Finite Group Databasebeta

← #11783244

Subgroups — #11783244

Order 1152.

930 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 183 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
1C22×#3787C211yesmaximal, characteristic
2C2×#63900C212yesmaximal
3#10590075C214yesmaximal, complemented
4C22×C4×C3⋊D3C2211yescharacteristic
5C22×#624—22no—
6C22×#622C2212yes—
7C2×#3787—24no—
8C2×#3787C414yescomplemented
9C2×C3×C4⋊Dic3—22no—
10C2×#3724C2214yes—
11#63900—24no—
12#63900C418yescomplemented
13C2×D3×C4⋊C4—62no—
14C23×C3⋊D3D411yescharacteristic
15C22×C32×C4D411yescharacteristic
16C22×C3⋊Dic3C2311yescharacteristic
17C2×C4×C3⋊D3C2×C412yes—
18C2×C4×C3⋊D3C2×C414yes—
19C2×C4×C3⋊D3D414yes—
20C2×C4×C3⋊D3Q812yes—
21C22×C3×Dic3—24no—
22C2×#624—28no—
23C2×#624—44no—
24C2×#624—44no—
25C2×#622—24no—
26C2×#622C2×C414yescomplemented
27#3787—28no—
28C3×C4⋊Dic3—28no—
29#3724—24no—
30#3724C2×C418yescomplemented
31C2×#340—91nomaximal, Sylow
32C22×C4×D3—62no—
33C22×C4×D3—64no—
34C2×C3×C4⋊C4—62no—
35C2×C4⋊Dic3—22no—
36C2×Dic3⋊C4—64no—
37D3×C4⋊C4—68no—
38D3×C4⋊C4—68no—
39C23×C32C2×D411yescharacteristic
40C22×C3⋊D3C22⋊C414yes—
41C22×C3⋊D3C4⋊C412yes—
42C22×C3⋊D3D812yes—
43C22×C3⋊D3SD1614yes—
44C22×C3⋊D3Q1612yes—
45C2×C32×C4C22⋊C414yes—
46C2×C32×C4C4⋊C412yes—
47C2×C3⋊Dic3C22×C411yescharacteristic
48C2×C3⋊Dic3C22×C412yes—
49C2×C3⋊Dic3C2×D412yes—
50C2×C3⋊Dic3C2×Q811yescharacteristic
51C4×C3⋊D3C4214yes—
52C4×C3⋊D3C22⋊C414yes—
53C4×C3⋊D3C4⋊C418yes—
54C2×C3×Dic3—28no—
55C2×C3×Dic3—44no—
56C2×C3×Dic3—44no—
57#624—416no—
58#622—24no—
59C23×C8—91no—
60C22×C4⋊C4—92no—
61#340—94no—
62C23×D3—62no—
63C22×C3×C4—22no—
64C22×C3×C4—64no—
65C22×Dic3—24no—
66C22×Dic3—62no—
67C2×C4×D3—64no—
68C2×C4×D3—64no—
69C2×C4×D3—64no—
70C2×C4×D3—64no—
71C2×C4×D3—64no—
72C2×C4×D3—64no—
73C2×C4×D3—616no—
74C2×C4×D3—128no—
75C2×C4×D3—128no—
76C3×C4⋊C4—68no—
77C4⋊Dic3—28no—
78Dic3⋊C4—68no—
79Dic3⋊C4—68no—
80C22×C32C2×C22⋊C412yes—
81C22×C32C2×C4⋊C411yescharacteristic
82C22×C32C2×D811yescharacteristic
83C22×C32C2×SD1612yes—
84C22×C32C2×Q1611yescharacteristic
85C2×C3⋊D3#9514yes—
86C2×C3⋊D3#10218yes—
87C2×C3⋊D3#10318yes—
88C2×C3⋊D3#10614yes—
89C2×C3⋊D3#10714yes—
90C32×C4#9514yes—
91C3⋊Dic3C2×C4211yescharacteristic
92C3⋊Dic3C2×C22⋊C411yescharacteristic
93C3⋊Dic3C2×C4⋊C412yes—
94C3×Dic3—48no—
95C23×C4—91no—
96C23×C4—182no—
97C22×C8—94no—
98C22×C8—92no—
99C22×C8—184no—
100C2×C4⋊C4—62no—
101C2×C4⋊C4—98no—
102C2×C4⋊C4—94no—
103C2×C4⋊C4—184no—
104C23×C3—22no—
105C22×D3—64no—
106C22×D3—64no—
107C22×D3—64no—
108C22×D3—64no—
109C22×D3—64no—
110C22×D3—64no—
111C22×D3—64no—
112C2×C3×C4—24no—
113C2×C3×C4—24no—
114C2×C3×C4—24no—
115C2×C3×C4—68no—
116C2×C3×C4—124no—
117C2×C3×C4—124no—
118C2×Dic3—28no—
119C2×Dic3—44no—
120C2×Dic3—44no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—62no—
127C4×D3—68no—
128C4×D3—68no—
129C4×D3—68no—
130C4×D3—68no—
131C4×D3—1232no—
132C2×C32C2×#9511yescharacteristic
133C2×C32C2×#10212yes—
134C2×C32C2×#10312yes—
135C2×C32C2×#10611yescharacteristic
136C2×C32C2×#10711yescharacteristic
137C3⋊D3#34018yescomplemented
138C24—91no—
139C22×C4—64no—
140C22×C4—91no—
141C22×C4—94no—
142C22×C4—94no—
143C22×C4—92no—
144C22×C4—92no—
145C22×C4—188no—
146C22×C4—364no—
147C22×C4—364no—
148C22×C4GO+(4,𝔽2)11yescharacteristic
149C2×C8—94no—
150C2×C8—188no—
151C2×C8—184no—
152C4⋊C4—68no—
153C4⋊C4—98no—
154C4⋊C4—184no—
155C22×C3—22no—
156C22×C3—22no—
157C22×C3—22no—
158C22×C3—22no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—22no—
162C2×D3—68no—
163C2×D3—68no—
164C2×D3—68no—
165C2×D3—68no—
166C2×D3—68no—
167C2×D3—68no—
168C2×D3—68no—
169C3×C4—28no—
170C3×C4—128no—
171Dic3—48no—
172Dic3—62no—
173Dic3—62no—
174Dic3—62no—
175Dic3—62no—
176C32C2×#34011yescharacteristic, complemented, Sylow
177C23—92no—
178C23—94no—
179C23—92no—
180C23—94no—
181C23—92no—
182C23C2×GO+(4,𝔽2)11yescharacteristic
183C2×C4—68no—
184C2×C4—92no—
185C2×C4—92no—
186C2×C4—91no—
187C2×C4—91no—
188C2×C4—94no—
189C2×C4—94no—
190C2×C4—98no—
191C2×C4—124no—
192C2×C4—124no—
193C2×C4—3616no—
194C2×C4D32⋊C414yes—
195C2×C4#377312yes—
196C8—184no—
197C2×C3—22no—
198C2×C3—22no—
199C2×C3—22no—
200C2×C3—22no—
201C2×C3—22no—
202C2×C3—22no—
203C2×C3—22no—
204D3—616no—
205C22—98no—
206C22—98no—
207C22—94no—
208C22—94no—
209C22—94no—
210C22#6422511yescharacteristic
211C22#6422712yes—
212C22#6422811yescharacteristic
213C22C2×D32⋊C412yes—
214C22C2×#377311yescharacteristic
215C4—91no—
216C4—91no—
217C4—92no—
218C4—128no—
219C4#6373714yes—
220C3—22no—
221C2—98no—
222C2#1059336512yes—
223C2#1059337512yes—
224C2#1059338711yescharacteristic
225C2#1059339611yescharacteristic
226C2C2×#6373711yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#340
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10590075C2semidirect
8. C2×#3787C4semidirect
12. #63900C4semidirect
26. C2×#622C2×C4semidirect
30. #3724C2×C4semidirect
137. C3⋊D3#340semidirect
176. C32C2×#340semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
C2×#639002
#105900752
C2×#3409