Finite Group Databasebeta

← #11782008

Subgroups — #11782008

Order 1152.

369 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 82 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#10592537C211yesmaximal, characteristic
2#10590312C211yesmaximal, characteristic, complemented
3#10590300C212yesmaximal
4C3×#4481C212yesmaximal, complemented
5#10589098C211yesmaximal, characteristic, complemented
6#68501—32nomaximal
7C2×#3743—21no—
8C4×C4⋊(C3⋊D3)C2211yescharacteristic
9C3×#869C2212yes—
10C32×C4⋊C8C2211yescharacteristic
11#63647—21no—
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×C4⋊(C3⋊C8)C2212yes—
14#63576—21no—
15#63576—21no—
16#63573—22no—
17#63564—22no—
18#5084—32no—
19#5078—32no—
20#4842—32no—
21#4838—32no—
22#4838—61no—
23C3×#333—32no—
24#4481D312yescomplemented
25#4480—32no—
26C2×C4⋊(C3⋊D3)D411yescharacteristic
27C2×C4×C3⋊D3—21no—
28C2×C3×Dic6—22no—
29C2×C32×C8—21no—
30C32×C42C2311yescharacteristic
31#3752—21no—
32C4⋊(C3⋊Dic3)D411yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35#3743—42no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8—22no—
39#1695—91noSylow
40C3×C4⋊Q8—32no—
41C2×ΓL(1,𝔽25)—62no—
42C2×ΓL(1,𝔽25)—62no—
43C4×D12—32no—
44C4×D12—61no—
45#869C2×D312yes—
46C3×C4⋊C8—21no—
47C3×C4⋊C8—32no—
48C3×C4⋊C8C2×D312yes—
49#821—62no—
50(C2×D3)⋊C8—62no—
51(C2×D3)⋊C8—62no—
52#817—62no—
53#809—62no—
54#808—62no—
55#807—62no—
56#807—62no—
57C4⋊(C3⋊C8)C2×D312yes—
58C4×C3⋊C8—32no—
59C4×C3⋊C8—61no—
60C22×C3⋊D3—21no—
61C2×C32×C4C2×D411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4#4111yescharacteristic
64C2×C3⋊Dic3—21no—
65C4⋊(C3⋊D3)—22no—
66C4×C3⋊D3—41no—
67C4×C3⋊D3—41no—
68C2×C3×Dic3—42no—
69C3×Dic6—82no—
70C32×C8—41no—
71C3⋊(C3⋊C8)—21no—
72C3⋊(C3⋊C8)SD1612yes—
73C3×C3⋊C8—42no—
74#500—91no—
75#476—92no—
76#436—91no—
77#334—91no—
78#333—32no—
79C2×C3×Q8—62no—
80C2×D12—32no—
81C2×D12—61no—
82C2×C4×D3—62no—
83C2×C4×D3—62no—
84C2×Dic6—22no—
85C2×C3×C8—22no—
86C2×C3×C8—22no—
87C2×C3×C8—62no—
88C3×C4⋊C4—62no—
89C3×C4⋊C4—62no—
90C3×C42—21no—
91C3×C42C22×D312yes—
92(C2×D3)⋊C4—62no—
93(C2×D3)⋊C4—62no—
94C4⋊Dic3—22no—
95C4⋊Dic3—22no—
96C4⋊Dic3—32no—
97C4⋊Dic3—61no—
98C2×C3⋊C8—22no—
99C2×C3⋊C8—32no—
100C2×C3⋊C8—32no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—61no—
103ΓL(1,𝔽25)—124no—
104ΓL(1,𝔽25)—124no—
105C22×C32#12111yescharacteristic
106C2×C3⋊D3—41no—
107C2×C3⋊D3—41no—
108C2×C3⋊D3—41no—
109C32×C4—21no—
110C32×C4C2×SD1611yescharacteristic
111C32×C4#13712yes—
112C32×C4#13711yescharacteristic
113C3⋊Dic3—41no—
114C3×Dic3—82no—
115C2×M16—181no—
116C4⋊Q8—32no—
117C4×D4—91no—
118#107—181no—
119#107—181no—
120#106—182no—
121C4⋊C8—32no—
122C4⋊C8D3211yescharacteristic
123#102—182no—
124C22⋊C8—181no—
125C4×C8—91no—
126C22×D3—62no—
127C22×D3—62no—
128C3×Q8—242no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—122no—
133C2×C3×C4#23512yes—
134C2×C3×C4D3×D412yes—
135C2×C3×C4D3×D412yes—
136C2×Dic3—42no—
137C2×Dic3—62no—
138C2×Dic3—62no—
139D12—62no—
140D12—62no—
141D12—122no—
142C4×D3—122no—
143C4×D3—122no—
144C4×D3—122no—
145C4×D3—122no—
146Dic6—82no—
147C3×C8—42no—
148C3×C8—42no—
149C3×C8—122no—
150C3⋊C8—34no—
151C3⋊C8—42no—
152C3⋊C8—62no—
153C3⋊C8—62no—
154C3⋊C8—121no—
155C2×C32#46111yescharacteristic
156C2×C32#47011yescharacteristic
157C2×C32#47211yescharacteristic
158C3⋊D3—81no—
159C2×Q8—62no—
160C2×D4—91no—
161C22×C4—181no—
162M16—362no—
163C2×C8—21no—
164C2×C8—62no—
165C2×C8—91no—
166C2×C8—91no—
167C4⋊C4—62no—
168C4⋊C4—62no—
169C4⋊C4—91no—
170C22⋊C4—181no—
171C42C2×D3211yescharacteristic
172C22×C3—21no—
173C22×C3#88412yes—
174C2×D3—122no—
175C2×D3—122no—
176C2×D3—122no—
177C2×D3—122no—
178C2×D3—122no—
179C2×D3—122no—
180C3×C4—22no—
181C3×C4—22no—
182C3×C4—21no—
183C3×C4—21no—
184C3×C4—41no—
185C3×C4—242no—
186C3×C4D3×SD1612yes—
187C3×C4#91512yes—
188C3×C4#91812yes—
189C3×C4#91812yes—
190Dic3—82no—
191Dic3—122no—
192Dic3—122no—
193C32#169511yescharacteristic, complemented, Sylow
194C23—181no—
195Q8—242no—
196D4—182no—
197C2×C4—122no—
198C2×C4—181no—
199C2×C4—361no—
200C2×C4—361no—
201C2×C4#379811yescharacteristic
202C2×C4#380211yescharacteristic
203C2×C4#381111yescharacteristic
204C8—41no—
205C8—92no—
206C8—122no—
207C8—181no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3#474912yes—
212C2×C3#481612yes—
213C2×C3#481812yes—
214D3—242no—
215D3—242no—
216C22—361no—
217C22—361no—
218C22—361no—
219C22#6391211yescharacteristic
220C4—21no—
221C4—242no—
222C4—361no—
223C4#6381112yes—
224C4#6393011yescharacteristic
225C4#6394511yescharacteristic
226C3—21no—
227C3#6850112yescomplemented
228C2—721no—
229C2#1059056511yescharacteristic
230C2#1059085611yescharacteristic
231C2#1059098811yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1695
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10590312C2semidirect
4. C3×#4481C2semidirect
5. #10589098C2semidirect
24. #4481D3semidirect
193. C32#1695semidirect
227. C3#68501semidirect

Maximal subgroups

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

subgroupindex
#105925372
#105903122
#105903002
C3×#44812
#105890982
#685013