Finite Group Databasebeta

← #11788192

Subgroups — #11788192

Order 1152.

1074 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 221 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
1#10596262C211yesmaximal, characteristic
2C2×#64135C211yesmaximal, characteristic, complemented
3C32×#407C211yesmaximal, characteristic, complemented
4C2×#63652C212yesmaximal, complemented
5#10589421C212yesmaximal, complemented
6#69966—34nomaximal
7C23×C32×C4C2211yescharacteristic
8C2×#3828C2211yescharacteristic
9C2×C32×M16C2212yes—
10#64162—21no—
11C2×#3757—21no—
12#64139C412yescomplemented
13#64138—21no—
14C4×#638—22no—
15#64135—24no—
16#64135C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)—21no—
18#64133C412yescomplemented
19C2×C4×C3⋊Dic3C2212yes—
20C32×C22⋊C8—22no—
21#63652—24no—
22#5791—34no—
23C2×#926—34no—
24C3×#407D314yescomplemented
25C2×#825—38no—
26#4555—38no—
27C24×C32D411yescharacteristic
28C22×C32×C4—22no—
29C22×C32×C4—22no—
30C22×C32×C4C2×C412yes—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D412yes—
33C22×C32×C4C2311yescharacteristic
34C2×#638—22no—
35C2×#638—21no—
36C22×C3⋊Dic3—22no—
37#3828—22no—
38#3828—22no—
39C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
40C2×C4×C3⋊D3—21no—
41C2×#634C2×C411yescharacteristic
42C32×M16—22no—
43C32×M16—22no—
44C2×C32×C8—22no—
45#3757—24no—
46#3757—22no—
47#3757—21no—
48#3752—22no—
49C4⋊(C3⋊Dic3)—24no—
50C4⋊(C3⋊Dic3)C2×C412yes—
51#3750—22no—
52C4×C3⋊Dic3—22no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3D414yescomplemented
55#1897—91noSylow
56C23×C3×C4C2×D314yes—
57C2×#235—34no—
58C2×C3×M16C2×D318yes—
59#953—64no—
60C2×#217—64no—
61#930—38no—
62#929—64no—
63C4×#67—68no—
64#926—34no—
65#926—616no—
66C2×C4⋊Dic3—64no—
67#924—38no—
68C2×C4×Dic3—38no—
69C3×C22⋊C8—28no—
70#825—616no—
71C23×C32—21no—
72C23×C32—21no—
73C23×C32—42no—
74C23×C32C22⋊C412yes—
75C23×C32C2×D411yescharacteristic
76C22×C3⋊D3—21no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—24no—
80C2×C32×C4—24no—
81C2×C32×C4C22⋊C412yes—
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C2×D412yes—
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4#4112yes—
86#638—44no—
87#638—41no—
88#638—41no—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3—44no—
93C4⋊(C3⋊D3)—22no—
94C4×C3⋊D3—42no—
95#634—22no—
96C32×C8—42no—
97#525—91no—
98C2×#117—91no—
99C2×#104—92no—
100#407C3⋊D311yescharacteristic, complemented
101#339—92no—
102C24×C3D1214yes—
103C22×C3×C4—28no—
104C22×C3×C4—28no—
105C22×C3×C4C4×D318yes—
106C22×C3×C4D1214yes—
107C22×C3×C4#6718yes—
108C22×C3×C4C22×D314yes—
109C2×#67—68no—
110C2×#67—64no—
111C22×Dic3—68no—
112#235—68no—
113#235—68no—
114C2×D12—34no—
115C2×C4×D3—64no—
116C2×Dic6—34no—
117C3×M16—28no—
118C3×M16—28no—
119C2×C3×C8—28no—
120#217—616no—
121#217—68no—
122#217—64no—
123(C2×D3)⋊C4—68no—
124C4⋊Dic3—38no—
125C4⋊Dic3—616no—
126Dic3⋊C4—68no—
127C4×Dic3—316no—
128C4×Dic3—68no—
129C4×Dic3—64no—
130C22×C32—22no—
131C22×C32—22no—
132C22×C32—22no—
133C22×C32—22no—
134C22×C32—42no—
135C22×C32—42no—
136C22×C32C2×C22⋊C411yescharacteristic
137C22×C32#12011yescharacteristic
138C22×C32#12311yescharacteristic
139C2×C3⋊D3—41no—
140C2×C3⋊D3—42no—
141C32×C4—22no—
142C32×C4C4×D412yes—
143C32×C4#12112yes—
144C3⋊Dic3—44no—
145C3⋊Dic3—41no—
146C3⋊Dic3—42no—
147C2×#41—91no—
148C23×C4C2×C3⋊D311yescharacteristic
149C2×M16C2×C3⋊D312yes—
150#123—181no—
151C22⋊Q8—92no—
152#121—92no—
153#120—181no—
154C4×D4—182no—
155#117—91no—
156#117—184no—
157C2×C4⋊C4—181no—
158C2×C22⋊C4—181no—
159C2×C42—92no—
160#104—184no—
161C22⋊C8—22no—
162C23×C3—24no—
163C23×C3—24no—
164C23×C3—48no—
165C23×C3(C2×D3)⋊C418yes—
166C23×C3C2×D1214yes—
167C22×D3—64no—
168C2×C3×C4—24no—
169C2×C3×C4—24no—
170C2×C3×C4—216no—
171C2×C3×C4—216no—
172C2×C3×C4(C2×D3)⋊C418yes—
173C2×C3×C4C2×C4×D314yes—
174C2×C3×C4D3×D418yes—
175C2×C3×C4#23718yes—
176C2×C3×C4C2×#6714yes—
177#67—1216no—
178#67—124no—
179#67—124no—
180C2×Dic3—616no—
181C2×Dic3—68no—
182C2×Dic3—64no—
183C2×Dic3—1216no—
184D12—68no—
185C4×D3—128no—
186Dic6—68no—
187C3×C8—48no—
188C2×C32—21no—
189C2×C32—21no—
190C2×C32—42no—
191C2×C32#38611yescharacteristic
192C2×C32#42112yes—
193C3⋊D3—81no—
194C24C4⋊(C3⋊D3)11yescharacteristic
195#41—182no—
196#41—182no—
197C2×Q8—91no—
198C2×D4—91no—
199C2×D4—182no—
200C2×D4—181no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—182no—
204C22×C4—181no—
205C22×C4C4×C3⋊D312yes—
206C22×C4C4⋊(C3⋊D3)11yescharacteristic
207C22×C4#63812yes—
208C22×C4C22×C3⋊D311yescharacteristic
209M16—22no—
210M16—22no—
211C2×C8—22no—
212C4⋊C4—92no—
213C4⋊C4—184no—
214C4⋊C4—182no—
215C22⋊C4—184no—
216C22⋊C4—182no—
217C22⋊C4—181no—
218C22⋊C4—182no—
219C42—94no—
220C42—182no—
221C42—181no—
222C22×C3—28no—
223C22×C3—28no—
224C22×C3—28no—
225C22×C3—28no—
226C22×C3—48no—
227C22×C3—48no—
228C22×C3#88214yes—
229C22×C3#88614yes—
230C22×C3C2×(C2×D3)⋊C414yes—
231C2×D3—128no—
232C2×D3—124no—
233C3×C4—28no—
234C3×C4#67⋊C418yes—
235C3×C4#93918yes—
236Dic3—1216no—
237Dic3—128no—
238Dic3—124no—
239C32#189711yescharacteristic, complemented, Sylow
240C23—21no—
241C23—21no—
242C23—42no—
243C23—181no—
244C23#375212yes—
245C23C2×C4⋊(C3⋊D3)11yescharacteristic
246Q8—182no—
247D4—182no—
248D4—364no—
249D4—361no—
250D4—361no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—184no—
256C2×C4—182no—
257C2×C4—181no—
258C2×C4—364no—
259C2×C4—362no—
260C2×C4#375212yes—
261C2×C4C2×C4×C3⋊D311yescharacteristic
262C2×C4D4×C3⋊D312yes—
263C2×C4#383012yes—
264C2×C4C2×#63811yescharacteristic
265C8—42no—
266C2×C3—24no—
267C2×C3—24no—
268C2×C3—48no—
269C2×C3#495814yes—
270C2×C3#513918yes—
271D3—244no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—362no—
279C22—361no—
280C22#6409111yescharacteristic
281C22#6409511yescharacteristic
282C22C2×#375211yescharacteristic
283C4—22no—
284C4—364no—
285C4—362no—
286C4—361no—
287C4#6409012yes—
288C4#6414812yes—
289C3#6996614yescomplemented
290C2—21no—
291C2—21no—
292C2—42no—
293C2—721no—
294C2#1059265711yescharacteristic
295C2#1059283812yes—
subgroupG/H
centerC2×C4C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radical#10596262C2
cosocleC22×C32×C4C23
hypercenter#407C3⋊D3
hypocenterC32#1897
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#64135C2semidirect
3. C32×#407C2semidirect
4. C2×#63652C2semidirect
5. #10589421C2semidirect
12. #64139C4semidirect
18. #64133C4semidirect
24. C3×#407D3semidirect
54. C4×C3⋊Dic3D4semidirect
100. #407C3⋊D3semidirect
239. C32#1897semidirect
289. C3#69966semidirect

Maximal subgroups

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

subgroupindex
#105962622
C2×#641352
C32×#4072
C2×#636522
#105894212
#699663