Finite Group Databasebeta

← #11779523

Subgroups — #11779523

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#10596197C211yesmaximal, characteristic
2#10592792C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4#10592541C211yesmaximal, characteristic, complemented
5C32×#332C211yesmaximal, characteristic, complemented
6#10589349C211yesmaximal, characteristic, complemented
7#10589349C211yesmaximal, characteristic, complemented
8#68434—34nomaximal
9C2×#3832—21no—
10C32×C4⋊Q8C2211yescharacteristic
11#64155—21no—
12#64104—21no—
13#64103—22no—
14C4⋊C4×C3⋊D3—21no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C32×C4⋊C8C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20#63648—21no—
21#63648—21no—
22#63644—21no—
23#63644—21no—
24#63637—22no—
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26#5726—34no—
27#5093—34no—
28#4842—34no—
29#4842—34no—
30C3×#332D314yescomplemented
31#4483—34no—
32#4483—34no—
33C2×C32×Q8—21no—
34#3832—42no—
35#3832—42no—
36C2×C4⋊(C3⋊D3)—22no—
37C2×C4⋊(C3⋊D3)D411yescharacteristic
38C2×C4⋊(C3⋊D3)D411yescharacteristic
39C2×C4×C3⋊D3—22no—
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3—21no—
42C2×#634—21no—
43C2×C32×C8—21no—
44C2×C32×C8—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4D412yes—
47C32×C42C2311yescharacteristic
48#3752—22no—
49#3752—21no—
50#3752—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4⋊(C3⋊Dic3)D411yescharacteristic
55#3750—22no—
56C2×C3⋊(C3⋊C8)—21no—
57#1635—91noSylow
58C2×#239—64no—
59C3×C4⋊Q8C2×D314yes—
60#946—64no—
61#895—64no—
62#894—68no—
63D3×C4⋊C4—64no—
64C4×D12—34no—
65C4×D12—34no—
66#869—34no—
67C3×C4⋊C8C2×D314yes—
68C3×C4⋊C8C2×D314yes—
69#821—64no—
70#821—64no—
71#817—64no—
72#817—64no—
73#810—68no—
74C4×C3⋊C8—34no—
75C22×C3⋊D3—21no—
76C22×C3⋊D3—21no—
77C32×Q8—41no—
78C32×Q8—41no—
79C2×C32×C4—22no—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—41no—
86C4⋊(C3⋊D3)—21no—
87C4⋊(C3⋊D3)—21no—
88C4⋊(C3⋊D3)—21no—
89C4⋊(C3⋊D3)—44no—
90C4⋊(C3⋊D3)SD1612yes—
91C4×C3⋊D3—44no—
92C4×C3⋊D3—41no—
93C4×C3⋊D3—41no—
94C4×C3⋊D3—41no—
95C4×C3⋊D3—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#332C3⋊D311yescharacteristic, complemented
105D4⋊C8—91no—
106D4⋊C8—91no—
107C2×C3×Q8—24no—
108#239—128no—
109#239—128no—
110C2×D12—34no—
111C2×D12—34no—
112C2×D12—68no—
113C2×C4×D3—68no—
114C2×C4×D3—64no—
115C2×C4×D3—64no—
116C2×Dic6—64no—
117C2×C3×C8—24no—
118C2×C3×C8—24no—
119C3×C4⋊C4—24no—
120C3×C4⋊C4D1218yes—
121C3×C42C22×D314yes—
122(C2×D3)⋊C4—68no—
123(C2×D3)⋊C4—64no—
124(C2×D3)⋊C4—64no—
125C4⋊Dic3—34no—
126C4⋊Dic3—34no—
127C4⋊Dic3—64no—
128C4⋊Dic3—64no—
129Dic3⋊C4—68no—
130C2×C3⋊C8—64no—
131C22×C32#12011yescharacteristic
132C2×C3⋊D3—22no—
133C2×C3⋊D3—41no—
134C2×C3⋊D3—41no—
135C2×C3⋊D3—41no—
136C2×C3⋊D3—41no—
137C2×C3⋊D3—41no—
138C32×C4—21no—
139C32×C4—42no—
140C32×C4C2×SD1611yescharacteristic
141C32×C4#13511yescharacteristic
142C32×C4AGL(1,ℤ/8)11yescharacteristic
143C32×C4#13711yescharacteristic
144C3⋊Dic3—41no—
145C3⋊Dic3—41no—
146C3⋊Dic3—81no—
147C2×#41—181no—
148C4⋊Q8—91no—
149C4⋊Q8C2×C3⋊D311yescharacteristic
150#123—182no—
151C22⋊Q8—181no—
152#121—181no—
153C4×D4—91no—
154C4×D4—91no—
155C2×C4⋊C4—181no—
156#106—181no—
157#106—181no—
158C4⋊C8C2×C3⋊D311yescharacteristic
159C4⋊C8C2×C3⋊D311yescharacteristic
160#103—182no—
161#102—181no—
162#102—181no—
163C4×C8—91no—
164C22×D3—64no—
165C22×D3—64no—
166C3×Q8—44no—
167C3×Q8—44no—
168C2×C3×C4—28no—
169C2×C3×C4C2×D1214yes—
170C2×C3×C4D3×D414yes—
171C2×C3×C4D3×D414yes—
172C2×Dic3—64no—
173C2×Dic3—64no—
174C2×Dic3—124no—
175D12—38no—
176D12—64no—
177D12—64no—
178D12—64no—
179D12—1216no—
180C4×D3—1216no—
181C4×D3—124no—
182C4×D3—124no—
183C4×D3—124no—
184C4×D3—124no—
185Dic6—128no—
186C3×C8—44no—
187C3×C8—44no—
188C3⋊C8—124no—
189C2×C32#45011yescharacteristic
190C2×C32#45211yescharacteristic
191C2×C32#45411yescharacteristic
192C3⋊D3—42no—
193C3⋊D3—81no—
194#41—362no—
195#41—362no—
196C2×Q8—21no—
197C2×Q8—181no—
198C2×D4—91no—
199C2×D4—91no—
200C2×D4—182no—
201C22×C4—182no—
202C22×C4—181no—
203C22×C4—181no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—181no—
207C4⋊C4—21no—
208C4⋊C4—91no—
209C4⋊C4—91no—
210C4⋊C4—182no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C4⋊C4C4⋊(C3⋊D3)12yes—
214C22⋊C4—182no—
215C22⋊C4—181no—
216C22⋊C4—181no—
217C42C22×C3⋊D311yescharacteristic
218C22×C3#88214yes—
219C2×D3—68no—
220C2×D3—124no—
221C2×D3—124no—
222C2×D3—124no—
223C2×D3—124no—
224C2×D3—124no—
225C3×C4—24no—
226C3×C4—48no—
227C3×C4#91114yes—
228C3×C4D3×SD1614yes—
229C3×C4#91614yes—
230C3×C4#91814yes—
231Dic3—124no—
232Dic3—124no—
233Dic3—244no—
234C32#163511yescharacteristic, complemented, Sylow
235C23—181no—
236C23—181no—
237Q8—41no—
238Q8—41no—
239Q8—362no—
240D4—92no—
241D4—181no—
242D4—181no—
243D4—181no—
244D4—364no—
245C2×C4—22no—
246C2×C4—181no—
247C2×C4—181no—
248C2×C4—364no—
249C2×C4—361no—
250C2×C4—361no—
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#475314yes—
261C2×C3#477614yes—
262C2×C3#480814yes—
263D3—128no—
264D3—244no—
265C22—182no—
266C22—361no—
267C22—361no—
268C22—361no—
269C22—361no—
270C22—361no—
271C22#6409111yescharacteristic
272C4—21no—
273C4—42no—
274C4—361no—
275C4—361no—
276C4—721no—
277C4#6412011yescharacteristic
278C4SD16×C3⋊D311yescharacteristic
279C4#6412511yescharacteristic
280C4#6412711yescharacteristic
281C3#6843414yescomplemented
282C2—362no—
283C2—721no—
284C2#1059245211yescharacteristic
285C2#1059247511yescharacteristic
286C2#1059250711yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#332C2
socleC22×C32#120
prime radical#10596197C2
hypercenter#332C3⋊D3
hypocenterC32#1635
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #10592792C2semidirect
3. #10592541C2semidirect
4. #10592541C2semidirect
5. C32×#332C2semidirect
6. #10589349C2semidirect
7. #10589349C2semidirect
30. C3×#332D3semidirect
104. #332C3⋊D3semidirect
234. C32#1635semidirect
281. C3#68434semidirect

Maximal subgroups

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

subgroupindex
#105961972
#105927922
#105925412
C32×#3322
#105893492
#684343