Finite Group Databasebeta

← #11875006

Subgroups — #11875006

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#10594810C212yesmaximal
2C2×C4×#622C211yesmaximal, characteristic
3#10593511C214yesmaximal
4#10593395C211yesmaximal, characteristic, complemented
5#10593390C214yesmaximal, complemented
6#10593388C211yesmaximal, characteristic, complemented
7#10593384C212yesmaximal, complemented
8C22×#622C2212yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C3×#924—22no—
11#63982—22no—
12#63957C2214yes—
13#63919C2212yes—
14#63873C2212yes—
15#63870C2214yes—
16#63843—22no—
17#63838—22no—
18C4×#622C2211yescharacteristic
19C4×#622C2211yescharacteristic
20C4×#622C2212yes—
21#63743C2214yes—
22#63743C2214yes—
23#63742C2218yes—
24#5622—62no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C2×C3×Dic6—22no—
29C2×#627—22no—
30C2×#622Q818yescomplemented
31C2×#622C2312yes—
32C2×#622C2312yes—
33C4×C3⋊Dic3D411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3C2311yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C3×#217—24no—
38C3×C4⋊Dic3—22no—
39C3×Dic3⋊C4—24no—
40#3724—22no—
41#3724C2314yes—
42#3724C2314yes—
43Dic3⋊Dic3—24no—
44Dic32—24no—
45#3160—91nomaximal, Sylow
46C3×C22⋊Q8—62no—
47Q8×Dic3—62no—
48#944—62no—
49#924—22no—
50C2×C4×Dic3—62no—
51#889—64no—
52#888—62no—
53#887—64no—
54#887—62no—
55#878—64no—
56#877—64no—
57C23×C32C2×D411yescharacteristic
58C2×C32×C4—22no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C32×C4C2×D411yescharacteristic
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3C2×D411yescharacteristic
63C2×C3⋊Dic3C2×D411yescharacteristic
64C2×C3⋊Dic3C2×D411yescharacteristic
65C2×C3⋊Dic3C2×Q814yes—
66C2×C3⋊Dic3C2411yescharacteristic
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—
81C22×C3×C4—22no—
82C22×Dic3—62no—
83C22×Dic3—62no—
84C2×Dic6—22no—
85C2×Dic6—64no—
86C3×C4⋊C4—62no—
87C3×C4⋊C4—64no—
88C3×C22⋊C4—64no—
89#217—24no—
90C4⋊Dic3—22no—
91C4⋊Dic3—64no—
92Dic3⋊C4—24no—
93Dic3⋊C4—64no—
94Dic3⋊C4—64no—
95Dic3⋊C4—64no—
96Dic3⋊C4—64no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C4×Dic3—62no—
100C4×Dic3—62no—
101C4×Dic3—64no—
102C4×Dic3—64no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32C4⋊Q812yes—
106C22×C32C22×D411yescharacteristic
107C32×C4—21no—
108C32×C4#13512yes—
109C3⋊Dic3—21no—
110C3⋊Dic3C4⋊Q812yes—
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—62no—
120C22⋊Q8—182no—
121C4×Q8—182no—
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—
131C23×C3—22no—
132C3×Q8—124no—
133C2×C3×C4—22no—
134C2×C3×C4—22no—
135C2×C3×C4—44no—
136C2×C3×C4—64no—
137C2×C3×C4—64no—
138C2×Dic3—24no—
139C2×Dic3—24no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142C2×Dic3—68no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—124no—
146Dic6—44no—
147Dic6—128no—
148C2×C32—22no—
149C2×C32C2×C4⋊Q811yescharacteristic
150C2×C32C2×#13511yescharacteristic
151C2×C32C2×#13511yescharacteristic
152C2×Q8—62no—
153C2×Q8—182no—
154C22×C4—91no—
155C22×C4—91no—
156C22×C4GO+(4,𝔽2)11yescharacteristic
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—64no—
167C42—91no—
168C42—91no—
169C42—91no—
170C42—91no—
171C42—184no—
172C22×C3—22no—
173C22×C3—24no—
174C22×C3—42no—
175C22×C3—42no—
176C3×C4—24no—
177C3×C4—42no—
178C3×C4—124no—
179C3×C4—124no—
180Dic3—44no—
181Dic3—44no—
182Dic3—64no—
183Dic3—64no—
184Dic3—64no—
185Dic3—122no—
186C32#316011yescharacteristic, complemented, Sylow
187C23C2×GO+(4,𝔽2)11yescharacteristic
188Q8—124no—
189Q8—364no—
190C2×C4—22no—
191C2×C4—64no—
192C2×C4—64no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4—94no—
197C2×C4—91no—
198C2×C4—182no—
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—
206C2×C3—44no—
207C22—21no—
208C22—21no—
209C22#6422212yes—
210C22C22×GO+(4,𝔽2)11yescharacteristic
211C4—21no—
212C4—92no—
213C4—92no—
214C4—92no—
215C4—124no—
216C4—124no—
217C4—181no—
218C4#6423712yes—
219C3—22no—
220C2—22no—
221C2C2×#6422211yescharacteristic
222C2#1059650011yescharacteristic
223C2C2×#6423711yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3160
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10593395C2semidirect
5. #10593390C2semidirect
6. #10593388C2semidirect
7. #10593384C2semidirect
30. C2×#622Q8semidirect
186. C32#3160semidirect

Maximal subgroups

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

subgroupindex
#105948102
C2×C4×#6222
#105935112
#105933952
#105933902
#105933882
#105933842
#31609