Finite Group Databasebeta

← C2×#20268022 #27204706

Subgroups — C2×#20268022 #27204706

Order 13184.

564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13110092C211yesmaximal, characteristic, complemented
2C23×C103⋊C8C211yesmaximal, characteristic, complemented
3C2×#15692995C211yesmaximal, characteristic
4#20268022C218yesmaximal, direct product factor
5C2×#15692952C211yesmaximal, characteristic, complemented
6C2×#15692945C211yesmaximal, characteristic, complemented
7C2×#15692941C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C103C211yesmaximal, characteristic, complemented
9C22×D412C2211yescharacteristic
10C22×C22⋊D103—21no—
11C2×#13110092—24no—
12C2×#13110092C2214yescomplemented
13C22×C103⋊C8—24no—
14C22×C103⋊C8C2211yescharacteristic
15C22×C103⋊C8C2211yescharacteristic
16C22×C103⋊C8C2214yescomplemented
17#15692995—22no—
18#15692995C2214yes—
19C2×C4⋊Dic103C2211yescharacteristic
20C2×(C2×D103)⋊C4—21no—
21#15692952C2214yescomplemented
22#15692945C2214yescomplemented
23#15692941C2214yescomplemented
24C22×Q8×C103C2211yescharacteristic
25C23×C4×C103C2211yescharacteristic
26C22⋊Q8×C103—22no—
27C22⋊Q8×C103C2214yescomplemented
28C2×C4⋊C4×C103—21no—
29C2×C4⋊C4×C103C2211yescharacteristic
30C2×C22⋊C4×C103—21no—
31C23×D103—21no—
32C2×D412—22no—
33C2×D412—22no—
34C2×D412—21no—
35C2×D412C2312yes—
36C2×C22⋊D103—24no—
37C2×C22⋊D103—44no—
38C22×Dic103—21no—
39#13110092—28no—
40C2×C103⋊C8—22no—
41C2×C103⋊C8—28no—
42C2×C103⋊C8D414yescomplemented
43C2×C103⋊C8C2312yes—
44C2×C103⋊C8C2312yes—
45C4⋊Dic103—21no—
46C4⋊Dic103C2312yes—
47(C2×D103)⋊C4—24no—
48C24×C103D411yescharacteristic
49C2×Q8×C103—21no—
50C2×Q8×C103—22no—
51C2×Q8×C103—22no—
52C2×Q8×C103C2312yes—
53C22×C4×C103—22no—
54C22×C4×C103—22no—
55C22×C4×C103—21no—
56C22×C4×C103—21no—
57C22×C4×C103D411yescharacteristic
58C22×C4×C103D412yes—
59C22×C4×C103C2312yes—
60C22×C4×C103C2311yescharacteristic
61C4⋊C4×C103—24no—
62C4⋊C4×C103—21no—
63C4⋊C4×C103C2312yes—
64C22⋊C4×C103—24no—
65C23×C103—22no—
66C23×C103—22no—
67C23×C103SD1614yescomplemented
68C23×C103C2×D412yes—
69C23×C103C2×D411yescharacteristic
70C22×D103—22no—
71C22×D103—42no—
72C22×D103—42no—
73C22×D103—42no—
74Q8×C103—22no—
75Q8×C103—22no—
76Q8×C103—42no—
77C2×C4×C103—22no—
78C2×C4×C103—24no—
79C2×C4×C103—22no—
80C2×C4×C103—22no—
81C2×C4×C103—22no—
82C2×C4×C103—22no—
83C2×C4×C103—42no—
84C2×C4×C103—42no—
85C2×C4×C103C2×D412yes—
86C2×C4×C103C2×D412yes—
87C2×C4×C103C2×D411yescharacteristic
88C2×C4×C103#4112yes—
89C2×C4×C103C2411yescharacteristic
90C22⋊D103—48no—
91C2×Dic103—22no—
92C2×Dic103—42no—
93D412—22no—
94D412—22no—
95D412—42no—
96C103⋊C8—22no—
97C103⋊C8C2×D414yescomplemented
98C22×C103—22no—
99C22×C103—22no—
100C22×C103—28no—
101C22×C103#12112yes—
102C22×C103C2×SD1612yes—
103C22×C103C2×SD1614yescomplemented
104C22×C103#13512yes—
105C22×C103C22×D411yescharacteristic
106C2×D103—42no—
107C2×D103—42no—
108C2×D103—42no—
109C2×D103—84no—
110C4×C103—22no—
111C4×C103—42no—
112C4×C103—42no—
113C4×C103#12112yes—
114C4×C103C22×D411yescharacteristic
115C4×C103C2×#4111yescharacteristic
116Dic103—42no—
117C2×C103—24no—
118C2×C103#46514yescomplemented
119C2×C103C2×#12111yescharacteristic
120C2×C103C22×SD1611yescharacteristic
121C2×C103C2×#13511yescharacteristic
122D103—82no—
123C2×#465—1031nomaximal, Sylow
124C103C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16—1031no—
126C23×C8—1031no—
127C2×C22⋊Q8D10311yescharacteristic, complemented
128C2×#121—1031no—
129#465—1038no—
130C2×#106—1031no—
131C2×#103—1031no—
132C2×#102—1031no—
133C22×Q8C2×D10311yescharacteristic
134C22×D4—1031no—
135C22×D4—2061no—
136C23×C4C2×D10311yescharacteristic
137C2×SD16—1034no—
138C2×SD16—2064no—
139C22×C8—1031no—
140C22×C8—1031no—
141C22×C8—1034no—
142C22×C8—2064no—
143C22⋊Q8—22no—
144C22⋊Q8C2×D10314yescomplemented
145#121—1034no—
146#121—2062no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—1031no—
149C2×C4⋊C4C2×D10311yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—2061no—
152#106—1034no—
153#103—1034no—
154#102—1034no—
155C24—2061no—
156C24C22⋊D10311yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D10312yes—
161C2×D4—1032no—
162C2×D4—4124no—
163C2×D4—2064no—
164C2×D4—2062no—
165C2×D4—2061no—
166C2×D4—2062no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—2061no—
172C22×C4C22⋊D10312yes—
173C22×C4C22⋊D10311yescharacteristic
174C22×C4C22×D10312yes—
175C22×C4C22×D10311yescharacteristic
176SD16—2068no—
177C2×C8—1034no—
178C2×C8—1032no—
179C2×C8—1032no—
180C2×C8—2068no—
181C2×C8—2062no—
182C4⋊C4—24no—
183C4⋊C4—21no—
184C4⋊C4—1032no—
185C4⋊C4—2061no—
186C4⋊C4C22×D10312yes—
187C22⋊C4—24no—
188C22⋊C4—2064no—
189C23—22no—
190C23—22no—
191C23—4122no—
192C23—4122no—
193C23—4122no—
194C23—2062no—
195C23#1311009214yescomplemented
196C23C2×C22⋊D10312yes—
197C23C2×C22⋊D10311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—4128no—
202D4—4122no—
203D4—2062no—
204D4—2062no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—4122no—
214C2×C4—2062no—
215C2×C4D4×D10312yes—
216C2×C4C2×C22⋊D10312yes—
217C2×C4C2×C22⋊D10311yescharacteristic
218C2×C4#1311010412yes—
219C2×C4C23×D10311yescharacteristic
220C8—1034no—
221C8—2062no—
222C22—22no—
223C22—28no—
224C22—22no—
225C22—8244no—
226C22—4122no—
227C22—4122no—
228C22—4122no—
229C22#1569299312yes—
230C22C2×#1311009212yes—
231C22C2×#1311009214yescomplemented
232C22#1569304112yes—
233C22C22×C22⋊D10311yescharacteristic
234C4—22no—
235C4—42no—
236C4—42no—
237C4—4122no—
238C4#1569299312yes—
239C4C2×D4×D10311yescharacteristic
240C4C2×#1311010411yescharacteristic
241C2—24no—
242C2—8242no—
243C2#2026802214yesdirect product factor
244C2C2×#1569299311yescharacteristic
245C2C22×#1311009211yescharacteristic
246C2C2×#1569304111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×C22⋊Q8×C103C2
socleC23×C103C2×D4
prime radicalC2×#15692995C2
hypercenterC2×C22⋊Q8D103
hypocenterC103C2×#465
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13110092C2semidirect
2. C23×C103⋊C8C2semidirect
4. #20268022C2direct (N × H)
5. C2×#15692952C2semidirect
6. C2×#15692945C2semidirect
7. C2×#15692941C2semidirect
8. C2×C22⋊Q8×C103C2semidirect
12. C2×#13110092C22semidirect
16. C22×C103⋊C8C22semidirect
21. #15692952C22semidirect
22. #15692945C22semidirect
23. #15692941C22semidirect
27. C22⋊Q8×C103C22semidirect
42. C2×C103⋊C8D4semidirect
67. C23×C103SD16semidirect
97. C103⋊C8C2×D4semidirect
103. C22×C103C2×SD16semidirect
118. C2×C103#465semidirect
124. C103C2×#465semidirect
127. C2×C22⋊Q8D103semidirect
144. C22⋊Q8C2×D103semidirect
195. C23#13110092semidirect
231. C22C2×#13110092semidirect
243. C2#20268022direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131100922
C23×C103⋊C82
C2×#156929952
#202680222
C2×#156929522
C2×#156929452
C2×#156929412
C2×C22⋊Q8×C1032
C2×#465103