Finite Group Databasebeta

← #27193645

Subgroups — #27193645

Order 13184.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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#20268301C211yesmaximal, characteristic
2#20267753C211yesmaximal, characteristic, complemented
3#95×D103C211yesmaximal, characteristic, complemented
4#20267529C211yesmaximal, characteristic, complemented
5#20267527C211yesmaximal, characteristic, complemented
6#20267525C211yesmaximal, characteristic, complemented
7#327×C103C211yesmaximal, characteristic, complemented
8C2×#13110104C411yescharacteristic, complemented
9C22×C4×D103—21no—
10C22×C4×D103C2211yescharacteristic
11C2×#13110088—21no—
12#15693003—21no—
13#15693001C411yescharacteristic, complemented
14#15693000C2211yescharacteristic
15#15692992C411yescharacteristic, complemented
16#15692989—21no—
17D4×Dic103—21no—
18(C22⋊D103)⋊C4—21no—
19#15692979C411yescharacteristic, complemented
20C22⋊(C103⋊C8)C2211yescharacteristic
21(C2×D103)⋊C8—21no—
22C103⋊#95—21no—
23C103⋊#95C2211yescharacteristic
24#121×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic
26#95×C103C2211yescharacteristic
27C23×D103D411yescharacteristic
28#13110104—42no—
29C2×Dic206C2×C411yescharacteristic, complemented
30C2×C22⋊D103—21no—
31C2×C22⋊D103—21no—
32C22×Dic103—21no—
33C22×Dic103—21no—
34C22×Dic103D411yescharacteristic
35C2×C4×D103—24no—
36C2×C4×D103—42no—
37C2×C4×D103—42no—
38C2×C4×D103—42no—
39C2×C4×D103C2×C411yescharacteristic
40C2×C4×D103C2×C411yescharacteristic
41C2×C4×D103D411yescharacteristic
42C2×C4×D103D411yescharacteristic
43#13110088—42no—
44C2×C103⋊C8—21no—
45C4⋊Dic103—21no—
46C4⋊Dic103C2×C411yescharacteristic, complemented
47Dic103⋊C4—21no—
48C22⋊Dic103—21no—
49C22⋊Dic103—21no—
50(C2×D103)⋊C4—21no—
51(C2×D103)⋊C4—21no—
52C4×Dic103—21no—
53C2×D4×C103—21no—
54C2×D4×C103C2×C411yescharacteristic, complemented
55C22×C4×C103—21no—
56C22×C4×C103C2311yescharacteristic
57C2×C8×C103—21no—
58C4⋊C4×C103C2×C411yescharacteristic, complemented
59C22⋊C4×C103—21no—
60C23×C103—21no—
61C23×C103C2×D411yescharacteristic
62C22×D103—21no—
63C22×D103—21no—
64C22×D103—22no—
65C22×D103—22no—
66C22×D103C22⋊C411yescharacteristic
67C22×D103C22⋊C411yescharacteristic
68D4×C103—41no—
69D4×C103—41no—
70D4×C103—41no—
71C2×C4×C103—22no—
72C2×C4×C103—21no—
73C2×C4×C103—41no—
74C2×C4×C103—41no—
75C2×C4×C103—41no—
76C2×C4×C103C22×C411yescharacteristic
77C2×C4×C103C2×D411yescharacteristic
78C22⋊D103—42no—
79C22⋊D103—42no—
80C2×Dic103—22no—
81C2×Dic103—21no—
82C2×Dic103—21no—
83C2×Dic103—41no—
84C2×Dic103—42no—
85C2×Dic103—41no—
86C2×Dic103—41no—
87C2×Dic103C22⋊C411yescharacteristic
88C2×Dic103C22⋊C411yescharacteristic
89C4×D103—22no—
90C4×D103—22no—
91C4×D103—41no—
92C4×D103—41no—
93C4×D103—48no—
94Dic206—41no—
95C8×C103—41no—
96C103⋊C8—41no—
97C22×C103—21no—
98C22×C103—21no—
99C22×C103—41no—
100C22×C103—41no—
101C22×C103—41no—
102C22×C103C2×C22⋊C411yescharacteristic
103C22×C103AGL(1,ℤ/8)11yescharacteristic
104C22×C103#13711yescharacteristic
105C2×D103—24no—
106C2×D103—24no—
107C2×D103—21no—
108C2×D103—21no—
109C2×D103—21no—
110C2×D103—21no—
111C2×D103#9912yes—
112C2×D103#10412yes—
113C4×C103—21no—
114C4×C103—21no—
115C4×C103—42no—
116C4×C103—41no—
117Dic103—21no—
118Dic103—21no—
119Dic103—42no—
120Dic103—41no—
121Dic103—41no—
122C2×C103—21no—
123C2×C103—21no—
124C2×C103—81no—
125C2×C103C2×#9911yescharacteristic
126C2×C103#41711yescharacteristic
127C2×C103C2×#10411yescharacteristic
128D103—22no—
129D103—22no—
130#1504—1031nomaximal, Sylow
131C103#150411yescharacteristic, complemented, Sylow
132#525—1031no—
133#407—1031no—
134C2×#95—1031no—
135#328—1031no—
136#328—1031no—
137#327—1031no—
138#327D10311yescharacteristic, complemented
139C2×#41—1031no—
140C23×C4—1031no—
141C23×C4—2061no—
142C2×M16—2061no—
143#123—2061no—
144C22⋊Q8—1031no—
145C22⋊Q8—1031no—
146#121—1031no—
147#121C2×D10311yescharacteristic
148#120—2061no—
149C4×D4—2061no—
150C4×D4—2061no—
151#117—1031no—
152C22⋊C8—1031no—
153C22⋊C8—2061no—
154C22⋊C8C2×D10311yescharacteristic
155#95—1031no—
156#95—2061no—
157#95C2×D10311yescharacteristic
158C24—1031no—
159#41—4122no—
160C2×Q8—1031no—
161C2×D4—21no—
162C2×D4—2061no—
163C2×D4—2061no—
164C2×D4C4×D10311yescharacteristic, complemented
165C22×C4—21no—
166C22×C4—1031no—
167C22×C4—1031no—
168C22×C4—1031no—
169C22×C4—1031no—
170C22×C4—1031no—
171C22×C4—4122no—
172C22×C4—4122no—
173C22×C4—4122no—
174C22×C4—2064no—
175C22×C4—2061no—
176C22×C4—2061no—
177C22×C4C22×D10311yescharacteristic
178M16—4122no—
179C2×C8—21no—
180C2×C8—2061no—
181C4⋊C4—1031no—
182C4⋊C4—2061no—
183C4⋊C4—2061no—
184C4⋊C4C4×D10311yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—2061no—
187C22⋊C4—2061no—
188C22⋊C4—2061no—
189C22⋊C4—2061no—
190C42—2061no—
191C23—21no—
192C23—1031no—
193C23—1031no—
194C23—2062no—
195C23—2062no—
196C23—2061no—
197C23—2061no—
198C23D4×D10311yescharacteristic
199Q8—4121no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—4122no—
204D4—4122no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—1031no—
211C2×C4—1031no—
212C2×C4—4121no—
213C2×C4—4121no—
214C2×C4—4128no—
215C2×C4—4121no—
216C2×C4—4121no—
217C2×C4—4122no—
218C2×C4—4121no—
219C2×C4—2062no—
220C2×C4—2062no—
221C2×C4—2062no—
222C2×C4—2061no—
223C2×C4—2061no—
224C2×C4C2×C4×D10311yescharacteristic
225C2×C4D4×D10311yescharacteristic
226C8—41no—
227C8—4121no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—1032no—
234C22—1032no—
235C22—2064no—
236C22—2064no—
237C22—2061no—
238C22—2061no—
239C22—2061no—
240C22—2061no—
241C22C22⋊C4×D10311yescharacteristic
242C22#1569304511yescharacteristic
243C22#1569305011yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—4122no—
249C4—4121no—
250C4—4121no—
251C4—2061no—
252C4—2061no—
253C2—21no—
254C2—21no—
255C2—81no—
256C2—2062no—
257C2—2062no—
258C2#99×D10311yescharacteristic
259C2#2026778911yescharacteristic
260C2#104×D10311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#327×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268301C2
cosocleC22×C4×C103C23
hypercenter#327D103
hypocenterC103#1504
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20267753C2semidirect
3. #95×D103C2semidirect
4. #20267529C2semidirect
5. #20267527C2semidirect
6. #20267525C2semidirect
7. #327×C103C2semidirect
8. C2×#13110104C4semidirect
13. #15693001C4semidirect
15. #15692992C4semidirect
19. #15692979C4semidirect
29. C2×Dic206C2×C4semidirect
46. C4⋊Dic103C2×C4semidirect
54. C2×D4×C103C2×C4semidirect
58. C4⋊C4×C103C2×C4semidirect
131. C103#1504semidirect
138. #327D103semidirect
164. C2×D4C4×D103semidirect
184. C4⋊C4C4×D103semidirect

Maximal subgroups

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

subgroupindex
#202683012
#202677532
#95×D1032
#202675292
#202675272
#202675252
#327×C1032
#1504103