Finite Group Databasebeta

← #25254253

Subgroups — #25254253

Order 11008.

486 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#19147580C211yesmaximal, characteristic, complemented
2#19147459C211yesmaximal, characteristic, complemented
3#19136825C211yesmaximal, characteristic, complemented
4#19136821C211yesmaximal, characteristic, complemented
5#19136757C211yesmaximal, characteristic, complemented
6#19136756C211yesmaximal, characteristic, complemented
7#19136740C211yesmaximal, characteristic, complemented
8#19136649C211yesmaximal, characteristic
9#19136647C211yesmaximal, characteristic
10#19136639C211yesmaximal, characteristic, complemented
11C16×Dic86C211yesmaximal, characteristic, complemented
12C4×#13063270C211yesmaximal, characteristic, complemented
13#19136444C211yesmaximal, characteristic, complemented
14#19136439C211yesmaximal, characteristic
15C43×#2242C211yesmaximal, characteristic, complemented
16#14583618—21no—
17#14583605—21no—
18C2×#13063270C2211yescharacteristic
19C2×#13063268C2211yescharacteristic
20C2×#13063266C2211yescharacteristic
21#14583303C2211yescharacteristic
22#14583300C2211yescharacteristic
23#14583282C2211yescharacteristic
24#14583277C2211yescharacteristic
25#14583198—21no—
26#14583196—21no—
27#14583188—21no—
28#14583119—21no—
29#14583118—21no—
30#14583102—21no—
31C8×Dic86C2211yescharacteristic
32C4×Dic172C2211yescharacteristic
33Q16×Dic43C2211yescharacteristic
34C4×D344C2211yescharacteristic
35D8×Dic43C2211yescharacteristic
36#14582981C2211yescharacteristic
37#14582981C2211yescharacteristic
38#14582727C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582724C2211yescharacteristic
41C4⋊(C43⋊C16)C2211yescharacteristic
42Dic43⋊C16C2211yescharacteristic
43Dic43⋊C16C2211yescharacteristic
44#14582704C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582702C2211yescharacteristic
47#14582702C2211yescharacteristic
48#14582701C2211yescharacteristic
49#14582700C2211yescharacteristic
50C16×Dic43C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C43×#499C2211yescharacteristic
53C43×#495C2211yescharacteristic
54C43×#358C2211yescharacteristic
55C43×#358C2211yescharacteristic
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C4×C16×C43C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621885—21no—
61C2×#10621883—21no—
62C2×D344C2311yescharacteristic
63#13063324—21no—
64#13063323—21no—
65#13063318—41no—
66#13063318—41no—
67#13063316—21no—
68#13063312—21no—
69#13063305—41no—
70#13063303—41no—
71#13063303—41no—
72#13063302—41no—
73Q8×Dic43—21no—
74C4×Dic86—21no—
75C4×Dic86D411yescharacteristic
76C4×D172—21no—
77D4×Dic43—21no—
78#13063287—21no—
79#13063287—21no—
80#13063281—41no—
81C4⋊C4×D43—41no—
82#13063270—22no—
83#13063268—22no—
84#13063266—22no—
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063258—21no—
90#13063256—21no—
91C4⋊(C43⋊C8)D411yescharacteristic
92Dic43⋊C8D411yescharacteristic
93Dic43⋊C8D411yescharacteristic
94#13063250—21no—
95#13063249—21no—
96#13063247—21no—
97#13063246—21no—
98#13063245—21no—
99#13063245—21no—
100C8×Dic43C2311yescharacteristic
101C8×Dic43C2311yescharacteristic
102C2×Q16×C43C2311yescharacteristic
103C2×SD16×C43—21no—
104C2×D8×C43C2311yescharacteristic
105#125×C43—21no—
106#124×C43—21no—
107C2×C16×C43C2311yescharacteristic
108C2×C16×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#106×C43—21no—
112C4×C8×C43C2311yescharacteristic
113C2×Q8×C43—21no—
114C2×D4×C43—21no—
115C22×Dic43—41no—
116C2×D172—21no—
117C2×C4×D43—41no—
118C2×C4×D43—41no—
119C2×C4×D43—41no—
120C2×Dic86—21no—
121C2×Dic86—41no—
122C2×Dic86D811yescharacteristic
123Q16×C43—21no—
124Q16×C43—21no—
125SD16×C43—81no—
126D8×C43—21no—
127D8×C43—21no—
128C2×C8×C43C2×D411yescharacteristic
129C2×C8×C43C2411yescharacteristic
130C4⋊C4×C43—21no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135C22⋊C4×C43—41no—
136C42×C43C2×D411yescharacteristic
137C22⋊Dic43—41no—
138C22⋊Dic43—41no—
139C22⋊Dic43—41no—
140#10621885—81no—
141#10621883—81no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4—41no—
145C4⋊Dic43—21no—
146C4⋊Dic43—21no—
147C4⋊Dic43—41no—
148C4⋊Dic43—41no—
149C4⋊Dic43D811yescharacteristic
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4D811yescharacteristic
156Dic43⋊C4D811yescharacteristic
157C4×Dic43—41no—
158C4×Dic43—41no—
159C4×Dic43C2×D411yescharacteristic
160C4×Dic43C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162C2×C43⋊C8C2×D411yescharacteristic
163Dic172—21no—
164Dic172—21no—
165D344—21no—
166D344#4112yes—
167C16×C43—21no—
168C16×C43—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C23×C43—41no—
172C22×D43—41no—
173Q8×C43—41no—
174Q8×C43—41no—
175D4×C43—41no—
176D4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43C2×D811yescharacteristic
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—82no—
187C2×Dic43C2×D811yescharacteristic
188C2×Dic43C2×D811yescharacteristic
189C2×Dic43C2×D811yescharacteristic
190C2×Dic43C2×D811yescharacteristic
191D172—22no—
192D172—41no—
193C4×D43—82no—
194C4×D43—161no—
195C4×D43—161no—
196Dic86—22no—
197Dic86—41no—
198Dic86—41no—
199Dic86—161no—
200C8×C43—21no—
201C8×C43C2×#4111yescharacteristic
202C8×C432−1+411yescharacteristic
203C43⋊C8—21no—
204C43⋊C8—21no—
205#33927—431nomaximal, Sylow
206C22×C43—81no—
207C22×C43—81no—
208C22×C43—81no—
209C22×C43C22×D811yescharacteristic
210C2×D43—42no—
211C2×D43—81no—
212C2×D43—81no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—81no—
216C4×C43—81no—
217C4×C43—81no—
218C4×C43#54811yescharacteristic
219C4×C43#57711yescharacteristic
220Dic43—21no—
221Dic43—21no—
222Dic43—21no—
223Dic43—81no—
224Dic43—81no—
225Dic43—81no—
226Dic43#50812yes—
227#3393—431no—
228#3380—431no—
229#2242—431no—
230#2242D4311yescharacteristic, complemented
231#2241—431no—
232#2229—431no—
233#2229—431no—
234#2226—431no—
235#2210—431no—
236#2210—431no—
237#2208—431no—
238Q8×C16—431no—
239C4×SD32—431no—
240C4×SD32—431no—
241C4×D16—431no—
242C2×C43—161no—
243C2×C43#335811yescharacteristic
244C2×C43C2×#50811yescharacteristic
245C2×C43#341611yescharacteristic
246D43—82no—
247#556—861no—
248#554—861no—
249C2×SD32—431no—
250C2×SD32—431no—
251C2×D16—431no—
252#500—431no—
253#499—431no—
254#499C2×D4311yescharacteristic
255#495—431no—
256#495C2×D4311yescharacteristic
257#494—431no—
258#478—861no—
259#478—861no—
260#476—861no—
261#464—861no—
262#464—861no—
263#461—861no—
264C8×Q8—431no—
265C4×Q16—431no—
266C4×Q16—431no—
267C4×D8—431no—
268C4×D8—431no—
269C4×D8—431no—
270C4×D8—431no—
271#367—431no—
272#367—431no—
273#366—431no—
274C4⋊C16—431no—
275C4⋊C16—431no—
276C4⋊C16—431no—
277#358—431no—
278#358—431no—
279#358—431no—
280#358—431no—
281#358C2×D4311yescharacteristic
282#358C2×D4311yescharacteristic
283#357—431no—
284#357—431no—
285#357C2×D4311yescharacteristic
286#357C2×D4311yescharacteristic
287C4×C16—431no—
288C4×C16—431no—
289C4×C16C2×D4311yescharacteristic
290C43#3392711yescharacteristic, complemented, Sylow
291C2×Q16—431no—
292C2×Q16—861no—
293C2×Q16C22×D4311yescharacteristic
294C2×SD16—21no—
295C2×SD16—861no—
296C2×D8—431no—
297C2×D8C22×D4311yescharacteristic
298C4⋊Q8—861no—
299C4⋊Q8—861no—
300#126—1721no—
301#126—1721no—
302#125—21no—
303#125—861no—
304#124—21no—
305#124—861no—
306C22⋊Q8—1721no—
307C22⋊Q8—1721no—
308C22⋊Q8—1721no—
309C22⋊Q8—1721no—
310C4×Q8—431no—
311C4×Q8—861no—
312C4×Q8—861no—
313C4×D4—861no—
314C4×D4—861no—
315C4×D4—861no—
316C4×D4—861no—
317#117—1721no—
318C2×C4⋊C4—1721no—
319SD32—862no—
320SD32—862no—
321D16—862no—
322C2×C16—431no—
323C2×C16—431no—
324C2×C16C22×D4311yescharacteristic
325C2×C16C22×D4311yescharacteristic
326#107—431no—
327#107—431no—
328#107—861no—
329#107C22×D4311yescharacteristic
330#107C22×D4311yescharacteristic
331#106—21no—
332#106—861no—
333C4⋊C8—431no—
334C4⋊C8—431no—
335C4⋊C8—431no—
336#103—861no—
337#103—861no—
338#102—861no—
339#102—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—861no—
351C22×C4—1721no—
352C22×C4—1721no—
353C22×C4—1721no—
354C22×C4—1721no—
355Q16—21no—
356Q16—21no—
357Q16—861no—
358Q16—861no—
359Q16—3441no—
360SD16—81no—
361SD16—3441no—
362D8—21no—
363D8—21no—
364D8—432no—
365D8—861no—
366C2×C8—431no—
367C2×C8—431no—
368C2×C8D4×D4311yescharacteristic
369C2×C8C23×D4311yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—431no—
375C4⋊C4—431no—
376C4⋊C4—431no—
377C4⋊C4—861no—
378C4⋊C4—861no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C4⋊C4—1721no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C42—431no—
395C42—431no—
396C42—1721no—
397C42—1721no—
398C42D4×D4311yescharacteristic
399C16—21no—
400C16—21no—
401C16—861no—
402C16—861no—
403C23—41no—
404C23—1721no—
405Q8—41no—
406Q8—41no—
407Q8—862no—
408Q8—1721no—
409Q8—1721no—
410Q8—6881no—
411D4—41no—
412D4—41no—
413D4—862no—
414D4—1721no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—431no—
419C2×C4—431no—
420C2×C4—431no—
421C2×C4—431no—
422C2×C4—3442no—
423C2×C4—3442no—
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—
435C8#41×D4311yescharacteristic
436C8#1306337211yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—3441no—
441C22—3441no—
442C22—1722no—
443C22C2×D8×D4311yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—432no—
450C4—861no—
451C4—861no—
452C4—861no—
453C4—3441no—
454C4—3441no—
455C4—3441no—
456C4#1458355711yescharacteristic
457C4#1458370511yescharacteristic
458C2—161no—
459C2—3442no—
460C2#1914722711yescharacteristic
461C2#508×D4311yescharacteristic
462C2#1914773811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2242C2
socleC22×C43C22×D8
prime radicalC2×#13063266C22
hypercenter#2242D43
hypocenterC43#33927
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
1. #19147580C2semidirect
2. #19147459C2semidirect
3. #19136825C2semidirect
4. #19136821C2semidirect
5. #19136757C2semidirect
6. #19136756C2semidirect
7. #19136740C2semidirect
10. #19136639C2semidirect
11. C16×Dic86C2semidirect
12. C4×#13063270C2semidirect
13. #19136444C2semidirect
15. C43×#2242C2semidirect
230. #2242D43semidirect
290. C43#33927semidirect

Maximal subgroups

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

subgroupindex
#191475802
#191474592
#191368252
#191368212
#191367572
#191367562
#191367402
#191366492
#191366472
#191366392
C16×Dic862
C4×#130632702
#191364442
#191364392
C43×#22422
#3392743