Finite Group Databasebeta

← #11783811

Subgroups — #11783811

Order 1152.

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

normal subgroups only

This group has 741 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
1C2×#64096C211yesmaximal, characteristic
2C2×#63561C212yesmaximal
3#10591060C212yesmaximal
4C3×#4530C212yesmaximal
5#68973—32nomaximal
6C22×#634C2211yescharacteristic
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×#3750C412yes—
9C2×C4×C3⋊Dic3C412yes—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11#64096—22no—
12#64096—22no—
13C2×C3×#208C2214yes—
14#63561C418yescomplemented
15#63555—22no—
16#63553—22no—
17C2×#887—32no—
18C2×#887—61no—
19C2×#824—34no—
20Dic3×M16—34no—
21C3×#343—32no—
22#4530D312yes—
23C22×C32×C4C2×C412yes—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3C2×C412yes—
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C2×#634—22no—
29C2×#634—22no—
30C2×#634C2×C414yes—
31C32×C4⋊C4—22no—
32#3750—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×Dic6—32no—
42C22×Dic6—61no—
43C2×C3×M16—34no—
44C2×C3×C4⋊C4—21no—
45C2×C3×C4⋊C4C2×D312yes—
46C2×Dic3⋊C4—34no—
47C2×Dic3⋊C4—62no—
48C2×C4×Dic3—32no—
49C2×C4×Dic3—34no—
50C2×C4×Dic3—62no—
51C2×C4×Dic3—61no—
52C2×#208C2×D314yes—
53#887—64no—
54#887—64no—
55#887—64no—
56#887—64no—
57#824—316no—
58#815—64no—
59C8×Dic3—64no—
60C23×C32C22×C411yescharacteristic
61C2×C32×C4—22no—
62C2×C32×C4—42no—
63C2×C32×C4C22×C412yes—
64C2×C32×C4C2×D412yes—
65C2×C32×C4#4112yes—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3—22no—
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3—41no—
70C2×C3⋊Dic3C4214yes—
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22⋊C412yes—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74#634—28no—
75C3×C3⋊C8—28no—
76C2×C4×Q8—91no—
77C2×#101—92no—
78C4×M16—92no—
79#343—32no—
80C22×C3×C4—22no—
81C22×C3×C4—21no—
82C22×C3×C4C4×D314yes—
83C22×C3×C4C22×D312yes—
84C22×Dic3—32no—
85C22×Dic3—34no—
86C22×Dic3—32no—
87C22×Dic3—61no—
88C22×Dic3—62no—
89C22×Dic3—61no—
90C2×Dic6—38no—
91C2×Dic6—64no—
92C2×Dic6—64no—
93C2×Dic6—64no—
94C2×Dic6—64no—
95C2×Dic6—62no—
96C2×Dic6—62no—
97C3×M16—38no—
98C3×M16—64no—
99C2×C3×C8—64no—
100C3×C4⋊C4—24no—
101C3×C4⋊C4—24no—
102Dic3⋊C4—68no—
103Dic3⋊C4—68no—
104C4×Dic3—34no—
105C4×Dic3—34no—
106C4×Dic3—62no—
107C4×Dic3—62no—
108C4×Dic3—64no—
109C4×Dic3—64no—
110C4×Dic3—64no—
111C4×Dic3—64no—
112#208—24no—
113#208C4×D318yes—
114C2×C3⋊C8—24no—
115C22×C32—21no—
116C22×C32—21no—
117C22×C32C2×C4211yescharacteristic
118C22×C32C2×C22⋊C411yescharacteristic
119C22×C32#11711yescharacteristic
120C32×C4—42no—
121C32×C4C4×D414yes—
122C3⋊Dic3—24no—
123C3⋊Dic3—21no—
124C3⋊Dic3—22no—
125C3⋊Dic3#10112yescomplemented
126C22×Q8—91no—
127C2×M16—34no—
128C4×Q8—182no—
129C4×Q8—182no—
130C2×C4⋊C4—92no—
131C2×C4⋊C4D3211yescharacteristic
132C2×C42—91no—
133C2×C42—92no—
134#101—98no—
135#97—182no—
136C4×C8—182no—
137C23×C3—21no—
138C23×C3C2×C4×D312yes—
139C2×C3×C4—24no—
140C2×C3×C4—24no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—22no—
144C2×C3×C4—44no—
145C2×C3×C4—44no—
146C2×C3×C4C2×C4×D314yes—
147C2×C3×C4D3×D414yes—
148C2×C3×C4#23712yes—
149C2×C3×C4#23912yes—
150C2×Dic3—32no—
151C2×Dic3—38no—
152C2×Dic3—32no—
153C2×Dic3—34no—
154C2×Dic3—64no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—62no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160C2×Dic3—64no—
161C2×Dic3—64no—
162C2×Dic3—64no—
163C2×Dic3—64no—
164C2×Dic3—122no—
165C2×Dic3—122no—
166Dic6—616no—
167Dic6—68no—
168Dic6—68no—
169C3×C8—68no—
170C3⋊C8—28no—
171C2×C32—21no—
172C2×C32—21no—
173C2×C32C4×C22⋊C411yescharacteristic
174C2×C32C2×#10111yescharacteristic
175C2×C32#41311yescharacteristic
176C2×Q8—94no—
177C2×Q8—182no—
178C2×Q8—182no—
179C22×C4—91no—
180C22×C4—92no—
181C22×C4—91no—
182C22×C4#62412yes—
183C22×C4C2×D3211yescharacteristic
184M16—38no—
185M16—64no—
186C2×C8—64no—
187C4⋊C4—22no—
188C4⋊C4—184no—
189C42—92no—
190C42—92no—
191C42—182no—
192C42—182no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—22no—
196C22×C3—22no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3C42×D312yes—
201C22×C3D3×C22⋊C412yes—
202C22×C3#89212yes—
203C3×C4—24no—
204C3×C4—44no—
205C3×C4—44no—
206C3×C4#67⋊C414yes—
207C3×C4#89314yes—
208Dic3—34no—
209Dic3—62no—
210Dic3—68no—
211Dic3—62no—
212Dic3—68no—
213Dic3—64no—
214Dic3—62no—
215Dic3—122no—
216C32C4×#10111yescharacteristic, complemented, Sylow
217C23C2×#62411yescharacteristic
218Q8—188no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—91no—
222C2×C4—94no—
223C2×C4—91no—
224C2×C4—92no—
225C2×C4—182no—
226C2×C4—182no—
227C2×C4—182no—
228C2×C4—361no—
229C2×C4#379612yes—
230C2×C4C4×D3212yes—
231C2×C4#381112yes—
232C8—68no—
233C2×C3—22no—
234C2×C3—22no—
235C2×C3—22no—
236C2×C3—22no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3#466612yes—
241C2×C3#474512yes—
242C2×C3D3×#10112yes—
243C22—21no—
244C22—21no—
245C22#6384911yescharacteristic
246C22C4×#62411yescharacteristic
247C22#6397411yescharacteristic
248C4—42no—
249C4—92no—
250C4—182no—
251C4—184no—
252C4—181no—
253C4#6388114yes—
254C3—21no—
255C3#6897312yescomplemented
256C2—21no—
257C2—21no—
258C2#1059126011yescharacteristic
259C2#1059150411yescharacteristic
260C2#1059163911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#101
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
14. #63561C4semidirect
125. C3⋊Dic3#101semidirect
216. C32C4×#101semidirect
255. C3#68973semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#635612
#105910602
C3×#45302
#689733