Finite Group Databasebeta

← #11777971

Subgroups — #11777971

Order 1152.

385 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 385 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C4×#3713C211yesmaximal, characteristic
2#10590339C212yesmaximal, complemented
3#10589320C211yesmaximal, characteristic, complemented
4C3×#4459C212yesmaximal, complemented
5#10589098C211yesmaximal, characteristic, complemented
6#68163—32nomaximal
7C3×C4×D12C2212yes—
8C2×#3713C411yescharacteristic
9C2×#3711—22no—
10C32×C4×C8C2211yescharacteristic
11C4×C3⋊(C3⋊C8)C2211yescharacteristic
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×C4⋊(C3⋊C8)C2212yes—
14#63576C411yescharacteristic
15#63562C412yes—
16(C2×D3)⋊(C3⋊C8)—22no—
17C4×#213—32no—
18#5012—32no—
19#4838—32no—
20C3×D4⋊C8—32no—
21#4480—32no—
22#4459D312yescomplemented
23#4454—32no—
24#4454—61no—
25C2×C3×D12C2×C412yes—
26C2×C3×C4×D3—22no—
27C2×C32×C8—21no—
28C32×C42C2311yescharacteristic
29C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
30C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
31C2×C3⋊(C3⋊C8)D412yes—
32C3×(C2×D3)⋊C4—22no—
33C3×C4⋊Dic3C2×C412yes—
34C2×C3×C3⋊C8—22no—
35#3713—22no—
36#3711—44no—
37#1594—91noSylow
38C3×C4×D4—32no—
39C2×#213—32no—
40C2×#208—62no—
41C2×ΓL(1,𝔽25)—62no—
42C4×D12C2×D312yes—
43C3×C4⋊C8—32no—
44C3×C4×C8—21no—
45C3×C4×C8C2×D312yes—
46#832—32no—
47#830—62no—
48(C2×D3)⋊C8—62no—
49#809—32no—
50#807—32no—
51C4⋊(C3⋊C8)C2×D312yes—
52C4×C3⋊C8—32no—
53C4×C3⋊C8—32no—
54C4×C3⋊C8—61no—
55C4×C3⋊C8—61no—
56C22×C3×D3—22no—
57C2×C32×C4C22×C411yescharacteristic
58C2×C32×C4C2×D411yescharacteristic
59C2×C32×C4#4111yescharacteristic
60C2×C3×Dic3—22no—
61C3×D12—22no—
62C3×D12—22no—
63C3×C4×D3—42no—
64C3×C4×D3—42no—
65C32×C8—41no—
66C3⋊(C3⋊C8)—21no—
67C3⋊(C3⋊C8)—22no—
68C3⋊(C3⋊C8)M1612yescomplemented
69C3×C3⋊C8—42no—
70C4×D8—91no—
71#436—92no—
72#334—91no—
73D4⋊C8—32no—
74#322—91no—
75C2×C3×D4—32no—
76C22×C3×C4—62no—
77C2×D12C4×D312yes—
78C2×C4×D3—22no—
79C2×C3×C8—22no—
80C2×C3×C8—22no—
81C2×C3×C8—62no—
82C3×C4⋊C4—32no—
83C3×C22⋊C4—62no—
84C3×C42—21no—
85C3×C42C22×D312yes—
86#213—64no—
87(C2×D3)⋊C4—22no—
88C4⋊Dic3C4×D312yes—
89#208—124no—
90C2×C3⋊C8—22no—
91C2×C3⋊C8—32no—
92C2×C3⋊C8—32no—
93C2×C3⋊C8—32no—
94C2×C3⋊C8—32no—
95C2×C3⋊C8—61no—
96C2×C3⋊C8—61no—
97C2×C3⋊C8—62no—
98ΓL(1,𝔽25)—124no—
99C22×C32C4×D411yescharacteristic
100C2×C3×D3—42no—
101C2×C3×D3—42no—
102C2×C3×D3—42no—
103C32×C4—21no—
104C32×C4C2×M1611yescharacteristic
105C32×C4#13111yescharacteristic
106C32×C4AGL(1,ℤ/8)12yes—
107C3×Dic3—42no—
108C2×D8—91no—
109C2×M16—182no—
110C4×D4—32no—
111#107—91no—
112C4⋊C8—32no—
113#102—92no—
114C22⋊C8—182no—
115C4×C8—91no—
116C4×C8—91no—
117C4×C8D3211yescharacteristic
118C23×C3—62no—
119C22×D3—22no—
120C3×D4—62no—
121C3×D4—62no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—62no—
126C2×C3×C4—122no—
127C2×C3×C4—122no—
128C2×C3×C4C2×C4×D312yes—
129C2×C3×C4D3×D412yes—
130C2×C3×C4#23712yes—
131C2×Dic3—22no—
132D12—22no—
133D12—22no—
134C4×D3—42no—
135C4×D3—42no—
136C3×C8—42no—
137C3×C8—42no—
138C3×C8—122no—
139C3⋊C8—34no—
140C3⋊C8—42no—
141C3⋊C8—62no—
142C3⋊C8—62no—
143C3⋊C8—62no—
144C3⋊C8—62no—
145C3⋊C8—62no—
146C3⋊C8—122no—
147C2×C32#43611yescharacteristic
148C2×C32#44211yescharacteristic
149C2×C32#44411yescharacteristic
150C3×D3—82no—
151C2×D4—32no—
152C22×C4—62no—
153D8—182no—
154M16—364no—
155C2×C8—21no—
156C2×C8—62no—
157C2×C8—91no—
158C2×C8—91no—
159C2×C8—92no—
160C4⋊C4—32no—
161C22⋊C4—62no—
162C42C2×D3211yescharacteristic
163C22×C3—21no—
164C22×C3—122no—
165C22×C3—122no—
166C22×C3—122no—
167C22×C3#67⋊C412yes—
168C2×D3—42no—
169C2×D3—42no—
170C2×D3—42no—
171C3×C4—22no—
172C3×C4—22no—
173C3×C4—21no—
174C3×C4—22no—
175C3×C4—21no—
176C3×C4—122no—
177C3×C4#90112yes—
178C3×C4D3×M1612yes—
179C3×C4#91112yes—
180C3×C4#91412yes—
181Dic3—42no—
182C32#159411yescharacteristic, complemented, Sylow
183C23—62no—
184D4—62no—
185D4—62no—
186C2×C4—62no—
187C2×C4—122no—
188C2×C4—122no—
189C2×C4C4×D3211yescharacteristic
190C2×C4#380211yescharacteristic
191C2×C4#380511yescharacteristic
192C8—41no—
193C8—92no—
194C8—122no—
195C8—182no—
196C8—181no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—242no—
201C2×C3#472912yes—
202C2×C3#478512yes—
203C2×C3#482312yes—
204D3—82no—
205C22—122no—
206C22—122no—
207C22—122no—
208C22#6390211yescharacteristic
209C4—21no—
210C4—122no—
211C4#6379111yescharacteristic
212C4#6379812yes—
213C4#6380311yescharacteristic
214C3—21no—
215C3#6816312yescomplemented
216C2—242no—
217C2#1059039011yescharacteristic
218C2#1059073411yescharacteristic
219C2#1059074111yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C4×D4
prime radicalC2×#3713C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1594
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10590339C2semidirect
3. #10589320C2semidirect
4. C3×#4459C2semidirect
5. #10589098C2semidirect
22. #4459D3semidirect
68. C3⋊(C3⋊C8)M16semidirect
182. C32#1594semidirect
215. C3#68163semidirect

Maximal subgroups

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

subgroupindex
C4×#37132
#105903392
#105893202
C3×#44592
#105890982
#681633