2×SD32C2×D4311yescharacteristic
260C2×SD32C2×D4311yescharacteristic
261#500—431no—
262#499—431no—
263#499—431no—
264#493—431no—
265#493—431no—
266#493C2×D4311yescharacteristic
267#479—861no—
268#479—861no—
269#475—861no—
270#459—861no—
271#459—861no—
272#459—861no—
273C8×Q8—431no—
274C4×Q16—431no—
275C4×Q16—431no—
276C4×Q16C2×D4311yescharacteristic
277C4×D8—431no—
278C4×D8—431no—
279C4×D8—431no—
280#367—431no—
281#366—431no—
282#366—431no—
283C4⋊C16—431no—
284C4⋊C16—431no—
285C4⋊C16C2×D4311yescharacteristic
286#358—431no—
287#357—431no—
288#357—431no—
289#357—431no—
290#357—431no—
291#357—431no—
292#357—431no—
293#357—431no—
294#357C2×D4311yescharacteristic
295#357C2×D4311yescharacteristic
296#346—431no—
297#346—431no—
298C4×C16—431no—
299C43#3393511yescharacteristic, complemented, Sylow
300C2×#41—1721no—
301C2×Q16C22×D4311yescharacteristic
302C2×D8—21no—
303C2×D8—431no—
304C2×D8—861no—
305C2×D8—861no—
306C2×D8C22×D4311yescharacteristic
307C2×D8C22×D4311yescharacteristic
308C4⋊Q8—861no—
309C4⋊Q8—1721no—
310#127—21no—
311#127—861no—
312#127—861no—
313#125—861no—
314#125—861no—
315#125—1721no—
316#125—1721no—
317#121—1721no—
318#121—1721no—
319#121—1721no—
320C4×Q8—21no—
321C4×Q8—431no—
322C4×Q8—861no—
323C4×Q8—861no—
324C4×Q8—1721no—
325C4×D4—861no—
326C4×D4—861no—
327C4×D4—861no—
328SD32—22no—
329SD32—22no—
330SD32—862no—
331C2×C16—431no—
332C2×C16—431no—
333C2×C16C22×D4311yescharacteristic
334C2×C16C22×D4311yescharacteristic
335#107—431no—
336#107—431no—
337#107—431no—
338#107—861no—
339#107C22×D4311yescharacteristic
340#106—861no—
341#106—861no—
342C4⋊C8—431no—
343C4⋊C8—431no—
344C4⋊C8—431no—
345#103—21no—
346#103—861no—
347#103—861no—
348#102—861no—
349#102—861no—
350#102—861no—
351C4×C8—431no—
352C4×C8—431no—
353C4×C8C22×D4311yescharacteristic
354#41—3444no—
355C2×Q8—21no—
356C2×Q8—431no—
357C2×Q8—1721no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—861no—
363C2×D4—1721no—
364C2×D4—1721no—
365C2×D4—1721no—
366C2×D4—1721no—
367C22×C4—1721no—
368C22×C4—1721no—
369C22×C4—1721no—
370Q16—21no—
371Q16#1062190012yescomplemented
372D8—21no—
373D8—21no—
374D8—21no—
375D8—21no—
376D8—81no—
377D8—861no—
378D8—861no—
379D8—3441no—
380D8—3441no—
381C2×C8—431no—
382C2×C8—431no—
383C2×C8D4×D4311yescharacteristic
384C2×C8C23×D4311yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—431no—
388C4⋊C4—431no—
389C4⋊C4—431no—
390C4⋊C4—861no—
391C4⋊C4—861no—
392C4⋊C4—861no—
393C4⋊C4—1721no—
394C4⋊C4—1721no—
395C4⋊C4—1721no—
396C4⋊C4—1721no—
397C4⋊C4—1721no—
398C4⋊C4—1721no—
399C4⋊C4—1721no—
400C22⋊C4—1721no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C42—41no—
404C42—431no—
405C42—431no—
406C42—1721no—
407C42—1721no—
408C42D4×D4311yescharacteristic
409C16—21no—
410C16—21no—
411C16—861no—
412C16—861no—
413C23—41no—
414C23—41no—
415C23—1721no—
416Q8—22no—
417Q8—41no—
418Q8—862no—
419Q8—3442no—
420D4—41no—
421D4—41no—
422D4—41no—
423D4—41no—
424D4—82no—
425D4—161no—
426D4—3442no—
427D4—3442no—
428D4—1721no—
429D4—1721no—
430D4—6881no—
431D4—6881no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—431no—
435C2×C4—431no—
436C2×C4—431no—
437C2×C4—431no—
438C2×C4—3442no—
439C2×C4—3442no—
440C2×C4—3442no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4D8×D4311yescharacteristic
445C2×C4D8×D4311yescharacteristic
446C2×C4C2×D4×D4311yescharacteristic
447C8—21no—
448C8—861no—
449C8—861no—
450C8C2×#1062190011yescharacteristic
451C8#1306337211yescharacteristic
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—3441no—
459C22—3441no—
460C22—3441no—
461C22C2×D8×D4311yescharacteristic
462C4—21no—
463C4—21no—
464C4—42no—
465C4—81no—
466C4—432no—
467C4—861no—
468C4—861no—
469C4—861no—
470C4—3441no—
471C4—3441no—
472C4—3441no—
473C4#1458355511yescharacteristic
474C4#1458370911yescharacteristic
475C2—161no—
476C2—161no—
477C2—6881no—
478C2#1914722511yescharacteristic
479C2#509×D4311yescharacteristic
480C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2207C2
socleC22×C43C22×D8
prime radical#19147568C2
hypercenter#2207D43
hypocenterC43#33935
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
2. #19147486C2semidirect
3. #19136836C2semidirect
4. #19136835C2semidirect
5. #19136817C2semidirect
6. #19136754C2semidirect
7. #19136753C2semidirect
8. #19136730C2semidirect
9. #19136633C2semidirect
10. #19136633C2semidirect
11. #19136502C2semidirect
12. #19136460C2semidirect
13. #19136457C2semidirect
14. SD32×Dic43C2semidirect
15. C43×#2207C2semidirect
130. Q16×C43#41semidirect
245. #2207D43semidirect
299. C43#33935semidirect
371. Q16#10621900semidirect

Maximal subgroups

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

subgroupindex
#191475682
#191474862
#191368362
#191368352
#191368172
#191367542
#191367532
#191367302
#191366332
#191365022
#191364602
#191364572
SD32×Dic432
C43×#22072
#3393543