Finite Group Databasebeta

← #11785960

Subgroups — #11785960

Order 1152.

518 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 106 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×#63779C212yesmaximal
2C42×C3⋊Dic3C211yesmaximal, characteristic
3#10590207C212yesmaximal
4#10590207C212yesmaximal
5C22×#622C2214yes—
6C2×C32×C42C411yescharacteristic
7C2×C4×C3⋊Dic3C411yescharacteristic
8C2×C4×C3⋊Dic3C411yescharacteristic
9C2×C4×C3⋊Dic3C411yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#63779—24no—
14C42×Dic3—62no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C32×C4C2×C411yescharacteristic
17C22×C32×C4C2×C411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C22×C3⋊Dic3C2×C411yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3C2311yescharacteristic
22C2×#622—24no—
23C2×#622—24no—
24C2×#622—24no—
25C32×C42—22no—
26C4×C3⋊Dic3—22no—
27C4×C3⋊Dic3—22no—
28C4×C3⋊Dic3—22no—
29C4×C3⋊Dic3—22no—
30C4×C3⋊Dic3C814yescomplemented
31C4×C3⋊Dic3D412yes—
32C4×C3⋊Dic3Q812yes—
33#1831—91nomaximal, Sylow
34C2×C3×C42—22no—
35C2×C4×Dic3—62no—
36C2×C4×Dic3—62no—
37C2×C4×Dic3—62no—
38C2×C4×Dic3—62no—
39C2×C4×Dic3—62no—
40C2×C4×Dic3—62no—
41C23×C32C22×C411yescharacteristic
42C2×C32×C4—21no—
43C2×C32×C4—21no—
44C2×C32×C4—21no—
45C2×C32×C4—21no—
46C2×C32×C4—21no—
47C2×C32×C4—21no—
48C2×C32×C4C4⋊C412yes—
49C2×C32×C4C2×C812yes—
50C2×C32×C4M1612yes—
51C2×C3⋊Dic3—21no—
52C2×C3⋊Dic3—21no—
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3C4⋊C412yes—
56C2×C3⋊Dic3C2×C812yes—
57C2×C3⋊Dic3C2×C812yes—
58C2×C3⋊Dic3M1612yes—
59C2×C3⋊Dic3M1612yes—
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3C2×Q811yescharacteristic
62C2×C3⋊Dic3#4112yes—
63C2×C3⋊Dic3#4112yes—
64#622—44no—
65C2×C4⋊C8—92no—
66C43—91no—
67#336—92no—
68#336—92no—
69C22×C3×C4—22no—
70C22×C3×C4—22no—
71C22×C3×C4—22no—
72C22×Dic3—62no—
73C22×Dic3—62no—
74C22×Dic3—62no—
75C22×Dic3—62no—
76C3×C42—28no—
77C4×Dic3—68no—
78C4×Dic3—64no—
79C4×Dic3—64no—
80C4×Dic3—68no—
81C4×Dic3—68no—
82C4×Dic3—68no—
83C4×Dic3—68no—
84C22×C32C2×C4⋊C411yescharacteristic
85C22×C32#11711yescharacteristic
86C22×C32#11711yescharacteristic
87C22×C32C22×C811yescharacteristic
88C22×C32C2×M1611yescharacteristic
89C22×C32C2×M1611yescharacteristic
90C22×C32C2×M1611yescharacteristic
91C32×C4—22no—
92C32×C4—22no—
93C32×C4—22no—
94C3⋊Dic3—22no—
95C3⋊Dic3—22no—
96C3⋊Dic3C4⋊C814yes—
97C3⋊Dic3#12412yes—
98C3⋊Dic3#12512yes—
99C22×C8—94no—
100C2×C42—91no—
101C2×C42—91no—
102C2×C42—91no—
103C2×C42—91no—
104C2×C42—91no—
105C2×C42—91no—
106C2×C42#15711yescharacteristic
107C4⋊C8—184no—
108C23×C3—22no—
109C2×C3×C4—24no—
110C2×C3×C4—24no—
111C2×C3×C4—24no—
112C2×C3×C4—24no—
113C2×C3×C4—24no—
114C2×C3×C4—24no—
115C2×C3×C4—24no—
116C2×C3×C4—24no—
117C2×C3×C4—24no—
118C2×Dic3—64no—
119C2×Dic3—64no—
120C2×Dic3—64no—
121C2×Dic3—64no—
122C2×Dic3—64no—
123C2×Dic3—62no—
124C2×Dic3—62no—
125C2×Dic3—64no—
126C2×Dic3—64no—
127C2×Dic3—64no—
128C2×Dic3—64no—
129C2×Dic3—64no—
130C2×Dic3—64no—
131C2×C32#38211yescharacteristic
132C2×C32C2×C4⋊C811yescharacteristic
133C2×C32#42311yescharacteristic
134C2×C32#43111yescharacteristic
135C2×C32#43111yescharacteristic
136C2×C32#43211yescharacteristic
137C2×C32#43211yescharacteristic
138C22×C4—91no—
139C22×C4—91no—
140C22×C4—91no—
141C22×C4—91no—
142C22×C4C2×#15711yescharacteristic
143C22×C4C2×#15711yescharacteristic
144C22×C4C2×#15711yescharacteristic
145C2×C8—184no—
146C2×C8—184no—
147C2×C8—184no—
148C42—22no—
149C42—94no—
150C42—92no—
151C42—92no—
152C42—182no—
153C42—182no—
154C42—182no—
155C42—182no—
156C22×C3—22no—
157C22×C3—22no—
158C22×C3—22no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—22no—
162C22×C3—22no—
163C3×C4—28no—
164C3×C4—28no—
165C3×C4—28no—
166Dic3—68no—
167Dic3—64no—
168Dic3—64no—
169Dic3—68no—
170Dic3—68no—
171C32#183111yescharacteristic, complemented, Sylow
172C23C22×#15711yescharacteristic
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—92no—
180C2×C4—92no—
181C2×C4—91no—
182C2×C4—92no—
183C2×C4—91no—
184C2×C4—92no—
185C2×C4—92no—
186C2×C4—92no—
187C2×C4—92no—
188C2×C4—181no—
189C2×C4—181no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4#378712yes—
193C2×C4C4⋊#15712yes—
194C2×C4#379212yes—
195C8—364no—
196C2×C3—22no—
197C2×C3—22no—
198C2×C3—22no—
199C2×C3—22no—
200C2×C3—22no—
201C2×C3—22no—
202C2×C3—22no—
203C22C2×#378711yescharacteristic
204C22#6428311yescharacteristic
205C22#6428311yescharacteristic
206C22C2×C4⋊#15711yescharacteristic
207C22#6428611yescharacteristic
208C22#6428611yescharacteristic
209C22C2×#379211yescharacteristic
210C4—22no—
211C4—22no—
212C4—22no—
213C4—94no—
214C4—92no—
215C4—92no—
216C4—182no—
217C4—182no—
218C3—22no—
219C2#1059372511yescharacteristic
220C2#1059372611yescharacteristic
221C2#1059373111yescharacteristic
222C2#1059373611yescharacteristic
223C2#1059380111yescharacteristic
224C2#1059380411yescharacteristic
225C2#1059380511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C22×C8
FittingC2×C32×C42C4
socle, prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C42#157
hypocenterC32#1831
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
30. C4×C3⋊Dic3C8semidirect
171. C32#1831semidirect

Maximal subgroups

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

subgroupindex
C2×#637792
C42×C3⋊Dic32
#105902072
#18319