Finite Group Databasebeta

← #11875005

Subgroups — #11875005

Order 1152.

578 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 125 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#10593882C212yesmaximal
2C4×#3787C211yesmaximal, characteristic
3#10593395C211yesmaximal, characteristic, complemented
4#10593390C214yesmaximal, complemented
5#10593389C214yesmaximal
6#10593388C211yesmaximal, characteristic, complemented
7#10593384C212yesmaximal, complemented
8C2×#3787C2212yes—
9C42×C3⋊D3C2211yescharacteristic
10C3×C4×Dic6—22no—
11#63919C2212yes—
12C4×#627—22no—
13#63874C2214yes—
14#63873C2212yes—
15#63871—22no—
16#63870C2214yes—
17#63865—22no—
18C4×#622C2211yescharacteristic
19C4×#622C2211yescharacteristic
20C4×#622C2212yes—
21#63743C2214yes—
22#63743C2214yes—
23#63742C2218yes—
24#5578—62no—
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×C3×Dic6—22no—
29C2×#627—22no—
30C2×#622C2312yes—
31C2×#622C2312yes—
32#3787Q818yescomplemented
33C32×C42D411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3C2311yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C3×C4⋊Dic3—22no—
38C3×Dic3⋊C4—24no—
39C3×C4×Dic3—24no—
40#3724—22no—
41#3724C2314yes—
42#3724C2314yes—
43Dic3⋊Dic3—24no—
44#3722—24no—
45#3160—91nomaximal, Sylow
46C3×C4×Q8—62no—
47#946—62no—
48#944—62no—
49#897—62no—
50#896—64no—
51#889—64no—
52#888—62no—
53#872—64no—
54C42×D3—62no—
55C4×Dic6—22no—
56C4×Dic6—64no—
57C22×C3⋊D3C2×D411yescharacteristic
58C2×C32×C4C2×D411yescharacteristic
59C2×C32×C4C2×D411yescharacteristic
60C2×C32×C4C2×D411yescharacteristic
61C2×C3⋊Dic3C2×D411yescharacteristic
62C2×C3⋊Dic3C2×D411yescharacteristic
63C2×C3⋊Dic3C2411yescharacteristic
64C4×C3⋊D3—22no—
65C4×C3⋊D3—22no—
66C4×C3⋊D3C2×Q814yes—
67C2×C3×Dic3—24no—
68C2×C3×Dic3—24no—
69C3×Dic6—44no—
70#627—44no—
71#622C2×Q814yes—
72#622C2×Q814yes—
73#533—92no—
74#500—91no—
75#500—91no—
76#499—94no—
77#498—92no—
78#427—94no—
79C2×C4×C8—91no—
80C2×C3×Q8—62no—
81C2×C4×D3—62no—
82C2×C4×D3—62no—
83C2×C4×D3—62no—
84C2×Dic6—22no—
85C2×Dic6—64no—
86C3×C4⋊C4—62no—
87C3×C4⋊C4—64no—
88C3×C42—22no—
89C3×C42—64no—
90(C2×D3)⋊C4—64no—
91(C2×D3)⋊C4—64no—
92C4⋊Dic3—22no—
93C4⋊Dic3—64no—
94Dic3⋊C4—24no—
95Dic3⋊C4—64no—
96Dic3⋊C4—64no—
97Dic3⋊C4—64no—
98Dic3⋊C4—64no—
99C4×Dic3—24no—
100C4×Dic3—62no—
101C4×Dic3—62no—
102C4×Dic3—62no—
103C22×C32C22×D411yescharacteristic
104C2×C3⋊D3—21no—
105C2×C3⋊D3—21no—
106C2×C3⋊D3C4⋊Q812yes—
107C32×C4—21no—
108C32×C4C4⋊Q812yes—
109C32×C4#13512yes—
110C3⋊Dic3—21no—
111C3⋊Dic3#13512yes—
112C3⋊Dic3C22×Q812yes—
113C3×Dic3—44no—
114C3×Dic3—44no—
115C22×C8—92no—
116C4⋊Q8—92no—
117C4⋊Q8—92no—
118#125—94no—
119C22⋊Q8—182no—
120C22⋊Q8—182no—
121C4×Q8—62no—
122C4×Q8—182no—
123#117—94no—
124C2×C42—91no—
125#107—94no—
126#107—94no—
127#106—98no—
128C4×C8—91no—
129C4×C8—92no—
130C4×C8—91no—
131C22×D3—62no—
132C3×Q8—124no—
133C2×C3×C4—22no—
134C2×C3×C4—22no—
135C2×C3×C4—22no—
136C2×C3×C4—64no—
137C2×C3×C4—64no—
138C2×Dic3—24no—
139C2×Dic3—24no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C4×D3—68no—
144C4×D3—124no—
145C4×D3—124no—
146Dic6—44no—
147Dic6—128no—
148C2×C32C2×C4⋊Q811yescharacteristic
149C2×C32C2×#13511yescharacteristic
150C2×C32C2×#13511yescharacteristic
151C3⋊D3—22no—
152C2×Q8—62no—
153C2×Q8—182no—
154C22×C4—91no—
155C22×C4—91no—
156C22×C4—91no—
157C2×C8—92no—
158C2×C8—92no—
159C2×C8—98no—
160C4⋊C4—64no—
161C4⋊C4—62no—
162C4⋊C4—94no—
163C4⋊C4—94no—
164C4⋊C4—184no—
165C4⋊C4—182no—
166C22⋊C4—184no—
167C42—64no—
168C42—91no—
169C42—91no—
170C42—91no—
171C42GO+(4,𝔽2)11yescharacteristic
172C22×C3—22no—
173C2×D3—64no—
174C2×D3—122no—
175C2×D3—122no—
176C3×C4—24no—
177C3×C4—24no—
178C3×C4—42no—
179C3×C4—124no—
180C3×C4—124no—
181Dic3—44no—
182Dic3—44no—
183Dic3—64no—
184Dic3—64no—
185Dic3—122no—
186C32#316011yescharacteristic, complemented, Sylow
187C23—91no—
188Q8—124no—
189Q8—364no—
190C2×C4—64no—
191C2×C4—64no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—94no—
195C2×C4—91no—
196C2×C4—182no—
197C2×C4—182no—
198C2×C4C2×GO+(4,𝔽2)11yescharacteristic
199C2×C4C2×GO+(4,𝔽2)11yescharacteristic
200C2×C4C2×GO+(4,𝔽2)11yescharacteristic
201C8—94no—
202C8—94no—
203C2×C3—22no—
204C2×C3—22no—
205C2×C3—22no—
206D3—124no—
207C22—92no—
208C22—181no—
209C22—181no—
210C22C22×GO+(4,𝔽2)11yescharacteristic
211C4—21no—
212C4—92no—
213C4—92no—
214C4—124no—
215C4—124no—
216C4—181no—
217C4#6422212yes—
218C4#6422312yes—
219C3—22no—
220C2—182no—
221C2C2×#6422211yescharacteristic
222C2C2×#6422311yescharacteristic
223C2#1059650011yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32#3160
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #10593395C2semidirect
4. #10593390C2semidirect
6. #10593388C2semidirect
7. #10593384C2semidirect
32. #3787Q8semidirect
186. C32#3160semidirect

Maximal subgroups

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

subgroupindex
#105938822
C4×#37872
#105933952
#105933902
#105933892
#105933882
#105933842
#31609