Finite Group Databasebeta

← #27203417

Subgroups — #27203417

Order 13184.

356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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#20267732C212yesmaximal
2#20267731C212yesmaximal
3#20267730C211yesmaximal, characteristic
4#20267712C212yesmaximal
5#20267712C212yesmaximal
6#20267711C212yesmaximal
7#20267656C211yesmaximal, characteristic
8#20267655C212yesmaximal
9#400×C103C211yesmaximal, characteristic
10C22×Dic206C2212yes—
11C2×C4⋊Dic103C2211yescharacteristic
12C2×C4⋊Dic103C2211yescharacteristic
13C2×C4⋊Dic103C2212yes—
14C2×Dic103⋊C4C2212yes—
15C2×Dic103⋊C4C2212yes—
16C2×Dic103⋊C4C2212yes—
17C2×C4×Dic103C2211yescharacteristic
18C103⋊#95C2212yes—
19C103⋊#95C2212yes—
20C103⋊#95C2212yes—
21C103⋊#95C2212yes—
22C103⋊#95C2212yes—
23C103⋊#95C2212yes—
24C103⋊#95C2212yes—
25C103⋊#95C2211yescharacteristic
26C2×C4⋊C4×C103C2211yescharacteristic
27C2×C4⋊C4×C103C2211yescharacteristic
28#95×C103C2212yes—
29#95×C103C2212yes—
30#95×C103C2211yescharacteristic
31C2×Dic206—42no—
32C2×Dic206—42no—
33C2×Dic206—42no—
34C22×Dic103C2312yes—
35C22×Dic103C2312yes—
36C22×Dic103C2312yes—
37C22×Dic103C2312yes—
38C4⋊Dic103—41no—
39C4⋊Dic103—41no—
40C4⋊Dic103—42no—
41Dic103⋊C4—42no—
42Dic103⋊C4—42no—
43Dic103⋊C4—42no—
44C4×Dic103Q814yescomplemented
45C22×C4×C103C2312yes—
46C22×C4×C103C2312yes—
47C22×C4×C103C2311yescharacteristic
48C22×C4×C103C2311yescharacteristic
49C22×C4×C103C2311yescharacteristic
50C4⋊C4×C103—41no—
51C4⋊C4×C103—41no—
52C23×C103C2411yescharacteristic
53C2×C4×C103—21no—
54C2×C4×C103—21no—
55C2×C4×C103—21no—
56C2×C4×C103—21no—
57C2×C4×C103—22no—
58C2×C4×C103—22no—
59C2×C4×C103—22no—
60C2×C4×C103—22no—
61C2×C4×C103—22no—
62C2×C4×C103—22no—
63C2×C4×C103—22no—
64C2×C4×C103—22no—
65C2×C4×C103C2×Q812yes—
66C2×Dic103—22no—
67C2×Dic103—22no—
68C2×Dic103—22no—
69C2×Dic103—22no—
70C2×Dic103—22no—
71C2×Dic103—22no—
72C2×Dic103—22no—
73C2×Dic103—22no—
74C2×Dic103—22no—
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103C2×Q814yes—
78Dic206—48no—
79C22×C103C22×Q811yescharacteristic
80C22×C103H(5,𝔽2)11yescharacteristic
81C22×C103H(5,𝔽2)12yes—
82C22×C1032−1+412yes—
83C22×C1032−1+411yescharacteristic
84C4×C103—22no—
85C4×C103—42no—
86C4×C103—41no—
87C4×C103—41no—
88C4×C103—42no—
89Dic103—24no—
90Dic103—42no—
91Dic103—42no—
92Dic103—42no—
93C2×C103#54411yescharacteristic
94C2×C103#54412yes—
95C2×C103H(3,𝔽4)11yescharacteristic
96C2×C103#56311yescharacteristic
97C2×C103#56312yes—
98#2844—1031nomaximal, Sylow
99C103#284411yescharacteristic, complemented, Sylow
100#400—1031no—
101#400—1032no—
102#400—1032no—
103#400D10311yescharacteristic
104#395—1032no—
105#395—1032no—
106#395—1032no—
107#382—1031no—
108#382—1032no—
109C22×Q8—1032no—
110C2×C4⋊C4—1032no—
111C2×C4⋊C4—1031no—
112C2×C4⋊C4—1032no—
113C2×C4⋊C4—1032no—
114C2×C4⋊C4—1031no—
115C2×C4⋊C4—1032no—
116C2×C4⋊C4C2×D10311yescharacteristic
117C2×C4⋊C4C2×D10311yescharacteristic
118C2×C42—1031no—
119#95—1032no—
120#95—1032no—
121#95—1032no—
122#95—1032no—
123#95—1032no—
124#95—1032no—
125#95—1032no—
126#95—1031no—
127#95C2×D10312yes—
128#95C2×D10312yes—
129#95C2×D10311yescharacteristic
130C2×Q8—4122no—
131C2×Q8—4122no—
132C2×Q8—4122no—
133C22×C4—1032no—
134C22×C4—1032no—
135C22×C4—1032no—
136C22×C4—1032no—
137C22×C4C22×D10311yescharacteristic
138C22×C4C22×D10311yescharacteristic
139C22×C4C22×D10312yes—
140C22×C4C22×D10312yes—
141C22×C4C22×D10311yescharacteristic
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—4122no—
145C4⋊C4—4122no—
146C4⋊C4—4122no—
147C4⋊C4—4121no—
148C4⋊C4—4121no—
149C4⋊C4—4122no—
150C42—1034no—
151C23C23×D10311yescharacteristic
152Q8—4128no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—1034no—
166C2×C4—2062no—
167C2×C4—2062no—
168C2×C4—2062no—
169C2×C4—2062no—
170C2×C4—2062no—
171C2×C4—2062no—
172C2×C4—2062no—
173C2×C4—2062no—
174C2×C4—2062no—
175C2×C4—2062no—
176C2×C4—2062no—
177C2×C4Q8×D10312yes—
178C22C2×Q8×D10311yescharacteristic
179C22#1569306611yescharacteristic
180C22#1569306712yes—
181C22#1569306812yes—
182C22#1569306811yescharacteristic
183C4—22no—
184C4—41no—
185C4—41no—
186C4—42no—
187C4—42no—
188C4—4122no—
189C4—4122no—
190C4—4122no—
191C4—2064no—
192C2#2026842011yescharacteristic
193C2#2026842112yes—
194C2#2026853311yescharacteristic
195C2#2026854312yes—
196C2#2026854411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutator, socle, prime radical, cosocleC23×C103C24
Fitting#400×C103C2
hypercenter#400D103
hypocenterC103#2844
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic103Q8semidirect
99. C103#2844semidirect

Maximal subgroups

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

subgroupindex
#202677322
#202677312
#202677302
#202677122
#202677112
#202676562
#202676552
#400×C1032
#2844103