Finite Group Databasebeta

← #11781943

Subgroups — #11781943

Order 1152.

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

normal subgroups only

This group has 393 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#10590379C212yesmaximal
3#10590312C211yesmaximal, characteristic, complemented
4C3×#4486C212yesmaximal, complemented
5#10589098C211yesmaximal, characteristic, complemented
6#68451—32nomaximal
7C2×#3743—21no—
8C4×C4⋊(C3⋊D3)C2211yescharacteristic
9C3×#869C2212yes—
10C2×#3717—22no—
11C32×C4⋊C8C2211yescharacteristic
12#63647—21no—
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×C4⋊(C3⋊C8)C2212yes—
15#63576—21no—
16#63576—21no—
17#63566—22no—
18#5083—32no—
19#5078—32no—
20#4841—32no—
21#4838—32no—
22#4838—61no—
23C3×#332—32no—
24#4486D312yescomplemented
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#3717—44no—
40#1693—91noSylow
41C3×C4⋊Q8—32no—
42C2×#215—62no—
43C2×#204—62no—
44C2×ΓL(1,𝔽25)—62no—
45C2×ΓL(1,𝔽25)—62no—
46C4×D12—32no—
47C4×D12—61no—
48#869C2×D312yes—
49C3×C4⋊C8—21no—
50C3×C4⋊C8—32no—
51C3×C4⋊C8C2×D312yes—
52#835—62no—
53(C2×D3)⋊C8—62no—
54(C2×D3)⋊C8—62no—
55#816—62no—
56#807—62no—
57#807—62no—
58C4⋊(C3⋊C8)C2×D312yes—
59C4×C3⋊C8—32no—
60C4×C3⋊C8—61no—
61C22×C3⋊D3—21no—
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C32×C4#4111yescharacteristic
65C2×C3⋊Dic3—21no—
66C4⋊(C3⋊D3)—22no—
67C4×C3⋊D3—41no—
68C4×C3⋊D3—41no—
69C2×C3×Dic3—42no—
70C3×Dic6—42no—
71C3×Dic6—42no—
72C32×C8—41no—
73C3⋊(C3⋊C8)—21no—
74C3⋊(C3⋊C8)SD1612yescomplemented
75C3×C3⋊C8—42no—
76#500—91no—
77#461—92no—
78#436—91no—
79#334—91no—
80#332—32no—
81C2×C3×Q8—62no—
82C2×D12—32no—
83C2×D12—61no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×Dic6—22no—
87C2×C3×C8—22no—
88C2×C3×C8—22no—
89C2×C3×C8—62no—
90C3×C4⋊C4—62no—
91C3×C4⋊C4—62no—
92C3×C42—21no—
93C3×C42C22×D312yes—
94#215—124no—
95(C2×D3)⋊C4—62no—
96(C2×D3)⋊C4—62no—
97C4⋊Dic3—22no—
98C4⋊Dic3—22no—
99C4⋊Dic3—32no—
100C4⋊Dic3—61no—
101C2×C3⋊C8—22no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—32no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106#204—124no—
107ΓL(1,𝔽25)—124no—
108ΓL(1,𝔽25)—124no—
109C22×C32#12111yescharacteristic
110C2×C3⋊D3—41no—
111C2×C3⋊D3—41no—
112C2×C3⋊D3—41no—
113C32×C4—21no—
114C32×C4C2×SD1611yescharacteristic
115C32×C4AGL(1,ℤ/8)12yes—
116C32×C4#13711yescharacteristic
117C3⋊Dic3—41no—
118C3×Dic3—82no—
119C2×SD16—182no—
120C2×M16—181no—
121C4⋊Q8—32no—
122C4×D4—91no—
123#107—181no—
124#107—181no—
125C4⋊C8—32no—
126C4⋊C8D3211yescharacteristic
127#103—182no—
128C22⋊C8—181no—
129C4×C8—91no—
130C22×D3—62no—
131C22×D3—62no—
132C3×Q8—122no—
133C3×Q8—122no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—122no—
138C2×C3×C4#23512yes—
139C2×C3×C4D3×D412yes—
140C2×C3×C4D3×D412yes—
141C2×Dic3—42no—
142C2×Dic3—62no—
143C2×Dic3—62no—
144D12—62no—
145D12—62no—
146D12—122no—
147C4×D3—122no—
148C4×D3—122no—
149C4×D3—122no—
150C4×D3—122no—
151Dic6—42no—
152Dic6—42no—
153C3×C8—42no—
154C3×C8—42no—
155C3×C8—122no—
156C3⋊C8—34no—
157C3⋊C8—42no—
158C3⋊C8—62no—
159C3⋊C8—62no—
160C3⋊C8—121no—
161C2×C32#46111yescharacteristic
162C2×C32#46911yescharacteristic
163C2×C32#47311yescharacteristic
164C3⋊D3—81no—
165C2×Q8—62no—
166C2×D4—91no—
167C22×C4—181no—
168SD16—364no—
169M16—362no—
170C2×C8—21no—
171C2×C8—62no—
172C2×C8—91no—
173C2×C8—91no—
174C4⋊C4—62no—
175C4⋊C4—62no—
176C4⋊C4—91no—
177C22⋊C4—181no—
178C42C2×D3211yescharacteristic
179C22×C3—21no—
180C22×C3#88412yes—
181C2×D3—122no—
182C2×D3—122no—
183C2×D3—122no—
184C2×D3—122no—
185C2×D3—122no—
186C2×D3—122no—
187C3×C4—22no—
188C3×C4—22no—
189C3×C4—21no—
190C3×C4—21no—
191C3×C4—41no—
192C3×C4—242no—
193C3×C4#91112yes—
194C3×C4D3×SD1612yes—
195C3×C4#91412yes—
196C3×C4#91812yes—
197Dic3—82no—
198Dic3—122no—
199Dic3—122no—
200C32#169311yescharacteristic, complemented, Sylow
201C23—181no—
202Q8—122no—
203Q8—122no—
204D4—182no—
205C2×C4—122no—
206C2×C4—181no—
207C2×C4—361no—
208C2×C4—361no—
209C2×C4#379811yescharacteristic
210C2×C4#380211yescharacteristic
211C2×C4#381111yescharacteristic
212C8—41no—
213C8—92no—
214C8—122no—
215C8—181no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3#475512yes—
220C2×C3#478212yes—
221C2×C3#481812yes—
222D3—242no—
223D3—242no—
224C22—361no—
225C22—361no—
226C22—361no—
227C22#6391211yescharacteristic
228C4—21no—
229C4—242no—
230C4—361no—
231C4#6379812yes—
232C4#6393011yescharacteristic
233C4#6394511yescharacteristic
234C3—21no—
235C3#6845112yescomplemented
236C2—721no—
237C2#1059056511yescharacteristic
238C2#1059084011yescharacteristic
239C2#1059099311yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1693
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
3. #10590312C2semidirect
4. C3×#4486C2semidirect
5. #10589098C2semidirect
24. #4486D3semidirect
74. C3⋊(C3⋊C8)SD16semidirect
200. C32#1693semidirect
235. C3#68451semidirect

Maximal subgroups

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

subgroupindex
#105925372
#105903792
#105903122
C3×#44862
#105890982
#684513