Finite Group Databasebeta

← #11796746

Subgroups — #11796746

Order 1152.

485 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 485 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C2×#63802C211yesmaximal, characteristic
2C2×#63625C211yesmaximal, characteristic
3#10590714C211yesmaximal, characteristic
4C3×#4503C212yesmaximal, complemented
5#10589117C212yesmaximal, complemented
6#69222—32nomaximal
7C2×#3797—21no—
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C3×Dic12C2212yes—
10#63849—21no—
11C2×#3718—21no—
12#63802—22no—
13#63802C414yescomplemented
14C2×C32×C16C2211yescharacteristic
15C2×C3⋊(C3⋊C16)C2211yescharacteristic
16#63625—22no—
17C3×#818C2212yes—
18#63574—21no—
19C2×D3×Q16—32no—
20C2×#798—32no—
21C2×#798—61no—
22#4880—32no—
23C3×#358—32no—
24#4564—32no—
25#4503D312yescomplemented
26#4492—32no—
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C3×Dic6—22no—
29C2×#627—41no—
30C2×#624—41no—
31#3797—24no—
32#3797—42no—
33C2×C32×C8C2311yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C8×C3⋊D3C2×C412yes—
36C8×C3⋊D3D412yes—
37C3×C4⋊Dic3—22no—
38C3×Dic12—22no—
39C3×Dic12C2×C414yes—
40#3722—41no—
41Dic32—41no—
42#3718—24no—
43C32×C16—21no—
44C3⋊(C3⋊C16)—21no—
45#2141—91noSylow
46C2×D3×Q8—62no—
47C2×C3×Q16—32no—
48C2×#216—62no—
49D3×Q16—38no—
50D3×Q16—64no—
51C2×Dic12C2×D312yes—
52C2×D3×C8—32no—
53C2×D3×C8—61no—
54#892—62no—
55C2×C3×C16—21no—
56C2×C3×C16C2×D312yes—
57C3×#107—32no—
58#818C2×D312yes—
59C2×C3⋊C16—32no—
60C2×C3⋊C16—61no—
61#808—62no—
62#798—64no—
63#798—64no—
64C22×C3⋊D3D811yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C3⋊Dic3D811yescharacteristic
67C4×C3⋊D3C22⋊C412yes—
68C4×C3⋊D3SD1612yes—
69C2×C3×Dic3—42no—
70C2×C3×Dic3—42no—
71C3×Dic6—24no—
72C3×Dic6—42no—
73#627—44no—
74#624—44no—
75C32×C8C22×C411yescharacteristic
76C32×C8C2×D411yescharacteristic
77C3⋊(C3⋊C8)C22⋊C412yes—
78C22×Q16—91no—
79C2×M32—91no—
80#427—91no—
81#358—32no—
82#358—92no—
83C2×C3×Q8—62no—
84D3×Q8—68no—
85D3×Q8—124no—
86C2×C4×D3—32no—
87C2×C4×D3—61no—
88C2×C4×D3—122no—
89C2×Dic6—22no—
90C2×Dic6—122no—
91C3×Q16—34no—
92C3×Q16—62no—
93C2×C3×C8—21no—
94C2×C3×C8C22×D312yes—
95C3×C4⋊C4—62no—
96#216—68no—
97(C2×D3)⋊C4—122no—
98C4⋊Dic3—22no—
99C4×Dic3—122no—
100C2×C3⋊C8—32no—
101C2×C3⋊C8—61no—
102Dic12—22no—
103Dic12C4×D314yes—
104D3×C8—34no—
105D3×C8—34no—
106D3×C8—62no—
107D3×C8—62no—
108C3×C16—22no—
109C3×C16—22no—
110C3⋊C16—62no—
111C3⋊C16—62no—
112C22×C32C2×D811yescharacteristic
113C2×C3⋊D3—22no—
114C2×C3⋊D3#10212yes—
115C32×C4C2×C22⋊C411yescharacteristic
116C32×C4C2×SD1611yescharacteristic
117C3⋊Dic3#10212yes—
118C3×Dic3—44no—
119C3×Dic3—82no—
120C22×Q8—181no—
121C2×Q16—32no—
122C2×Q16—94no—
123C2×Q16—182no—
124C2×Q16—181no—
125C22×C8—91no—
126#117—181no—
127M32—182no—
128C2×C16—91no—
129C2×C16D3211yescharacteristic
130#107—32no—
131#106—181no—
132C22×D3—32no—
133C22×D3—61no—
134C3×Q8—64no—
135C3×Q8—122no—
136C2×C3×C4—21no—
137C2×C3×C4—122no—
138C2×C3×C4—122no—
139C2×C3×C4D3×D412yes—
140C2×Dic3—32no—
141C2×Dic3—42no—
142C2×Dic3—42no—
143C2×Dic3—61no—
144C4×D3—34no—
145C4×D3—34no—
146C4×D3—62no—
147C4×D3—62no—
148C4×D3—128no—
149Dic6—24no—
150Dic6—42no—
151Dic6—128no—
152C3×C8—21no—
153C3×C8—21no—
154C3×C8C2×C4×D312yes—
155C3×C8D3×D412yes—
156C3⋊C8—34no—
157C3⋊C8—62no—
158C2×C32C2×#10211yescharacteristic
159C2×C32#51012yes—
160C3⋊D3—22no—
161C2×Q8—62no—
162C2×Q8—184no—
163C2×Q8—361no—
164C2×Q8—362no—
165C22×C4—91no—
166C22×C4—361no—
167Q16—34no—
168Q16—62no—
169Q16—184no—
170C2×C8—91no—
171C2×C8—92no—
172C2×C8—92no—
173C2×C8C2×D3211yescharacteristic
174C4⋊C4—62no—
175C22⋊C4—361no—
176C42—361no—
177C16—21no—
178C16—181no—
179C22×C3—21no—
180C22×C3D3×D812yes—
181C2×D3—34no—
182C2×D3—62no—
183C2×D3—62no—
184C2×D3—62no—
185C2×D3—122no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—124no—
189C3×C4—242no—
190C3×C4D3×C22⋊C412yes—
191C3×C4D3×SD1612yes—
192Dic3—34no—
193Dic3—44no—
194Dic3—62no—
195Dic3—82no—
196C32#214111yescharacteristic, complemented, Sylow
197C23—91no—
198Q8—64no—
199Q8—122no—
200Q8—364no—
201C2×C4—91no—
202C2×C4—92no—
203C2×C4—92no—
204C2×C4—122no—
205C2×C4—122no—
206C2×C4—364no—
207C2×C4#380211yescharacteristic
208C8—92no—
209C8C4×D3211yescharacteristic
210C8#381111yescharacteristic
211C2×C3—22no—
212C2×C3—21no—
213C2×C3D3×#10212yes—
214C2×C3#491512yes—
215C2×C3#491812yes—
216D3—64no—
217D3—122no—
218C22—92no—
219C22—182no—
220C22#6379711yescharacteristic
221C4—92no—
222C4—124no—
223C4—242no—
224C4#6379611yescharacteristic
225C4#6392111yescharacteristic
226C3—21no—
227C3#6922212yescomplemented
228C2—182no—
229C2#1059024612yes—
230C2#1059094011yescharacteristic
subgroupG/H
centerC22#63797
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC22×C32C2×D8
prime radicalC22×C3⋊D3D8
cosocleC2×C32×C8C23
hypercenterC2×C16D32
hypocenterC32#2141
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
4. C3×#4503C2semidirect
5. #10589117C2semidirect
13. #63802C4semidirect
25. #4503D3semidirect
196. C32#2141semidirect
227. C3#69222semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
C2×#636252
#105907142
C3×#45032
#105891172
#692223