Finite Group Databasebeta

← #25251524

Subgroups — #25251524

Order 11008.

610 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145176C211yesmaximal, characteristic, complemented
2C2×D8×Dic43C211yesmaximal, characteristic
3#19136793C211yesmaximal, characteristic, complemented
4#19136790C211yesmaximal, characteristic, complemented
5#19136740C212yesmaximal, complemented
6#19136638C212yesmaximal, complemented
7#19136524C211yesmaximal, characteristic
8#19136450C212yesmaximal, complemented
9SD32×Dic43C212yesmaximal, complemented
10#19136391C211yesmaximal, characteristic, complemented
11C43×#2187C211yesmaximal, characteristic
12#14583451—21no—
13C2×D4×Dic43—21no—
14C2×#13063269C2212yes—
15#14583303C2211yescharacteristic, complemented
16#14583277C2211yescharacteristic, complemented
17#14583248—21no—
18#14583140C2211yescharacteristic
19#14583138—21no—
20Q16×Dic43C2211yescharacteristic, complemented
21#14582993C2211yescharacteristic, complemented
22#14582991—21no—
23D8×Dic43—21no—
24D8×Dic43—21no—
25D8×Dic43C2212yes—
26D8×Dic43C2212yes—
27C2×#13063259C2211yescharacteristic
28C2×#13063246—21no—
29C2×C8×Dic43C2211yescharacteristic
30#14582727C2212yescomplemented
31#14582726C2212yescomplemented
32Dic43⋊C16C2212yescomplemented
33#14582704C2212yescomplemented
34#14582703C2212yescomplemented
35#14582700C2212yes—
36C22⋊(C43⋊C16)C2211yescharacteristic
37C16×Dic43C2212yescomplemented
38C22×D8×C43C2211yescharacteristic
39C2×SD32×C43C2212yes—
40C43×#467C2211yescharacteristic
41C43×#357C2212yes—
42C43×C22⋊C16C2211yescharacteristic
43C23×Dic43—41no—
44C2×Dic172C2311yescharacteristic
45C2×#10621885—21no—
46C22×C43⋊C8D411yescharacteristic
47#13063324—21no—
48#13063323—21no—
49#13063315—41no—
50#13063304—21no—
51#13063302—41no—
52Q8×Dic43—21no—
53#13063290—21no—
54#13063290—41no—
55D4×Dic43—22no—
56D4×Dic43—22no—
57D4×Dic43—41no—
58D4×Dic43—41no—
59#13063281—41no—
60C2×C4⋊Dic43—21no—
61C2×C22⋊Dic43—41no—
62C2×C4×Dic43D411yescharacteristic
63#13063269—24no—
64C2×C43⋊C16C2312yes—
65#13063259—21no—
66#13063259C2311yescharacteristic
67#13063259C2312yes—
68#13063258—21no—
69#13063250—21no—
70#13063249—21no—
71#13063248—21no—
72#13063246—22no—
73#13063246—22no—
74C8×Dic43D411yescharacteristic
75C8×Dic43D411yescharacteristic
76C8×Dic43C2311yescharacteristic
77C8×Dic43C2311yescharacteristic
78C22×D4×C43—21no—
79C2×Q16×C43C2311yescharacteristic
80C2×D8×C43—24no—
81C2×D8×C43—21no—
82C2×D8×C43C2312yes—
83C22×C8×C43C2311yescharacteristic
84C22⋊Q8×C43—21no—
85SD32×C43—24no—
86C2×C16×C43C2312yes—
87#107×C43C2311yescharacteristic
88#103×C43—21no—
89C24×C43—41no—
90C2×Q8×C43—21no—
91C2×D4×C43—24no—
92C2×D4×C43—22no—
93C2×D4×C43—42no—
94C2×D4×C43—41no—
95C22×C4×C43C2×D411yescharacteristic
96C22×Dic43—42no—
97C22×Dic43—42no—
98C22×Dic43—41no—
99C22×Dic43—84no—
100C22×Dic43D811yescharacteristic
101C22×Dic43D811yescharacteristic
102C2×Dic86—21no—
103C2×Dic86—41no—
104Q16×C43—22no—
105D8×C43—24no—
106D8×C43—22no—
107D8×C43#4114yes—
108C2×C8×C43—22no—
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2411yescharacteristic
111C4⋊C4×C43—21no—
112C4⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊Dic43—42no—
115C22⋊Dic43—42no—
116C22⋊Dic43—41no—
117#10621885—42no—
118C4⋊Dic43—22no—
119C4⋊Dic43—21no—
120C4⋊Dic43—41no—
121C4⋊Dic43—41no—
122Dic43⋊C4—41no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127C4×Dic43—41no—
128C4×Dic43—41no—
129C4×Dic43D811yescharacteristic
130C4×Dic43D811yescharacteristic
131C4×Dic43C2×D411yescharacteristic
132C4×Dic43C2×D411yescharacteristic
133C2×C43⋊C8—41no—
134C2×C43⋊C8C2×D411yescharacteristic
135C2×C43⋊C8C2×D411yescharacteristic
136Dic172—22no—
137C16×C43—22no—
138C43⋊C16—22no—
139C23×C43—44no—
140C23×C43—42no—
141C23×C43—82no—
142C23×C43—82no—
143C23×C43C2×D811yescharacteristic
144Q8×C43—41no—
145Q8×C43—41no—
146D4×C43—24no—
147D4×C43—44no—
148D4×C43—42no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43C2×D811yescharacteristic
154C2×C4×C43C22×D411yescharacteristic
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—42no—
159C2×Dic43—82no—
160C2×Dic43—84no—
161C2×Dic43—84no—
162C2×Dic43SD3214yescomplemented
163C2×Dic43C2×D811yescharacteristic
164C2×Dic43C2×D811yescharacteristic
165C2×Dic43C2×D811yescharacteristic
166C2×Dic43C2×D811yescharacteristic
167Dic86—41no—
168Dic86—41no—
169Dic86—82no—
170C8×C43—21no—
171C8×C43C2×#4112yes—
172C43⋊C8—21no—
173C43⋊C8—21no—
174#33661—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—44no—
178C22×C43—88no—
179C22×C43—82no—
180C22×C43—82no—
181C22×C43C2×SD3212yes—
182C22×C43C22×D811yescharacteristic
183C4×C43—21no—
184C4×C43—81no—
185C4×C43—81no—
186C4×C43#52511yescharacteristic
187C4×C43#57511yescharacteristic
188Dic43—21no—
189Dic43—21no—
190Dic43—81no—
191Dic43—82no—
192Dic43—81no—
193Dic43C2×SD3212yes—
194Dic43C2×SD3212yes—
195#3170—431no—
196C2×C4×D8—431no—
197#2235—431no—
198#2235—431no—
199#2226—432no—
200#2208—432no—
201#2187—431no—
202#2187D4311yescharacteristic
203C4×SD32—432no—
204C4×SD32—432no—
205#2162—431no—
206C2×C43—22no—
207C2×C43—84no—
208C2×C43#310011yescharacteristic
209C2×C43C22×SD3211yescharacteristic
210C2×C43#341411yescharacteristic
211C22×D8C2×D4311yescharacteristic
212#533—861no—
213C2×C4×D4—861no—
214C2×SD32—432no—
215C2×SD32C2×D4312yes—
216#500—431no—
217#494—431no—
218#487—861no—
219#467—431no—
220#467—861no—
221#467C2×D4311yescharacteristic
222C4×Q16—431no—
223C4×Q16—431no—
224C4×Q16—861no—
225C4×D8—432no—
226C4×D8—432no—
227C4×D8—861no—
228C4×D8—861no—
229C2×#107—431no—
230C2×#102—861no—
231C2×C4×C8—431no—
232#367—432no—
233#367—432no—
234C4⋊C16—432no—
235#358—432no—
236#358—432no—
237#357—432no—
238#357C2×D4312yes—
239C22⋊C16—431no—
240C22⋊C16C2×D4311yescharacteristic
241C4×C16—432no—
242C43#3366111yescharacteristic, complemented, Sylow
243C22×D4—21no—
244C23×C4—1721no—
245C2×Q16—431no—
246C2×Q16—861no—
247C2×Q16C22×D4311yescharacteristic
248C2×D8—24no—
249C2×D8—21no—
250C2×D8C22×D4312yes—
251C22×C8—431no—
252C22×C8C22×D4311yescharacteristic
253C4⋊Q8—861no—
254C4⋊Q8—861no—
255#125—1721no—
256C22⋊Q8—21no—
257C22⋊Q8—861no—
258C22⋊Q8—1721no—
259C4×Q8—861no—
260C4×Q8—861no—
261C4×Q8—1721no—
262C4×D4—862no—
263C4×D4—862no—
264C4×D4—1721no—
265C4×D4—1721no—
266#117—1721no—
267C2×C4⋊C4—861no—
268C2×C22⋊C4—1721no—
269C2×C42—431no—
270SD32—24no—
271SD32—864no—
272C2×C16—432no—
273C2×C16C22×D4312yes—
274#107—431no—
275#107—432no—
276#107—861no—
277#107—861no—
278#107C22×D4311yescharacteristic
279#103—21no—
280#103—861no—
281#103—861no—
282#103—861no—
283#102—862no—
284#102—862no—
285C4×C8—431no—
286C4×C8—431no—
287C4×C8—431no—
288C4×C8—431no—
289C24—41no—
290C2×Q8—21no—
291C2×Q8—861no—
292C2×Q8—1721no—
293C2×D4—24no—
294C2×D4—22no—
295C2×D4—42no—
296C2×D4—41no—
297C22×C4—431no—
298C22×C4—431no—
299C22×C4—3444no—
300C22×C4—1722no—
301C22×C4—1722no—
302C22×C4—1721no—
303C22×C4D4×D4311yescharacteristic
304Q16—22no—
305Q16—862no—
306Q16—1722no—
307D8—24no—
308D8—22no—
309D8#1062190014yes—
310C2×C8—22no—
311C2×C8—431no—
312C2×C8—431no—
313C2×C8—1721no—
314C2×C8D4×D4311yescharacteristic
315C2×C8C23×D4311yescharacteristic
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—862no—
319C4⋊C4—861no—
320C4⋊C4—1721no—
321C4⋊C4—1721no—
322C4⋊C4—1721no—
323C4⋊C4—1721no—
324C4⋊C4—1721no—
325C4⋊C4—1721no—
326C4⋊C4—1721no—
327C22⋊C4—41no—
328C22⋊C4—1722no—
329C22⋊C4—1722no—
330C22⋊C4—1721no—
331C42—431no—
332C42—431no—
333C42—431no—
334C42—431no—
335C42—1721no—
336C42—1721no—
337C16—22no—
338C16—862no—
339C23—44no—
340C23—42no—
341C23—82no—
342C23—82no—
343C23D8×D4311yescharacteristic
344Q8—41no—
345Q8—41no—
346Q8—3442no—
347Q8—1721no—
348Q8—1721no—
349D4—24no—
350D4—44no—
351D4—42no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—434no—
357C2×C4—431no—
358C2×C4—431no—
359C2×C4—431no—
360C2×C4—431no—
361C2×C4—3444no—
362C2×C4—3444no—
363C2×C4—3442no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1722no—
368C2×C4D8×D4311yescharacteristic
369C2×C4C2×D4×D4311yescharacteristic
370C8—21no—
371C8—861no—
372C8—861no—
373C8C2×#1062190012yes—
374C22—21no—
375C22—21no—
376C22—44no—
377C22—88no—
378C22—82no—
379C22—82no—
380C22SD32×D4312yes—
381C22C2×D8×D4311yescharacteristic
382C4—21no—
383C4—81no—
384C4—81no—
385C4—432no—
386C4—432no—
387C4—861no—
388C4—861no—
389C4—3441no—
390C4—3442no—
391C4—3441no—
392C4#1458340511yescharacteristic
393C4#1458369511yescharacteristic
394C2—22no—
395C2—84no—
396C2#1914459011yescharacteristic
397C2C2×SD32×D4311yescharacteristic
398C2#1914772711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2187C2
socleC22×C43C22×D8
prime radicalC22×D8×C43C22
hypercenter#2187D43
hypocenterC43#33661
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #19145176C2semidirect
3. #19136793C2semidirect
4. #19136790C2semidirect
5. #19136740C2semidirect
6. #19136638C2semidirect
8. #19136450C2semidirect
9. SD32×Dic43C2semidirect
10. #19136391C2semidirect
15. #14583303C22semidirect
16. #14583277C22semidirect
20. Q16×Dic43C22semidirect
21. #14582993C22semidirect
30. #14582727C22semidirect
31. #14582726C22semidirect
32. Dic43⋊C16C22semidirect
33. #14582704C22semidirect
34. #14582703C22semidirect
37. C16×Dic43C22semidirect
162. C2×Dic43SD32semidirect
242. C43#33661semidirect

Maximal subgroups

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

subgroupindex
#191451762
C2×D8×Dic432
#191367932
#191367902
#191367402
#191366382
#191365242
#191364502
SD32×Dic432
#191363912
C43×#21872
#3366143