Finite Group Databasebeta

← #11774824

Subgroups — #11774824

Order 1152.

648 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 181 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#10595950C211yesmaximal, characteristic
2C32×#423C211yesmaximal, characteristic, complemented
3#10592624C211yesmaximal, characteristic, complemented
4#10589350C212yesmaximal, complemented
5#10589349C212yesmaximal, complemented
6#70499—34nomaximal
7C2×C32×M16—21no—
8C2×C32×C42C2211yescharacteristic
9#64139C411yescharacteristic
10#64138—21no—
11C4×#638—21no—
12#64133C411yescharacteristic
13#64085—21no—
14#64084C411yescharacteristic
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64081—21no—
17#64079C411yescharacteristic
18C4×#634C2211yescharacteristic
19C32×C4⋊C8—21no—
20C32×C4⋊C8C2212yes—
21#63657—21no—
22C4⋊(C3⋊(C3⋊C8))—21no—
23C4×C3⋊(C3⋊C8)C2212yes—
24#5479—34no—
25C3×#423D314yescomplemented
26#4925—34no—
27#4484—38no—
28#4483—38no—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C2×#638—21no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×#634C2×C411yescharacteristic
36C32×M16—42no—
37C2×C32×C8—22no—
38C32×C42C2×C411yescharacteristic
39C32×C42D411yescharacteristic
40C32×C42D411yescharacteristic
41C32×C42C2311yescharacteristic
42#3757—21no—
43#3752—21no—
44#3752—21no—
45#3752—21no—
46#3752—21no—
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48C4⋊(C3⋊Dic3)C2×C411yescharacteristic
49#3750—21no—
50#3750—21no—
51#3750—21no—
52#3750—21no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—22no—
55#1495—91noSylow
56C2×C3×M16—24no—
57C2×C3×C42C2×D314yes—
58#930—34no—
59#929—64no—
60C4×#67—64no—
61#924—34no—
62#876—64no—
63#875—34no—
64C4×D12—34no—
65#872—64no—
66#870—34no—
67C4×Dic6—34no—
68C3×C4⋊C8—24no—
69C3×C4⋊C8C2×D318yes—
70#830—64no—
71C4⋊(C3⋊C8)—64no—
72C4×C3⋊C8—38no—
73C23×C32C22⋊C411yescharacteristic
74C22×C3⋊D3—21no—
75C2×C32×C4—22no—
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4—41no—
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85#638—42no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3—21no—
89C4⋊(C3⋊D3)—22no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3—41no—
92#634—22no—
93C32×C8—42no—
94C3⋊(C3⋊C8)—42no—
95#529—91no—
96#431—91no—
97#423C3⋊D311yescharacteristic, complemented
98Q8⋊C8—92no—
99D4⋊C8—92no—
100C22×C3×C4C4×D314yes—
101C22×C3×C4D1214yes—
102C22×C3×C4#6714yes—
103C2×#67—64no—
104C2×D12—34no—
105C2×C4×D3—64no—
106C2×Dic6—34no—
107C3×M16—48no—
108C2×C3×C8—28no—
109C3×C42C4×D314yes—
110C3×C42D1214yes—
111C3×C42#6714yes—
112C3×C42C22×D314yes—
113#217—64no—
114(C2×D3)⋊C4—64no—
115(C2×D3)⋊C4—64no—
116(C2×D3)⋊C4—64no—
117(C2×D3)⋊C4—64no—
118C4⋊Dic3—34no—
119C4⋊Dic3—34no—
120Dic3⋊C4—64no—
121Dic3⋊C4—64no—
122Dic3⋊C4—64no—
123Dic3⋊C4—64no—
124C4×Dic3—64no—
125C2×C3⋊C8—68no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32C2×C22⋊C411yescharacteristic
130C2×C3⋊D3—41no—
131C2×C3⋊D3—41no—
132C2×C3⋊D3—41no—
133C32×C4—21no—
134C32×C4—21no—
135C32×C4—21no—
136C32×C4—21no—
137C32×C4#13112yes—
138C32×C4AGL(1,ℤ/8)11yescharacteristic
139C32×C4#13711yescharacteristic
140C3⋊Dic3—41no—
141C3⋊Dic3—41no—
142C3⋊Dic3—41no—
143C2×M16—21no—
144#126—181no—
145#125—91no—
146#124—91no—
147#123—181no—
148C22⋊Q8—91no—
149#121—91no—
150C4×Q8—91no—
151C4×D4—91no—
152C4×D4—181no—
153#117—181no—
154C2×C42C2×C3⋊D311yescharacteristic
155C4⋊C8—21no—
156C4⋊C8—181no—
157C4⋊C8C2×C3⋊D312yes—
158C22⋊C8—181no—
159C4×C8—92no—
160C23×C3(C2×D3)⋊C414yes—
161C22×D3—64no—
162C2×C3×C4—28no—
163C2×C3×C4—24no—
164C2×C3×C4—24no—
165C2×C3×C4—44no—
166C2×C3×C4(C2×D3)⋊C414yes—
167C2×C3×C4(C2×D3)⋊C414yes—
168C2×C3×C4(C2×D3)⋊C414yes—
169C2×C3×C4C2×C4×D314yes—
170C2×C3×C4C2×D1214yes—
171C2×C3×C4C2×#6714yes—
172#67—128no—
173C2×Dic3—64no—
174C2×Dic3—64no—
175C2×Dic3—64no—
176D12—68no—
177C4×D3—124no—
178C4×D3—124no—
179Dic6—68no—
180C3×C8—48no—
181C3⋊C8—128no—
182C2×C32—41no—
183C2×C32#40811yescharacteristic
184C2×C32#41711yescharacteristic
185C2×C32#42111yescharacteristic
186C3⋊D3—81no—
187C2×Q8—91no—
188C2×D4—91no—
189C2×D4—181no—
190C22×C4—181no—
191C22×C4C4×C3⋊D311yescharacteristic
192C22×C4C4⋊(C3⋊D3)11yescharacteristic
193C22×C4#63811yescharacteristic
194M16—42no—
195C2×C8—22no—
196C2×C8—182no—
197C4⋊C4—91no—
198C4⋊C4—91no—
199C4⋊C4—181no—
200C4⋊C4—181no—
201C4⋊C4—181no—
202C4⋊C4—181no—
203C22⋊C4—181no—
204C22⋊C4—181no—
205C22⋊C4—181no—
206C22⋊C4—181no—
207C22⋊C4—181no—
208C42—181no—
209C42C4×C3⋊D311yescharacteristic
210C42C4⋊(C3⋊D3)11yescharacteristic
211C42#63811yescharacteristic
212C42C22×C3⋊D311yescharacteristic
213C22×C3—24no—
214C22×C3—24no—
215C22×C3—24no—
216C22×C3C2×(C2×D3)⋊C414yes—
217C2×D3—124no—
218C2×D3—124no—
219C2×D3—124no—
220C3×C4—24no—
221C3×C4—24no—
222C3×C4—24no—
223C3×C4—24no—
224C3×C4#90718yes—
225C3×C4#93214yes—
226C3×C4#94214yes—
227Dic3—124no—
228Dic3—124no—
229Dic3—124no—
230C32#149511yescharacteristic, complemented, Sylow
231C23—181no—
232C23#375211yescharacteristic
233Q8—182no—
234D4—182no—
235D4—362no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4—181no—
243C2×C4—361no—
244C2×C4—361no—
245C2×C4#375211yescharacteristic
246C2×C4#375211yescharacteristic
247C2×C4#375211yescharacteristic
248C2×C4C2×C4×C3⋊D311yescharacteristic
249C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
250C2×C4C2×#63811yescharacteristic
251C8—42no—
252C8—362no—
253C2×C3—44no—
254C2×C3#496614yes—
255C2×C3#512914yes—
256C2×C3#513914yes—
257D3—244no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—361no—
262C22—361no—
263C22—361no—
264C22C2×#375211yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—361no—
270C4—361no—
271C4—361no—
272C4#6411612yes—
273C4#6414111yescharacteristic
274C4#6415111yescharacteristic
275C3#7049914yescomplemented
276C2—41no—
277C2—721no—
278C2#1059266511yescharacteristic
279C2#1059282811yescharacteristic
280C2#1059283811yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#423C2
socleC22×C32C2×C22⋊C4
prime radical#64139C4
cosocleC32×C42C23
hypercenter#423C3⋊D3
hypocenterC32#1495
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C32×#423C2semidirect
3. #10592624C2semidirect
4. #10589350C2semidirect
5. #10589349C2semidirect
25. C3×#423D3semidirect
97. #423C3⋊D3semidirect
230. C32#1495semidirect
275. C3#70499semidirect

Maximal subgroups

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

subgroupindex
#105959502
C32×#4232
#105926242
#105893502
#105893492
#704993