Finite Group Databasebeta

← #25254218

Subgroups — #25254218

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147023C211yesmaximal, characteristic
2#19146985C211yesmaximal, characteristic
3#19136876C211yesmaximal, characteristic, complemented
4#19136805C211yesmaximal, characteristic, complemented
5#19136803C211yesmaximal, characteristic, complemented
6#19136794C211yesmaximal, characteristic, complemented
7#19136792C211yesmaximal, characteristic, complemented
8#19136746C211yesmaximal, characteristic, complemented
9#19136736C211yesmaximal, characteristic, complemented
10#19136704C211yesmaximal, characteristic, complemented
11#19136703C211yesmaximal, characteristic, complemented
12#19136453C211yesmaximal, characteristic, complemented
13#19136425C211yesmaximal, characteristic
14#19136380C211yesmaximal, characteristic, complemented
15C43×#2159C211yesmaximal, characteristic, complemented
16#14583617—21no—
17#14583604—21no—
18C2×Dic344C2211yescharacteristic
19C2×#13063264C2211yescharacteristic
20#14583303C2211yescharacteristic
21#14583303C2211yescharacteristic
22#14583243—21no—
23#14583240—21no—
24#14583236—21no—
25#14583234—21no—
26#14583193—21no—
27#14583183—21no—
28#14583141C2211yescharacteristic
29#14583141C2211yescharacteristic
30#14583140C2211yescharacteristic
31#14583140C2211yescharacteristic
32#14582993C2211yescharacteristic
33#14582993C2211yescharacteristic
34C8×C22⋊D43C2211yescharacteristic
35#14582936C2211yescharacteristic
36#107×D43C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582726C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582726C2211yescharacteristic
41#14582724C2211yescharacteristic
42Dic43⋊C16C2211yescharacteristic
43#14582704C2211yescharacteristic
44#14582704C2211yescharacteristic
45#14582702C2211yescharacteristic
46#14582702C2211yescharacteristic
47#14582702C2211yescharacteristic
48#14582702C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×M32×C43C2211yescharacteristic
53C43×#427C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C43×#367C2211yescharacteristic
56C43×#367C2211yescharacteristic
57C43×#366C2211yescharacteristic
58C43×#366C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×Dic172C2311yescharacteristic
61C2×C8×D43C2311yescharacteristic
62#13063324—21no—
63#13063324—21no—
64#13063319—41no—
65#13063318—41no—
66#13063315—41no—
67#13063311—41no—
68#13063305—21no—
69#13063305—21no—
70#13063304—21no—
71#13063304—21no—
72#13063304—41no—
73#13063303—41no—
74C4×Dic86—41no—
75#13063290—21no—
76#13063290—21no—
77C4×C22⋊D43—41no—
78C4×C22⋊D43D411yescharacteristic
79#13063283—21no—
80C4⋊C4×D43—21no—
81Dic344—22no—
82#13063264—22no—
83C2×C43⋊C16C2311yescharacteristic
84C2×C43⋊C16C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063256—21no—
91Dic43⋊C8D411yescharacteristic
92#13063250—21no—
93#13063250—21no—
94#13063248—21no—
95#13063248—21no—
96#13063248—21no—
97#13063248—21no—
98C22⋊(C43⋊C8)D411yescharacteristic
99(C2×D43)⋊C8D411yescharacteristic
100C8×Dic43C2311yescharacteristic
101C22×C8×C43C2311yescharacteristic
102#117×C43—21no—
103C2×C4⋊C4×C43—21no—
104M32×C43—22no—
105C2×C16×C43C2311yescharacteristic
106C2×C16×C43C2311yescharacteristic
107#107×C43—21no—
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#106×C43—21no—
113C22×C4×C43—41no—
114C22×C4×C43C2×D411yescharacteristic
115C2×C22⋊D43D811yescharacteristic
116C2×C4×D43—41no—
117C2×C4×D43C2×D411yescharacteristic
118C2×Dic86—21no—
119C2×Dic86—21no—
120C2×Dic86—41no—
121C2×Dic86—41no—
122C2×C8×C43—21no—
123C2×C8×C43—21no—
124C2×C8×C43C2×D411yescharacteristic
125C2×C8×C43C2411yescharacteristic
126C4⋊C4×C43—21no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—41no—
131C22⋊C4×C43—41no—
132C42×C43—41no—
133C22⋊Dic43—41no—
134C22⋊Dic43—41no—
135C22⋊Dic43D811yescharacteristic
136(C2×D43)⋊C4—41no—
137(C2×D43)⋊C4—41no—
138(C2×D43)⋊C4—41no—
139(C2×D43)⋊C4D811yescharacteristic
140C4⋊Dic43—21no—
141C4⋊Dic43—21no—
142C4⋊Dic43—41no—
143C4⋊Dic43—41no—
144Dic43⋊C4—41no—
145Dic43⋊C4—41no—
146Dic43⋊C4—41no—
147Dic43⋊C4—41no—
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4D811yescharacteristic
152C4×Dic43—41no—
153C4×Dic43—41no—
154C4×Dic43—41no—
155C4×Dic43C2×D411yescharacteristic
156C2×C43⋊C8C2×D411yescharacteristic
157C2×C43⋊C8C2×D411yescharacteristic
158Dic172—21no—
159Dic172—21no—
160Dic172—21no—
161Dic172—21no—
162C8×D43—21no—
163C8×D43—21no—
164C16×C43—21no—
165C16×C43#4112yes—
166C43⋊C16—21no—
167C43⋊C16—21no—
168C23×C43C2×D811yescharacteristic
169C22×D43C2×D811yescharacteristic
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—161no—
177C2×C4×C43C2×D811yescharacteristic
178C2×C4×C43C22×D411yescharacteristic
179C22⋊D43—22no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43C2×D811yescharacteristic
185C2×Dic43C2×D811yescharacteristic
186C2×Dic43C2×D811yescharacteristic
187C4×D43—21no—
188C4×D43—21no—
189C4×D43—161no—
190Dic86—41no—
191Dic86—41no—
192Dic86—41no—
193Dic86—41no—
194Dic86—82no—
195Dic86—161no—
196C8×C43—21no—
197C8×C43C2×#4111yescharacteristic
198C8×C432−1+411yescharacteristic
199C43⋊C8—21no—
200C43⋊C8—21no—
201#33923—431nomaximal, Sylow
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—21no—
205C22×C43C22×D811yescharacteristic
206C2×D43—21no—
207C2×D43—21no—
208C2×D43—21no—
209C4×C43—21no—
210C4×C43—81no—
211C4×C43—81no—
212C4×C43—81no—
213C4×C43—81no—
214C4×C43#54711yescharacteristic
215C4×C43#57811yescharacteristic
216Dic43—21no—
217Dic43—21no—
218Dic43—81no—
219Dic43—81no—
220Dic43—81no—
221Dic43—81no—
222Dic43#51012yes—
223#3342—431no—
224#3338—431no—
225#2254—431no—
226#2237—431no—
227#2237—431no—
228#2235—431no—
229#2235—431no—
230#2227—431no—
231#2225—431no—
232#2219—431no—
233#2219—431no—
234C4×Q32—431no—
235#2169—431no—
236#2159—431no—
237#2159D4311yescharacteristic, complemented
238C2×C43—41no—
239C2×C43#333411yescharacteristic
240C2×C43C2×#51011yescharacteristic
241C2×C43#341611yescharacteristic
242D43—41no—
243#556—861no—
244#554—861no—
245C2×Q32—431no—
246C2×M32—431no—
247C2×M32C2×D4311yescharacteristic
248#500—431no—
249#500—431no—
250#485—861no—
251#485—861no—
252#484—861no—
253#484—861no—
254#477—861no—
255#475—861no—
256#467—431no—
257#467—431no—
258#467—431no—
259#467—431no—
260C4×Q16—431no—
261C4×Q16—431no—
262C8×D4—431no—
263#427—431no—
264#427C2×D4311yescharacteristic
265C2×#107—431no—
266C2×#107C2×D4311yescharacteristic
267#367—431no—
268#367—431no—
269#367—431no—
270#367—431no—
271#367C2×D4311yescharacteristic
272#367C2×D4311yescharacteristic
273#366—431no—
274#366C2×D4311yescharacteristic
275#366C2×D4311yescharacteristic
276C4⋊C16—431no—
277#358—431no—
278#358—431no—
279#358—431no—
280#358—431no—
281#358—431no—
282#358—431no—
283C22⋊C16—431no—
284C22⋊C16—431no—
285C4×C16—431no—
286C43#3392311yescharacteristic, complemented, Sylow
287C2×Q16—431no—
288C2×Q16—431no—
289C22×C8—431no—
290C22×C8C22×D4311yescharacteristic
291C4⋊Q8—861no—
292C4⋊Q8—861no—
293#126—1721no—
294#126—1721no—
295#125—1721no—
296#124—1721no—
297C22⋊Q8—861no—
298C22⋊Q8—861no—
299C22⋊Q8—861no—
300C22⋊Q8—861no—
301C22⋊Q8—1721no—
302C22⋊Q8—1721no—
303C4×Q8—861no—
304C4×Q8—861no—
305C4×Q8—1721no—
306C4×D4—431no—
307C4×D4—1721no—
308#117—21no—
309#117—861no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—861no—
312Q32—862no—
313M32—22no—
314M32—862no—
315C2×C16—431no—
316C2×C16—431no—
317C2×C16C22×D4311yescharacteristic
318C2×C16C22×D4311yescharacteristic
319#107—21no—
320#107—431no—
321#107—431no—
322#107—861no—
323#107—861no—
324#107—861no—
325#107C22×D4311yescharacteristic
326#107C22×D4311yescharacteristic
327#107C22×D4311yescharacteristic
328#107C22×D4311yescharacteristic
329#106—21no—
330#106—861no—
331C4⋊C8—431no—
332#103—861no—
333#103—861no—
334#103—861no—
335#103—861no—
336#103—861no—
337#103—861no—
338C22⋊C8—431no—
339C22⋊C8—431no—
340C4×C8—431no—
341C2×Q8—861no—
342C2×Q8—861no—
343C2×Q8—1721no—
344C2×Q8—1721no—
345C2×D4—431no—
346C22×C4—41no—
347C22×C4—431no—
348C22×C4—1721no—
349C22×C4D4×D4311yescharacteristic
350Q16—861no—
351Q16—861no—
352Q16—861no—
353Q16—861no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—431no—
357C2×C8—431no—
358C2×C8—861no—
359C2×C8—861no—
360C2×C8D4×D4311yescharacteristic
361C2×C8C23×D4311yescharacteristic
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—41no—
367C4⋊C4—431no—
368C4⋊C4—861no—
369C4⋊C4—861no—
370C4⋊C4—1721no—
371C4⋊C4—1721no—
372C4⋊C4—1721no—
373C4⋊C4—1721no—
374C4⋊C4—1721no—
375C4⋊C4—1721no—
376C4⋊C4—1721no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C22⋊C4—41no—
380C22⋊C4—431no—
381C22⋊C4—431no—
382C22⋊C4—1721no—
383C22⋊C4—1721no—
384C22⋊C4—1721no—
385C22⋊C4—1721no—
386C22⋊C4—1721no—
387C42—41no—
388C42—431no—
389C42—1721no—
390C42—1721no—
391C42—1721no—
392C16—21no—
393C16—861no—
394C16—861no—
395C16#1062189812yes—
396C23—431no—
397C23D8×D4311yescharacteristic
398Q8—3442no—
399Q8—1721no—
400Q8—1721no—
401Q8—1721no—
402Q8—1721no—
403Q8—6881no—
404D4—862no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—161no—
412C2×C4—431no—
413C2×C4—431no—
414C2×C4—431no—
415C2×C4—861no—
416C2×C4—861no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—1721no—
420C2×C4—1721no—
421C2×C4—6881no—
422C2×C4D8×D4311yescharacteristic
423C2×C4C2×D4×D4311yescharacteristic
424C8—21no—
425C8—861no—
426C8—861no—
427C8C2×#1062189811yescharacteristic
428C8#1306337311yescharacteristic
429C22—21no—
430C22—21no—
431C22—21no—
432C22—861no—
433C22—861no—
434C22—861no—
435C22C2×D8×D4311yescharacteristic
436C4—21no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—81no—
441C4—432no—
442C4—861no—
443C4—861no—
444C4—3441no—
445C4—3441no—
446C4—3441no—
447C4—3441no—
448C4#1458355011yescharacteristic
449C4#1458371211yescharacteristic
450C2—41no—
451C2—1721no—
452C2#1914694011yescharacteristic
453C2#510×D4311yescharacteristic
454C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2159C2
socleC22×C43C22×D8
prime radicalC2×C22⋊D43D8
hypercenter#2159D43
hypocenterC43#33923
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
3. #19136876C2semidirect
4. #19136805C2semidirect
5. #19136803C2semidirect
6. #19136794C2semidirect
7. #19136792C2semidirect
8. #19136746C2semidirect
9. #19136736C2semidirect
10. #19136704C2semidirect
11. #19136703C2semidirect
12. #19136453C2semidirect
14. #19136380C2semidirect
15. C43×#2159C2semidirect
237. #2159D43semidirect
286. C43#33923semidirect

Maximal subgroups

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

subgroupindex
#191470232
#191469852
#191368762
#191368052
#191368032
#191367942
#191367922
#191367462
#191367362
#191367042
#191367032
#191364532
#191364252
#191363802
C43×#21592
#3392343