Finite Group Databasebeta

← #11783418

Subgroups — #11783418

Order 1152.

718 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 130 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×#64283C212yesmaximal
2C2×#64081C211yesmaximal, characteristic
3#10590208C214yesmaximal, complemented
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×#3792C2214yes—
6#64283—24no—
7#64283C418yescomplemented
8C2×#3788—22no—
9C2×#3787—22no—
10C2×C32×C42C411yescharacteristic
11C2×#3752C412yes—
12C2×#3750C2212yes—
13C2×C4×C3⋊Dic3C411yescharacteristic
14#64081—22no—
15#64081—22no—
16C2×#872—62no—
17C23×C3⋊D3C2×C411yescharacteristic
18C22×C32×C4C2×C412yes—
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3C2×C412yes—
21C22×C3⋊Dic3C2311yescharacteristic
22C2×C4×C3⋊D3C2×C414yes—
23C2×C4×C3⋊D3D412yes—
24C2×C4×C3⋊D3D412yes—
25C2×C4×C3⋊D3D412yes—
26C2×C4×C3⋊D3Q812yes—
27#3792—24no—
28#3792C2×C418yes—
29C2×#622—24no—
30#3788—28no—
31#3787—28no—
32C32×C42—21no—
33C32×C42—21no—
34#3752—24no—
35#3750—24no—
36C4×C3⋊Dic3—21no—
37C4×C3⋊Dic3—21no—
38#1742—91nomaximal, Sylow
39C22×C4×D3—62no—
40C2×C3×C42—22no—
41C2×(C2×D3)⋊C4—64no—
42C2×Dic3⋊C4—64no—
43C2×C4×Dic3—62no—
44#872—68no—
45#872—68no—
46C23×C32C22×C411yescharacteristic
47C22×C3⋊D3—42no—
48C22×C3⋊D3C4212yes—
49C22×C3⋊D3C22⋊C412yes—
50C22×C3⋊D3C4⋊C412yes—
51C2×C32×C4—22no—
52C2×C32×C4—42no—
53C2×C32×C4C4212yes—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4C4⋊C412yes—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3—42no—
59C2×C3⋊Dic3C22×C412yes—
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3C2×D412yes—
62C2×C3⋊Dic3C2×Q811yescharacteristic
63C4×C3⋊D3C22⋊C414yes—
64C4×C3⋊D3C22⋊C414yes—
65C4×C3⋊D3C4⋊C414yes—
66C4×C3⋊D3C4⋊C414yes—
67#622—28no—
68C22×M16—92no—
69C2×#117—91no—
70#343—94no—
71C23×D3—62no—
72C22×C3×C4—24no—
73C22×C3×C4—22no—
74C22×Dic3—62no—
75C22×Dic3—64no—
76C2×C4×D3—64no—
77C2×C4×D3—64no—
78C2×C4×D3—68no—
79C2×C4×D3—64no—
80C2×C4×D3—64no—
81C3×C42—24no—
82C3×C42—24no—
83(C2×D3)⋊C4—616no—
84Dic3⋊C4—616no—
85C4×Dic3—64no—
86C4×Dic3—64no—
87C22×C32—22no—
88C22×C32C2×C4211yescharacteristic
89C22×C32C2×C22⋊C411yescharacteristic
90C22×C32C2×C4⋊C411yescharacteristic
91C2×C3⋊D3—24no—
92C2×C3⋊D3—42no—
93C2×C3⋊D3—42no—
94C2×C3⋊D3#9514yes—
95C32×C4—42no—
96C32×C4#9512yes—
97C32×C4#9512yes—
98C3⋊Dic3—42no—
99C3⋊Dic3C2×C22⋊C412yes—
100C3⋊Dic3C2×C4⋊C412yes—
101C23×C4—91no—
102C2×M16—98no—
103C2×M16—94no—
104C2×M16—182no—
105C2×M16—184no—
106C22×C8—182no—
107#117—182no—
108#117—182no—
109C2×C4⋊C4—92no—
110C2×C22⋊C4—92no—
111C2×C42—91no—
112C2×C42#15711yescharacteristic
113C23×C3—22no—
114C22×D3—64no—
115C22×D3—64no—
116C22×D3—64no—
117C22×D3—128no—
118C2×C3×C4—28no—
119C2×C3×C4—24no—
120C2×C3×C4—24no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—48no—
124C2×Dic3—64no—
125C2×Dic3—64no—
126C2×Dic3—62no—
127C2×Dic3—62no—
128C2×Dic3—68no—
129C2×Dic3—128no—
130C4×D3—68no—
131C4×D3—68no—
132C4×D3—68no—
133C4×D3—68no—
134C2×C32—21no—
135C2×C32—21no—
136C2×C32C2×#9511yescharacteristic
137C2×C32#41312yes—
138C3⋊D3—24no—
139C24—91no—
140C22×C4—91no—
141C22×C4—94no—
142C22×C4—92no—
143C22×C4—92no—
144C22×C4—92no—
145C22×C4—92no—
146C22×C4—92no—
147C22×C4C2×#15712yes—
148C22×C4C2×#15711yescharacteristic
149M16—98no—
150M16—188no—
151M16—184no—
152C2×C8—188no—
153C2×C8—184no—
154C4⋊C4—184no—
155C22⋊C4—184no—
156C42—21no—
157C42—21no—
158C42—181no—
159C42—181no—
160C22×C3—28no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—22no—
164C2×D3—68no—
165C2×D3—128no—
166C2×D3—128no—
167C2×D3—128no—
168C3×C4—24no—
169C3×C4—24no—
170C3×C4—48no—
171Dic3—64no—
172Dic3—64no—
173Dic3—128no—
174C32#174211yescharacteristic, complemented, Sylow
175C23—92no—
176C23—92no—
177C23—92no—
178C23—362no—
179C23C22×#15711yescharacteristic
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—92no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—92no—
186C2×C4—94no—
187C2×C4—94no—
188C2×C4—94no—
189C2×C4—94no—
190C2×C4—182no—
191C2×C4—362no—
192C2×C4C4×#15712yes—
193C2×C4C4⋊#15712yes—
194C2×C4C22⋊#15711yescharacteristic
195C2×C4C22⋊#15711yescharacteristic
196C8—188no—
197C2×C3—24no—
198C2×C3—24no—
199C2×C3—24no—
200C2×C3—22no—
201D3—128no—
202C22—22no—
203C22—94no—
204C22—184no—
205C22—362no—
206C22—362no—
207C22C2×C4×#15711yescharacteristic
208C22C2×C4⋊#15711yescharacteristic
209C22C2×C22⋊#15711yescharacteristic
210C4—42no—
211C4—92no—
212C4—92no—
213C4—362no—
214C4#6378112yes—
215C4#6378112yes—
216C3—22no—
217C2—21no—
218C2—21no—
219C2—184no—
220C2#1059380812yes—
221C2C2×#6378111yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC2×C32×C42C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C42#157
hypocenterC32#1742
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #10590208C2semidirect
7. #64283C4semidirect
174. C32#1742semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
C2×#640812
#105902082
#17429