Finite Group Databasebeta

← #25254389

Subgroups — #25254389

Order 11008.

476 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#19147600C211yesmaximal, characteristic, complemented
2#19147462C211yesmaximal, characteristic
3#19136841C211yesmaximal, characteristic, complemented
4#19136839C211yesmaximal, characteristic, complemented
5#19136821C211yesmaximal, characteristic, complemented
6#19136759C211yesmaximal, characteristic, complemented
7#19136758C211yesmaximal, characteristic, complemented
8#19136746C211yesmaximal, characteristic, complemented
9#19136640C211yesmaximal, characteristic
10#19136638C211yesmaximal, characteristic
11#19136638C211yesmaximal, characteristic
12#19136501C211yesmaximal, characteristic, complemented
13#19136456C211yesmaximal, characteristic
14#19136450C211yesmaximal, characteristic
15C43×#2175C211yesmaximal, characteristic
16#14583627—21no—
17#14583608—21no—
18C2×#13063269C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20#14583303C2211yescharacteristic
21#14583301C2211yescharacteristic
22#14583300C2211yescharacteristic
23#14583279C2211yescharacteristic
24#14583277C2211yescharacteristic
25#14583277C2211yescharacteristic
26#14583201—21no—
27#14583199—21no—
28#14583187—21no—
29#14583109—21no—
30#14583108—21no—
31#14583108—21no—
32C8×Dic86C2211yescharacteristic
33#14582993C2211yescharacteristic
34#14582993C2211yescharacteristic
35D8×Dic43C2211yescharacteristic
36D8×Dic43C2211yescharacteristic
37#14582726C2211yescharacteristic
38#14582724C2211yescharacteristic
39C4⋊(C43⋊C16)C2211yescharacteristic
40Dic43⋊C16C2211yescharacteristic
41Dic43⋊C16C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582704C2211yescharacteristic
44#14582704C2211yescharacteristic
45#14582704C2211yescharacteristic
46#14582703C2211yescharacteristic
47#14582703C2211yescharacteristic
48#14582702C2211yescharacteristic
49#14582702C2211yescharacteristic
50#14582674C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×SD32×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C4×D8×C43C2211yescharacteristic
55C43×#366C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×#346C2211yescharacteristic
59C2×Dic172—21no—
60C2×Dic172C2311yescharacteristic
61C2×Dic172C2311yescharacteristic
62C2×#10621885—21no—
63C2×#10621885—21no—
64#13063325—21no—
65#13063324—21no—
66#13063323—21no—
67#13063323—21no—
68#13063317—21no—
69#13063317—41no—
70#13063316—21no—
71#13063315—41no—
72#13063315—41no—
73#13063304—41no—
74#13063302—41no—
75#13063302—41no—
76C4×Dic86—41no—
77C4×Dic86D411yescharacteristic
78#13063290—21no—
79#13063290—21no—
80D4×Dic43—21no—
81D4×Dic43—21no—
82C2×Dic43⋊C4—41no—
83#13063269—22no—
84#13063269—22no—
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063258—21no—
90#13063257—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)D411yescharacteristic
93Dic43⋊C8D411yescharacteristic
94Dic43⋊C8D411yescharacteristic
95#13063248—21no—
96#13063248—21no—
97#13063246—21no—
98#13063246—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×Dic86—21no—
119C2×Dic86—21no—
120C2×Dic86—41no—
121C2×Dic86D811yescharacteristic
122Q16×C43—21no—
123Q16×C43—21no—
124D8×C43—21no—
125D8×C43#4112yes—
126C2×C8×C43C2×D411yescharacteristic
127C2×C8×C43C2411yescharacteristic
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—41no—
131C22⋊C4×C43—41no—
132C42×C43—41no—
133C42×C43C2×D411yescharacteristic
134C22⋊Dic43—41no—
135C22⋊Dic43—41no—
136#10621885—81no—
137#10621885—81no—
138C4⋊Dic43—21no—
139C4⋊Dic43—21no—
140C4⋊Dic43—41no—
141C4⋊Dic43—41no—
142C4⋊Dic43—41no—
143C4⋊Dic43D811yescharacteristic
144Dic43⋊C4—41no—
145Dic43⋊C4—41no—
146Dic43⋊C4—41no—
147Dic43⋊C4—41no—
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4D811yescharacteristic
155Dic43⋊C4D811yescharacteristic
156C4×Dic43—41no—
157C4×Dic43—41no—
158C4×Dic43C2×D411yescharacteristic
159C4×Dic43C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162Dic172—21no—
163Dic172—21no—
164Dic172—21no—
165Dic172—21no—
166Dic172—81no—
167C16×C43—21no—
168C16×C43—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C23×C43—41no—
172Q8×C43—41no—
173Q8×C43—41no—
174D4×C43—22no—
175D4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—161no—
180C2×C4×C43C2×D811yescharacteristic
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—82no—
188C2×Dic43—161no—
189C2×Dic43C2×D811yescharacteristic
190C2×Dic43C2×D811yescharacteristic
191C2×Dic43C2×D811yescharacteristic
192C2×Dic43C2×D811yescharacteristic
193Dic86—22no—
194Dic86—41no—
195Dic86—41no—
196Dic86—41no—
197Dic86—41no—
198Dic86—161no—
199C8×C43—21no—
200C8×C43C2×#4111yescharacteristic
201C8×C432−1+411yescharacteristic
202C43⋊C8—21no—
203C43⋊C8—21no—
204#33939—431nomaximal, Sylow
205C22×C43—42no—
206C22×C43—81no—
207C22×C43—81no—
208C22×C43C22×D811yescharacteristic
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—81no—
212C4×C43—81no—
213C4×C43—81no—
214C4×C43#54811yescharacteristic
215C4×C43#57711yescharacteristic
216Dic43—21no—
217Dic43—21no—
218Dic43—21no—
219Dic43—81no—
220Dic43—81no—
221Dic43—81no—
222Dic43—81no—
223Dic43#51012yes—
224#3395—431no—
225#3380—431no—
226#2245—431no—
227#2245—431no—
228#2241—431no—
229#2229—431no—
230#2229—431no—
231#2227—431no—
232#2208—431no—
233#2208—431no—
234#2208—431no—
235#2183—431no—
236#2175—431no—
237#2175D4311yescharacteristic
238C4×SD32—431no—
239C2×C43—82no—
240C2×C43#335811yescharacteristic
241C2×C43C2×#51011yescharacteristic
242C2×C43#341611yescharacteristic
243#557—861no—
244#554—861no—
245C2×SD32—431no—
246C2×SD32—431no—
247C2×SD32C2×D4311yescharacteristic
248#500—431no—
249#499—431no—
250#499—431no—
251#494—431no—
252#494—431no—
253#494—431no—
254#478—861no—
255#478—861no—
256#476—861no—
257#462—861no—
258#462—861no—
259#462—861no—
260C8×Q8—431no—
261C4×Q16—431no—
262C4×Q16—431no—
263C4×Q16C2×D4311yescharacteristic
264C4×D8—431no—
265C4×D8—431no—
266C4×D8C2×D4311yescharacteristic
267#367—431no—
268#366—431no—
269#366C2×D4311yescharacteristic
270C4⋊C16—431no—
271C4⋊C16—431no—
272C4⋊C16—431no—
273#358—431no—
274#358—431no—
275#358—431no—
276#358—431no—
277#358—431no—
278#358—431no—
279#358—431no—
280#358—431no—
281#358C2×D4311yescharacteristic
282#357C2×D4311yescharacteristic
283#346—431no—
284#346C2×D4311yescharacteristic
285C4×C16—431no—
286C43#3393911yescharacteristic, complemented, Sylow
287C2×Q16—431no—
288C2×Q16—431no—
289C2×Q16—861no—
290C2×Q16—861no—
291C2×Q16—861no—
292C2×Q16C22×D4311yescharacteristic
293C2×D8C22×D4311yescharacteristic
294C4⋊Q8—861no—
295C4⋊Q8—861no—
296C4⋊Q8—861no—
297C4⋊Q8—861no—
298#125—861no—
299#125—861no—
300#125—1721no—
301#125—1721no—
302#125—1721no—
303C22⋊Q8—1721no—
304C22⋊Q8—1721no—
305C22⋊Q8—1721no—
306C4×Q8—21no—
307C4×Q8—431no—
308C4×Q8—861no—
309C4×Q8—861no—
310C4×Q8—1721no—
311C4×D4—21no—
312C4×D4—861no—
313C4×D4—861no—
314C2×C4⋊C4—1721no—
315SD32—22no—
316SD32—862no—
317SD32—862no—
318C2×C16—431no—
319C2×C16—431no—
320C2×C16C22×D4311yescharacteristic
321C2×C16C22×D4311yescharacteristic
322#107—431no—
323#107—431no—
324#107—861no—
325#107C22×D4311yescharacteristic
326#107C22×D4311yescharacteristic
327#106—861no—
328#106—861no—
329C4⋊C8—431no—
330C4⋊C8—431no—
331C4⋊C8—431no—
332#103—21no—
333#103—861no—
334#103—861no—
335#102—21no—
336#102—861no—
337#102—861no—
338C4×C8—431no—
339C4×C8—431no—
340C4×C8C22×D4311yescharacteristic
341C2×Q8—21no—
342C2×Q8—431no—
343C2×Q8—861no—
344C2×Q8—861no—
345C2×Q8—1721no—
346C2×D4—21no—
347C22×C4—41no—
348C22×C4—1721no—
349C22×C4—1721no—
350Q16—21no—
351Q16—21no—
352Q16—861no—
353Q16—861no—
354Q16—861no—
355Q16—861no—
356Q16—3441no—
357Q16—3441no—
358Q16—3441no—
359D8—21no—
360D8#1062189812yes—
361C2×C8—431no—
362C2×C8—431no—
363C2×C8D4×D4311yescharacteristic
364C2×C8C23×D4311yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—41no—
368C4⋊C4—431no—
369C4⋊C4—431no—
370C4⋊C4—431no—
371C4⋊C4—861no—
372C4⋊C4—861no—
373C4⋊C4—1721no—
374C4⋊C4—1721no—
375C4⋊C4—1721no—
376C4⋊C4—1721no—
377C4⋊C4—1721no—
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—41no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C42—41no—
390C42—431no—
391C42—431no—
392C42—1721no—
393C42—1721no—
394C42D4×D4311yescharacteristic
395C16—21no—
396C16—21no—
397C16—861no—
398C16—861no—
399C23—41no—
400Q8—41no—
401Q8—41no—
402Q8—862no—
403Q8—1721no—
404Q8—1721no—
405Q8—1721no—
406Q8—1721no—
407Q8—6881no—
408D4—22no—
409D4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—161no—
414C2×C4—431no—
415C2×C4—431no—
416C2×C4—431no—
417C2×C4—431no—
418C2×C4—3442no—
419C2×C4—1721no—
420C2×C4—1721no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—6881no—
424C2×C4D8×D4311yescharacteristic
425C2×C4D8×D4311yescharacteristic
426C2×C4C2×D4×D4311yescharacteristic
427C8—21no—
428C8—861no—
429C8—861no—
430C8C2×#1062189811yescharacteristic
431C8#1306337211yescharacteristic
432C22—42no—
433C22—81no—
434C22—81no—
435C22C2×D8×D4311yescharacteristic
436C4—21no—
437C4—21no—
438C4—81no—
439C4—81no—
440C4—81no—
441C4—432no—
442C4—861no—
443C4—861no—
444C4—861no—
445C4—3441no—
446C4—3441no—
447C4—3441no—
448C4—3441no—
449C4#1458355811yescharacteristic
450C4#1458370611yescharacteristic
451C2—82no—
452C2#1914722811yescharacteristic
453C2#510×D4311yescharacteristic
454C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2175C2
socleC22×C43C22×D8
prime radicalC2×D8×C43C23
hypercenter#2175D43
hypocenterC43#33939
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. #19147600C2semidirect
3. #19136841C2semidirect
4. #19136839C2semidirect
5. #19136821C2semidirect
6. #19136759C2semidirect
7. #19136758C2semidirect
8. #19136746C2semidirect
12. #19136501C2semidirect
286. C43#33939semidirect

Maximal subgroups

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

subgroupindex
#191476002
#191474622
#191368412
#191368392
#191368212
#191367592
#191367582
#191367462
#191366402
#191366382
#191365012
#191364562
#191364502
C43×#21752
#3393943