Finite Group Databasebeta

← #27206615

Subgroups — #27206615

Order 13184.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#20268412C212yesmaximal, complemented
2#20268082C212yesmaximal, complemented
3#20268077C212yesmaximal, complemented
4#20268049C211yesmaximal, characteristic, complemented
5#20268044C211yesmaximal, characteristic
6#20268020C212yesmaximal, complemented
7#20268014C212yesmaximal, complemented
8#20268007C212yesmaximal, complemented
9#424×C103C211yesmaximal, characteristic, complemented
10C2×Dic412C2211yescharacteristic
11C2×#13110094C2212yes—
12C2×D824C2211yescharacteristic
13#15693021C2212yes—
14#15693016—22no—
15#15693009C2212yes—
16#15693007—22no—
17#15693003—22no—
18#15693000C2212yes—
19#15692999—22no—
20#15692995C2212yes—
21C4×Dic206C2212yes—
22C4×D412C2212yes—
23#15692953C2211yescharacteristic
24#15692953C2211yescharacteristic
25#15692953C2212yes—
26#15692946C2212yes—
27#15692946C2212yes—
28#15692943C2212yes—
29#15692943C2212yes—
30C2×M16×C103C2211yescharacteristic
31C22×C8×C103C2211yescharacteristic
32#117×C103C2211yescharacteristic
33C4⋊C8×C103C2212yes—
34C4⋊C8×C103C2212yes—
35C2×Dic206—22no—
36C2×Dic206C2312yes—
37C2×D412C2312yes—
38C2×C22⋊D103—22no—
39C2×C4×D103—22no—
40Dic412—41no—
41#13110094—42no—
42D824—41no—
43C4⋊Dic103—22no—
44C4⋊Dic103C2312yes—
45C4⋊Dic103C2312yes—
46Dic103⋊C4—22no—
47Dic103⋊C4—22no—
48C22⋊Dic103—22no—
49(C2×D103)⋊C4—22no—
50(C2×D103)⋊C4—22no—
51(C2×D103)⋊C4—22no—
52(C2×D103)⋊C4—22no—
53C4×Dic103—22no—
54C22×C4×C103C2311yescharacteristic
55M16×C103—41no—
56C2×C8×C103—41no—
57C2×C8×C103C2312yes—
58C2×C8×C103C2311yescharacteristic
59C2×C8×C103C2311yescharacteristic
60C4⋊C4×C103D412yes—
61C22⋊C4×C103D411yescharacteristic
62C22⋊C4×C103D411yescharacteristic
63C42×C103C2312yes—
64C23×C103C2×D411yescharacteristic
65C22×D103—22no—
66C2×C4×C103—21no—
67C2×C4×C103—21no—
68C2×C4×C103C2×D412yes—
69C2×C4×C103C2×D412yes—
70C2×C4×C103C2×D411yescharacteristic
71C2×C4×C103C2411yescharacteristic
72C22⋊D103—82no—
73C2×Dic103—22no—
74C2×Dic103—22no—
75C2×Dic103—22no—
76D412—22no—
77D412—22no—
78C4×D103—82no—
79Dic206—22no—
80Dic206—22no—
81Dic206—82no—
82C8×C103—22no—
83C8×C103—21no—
84C8×C103—21no—
85C22×C103—21no—
86C22×C103—22no—
87C22×C103C22×D411yescharacteristic
88C2×D103—42no—
89C2×D103—42no—
90C2×D103—42no—
91C4×C103—21no—
92C4×C103—22no—
93C4×C103—22no—
94C4×C103H(5,𝔽2)11yescharacteristic
95C4×C1032−1+411yescharacteristic
96Dic103—42no—
97Dic103—42no—
98Dic103—42no—
99C2×C103—41no—
100C2×C103#53711yescharacteristic
101C2×C103#57712yes—
102D103—82no—
103#3263—1031nomaximal, Sylow
104C103#326311yescharacteristic, complemented, Sylow
105#542—1032no—
106#476—1032no—
107#475—1032no—
108#470—1031no—
109#469—1031no—
110#465—1032no—
111#464—1032no—
112#463—1032no—
113#424D10311yescharacteristic, complemented
114C2×Q16—1031no—
115C2×SD16—1032no—
116C2×D8—1031no—
117C2×M16C2×D10311yescharacteristic
118C22×C8C2×D10311yescharacteristic
119C4⋊Q8—1032no—
120#126—2062no—
121#124—1032no—
122#124—2062no—
123#123—2062no—
124C22⋊Q8—1032no—
125C22⋊Q8—2062no—
126#121—1032no—
127C4×Q8—1032no—
128C4×D4—1032no—
129#117C2×D10311yescharacteristic
130#106—1032no—
131#106—1031no—
132#106—1031no—
133C4⋊C8C2×D10312yes—
134C4⋊C8C2×D10312yes—
135#103—1032no—
136#103—1032no—
137#102—1032no—
138#102—1032no—
139C2×Q8—1032no—
140C2×Q8—2062no—
141C2×D4—1032no—
142C2×D4—2062no—
143C22×C4—2062no—
144C22×C4C22×D10311yescharacteristic
145Q16—4121no—
146SD16—4122no—
147D8—4121no—
148M16—41no—
149C2×C8—41no—
150C2×C8C22×D10311yescharacteristic
151C2×C8C22×D10312yes—
152C2×C8C22×D10311yescharacteristic
153C4⋊C4—1032no—
154C4⋊C4—1032no—
155C4⋊C4—2062no—
156C4⋊C4—2062no—
157C4⋊C4—2062no—
158C4⋊C4D41212yes—
159C22⋊C4—2062no—
160C22⋊C4—2062no—
161C22⋊C4—2062no—
162C22⋊C4—2062no—
163C22⋊C4—2062no—
164C22⋊C4D41211yescharacteristic
165C22⋊C4D41211yescharacteristic
166C42—2062no—
167C42C22×D10312yes—
168C23—2062no—
169C23C2×D41211yescharacteristic
170Q8—8242no—
171Q8—2062no—
172Q8—2062no—
173D4—8242no—
174D4—2062no—
175D4—2062no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—8242no—
179C2×C4—2062no—
180C2×C4—2062no—
181C2×C4—2062no—
182C2×C4C2×D41212yes—
183C2×C4C2×D41212yes—
184C2×C4C2×D41211yescharacteristic
185C2×C4C23×D10311yescharacteristic
186C8—22no—
187C8—21no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—4122no—
192C22—4122no—
193C22—4122no—
194C22C22×D41211yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—4122no—
199C4—4122no—
200C4—4122no—
201C4#1569306611yescharacteristic
202C4#1569306911yescharacteristic
203C2—41no—
204C2—8242no—
205C2#2026837211yescharacteristic
206C2#2026860312yes—
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#424×C103C2
socleC22×C103C22×D4
prime radical#20268044C2
hypercenter#424D103
hypocenterC103#3263
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #20268412C2semidirect
2. #20268082C2semidirect
3. #20268077C2semidirect
4. #20268049C2semidirect
6. #20268020C2semidirect
7. #20268014C2semidirect
8. #20268007C2semidirect
9. #424×C103C2semidirect
104. C103#3263semidirect
113. #424D103semidirect

Maximal subgroups

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

subgroupindex
#202684122
#202680822
#202680772
#202680492
#202680442
#202680202
#202680142
#202680072
#424×C1032
#3263103