Finite Group Databasebeta

← #25254368

Subgroups — #25254368

Order 11008.

480 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147609C211yesmaximal, characteristic
2#19147486C211yesmaximal, characteristic, complemented
3#19136836C211yesmaximal, characteristic
4#19136830C211yesmaximal, characteristic, complemented
5#19136825C211yesmaximal, characteristic, complemented
6#19136760C211yesmaximal, characteristic, complemented
7#19136750C211yesmaximal, characteristic, complemented
8#19136740C211yesmaximal, characteristic, complemented
9#19136655C211yesmaximal, characteristic, complemented
10#19136655C211yesmaximal, characteristic, complemented
11#19136502C211yesmaximal, characteristic, complemented
12#19136464C211yesmaximal, characteristic, complemented
13#19136460C211yesmaximal, characteristic, complemented
14SD32×Dic43C211yesmaximal, characteristic, complemented
15C43×#2207C211yesmaximal, characteristic
16#14583635—21no—
17#14583625—21no—
18C2×#13063271C2211yescharacteristic
19#14583303C2211yescharacteristic
20#14583301C2211yescharacteristic
21#14583300C2211yescharacteristic
22#14583282C2211yescharacteristic
23#14583282C2211yescharacteristic
24#14583206—21no—
25#14583204—21no—
26#14583182—21no—
27#14583112—21no—
28#14583112—21no—
29#14583096—21no—
30C8×Dic86C2211yescharacteristic
31C4×Dic172C2211yescharacteristic
32Q16×Dic43C2211yescharacteristic
33Q16×Dic43C2211yescharacteristic
34D8×Dic43C2211yescharacteristic
35D8×Dic43C2211yescharacteristic
36#14582727C2211yescharacteristic
37#14582726C2211yescharacteristic
38#14582725C2211yescharacteristic
39Dic43⋊C16C2211yescharacteristic
40Dic43⋊C16C2211yescharacteristic
41#14582704C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582703C2211yescharacteristic
44#14582702C2211yescharacteristic
45#14582700C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic
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×Dic172C2311yescharacteristic
60C2×#10621883—21no—
61C2×#10621883—21no—
62#13063324—21no—
63#13063324—41no—
64#13063317—21no—
65#13063317—41no—
66#13063316—21no—
67#13063316—41no—
68#13063312—21no—
69#13063312—21no—
70#13063312—41no—
71#13063306—41no—
72#13063306—41no—
73Q8×Dic43—21no—
74Q8×Dic43—21no—
75C4×Dic86—21no—
76C4×Dic86—41no—
77C4×Dic86D411yescharacteristic
78D4×Dic43—21no—
79D4×Dic43—21no—
80D4×Dic43—41no—
81#13063271—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#13063250—21no—
94#13063249—21no—
95#13063249—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—
118C22×Dic43—41no—
119C22×Dic43—41no—
120C2×Dic86—21no—
121C2×Dic86—41no—
122C2×Dic86D811yescharacteristic
123Q16×C43—21no—
124Q16×C43#4112yes—
125D8×C43—21no—
126D8×C43—21no—
127D8×C43—21no—
128D8×C43—21no—
129D8×C43—81no—
130C2×C8×C43C2×D411yescharacteristic
131C2×C8×C43C2411yescharacteristic
132C4⋊C4×C43—21no—
133C4⋊C4×C43—41no—
134C42×C43—41no—
135C42×C43C2×D411yescharacteristic
136C22⋊Dic43—41no—
137C22⋊Dic43—41no—
138C22⋊Dic43—41no—
139C22⋊Dic43—41no—
140C22⋊Dic43—41no—
141C22⋊Dic43—41no—
142#10621883—81no—
143#10621883—81no—
144C4⋊Dic43—21no—
145C4⋊Dic43—21no—
146C4⋊Dic43—21no—
147C4⋊Dic43—41no—
148C4⋊Dic43—41no—
149C4⋊Dic43—41no—
150C4⋊Dic43D811yescharacteristic
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4—41no—
156Dic43⋊C4D811yescharacteristic
157Dic43⋊C4D811yescharacteristic
158C4×Dic43—41no—
159C4×Dic43—41no—
160C4×Dic43—41no—
161C4×Dic43C2×D411yescharacteristic
162C4×Dic43C2×D411yescharacteristic
163C2×C43⋊C8C2×D411yescharacteristic
164C2×C43⋊C8C2×D411yescharacteristic
165Dic172—21no—
166Dic172—21no—
167C16×C43—21no—
168C16×C43—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C23×C43—41no—
172C23×C43—41no—
173Q8×C43—22no—
174Q8×C43—41no—
175D4×C43—41no—
176D4×C43—41no—
177D4×C43—41no—
178D4×C43—41no—
179D4×C43—82no—
180D4×C43—161no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43C2×D811yescharacteristic
184C2×C4×C43C2×D811yescharacteristic
185C2×C4×C43C22×D411yescharacteristic
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—161no—
191C2×Dic43—161no—
192C2×Dic43C2×D811yescharacteristic
193C2×Dic43C2×D811yescharacteristic
194C2×Dic43C2×D811yescharacteristic
195C2×Dic43C2×D811yescharacteristic
196Dic86—41no—
197Dic86—41no—
198Dic86—41no—
199Dic86—82no—
200C8×C43—21no—
201C8×C43C2×#4111yescharacteristic
202C8×C432−1+411yescharacteristic
203C43⋊C8—21no—
204C43⋊C8—21no—
205#33938—431nomaximal, Sylow
206C22×C43—81no—
207C22×C43—81no—
208C22×C43—81no—
209C22×C43—81no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43C22×D811yescharacteristic
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—42no—
216C4×C43—81no—
217C4×C43#54811yescharacteristic
218C4×C43#57711yescharacteristic
219Dic43—21no—
220Dic43—21no—
221Dic43—21no—
222Dic43—21no—
223Dic43—81no—
224Dic43—81no—
225Dic43—81no—
226Dic43—81no—
227#3396—431no—
228#3383—431no—
229#2244—431no—
230#2243—431no—
231#2242—431no—
232#2229—431no—
233#2228—431no—
234#2226—431no—
235#2211—431no—
236#2211—431no—
237#2207D4311yescharacteristic
238#2183—431no—
239#2176—431no—
240#2175—431no—
241C4×SD32—431no—
242C2×C43—161no—
243C2×C43—161no—
244C2×C43#335811yescharacteristic
245C2×C43#341411yescharacteristic
246C2×C43#341611yescharacteristic
247#559—861no—
248#557—861no—
249C2×Q32—431no—
250C2×SD32C2×D4311yescharacteristic
251C2×SD32C2×D4311yescharacteristic
252#500—431no—
253#499—431no—
254#499—431no—
255#495—431no—
256#495—431no—
257#493C2×D4311yescharacteristic
258#479—861no—
259#479—861no—
260#475—861no—
261#463—861no—
262#463—861no—
263#460—861no—
264C8×Q8—431no—
265C4×Q16—431no—
266C4×Q16—431no—
267C4×Q16—431no—
268C4×Q16C2×D4311yescharacteristic
269C4×D8—431no—
270C4×D8—431no—
271#367—431no—
272#367—431no—
273#366—431no—
274C4⋊C16—431no—
275C4⋊C16—431no—
276C4⋊C16C2×D4311yescharacteristic
277#358—431no—
278#358—431no—
279#358—431no—
280#358—431no—
281#357—431no—
282#357—431no—
283#357—431no—
284#357—431no—
285#357C2×D4311yescharacteristic
286#357C2×D4311yescharacteristic
287#346—431no—
288#346—431no—
289C4×C16—431no—
290C43#3393811yescharacteristic, complemented, Sylow
291C2×Q16—431no—
292C2×Q16C22×D4311yescharacteristic
293C2×SD16—861no—
294C2×SD16—861no—
295C2×D8—21no—
296C2×D8C22×D4311yescharacteristic
297C2×D8C22×D4311yescharacteristic
298C4⋊Q8—861no—
299C4⋊Q8—1721no—
300#127—21no—
301#125—861no—
302#125—861no—
303#125—1721no—
304#125—1721no—
305#124—861no—
306#124—861no—
307#124—1721no—
308#123—1721no—
309#123—1721no—
310C4×Q8—21no—
311C4×Q8—431no—
312C4×Q8—861no—
313C4×Q8—861no—
314C4×Q8—861no—
315C4×Q8—1721no—
316C4×D4—861no—
317C4×D4—861no—
318C4×D4—1721no—
319Q32—862no—
320SD32—22no—
321SD32—22no—
322C2×C16—431no—
323C2×C16—431no—
324C2×C16C22×D4311yescharacteristic
325C2×C16C22×D4311yescharacteristic
326#107—431no—
327#107—431no—
328#107—431no—
329#107—861no—
330#107C22×D4311yescharacteristic
331#106—861no—
332#106—861no—
333C4⋊C8—431no—
334C4⋊C8—431no—
335C4⋊C8—431no—
336#103—21no—
337#103—861no—
338#103—861no—
339#103—861no—
340#102—861no—
341#102—861no—
342C4×C8—431no—
343C4×C8—431no—
344C4×C8C22×D4311yescharacteristic
345C2×Q8—21no—
346C2×Q8—431no—
347C2×Q8—861no—
348C2×Q8—1721no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—41no—
353C22×C4—1721no—
354C22×C4—1721no—
355Q16—21no—
356Q16—861no—
357Q16—861no—
358Q16#1062190012yes—
359SD16—3441no—
360SD16—3441no—
361D8—21no—
362D8—21no—
363D8—21no—
364D8—21no—
365D8—81no—
366C2×C8—431no—
367C2×C8—431no—
368C2×C8D4×D4311yescharacteristic
369C2×C8C23×D4311yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—431no—
373C4⋊C4—431no—
374C4⋊C4—431no—
375C4⋊C4—861no—
376C4⋊C4—861no—
377C4⋊C4—861no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C4⋊C4—1721no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C42—41no—
393C42—431no—
394C42—431no—
395C42—1721no—
396C42—1721no—
397C42—1721no—
398C42D4×D4311yescharacteristic
399C16—21no—
400C16—21no—
401C16—861no—
402C16—861no—
403C23—41no—
404C23—41no—
405Q8—22no—
406Q8—41no—
407Q8—3442no—
408Q8—1721no—
409Q8—1721no—
410Q8—1721no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—82no—
416D4—161no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—431no—
420C2×C4—431no—
421C2×C4—431no—
422C2×C4—431no—
423C2×C4—1721no—
424C2×C4—1721no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4—6881no—
428C2×C4—6881no—
429C2×C4D8×D4311yescharacteristic
430C2×C4D8×D4311yescharacteristic
431C2×C4C2×D4×D4311yescharacteristic
432C8—21no—
433C8—861no—
434C8—861no—
435C8C2×#1062190011yescharacteristic
436C8#1306337211yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C2×D8×D4311yescharacteristic
444C4—21no—
445C4—21no—
446C4—42no—
447C4—81no—
448C4—861no—
449C4—861no—
450C4—861no—
451C4—861no—
452C4—3441no—
453C4—3441no—
454C4—3441no—
455C4—3441no—
456C4#1458355511yescharacteristic
457C4#1458370911yescharacteristic
458C2—161no—
459C2—161no—
460C2#1914722511yescharacteristic
461C2#1914772711yescharacteristic
462C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2207C2
socleC22×C43C22×D8
prime radicalC43×#493C22
hypercenter#2207D43
hypocenterC43#33938
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
4. #19136830C2semidirect
5. #19136825C2semidirect
6. #19136760C2semidirect
7. #19136750C2semidirect
8. #19136740C2semidirect
9. #19136655C2semidirect
10. #19136655C2semidirect
11. #19136502C2semidirect
12. #19136464C2semidirect
13. #19136460C2semidirect
14. SD32×Dic43C2semidirect
290. C43#33938semidirect

Maximal subgroups

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

subgroupindex
#191476092
#191474862
#191368362
#191368302
#191368252
#191367602
#191367502
#191367402
#191366552
#191365022
#191364642
#191364602
SD32×Dic432
C43×#22072
#3393843