Finite Group Databasebeta

← #11783818

Subgroups — #11783818

Order 1152.

741 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 741 conjugacy classes of subgroups — too many to draw. Only its 190 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×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#836C212yesmaximal
3#10591060C212yesmaximal
4#10589168C212yesmaximal
5Dic3×#101—32nomaximal
6C22×C32×Q8C2211yescharacteristic
7Q8×C3⋊Dic3—22no—
8Q8×C3⋊Dic3—22no—
9C2×C4⋊(C3⋊Dic3)C412yes—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×C4×C3⋊Dic3C412yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×#208C2214yes—
14C3×#836C418yescomplemented
15#63555—22no—
16#63553—22no—
17C2×Q8×Dic3—32no—
18C2×Q8×Dic3—61no—
19C2×C3×#101—32no—
20C2×#836D312yes—
21Dic3×M16—34no—
22#4554—34no—
23C2×C32×Q8—22no—
24C2×C32×Q8—22no—
25C2×C32×Q8C2×C414yes—
26C22×C32×C4C2×C412yes—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C412yes—
30C22×C3⋊Dic3C2×C411yescharacteristic
31C4⋊(C3⋊Dic3)—22no—
32C4⋊(C3⋊Dic3)—24no—
33C4×C3⋊Dic3—22no—
34C4×C3⋊Dic3—22no—
35C4×C3⋊Dic3D412yes—
36C4×C3⋊Dic3D412yes—
37C3×#208—24no—
38C3×#208C2×C418yes—
39C2×C3×C3⋊C8—24no—
40C4×#101—91noSylow
41C22×C3×Q8—21no—
42C22×C3×Q8C2×D312yes—
43C2×C3×M16—34no—
44Q8×Dic3—64no—
45Q8×Dic3—64no—
46Q8×Dic3—64no—
47Q8×Dic3—64no—
48C2×C4⋊Dic3—34no—
49C2×C4⋊Dic3—32no—
50C2×C4⋊Dic3—62no—
51C2×C4⋊Dic3—61no—
52C2×C4×Dic3—32no—
53C2×C4×Dic3—34no—
54C2×C4×Dic3—62no—
55C2×C4×Dic3—61no—
56C2×#208C2×D314yes—
57C3×#101—38no—
58#836Dic318yescomplemented
59#815—64no—
60C8×Dic3—64no—
61C23×C32C22×C411yescharacteristic
62C32×Q8—28no—
63C2×C32×C4—22no—
64C2×C32×C4—22no—
65C2×C32×C4C4214yes—
66C2×C32×C4C22×C412yes—
67C2×C32×C4C2×D412yes—
68C2×C32×C4#4112yes—
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3—42no—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C22⋊C412yes—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C3×C3⋊C8—28no—
77C2×C4×Q8—91no—
78C2×#101—32no—
79C4×M16—92no—
80#343—92no—
81C2×C3×Q8—24no—
82C2×C3×Q8—24no—
83C2×C3×Q8—24no—
84C2×C3×Q8—24no—
85C2×C3×Q8—24no—
86C2×C3×Q8C4×D314yes—
87C2×C3×Q8C2×Dic314yes—
88C22×C3×C4—22no—
89C22×C3×C4—21no—
90C22×C3×C4C4×D314yes—
91C22×C3×C4C22×D312yes—
92C22×Dic3—32no—
93C22×Dic3—32no—
94C22×Dic3—34no—
95C22×Dic3—61no—
96C22×Dic3—61no—
97C22×Dic3—62no—
98C3×M16—38no—
99C3×M16—64no—
100C2×C3×C8—64no—
101C4⋊Dic3—68no—
102C4⋊Dic3—68no—
103C4⋊Dic3—64no—
104C4⋊Dic3—64no—
105C4×Dic3—34no—
106C4×Dic3—34no—
107C4×Dic3—62no—
108C4×Dic3—62no—
109C4×Dic3—64no—
110C4×Dic3—64no—
111C4×Dic3—64no—
112C4×Dic3—64no—
113#208—24no—
114#208C2×Dic318yes—
115C2×C3⋊C8—24no—
116C22×C32—21no—
117C22×C32—21no—
118C22×C32C2×C4211yescharacteristic
119C22×C32C2×C22⋊C411yescharacteristic
120C22×C32#11711yescharacteristic
121C32×C4—24no—
122C32×C4C4×D414yes—
123C3⋊Dic3—21no—
124C3⋊Dic3—22no—
125C3⋊Dic3—42no—
126C3⋊Dic3#10112yescomplemented
127C22×Q8D3211yescharacteristic
128C2×M16—34no—
129C4×Q8—182no—
130C4×Q8—182no—
131C2×C4⋊C4—92no—
132C2×C4⋊C4—91no—
133C2×C42—91no—
134C2×C42—92no—
135#101—38no—
136#97—182no—
137C4×C8—182no—
138C23×C3—21no—
139C23×C3C2×C4×D312yes—
140C3×Q8—216no—
141C3×Q8—28no—
142C3×Q8—28no—
143C2×C3×C4—24no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—24no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4C4×Dic318yes—
152C2×C3×C4C2×C4×D312yes—
153C2×C3×C4D3×D414yes—
154C2×C3×C4#23714yes—
155C2×C3×C4C22×Dic312yes—
156C2×Dic3—32no—
157C2×Dic3—32no—
158C2×Dic3—34no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—62no—
162C2×Dic3—64no—
163C2×Dic3—64no—
164C2×Dic3—64no—
165C2×Dic3—64no—
166C2×Dic3—122no—
167C2×Dic3—122no—
168C2×Dic3—124no—
169C2×Dic3—124no—
170C3×C8—68no—
171C3⋊C8—28no—
172C2×C32—21no—
173C2×C32—21no—
174C2×C32C4×C22⋊C411yescharacteristic
175C2×C32C2×#10111yescharacteristic
176C2×C32#41311yescharacteristic
177C2×Q8—22no—
178C2×Q8—22no—
179C2×Q8D3×Dic314yes—
180C22×C4—91no—
181C22×C4—91no—
182C22×C4—92no—
183C22×C4#62412yes—
184C22×C4C2×D3211yescharacteristic
185M16—38no—
186M16—64no—
187C2×C8—64no—
188C4⋊C4—184no—
189C4⋊C4—182no—
190C42—92no—
191C42—92no—
192C42—182no—
193C42—182no—
194C22×C3—22no—
195C22×C3—22no—
196C22×C3—22no—
197C22×C3—22no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—21no—
201C22×C3#87712yes—
202C22×C3D3×C22⋊C412yes—
203C22×C3C2×C4×Dic312yes—
204C3×C4—28no—
205C3×C4—28no—
206C3×C4—24no—
207C3×C4#67⋊C414yes—
208C3×C4D4×Dic314yes—
209Dic3—34no—
210Dic3—62no—
211Dic3—62no—
212Dic3—62no—
213Dic3—64no—
214Dic3—122no—
215Dic3—124no—
216Dic3—124no—
217C32C4×#10111yescharacteristic, complemented, Sylow
218C23C2×#62411yescharacteristic
219Q8—28no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—92no—
225C2×C4—182no—
226C2×C4—182no—
227C2×C4—361no—
228C2×C4—362no—
229C2×C4Dic3214yes—
230C2×C4C2×D3×Dic312yes—
231C2×C4#380512yes—
232C2×C4#381112yes—
233C8—68no—
234C2×C3—22no—
235C2×C3—22no—
236C2×C3—22no—
237C2×C3—22no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3D3×#10112yes—
242C2×C3#475112yes—
243C2×C3Dic3×C22⋊C412yes—
244C22—21no—
245C22—21no—
246C22C2×Dic3211yescharacteristic
247C22#6395711yescharacteristic
248C22#6397411yescharacteristic
249C4—24no—
250C4—92no—
251C4—181no—
252C4—182no—
253C4—362no—
254C4#67⋊Dic314yes—
255C3—21no—
256C3Dic3×#10112yescomplemented
257C2—21no—
258C2—21no—
259C2#1059163911yescharacteristic
260C2#1059164011yescharacteristic
261C2#1059170511yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32C4×#101
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
14. C3×#836C4semidirect
58. #836Dic3semidirect
126. C3⋊Dic3#101semidirect
217. C32C4×#101semidirect
256. C3Dic3×#101semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×C3×#8362
#105910602
#105891682
Dic3×#1013