Finite Group Databasebeta

← #11783397

Subgroups — #11783397

Order 1152.

850 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 138 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×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
3#10590208C214yesmaximal, complemented
4C22×C4×C3⋊D3C412yes—
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3792C2214yes—
7#64283—24no—
8#64283C418yescomplemented
9C2×#3788—22no—
10C2×#3787—22no—
11C2×C32×C4⋊C4C411yescharacteristic
12C2×C4⋊(C3⋊Dic3)C411yescharacteristic
13C2×#3750C2212yes—
14C4⋊C4×C3⋊D3—22no—
15C4⋊C4×C3⋊D3—22no—
16C2×D3×C4⋊C4—62no—
17C23×C3⋊D3C2×C411yescharacteristic
18C22×C32×C4C2×C412yes—
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3C2×C412yes—
21C22×C3⋊Dic3C2311yescharacteristic
22C2×C4×C3⋊D3—22no—
23C2×C4×C3⋊D3—22no—
24C2×C4×C3⋊D3—44no—
25C2×C4×C3⋊D3C2×C414yes—
26C2×C4×C3⋊D3D412yes—
27C2×C4×C3⋊D3D412yes—
28C2×C4×C3⋊D3D412yes—
29C2×C4×C3⋊D3Q812yes—
30#3792—24no—
31#3792C2×C418yescomplemented
32C2×#622—24no—
33#3788—28no—
34#3787—28no—
35C32×C4⋊C4—22no—
36C4⋊(C3⋊Dic3)—22no—
37#3750—24no—
38C2×#343—91nomaximal, Sylow
39C22×C4×D3—62no—
40C22×C4×D3—64no—
41C2×C3×C4⋊C4—22no—
42C2×C4⋊Dic3—62no—
43C2×Dic3⋊C4—64no—
44D3×C4⋊C4—68no—
45D3×C4⋊C4—68no—
46C23×C32C22×C411yescharacteristic
47C22×C3⋊D3—22no—
48C22×C3⋊D3—22no—
49C22×C3⋊D3C4212yes—
50C22×C3⋊D3C22⋊C411yescharacteristic
51C22×C3⋊D3C22⋊C411yescharacteristic
52C22×C3⋊D3C4⋊C412yes—
53C2×C32×C4—22no—
54C2×C32×C4—42no—
55C2×C32×C4C4212yes—
56C2×C32×C4C22⋊C412yes—
57C2×C32×C4C4⋊C412yes—
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3—42no—
60C2×C3⋊Dic3C22×C412yes—
61C2×C3⋊Dic3C2×D411yescharacteristic
62C2×C3⋊Dic3C2×D412yes—
63C2×C3⋊Dic3C2×Q811yescharacteristic
64C4×C3⋊D3—44no—
65C4×C3⋊D3—44no—
66C4×C3⋊D3C22⋊C414yes—
67C4×C3⋊D3C22⋊C414yes—
68C4×C3⋊D3C4⋊C414yes—
69C4×C3⋊D3C4⋊C414yes—
70#622—28no—
71C22×M16—92no—
72C22×C4⋊C4—91no—
73#343—94no—
74C23×D3—62no—
75C22×C3×C4—24no—
76C22×C3×C4—22no—
77C22×Dic3—62no—
78C22×Dic3—64no—
79C2×C4×D3—64no—
80C2×C4×D3—64no—
81C2×C4×D3—68no—
82C2×C4×D3—64no—
83C2×C4×D3—64no—
84C2×C4×D3—68no—
85C2×C4×D3—68no—
86C2×C4×D3—1216no—
87C3×C4⋊C4—28no—
88C4⋊Dic3—68no—
89Dic3⋊C4—616no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32C2×C4211yescharacteristic
93C22×C32C2×C22⋊C411yescharacteristic
94C22×C32C2×C4⋊C411yescharacteristic
95C2×C3⋊D3—21no—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—24no—
98C2×C3⋊D3—24no—
99C2×C3⋊D3#9512yes—
100C2×C3⋊D3#9512yes—
101C2×C3⋊D3#10012yes—
102C2×C3⋊D3#10112yes—
103C32×C4—42no—
104C32×C4#9514yes—
105C3⋊Dic3—42no—
106C3⋊Dic3C2×C22⋊C412yes—
107C3⋊Dic3C2×C4⋊C412yes—
108C23×C4—91no—
109C23×C4—92no—
110C2×M16—98no—
111C2×M16—94no—
112C2×M16—182no—
113C2×M16—184no—
114C22×C8—182no—
115C2×C4⋊C4—92no—
116C2×C4⋊C4—91no—
117C2×C4⋊C4—182no—
118C2×C4⋊C4—182no—
119C2×C4⋊C4#15711yescharacteristic
120C23×C3—22no—
121C22×D3—64no—
122C22×D3—62no—
123C22×D3—62no—
124C22×D3—64no—
125C22×D3—68no—
126C22×D3—68no—
127C2×C3×C4—28no—
128C2×C3×C4—24no—
129C2×C3×C4—24no—
130C2×C3×C4—24no—
131C2×C3×C4—48no—
132C2×Dic3—64no—
133C2×Dic3—64no—
134C2×Dic3—62no—
135C2×Dic3—62no—
136C2×Dic3—68no—
137C2×Dic3—128no—
138C4×D3—68no—
139C4×D3—68no—
140C4×D3—68no—
141C4×D3—68no—
142C4×D3—1216no—
143C4×D3—1216no—
144C2×C32—21no—
145C2×C32—21no—
146C2×C32C2×#9511yescharacteristic
147C2×C32C2×#10011yescharacteristic
148C2×C32C2×#10111yescharacteristic
149C3⋊D3—22no—
150C3⋊D3#34314yescomplemented
151C24—91no—
152C22×C4—91no—
153C22×C4—94no—
154C22×C4—92no—
155C22×C4—92no—
156C22×C4—92no—
157C22×C4—92no—
158C22×C4—92no—
159C22×C4—182no—
160C22×C4—182no—
161C22×C4—364no—
162C22×C4C2×#15712yes—
163C22×C4C2×#15711yescharacteristic
164M16—98no—
165M16—188no—
166M16—184no—
167C2×C8—188no—
168C2×C8—184no—
169C4⋊C4—22no—
170C4⋊C4—184no—
171C4⋊C4—182no—
172C22×C3—24no—
173C22×C3—24no—
174C22×C3—22no—
175C22×C3—22no—
176C22×C3—22no—
177C2×D3—64no—
178C2×D3—64no—
179C2×D3—64no—
180C2×D3—64no—
181C2×D3—64no—
182C2×D3—616no—
183C2×D3—616no—
184C2×D3—64no—
185C3×C4—28no—
186C3×C4—48no—
187Dic3—64no—
188Dic3—64no—
189Dic3—128no—
190C32C2×#34311yescharacteristic, complemented, Sylow
191C23—91no—
192C23—92no—
193C23—92no—
194C23—91no—
195C23—182no—
196C23—182no—
197C23C22×#15711yescharacteristic
198C2×C4—22no—
199C2×C4—42no—
200C2×C4—92no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—92no—
204C2×C4—94no—
205C2×C4—94no—
206C2×C4—94no—
207C2×C4—94no—
208C2×C4—182no—
209C2×C4—364no—
210C2×C4—364no—
211C2×C4—362no—
212C2×C4C4×#15712yes—
213C2×C4C4⋊#15712yes—
214C2×C4C22⋊#15712yes—
215C8—188no—
216C2×C3—24no—
217C2×C3—24no—
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—22no—
221D3—68no—
222D3—68no—
223C22—21no—
224C22—21no—
225C22—92no—
226C22—92no—
227C22—92no—
228C22—92no—
229C22—184no—
230C22—184no—
231C22—181no—
232C22—181no—
233C22C2×C4×#15711yescharacteristic
234C22C2×C4⋊#15711yescharacteristic
235C22C2×C22⋊#15711yescharacteristic
236C4—42no—
237C4—92no—
238C4—92no—
239C4—362no—
240C4#6378114yes—
241C3—22no—
242C2—21no—
243C2—21no—
244C2—94no—
245C2—182no—
246C2C2×#6378111yescharacteristic
247C2#1059382511yescharacteristic
248C2#1059383611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32C2×#343
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10590208C2semidirect
8. #64283C4semidirect
31. #3792C2×C4semidirect
150. C3⋊D3#343semidirect
190. C32C2×#343semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
C2×C4⋊C4×C3⋊D32
#105902082
C2×#3439