Finite Group Databasebeta

← #11786129

Subgroups — #11786129

Order 1152.

498 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C42×C3⋊Dic3C211yesmaximal, characteristic
2#10590207C212yesmaximal
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
13C42×Dic3—62no—
14C22×C32×C4C2×C411yescharacteristic
15C22×C32×C4C2×C411yescharacteristic
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3C2×C411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C22×C3⋊Dic3C2×C411yescharacteristic
20C22×C3⋊Dic3C2311yescharacteristic
21C2×#622—24no—
22C2×#622—24no—
23C2×#622—24no—
24C32×C42—22no—
25C4×C3⋊Dic3—22no—
26C4×C3⋊Dic3—22no—
27C4×C3⋊Dic3—22no—
28C4×C3⋊Dic3—22no—
29C4×C3⋊Dic3—22no—
30C4×C3⋊Dic3C814yescomplemented
31#1839—91nomaximal, Sylow
32C2×C3×C42—22no—
33C2×C4×Dic3—62no—
34C2×C4×Dic3—62no—
35C2×C4×Dic3—62no—
36C2×C4×Dic3—62no—
37C2×C4×Dic3—62no—
38C2×C4×Dic3—62no—
39C23×C32C22×C411yescharacteristic
40C2×C32×C4—21no—
41C2×C32×C4—21no—
42C2×C32×C4—21no—
43C2×C32×C4—21no—
44C2×C32×C4—21no—
45C2×C32×C4—21no—
46C2×C32×C4C2×C812yes—
47C2×C32×C4M1612yes—
48C2×C32×C4M1612yes—
49C2×C3⋊Dic3—21no—
50C2×C3⋊Dic3—21no—
51C2×C3⋊Dic3—21no—
52C2×C3⋊Dic3—21no—
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3C2×C812yes—
56C2×C3⋊Dic3C2×C812yes—
57C2×C3⋊Dic3M1612yes—
58C2×C3⋊Dic3#4112yes—
59C2×C3⋊Dic3#4112yes—
60C2×C3⋊Dic3#4112yes—
61#622—44no—
62C43—91no—
63#336—92no—
64#336—92no—
65#336—92no—
66C22×C3×C4—22no—
67C22×C3×C4—22no—
68C22×C3×C4—22no—
69C22×Dic3—62no—
70C22×Dic3—62no—
71C22×Dic3—62no—
72C22×Dic3—62no—
73C3×C42—28no—
74C4×Dic3—68no—
75C4×Dic3—68no—
76C4×Dic3—68no—
77C4×Dic3—68no—
78C4×Dic3—68no—
79C4×Dic3—68no—
80C22×C32#11711yescharacteristic
81C22×C32#11711yescharacteristic
82C22×C32#11711yescharacteristic
83C22×C32C22×C811yescharacteristic
84C22×C32C2×M1611yescharacteristic
85C22×C32C2×M1611yescharacteristic
86C22×C32C2×M1611yescharacteristic
87C32×C4—22no—
88C32×C4—22no—
89C32×C4—22no—
90C3⋊Dic3—22no—
91C3⋊Dic3—22no—
92C3⋊Dic3—22no—
93C3⋊Dic3#12614yes—
94C22×C8—94no—
95C2×C42—91no—
96C2×C42—91no—
97C2×C42—91no—
98C2×C42—91no—
99C2×C42—91no—
100C2×C42—91no—
101C2×C42#15711yescharacteristic
102C23×C3—22no—
103C2×C3×C4—24no—
104C2×C3×C4—24no—
105C2×C3×C4—24no—
106C2×C3×C4—24no—
107C2×C3×C4—24no—
108C2×C3×C4—24no—
109C2×C3×C4—24no—
110C2×C3×C4—24no—
111C2×C3×C4—24no—
112C2×Dic3—64no—
113C2×Dic3—64no—
114C2×Dic3—64no—
115C2×Dic3—64no—
116C2×Dic3—64no—
117C2×Dic3—64no—
118C2×Dic3—64no—
119C2×Dic3—64no—
120C2×Dic3—64no—
121C2×Dic3—64no—
122C2×Dic3—64no—
123C2×Dic3—64no—
124C2×C32#38311yescharacteristic
125C2×C32#43111yescharacteristic
126C2×C32#43111yescharacteristic
127C2×C32#43111yescharacteristic
128C2×C32#43211yescharacteristic
129C2×C32#43211yescharacteristic
130C2×C32#43211yescharacteristic
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—91no—
134C22×C4—91no—
135C22×C4C2×#15711yescharacteristic
136C22×C4C2×#15711yescharacteristic
137C22×C4C2×#15711yescharacteristic
138C2×C8—184no—
139C2×C8—184no—
140C2×C8—184no—
141C42—22no—
142C42—94no—
143C42—182no—
144C42—182no—
145C42—182no—
146C42—182no—
147C42—182no—
148C22×C3—22no—
149C22×C3—22no—
150C22×C3—22no—
151C22×C3—22no—
152C22×C3—22no—
153C22×C3—22no—
154C22×C3—22no—
155C3×C4—28no—
156C3×C4—28no—
157C3×C4—28no—
158Dic3—68no—
159Dic3—68no—
160Dic3—68no—
161Dic3—68no—
162C32#183911yescharacteristic, complemented, Sylow
163C23C22×#15711yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—92no—
171C2×C4—92no—
172C2×C4—92no—
173C2×C4—92no—
174C2×C4—92no—
175C2×C4—92no—
176C2×C4—181no—
177C2×C4—181no—
178C2×C4—181no—
179C2×C4—181no—
180C2×C4—181no—
181C2×C4—181no—
182C2×C4#378712yes—
183C2×C4#378812yes—
184C2×C4#379212yes—
185C8—364no—
186C2×C3—22no—
187C2×C3—22no—
188C2×C3—22no—
189C2×C3—22no—
190C2×C3—22no—
191C2×C3—22no—
192C2×C3—22no—
193C22C2×#378711yescharacteristic
194C22C2×#378811yescharacteristic
195C22#6428311yescharacteristic
196C22#6428611yescharacteristic
197C22#6428611yescharacteristic
198C22#6428611yescharacteristic
199C22C2×#379211yescharacteristic
200C4—22no—
201C4—22no—
202C4—22no—
203C4—94no—
204C4—182no—
205C4—182no—
206C4—182no—
207C3—22no—
208C2#1059372511yescharacteristic
209C2#1059372711yescharacteristic
210C2#1059373011yescharacteristic
211C2#1059373711yescharacteristic
212C2#1059380111yescharacteristic
213C2#1059380411yescharacteristic
214C2#1059380611yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C22×C8
FittingC2×C32×C42C4
socle, prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C42#157
hypocenterC32#1839
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
162. C32#1839semidirect

Maximal subgroups

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

subgroupindex
C42×C3⋊Dic32
#105902072
#18399