Finite Group Databasebeta

← #11775353

Subgroups — #11775353

Order 1152.

666 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 169 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×#432C211yesmaximal, characteristic, complemented
3#10592635C211yesmaximal, characteristic, complemented
4#10589336C212yesmaximal
5#10589333C212yesmaximal, complemented
6#70834—34nomaximal
7C2×C32×C42C2211yescharacteristic
8#64139C2211yescharacteristic
9#64138—21no—
10C4×#638—21no—
11C2×C4⋊(C3⋊Dic3)—21no—
12#64133C2211yescharacteristic
13#64085—21no—
14#64084C411yescharacteristic, complemented
15C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
16#64081—21no—
17#64079C411yescharacteristic, complemented
18C4×#634C411yescharacteristic, complemented
19C32×C4⋊C8—21no—
20C32×C22⋊C8C2212yes—
21C32×#97—21no—
22#63658—21no—
23#63658C2212yes—
24#5479—34no—
25C3×#432D314yescomplemented
26#4936—34no—
27#4470—38no—
28#4467—38no—
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4C2311yescharacteristic
32C2×#638—21no—
33C22×C3⋊Dic3—22no—
34C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
35C2×C4×C3⋊D3—21no—
36C2×#634C2×C411yescharacteristic
37C2×C32×C8—22no—
38C32×C42C2×C411yescharacteristic
39C32×C42C2×C411yescharacteristic
40C32×C42D411yescharacteristic
41C32×C42D411yescharacteristic
42#3757—21no—
43#3752—21no—
44#3752—21no—
45#3752—21no—
46#3752—21no—
47C4⋊(C3⋊Dic3)—42no—
48C4⋊(C3⋊Dic3)C2×C411yescharacteristic
49C4⋊(C3⋊Dic3)C2×C411yescharacteristic
50#3750—21no—
51#3750—21no—
52#3750—21no—
53#3750—21no—
54C4×C3⋊Dic3—21no—
55#1512—91noSylow
56C2×C3×C42C2×D314yes—
57#930—34no—
58#929—64no—
59C4×#67—64no—
60C2×C4⋊Dic3—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×C22⋊C8C2×D318yes—
70C3×#97—24no—
71C3⋊#95—38no—
72C3⋊#95—64no—
73C23×C32C2×D411yescharacteristic
74C22×C3⋊D3—21no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85#638—41no—
86#638—41no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3—21no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—42no—
91C2×C3⋊Dic3—42no—
92C2×C3⋊Dic3—42no—
93C4⋊(C3⋊D3)—41no—
94C4×C3⋊D3—42no—
95#634—41no—
96C32×C8—42no—
97#529—91no—
98#432C3⋊D311yescharacteristic, complemented
99#382—91no—
100#328—92no—
101#327—92no—
102C22×C3×C4D1214yes—
103C22×C3×C4D1214yes—
104C22×C3×C4C22×D314yes—
105C2×#67—64no—
106C22×Dic3—68no—
107C2×D12—34no—
108C2×C4×D3—64no—
109C2×Dic6—34no—
110C2×C3×C8—28no—
111C3×C42C4×D314yes—
112C3×C42C4×D314yes—
113C3×C42#6714yes—
114C3×C42#6714yes—
115#217—64no—
116(C2×D3)⋊C4—64no—
117(C2×D3)⋊C4—64no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—64no—
120C4⋊Dic3—34no—
121C4⋊Dic3—34no—
122C4⋊Dic3—128no—
123Dic3⋊C4—64no—
124Dic3⋊C4—64no—
125Dic3⋊C4—64no—
126Dic3⋊C4—64no—
127C4×Dic3—64no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32C2×C22⋊C411yescharacteristic
131C22×C32AGL(1,ℤ/8)11yescharacteristic
132C22×C32#13711yescharacteristic
133C2×C3⋊D3—41no—
134C2×C3⋊D3—41no—
135C2×C3⋊D3—41no—
136C32×C4—21no—
137C32×C4—21no—
138C32×C4—21no—
139C32×C4—21no—
140C32×C4—21no—
141C32×C4—21no—
142C3⋊Dic3—41no—
143C3⋊Dic3—41no—
144C3⋊Dic3—41no—
145C3⋊Dic3—82no—
146#126—181no—
147#125—91no—
148#124—91no—
149#123—181no—
150C22⋊Q8—91no—
151#121—91no—
152C4×Q8—91no—
153C4×D4—91no—
154C4×D4—181no—
155#117—181no—
156C2×C4⋊C4—181no—
157C2×C42C2×C3⋊D311yescharacteristic
158C4⋊C8—21no—
159C22⋊C8C2×C3⋊D312yes—
160#97—21no—
161#95—92no—
162#95—181no—
163C23×C3C2×D1214yes—
164C22×D3—64no—
165C2×C3×C4—24no—
166C2×C3×C4—24no—
167C2×C3×C4—44no—
168C2×C3×C4—44no—
169C2×C3×C4(C2×D3)⋊C414yes—
170C2×C3×C4(C2×D3)⋊C414yes—
171C2×C3×C4(C2×D3)⋊C414yes—
172C2×C3×C4(C2×D3)⋊C414yes—
173C2×C3×C4C2×C4×D314yes—
174C2×C3×C4C2×#6714yes—
175#67—124no—
176#67—124no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C2×Dic3—64no—
180C2×Dic3—128no—
181C2×Dic3—128no—
182C2×Dic3—128no—
183D12—124no—
184C4×D3—128no—
185Dic6—124no—
186C3×C8—48no—
187C2×C32—21no—
188C2×C32—21no—
189C2×C32#41011yescharacteristic
190C2×C32#41711yescharacteristic
191C2×C32#42111yescharacteristic
192C3⋊D3—81no—
193C2×Q8—91no—
194C2×D4—91no—
195C2×D4—181no—
196C22×C4—181no—
197C22×C4—182no—
198C22×C4C4⋊(C3⋊D3)11yescharacteristic
199C22×C4C4⋊(C3⋊D3)11yescharacteristic
200C22×C4C22×C3⋊D311yescharacteristic
201C2×C8—22no—
202C4⋊C4—91no—
203C4⋊C4—91no—
204C4⋊C4—181no—
205C4⋊C4—181no—
206C4⋊C4—181no—
207C4⋊C4—181no—
208C4⋊C4—362no—
209C22⋊C4—181no—
210C22⋊C4—181no—
211C22⋊C4—181no—
212C22⋊C4—181no—
213C22⋊C4—181no—
214C42—181no—
215C42C4×C3⋊D311yescharacteristic
216C42C4×C3⋊D311yescharacteristic
217C42#63811yescharacteristic
218C42#63811yescharacteristic
219C22×C3—24no—
220C22×C3—24no—
221C22×C3#90814yes—
222C22×C3#90914yes—
223C22×C3C2×(C2×D3)⋊C414yes—
224C2×D3—124no—
225C2×D3—124no—
226C2×D3—124no—
227C3×C4—24no—
228C3×C4—24no—
229C3×C4—24no—
230C3×C4—24no—
231C3×C4—24no—
232C3×C4—24no—
233Dic3—124no—
234Dic3—124no—
235Dic3—124no—
236Dic3—248no—
237C32#151211yescharacteristic, complemented, Sylow
238C23—181no—
239C23C2×C4⋊(C3⋊D3)11yescharacteristic
240Q8—361no—
241D4—361no—
242D4—361no—
243D4—361no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—181no—
249C2×C4—181no—
250C2×C4—181no—
251C2×C4—362no—
252C2×C4—362no—
253C2×C4—362no—
254C2×C4—362no—
255C2×C4#375211yescharacteristic
256C2×C4#375211yescharacteristic
257C2×C4#375211yescharacteristic
258C2×C4#375211yescharacteristic
259C2×C4C2×C4×C3⋊D311yescharacteristic
260C2×C4C2×#63811yescharacteristic
261C8—42no—
262C2×C3—24no—
263C2×C3—24no—
264C2×C3#500614yes—
265C2×C3#513314yes—
266C2×C3#513914yes—
267D3—244no—
268C22—21no—
269C22—21no—
270C22—361no—
271C22—361no—
272C22—361no—
273C22#6411711yescharacteristic
274C22#6411811yescharacteristic
275C22C2×#375211yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—361no—
283C4—361no—
284C4—361no—
285C4—722no—
286C3#7083414yescomplemented
287C2—21no—
288C2—21no—
289C2—721no—
290C2#1059270511yescharacteristic
291C2#1059283211yescharacteristic
292C2#1059283811yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#432C2
socleC22×C32C2×C22⋊C4
prime radical#64139C22
cosocleC22×C32×C4C23
hypercenter#432C3⋊D3
hypocenterC32#1512
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C32×#432C2semidirect
3. #10592635C2semidirect
5. #10589333C2semidirect
14. #64084C4semidirect
15. C4×C4⋊(C3⋊D3)C4semidirect
17. #64079C4semidirect
18. C4×#634C4semidirect
25. C3×#432D3semidirect
98. #432C3⋊D3semidirect
237. C32#1512semidirect
286. C3#70834semidirect

Maximal subgroups

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

subgroupindex
#105959502
C32×#4322
#105926352
#105893362
#105893332
#708343