Finite Group Databasebeta

← #27195592

Subgroups — #27195592

Order 13184.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#20268302C211yesmaximal, characteristic
2C2×#15692949C212yesmaximal, complemented
3#20267755C211yesmaximal, characteristic, complemented
4#20267551C212yesmaximal, complemented
5C2×#117×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C2211yescharacteristic
7C2×#13110089C2212yes—
8#15693004—21no—
9#15693000C412yescomplemented
10#15692995C412yescomplemented
11#15692990—21no—
12C4×C22⋊D103—22no—
13#15692980C2211yescharacteristic
14#15692949—24no—
15C22⋊(C103⋊C8)—22no—
16C23×C4×C103C2211yescharacteristic
17#117×C103—24no—
18C2×C4⋊C4×C103—21no—
19C2×C22⋊C4×C103—21no—
20C2×C42×C103C2212yes—
21#13110105—22no—
22#13110105—22no—
23C2×Dic206C2×C411yescharacteristic
24C2×D412C2×C411yescharacteristic
25C2×C22⋊D103—22no—
26C2×C22⋊D103—21no—
27C2×C4×D103—21no—
28#13110089—22no—
29#13110089—22no—
30C2×C103⋊C8—22no—
31C4⋊Dic103C2×C412yes—
32Dic103⋊C4—22no—
33C22⋊Dic103—22no—
34C22⋊Dic103—21no—
35(C2×D103)⋊C4—22no—
36C4×Dic103—21no—
37C24×C103D411yescharacteristic
38C22×C4×C103—22no—
39C22×C4×C103—22no—
40C22×C4×C103—22no—
41C22×C4×C103C2×C412yes—
42C22×C4×C103D412yes—
43C22×C4×C103D411yescharacteristic
44C22×C4×C103C2311yescharacteristic
45C4⋊C4×C103—24no—
46C22⋊C4×C103—24no—
47C42×C103—22no—
48C42×C103D414yescomplemented
49C23×C103—21no—
50C23×C103—21no—
51C23×C103—42no—
52C23×C103C22⋊C412yes—
53C23×C103C2×D411yescharacteristic
54C22×D103—21no—
55C2×C4×C103—21no—
56C2×C4×C103—21no—
57C2×C4×C103—24no—
58C2×C4×C103—24no—
59C2×C4×C103—24no—
60C2×C4×C103—44no—
61C2×C4×C103C22⋊C412yes—
62C2×C4×C103C22×C411yescharacteristic
63C2×C4×C103C2×D412yes—
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103#4112yes—
66C22⋊D103—44no—
67C22⋊D103—41no—
68C22⋊D103—41no—
69C2×Dic103—22no—
70C2×Dic103—21no—
71D412—22no—
72C4×D103—42no—
73Dic206—22no—
74C103⋊C8—42no—
75C22×C103—22no—
76C22×C103—22no—
77C22×C103—22no—
78C22×C103—22no—
79C22×C103—42no—
80C22×C103—42no—
81C22×C103C2×C22⋊C411yescharacteristic
82C22×C103#12011yescharacteristic
83C22×C103#12311yescharacteristic
84C2×D103—41no—
85C2×D103—42no—
86C4×C103—22no—
87C4×C103—44no—
88C4×C103C4×D412yes—
89C4×C103#12112yes—
90Dic103—41no—
91Dic103—42no—
92C2×C103—21no—
93C2×C103—21no—
94C2×C103—42no—
95C2×C103#38611yescharacteristic
96C2×C103#42112yes—
97D103—81no—
98#1897—1031nomaximal, Sylow
99C103#189711yescharacteristic, complemented, Sylow
100#525—1031no—
101C2×#117D10311yescharacteristic, complemented
102C2×#104—1032no—
103#407—1031no—
104#339—1032no—
105C2×#41—1031no—
106C23×C4C2×D10311yescharacteristic
107C2×M16—1032no—
108#123—2061no—
109C22⋊Q8—1032no—
110#121—1032no—
111#120—2061no—
112C4×D4—2062no—
113#117—24no—
114#117—1031no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D10312yes—
118#104—2064no—
119C22⋊C8—2062no—
120C24C22⋊D10311yescharacteristic
121#41—2062no—
122#41—2062no—
123C2×Q8—1031no—
124C2×D4—1031no—
125C2×D4—2062no—
126C2×D4—2061no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—2061no—
131C22×C4C4×D10312yes—
132C22×C4D41212yes—
133C22×C4C22⋊D10311yescharacteristic
134C22×C4C22×D10311yescharacteristic
135M16—2062no—
136M16—2062no—
137C2×C8—2062no—
138C4⋊C4—24no—
139C4⋊C4—1032no—
140C4⋊C4—2062no—
141C22⋊C4—24no—
142C22⋊C4—2062no—
143C22⋊C4—2061no—
144C22⋊C4—2062no—
145C42—22no—
146C42—2061no—
147C42C22⋊D10314yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—2061no—
152C23(C2×D103)⋊C412yes—
153C23C2×C22⋊D10311yescharacteristic
154Q8—2062no—
155D4—4124no—
156D4—4121no—
157D4—4121no—
158D4—2062no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—4122no—
166C2×C4—2062no—
167C2×C4—2061no—
168C2×C4(C2×D103)⋊C412yes—
169C2×C4C2×C4×D10311yescharacteristic
170C2×C4C2×C22⋊D10312yes—
171C2×C4C2×D41211yescharacteristic
172C2×C4#1311010512yes—
173C8—4122no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—4122no—
181C22—4121no—
182C22C2×(C2×D103)⋊C411yescharacteristic
183C22#1569299011yescharacteristic
184C22#1569300411yescharacteristic
185C4—22no—
186C4—44no—
187C4—4122no—
188C4—4121no—
189C4C4×C22⋊D10312yes—
190C4#1569299512yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—8241no—
195C2#2026767011yescharacteristic
196C2#2026780912yes—
subgroupG/H
centerC2×C4C2×D412
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×#117×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268302C2
cosocleC22×C4×C103C23
hypercenterC2×#117D103
hypocenterC103#1897
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#15692949C2semidirect
3. #20267755C2semidirect
4. #20267551C2semidirect
5. C2×#117×C103C2semidirect
9. #15693000C4semidirect
10. #15692995C4semidirect
48. C42×C103D4semidirect
99. C103#1897semidirect
101. C2×#117D103semidirect
147. C42C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
C2×#156929492
#202677552
#202675512
C2×#117×C1032
#1897103