Finite Group Databasebeta

← #11796739

Subgroups — #11796739

Order 1152.

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

normal subgroups only

This group has 497 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
2#10592579C211yesmaximal, characteristic
3C2×#63544C211yesmaximal, characteristic
4C3×#4492C212yesmaximal, complemented
5#10589118C212yesmaximal, complemented
6#69222—32nomaximal
7C2×#3797—21no—
8C2×C8×C3⋊D3C2211yescharacteristic
9#64101—21no—
10C2×C3×Dic12C2212yes—
11C2×#3718—21no—
12#63802—22no—
13#63802C414yescomplemented
14C32×#107C2211yescharacteristic
15#63645C2211yescharacteristic
16#63635—21no—
17C2×C3×C3⋊C16C2212yes—
18#63544—22no—
19C2×D3×Q16—32no—
20C2×#798—32no—
21#4880—32no—
22#4880—61no—
23C3×#358—32no—
24#4564—32no—
25#4503—32no—
26#4492D312yescomplemented
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C3×Dic6—22no—
29C2×#627—41no—
30C2×#624—41no—
31#3797—24no—
32#3797—42no—
33C2×C32×C8C2311yescharacteristic
34C32×C4⋊C4—21no—
35#3752—41no—
36C4⋊(C3⋊Dic3)—21no—
37C4×C3⋊Dic3—41no—
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39C8×C3⋊D3C2×C412yes—
40C8×C3⋊D3D412yes—
41C3×Dic12—22no—
42C3×Dic12C2×C414yes—
43#3718—24no—
44C3×C3⋊C16—22no—
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—
55#892—62no—
56C2×C3×C16—32no—
57C3×#107—21no—
58C3×#107C2×D312yes—
59#818—32no—
60#818—61no—
61C2×C3⋊C16C2×D312yes—
62#808—62no—
63#808—62no—
64#798—64no—
65C22×C3⋊D3D811yescharacteristic
66C2×C32×C4—41no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3D811yescharacteristic
70C4×C3⋊D3C22⋊C412yes—
71C4×C3⋊D3SD1612yes—
72C2×C3×Dic3—42no—
73C3×Dic6—24no—
74C3×Dic6—42no—
75#627—44no—
76#624—44no—
77C32×C8C22×C411yescharacteristic
78C32×C8C2×D411yescharacteristic
79C3⋊(C3⋊C8)C22⋊C412yes—
80C22×Q16—91no—
81C2×M32—91no—
82#427—91no—
83#358—32no—
84#358—92no—
85C2×C3×Q8—62no—
86D3×Q8—68no—
87D3×Q8—124no—
88C2×C4×D3—32no—
89C2×C4×D3—61no—
90C2×C4×D3—122no—
91C2×Dic6—22no—
92C2×Dic6—122no—
93C3×Q16—34no—
94C3×Q16—62no—
95C2×C3×C8—21no—
96C2×C3×C8C22×D312yes—
97C3×C4⋊C4—22no—
98C3×C4⋊C4—22no—
99#216—68no—
100(C2×D3)⋊C4—122no—
101(C2×D3)⋊C4—122no—
102C4⋊Dic3—62no—
103C4⋊Dic3—62no—
104C4×Dic3—122no—
105C4×Dic3—122no—
106C2×C3⋊C8—32no—
107C2×C3⋊C8—61no—
108Dic12—22no—
109Dic12C4×D314yes—
110D3×C8—34no—
111D3×C8—34no—
112D3×C8—62no—
113D3×C8—62no—
114C3×C16—62no—
115C3⋊C16—22no—
116C22×C32C2×D811yescharacteristic
117C2×C3⋊D3—21no—
118C2×C3⋊D3—21no—
119C2×C3⋊D3#10212yes—
120C32×C4—81no—
121C32×C4C2×C22⋊C411yescharacteristic
122C32×C4C2×SD1611yescharacteristic
123C3⋊Dic3—81no—
124C3⋊Dic3#10212yes—
125C3×Dic3—44no—
126C22×Q8—181no—
127C2×Q16—32no—
128C2×Q16—94no—
129C2×Q16—182no—
130C2×Q16—181no—
131C22×C8—91no—
132#117—181no—
133M32—182no—
134C2×C16—32no—
135#107—91no—
136#107D3211yescharacteristic
137#106—181no—
138C22×D3—32no—
139C22×D3—61no—
140C3×Q8—64no—
141C3×Q8—122no—
142C2×C3×C4—21no—
143C2×C3×C4—42no—
144C2×C3×C4—42no—
145C2×C3×C4—122no—
146C2×C3×C4D3×D412yes—
147C2×Dic3—32no—
148C2×Dic3—42no—
149C2×Dic3—61no—
150C2×Dic3—122no—
151C2×Dic3—122no—
152C4×D3—34no—
153C4×D3—34no—
154C4×D3—62no—
155C4×D3—62no—
156C4×D3—128no—
157Dic6—24no—
158Dic6—42no—
159Dic6—128no—
160C3×C8—21no—
161C3×C8—21no—
162C3×C8C2×C4×D312yes—
163C3×C8D3×D412yes—
164C3⋊C8—34no—
165C3⋊C8—62no—
166C2×C32C2×#10211yescharacteristic
167C2×C32#51011yescharacteristic
168C2×C32#51011yescharacteristic
169C3⋊D3—22no—
170C2×Q8—62no—
171C2×Q8—184no—
172C2×Q8—361no—
173C2×Q8—362no—
174C22×C4—91no—
175C22×C4—361no—
176Q16—34no—
177Q16—62no—
178Q16—184no—
179C2×C8—91no—
180C2×C8—92no—
181C2×C8—92no—
182C2×C8C2×D3211yescharacteristic
183C4⋊C4—21no—
184C4⋊C4—181no—
185C22⋊C4—361no—
186C42—361no—
187C16—62no—
188C22×C3—21no—
189C22×C3D3×D812yes—
190C2×D3—34no—
191C2×D3—62no—
192C2×D3—62no—
193C2×D3—62no—
194C2×D3—121no—
195C2×D3—121no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—82no—
199C3×C4—82no—
200C3×C4—124no—
201C3×C4D3×C22⋊C412yes—
202C3×C4D3×SD1612yes—
203Dic3—34no—
204Dic3—44no—
205Dic3—62no—
206Dic3—242no—
207Dic3—242no—
208C32#214111yescharacteristic, complemented, Sylow
209C23—91no—
210Q8—64no—
211Q8—122no—
212Q8—364no—
213C2×C4—41no—
214C2×C4—91no—
215C2×C4—92no—
216C2×C4—92no—
217C2×C4—122no—
218C2×C4—364no—
219C2×C4—361no—
220C2×C4#381111yescharacteristic
221C8—92no—
222C8C4×D3211yescharacteristic
223C8#380211yescharacteristic
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3D3×#10212yes—
228C2×C3#491512yes—
229C2×C3#491812yes—
230D3—64no—
231D3—122no—
232C22—92no—
233C22—181no—
234C22—181no—
235C22#6392611yescharacteristic
236C4—81no—
237C4—92no—
238C4—124no—
239C4—721no—
240C4#6392111yescharacteristic
241C4#6394011yescharacteristic
242C3—21no—
243C3#6922212yescomplemented
244C2—182no—
245C2#1059059311yescharacteristic
246C2#1059103011yescharacteristic
247C2#1059104411yescharacteristic
subgroupG/H
centerC22#63926
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC22×C3⋊D3D8
cosocleC2×C32×C8C23
hypercenter#107D32
hypocenterC32#2141
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
4. C3×#4492C2semidirect
5. #10589118C2semidirect
13. #63802C4semidirect
26. #4492D3semidirect
208. C32#2141semidirect
243. C3#69222semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
#105925792
C2×#635442
C3×#44922
#105891182
#692223