Finite Group Databasebeta

← #27193671

Subgroups — #27193671

Order 13184.

326 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 63 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#121×D103C211yesmaximal, characteristic
2#20267753C211yesmaximal, characteristic, complemented
3#20267653C211yesmaximal, characteristic, complemented
4#20267526C211yesmaximal, characteristic, complemented
5#20267525C211yesmaximal, characteristic, complemented
6#20267524C211yesmaximal, characteristic, complemented
7#327×C103C211yesmaximal, characteristic, complemented
8C2×D4×D103—21no—
9C2×D4×D103C411yescharacteristic, complemented
10C22×C4×D103C2211yescharacteristic
11C2×#13110088—21no—
12#15692996C411yescharacteristic, complemented
13#15692995C2211yescharacteristic
14#15692994—21no—
15#15692993—21no—
16#15692992C411yescharacteristic, complemented
17C4⋊C4×D103C411yescharacteristic, complemented
18C2×(C2×D103)⋊C4—21no—
19C22⋊C4×D103—21no—
20C22⋊(C103⋊C8)C2211yescharacteristic, complemented
21(C2×D103)⋊C8—21no—
22C103⋊#95—21no—
23C103⋊#95C2211yescharacteristic, complemented
24#121×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic, complemented
26#95×C103C2211yescharacteristic, complemented
27C23×D103—21no—
28C23×D103D411yescharacteristic
29C2×D412—21no—
30C2×D412C2×C411yescharacteristic
31C2×C22⋊D103—21no—
32C2×C22⋊D103—21no—
33C2×C22⋊D103—21no—
34D4×D103—42no—
35D4×D103—42no—
36D4×D103—42no—
37C22×Dic103—21no—
38C22×Dic103D411yescharacteristic
39C2×C4×D103—21no—
40C2×C4×D103—42no—
41C2×C4×D103C2×C411yescharacteristic
42C2×C4×D103C2×C411yescharacteristic
43C2×C4×D103D411yescharacteristic
44C2×C4×D103D411yescharacteristic
45#13110088—42no—
46C2×C103⋊C8—21no—
47C4⋊Dic103C2×C411yescharacteristic
48Dic103⋊C4—21no—
49C22⋊Dic103—21no—
50(C2×D103)⋊C4—21no—
51(C2×D103)⋊C4—21no—
52(C2×D103)⋊C4—42no—
53C2×D4×C103—21no—
54C2×D4×C103C2×C411yescharacteristic
55C22×C4×C103—21no—
56C22×C4×C103C2311yescharacteristic
57C2×C8×C103—21no—
58C4⋊C4×C103C2×C411yescharacteristic
59C22⋊C4×C103—21no—
60C23×C103—21no—
61C23×C103C2×D411yescharacteristic
62C22×D103—21no—
63C22×D103—21no—
64C22×D103—22no—
65C22×D103—21no—
66C22×D103—41no—
67C22×D103—42no—
68C22×D103—42no—
69C22×D103—42no—
70C22×D103C22⋊C411yescharacteristic
71C22×D103C22⋊C411yescharacteristic
72D4×C103—41no—
73D4×C103—41no—
74D4×C103—41no—
75C2×C4×C103—21no—
76C2×C4×C103—41no—
77C2×C4×C103—41no—
78C2×C4×C103—41no—
79C2×C4×C103—41no—
80C2×C4×C103C22×C411yescharacteristic
81C2×C4×C103C2×D411yescharacteristic
82C22⋊D103—42no—
83C22⋊D103—42no—
84C22⋊D103—41no—
85C22⋊D103—41no—
86C2×Dic103—21no—
87C2×Dic103—41no—
88C2×Dic103—41no—
89C2×Dic103—41no—
90C2×Dic103—41no—
91C2×Dic103C22⋊C411yescharacteristic
92C2×Dic103C22⋊C411yescharacteristic
93D412—41no—
94D412—42no—
95C4×D103—22no—
96C4×D103—22no—
97C4×D103—41no—
98C4×D103—41no—
99C4×D103—42no—
100C8×C103—41no—
101C103⋊C8—41no—
102C22×C103—21no—
103C22×C103—21no—
104C22×C103—41no—
105C22×C103—41no—
106C22×C103—41no—
107C22×C103C2×C22⋊C411yescharacteristic
108C22×C103AGL(1,ℤ/8)11yescharacteristic
109C22×C103AGL(1,ℤ/8)11yescharacteristic
110C2×D103—21no—
111C2×D103—21no—
112C2×D103—21no—
113C2×D103—21no—
114C2×D103—21no—
115C2×D103—42no—
116C2×D103—42no—
117C2×D103—41no—
118C2×D103—41no—
119C2×D103—41no—
120C2×D103—84no—
121C2×D103#9912yes—
122C4×C103—21no—
123C4×C103—21no—
124C4×C103—41no—
125C4×C103—81no—
126Dic103—21no—
127Dic103—21no—
128Dic103—41no—
129Dic103—81no—
130C2×C103—21no—
131C2×C103—21no—
132C2×C103—81no—
133C2×C103C2×#9911yescharacteristic
134C2×C103#41811yescharacteristic
135C2×C103#42111yescharacteristic
136D103—22no—
137D103—41no—
138D103—81no—
139#1510—1031nomaximal, Sylow
140C103#151011yescharacteristic, complemented, Sylow
141C2×#121—1031no—
142#407—1031no—
143#381—1031no—
144#327—1031no—
145#327—1031no—
146#327—1031no—
147#327D10311yescharacteristic, complemented
148C22×D4—1031no—
149C22×D4—2061no—
150C23×C4—1031no—
151C2×M16—2061no—
152#121—1031no—
153#121—1031no—
154#121—1031no—
155#121—2061no—
156#121—2061no—
157#121C2×D10311yescharacteristic
158C2×C4⋊C4—1031no—
159C2×C22⋊C4—2061no—
160C2×C22⋊C4—2061no—
161C22⋊C8—1031no—
162C22⋊C8—2061no—
163C22⋊C8C2×D10311yescharacteristic, complemented
164#95—1031no—
165#95—2061no—
166#95C2×D10311yescharacteristic, complemented
167C24—1031no—
168C24—2061no—
169C2×D4—21no—
170C2×D4—1031no—
171C2×D4—4122no—
172C2×D4—4122no—
173C2×D4—4122no—
174C2×D4—2061no—
175C2×D4—2061no—
176C2×D4—2061no—
177C2×D4—2061no—
178C2×D4C4×D10311yescharacteristic
179C22×C4—21no—
180C22×C4—1031no—
181C22×C4—1031no—
182C22×C4—1031no—
183C22×C4—1031no—
184C22×C4—1031no—
185C22×C4—4122no—
186C22×C4—2061no—
187C22×C4—2061no—
188C22×C4C22×D10311yescharacteristic
189M16—4122no—
190C2×C8—21no—
191C2×C8—2061no—
192C4⋊C4—1031no—
193C4⋊C4—2061no—
194C4⋊C4C4×D10311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—4122no—
197C22⋊C4—2061no—
198C22⋊C4—2061no—
199C22⋊C4—2061no—
200C23—21no—
201C23—1031no—
202C23—1031no—
203C23—4121no—
204C23—4122no—
205C23—4122no—
206C23—4122no—
207C23—2062no—
208C23—2061no—
209C23—2061no—
210C23—2061no—
211C23D4×D10311yescharacteristic
212D4—41no—
213D4—41no—
214D4—41no—
215D4—4121no—
216D4—4122no—
217D4—4122no—
218D4—4121no—
219D4—4121no—
220D4—4122no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—1031no—
227C2×C4—1031no—
228C2×C4—4121no—
229C2×C4—4121no—
230C2×C4—4122no—
231C2×C4—4121no—
232C2×C4—4121no—
233C2×C4—4121no—
234C2×C4—4121no—
235C2×C4—2062no—
236C2×C4—2062no—
237C2×C4—2061no—
238C2×C4C2×C4×D10311yescharacteristic
239C2×C4D4×D10311yescharacteristic
240C8—41no—
241C8—4121no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—8244no—
248C22—1032no—
249C22—4122no—
250C22—4122no—
251C22—4121no—
252C22—4121no—
253C22—4121no—
254C22—2061no—
255C22—2061no—
256C22—2061no—
257C22—2061no—
258C22—2061no—
259C22C22⋊C4×D10311yescharacteristic
260C22#1569304511yescharacteristic
261C22#1569304811yescharacteristic
262C4—21no—
263C4—21no—
264C4—41no—
265C4—81no—
266C4—8241no—
267C4—4121no—
268C4—2061no—
269C4—2061no—
270C2—21no—
271C2—21no—
272C2—81no—
273C2—8241no—
274C2—4121no—
275C2—2062no—
276C2#99×D10311yescharacteristic
277C2#2026779411yescharacteristic
278C2#2026780611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#327×C103C2
socleC22×C103C2×C22⋊C4
prime radical#121×D103C2
cosocleC22×C4×C103C23
hypercenter#327D103
hypocenterC103#1510
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. #20267653C2semidirect
4. #20267526C2semidirect
5. #20267525C2semidirect
6. #20267524C2semidirect
7. #327×C103C2semidirect
9. C2×D4×D103C4semidirect
12. #15692996C4semidirect
16. #15692992C4semidirect
17. C4⋊C4×D103C4semidirect
20. C22⋊(C103⋊C8)C22semidirect
23. C103⋊#95C22semidirect
25. C22⋊C8×C103C22semidirect
26. #95×C103C22semidirect
140. C103#1510semidirect
147. #327D103semidirect
163. C22⋊C8C2×D103semidirect
166. #95C2×D103semidirect

Maximal subgroups

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

subgroupindex
#121×D1032
#202677532
#202676532
#202675262
#202675252
#202675242
#327×C1032
#1510103