Finite Group Databasebeta

← #11779764

Subgroups — #11779764

Order 1152.

636 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#10596056C211yesmaximal, characteristic
2#10592730C211yesmaximal, characteristic, complemented
3#10592550C211yesmaximal, characteristic, complemented
4#10592393C211yesmaximal, characteristic
5C32×Q8⋊C8C211yesmaximal, characteristic, complemented
6#10589351C211yesmaximal, characteristic
7#10589322C211yesmaximal, characteristic, complemented
8#68262—34nomaximal
9C32×C4×Q8C2211yescharacteristic
10#64156—21no—
11C2×#3756—21no—
12#64103—22no—
13#64102—21no—
14#64084—21no—
15#64083C2211yescharacteristic
16C4×C4⋊(C3⋊D3)—21no—
17#64078C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4×C8C2211yescharacteristic
21#63648—22no—
22#63644—21no—
23#63643—21no—
24#63637—21no—
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26#5585—34no—
27#5031—34no—
28#4851—34no—
29#4694—34no—
30C3×Q8⋊C8D314yescomplemented
31#4485—34no—
32#4456—34no—
33C2×C32×Q8D411yescharacteristic
34C2×C4⋊(C3⋊D3)—21no—
35C2×C4⋊(C3⋊D3)—21no—
36C2×C4⋊(C3⋊D3)D412yes—
37C2×C4×C3⋊D3—22no—
38C2×#634—21no—
39C2×#634D411yescharacteristic
40C2×C32×C8—21no—
41C2×C32×C8—21no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4D411yescharacteristic
44C32×C42—21no—
45C32×C42C2311yescharacteristic
46#3756—42no—
47#3752—22no—
48#3752—22no—
49#3752—22no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—21no—
54C4×C3⋊Dic3—21no—
55C2×C3⋊(C3⋊C8)—21no—
56#1640—91noSylow
57C3×C4×Q8C2×D314yes—
58#947—64no—
59C2×#216—64no—
60#894—68no—
61#893—64no—
62#875—64no—
63#874—34no—
64C4×D12—64no—
65#869—34no—
66C4×Dic6—34no—
67C3×C4⋊C8C2×D314yes—
68C3×C4×C8C2×D314yes—
69#821—68no—
70#817—64no—
71#816—64no—
72#810—64no—
73C4⋊(C3⋊C8)—34no—
74C22×C3⋊D3—22no—
75C32×Q8—21no—
76C32×Q8—21no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—41no—
85C4⋊(C3⋊D3)—42no—
86C4⋊(C3⋊D3)—41no—
87C4⋊(C3⋊D3)—41no—
88C4⋊(C3⋊D3)—41no—
89C4⋊(C3⋊D3)—41no—
90C4×C3⋊D3—82no—
91#634—21no—
92#634—21no—
93#634—41no—
94#634—41no—
95C32×C8—41no—
96C32×C8—41no—
97C3⋊(C3⋊C8)—41no—
98#559—91no—
99#486—91no—
100#475—91no—
101#462—91no—
102#331—91no—
103Q8⋊C8—91no—
104Q8⋊C8C3⋊D311yescharacteristic, complemented
105C2×C3×Q8D1214yes—
106C2×D12—38no—
107C2×D12—64no—
108C2×D12—64no—
109C2×C4×D3—68no—
110C2×Dic6—34no—
111C2×Dic6—64no—
112C2×C3×C8—24no—
113C2×C3×C8—24no—
114C3×C4⋊C4—24no—
115C3×C4⋊C4D1214yes—
116C3×C42—24no—
117C3×C42C22×D314yes—
118#216—128no—
119(C2×D3)⋊C4—68no—
120(C2×D3)⋊C4—68no—
121(C2×D3)⋊C4—68no—
122C4⋊Dic3—34no—
123C4⋊Dic3—64no—
124C4⋊Dic3—64no—
125Dic3⋊C4—64no—
126C4×Dic3—64no—
127C2×C3⋊C8—64no—
128C22×C32#12011yescharacteristic
129C2×C3⋊D3—42no—
130C2×C3⋊D3—42no—
131C2×C3⋊D3—42no—
132C32×C4—21no—
133C32×C4—41no—
134C32×C4—41no—
135C32×C4#13511yescharacteristic
136C32×C4#13511yescharacteristic
137C32×C4AGL(1,ℤ/8)11yescharacteristic
138C32×C4#13711yescharacteristic
139C3⋊Dic3—41no—
140C3⋊Dic3—41no—
141C3⋊Dic3—81no—
142C2×Q16—181no—
143C4⋊Q8—91no—
144#127—91no—
145#124—181no—
146#124—181no—
147#123—182no—
148C4×Q8—91no—
149C4×Q8C2×C3⋊D311yescharacteristic
150C4×D4—181no—
151C4×D4—181no—
152#106—181no—
153C4⋊C8—91no—
154C4⋊C8C2×C3⋊D311yescharacteristic
155#103—181no—
156#103—181no—
157#102—182no—
158C4×C8C2×C3⋊D311yescharacteristic
159C22×D3—68no—
160C3×Q8—24no—
161C3×Q8—24no—
162C2×C3×C4—24no—
163C2×C3×C4—24no—
164C2×C3×C4C2×D1214yes—
165C2×C3×C4D3×D414yes—
166C2×C3×C4D3×D414yes—
167C2×Dic3—64no—
168C2×Dic3—64no—
169C2×Dic3—124no—
170D12—128no—
171D12—124no—
172D12—124no—
173D12—124no—
174D12—124no—
175C4×D3—248no—
176Dic6—64no—
177Dic6—64no—
178Dic6—124no—
179Dic6—124no—
180C3×C8—44no—
181C3×C8—44no—
182C3⋊C8—124no—
183C2×C32#44911yescharacteristic
184C2×C32#45211yescharacteristic
185C2×C32#45511yescharacteristic
186C3⋊D3—82no—
187C2×Q8—91no—
188C2×Q8—181no—
189C2×Q8C4⋊(C3⋊D3)11yescharacteristic
190C2×D4—92no—
191C2×D4—181no—
192C2×D4—181no—
193C22×C4—182no—
194Q16—362no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—181no—
198C4⋊C4—21no—
199C4⋊C4—91no—
200C4⋊C4—181no—
201C4⋊C4—181no—
202C4⋊C4—181no—
203C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
204C22⋊C4—182no—
205C22⋊C4—182no—
206C22⋊C4—182no—
207C42—21no—
208C42—181no—
209C42C22×C3⋊D311yescharacteristic
210C22×C3#88214yes—
211C2×D3—128no—
212C2×D3—128no—
213C2×D3—128no—
214C3×C4—24no—
215C3×C4—44no—
216C3×C4—44no—
217C3×C4#90414yes—
218C3×C4#90814yes—
219C3×C4#91614yes—
220C3×C4#91814yes—
221Dic3—124no—
222Dic3—124no—
223Dic3—244no—
224C32#164011yescharacteristic, complemented, Sylow
225C23—182no—
226Q8—21no—
227Q8—21no—
228Q8—181no—
229Q8—181no—
230Q8—361no—
231Q8—361no—
232D4—362no—
233D4—361no—
234D4—361no—
235D4—361no—
236D4—361no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—361no—
242C2×C4—722no—
243C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
244C2×C4D4×C3⋊D311yescharacteristic
245C2×C4D4×C3⋊D311yescharacteristic
246C8—41no—
247C8—41no—
248C8—361no—
249C2×C3#473414yes—
250C2×C3#480814yes—
251C2×C3#482514yes—
252D3—248no—
253C22—362no—
254C22—362no—
255C22—362no—
256C22#6409111yescharacteristic
257C4—21no—
258C4—41no—
259C4—41no—
260C4—361no—
261C4—361no—
262C4—721no—
263C4#6411311yescharacteristic
264C4#6411711yescharacteristic
265C4#6412511yescharacteristic
266C4#6412711yescharacteristic
267C3#6826214yescomplemented
268C2—722no—
269C2#1059243311yescharacteristic
270C2#1059250711yescharacteristic
271C2#1059252411yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×Q8⋊C8C2
socleC22×C32#120
prime radical#64083C22
hypercenterQ8⋊C8C3⋊D3
hypocenterC32#1640
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592730C2semidirect
3. #10592550C2semidirect
5. C32×Q8⋊C8C2semidirect
7. #10589322C2semidirect
30. C3×Q8⋊C8D3semidirect
104. Q8⋊C8C3⋊D3semidirect
224. C32#1640semidirect
267. C3#68262semidirect

Maximal subgroups

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

subgroupindex
#105960562
#105927302
#105925502
#105923932
C32×Q8⋊C82
#105893512
#105893222
#682623