Finite Group Databasebeta

← C2×#20268043 #27204739

Subgroups — C2×#20268043 #27204739

Order 13184.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#13110090C211yesmaximal, characteristic, complemented
2C22×#13110088C211yesmaximal, characteristic, complemented
3C2×#15692996C211yesmaximal, characteristic, complemented
4C2×#15692992C211yesmaximal, characteristic, complemented
5#20268043C218yesmaximal, direct product factor
6C2×#15692952C211yesmaximal, characteristic, complemented
7C2×#15692943C211yesmaximal, characteristic, complemented
8C2×#102×C103C211yesmaximal, characteristic, complemented
9C22×D412—21no—
10C22×D412C2211yescharacteristic
11C22×C22⋊D103—21no—
12C22×C4×D103C2211yescharacteristic
13C2×#13110090—24no—
14C2×#13110090C2214yescomplemented
15C2×#13110088—24no—
16C2×#13110088C2214yescomplemented
17C22×C103⋊C8C2211yescharacteristic
18#15692996—22no—
19#15692996C2214yescomplemented
20#15692992—22no—
21#15692992C2214yescomplemented
22C2×C4⋊Dic103C2211yescharacteristic
23C2×C22⋊Dic103—21no—
24C2×(C2×D103)⋊C4—21no—
25#15692952C2214yescomplemented
26#15692943C2214yescomplemented
27C22×D4×C103C2211yescharacteristic
28C22×C8×C103C2211yescharacteristic
29C2×C4⋊C4×C103C2211yescharacteristic
30#102×C103C2214yescomplemented
31C23×D103—21no—
32C23×D103D411yescharacteristic
33C2×D412—22no—
34C2×D412—22no—
35C2×D412—24no—
36C2×D412—21no—
37C2×D412—44no—
38C2×D412C2312yes—
39C2×C22⋊D103—24no—
40C2×C22⋊D103—44no—
41C22×Dic103—21no—
42C22×Dic103D411yescharacteristic
43C2×C4×D103—22no—
44C2×C4×D103—22no—
45C2×C4×D103D412yes—
46C2×C4×D103C2312yes—
47#13110090—28no—
48#13110088—28no—
49C2×C103⋊C8D414yescomplemented
50C2×C103⋊C8C2312yes—
51C4⋊Dic103—21no—
52C4⋊Dic103C2312yes—
53C22⋊Dic103—24no—
54(C2×D103)⋊C4—24no—
55C24×C103—21no—
56C2×D4×C103—22no—
57C2×D4×C103—21no—
58C2×D4×C103—22no—
59C2×D4×C103C2312yes—
60C22×C4×C103—21no—
61C22×C4×C103C2311yescharacteristic
62C2×C8×C103—22no—
63C2×C8×C103C2312yes—
64C4⋊C4×C103—21no—
65C4⋊C4×C103C2312yes—
66C23×C103—22no—
67C23×C103—42no—
68C23×C103—42no—
69C23×C103—42no—
70C23×C103C2×D411yescharacteristic
71C22×D103—22no—
72C22×D103—22no—
73C22×D103—22no—
74C22×D103—22no—
75C22×D103—42no—
76C22×D103—42no—
77C22×D103—42no—
78C22×D103C2×D412yes—
79D4×C103—22no—
80D4×C103—22no—
81D4×C103—42no—
82C2×C4×C103—22no—
83C2×C4×C103—42no—
84C2×C4×C103C2×D411yescharacteristic
85C2×C4×C103C2×D412yes—
86C2×C4×C103#4112yes—
87C2×C4×C103C2411yescharacteristic
88C22⋊D103—48no—
89C2×Dic103—22no—
90C2×Dic103—22no—
91C2×Dic103—42no—
92C2×Dic103C2×D412yes—
93D412—22no—
94D412—22no—
95D412—48no—
96D412—42no—
97C4×D103—24no—
98C4×D103—22no—
99C4×D103—22no—
100C8×C103—22no—
101C103⋊C8C2×D414yescomplemented
102C22×C103—42no—
103C22×C103—42no—
104C22×C103—42no—
105C22×C103—84no—
106C22×C103#12112yes—
107C22×C103AGL(1,ℤ/8)12yes—
108C22×C103AGL(1,ℤ/8)12yes—
109C22×C103C22×D411yescharacteristic
110C2×D103—22no—
111C2×D103—22no—
112C2×D103—22no—
113C2×D103—44no—
114C2×D103—42no—
115C2×D103—42no—
116C2×D103—42no—
117C2×D103—84no—
118C4×C103—42no—
119C4×C103#12112yes—
120C4×C103C22×D411yescharacteristic
121C4×C103C2×#4111yescharacteristic
122Dic103—22no—
123Dic103—42no—
124C2×C103—82no—
125C2×C103#46914yescomplemented
126C2×C103C2×#12111yescharacteristic
127C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
129D103—42no—
130D103—82no—
131C2×#469—1031nomaximal, Sylow
132C103C2×#46911yescharacteristic, complemented, Sylow
133C22×D8—1031no—
134C22×M16—1031no—
135C2×#121—1031no—
136C2×#121—1031no—
137#469—1038no—
138C2×#106—1031no—
139C2×#102—1031no—
140C2×#102D10311yescharacteristic, complemented
141C22×D4—1031no—
142C22×D4—2061no—
143C22×D4—2061no—
144C22×D4C2×D10311yescharacteristic
145C23×C4—1031no—
146C2×D8—1034no—
147C2×D8—2064no—
148C2×M16—1034no—
149C2×M16—2064no—
150C22×C8—1031no—
151C22×C8C2×D10311yescharacteristic
152#121—1034no—
153#121—1034no—
154#121—2062no—
155#121—2062no—
156C2×C4⋊C4—1031no—
157C2×C4⋊C4C2×D10311yescharacteristic
158C2×C22⋊C4—2061no—
159C2×C22⋊C4—2061no—
160#106—1034no—
161#102—1034no—
162#102C2×D10314yescomplemented
163C24—21no—
164C24—1031no—
165C24—2061no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—1032no—
170C2×D4—4124no—
171C2×D4—4124no—
172C2×D4—2064no—
173C2×D4—2064no—
174C2×D4—2061no—
175C2×D4—2062no—
176C2×D4—2062no—
177C2×D4C22×D10312yes—
178C22×C4—21no—
179C22×C4—1031no—
180C22×C4—1032no—
181C22×C4—1032no—
182C22×C4—2061no—
183C22×C4—2062no—
184C22×C4—2062no—
185C22×C4C22×D10311yescharacteristic
186D8—2068no—
187M16—2068no—
188C2×C8—22no—
189C2×C8—1034no—
190C2×C8—1032no—
191C2×C8C22×D10312yes—
192C4⋊C4—21no—
193C4⋊C4—1032no—
194C4⋊C4—2061no—
195C4⋊C4C22×D10312yes—
196C22⋊C4—2064no—
197C22⋊C4—2064no—
198C23—22no—
199C23—42no—
200C23—42no—
201C23—42no—
202C23—1032no—
203C23—4122no—
204C23—4122no—
205C23—4122no—
206C23—2062no—
207C23—2062no—
208C23—2062no—
209C23—2062no—
210C23D4×D10311yescharacteristic
211D4—22no—
212D4—22no—
213D4—42no—
214D4—4128no—
215D4—4128no—
216D4—4122no—
217D4—2062no—
218D4—2062no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—1032no—
222C2×C4—4122no—
223C2×C4—2062no—
224C2×C4—2062no—
225C2×C4—2062no—
226C2×C4—2062no—
227C2×C4—2064no—
228C2×C4D4×D10312yes—
229C2×C4D4×D10311yescharacteristic
230C2×C4#1311010512yes—
231C2×C4C23×D10311yescharacteristic
232C8—22no—
233C8—1034no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—84no—
238C22—8244no—
239C22—4122no—
240C22—4122no—
241C22—4122no—
242C22—4124no—
243C22—2062no—
244C22—2062no—
245C22—2062no—
246C22#1569299412yes—
247C22#1569304512yes—
248C22#1569304812yes—
249C22C2×D4×D10311yescharacteristic
250C4—42no—
251C4—4122no—
252C4—2062no—
253C4#1569299412yes—
254C4C2×D4×D10311yescharacteristic
255C4C2×#1311010511yescharacteristic
256C2—82no—
257C2—8242no—
258C2—4122no—
259C2#2026804314yesdirect product factor
260C2C2×#1569299411yescharacteristic
261C2C2×#1569304511yescharacteristic
262C2C2×#1569304811yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#102×C103C2
socleC23×C103C2×D4
hypercenterC2×#102D103
hypocenterC103C2×#469
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#13110090C2semidirect
2. C22×#13110088C2semidirect
3. C2×#15692996C2semidirect
4. C2×#15692992C2semidirect
5. #20268043C2direct (N × H)
6. C2×#15692952C2semidirect
7. C2×#15692943C2semidirect
8. C2×#102×C103C2semidirect
14. C2×#13110090C22semidirect
16. C2×#13110088C22semidirect
19. #15692996C22semidirect
21. #15692992C22semidirect
25. #15692952C22semidirect
26. #15692943C22semidirect
30. #102×C103C22semidirect
49. C2×C103⋊C8D4semidirect
101. C103⋊C8C2×D4semidirect
125. C2×C103#469semidirect
132. C103C2×#469semidirect
140. C2×#102D103semidirect
162. #102C2×D103semidirect
259. C2#20268043direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131100902
C22×#131100882
C2×#156929962
C2×#156929922
#202680432
C2×#156929522
C2×#156929432
C2×#102×C1032
C2×#469103