Finite Group Databasebeta

← #11781423

Subgroups — #11781423

Order 1152.

546 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 119 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#10592771C211yesmaximal, characteristic
2#10592769C211yesmaximal, characteristic, complemented
3#10592540C211yesmaximal, characteristic, complemented
4#10592533C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic, complemented
6#10589352C211yesmaximal, characteristic, complemented
7#10589345C211yesmaximal, characteristic, complemented
8#68397—34nomaximal
9C32×#127C2211yescharacteristic
10C2×#3753—21no—
11C2×#3744—21no—
12C2×C8×C3⋊D3—21no—
13C4×C4⋊(C3⋊D3)C2211yescharacteristic
14#64078C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17#63659—21no—
18#63659—21no—
19#63659—21no—
20#63647—21no—
21#63643—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5072—34no—
25#5070—34no—
26#4841—34no—
27#4834—34no—
28C3×#331D314yescomplemented
29#4486—34no—
30#4479—34no—
31C2×C32×D4—21no—
32C2×C32×D4—21no—
33C2×C32×D4—21no—
34C2×C4⋊(C3⋊D3)D411yescharacteristic
35C2×C4×C3⋊D3—21no—
36C2×#634—21no—
37C2×C32×C8—21no—
38C2×C32×C8—21no—
39C32×C42C2311yescharacteristic
40#3753—42no—
41#3752—21no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)D411yescharacteristic
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48#3744—42no—
49C8×C3⋊D3—42no—
50#1681—91noSylow
51C3×#127C2×D314yes—
52C2×#213—64no—
53C2×#204—64no—
54C2×D3×C8—64no—
55C4×D12—34no—
56#869—34no—
57C3×C4⋊C8C2×D314yes—
58C3×C4⋊C8C2×D314yes—
59#832—64no—
60#832—64no—
61#832—64no—
62(C2×D3)⋊C8—64no—
63#816—64no—
64C4⋊(C3⋊C8)—34no—
65C4×C3⋊C8—34no—
66C23×C32—41no—
67C22×C3⋊D3—21no—
68C32×D4—41no—
69C32×D4—41no—
70C32×D4—41no—
71C32×D4—41no—
72C32×D4—81no—
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4#4111yescharacteristic
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—41no—
78C4⋊(C3⋊D3)—21no—
79C4⋊(C3⋊D3)D812yes—
80C4×C3⋊D3—41no—
81C4×C3⋊D3—41no—
82#634—41no—
83#634—41no—
84C32×C8—41no—
85C32×C8—41no—
86C3⋊(C3⋊C8)—21no—
87C3⋊(C3⋊C8)—21no—
88C3⋊(C3⋊C8)—41no—
89#486—91no—
90#461—91no—
91#459—91no—
92C8×D4—91no—
93#335—91no—
94#332—91no—
95#331C3⋊D311yescharacteristic, complemented
96C2×C3×D4—24no—
97C2×C3×D4—24no—
98C2×C3×D4—24no—
99C2×D12—34no—
100C2×C4×D3—64no—
101C2×Dic6—64no—
102C2×C3×C8—24no—
103C2×C3×C8—24no—
104C3×C42C22×D314yes—
105#213—128no—
106(C2×D3)⋊C4—64no—
107C4⋊Dic3—34no—
108C4⋊Dic3—64no—
109C4⋊Dic3—64no—
110C2×C3⋊C8—34no—
111C2×C3⋊C8—34no—
112C2×C3⋊C8—64no—
113#204—128no—
114D3×C8—128no—
115C22×C32—81no—
116C22×C32—81no—
117C22×C32—81no—
118C22×C32#12111yescharacteristic
119C2×C3⋊D3—22no—
120C2×C3⋊D3—41no—
121C2×C3⋊D3—41no—
122C32×C4—21no—
123C32×C4C2×D811yescharacteristic
124C32×C4#13511yescharacteristic
125C32×C4#13511yescharacteristic
126C32×C4AGL(1,ℤ/8)11yescharacteristic
127C3⋊Dic3—41no—
128C3⋊Dic3—81no—
129C2×SD16—181no—
130C2×D8—181no—
131C22×C8—181no—
132C4⋊Q8—91no—
133#127C2×C3⋊D311yescharacteristic
134C4×D4—91no—
135C4⋊C8—91no—
136C4⋊C8C2×C3⋊D311yescharacteristic
137C4⋊C8C2×C3⋊D311yescharacteristic
138#103—181no—
139#102—181no—
140#102—181no—
141#102—181no—
142C22⋊C8—181no—
143C4×C8—91no—
144C23×C3—44no—
145C22×D3—64no—
146C3×D4—44no—
147C3×D4—44no—
148C3×D4—44no—
149C3×D4—44no—
150C3×D4—84no—
151C2×C3×C4#23514yes—
152C2×C3×C4D3×D414yes—
153C2×C3×C4D3×D414yes—
154C2×Dic3—64no—
155C2×Dic3—124no—
156D12—38no—
157D12—64no—
158C4×D3—124no—
159C4×D3—124no—
160Dic6—124no—
161Dic6—124no—
162C3×C8—44no—
163C3×C8—44no—
164C3⋊C8—64no—
165C3⋊C8—64no—
166C3⋊C8—124no—
167C2×C32—161no—
168C2×C32#46311yescharacteristic
169C2×C32#46611yescharacteristic
170C2×C32#47111yescharacteristic
171C3⋊D3—42no—
172C2×Q8—181no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—91no—
177C22×C4—181no—
178SD16—362no—
179D8—362no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—91no—
183C2×C8—91no—
184C2×C8—181no—
185C2×C8—362no—
186C4⋊C4—91no—
187C4⋊C4—181no—
188C4⋊C4—181no—
189C22⋊C4—181no—
190C42C22×C3⋊D311yescharacteristic
191C22×C3—84no—
192C22×C3—84no—
193C22×C3—84no—
194C22×C3#88414yes—
195C2×D3—68no—
196C2×D3—124no—
197C2×D3—124no—
198C3×C4—24no—
199C3×C4D3×D814yes—
200C3×C4#91114yes—
201C3×C4#91614yes—
202C3×C4#91614yes—
203Dic3—124no—
204Dic3—244no—
205C32#168111yescharacteristic, complemented, Sylow
206C23—41no—
207C23—181no—
208Q8—361no—
209Q8—361no—
210D4—41no—
211D4—41no—
212D4—41no—
213D4—41no—
214D4—81no—
215D4—92no—
216D4—181no—
217C2×C4—181no—
218C2×C4—361no—
219C2×C4—361no—
220C2×C4—361no—
221C2×C4#382811yescharacteristic
222C2×C4D4×C3⋊D311yescharacteristic
223C2×C4D4×C3⋊D311yescharacteristic
224C8—41no—
225C8—41no—
226C8—181no—
227C8—181no—
228C8—361no—
229C2×C3—164no—
230C2×C3#474814yes—
231C2×C3#477514yes—
232C2×C3#478714yes—
233D3—128no—
234C22—81no—
235C22—81no—
236C22—81no—
237C22—182no—
238C22—361no—
239C22—361no—
240C22#6409311yescharacteristic
241C4—21no—
242C4—361no—
243C4—721no—
244C4D8×C3⋊D311yescharacteristic
245C4#6412011yescharacteristic
246C4#6412511yescharacteristic
247C4#6412511yescharacteristic
248C3#6839714yescomplemented
249C2—161no—
250C2—362no—
251C2#1059244711yescharacteristic
252C2#1059247411yescharacteristic
253C2#1059248611yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#331C2
socleC22×C32#121
prime radical#10592771C2
hypercenter#331C3⋊D3
hypocenterC32#1681
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #10592769C2semidirect
3. #10592540C2semidirect
4. #10592533C2semidirect
5. C32×#331C2semidirect
6. #10589352C2semidirect
7. #10589345C2semidirect
28. C3×#331D3semidirect
95. #331C3⋊D3semidirect
205. C32#1681semidirect
248. C3#68397semidirect

Maximal subgroups

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

subgroupindex
#105927712
#105927692
#105925402
#105925332
C32×#3312
#105893522
#105893452
#683973