Finite Group Databasebeta

← #11797892

Subgroups — #11797892

Order 1152.

330 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592603C211yesmaximal, characteristic
2#10590917C212yesmaximal, complemented
3C3×#4506C211yesmaximal, characteristic, complemented
4C3×#4502C211yesmaximal, characteristic, complemented
5#10589122C212yesmaximal, complemented
6#69358—31nomaximal
7#69085—31nomaximal
8#64113C2212yes—
9#63817—22no—
10C2×C32×C16C2211yescharacteristic
11#63628C411yescharacteristic, complemented
12#63627C412yescomplemented
13#63626C411yescharacteristic, complemented
14C3×#819C2212yes—
15C3×C8×Dic3C2211yescharacteristic
16C2×C3×C3⋊C16C2211yescharacteristic
17#63570—22no—
18#4904—31no—
19#4904—31no—
20#4904—61no—
21#4895—32no—
22#4700—32no—
23C3×#368—31no—
24C3×#346—31no—
25#4510—32no—
26#4506D311yescharacteristic, complemented
27#4502D311yescharacteristic, complemented
28#4497—32no—
29#3828—22no—
30C2×C32×C8C2311yescharacteristic
31#3746C2×C412yes—
32#3745C2×C412yes—
33#3744—22no—
34C3×C4×Dic3D411yescharacteristic
35C3×#208—22no—
36C2×C3×C3⋊C8D411yescharacteristic
37#3712—42no—
38#3710—42no—
39C32×C16C2×C411yescharacteristic
40C32×C16C2×C411yescharacteristic
41C3×C3⋊C16—21no—
42#2179—91noSylow
43#907—62no—
44#904—32no—
45#904—32no—
46#904—62no—
47#901—62no—
48C2×C3×C16—21no—
49C2×C3×C16—31no—
50C2×C3×C16C2×D311yescharacteristic
51C2×C3×C16C2×D311yescharacteristic
52C3×#108—32no—
53C3×C4×C8—31no—
54#825—62no—
55#819C2×D312yes—
56C8×Dic3C2×D311yescharacteristic
57C2×C3⋊C16C2×D311yescharacteristic
58#805—62no—
59Dic24—31no—
60Dic24—31no—
61Dic24—61no—
62#800—32no—
63#800—32no—
64#800—62no—
65D48—31no—
66D48—31no—
67D48—61no—
68C2×C32×C4C2×D411yescharacteristic
69#638—42no—
70C4⋊(C3⋊D3)—22no—
71C4×C3⋊D3—42no—
72#634—22no—
73C2×C3×Dic3—21no—
74C32×C8C22×C411yescharacteristic
75C32×C8#4111yescharacteristic
76C3×C3⋊C8—42no—
77C3×C3⋊C8D812yes—
78#508—91no—
79#443—92no—
80#368—31no—
81#359—92no—
82#346—31no—
83#235—62no—
84#235—62no—
85#235—122no—
86C3×M16—62no—
87C2×C3×C8—21no—
88C2×C3×C8—31no—
89C2×C3×C8C22×D311yescharacteristic
90C2×C3×C8C22×D311yescharacteristic
91C3×C42—31no—
92C4×Dic3D1211yescharacteristic
93#208—22no—
94C2×C3⋊C8D1211yescharacteristic
95Dic12—32no—
96Dic12—32no—
97Dic12—62no—
98D24—32no—
99D24—32no—
100D24—62no—
101#204—62no—
102#204—62no—
103#204—122no—
104ΓL(1,𝔽25)—122no—
105ΓL(1,𝔽25)—122no—
106D3×C8—122no—
107D3×C8—122no—
108C3×C16—21no—
109C3×C16—21no—
110C3×C16—61no—
111C3×C16C4×D311yescharacteristic
112C3×C16C4×D311yescharacteristic
113C3×C16C4×D311yescharacteristic
114C3×C16C4×D311yescharacteristic
115C3⋊C16—21no—
116C22×C32#13511yescharacteristic
117C2×C3⋊D3—42no—
118C32×C4C4×D411yescharacteristic
119C32×C4C2×D811yescharacteristic
120C3⋊Dic3—42no—
121C3×Dic3—41no—
122#135—92no—
123#131—182no—
124Q32—91no—
125SD32—92no—
126D16—91no—
127C2×C16—31no—
128C2×C16D3211yescharacteristic
129#108—32no—
130#104—182no—
131C4×C8—31no—
132C2×C3×C4—21no—
133C2×C3×C4—61no—
134C2×C3×C4C2×D1211yescharacteristic
135C2×C3×C4D3×D411yescharacteristic
136#67—122no—
137#67—122no—
138#67—242no—
139C2×Dic3—21no—
140D12—62no—
141D12—62no—
142D12—122no—
143C4×D3—122no—
144C4×D3—122no—
145C4×D3—242no—
146Dic6—62no—
147Dic6—62no—
148Dic6—122no—
149C3×C8—21no—
150C3×C8—21no—
151C3×C8—32no—
152C3×C8—122no—
153C3×C8C2×C4×D311yescharacteristic
154C3×C8C2×C4×D311yescharacteristic
155C3×C8#23511yescharacteristic
156C3×C8#23911yescharacteristic
157C3⋊C8—42no—
158C3⋊C8D2412yes—
159C2×C32—21no—
160C2×C32C4×D811yescharacteristic
161C3⋊D3—82no—
162#41—182no—
163Q16—92no—
164SD16—182no—
165D8—92no—
166M16—62no—
167M16—362no—
168C2×C8—31no—
169C2×C8—362no—
170C2×C8C2×D3211yescharacteristic
171C42—31no—
172C16—61no—
173C16#62411yescharacteristic
174C16#62411yescharacteristic
175C22×C3—21no—
176C22×C3#90411yescharacteristic
177C22×C3#91911yescharacteristic
178C2×D3—122no—
179C2×D3—122no—
180C2×D3—242no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—121no—
184C3×C4C4×D1211yescharacteristic
185C3×C4#89311yescharacteristic
186C3×C4C2×D2411yescharacteristic
187C3×C4D3×D811yescharacteristic
188Dic3—41no—
189Dic3—122no—
190Dic3—122no—
191Dic3—242no—
192C32#217911yescharacteristic, complemented, Sylow
193Q8—182no—
194D4—182no—
195D4—362no—
196C2×C4—61no—
197C2×C4—362no—
198C2×C4D3×D1211yescharacteristic
199C8—32no—
200C8—122no—
201C8#379911yescharacteristic
202C8C2×#62411yescharacteristic
203C2×C3—21no—
204C2×C3—21no—
205C2×C3—21no—
206C2×C3—41no—
207C2×C3C4×D2411yescharacteristic
208C2×C3#487211yescharacteristic
209D3—242no—
210D3—242no—
211D3—482no—
212C22—362no—
213C22#6380811yescharacteristic
214C4—121no—
215C4—362no—
216C4D3×D2411yescharacteristic
217C4#6389411yescharacteristic
218C3—21no—
219C3#6908511yescharacteristic, complemented
220C3#6935811yescharacteristic, complemented
221C2—21no—
222C2—722no—
223C2#1059076311yescharacteristic
subgroupG/H
centerC4D3×D24
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC2×C32C4×D8
prime radical#10592603C2
cosocleC2×C32×C8C23
hypercenterC2×C16D32
hypocenterC32#2179
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. #10590917C2semidirect
3. C3×#4506C2semidirect
4. C3×#4502C2semidirect
5. #10589122C2semidirect
11. #63628C4semidirect
12. #63627C4semidirect
13. #63626C4semidirect
26. #4506D3semidirect
27. #4502D3semidirect
192. C32#2179semidirect
219. C3#69085semidirect
220. C3#69358semidirect

Maximal subgroups

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

subgroupindex
#105926032
#105909172
C3×#45062
C3×#45022
#105891222
#693583
#690853