Finite Group Databasebeta

← #11795229

Subgroups — #11795229

Order 1152.

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

normal subgroups only

This group has 517 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×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
2C3×#4928C212yesmaximal
3C2×#63576C211yesmaximal, characteristic
4#10589163C212yesmaximal
5#10589163C211yesmaximal, characteristic
6#69623—32nomaximal
7C2×C32×C42C2211yescharacteristic
8C22×C3⋊(C3⋊C8)C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×Dic3⋊C4—22no—
13C4⋊(C3⋊(C3⋊C8))—22no—
14C3×C3⋊#95—22no—
15#63576—22no—
16C3×#389—32no—
17C2×#807—32no—
18#4928D312yes—
19C2×C4⋊(C3⋊C8)—32no—
20C2×C4⋊(C3⋊C8)—61no—
21#4529—32no—
22#4529—32no—
23#4529—32no—
24C22×C32×C4D411yescharacteristic
25C22×C32×C4D411yescharacteristic
26C22×C32×C4C2311yescharacteristic
27C22×C3×Dic3—22no—
28C22×C3×Dic3—22no—
29C32×C42—21no—
30C32×C42—21no—
31C2×C3⋊(C3⋊C8)—22no—
32C2×C3⋊(C3⋊C8)—21no—
33C2×C3⋊(C3⋊C8)—22no—
34C2×C3⋊(C3⋊C8)D412yes—
35C3×C4⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C3×C4⋊Dic3Q814yes—
39C3×Dic3⋊C4—44no—
40#2087—91noSylow
41C2×C3×C4⋊C4—32no—
42C2×C3×C4⋊C4—32no—
43C2×C3×C4⋊C4—62no—
44C2×C3×C42—21no—
45C2×C3×C42C2×D312yes—
46C2×C4⋊Dic3C2×D312yes—
47C2×C4⋊Dic3C2×D312yes—
48C2×Dic3⋊C4—22no—
49C22×C3⋊C8—32no—
50C22×C3⋊C8—32no—
51C22×C3⋊C8—61no—
52C22×C3⋊C8—61no—
53C3×#95—62no—
54C3⋊#95—22no—
55#807—64no—
56C4⋊(C3⋊C8)—64no—
57C4⋊(C3⋊C8)—64no—
58C23×C32C2×D411yescharacteristic
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—22no—
63C2×C32×C4Q1612yes—
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4C2×Q812yes—
66C2×C32×C4#4112yes—
67C2×C32×C4#4111yescharacteristic
68C2×C3×Dic3—24no—
69C2×C3×Dic3—42no—
70C2×C3×Dic3—42no—
71C2×C3×Dic3—42no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—42no—
74C3⋊(C3⋊C8)—22no—
75C3⋊(C3⋊C8)—41no—
76C2×#107—91no—
77C2×C4⋊C8—91no—
78#389—32no—
79#340—91no—
80#340—92no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×C3×C4—21no—
84C22×C3×C4—62no—
85C22×C3×C4—62no—
86C22×C3×C4#6712yes—
87C22×C3×C4#6712yes—
88C22×C3×C4C22×D312yes—
89C22×Dic3—22no—
90C22×Dic3—22no—
91C3×C4⋊C4—34no—
92C3×C4⋊C4—62no—
93C3×C4⋊C4—62no—
94C3×C4⋊C4—62no—
95C3×C4⋊C4—124no—
96C3×C42—22no—
97C3×C42—22no—
98C3×C42—22no—
99C3×C42—22no—
100C4⋊Dic3—22no—
101C4⋊Dic3—22no—
102C4⋊Dic3—22no—
103C4⋊Dic3Dic614yes—
104Dic3⋊C4—44no—
105C2×C3⋊C8—34no—
106C2×C3⋊C8—62no—
107C2×C3⋊C8—62no—
108C2×C3⋊C8—62no—
109C2×C3⋊C8—62no—
110C2×C3⋊C8—62no—
111C2×C3⋊C8—62no—
112C2×C3⋊C8—62no—
113C2×C3⋊C8—122no—
114C2×C3⋊C8—122no—
115C22×C32#12111yescharacteristic
116C22×C32C22⋊Q812yes—
117C22×C32C2×Q1611yescharacteristic
118C22×C32#13511yescharacteristic
119C22×C32AGL(1,ℤ/8)12yes—
120C32×C4—22no—
121C32×C4—41no—
122C32×C4#12311yescharacteristic
123C32×C4#12512yes—
124C32×C4C4⋊Q811yescharacteristic
125C3×Dic3—44no—
126C3×Dic3—82no—
127C22×C8—91no—
128C22×C8—91no—
129C2×C4⋊C4—32no—
130C2×C4⋊C4—32no—
131C2×C4⋊C4—62no—
132C2×C42D3211yescharacteristic
133#107—182no—
134C4⋊C8—182no—
135#95—62no—
136C23×C3—21no—
137C23×C3C2×#6712yes—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—42no—
152C2×C3×C4—64no—
153C2×C3×C4—122no—
154C2×C3×C4—122no—
155C2×C3×C4—122no—
156C2×C3×C4—122no—
157C2×C3×C4—122no—
158C2×C3×C4#21614yes—
159C2×C3×C4C2×Dic612yes—
160C2×C3×C4#23512yes—
161C2×C3×C4D3×D412yes—
162C2×C3×C4#23712yes—
163C2×C3×C4D3×Q812yes—
164C2×C3×C4#23912yes—
165C2×Dic3—24no—
166C2×Dic3—42no—
167C2×Dic3—42no—
168C2×Dic3—42no—
169C2×Dic3—42no—
170C2×Dic3—42no—
171C3⋊C8—64no—
172C3⋊C8—122no—
173C3⋊C8—122no—
174C3⋊C8—122no—
175C2×C32#39811yescharacteristic
176C2×C32#46711yescharacteristic
177C2×C32#46911yescharacteristic
178C2×C32#47712yes—
179C2×C32#47812yes—
180C22×C4—62no—
181C22×C4—62no—
182C22×C4#62511yescharacteristic
183C22×C4#62511yescharacteristic
184C22×C4C2×D3211yescharacteristic
185C2×C8—92no—
186C2×C8—182no—
187C2×C8—182no—
188C2×C8—181no—
189C4⋊C4—34no—
190C4⋊C4—62no—
191C4⋊C4—62no—
192C4⋊C4—62no—
193C4⋊C4—124no—
194C42—21no—
195C42—21no—
196C22×C3—21no—
197C22×C3—22no—
198C22×C3—21no—
199C22×C3—22no—
200C22×C3—21no—
201C22×C3#92412yes—
202C22×C3#93212yes—
203C22×C3#93912yes—
204C22×C3C2×#21612yes—
205C22×C3#94612yes—
206C22×C3#94912yes—
207C22×C3#95012yes—
208C3×C4—24no—
209C3×C4—24no—
210C3×C4—21no—
211C3×C4—22no—
212C3×C4—21no—
213C3×C4—42no—
214C3×C4—42no—
215C3×C4—124no—
216C3×C4—242no—
217C3×C4#88812yes—
218C3×C4#88912yes—
219C3×C4#89012yes—
220C3×C4#89412yes—
221Dic3—44no—
222Dic3—82no—
223C32#208711yescharacteristic, complemented, Sylow
224C23C2×#62511yescharacteristic
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—64no—
230C2×C4—122no—
231C2×C4—122no—
232C2×C4—122no—
233C2×C4—122no—
234C2×C4—122no—
235C2×C4#371812yes—
236C2×C4D3×Dic612yes—
237C2×C4#379912yes—
238C2×C4#380511yescharacteristic
239C2×C4#381111yescharacteristic
240C8—182no—
241C8—361no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3#498212yes—
248C2×C3#500912yes—
249C2×C3#502112yes—
250C2×C3#503912yes—
251C2×C3#505112yes—
252C2×C3#506612yes—
253C2×C3#509112yes—
254C22#6382211yescharacteristic
255C22#6382312yes—
256C22C2×#371811yescharacteristic
257C22#6385612yes—
258C22#6398011yescharacteristic
259C4—22no—
260C4—41no—
261C4—124no—
262C4—242no—
263C4#6384011yescharacteristic
264C4#6384512yes—
265C4#6389711yescharacteristic
266C3—21no—
267C3#6962312yescomplemented
268C2#1059027012yes—
269C2#1059031012yes—
270C2#1059116711yescharacteristic
271C2#1059118811yescharacteristic
272C2#1059121511yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C42D32
hypocenterC32#2087
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
223. C32#2087semidirect
267. C3#69623semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊(C3⋊C8))2
C3×#49282
C2×#635762
#105891632
#696233