Finite Group Databasebeta

← #11783085

Subgroups — #11783085

Order 1152.

978 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 978 conjugacy classes of subgroups — too many to draw. Only its 158 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
1C22×#3788C212yesmaximal
2C2×C42×C3⋊D3C211yesmaximal, characteristic
3#10590207C214yesmaximal, complemented
4C22×C4×C3⋊D3C412yes—
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#622C2214yes—
7C2×#3788—24no—
8C2×#3788—24no—
9C2×#3788C418yescomplemented
10C2×C32×C42C411yescharacteristic
11C2×C4×C3⋊Dic3C411yescharacteristic
12C2×C4×C3⋊Dic3C2212yes—
13C42×C3⋊D3—24no—
14C2×C42×D3—62no—
15C23×C3⋊D3C2×C411yescharacteristic
16C22×C32×C4C2×C412yes—
17C22×C32×C4C2×C411yescharacteristic
18C22×C3⋊Dic3C2×C412yes—
19C22×C3⋊Dic3C2311yescharacteristic
20C2×C4×C3⋊D3—24no—
21C2×C4×C3⋊D3—24no—
22C2×C4×C3⋊D3—24no—
23C2×C4×C3⋊D3C2×C414yes—
24C2×C4×C3⋊D3D412yes—
25C2×C4×C3⋊D3D414yes—
26C2×C4×C3⋊D3Q812yes—
27C2×#622—24no—
28C2×#622—24no—
29C2×#622C2×C418yescomplemented
30#3788—216no—
31C32×C42—22no—
32C4×C3⋊Dic3—22no—
33C4×C3⋊Dic3—24no—
34#1728—91nomaximal, Sylow
35C22×C4×D3—64no—
36C22×C4×D3—62no—
37C2×C3×C42—22no—
38C2×C4×Dic3—62no—
39C2×C4×Dic3—64no—
40C42×D3—616no—
41C23×C32C22×C411yescharacteristic
42C22×C3⋊D3—22no—
43C22×C3⋊D3—22no—
44C22×C3⋊D3C4212yes—
45C22×C3⋊D3C22⋊C412yes—
46C22×C3⋊D3C4⋊C412yes—
47C2×C32×C4—22no—
48C2×C32×C4—22no—
49C2×C32×C4C4212yes—
50C2×C32×C4C22⋊C412yes—
51C2×C32×C4C4⋊C412yes—
52C2×C32×C4M1614yescomplemented
53C2×C3⋊Dic3—22no—
54C2×C3⋊Dic3—22no—
55C2×C3⋊Dic3M1614yescomplemented
56C2×C3⋊Dic3C22×C412yes—
57C2×C3⋊Dic3C2×D411yescharacteristic
58C2×C3⋊Dic3C2×D412yes—
59C2×C3⋊Dic3C2×Q811yescharacteristic
60C4×C3⋊D3—216no—
61C4×C3⋊D3C22⋊C418yes—
62C4×C3⋊D3C4⋊C418yes—
63#622—28no—
64C22×M16—92no—
65C22×C42—91no—
66#336—94no—
67C23×D3—62no—
68C22×C3×C4—24no—
69C22×C3×C4—22no—
70C22×Dic3—64no—
71C22×Dic3—62no—
72C2×C4×D3—68no—
73C2×C4×D3—68no—
74C2×C4×D3—64no—
75C2×C4×D3—64no—
76C2×C4×D3—616no—
77C2×C4×D3—616no—
78C2×C4×D3—616no—
79C3×C42—28no—
80C4×Dic3—616no—
81C4×Dic3—68no—
82C22×C32C2×C4211yescharacteristic
83C22×C32C2×C22⋊C411yescharacteristic
84C22×C32C2×C4⋊C411yescharacteristic
85C22×C32C2×M1612yes—
86C22×C32C2×M1612yes—
87C2×C3⋊D3—24no—
88C2×C3⋊D3—24no—
89C2×C3⋊D3—22no—
90C2×C3⋊D3—22no—
91C2×C3⋊D3#9514yes—
92C32×C4—24no—
93C32×C4#9514yes—
94C3⋊Dic3—24no—
95C3⋊Dic3C2×C22⋊C412yes—
96C3⋊Dic3C2×C4⋊C412yes—
97C23×C4—91no—
98C23×C4—92no—
99C2×M16—98no—
100C2×M16—184no—
101C2×M16—184no—
102C22×C8—94no—
103C2×C42—92no—
104C2×C42—91no—
105C2×C42—184no—
106C2×C42#15711yescharacteristic
107C23×C3—22no—
108C22×D3—64no—
109C22×D3—64no—
110C22×D3—64no—
111C22×D3—68no—
112C22×D3—68no—
113C2×C3×C4—28no—
114C2×C3×C4—28no—
115C2×C3×C4—28no—
116C2×C3×C4—24no—
117C2×C3×C4—24no—
118C2×C3×C4—24no—
119C2×Dic3—68no—
120C2×Dic3—64no—
121C2×Dic3—64no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—68no—
125C2×Dic3—68no—
126C4×D3—616no—
127C4×D3—616no—
128C4×D3—664no—
129C2×C32C2×#9511yescharacteristic
130C2×C32C4×M1612yes—
131C2×C32#40712yes—
132C2×C32#42311yescharacteristic
133C2×C32#42311yescharacteristic
134C3⋊D3—24no—
135C24—91no—
136C22×C4—91no—
137C22×C4—94no—
138C22×C4—92no—
139C22×C4—92no—
140C22×C4—94no—
141C22×C4—92no—
142C22×C4—184no—
143C22×C4—184no—
144C22×C4—184no—
145C22×C4C2×#15712yes—
146C22×C4C2×#15711yescharacteristic
147M16—1816no—
148C2×C8—98no—
149C2×C8—184no—
150C2×C8—184no—
151C42—22no—
152C42—184no—
153C42—182no—
154C22×C3—24no—
155C22×C3—24no—
156C22×C3—22no—
157C22×C3—22no—
158C22×C3—22no—
159C2×D3—68no—
160C2×D3—616no—
161C2×D3—616no—
162C2×D3—68no—
163C2×D3—68no—
164C3×C4—216no—
165C3×C4—28no—
166Dic3—64no—
167Dic3—64no—
168Dic3—616no—
169C32#172811yescharacteristic, complemented, Sylow
170C23—92no—
171C23—92no—
172C23—92no—
173C23—182no—
174C23—182no—
175C23C22×#15711yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—92no—
179C2×C4—91no—
180C2×C4—91no—
181C2×C4—92no—
182C2×C4—98no—
183C2×C4—98no—
184C2×C4—94no—
185C2×C4—1816no—
186C2×C4—182no—
187C2×C4—182no—
188C2×C4#378814yescomplemented
189C2×C4C4×#15712yes—
190C2×C4C4⋊#15712yes—
191C2×C4C22⋊#15712yes—
192C8—188no—
193C2×C3—24no—
194C2×C3—22no—
195C2×C3—24no—
196C2×C3—22no—
197C2×C3—22no—
198D3—616no—
199C22—94no—
200C22—184no—
201C22—184no—
202C22—182no—
203C22—182no—
204C22C2×#378812yes—
205C22#6428312yes—
206C22C2×C4×#15711yescharacteristic
207C22C2×C4⋊#15711yescharacteristic
208C22C2×C22⋊#15711yescharacteristic
209C4—24no—
210C4—92no—
211C4—92no—
212C4—184no—
213C4#6378114yes—
214C3—22no—
215C2—184no—
216C2C4×#378812yes—
217C2#1059372811yescharacteristic
218C2#1059372911yescharacteristic
219C2#1059380312yes—
220C2C2×#6378111yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC2×C32×C42C4
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C42#157
hypocenterC32#1728
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #10590207C2semidirect
9. C2×#3788C4semidirect
29. C2×#622C2×C4semidirect
52. C2×C32×C4M16semidirect
55. C2×C3⋊Dic3M16semidirect
169. C32#1728semidirect
188. C2×C4#3788semidirect

Maximal subgroups

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

subgroupindex
C22×#37882
C2×C42×C3⋊D32
#105902072
#17289