Finite Group Databasebeta

← #11779313

Subgroups — #11779313

Order 1152.

699 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 699 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D122C211yesmaximal, characteristic
2#10592392C211yesmaximal, characteristic, complemented
3#10590268C212yesmaximal, complemented
4C3×#4459C212yesmaximal, complemented
5#10589091C211yesmaximal, characteristic, complemented
6#68195—32nomaximal
7C2×D3×D12—22no—
8C2×#3744—22no—
9#64083C2211yescharacteristic
10#64078C2211yescharacteristic, complemented
11C3×C4×D12C2212yes—
12#63923—22no—
13#63909—22no—
14C32×C4×C8C2211yescharacteristic, complemented
15C3×C4⋊(C3⋊C8)C2212yescomplemented
16#63573—22no—
17#63563—22no—
18D4×D12—32no—
19#5008—32no—
20#4842—32no—
21#4693—32no—
22#4693—61no—
23C3×D4⋊C8—32no—
24#4485—32no—
25#4459D312yescomplemented
26C22×D32—22no—
27C2×C4⋊(C3⋊D3)—22no—
28C2×C4⋊(C3⋊D3)D412yes—
29C2×#634—21no—
30C2×C3×D12D412yes—
31C2×C3×C4×D3—22no—
32C2×#626—24no—
33D3×D12—44no—
34D3×D12—44no—
35C2×C32×C8—21no—
36C32×C42C2311yescharacteristic
37C4⋊(C3⋊Dic3)—22no—
38#3744—44no—
39C3×(C2×D3)⋊C4—22no—
40C3×C4⋊Dic3D412yes—
41C2×C3×C3⋊C8—22no—
42#3722—22no—
43#1629—91noSylow
44C2×D3×D4—62no—
45C22×D12—62no—
46C3×C4×D4—32no—
47#930—62no—
48C2×#204—64no—
49C2×#204—64no—
50#895—62no—
51#882—64no—
52#874—32no—
53#874—61no—
54C4×D12C2×D312yes—
55#869—32no—
56#869—61no—
57C3×C4⋊C8—32no—
58C3×C4×C8—21no—
59C3×C4×C8C2×D312yescomplemented
60#832—62no—
61#821—62no—
62#817—62no—
63#808—62no—
64C4⋊(C3⋊C8)C2×D312yescomplemented
65C22×C3⋊D3—22no—
66C22×C3×D3—22no—
67C2×D32—48no—
68C2×D32—82no—
69C2×C32×C4C2×D412yes—
70C2×C32×C4C2×D411yescharacteristic
71C2×C3⋊Dic3—41no—
72C4⋊(C3⋊D3)—42no—
73C4⋊(C3⋊D3)—42no—
74C4⋊(C3⋊D3)—42no—
75#634—42no—
76C2×C3×Dic3—22no—
77C3×D12—22no—
78C3×D12SD1614yescomplemented
79C3×C4×D3—42no—
80C3×C4×D3—42no—
81#626—48no—
82C32×C8—22no—
83C3×C3⋊C8—42no—
84D42—91no—
85#492—91no—
86#476—92no—
87#331—91no—
88D4⋊C8—32no—
89C23×D3—64no—
90C2×C3×D4—32no—
91C22×C3×C4—62no—
92C2×#67—64no—
93D3×D4—124no—
94D3×D4—124no—
95C2×D12—34no—
96C2×D12—62no—
97C2×D12—64no—
98C2×D12—62no—
99C2×D12—62no—
100C2×D12—122no—
101C2×D12—124no—
102C2×D12—124no—
103C2×D12D1212yes—
104C2×C4×D3—22no—
105C2×Dic6—62no—
106C2×Dic6—62no—
107C2×C3×C8—22no—
108C2×C3×C8—22no—
109C2×C3×C8—62no—
110C3×C4⋊C4—32no—
111C3×C22⋊C4—62no—
112C3×C42—21no—
113C3×C42C22×D312yes—
114(C2×D3)⋊C4—22no—
115(C2×D3)⋊C4—64no—
116C4⋊Dic3—62no—
117C4⋊Dic3—62no—
118C4⋊Dic3—122no—
119C4⋊Dic3D1212yes—
120C2×C3⋊C8—22no—
121#204—128no—
122#204—128no—
123C22×C32#12011yescharacteristic
124C2×C3⋊D3—44no—
125C2×C3⋊D3—42no—
126C2×C3×D3—24no—
127C2×C3×D3—42no—
128C2×C3×D3—42no—
129D32—88no—
130C32×C4—21no—
131C32×C4C2×SD1612yes—
132C32×C4AGL(1,ℤ/8)12yes—
133C3⋊Dic3—81no—
134C3×Dic3—42no—
135C22×D4—182no—
136C2×SD16—182no—
137C4⋊Q8—91no—
138#127—91no—
139#121—182no—
140#120—182no—
141C4×D4—32no—
142#106—182no—
143C4⋊C8—32no—
144#102—182no—
145C4×C8D3211yescharacteristic, complemented
146C23×C3—62no—
147C22×D3—22no—
148C22×D3—64no—
149C22×D3—122no—
150C22×D3—128no—
151C22×D3—128no—
152C22×D3—244no—
153C3×D4—34no—
154C3×D4—62no—
155C2×C3×C4—22no—
156C2×C3×C4—21no—
157C2×C3×C4—62no—
158C2×C3×C4—122no—
159C2×C3×C4—122no—
160C2×C3×C4C2×D1212yes—
161C2×C3×C4D3×D412yes—
162C2×C3×C4D3×D412yes—
163#67—128no—
164C2×Dic3—22no—
165C2×Dic3—122no—
166C2×Dic3—122no—
167D12—22no—
168D12—124no—
169D12—124no—
170D12—128no—
171D12—122no—
172D12—122no—
173D12—122no—
174D12—122no—
175D12—242no—
176D12—242no—
177D12#20414yescomplemented
178C4×D3—42no—
179C4×D3—42no—
180Dic6—124no—
181Dic6—124no—
182C3×C8—24no—
183C3×C8—24no—
184C3×C8—122no—
185C3⋊C8—42no—
186C2×C32#45012yes—
187C2×C32#45311yescharacteristic
188C3⋊D3—82no—
189C3×D3—44no—
190C24—182no—
191C2×Q8—181no—
192C2×D4—32no—
193C2×D4—92no—
194C2×D4—184no—
195C2×D4—182no—
196C2×D4—364no—
197C2×D4—364no—
198C22×C4—62no—
199SD16—364no—
200C2×C8—21no—
201C2×C8—62no—
202C4⋊C4—32no—
203C4⋊C4—182no—
204C22⋊C4—62no—
205C22⋊C4—182no—
206C42C2×D3211yescharacteristic
207C22×C3—21no—
208C22×C3—64no—
209C22×C3—122no—
210C22×C3—122no—
211C22×C3#88212yes—
212C2×D3—24no—
213C2×D3—42no—
214C2×D3—42no—
215C2×D3—124no—
216C2×D3—124no—
217C2×D3—124no—
218C2×D3—242no—
219C2×D3—244no—
220C2×D3—2416no—
221C3×C4—22no—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—22no—
225C3×C4—122no—
226C3×C4C2×#20412yes—
227C3×C4#90812yes—
228C3×C4#91112yes—
229C3×C4D3×SD1612yes—
230Dic3—42no—
231Dic3—242no—
232Dic3—242no—
233C32#162911yescharacteristic, complemented, Sylow
234C23—62no—
235C23—182no—
236C23—368no—
237C23—722no—
238Q8—362no—
239D4—34no—
240D4—62no—
241D4—362no—
242D4—368no—
243D4—362no—
244D4—362no—
245C2×C4—62no—
246C2×C4—122no—
247C2×C4—122no—
248C2×C4—361no—
249C2×C4D3×D1212yes—
250C2×C4#381111yescharacteristic
251C8—22no—
252C8—122no—
253C2×C3—21no—
254C2×C3—22no—
255C2×C3—124no—
256C2×C3#473112yes—
257C2×C3#477612yes—
258C2×C3#482212yes—
259D3—44no—
260D3—244no—
261D3—482no—
262C22—64no—
263C22—122no—
264C22—122no—
265C22—362no—
266C22—364no—
267C22—728no—
268C22#6392311yescharacteristic
269C4—21no—
270C4—122no—
271C4—721no—
272C4D3×#20412yes—
273C4#6379512yes—
274C3—21no—
275C3#6819512yescomplemented
276C2—124no—
277C2—722no—
278C2#1059039711yescharacteristic
279C2#1059094612yes—
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radicalD122C2
hypercenterC4×C8D32
hypocenterC32#1629
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10592392C2semidirect
3. #10590268C2semidirect
4. C3×#4459C2semidirect
5. #10589091C2semidirect
10. #64078C22semidirect
14. C32×C4×C8C22semidirect
15. C3×C4⋊(C3⋊C8)C22semidirect
25. #4459D3semidirect
59. C3×C4×C8C2×D3semidirect
64. C4⋊(C3⋊C8)C2×D3semidirect
78. C3×D12SD16semidirect
145. C4×C8D32semidirect
177. D12#204semidirect
233. C32#1629semidirect
275. C3#68195semidirect

Maximal subgroups

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

subgroupindex
D1222
#105923922
#105902682
C3×#44592
#105890912
#681953