Finite Group Databasebeta

← C2×#20268000 #27204581

Subgroups — C2×#20268000 #27204581

Order 13184.

480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×Dic412C211yesmaximal, characteristic
2C22×#13110095C211yesmaximal, characteristic
3C2×#15693019C211yesmaximal, characteristic
4C2×#15692986C211yesmaximal, characteristic
5#20268000C218yesmaximal, direct product factor
6C2×Dic103⋊C8C211yesmaximal, characteristic
7C2×#15692944C211yesmaximal, characteristic
8C2×#103×C103C211yesmaximal, characteristic
9C22×Dic206C2211yescharacteristic
10C22×Dic206C2211yescharacteristic
11C2×Dic412—24no—
12C2×Dic412C2214yes—
13C2×#13110095—24no—
14C2×#13110095C2214yes—
15C22×C103⋊C8C2211yescharacteristic
16#15693019—22no—
17#15693019C2214yes—
18#15692986—22no—
19#15692986C2214yes—
20C2×Dic103⋊C4—21no—
21C2×Dic103⋊C4—21no—
22C2×Dic103⋊C4—21no—
23C2×C4×Dic103—21no—
24C2×C4×Dic103C2211yescharacteristic
25Dic103⋊C8C2214yes—
26#15692944C2214yes—
27C22×Q8×C103C2211yescharacteristic
28C22×C8×C103C2211yescharacteristic
29C2×C4⋊C4×C103C2211yescharacteristic
30#103×C103C2214yes—
31C2×Dic206—21no—
32C2×Dic206—22no—
33C2×Dic206—22no—
34C2×Dic206—22no—
35C2×Dic206—21no—
36C2×Dic206D414yes—
37C2×Dic206C2312yes—
38C2×Dic206C2312yes—
39C22×Dic103—21no—
40C22×Dic103—21no—
41C22×Dic103D411yescharacteristic
42C22×Dic103D411yescharacteristic
43Dic412—28no—
44#13110095—28no—
45C2×C103⋊C8—22no—
46C2×C103⋊C8C2312yes—
47Dic103⋊C4—24no—
48Dic103⋊C4—24no—
49Dic103⋊C4—24no—
50C4×Dic103—24no—
51C4×Dic103D412yes—
52C4×Dic103C2312yes—
53C2×Q8×C103—21no—
54C2×Q8×C103—22no—
55C2×Q8×C103—22no—
56C2×Q8×C103C2312yes—
57C22×C4×C103—21no—
58C22×C4×C103—21no—
59C22×C4×C103C2311yescharacteristic
60C2×C8×C103—22no—
61C2×C8×C103C2312yes—
62C4⋊C4×C103—21no—
63C4⋊C4×C103C2312yes—
64C23×C103C2×D411yescharacteristic
65Q8×C103—22no—
66Q8×C103—22no—
67Q8×C103—42no—
68C2×C4×C103—22no—
69C2×C4×C103—22no—
70C2×C4×C103—42no—
71C2×C4×C103—42no—
72C2×C4×C103C2×D411yescharacteristic
73C2×C4×C103C2×D412yes—
74C2×C4×C103#4112yes—
75C2×C4×C103C2411yescharacteristic
76C2×Dic103—24no—
77C2×Dic103—22no—
78C2×Dic103—22no—
79C2×Dic103—22no—
80C2×Dic103—42no—
81C2×Dic103Q1614yescomplemented
82C2×Dic103C2×D412yes—
83C2×Dic103C2×D412yes—
84Dic206—24no—
85Dic206—22no—
86Dic206—22no—
87Dic206—22no—
88Dic206—42no—
89Dic206C2×D414yes—
90C8×C103—22no—
91C103⋊C8—22no—
92C22×C103#12112yes—
93C22×C103C2×Q1612yes—
94C22×C103#13712yes—
95C22×C103C22×D411yescharacteristic
96C4×C103—42no—
97C4×C103—42no—
98C4×C103#12112yes—
99C4×C103C22×D411yescharacteristic
100C4×C103C2×#4111yescharacteristic
101Dic103—24no—
102Dic103—22no—
103Dic103—42no—
104Dic103C2×Q1614yescomplemented
105C2×C103#46214yescomplemented
106C2×C103C2×#12111yescharacteristic
107C2×C103C22×Q1611yescharacteristic
108C2×C103C2×#13711yescharacteristic
109C2×#462—1031nomaximal, Sylow
110C103C2×#46211yescharacteristic, complemented, Sylow
111C22×Q16—1031no—
112C22×Q16—1031no—
113C2×C4⋊Q8—1031no—
114C2×C4×Q8—1031no—
115#462—1038no—
116C2×C4⋊C8—1031no—
117C2×#103—1031no—
118C2×#103D10311yescharacteristic
119C22×Q8—1031no—
120C22×Q8—1031no—
121C22×Q8C2×D10311yescharacteristic
122C2×Q16—1034no—
123C2×Q16—1034no—
124C2×Q16—2064no—
125C2×Q16—2064no—
126C22×C8—1031no—
127C22×C8C2×D10311yescharacteristic
128C4⋊Q8—1034no—
129C4⋊Q8—2062no—
130C4×Q8—1034no—
131C4×Q8—2062no—
132C2×C4⋊C4—2061no—
133C2×C4⋊C4—2061no—
134C2×C4⋊C4—2061no—
135C2×C4⋊C4C2×D10311yescharacteristic
136C2×C42—1031no—
137C2×C42—2061no—
138C4⋊C8—1034no—
139#103—1034no—
140#103C2×D10314yes—
141C2×Q8—21no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—1034no—
145C2×Q8—1032no—
146C2×Q8—1032no—
147C2×Q8—2062no—
148C2×Q8—2062no—
149C2×Q8—2061no—
150C2×Q8—2061no—
151C2×Q8—2062no—
152C2×Q8C22×D10312yes—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—1031no—
156C22×C4—1031no—
157C22×C4—2061no—
158C22×C4—2061no—
159C22×C4C22×D10311yescharacteristic
160Q16—2068no—
161Q16—2068no—
162C2×C8—22no—
163C2×C8—1032no—
164C2×C8—2062no—
165C2×C8C22×D10312yes—
166C4⋊C4—21no—
167C4⋊C4—2064no—
168C4⋊C4—2064no—
169C4⋊C4—2064no—
170C4⋊C4C22×D10312yes—
171C42—1032no—
172C42—1032no—
173C42—2064no—
174C23D4×D10311yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—42no—
178Q8—1034no—
179Q8—4122no—
180Q8—2062no—
181Q8—2062no—
182Q8—2062no—
183Q8—2064no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—1032no—
189C2×C4—1034no—
190C2×C4—1032no—
191C2×C4—4122no—
192C2×C4—2062no—
193C2×C4—2062no—
194C2×C4—2064no—
195C2×C4—2062no—
196C2×C4D4×D10312yes—
197C2×C4D4×D10311yescharacteristic
198C2×C4#1311010512yes—
199C2×C4C23×D10311yescharacteristic
200C8—22no—
201C8—2062no—
202C22#1569299412yes—
203C22Q16×D10312yes—
204C22#1569305012yes—
205C22C2×D4×D10311yescharacteristic
206C4—42no—
207C4—42no—
208C4—1034no—
209C4—4122no—
210C4—2062no—
211C4—2064no—
212C4#1569299412yes—
213C4C2×D4×D10311yescharacteristic
214C4C2×#1311010511yescharacteristic
215C2#2026800014yesdirect product factor
216C2C2×#1569299411yescharacteristic
217C2C2×Q16×D10311yescharacteristic
218C2C2×#1569305011yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#103×C103C2
socle, prime radicalC23×C103C2×D4
hypercenterC2×#103D103
hypocenterC103C2×#462
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
5. #20268000C2direct (N × H)
81. C2×Dic103Q16semidirect
104. Dic103C2×Q16semidirect
105. C2×C103#462semidirect
110. C103C2×#462semidirect
215. C2#20268000direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Dic4122
C22×#131100952
C2×#156930192
C2×#156929862
#202680002
C2×Dic103⋊C82
C2×#156929442
C2×#103×C1032
C2×#462103