Finite Group Databasebeta

← #11795234

Subgroups — #11795234

Order 1152.

517 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 517 conjugacy classes of subgroups — too many to draw. Only its 146 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×#63641C211yesmaximal, characteristic
2#10591357C212yesmaximal
3C2×#63576C211yesmaximal, characteristic
4C3×#4551C212yesmaximal
5#10589163C211yesmaximal, characteristic
6#68808—32nomaximal
7C22×C32×C8C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×C4⋊Dic3C2212yes—
12C2×Dic3⋊Dic3—22no—
13#63641—22no—
14#63579—22no—
15#63576—22no—
16C2×Dic3⋊C8—32no—
17C2×Dic3⋊C8—61no—
18#4984—32no—
19#4972—32no—
20C2×#807—32no—
21C3×#340—32no—
22#4551D312yes—
23#4529—32no—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3×Dic3—22no—
28C22×C3×Dic3—22no—
29C2×C32×C8—21no—
30C2×C32×C8—22no—
31C4×C3⋊Dic3—21no—
32C4×C3⋊Dic3—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—
39Dic3⋊Dic3—44no—
40#2087—91noSylow
41C22×C3×C8—21no—
42C22×C3×C8C2×D312yes—
43C2×C3×C4⋊C4—32no—
44C2×C3×C4⋊C4—32no—
45C2×C4⋊Dic3—62no—
46C2×C4⋊Dic3C2×D312yes—
47C2×C4⋊Dic3C2×D312yes—
48C2×Dic3⋊C4—62no—
49C2×C4×Dic3—32no—
50C2×C4×Dic3—61no—
51C22×C3⋊C8—32no—
52C22×C3⋊C8—61no—
53C3⋊#95—62no—
54C3⋊#95—62no—
55Dic3⋊C8—64no—
56Dic3⋊C8—64no—
57#807—64no—
58C23×C32C2×D411yescharacteristic
59C2×C32×C4C2×D411yescharacteristic
60C2×C32×C4C2×Q812yes—
61C2×C32×C4#4111yescharacteristic
62C2×C32×C4#4112yes—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3—21no—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3Q1612yes—
68C2×C3×Dic3—24no—
69C2×C3×Dic3—42no—
70C2×C3×Dic3—42no—
71C2×C3×Dic3—42no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—42no—
74C32×C8—41no—
75C3⋊(C3⋊C8)—22no—
76C2×#107—91no—
77C2×C4⋊C8—91no—
78#389—92no—
79#340—32no—
80#340—91no—
81C22×C3×C4—21no—
82C22×C3×C4—62no—
83C22×C3×C4—62no—
84C22×C3×C4C22×D312yes—
85C22×Dic3—22no—
86C22×Dic3—22no—
87C22×Dic3—32no—
88C22×Dic3—32no—
89C22×Dic3—61no—
90C22×Dic3—61no—
91C2×C3×C8—22no—
92C2×C3×C8—22no—
93C2×C3×C8—22no—
94C2×C3×C8—22no—
95C2×C3×C8—42no—
96C3×C4⋊C4—34no—
97C3×C4⋊C4—62no—
98C3×C4⋊C4—62no—
99C3×C4⋊C4—62no—
100C4⋊Dic3—22no—
101C4⋊Dic3—22no—
102C4⋊Dic3—22no—
103C4⋊Dic3—124no—
104C4⋊Dic3Dic614yes—
105Dic3⋊C4—124no—
106C4×Dic3—62no—
107C4×Dic3—62no—
108C4×Dic3—62no—
109C4×Dic3—62no—
110C2×C3⋊C8—34no—
111C2×C3⋊C8—62no—
112C2×C3⋊C8—62no—
113C2×C3⋊C8—62no—
114C2×C3⋊C8—122no—
115C22×C32#12111yescharacteristic
116C22×C32C22⋊Q812yes—
117C22×C32C2×Q1611yescharacteristic
118C22×C32#13511yescharacteristic
119C22×C32AGL(1,ℤ/8)12yes—
120C32×C4#12311yescharacteristic
121C32×C4#12512yes—
122C32×C4C4⋊Q811yescharacteristic
123C3⋊Dic3—22no—
124C3⋊Dic3—41no—
125C3×Dic3—44no—
126C3×Dic3—82no—
127C22×C8—91no—
128C22×C8D3211yescharacteristic
129C2×C4⋊C4—32no—
130C2×C4⋊C4—32no—
131C2×C4⋊C4—182no—
132C2×C42—91no—
133#107—182no—
134C4⋊C8—182no—
135#95—182no—
136C23×C3—21no—
137C23×C3D3×D412yes—
138C2×C3×C4—22no—
139C2×C3×C4—21no—
140C2×C3×C4—22no—
141C2×C3×C4—21no—
142C2×C3×C4—64no—
143C2×C3×C4—122no—
144C2×C3×C4—122no—
145C2×C3×C4—122no—
146C2×C3×C4—122no—
147C2×C3×C4—122no—
148C2×C3×C4C2×Dic612yes—
149C2×C3×C4#23512yes—
150C2×C3×C4#23512yes—
151C2×C3×C4D3×D412yes—
152C2×C3×C4#23712yes—
153C2×C3×C4D3×Q812yes—
154C2×Dic3—24no—
155C2×Dic3—34no—
156C2×Dic3—42no—
157C2×Dic3—42no—
158C2×Dic3—42no—
159C2×Dic3—42no—
160C2×Dic3—42no—
161C2×Dic3—62no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164C2×Dic3—62no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—122no—
171C3×C8—42no—
172C3×C8—42no—
173C3⋊C8—64no—
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—91no—
183C22×C4—91no—
184C22×C4C2×D3211yescharacteristic
185C2×C8—22no—
186C2×C8—21no—
187C2×C8—92no—
188C2×C8—182no—
189C4⋊C4—34no—
190C4⋊C4—62no—
191C4⋊C4—62no—
192C4⋊C4—62no—
193C4⋊C4—364no—
194C42—181no—
195C42—181no—
196C22×C3—22no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—22no—
200C22×C3—21no—
201C22×C3#87812yes—
202C22×C3#88412yes—
203C22×C3#89612yes—
204C22×C3#91112yes—
205C22×C3#91412yes—
206C22×C3#91612yes—
207C22×C3D3×Q1612yes—
208C3×C4—21no—
209C3×C4—22no—
210C3×C4—21no—
211C3×C4—124no—
212C3×C4—242no—
213C3×C4#87012yes—
214C3×C4#88312yes—
215C3×C4#88812yes—
216C3×C4#88912yes—
217Dic3—44no—
218Dic3—64no—
219Dic3—64no—
220Dic3—82no—
221Dic3—122no—
222Dic3—122no—
223C32#208711yescharacteristic, complemented, Sylow
224C23#380211yescharacteristic
225C2×C4—64no—
226C2×C4—92no—
227C2×C4—122no—
228C2×C4—122no—
229C2×C4—122no—
230C2×C4—122no—
231C2×C4—122no—
232C2×C4—181no—
233C2×C4—181no—
234C2×C4—182no—
235C2×C4—181no—
236C2×C4D3×Dic612yes—
237C2×C4#379811yescharacteristic
238C2×C4#380412yes—
239C2×C4#381111yescharacteristic
240C8—41no—
241C8—182no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3#465712yes—
248C2×C3#476312yes—
249C2×C3#478212yes—
250C2×C3#479312yes—
251C2×C3#481312yes—
252C2×C3#487112yes—
253C2×C3#487512yes—
254C22#6379812yes—
255C22#6380211yescharacteristic
256C22#6380911yescharacteristic
257C22#6389912yes—
258C22#6391211yescharacteristic
259C4—124no—
260C4—182no—
261C4—242no—
262C4—361no—
263C4#6384011yescharacteristic
264C4#6386712yes—
265C4#6397511yescharacteristic
266C3—21no—
267C3#6880812yescomplemented
268C2#1059078212yes—
269C2#1059081712yes—
270C2#1059084011yescharacteristic
271C2#1059085511yescharacteristic
272C2#1059135611yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socle, prime radicalC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32#2087
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
223. C32#2087semidirect
267. C3#68808semidirect

Maximal subgroups

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

subgroupindex
C2×#636412
#105913572
C2×#635762
C3×#45512
#105891632
#688083