Finite Group Databasebeta

← #11797100

Subgroups — #11797100

Order 1152.

369 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3⋊D3×#106C211yesmaximal, characteristic
2#10590913C211yesmaximal, characteristic
3#10590625C211yesmaximal, characteristic
4C3×#4487C212yesmaximal, complemented
5#10589137C212yesmaximal, complemented
6D3×#365—32nomaximal
7C2×C8×C3⋊D3C2211yescharacteristic
8C4⋊C4×C3⋊D3—21no—
9#63818—21no—
10C32×#106C2211yescharacteristic
11#63644C2211yescharacteristic
12#63635—21no—
13C3×#819C2212yes—
14C3×#812C2212yes—
15#63578—21no—
16#63544C412yescomplemented
17#63542C412yescomplemented
18D3×M32—32no—
19D3×#108—32no—
20D3×#106—32no—
21D3×#106—61no—
22C3×#365—32no—
23#4513—32no—
24#4494—32no—
25#4487D312yescomplemented
26C2×C4×C3⋊D3—41no—
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C32×C8C2311yescharacteristic
29C32×C4⋊C4—21no—
30C4⋊(C3⋊Dic3)—21no—
31#3750—41no—
32C2×C3⋊(C3⋊C8)D411yescharacteristic
33C8×C3⋊D3C2×C411yescharacteristic
34C8×C3⋊D3C2×C411yescharacteristic
35C8×C3⋊D3Q811yescharacteristic
36C8×C3⋊D3Q811yescharacteristic
37C3×#208—22no—
38#3712—41no—
39#3710—41no—
40C3×C3⋊C16C2×C414yescomplemented
41C2×#365—91noSylow
42D3×M16—62no—
43C2×D3×C8—32no—
44C2×D3×C8—61no—
45D3×C4⋊C4—62no—
46D3×C4⋊C4—62no—
47C3×M32—32no—
48C3×#108—32no—
49C3×#106—21no—
50C3×#106C2×D312yes—
51#822—62no—
52#819C2×D312yes—
53#817—32no—
54#817—61no—
55#812C2×D312yes—
56#808—62no—
57#808—62no—
58#798—34no—
59D3×C16—34no—
60C22×C3⋊D3SD1611yescharacteristic
61C2×C32×C4—41no—
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3SD1611yescharacteristic
65C4×C3⋊D3—82no—
66C4×C3⋊D3C4⋊C411yescharacteristic
67C4×C3⋊D3C4⋊C411yescharacteristic
68C4×C3⋊D3SD1611yescharacteristic
69C4×C3⋊D3SD1611yescharacteristic
70C32×C8C22×C411yescharacteristic
71C32×C8C2×Q811yescharacteristic
72C3⋊(C3⋊C8)C4⋊C411yescharacteristic
73C3⋊(C3⋊C8)C4⋊C411yescharacteristic
74C3×C3⋊C8—42no—
75C2×M32—91no—
76C2×#108—91no—
77C2×#106—91no—
78#365—32no—
79#365—92no—
80C2×C4×D3—32no—
81C2×C4×D3—61no—
82C2×C4×D3—122no—
83C2×C4×D3—122no—
84C3×M16—62no—
85C2×C3×C8—21no—
86C2×C3×C8C22×D312yes—
87C3×C4⋊C4—22no—
88C3×C4⋊C4—22no—
89C4⋊Dic3—62no—
90C4⋊Dic3—62no—
91Dic3⋊C4—122no—
92Dic3⋊C4—122no—
93#208—22no—
94C2×C3⋊C8—32no—
95C2×C3⋊C8—61no—
96ΓL(1,𝔽25)—122no—
97D3×C8—32no—
98D3×C8—32no—
99D3×C8—32no—
100D3×C8—32no—
101D3×C8—61no—
102D3×C8—61no—
103D3×C8—61no—
104D3×C8—61no—
105D3×C8—122no—
106C3×C16—34no—
107C3⋊C16C4×D314yescomplemented
108C22×C32C2×SD1611yescharacteristic
109C2×C3⋊D3—22no—
110C2×C3⋊D3#10611yescharacteristic
111C2×C3⋊D3#10611yescharacteristic
112C32×C4—81no—
113C32×C4C2×C4⋊C411yescharacteristic
114C32×C4C2×SD1611yescharacteristic
115C3⋊Dic3—81no—
116C3⋊Dic3#10611yescharacteristic
117C3⋊Dic3#10611yescharacteristic
118C2×M16—181no—
119C22×C8—91no—
120C2×C4⋊C4—181no—
121M32—32no—
122M32—92no—
123C2×C16—92no—
124#108—32no—
125#108—181no—
126#106—91no—
127#106—181no—
128#106D3211yescharacteristic
129C22×D3—32no—
130C22×D3—61no—
131C2×C3×C4—21no—
132C2×C3×C4—42no—
133C2×C3×C4—42no—
134C2×C3×C4D3×D412yes—
135C2×Dic3—32no—
136C2×Dic3—61no—
137C2×Dic3—122no—
138C2×Dic3—122no—
139C4×D3—32no—
140C4×D3—32no—
141C4×D3—32no—
142C4×D3—32no—
143C4×D3—61no—
144C4×D3—61no—
145C4×D3—61no—
146C4×D3—61no—
147C4×D3—244no—
148C4×D3—244no—
149C3×C8—21no—
150C3×C8—21no—
151C3×C8—122no—
152C3×C8C2×C4×D312yes—
153C3×C8D3×Q812yes—
154C3⋊C8—32no—
155C3⋊C8—32no—
156C3⋊C8—42no—
157C3⋊C8—61no—
158C3⋊C8—61no—
159C2×C32—21no—
160C2×C32C2×#10611yescharacteristic
161C3⋊D3—21no—
162C3⋊D3#36512yescomplemented
163C22×C4—91no—
164C22×C4—361no—
165M16—62no—
166M16—361no—
167C2×C8—91no—
168C2×C8—91no—
169C2×C8—91no—
170C2×C8—91no—
171C2×C8—91no—
172C2×C8—361no—
173C2×C8C2×D3211yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—181no—
176C4⋊C4—361no—
177C16—34no—
178C22×C3—21no—
179C22×C3D3×SD1612yes—
180C2×D3—32no—
181C2×D3—32no—
182C2×D3—61no—
183C2×D3—61no—
184C2×D3—64no—
185C2×D3—64no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—82no—
189C3×C4—82no—
190C3×C4D3×C4⋊C412yes—
191C3×C4D3×SD1612yes—
192Dic3—32no—
193Dic3—32no—
194Dic3—61no—
195Dic3—61no—
196Dic3—242no—
197Dic3—242no—
198C32C2×#36511yescharacteristic, complemented, Sylow
199C23—91no—
200C2×C4—41no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—91no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—361no—
207C2×C4—722no—
208C2×C4#381111yescharacteristic
209C8—91no—
210C8—91no—
211C8—122no—
212C8#379711yescharacteristic
213C8C4×D3211yescharacteristic
214C2×C3—22no—
215C2×C3—22no—
216C2×C3—21no—
217C2×C3D3×#10612yes—
218D3—34no—
219D3—62no—
220D3—62no—
221D3—62no—
222C22—91no—
223C22—91no—
224C22—182no—
225C22#6393011yescharacteristic
226C4—81no—
227C4—91no—
228C4—91no—
229C4—721no—
230C4#6388311yescharacteristic
231C4#6394011yescharacteristic
232C3—21no—
233C3D3×#36512yescomplemented
234C2—21no—
235C2—92no—
236C2—181no—
237C2#1059057511yescharacteristic
subgroupG/H
centerC2#10590575
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#106C22
socleC2×C32C2×#106
prime radicalC22×C3⋊D3SD16
cosocleC2×C32×C8C23
hypercenter#106D32
hypocenterC32C2×#365
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
4. C3×#4487C2semidirect
5. #10589137C2semidirect
16. #63544C4semidirect
17. #63542C4semidirect
25. #4487D3semidirect
40. C3×C3⋊C16C2×C4semidirect
107. C3⋊C16C4×D3semidirect
162. C3⋊D3#365semidirect
198. C32C2×#365semidirect
233. C3D3×#365semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1062
#105909132
#105906252
C3×#44872
#105891372
D3×#3653