Finite Group Databasebeta

← #11797107

Subgroups — #11797107

Order 1152.

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

normal subgroups only

This group has 357 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×#108C211yesmaximal, characteristic
2#10590685C211yesmaximal, characteristic
3#10590625C211yesmaximal, characteristic
4C3×#4494C212yesmaximal, complemented
5#10589136C212yesmaximal, complemented
6D3×#365—32nomaximal
7M16×C3⋊D3—21no—
8C2×C8×C3⋊D3C2211yescharacteristic
9#63900—21no—
10C32×#108C2211yescharacteristic
11#63649—21no—
12#63646C2211yescharacteristic
13C3×#817C2212yes—
14C3×#812C2212yes—
15#63574—21no—
16#63544C412yescomplemented
17#63542C412yescomplemented
18D3×M32—32no—
19D3×#108—32no—
20D3×#108—61no—
21D3×#106—32no—
22C3×#365—32no—
23#4513—32no—
24#4494D312yescomplemented
25#4487—32no—
26C2×C4×C3⋊D3D411yescharacteristic
27C2×#624—41no—
28C32×M16—21no—
29C2×C32×C8C2311yescharacteristic
30#3748—21no—
31C2×C3⋊(C3⋊C8)D411yescharacteristic
32#3743—41no—
33C8×C3⋊D3—41no—
34C8×C3⋊D3C2×C411yescharacteristic
35C8×C3⋊D3C2×C411yescharacteristic
36C8×C3⋊D3Q811yescharacteristic
37C8×C3⋊D3Q811yescharacteristic
38C3×C4⋊Dic3—22no—
39#3724—41no—
40C3×C3⋊C16C2×C414yescomplemented
41C2×#365—91noSylow
42D3×M16—62no—
43D3×M16—62no—
44C2×D3×C8—32no—
45C2×D3×C8—61no—
46D3×C4⋊C4—62no—
47C3×M32—32no—
48C3×#108—21no—
49C3×#108C2×D312yes—
50C3×#106—32no—
51#822—62no—
52#822—62no—
53#819—32no—
54#819—61no—
55#817C2×D312yes—
56#812C2×D312yes—
57#808—62no—
58#798—34no—
59D3×C16—34no—
60C22×C3⋊D3SD1611yescharacteristic
61C2×C32×C4C2×D411yescharacteristic
62C2×C3⋊Dic3SD1611yescharacteristic
63C4×C3⋊D3C4⋊C411yescharacteristic
64C4×C3⋊D3C4⋊C411yescharacteristic
65C4×C3⋊D3SD1611yescharacteristic
66C4×C3⋊D3SD1611yescharacteristic
67C2×C3×Dic3—42no—
68#624—82no—
69C32×C8—41no—
70C32×C8C22×C411yescharacteristic
71C32×C8C2×Q811yescharacteristic
72C3⋊(C3⋊C8)—41no—
73C3⋊(C3⋊C8)C4⋊C411yescharacteristic
74C3⋊(C3⋊C8)C4⋊C411yescharacteristic
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—
83C3×M16—22no—
84C3×M16—22no—
85C2×C3×C8—21no—
86C2×C3×C8C22×D312yes—
87C3×C4⋊C4—62no—
88C4⋊Dic3—22no—
89Dic3⋊C4—122no—
90#208—62no—
91#208—62no—
92C2×C3⋊C8—32no—
93C2×C3⋊C8—61no—
94ΓL(1,𝔽25)—122no—
95ΓL(1,𝔽25)—122no—
96D3×C8—32no—
97D3×C8—32no—
98D3×C8—32no—
99D3×C8—32no—
100D3×C8—61no—
101D3×C8—61no—
102D3×C8—61no—
103D3×C8—61no—
104D3×C8—122no—
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×C4C2×C4⋊C411yescharacteristic
113C32×C4C2×SD1611yescharacteristic
114C3⋊Dic3#10611yescharacteristic
115C3⋊Dic3#10611yescharacteristic
116C3×Dic3—82no—
117C2×M16—181no—
118C22×C8—91no—
119C2×C4⋊C4—181no—
120M32—32no—
121M32—92no—
122C2×C16—92no—
123#108—91no—
124#108—181no—
125#108D3211yescharacteristic
126#106—32no—
127#106—181no—
128C22×D3—32no—
129C22×D3—61no—
130C2×C3×C4—21no—
131C2×C3×C4—122no—
132C2×C3×C4D3×D412yes—
133C2×Dic3—32no—
134C2×Dic3—42no—
135C2×Dic3—61no—
136C4×D3—32no—
137C4×D3—32no—
138C4×D3—32no—
139C4×D3—32no—
140C4×D3—61no—
141C4×D3—61no—
142C4×D3—61no—
143C4×D3—61no—
144C4×D3—244no—
145C3×C8—21no—
146C3×C8—21no—
147C3×C8—42no—
148C3×C8—42no—
149C3×C8C2×C4×D312yes—
150C3×C8D3×Q812yes—
151C3⋊C8—32no—
152C3⋊C8—32no—
153C3⋊C8—61no—
154C3⋊C8—61no—
155C3⋊C8—122no—
156C3⋊C8—122no—
157C2×C32—21no—
158C2×C32C2×#10611yescharacteristic
159C3⋊D3—21no—
160C3⋊D3#36512yescomplemented
161C22×C4—91no—
162C22×C4—361no—
163M16—21no—
164M16—181no—
165M16—361no—
166C2×C8—91no—
167C2×C8—91no—
168C2×C8—91no—
169C2×C8—91no—
170C2×C8—91no—
171C2×C8—361no—
172C2×C8C2×D3211yescharacteristic
173C4⋊C4—62no—
174C4⋊C4—361no—
175C16—34no—
176C22×C3—21no—
177C22×C3D3×SD1612yes—
178C2×D3—32no—
179C2×D3—32no—
180C2×D3—61no—
181C2×D3—61no—
182C2×D3—64no—
183C2×D3—122no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—242no—
187C3×C4D3×C4⋊C412yes—
188C3×C4D3×SD1612yes—
189Dic3—32no—
190Dic3—32no—
191Dic3—61no—
192Dic3—61no—
193Dic3—82no—
194C32C2×#36511yescharacteristic, complemented, Sylow
195C23—91no—
196C2×C4—91no—
197C2×C4—91no—
198C2×C4—91no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—122no—
202C2×C4—722no—
203C2×C4#381111yescharacteristic
204C8—41no—
205C8—91no—
206C8—91no—
207C8—361no—
208C8#379711yescharacteristic
209C8C4×D3211yescharacteristic
210C2×C3—22no—
211C2×C3—21no—
212C2×C3—41no—
213C2×C3D3×#10612yes—
214D3—34no—
215D3—62no—
216D3—62no—
217D3—121no—
218C22—91no—
219C22—91no—
220C22—182no—
221C22#6394011yescharacteristic
222C4—91no—
223C4—91no—
224C4—242no—
225C4#6388311yescharacteristic
226C4#6393011yescharacteristic
227C3—21no—
228C3D3×#36512yescomplemented
229C2—21no—
230C2—92no—
231C2—181no—
232C2#1059057511yescharacteristic
subgroupG/H
centerC2#10590575
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32C2×#106
prime radicalC22×C3⋊D3SD16
cosocleC2×C32×C8C23
hypercenter#108D32
hypocenterC32C2×#365
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
4. C3×#4494C2semidirect
5. #10589136C2semidirect
16. #63544C4semidirect
17. #63542C4semidirect
24. #4494D3semidirect
40. C3×C3⋊C16C2×C4semidirect
107. C3⋊C16C4×D3semidirect
160. C3⋊D3#365semidirect
194. C32C2×#365semidirect
228. C3D3×#365semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1082
#105906852
#105906252
C3×#44942
#105891362
D3×#3653