Finite Group Databasebeta

← #27195588

Subgroups — #27195588

Order 13184.

442 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 105 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×C4×Dic103C211yesmaximal, characteristic, complemented
2C2×#15692948C212yesmaximal, complemented
3#20267755C211yesmaximal, characteristic, complemented
4#20267550C212yesmaximal, complemented
5#525×C103C211yesmaximal, characteristic
6C23×Dic103—21no—
7C2×#13110089C2212yes—
8C2×C4×Dic103—24no—
9C2×C4×Dic103—21no—
10C2×C4×Dic103C2212yes—
11#15692948—24no—
12C22⋊(C103⋊C8)—22no—
13C2×#41×C103C2211yescharacteristic
14C23×C4×C103C2211yescharacteristic
15#123×C103—21no—
16C22⋊Q8×C103C412yescomplemented
17#121×C103C412yescomplemented
18#120×C103—21no—
19C4×D4×C103—22no—
20#117×C103C2211yescharacteristic
21C22×Dic103—28no—
22C22×Dic103—24no—
23C22×Dic103—22no—
24#13110089—22no—
25#13110089—22no—
26C2×C103⋊C8—22no—
27C4×Dic103—24no—
28C4×Dic103—22no—
29C4×Dic103D414yescomplemented
30C24×C103D411yescharacteristic
31#41×C103—22no—
32#41×C103—22no—
33C2×Q8×C103C2×C411yescharacteristic, complemented
34C2×D4×C103—22no—
35C2×D4×C103—21no—
36C2×D4×C103C2×C411yescharacteristic, complemented
37C22×C4×C103—22no—
38C22×C4×C103—22no—
39C22×C4×C103—21no—
40C22×C4×C103C2×C412yes—
41C22×C4×C103D411yescharacteristic
42C22×C4×C103D412yes—
43C22×C4×C103C2311yescharacteristic
44C4⋊C4×C103—22no—
45C4⋊C4×C103C2×C412yescomplemented
46C22⋊C4×C103—22no—
47C22⋊C4×C103—21no—
48C22⋊C4×C103—22no—
49C42×C103—21no—
50C23×C103—24no—
51C23×C103—21no—
52C23×C103—21no—
53C23×C103—21no—
54C23×C103C22⋊C412yes—
55C23×C103C2×D411yescharacteristic
56Q8×C103—22no—
57D4×C103—22no—
58D4×C103—44no—
59D4×C103—41no—
60D4×C103—41no—
61C2×C4×C103—21no—
62C2×C4×C103—21no—
63C2×C4×C103—24no—
64C2×C4×C103—24no—
65C2×C4×C103—22no—
66C2×C4×C103—21no—
67C2×C4×C103—42no—
68C2×C4×C103C22⋊C412yes—
69C2×C4×C103C22×C411yescharacteristic
70C2×C4×C103C2×D412yes—
71C2×C4×C103C2×D411yescharacteristic
72C2×C4×C103#4112yes—
73C2×Dic103—216no—
74C2×Dic103—28no—
75C2×Dic103—24no—
76C103⋊C8—42no—
77C22×C103—24no—
78C22×C103—24no—
79C22×C103—22no—
80C22×C103—22no—
81C22×C103—22no—
82C22×C103—41no—
83C22×C103—42no—
84C22×C103#10414yescomplemented
85C22×C103C2×C22⋊C411yescharacteristic
86C22×C103#12011yescharacteristic
87C22×C103#12311yescharacteristic
88C4×C103—22no—
89C4×C103—41no—
90C4×C103—42no—
91C4×C103C4×D412yes—
92C4×C103#12112yes—
93Dic103—28no—
94C2×C103—21no—
95C2×C103—24no—
96C2×C103—21no—
97C2×C103—81no—
98C2×C103#38611yescharacteristic
99C2×C103C2×#10412yes—
100#1896—1031nomaximal, Sylow
101C103#189611yescharacteristic, complemented, Sylow
102#525D10311yescharacteristic
103C22×C42—1031no—
104C2×#104—1032no—
105#407—1031no—
106#339—1032no—
107C2×#41C2×D10311yescharacteristic
108C23×C4—2061no—
109C23×C4C2×D10311yescharacteristic
110C2×M16—1032no—
111#123—21no—
112C22⋊Q8Dic10312yescomplemented
113#121Dic10312yescomplemented
114#120—21no—
115C4×D4—22no—
116#117C2×D10311yescharacteristic
117C2×C42—1032no—
118C2×C42—2064no—
119C2×C42—2061no—
120#104—2064no—
121C22⋊C8—2062no—
122C24C22⋊D10311yescharacteristic
123#41—22no—
124#41—22no—
125C2×Q8C2×Dic10311yescharacteristic, complemented
126C2×D4—22no—
127C2×D4—21no—
128C2×D4C2×Dic10311yescharacteristic, complemented
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—2064no—
133C22×C4—2068no—
134C22×C4—2062no—
135C22×C4C2×Dic10312yes—
136C22×C4C22⋊D10311yescharacteristic
137C22×C4C22⋊D10312yes—
138C22×C4C22×D10311yescharacteristic
139M16—2062no—
140M16—2062no—
141C2×C8—2062no—
142C4⋊C4—22no—
143C4⋊C4C2×Dic10312yescomplemented
144C22⋊C4—22no—
145C22⋊C4—21no—
146C22⋊C4—22no—
147C42—21no—
148C42—1034no—
149C42—2064no—
150C42—2062no—
151C23—24no—
152C23—21no—
153C23—21no—
154C23—21no—
155C23C22⋊Dic10312yes—
156C23C2×C22⋊D10311yescharacteristic
157Q8—22no—
158D4—22no—
159D4—44no—
160D4—41no—
161D4—41no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—20616no—
170C2×C4—2068no—
171C2×C4—2064no—
172C2×C4C22⋊Dic10312yes—
173C2×C4C22×Dic10311yescharacteristic
174C2×C4D4×D10312yes—
175C2×C4C2×C22⋊D10311yescharacteristic
176C2×C4#1311010412yes—
177C8—4122no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—42no—
184C22—41no—
185C22#1569294814yescomplemented
186C22C2×C22⋊Dic10311yescharacteristic
187C22#1569298911yescharacteristic
188C22#1569300211yescharacteristic
189C4—22no—
190C4—42no—
191C4—41no—
192C4—2068no—
193C4D4×Dic10312yes—
194C4#1569299312yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—81no—
199C2#2026767111yescharacteristic
200C2C2×#1569294812yes—
subgroupG/H
centerC2×C4C2×C22⋊D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting, prime radical#525×C103C2
socleC22×C103C2×C22⋊C4
cosocleC22×C4×C103C23
hypercenter#525D103
hypocenterC103#1896
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic103C2semidirect
2. C2×#15692948C2semidirect
3. #20267755C2semidirect
4. #20267550C2semidirect
16. C22⋊Q8×C103C4semidirect
17. #121×C103C4semidirect
29. C4×Dic103D4semidirect
33. C2×Q8×C103C2×C4semidirect
36. C2×D4×C103C2×C4semidirect
45. C4⋊C4×C103C2×C4semidirect
84. C22×C103#104semidirect
101. C103#1896semidirect
112. C22⋊Q8Dic103semidirect
113. #121Dic103semidirect
125. C2×Q8C2×Dic103semidirect
128. C2×D4C2×Dic103semidirect
143. C4⋊C4C2×Dic103semidirect
185. C22#15692948semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic1032
C2×#156929482
#202677552
#202675502
#525×C1032
#1896103