Finite Group Databasebeta

← #11872714

Subgroups — #11872714

Order 1152.

1254 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#518C211yesmaximal, characteristic, complemented
2#10596006C211yesmaximal, characteristic, complemented
3#10592916C212yesmaximal, complemented
4#10592714C212yesmaximal, complemented
5#10592713C212yesmaximal, complemented
6C4×#3753C212yesmaximal, complemented
7#10592708C212yesmaximal, complemented
8#10592702C212yesmaximal, complemented
9#10592699C211yesmaximal, characteristic, complemented
10#82542—34nomaximal
11C22×C32×D4C2211yescharacteristic
12C32×C4×D4—22no—
13C32×C4×D4C2212yes—
14C32×C4×D4C2212yes—
15C32×#117C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C32×C22⋊C4—22no—
18C2×#3753C2212yes—
19C2×#3753C2212yes—
20#64139C2212yes—
21#64103—22no—
22#64093—22no—
23#64083C2211yescharacteristic, complemented
24C4×C4⋊(C3⋊D3)C2212yescomplemented
25#64079C2211yescharacteristic, complemented
26#63659C2212yes—
27#63659C2212yes—
28#63657C2212yes—
29#63636C2212yescomplemented
30#63636C2212yescomplemented
31#63635C2212yescomplemented
32#63634C2212yescomplemented
33C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
34#63630C2211yescharacteristic, complemented
35C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
36C3×#518D314yescomplemented
37#5535—34no—
38#5217—38no—
39#5015—38no—
40#5014—38no—
41C4×#213—38no—
42#5009—38no—
43#5003—38no—
44#5000—34no—
45C24×C32—21no—
46C2×C32×D4—24no—
47C2×C32×D4—21no—
48C2×C32×D4C2312yes—
49C22×C32×C4—22no—
50C22×C32×C4—22no—
51C22×C32×C4C2311yescharacteristic
52C2×#638—22no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×C4×C3⋊D3—22no—
56C32×C4⋊C4D412yes—
57C32×C4⋊C4C2312yes—
58C32×C22⋊C4—21no—
59C32×C22⋊C4—22no—
60C32×C22⋊C4—22no—
61C32×C22⋊C4D412yes—
62C32×C42—21no—
63C32×C42C2311yescharacteristic
64C32×C42C2311yescharacteristic
65#3753—24no—
66#3753—24no—
67#3752—22no—
68#3752—22no—
69C4⋊(C3⋊Dic3)C2312yes—
70#3750—22no—
71C2×C3⋊(C3⋊C8)C2312yes—
72C2×C3⋊(C3⋊C8)C2312yes—
73#3122—91noSylow
74C22×C3×D4C2×D314yes—
75C3×C4×D4—28no—
76C3×C4×D4C2×D318yes—
77C3×C4×D4C2×D318yes—
78C3×#117C2×D314yes—
79C3×#117C2×D314yes—
80C2×C3×C22⋊C4—28no—
81C2×#213—38no—
82C2×#213—38no—
83#930—38no—
84#894—68no—
85#884—68no—
86#874—34no—
87C4×D12—38no—
88#870—34no—
89#832—38no—
90#832—38no—
91#830—38no—
92#809—38no—
93#809—38no—
94#808—38no—
95#807—38no—
96C4⋊(C3⋊C8)—38no—
97#803—34no—
98C4×C3⋊C8—34no—
99C23×C32—24no—
100C23×C32—22no—
101C23×C32—82no—
102C23×C32C2×D411yescharacteristic
103C22×C3⋊D3—22no—
104C32×D4—24no—
105C32×D4—22no—
106C32×D4#4114yes—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—82no—
110C2×C32×C4—82no—
111C2×C32×C4C2×D412yes—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D412yes—
114C2×C32×C4C2411yescharacteristic
115#638—82no—
116C2×C3⋊Dic3—22no—
117C4⋊(C3⋊D3)—22no—
118C4⋊(C3⋊D3)—22no—
119C4⋊(C3⋊D3)—82no—
120C4×C3⋊D3—82no—
121C3⋊(C3⋊C8)—22no—
122C3⋊(C3⋊C8)—22no—
123#540—91no—
124#518C3⋊D311yescharacteristic, complemented
125#482—92no—
126#478—92no—
127#459—92no—
128#447—92no—
129#442—92no—
130C4×D8—92no—
131#433—91no—
132C24×C3—24no—
133C2×C3×D4—216no—
134C2×C3×D4—24no—
135C2×C3×D4C22×D318yes—
136C22×C3×C4—28no—
137C22×C3×C4—28no—
138C22×C3×C4C22×D314yes—
139C2×#67—68no—
140C2×D12—38no—
141C2×D12—68no—
142C2×C4×D3—68no—
143C3×C4⋊C4#6718yes—
144C3×C4⋊C4C22×D318yes—
145C3×C22⋊C4—24no—
146C3×C22⋊C4—28no—
147C3×C22⋊C4—28no—
148C3×C22⋊C4#6718yes—
149C3×C42—24no—
150C3×C42C22×D314yes—
151C3×C42C22×D314yes—
152#213—616no—
153#213—616no—
154(C2×D3)⋊C4—68no—
155(C2×D3)⋊C4—68no—
156C4⋊Dic3—38no—
157Dic3⋊C4—68no—
158C2×C3⋊C8—38no—
159C2×C3⋊C8—38no—
160C22×C32—21no—
161C22×C32—24no—
162C22×C32—22no—
163C22×C32—42no—
164C22×C32—42no—
165C22×C32—84no—
166C22×C32C22×D411yescharacteristic
167C2×C3⋊D3—42no—
168C2×C3⋊D3—42no—
169C2×C3⋊D3—42no—
170C32×C4—21no—
171C32×C4—22no—
172C32×C4—22no—
173C32×C4—42no—
174C32×C4C2×#4112yes—
175C3⋊Dic3—42no—
176C22×D4C2×C3⋊D311yescharacteristic
177C2×D8—92no—
178C2×D8—92no—
179#127—91no—
180#125—91no—
181#123—182no—
182#121—92no—
183#121—182no—
184C4×D4—22no—
185C4×D4—92no—
186C4×D4C2×C3⋊D312yes—
187C4×D4C2×C3⋊D312yes—
188#117C2×C3⋊D311yescharacteristic
189#117C2×C3⋊D311yescharacteristic
190C2×C22⋊C4—22no—
191#107—92no—
192#106—92no—
193C4⋊C8—92no—
194#102—92no—
195#102—92no—
196#102—92no—
197#102—92no—
198C22⋊C8—92no—
199#97—91no—
200C4×C8—91no—
201C23×C3—216no—
202C23×C3—28no—
203C23×C3—88no—
204C23×C3C2×#6714yes—
205C22×D3—68no—
206C3×D4—216no—
207C3×D4—28no—
208C3×D4#235116yes—
209C2×C3×C4—28no—
210C2×C3×C4—28no—
211C2×C3×C4—88no—
212C2×C3×C4—88no—
213C2×C3×C4C2×#6718yes—
214C2×C3×C4C2×#6714yes—
215C2×C3×C4C2×#6718yes—
216C2×C3×C4C23×D314yes—
217#67—248no—
218C2×Dic3—68no—
219D12—68no—
220D12—68no—
221D12—248no—
222C4×D3—248no—
223C3⋊C8—68no—
224C3⋊C8—68no—
225C2×C32—41no—
226C2×C32—44no—
227C2×C32#52511yescharacteristic
228C2×C32#57612yes—
229C3⋊D3—82no—
230C24—21no—
231C2×D4—24no—
232C2×D4—21no—
233C2×D4—92no—
234C2×D4—182no—
235C2×D4—182no—
236C2×D4C22×C3⋊D312yes—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—182no—
240C22×C4C22×C3⋊D311yescharacteristic
241D8—184no—
242D8—184no—
243C2×C8—92no—
244C2×C8—92no—
245C4⋊C4—92no—
246C4⋊C4—182no—
247C4⋊C4#63812yes—
248C4⋊C4C22×C3⋊D312yes—
249C22⋊C4—21no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—182no—
253C22⋊C4—182no—
254C22⋊C4#63812yes—
255C42—21no—
256C42C22×C3⋊D311yescharacteristic
257C42C22×C3⋊D311yescharacteristic
258C22×C3—24no—
259C22×C3—216no—
260C22×C3—28no—
261C22×C3—48no—
262C22×C3—48no—
263C22×C3—816no—
264C22×C3C22×#6714yes—
265C2×D3—128no—
266C2×D3—128no—
267C2×D3—128no—
268C3×C4—24no—
269C3×C4—28no—
270C3×C4—28no—
271C3×C4—48no—
272C3×C4C2×#23518yes—
273Dic3—128no—
274C32#312211yescharacteristic, complemented, Sylow
275C23—24no—
276C23—22no—
277C23—82no—
278C23—182no—
279C23C2×#63811yescharacteristic
280D4—24no—
281D4—22no—
282D4—182no—
283D4—182no—
284D4—722no—
285D4—722no—
286D4#382814yes—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—182no—
292C2×C4—722no—
293C2×C4C2×#63811yescharacteristic
294C2×C4C2×#63812yes—
295C2×C4C2×#63812yes—
296C2×C4C23×C3⋊D311yescharacteristic
297C8—182no—
298C8—182no—
299C2×C3—44no—
300C2×C3—416no—
301C2×C3#579114yes—
302C2×C3#583518yes—
303D3—248no—
304C22—21no—
305C22—24no—
306C22—22no—
307C22—42no—
308C22—42no—
309C22—84no—
310C22—362no—
311C22—362no—
312C22—362no—
313C22C22×#63811yescharacteristic
314C4—21no—
315C4—22no—
316C4—22no—
317C4—42no—
318C4—362no—
319C4C2×#382812yes—
320C3#8254214yescomplemented
321C2—41no—
322C2—44no—
323C2—722no—
324C2#1059626211yescharacteristic
325C2#1059630612yes—
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#518C2
socleC22×C32C22×D4
hypercenter#518C3⋊D3
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C32×#518C2semidirect
2. #10596006C2semidirect
3. #10592916C2semidirect
4. #10592714C2semidirect
5. #10592713C2semidirect
6. C4×#3753C2semidirect
7. #10592708C2semidirect
8. #10592702C2semidirect
9. #10592699C2semidirect
23. #64083C22semidirect
24. C4×C4⋊(C3⋊D3)C22semidirect
25. #64079C22semidirect
29. #63636C22semidirect
30. #63636C22semidirect
31. #63635C22semidirect
32. #63634C22semidirect
33. C4⋊(C3⋊(C3⋊C8))C22semidirect
34. #63630C22semidirect
35. C4×C3⋊(C3⋊C8)C22semidirect
36. C3×#518D3semidirect
124. #518C3⋊D3semidirect
274. C32#3122semidirect
320. C3#82542semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
#105960062
#105929162
#105927142
#105927132
C4×#37532
#105927082
#105927022
#105926992
#825423