Finite Group Databasebeta

← #25254326

Subgroups — #25254326

Order 11008.

508 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147583C211yesmaximal, characteristic, complemented
2D8×Dic86C211yesmaximal, characteristic, complemented
3#19136833C211yesmaximal, characteristic, complemented
4#19136832C211yesmaximal, characteristic, complemented
5#19136821C211yesmaximal, characteristic, complemented
6#19136747C211yesmaximal, characteristic, complemented
7#19136746C211yesmaximal, characteristic, complemented
8#19136731C211yesmaximal, characteristic, complemented
9#19136652C211yesmaximal, characteristic
10#19136650C211yesmaximal, characteristic
11#19136638C211yesmaximal, characteristic, complemented
12#19136501C211yesmaximal, characteristic, complemented
13#19136456C211yesmaximal, characteristic, complemented
14#19136439C211yesmaximal, characteristic
15C43×#2175C211yesmaximal, characteristic, complemented
16#14583621—21no—
17D4×Dic86—21no—
18C2×#13063269C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20#14583304C2211yescharacteristic
21#14583303C2211yescharacteristic
22#14583303C2211yescharacteristic
23#14583284C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583277C2211yescharacteristic
26#14583179—21no—
27#14583177—21no—
28#14583177—21no—
29#14583124—21no—
30#14583121—21no—
31#14583103—21no—
32C8×Dic86C2211yescharacteristic
33#14582993C2211yescharacteristic
34D8×Dic43C2211yescharacteristic
35D8×Dic43C2211yescharacteristic
36#14582981C2211yescharacteristic
37#14582724C2211yescharacteristic
38#14582724C2211yescharacteristic
39C4⋊(C43⋊C16)C2211yescharacteristic
40Dic43⋊C16C2211yescharacteristic
41Dic43⋊C16C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582704C2211yescharacteristic
44#14582703C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582702C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582701C2211yescharacteristic
49#14582699C2211yescharacteristic
50#14582674C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×SD32×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C4×D8×C43C2211yescharacteristic
55C43×#366C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×#346C2211yescharacteristic
59C22×Dic86—41no—
60C2×Dic172C2311yescharacteristic
61C2×#10621885—21no—
62C2×#10621873—21no—
63C2×#10621884—21no—
64C2×D344C2311yescharacteristic
65#13063325—21no—
66#13063324—21no—
67#13063324—21no—
68#13063323—21no—
69#13063320—41no—
70#13063319—41no—
71#13063314—21no—
72#13063313—21no—
73#13063304—41no—
74#13063303—41no—
75#13063302—41no—
76#13063302—41no—
77C4×Dic86D411yescharacteristic
78#13063290—21no—
79D4×Dic43—21no—
80D4×Dic43—21no—
81#13063287—21no—
82#13063282—41no—
83#13063269—22no—
84#13063266—22no—
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87#13063259—21no—
88#13063259C2311yescharacteristic
89#13063259C2311yescharacteristic
90#13063258—21no—
91#13063258—21no—
92C4⋊(C43⋊C8)D411yescharacteristic
93Dic43⋊C8D411yescharacteristic
94Dic43⋊C8D411yescharacteristic
95#13063248—21no—
96#13063246—21no—
97#13063246—21no—
98#13063245—21no—
99C8×Dic43C2311yescharacteristic
100C8×Dic43C2311yescharacteristic
101C2×Q16×C43C2311yescharacteristic
102C2×D8×C43C2311yescharacteristic
103C4×Q8×C43—21no—
104C4×D4×C43—21no—
105SD32×C43—22no—
106C2×C16×C43C2311yescharacteristic
107C2×C16×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#103×C43—21no—
111#102×C43—21no—
112C4×C8×C43C2311yescharacteristic
113C2×Q8×C43—21no—
114C2×D4×C43—21no—
115C22×C4×C43—41no—
116C22×Dic43—41no—
117C22×Dic43—41no—
118C2×D172—21no—
119C2×C4×D43—41no—
120C2×Dic86—21no—
121C2×Dic86—41no—
122C2×Dic86—41no—
123C2×Dic86—41no—
124C2×Dic86—84no—
125C2×Dic86D811yescharacteristic
126Q16×C43—21no—
127Q16×C43—21no—
128D8×C43—21no—
129D8×C43#4112yes—
130C2×C8×C43C2×D411yescharacteristic
131C2×C8×C43C2411yescharacteristic
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—41no—
135C22⋊C4×C43—41no—
136C42×C43—41no—
137C42×C43C2×D411yescharacteristic
138C22⋊Dic43—41no—
139C22⋊Dic43—41no—
140#10621885—81no—
141#10621884—81no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4—41no—
146(C2×D43)⋊C4—41no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
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×Dic43C2×D411yescharacteristic
160C4×Dic43C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162C2×C43⋊C8C2×D411yescharacteristic
163Dic172—21no—
164Dic172—21no—
165D344—21no—
166D344—21no—
167#10621873—81no—
168C16×C43—21no—
169C16×C43—21no—
170C43⋊C16—21no—
171C43⋊C16—21no—
172C23×C43—41no—
173C22×D43—41no—
174Q8×C43—41no—
175Q8×C43—41no—
176D4×C43—22no—
177D4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—82no—
182C2×C4×C43C2×D811yescharacteristic
183C2×C4×C43C2×D811yescharacteristic
184C2×C4×C43C22×D411yescharacteristic
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—82no—
189C2×Dic43—82no—
190C2×Dic43C2×D811yescharacteristic
191C2×Dic43C2×D811yescharacteristic
192C2×Dic43C2×D811yescharacteristic
193C2×Dic43C2×D811yescharacteristic
194D172—41no—
195D172—41no—
196C4×D43—82no—
197Dic86—22no—
198Dic86—41no—
199Dic86—41no—
200Dic86—82no—
201Dic86—82no—
202Dic86—82no—
203C8×C43—21no—
204C8×C43C2×#4111yescharacteristic
205C8×C432−1+411yescharacteristic
206C43⋊C8—21no—
207C43⋊C8—21no—
208#33934—431nomaximal, Sylow
209C22×C43—42no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43C22×D811yescharacteristic
213C2×D43—81no—
214C2×D43—81no—
215C2×D43—81no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—81no—
219C4×C43—81no—
220C4×C43—81no—
221C4×C43#54811yescharacteristic
222C4×C43#57711yescharacteristic
223Dic43—21no—
224Dic43—21no—
225Dic43—21no—
226Dic43—81no—
227Dic43—81no—
228Dic43—81no—
229Dic43#50912yes—
230#3393—431no—
231Q8×D8—431no—
232#2243—431no—
233#2243—431no—
234#2241—431no—
235#2227—431no—
236#2227—431no—
237#2224—431no—
238#2210—431no—
239#2210—431no—
240#2208—431no—
241#2183—431no—
242#2175—431no—
243#2175D4311yescharacteristic, complemented
244C4×D16—431no—
245C2×C43—82no—
246C2×C43#335811yescharacteristic
247C2×C43C2×#50911yescharacteristic
248C2×C43#341711yescharacteristic
249D43—161no—
250#556—861no—
251D4×Q8—861no—
252C2×SD32—431no—
253C2×SD32C2×D4311yescharacteristic
254C2×D16—431no—
255#500—431no—
256#500—431no—
257#500—431no—
258#495—431no—
259#495—431no—
260#494—431no—
261#474—861no—
262#474—861no—
263#474—861no—
264#464—861no—
265#464—861no—
266#461—861no—
267C8×Q8—431no—
268C4×Q16—431no—
269C4×Q16C2×D4311yescharacteristic
270C4×D8—431no—
271C4×D8—431no—
272C4×D8—431no—
273C4×D8C2×D4311yescharacteristic
274#366—431no—
275#366—431no—
276#366C2×D4311yescharacteristic
277C4⋊C16—431no—
278C4⋊C16—431no—
279C4⋊C16—431no—
280#358—431no—
281#358—431no—
282#358—431no—
283#358—431no—
284#358—431no—
285#358C2×D4311yescharacteristic
286#357—431no—
287#357—431no—
288#357—431no—
289#357C2×D4311yescharacteristic
290#346—431no—
291#346C2×D4311yescharacteristic
292C4×C16—431no—
293C43#3393411yescharacteristic, complemented, Sylow
294C22×Q8—1721no—
295C2×Q16—431no—
296C2×Q16—861no—
297C2×Q16C22×D4311yescharacteristic
298C2×SD16—861no—
299C2×SD16—861no—
300C2×D8—431no—
301C2×D8C22×D4311yescharacteristic
302C4⋊Q8—861no—
303C4⋊Q8—861no—
304C4⋊Q8—861no—
305C4⋊Q8—861no—
306#126—1721no—
307#126—1721no—
308#124—861no—
309#124—861no—
310C22⋊Q8—1721no—
311C22⋊Q8—1721no—
312C22⋊Q8—1721no—
313C22⋊Q8—1721no—
314C4×Q8—21no—
315C4×Q8—431no—
316C4×Q8—861no—
317C4×D4—21no—
318C4×D4—861no—
319C4×D4—861no—
320C4×D4—861no—
321#117—1721no—
322SD32—22no—
323SD32—862no—
324D16—862no—
325C2×C16—431no—
326C2×C16—431no—
327C2×C16C22×D4311yescharacteristic
328C2×C16C22×D4311yescharacteristic
329#107—431no—
330#107—431no—
331#107—861no—
332#107—861no—
333#107—861no—
334#107C22×D4311yescharacteristic
335#107C22×D4311yescharacteristic
336C4⋊C8—431no—
337C4⋊C8—431no—
338C4⋊C8—431no—
339#103—21no—
340#103—861no—
341#102—21no—
342#102—861no—
343#102—861no—
344#102—861no—
345C4×C8—431no—
346C4×C8—431no—
347C4×C8C22×D4311yescharacteristic
348C2×Q8—21no—
349C2×Q8—431no—
350C2×Q8—861no—
351C2×Q8—3444no—
352C2×Q8—1721no—
353C2×Q8—1721no—
354C2×Q8—1721no—
355C2×D4—21no—
356C2×D4—861no—
357C22×C4—41no—
358C22×C4—1721no—
359C22×C4—1721no—
360C22×C4—1721no—
361Q16—21no—
362Q16—21no—
363Q16—861no—
364Q16—861no—
365Q16—3441no—
366SD16—3441no—
367SD16—3441no—
368D8—21no—
369D8—861no—
370D8—861no—
371D8#1062189812yes—
372C2×C8—431no—
373C2×C8—431no—
374C2×C8D4×D4311yescharacteristic
375C2×C8C23×D4311yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—431no—
380C4⋊C4—431no—
381C4⋊C4—431no—
382C4⋊C4—861no—
383C4⋊C4—861no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C4⋊C4—1721no—
387C4⋊C4—1721no—
388C4⋊C4—1721no—
389C4⋊C4—1721no—
390C22⋊C4—41no—
391C22⋊C4—1721no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C22⋊C4—1721no—
395C22⋊C4—1721no—
396C22⋊C4—1721no—
397C22⋊C4—1721no—
398C42—41no—
399C42—431no—
400C42—431no—
401C42—1721no—
402C42D4×D4311yescharacteristic
403C16—21no—
404C16—21no—
405C16—861no—
406C16—861no—
407C23—41no—
408C23—1721no—
409Q8—41no—
410Q8—41no—
411Q8—862no—
412Q8—3442no—
413Q8—3442no—
414Q8—3442no—
415Q8—1721no—
416Q8—1721no—
417D4—22no—
418D4—41no—
419D4—1721no—
420D4—1721no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—82no—
425C2×C4—431no—
426C2×C4—431no—
427C2×C4—431no—
428C2×C4—431no—
429C2×C4—3442no—
430C2×C4—3442no—
431C2×C4—3442no—
432C2×C4—1721no—
433C2×C4—1721no—
434C2×C4—1721no—
435C2×C4D8×D4311yescharacteristic
436C2×C4D8×D4311yescharacteristic
437C2×C4C2×D4×D4311yescharacteristic
438C8—21no—
439C8—861no—
440C8—861no—
441C8C2×#1062189811yescharacteristic
442C8#1306337211yescharacteristic
443C22—42no—
444C22—81no—
445C22—81no—
446C22—3441no—
447C22—3441no—
448C22—3441no—
449C22C2×D8×D4311yescharacteristic
450C4—21no—
451C4—21no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—432no—
456C4—861no—
457C4—861no—
458C4—861no—
459C4—3441no—
460C4—3441no—
461C4—3441no—
462C4#1458355811yescharacteristic
463C4#1458370611yescharacteristic
464C2—82no—
465C2—6881no—
466C2#1914722811yescharacteristic
467C2#509×D4311yescharacteristic
468C2#1914774711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2175C2
socleC22×C43C22×D8
prime radicalC2×#13063266C22
hypercenter#2175D43
hypocenterC43#33934
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. #19147583C2semidirect
2. D8×Dic86C2semidirect
3. #19136833C2semidirect
4. #19136832C2semidirect
5. #19136821C2semidirect
6. #19136747C2semidirect
7. #19136746C2semidirect
8. #19136731C2semidirect
11. #19136638C2semidirect
12. #19136501C2semidirect
13. #19136456C2semidirect
15. C43×#2175C2semidirect
243. #2175D43semidirect
293. C43#33934semidirect

Maximal subgroups

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

subgroupindex
#191475832
D8×Dic862
#191368332
#191368322
#191368212
#191367472
#191367462
#191367312
#191366522
#191366502
#191366382
#191365012
#191364562
#191364392
C43×#21752
#3393443