Finite Group Databasebeta

← #11779529

Subgroups — #11779529

Order 1152.

702 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 131 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#10596022C211yesmaximal, characteristic
2#10592707C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4#10592380C211yesmaximal, characteristic, complemented
5C32×D4⋊C8C211yesmaximal, characteristic, complemented
6#10589348C211yesmaximal, characteristic, complemented
7#10589325C211yesmaximal, characteristic, complemented
8#68181—34nomaximal
9C2×#3828—21no—
10C32×C4×D4C2211yescharacteristic
11#64147—21no—
12#64133—21no—
13C4⋊C4×C3⋊D3—21no—
14#64092—22no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64078C2211yescharacteristic
17#64078C2211yescharacteristic
18C32×C4⋊C8C2211yescharacteristic
19C32×C4×C8C2211yescharacteristic
20#63659—21no—
21#63648—21no—
22#63644—21no—
23#63643—22no—
24#63635—21no—
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26#5551—34no—
27#5008—34no—
28#4842—34no—
29#4681—34no—
30C3×D4⋊C8D314yescomplemented
31#4482—34no—
32#4459—34no—
33C2×C32×D4D411yescharacteristic
34C22×C32×C4—21no—
35C2×#638—22no—
36#3828—42no—
37#3828—42no—
38C2×C4⋊(C3⋊D3)D411yescharacteristic
39C2×C4×C3⋊D3—22no—
40C2×C4×C3⋊D3—21no—
41C2×#634—21no—
42C2×#634—21no—
43C2×C32×C8—21no—
44C2×C32×C8—21no—
45C32×C4⋊C4D411yescharacteristic
46C32×C22⋊C4—21no—
47C32×C42C2311yescharacteristic
48#3757—22no—
49#3752—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)D412yes—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55#3750—22no—
56C2×C3⋊(C3⋊C8)—21no—
57#1635—91noSylow
58C2×#235—64no—
59C3×C4×D4C2×D314yes—
60#938—64no—
61#924—64no—
62D3×C4⋊C4—64no—
63#883—68no—
64C4×D12—34no—
65#869—34no—
66#869—34no—
67C3×C4⋊C8C2×D314yes—
68C3×C4×C8C2×D314yes—
69#832—64no—
70#821—64no—
71#817—64no—
72#816—68no—
73#808—64no—
74C4⋊(C3⋊C8)—34no—
75C23×C32—21no—
76C22×C3⋊D3—21no—
77C32×D4—21no—
78C32×D4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85#638—44no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—41no—
89C4⋊(C3⋊D3)—21no—
90C4⋊(C3⋊D3)SD1612yes—
91C4×C3⋊D3—44no—
92C4×C3⋊D3—41no—
93C4×C3⋊D3—41no—
94#634—41no—
95#634—41no—
96#634—42no—
97C32×C8—41no—
98C32×C8—41no—
99C3⋊(C3⋊C8)—41no—
100#547—91no—
101#487—91no—
102#476—91no—
103#476—91no—
104#332—91no—
105D4⋊C8—91no—
106D4⋊C8C3⋊D311yescharacteristic, complemented
107C2×C3×D4D1214yes—
108C22×C3×C4—24no—
109C2×#67—68no—
110#235—128no—
111#235—128no—
112C2×D12—34no—
113C2×C4×D3—68no—
114C2×C4×D3—64no—
115C2×Dic6—64no—
116C2×Dic6—64no—
117C2×C3×C8—24no—
118C2×C3×C8—24no—
119C3×C4⋊C4D1214yes—
120C3×C22⋊C4—24no—
121C3×C42C22×D314yes—
122#217—68no—
123(C2×D3)⋊C4—64no—
124C4⋊Dic3—38no—
125C4⋊Dic3—34no—
126C4⋊Dic3—64no—
127C4⋊Dic3—64no—
128C4⋊Dic3—64no—
129Dic3⋊C4—68no—
130C2×C3⋊C8—64no—
131C22×C32—41no—
132C22×C32—41no—
133C22×C32—41no—
134C22×C32#12011yescharacteristic
135C2×C3⋊D3—22no—
136C2×C3⋊D3—41no—
137C2×C3⋊D3—41no—
138C32×C4—21no—
139C32×C4—41no—
140C32×C4C2×SD1611yescharacteristic
141C32×C4#13511yescharacteristic
142C32×C4AGL(1,ℤ/8)11yescharacteristic
143C32×C4#13711yescharacteristic
144C3⋊Dic3—42no—
145C3⋊Dic3—41no—
146C3⋊Dic3—81no—
147C2×#41—181no—
148C4⋊Q8—91no—
149C4⋊Q8—91no—
150#123—182no—
151C22⋊Q8—181no—
152#121—181no—
153C4×D4—91no—
154C4×D4C2×C3⋊D311yescharacteristic
155C2×C4⋊C4—181no—
156#106—181no—
157#106—181no—
158C4⋊C8—91no—
159C4⋊C8C2×C3⋊D311yescharacteristic
160#103—182no—
161#102—181no—
162#102—181no—
163C4×C8C2×C3⋊D311yescharacteristic
164C23×C3—24no—
165C22×D3—64no—
166C3×D4—24no—
167C3×D4—24no—
168C2×C3×C4—24no—
169C2×C3×C4—44no—
170C2×C3×C4—44no—
171C2×C3×C4C2×D1214yes—
172C2×C3×C4D3×D414yes—
173C2×C3×C4D3×D414yes—
174#67—1216no—
175C2×Dic3—64no—
176C2×Dic3—68no—
177C2×Dic3—124no—
178D12—38no—
179D12—64no—
180C4×D3—1216no—
181C4×D3—124no—
182C4×D3—124no—
183Dic6—124no—
184Dic6—124no—
185Dic6—128no—
186C3×C8—44no—
187C3×C8—44no—
188C3⋊C8—124no—
189C2×C32—81no—
190C2×C32#45011yescharacteristic
191C2×C32#45211yescharacteristic
192C2×C32#45411yescharacteristic
193C3⋊D3—42no—
194#41—362no—
195#41—362no—
196C2×Q8—181no—
197C2×Q8—181no—
198C2×D4—91no—
199C2×D4—182no—
200C2×D4C4⋊(C3⋊D3)11yescharacteristic
201C22×C4—21no—
202C22×C4—182no—
203C22×C4—181no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—181no—
207C4⋊C4—92no—
208C4⋊C4—91no—
209C4⋊C4—182no—
210C4⋊C4—181no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—182no—
216C22⋊C4—181no—
217C42C22×C3⋊D311yescharacteristic
218C22×C3—44no—
219C22×C3—44no—
220C22×C3—44no—
221C22×C3#88214yes—
222C2×D3—68no—
223C2×D3—124no—
224C2×D3—124no—
225C3×C4—24no—
226C3×C4—44no—
227C3×C4#90414yes—
228C3×C4#90914yes—
229C3×C4#91114yes—
230C3×C4D3×SD1614yes—
231Dic3—124no—
232Dic3—128no—
233Dic3—244no—
234C32#163511yescharacteristic, complemented, Sylow
235C23—21no—
236C23—181no—
237Q8—362no—
238Q8—361no—
239Q8—361no—
240D4—21no—
241D4—21no—
242D4—92no—
243D4—181no—
244D4—364no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—181no—
249C2×C4—182no—
250C2×C4—364no—
251C2×C4—361no—
252C2×C4—361no—
253C2×C4—361no—
254C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
255C2×C4D4×C3⋊D311yescharacteristic
256C2×C4D4×C3⋊D311yescharacteristic
257C8—41no—
258C8—41no—
259C8—361no—
260C2×C3—84no—
261C2×C3#473314yes—
262C2×C3#477614yes—
263C2×C3#482714yes—
264D3—128no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—182no—
269C22—361no—
270C22—361no—
271C22#6409111yescharacteristic
272C4—21no—
273C4—41no—
274C4—361no—
275C4—362no—
276C4—721no—
277C4#6411311yescharacteristic
278C4#6411811yescharacteristic
279C4#6412011yescharacteristic
280C4SD16×C3⋊D311yescharacteristic
281C3#6818114yescomplemented
282C2—81no—
283C2—362no—
284C2#1059243211yescharacteristic
285C2#1059247511yescharacteristic
286C2#1059252611yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×D4⋊C8C2
socleC22×C32#120
prime radical#10596022C2
hypercenterD4⋊C8C3⋊D3
hypocenterC32#1635
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592707C2semidirect
3. #10592541C2semidirect
4. #10592380C2semidirect
5. C32×D4⋊C8C2semidirect
6. #10589348C2semidirect
7. #10589325C2semidirect
30. C3×D4⋊C8D3semidirect
106. D4⋊C8C3⋊D3semidirect
234. C32#1635semidirect
281. C3#68181semidirect

Maximal subgroups

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

subgroupindex
#105960222
#105927072
#105925412
#105923802
C32×D4⋊C82
#105893482
#105893252
#681813