Finite Group Databasebeta

← #11874889

Subgroups — #11874889

Order 1152.

929 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 929 conjugacy classes of subgroups — too many to draw. Only its 220 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#10593909C212yesmaximal
2C4×C8×C3⋊D3C211yesmaximal, characteristic
3C3×#4680C212yesmaximal, complemented
4#10590900C214yesmaximal, complemented
5#10590685C214yesmaximal
6#10590309C212yesmaximal, complemented
7D3×#498—32nomaximal
8C2×#3797—22no—
9C2×C8×C3⋊D3C2212yes—
10C42×C3⋊D3C2211yescharacteristic
11C3×#869C2214yes—
12#63919—22no—
13#63919C2214yes—
14#63900—22no—
15#63900C2214yes—
16#63873—22no—
17C32×C4×C8C2211yescharacteristic
18C8×C3⋊Dic3C2212yes—
19C4×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×#817C2218yes—
21#63574C2218yes—
22D3×C4⋊Q8—34no—
23C3×#498—32no—
24#5080—34no—
25D3×#106—38no—
26#4855—38no—
27C4×D3×C8—32no—
28C4×D3×C8—61no—
29#4680D312yescomplemented
30C2×C4×C3⋊D3D412yes—
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×C3×Dic6—24no—
33C2×#627—24no—
34C2×#624—24no—
35#3797—48no—
36C2×C32×C8C2312yes—
37C32×C42C2311yescharacteristic
38C4×C3⋊Dic3D412yes—
39C4×C3⋊Dic3C2311yescharacteristic
40C2×C3⋊(C3⋊C8)C2312yes—
41C8×C3⋊D3Q818yescomplemented
42C3×C4⋊Dic3—24no—
43C3×C4⋊Dic3C2318yes—
44#3724—24no—
45#3724—24no—
46C2×#498—91noSylow
47C2×D3×Q8—64no—
48C3×C4⋊Q8—34no—
49#944—64no—
50C2×D3×C8—34no—
51C2×D3×C8—62no—
52D3×C4⋊C4—38no—
53D3×C4⋊C4—64no—
54#888—38no—
55#888—64no—
56C42×D3—32no—
57C42×D3—61no—
58#869C2×D314yes—
59C3×#106—38no—
60C3×C4×C8—21no—
61C3×C4×C8C2×D312yes—
62#817C2×D318yes—
63C8×Dic3—34no—
64C8×Dic3—62no—
65#808—316no—
66C4×C3⋊C8—32no—
67C4×C3⋊C8—61no—
68C22×C3⋊D3C2×D411yescharacteristic
69C2×C32×C4C2×D412yes—
70C2×C32×C4C2411yescharacteristic
71C2×C3⋊Dic3C2×D411yescharacteristic
72C2×C3⋊Dic3C2×D412yes—
73C4×C3⋊D3SD1618yes—
74C4×C3⋊D3C2×Q814yes—
75C2×C3×Dic3—28no—
76C3×Dic6—48no—
77#627—48no—
78#624—48no—
79C32×C8C2×Q814yescomplemented
80C3⋊(C3⋊C8)C2×Q814yescomplemented
81C2×C4⋊Q8—92no—
82#498—32no—
83#498—94no—
84#498—92no—
85C2×#106—94no—
86C2×C4×C8—91no—
87C2×C3×Q8—64no—
88D3×Q8—1216no—
89C2×C4×D3—34no—
90C2×C4×D3—32no—
91C2×C4×D3—61no—
92C2×C4×D3—62no—
93C2×C4×D3—68no—
94C2×Dic6—24no—
95C2×Dic6—68no—
96C2×C3×C8—22no—
97C2×C3×C8C22×D314yes—
98C3×C4⋊C4—38no—
99C3×C4⋊C4—64no—
100C3×C42—21no—
101C3×C42C22×D312yes—
102C4⋊Dic3—24no—
103C4⋊Dic3C22×D318yes—
104Dic3⋊C4—68no—
105Dic3⋊C4—68no—
106C4×Dic3—34no—
107C4×Dic3—32no—
108C4×Dic3—61no—
109C4×Dic3—62no—
110C2×C3⋊C8—34no—
111C2×C3⋊C8—62no—
112D3×C8—316no—
113D3×C8—68no—
114C22×C32C22×D411yescharacteristic
115C2×C3⋊D3C4⋊Q812yes—
116C2×C3⋊D3C2×SD1614yes—
117C32×C4C2×SD1614yes—
118C32×C4C22×Q812yes—
119C3⋊Dic3C4⋊Q812yes—
120C3⋊Dic3C2×SD1614yes—
121C3×Dic3—48no—
122C22×Q8—182no—
123C22×C8—92no—
124C4⋊Q8—34no—
125C4⋊Q8—94no—
126C4⋊Q8—182no—
127C4⋊Q8—182no—
128C2×C4⋊C4—94no—
129C2×C4⋊C4—182no—
130C2×C42—91no—
131#106—38no—
132#106—98no—
133C4×C8—92no—
134C4×C8—91no—
135C4×C8D3211yescharacteristic
136C22×D3—32no—
137C22×D3—61no—
138C3×Q8—128no—
139C2×C3×C4—21no—
140C2×C3×C4—22no—
141C2×C3×C4—68no—
142C2×C3×C4D3×D414yes—
143C2×C3×C4C23×D312yes—
144C2×Dic3—28no—
145C2×Dic3—32no—
146C2×Dic3—34no—
147C2×Dic3—61no—
148C2×Dic3—62no—
149C4×D3—316no—
150C4×D3—38no—
151C4×D3—68no—
152C4×D3—64no—
153C4×D3—1216no—
154Dic6—48no—
155Dic6—1216no—
156C3×C8—24no—
157C3×C8D3×Q818yescomplemented
158C3⋊C8—38no—
159C3⋊C8—64no—
160C2×C32C2×C4⋊Q811yescharacteristic
161C2×C32C22×SD1612yes—
162C3⋊D3#49814yescomplemented
163C2×Q8—64no—
164C2×Q8—184no—
165C2×Q8—368no—
166C22×C4—91no—
167C22×C4—92no—
168C22×C4—184no—
169C2×C8—92no—
170C2×C8—98no—
171C2×C8C2×D3212yes—
172C4⋊C4—38no—
173C4⋊C4—64no—
174C4⋊C4—184no—
175C4⋊C4—184no—
176C42—91no—
177C42—92no—
178C42C2×D3211yescharacteristic
179C22×C3—21no—
180C22×C3C2×D3×D412yes—
181C2×D3—34no—
182C2×D3—38no—
183C2×D3—62no—
184C2×D3—64no—
185C3×C4—22no—
186C3×C4—24no—
187C3×C4—128no—
188C3×C4D3×SD1618yes—
189C3×C4C2×D3×Q814yes—
190Dic3—34no—
191Dic3—38no—
192Dic3—48no—
193Dic3—62no—
194Dic3—64no—
195C32C2×#49811yescharacteristic, complemented, Sylow
196C23—91no—
197Q8—128no—
198Q8—368no—
199C2×C4—68no—
200C2×C4—91no—
201C2×C4—92no—
202C2×C4—94no—
203C2×C4—98no—
204C2×C4—368no—
205C2×C4#380212yes—
206C2×C4C22×D3211yescharacteristic
207C8—94no—
208C8#379714yescomplemented
209C2×C3—21no—
210C2×C3—22no—
211C2×C3D3×C4⋊Q812yes—
212C2×C3C2×D3×SD1614yes—
213D3—38no—
214D3—64no—
215C22—92no—
216C22—94no—
217C22C2×#380211yescharacteristic
218C4—92no—
219C4—94no—
220C4—128no—
221C4#6379614yes—
222C4C2×#379712yes—
223C3—21no—
224C3D3×#49812yescomplemented
225C2—94no—
226C2#1059390911yescharacteristic
227C2C2×#6379612yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×C8D32
hypocenterC32C2×#498
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. C3×#4680C2semidirect
4. #10590900C2semidirect
6. #10590309C2semidirect
29. #4680D3semidirect
41. C8×C3⋊D3Q8semidirect
79. C32×C8C2×Q8semidirect
80. C3⋊(C3⋊C8)C2×Q8semidirect
157. C3×C8D3×Q8semidirect
162. C3⋊D3#498semidirect
195. C32C2×#498semidirect
208. C8#3797semidirect
224. C3D3×#498semidirect

Maximal subgroups

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

subgroupindex
#105939092
C4×C8×C3⋊D32
C3×#46802
#105909002
#105906852
#105903092
D3×#4983