Finite Group Databasebeta

← #25254342

Subgroups — #25254342

Order 11008.

474 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#19147580C211yesmaximal, characteristic
2Q16×Dic86C211yesmaximal, characteristic, complemented
3#19136831C211yesmaximal, characteristic
4#19136830C211yesmaximal, characteristic
5#19136821C211yesmaximal, characteristic, complemented
6#19136740C211yesmaximal, characteristic
7#19136738C211yesmaximal, characteristic, complemented
8#19136735C211yesmaximal, characteristic, complemented
9#19136655C211yesmaximal, characteristic
10#19136643C211yesmaximal, characteristic, complemented
11#19136502C211yesmaximal, characteristic, complemented
12#19136466C211yesmaximal, characteristic, complemented
13#19136464C211yesmaximal, characteristic, complemented
14SD32×Dic43C211yesmaximal, characteristic
15C43×#2211C211yesmaximal, characteristic
16Q8×Dic86—21no—
17#14583618—21no—
18C2×#13063271C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583303C2211yescharacteristic
21#14583303C2211yescharacteristic
22#14583282C2211yescharacteristic
23#14583277C2211yescharacteristic
24#14583194—21no—
25#14583192—21no—
26#14583192—21no—
27#14583119—21no—
28#14583118—21no—
29#14583102—21no—
30C8×Dic86C2211yescharacteristic
31C4×Dic172C2211yescharacteristic
32Q16×Dic43C2211yescharacteristic
33Q16×Dic43C2211yescharacteristic
34Q16×Dic43C2211yescharacteristic
35D8×Dic43C2211yescharacteristic
36#14582727C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582726C2211yescharacteristic
39Dic43⋊C16C2211yescharacteristic
40Dic43⋊C16C2211yescharacteristic
41#14582704C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582703C2211yescharacteristic
44#14582703C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582702C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic
49#14582675C2211yescharacteristic
50#14582674C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×Q32×C43C2211yescharacteristic
53C2×SD32×C43C2211yescharacteristic
54C43×#495C2211yescharacteristic
55C4×Q16×C43C2211yescharacteristic
56C43×C4⋊C16C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621885—21no—
61C2×#10621883—21no—
62#13063325—21no—
63#13063325—41no—
64#13063324—21no—
65#13063324—21no—
66#13063324—41no—
67#13063324—41no—
68#13063323—21no—
69#13063318—41no—
70#13063318—41no—
71#13063312—21no—
72#13063302—41no—
73Q8×Dic43—21no—
74Q8×Dic43—21no—
75Q8×Dic43—21no—
76C4×Dic86—21no—
77C4×Dic86—41no—
78C4×Dic86D411yescharacteristic
79D4×Dic43—21no—
80#13063281—41no—
81#13063271—22no—
82C2×C43⋊C16C2311yescharacteristic
83C2×C43⋊C16C2311yescharacteristic
84#13063259—21no—
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063258—21no—
89#13063258—21no—
90C4⋊(C43⋊C8)D411yescharacteristic
91Dic43⋊C8D411yescharacteristic
92Dic43⋊C8D411yescharacteristic
93#13063250—21no—
94#13063249—21no—
95#13063249—21no—
96#13063249—21no—
97#13063246—21no—
98C8×Dic43C2311yescharacteristic
99C8×Dic43C2311yescharacteristic
100C2×Q16×C43C2311yescharacteristic
101C2×Q16×C43C2311yescharacteristic
102C2×SD16×C43—21no—
103C2×D8×C43C2311yescharacteristic
104#124×C43—21no—
105C4×Q8×C43—21no—
106Q32×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×Q8×C43—21no—
115C2×D4×C43—21no—
116C22×Dic43—41no—
117C2×Dic86—21no—
118C2×Dic86—41no—
119C2×Dic86—41no—
120C2×Dic86—41no—
121C2×Dic86D811yescharacteristic
122Q16×C43—21no—
123Q16×C43—21no—
124Q16×C43—21no—
125Q16×C43#4112yes—
126SD16×C43—81no—
127D8×C43—21no—
128D8×C43—21no—
129C2×C8×C43C2×D411yescharacteristic
130C2×C8×C43C2411yescharacteristic
131C4⋊C4×C43—21no—
132C4⋊C4×C43—41no—
133C22⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135C42×C43—41no—
136C42×C43C2×D411yescharacteristic
137C22⋊Dic43—41no—
138C22⋊Dic43—41no—
139C22⋊Dic43—41no—
140#10621885—81no—
141#10621883—81no—
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C4⋊Dic43—21no—
145C4⋊Dic43—41no—
146C4⋊Dic43—41no—
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×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—
172Q8×C43—22no—
173Q8×C43—41no—
174Q8×C43—41no—
175Q8×C43—41no—
176D4×C43—41no—
177D4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C2×D811yescharacteristic
183C2×C4×C43C22×D411yescharacteristic
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—82no—
189C2×Dic43C2×D811yescharacteristic
190C2×Dic43C2×D811yescharacteristic
191C2×Dic43C2×D811yescharacteristic
192C2×Dic43C2×D811yescharacteristic
193Dic86—22no—
194Dic86—41no—
195Dic86—41no—
196Dic86—161no—
197Dic86—161no—
198Dic86—161no—
199C8×C43—21no—
200C8×C43C2×#4111yescharacteristic
201C8×C432−1+411yescharacteristic
202C43⋊C8—21no—
203C43⋊C8—21no—
204#33936—431nomaximal, Sylow
205C22×C43—81no—
206C22×C43—81no—
207C22×C43—81no—
208C22×C43C22×D811yescharacteristic
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—42no—
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#3393—431no—
225Q8×Q16—431no—
226#2243—431no—
227#2243—431no—
228#2241—431no—
229#2226—431no—
230#2225—431no—
231#2225—431no—
232#2211—431no—
233#2211D4311yescharacteristic
234#2209—431no—
235#2183—431no—
236#2176—431no—
237#2176—431no—
238C4×SD32—431no—
239C2×C43—161no—
240C2×C43#335811yescharacteristic
241C2×C43C2×#51011yescharacteristic
242C2×C43#341611yescharacteristic
243Q82—861no—
244#556—861no—
245C2×Q32—431no—
246C2×Q32C2×D4311yescharacteristic
247C2×SD32C2×D4311yescharacteristic
248#500—431no—
249#500—431no—
250#500—431no—
251#495—431no—
252#495C2×D4311yescharacteristic
253#494—431no—
254#477—861no—
255#477—861no—
256#477—861no—
257#464—861no—
258#464—861no—
259#461—861no—
260C8×Q8—431no—
261C4×Q16—431no—
262C4×Q16—431no—
263C4×Q16—431no—
264C4×Q16—431no—
265C4×Q16C2×D4311yescharacteristic
266C4×D8—431no—
267#367—431no—
268#367—431no—
269#367—431no—
270C4⋊C16—431no—
271C4⋊C16—431no—
272C4⋊C16C2×D4311yescharacteristic
273#358—431no—
274#358—431no—
275#358—431no—
276#358—431no—
277#358—431no—
278#358—431no—
279#358C2×D4311yescharacteristic
280#357—431no—
281#357—431no—
282#357C2×D4311yescharacteristic
283#346—431no—
284#346—431no—
285C4×C16—431no—
286C43#3393611yescharacteristic, complemented, Sylow
287C2×Q16—431no—
288C2×Q16—861no—
289C2×Q16C22×D4311yescharacteristic
290C2×Q16C22×D4311yescharacteristic
291C2×SD16—21no—
292C2×SD16—861no—
293C2×D8C22×D4311yescharacteristic
294C4⋊Q8—861no—
295C4⋊Q8—861no—
296C4⋊Q8—861no—
297C4⋊Q8—861no—
298C4⋊Q8—1721no—
299C4⋊Q8—1721no—
300C4⋊Q8—1721no—
301#126—1721no—
302#126—1721no—
303#124—21no—
304#124—861no—
305C22⋊Q8—1721no—
306C4×Q8—21no—
307C4×Q8—431no—
308C4×Q8—861no—
309C4×Q8—861no—
310C4×Q8—861no—
311C4×Q8—861no—
312C4×Q8—1721no—
313C4×D4—861no—
314#117—1721no—
315Q32—22no—
316Q32—862no—
317SD32—22no—
318C2×C16—431no—
319C2×C16—431no—
320C2×C16C22×D4311yescharacteristic
321C2×C16C22×D4311yescharacteristic
322#107—431no—
323#107—431no—
324#107—431no—
325#107—861no—
326#107—861no—
327#107—861no—
328#107C22×D4311yescharacteristic
329C4⋊C8—431no—
330C4⋊C8—431no—
331C4⋊C8—431no—
332#103—21no—
333#103—861no—
334#103—861no—
335#103—861no—
336#103—861no—
337#102—861no—
338C4×C8—431no—
339C4×C8—431no—
340C4×C8C22×D4311yescharacteristic
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—431no—
344C2×Q8—861no—
345C2×Q8—1721no—
346C2×Q8—1721no—
347C2×Q8—1721no—
348C2×D4—21no—
349C22×C4—1721no—
350Q16—21no—
351Q16—21no—
352Q16—21no—
353Q16—861no—
354Q16—861no—
355Q16—3441no—
356Q16#1062190012yes—
357SD16—81no—
358SD16—3441no—
359D8—21no—
360D8—21no—
361C2×C8—431no—
362C2×C8—431no—
363C2×C8D4×D4311yescharacteristic
364C2×C8C23×D4311yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—41no—
367C4⋊C4—431no—
368C4⋊C4—431no—
369C4⋊C4—431no—
370C4⋊C4—861no—
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—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—1721no—
385C22⋊C4—1721no—
386C22⋊C4—1721no—
387C42—41no—
388C42—431no—
389C42—431no—
390C42—1721no—
391C42—1721no—
392C42—1721no—
393C42—1721no—
394C42D4×D4311yescharacteristic
395C16—21no—
396C16—21no—
397C16—861no—
398C16—861no—
399C23—41no—
400Q8—22no—
401Q8—41no—
402Q8—41no—
403Q8—41no—
404Q8—862no—
405Q8—1721no—
406Q8—1721no—
407Q8—6881no—
408Q8—6881no—
409Q8—6881no—
410D4—41no—
411D4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—431no—
416C2×C4—431no—
417C2×C4—431no—
418C2×C4—431no—
419C2×C4—3442no—
420C2×C4—1721no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—1721no—
424C2×C4D8×D4311yescharacteristic
425C2×C4D8×D4311yescharacteristic
426C2×C4C2×D4×D4311yescharacteristic
427C8—21no—
428C8—861no—
429C8—861no—
430C8C2×#1062190011yescharacteristic
431C8#1306337211yescharacteristic
432C22—81no—
433C22—81no—
434C22—81no—
435C22C2×D8×D4311yescharacteristic
436C4—21no—
437C4—21no—
438C4—42no—
439C4—81no—
440C4—81no—
441C4—432no—
442C4—861no—
443C4—861no—
444C4—861no—
445C4—3441no—
446C4—3441no—
447C4—3441no—
448C4—3441no—
449C4#1458355511yescharacteristic
450C4#1458370911yescharacteristic
451C2—161no—
452C2#1914722511yescharacteristic
453C2#510×D4311yescharacteristic
454C2#1914773811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2211C2
socleC22×C43C22×D8
prime radicalC2×D8×C43C23
hypercenter#2211D43
hypocenterC43#33936
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2211

Complements

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

NH ≅ G/Ntype
2. Q16×Dic86C2semidirect
5. #19136821C2semidirect
7. #19136738C2semidirect
8. #19136735C2semidirect
10. #19136643C2semidirect
11. #19136502C2semidirect
12. #19136466C2semidirect
13. #19136464C2semidirect
286. C43#33936semidirect

Maximal subgroups

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

subgroupindex
#191475802
Q16×Dic862
#191368312
#191368302
#191368212
#191367402
#191367382
#191367352
#191366552
#191366432
#191365022
#191364662
#191364642
SD32×Dic432
C43×#22112
#3393643