Finite Group Databasebeta

← #27198329

Subgroups — #27198329

Order 13184.

408 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#15693013C211yesmaximal, characteristic
2#20267688C212yesmaximal
3#20267686C212yesmaximal
4#20267678C212yesmaximal
5#20267676C212yesmaximal
6#20267674C212yesmaximal
7#20267672C212yesmaximal
8#20267657C211yesmaximal, characteristic
9#382×C103C211yesmaximal, characteristic
10#15693013C418yescomplemented
11C2×C4⋊Dic103C2211yescharacteristic
12C2×C4⋊Dic103C2211yescharacteristic
13C2×C4⋊Dic103C2211yescharacteristic
14C2×C4⋊Dic103C2211yescharacteristic
15C2×Dic103⋊C4C2212yes—
16C2×Dic103⋊C4C2212yes—
17C2×Dic103⋊C4C2212yes—
18C2×Dic103⋊C4C2212yes—
19C2×C4×Dic103C2212yes—
20C2×C4×Dic103C2212yes—
21C103⋊#95C2212yes—
22C103⋊#95C2212yes—
23C103⋊#95C2212yes—
24C103⋊#95C2212yes—
25C103⋊#95C2212yes—
26C103⋊#95C2212yes—
27C2×C4⋊C4×C103C2211yescharacteristic
28C2×C4⋊C4×C103C2211yescharacteristic
29C2×C42×C103C2211yescharacteristic
30#95×C103C2212yes—
31#95×C103C2212yes—
32C22×Dic103C2312yes—
33C22×Dic103C2312yes—
34C22×Dic103C2312yes—
35C22×Dic103C2312yes—
36C4⋊Dic103—41no—
37C4⋊Dic103—41no—
38C4⋊Dic103C2×C414yes—
39C4⋊Dic103C2×C414yes—
40Dic103⋊C4—42no—
41Dic103⋊C4—42no—
42Dic103⋊C4C2×C418yes—
43Dic103⋊C4C2×C418yes—
44C4×Dic103—42no—
45C4×Dic103—42no—
46C22×C4×C103C2312yes—
47C22×C4×C103C2312yes—
48C22×C4×C103C2311yescharacteristic
49C22×C4×C103C2311yescharacteristic
50C22×C4×C103C2311yescharacteristic
51C4⋊C4×C103—41no—
52C4⋊C4×C103—41no—
53C42×C103C2×C414yes—
54C23×C103C2411yescharacteristic
55C2×C4×C103—21no—
56C2×C4×C103—21no—
57C2×C4×C103—21no—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—22no—
62C2×C4×C103—22no—
63C2×C4×C103—22no—
64C2×C4×C103—22no—
65C2×C4×C103—22no—
66C2×C4×C103—22no—
67C2×C4×C103C22×C412yes—
68C2×C4×C103C22×C412yes—
69C2×C4×C103C22×C412yes—
70C2×Dic103—22no—
71C2×Dic103—22no—
72C2×Dic103—22no—
73C2×Dic103—22no—
74C2×Dic103—22no—
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103—22no—
78C2×Dic103—22no—
79C2×Dic103—22no—
80C2×Dic103C22×C414yes—
81C2×Dic103C22×C414yes—
82C22×C103C23×C411yescharacteristic
83C22×C103H(5,𝔽2)11yescharacteristic
84C22×C103H(5,𝔽2)11yescharacteristic
85C22×C1032−1+411yescharacteristic
86C22×C1032−1+411yescharacteristic
87C22×C1032−1+411yescharacteristic
88C22×C1032−1+411yescharacteristic
89C4×C103—22no—
90C4×C103—22no—
91C4×C103—22no—
92C4×C103—42no—
93C4×C103—42no—
94Dic103—24no—
95Dic103—24no—
96Dic103—42no—
97Dic103—42no—
98C2×C103#51911yescharacteristic
99C2×C103#52011yescharacteristic
100C2×C103#52011yescharacteristic
101C2×C103#56211yescharacteristic
102C2×C103#56311yescharacteristic
103C2×C103#56311yescharacteristic
104C2×C103#56411yescharacteristic
105#2382—1031nomaximal, Sylow
106C103#238211yescharacteristic, complemented, Sylow
107C2×#125—1031no—
108#389—1032no—
109#389—1032no—
110#387—1032no—
111#387—1032no—
112#387—1032no—
113#387—1032no—
114#382—1031no—
115#382D10311yescharacteristic
116#125—1038no—
117C2×C4⋊C4—1031no—
118C2×C4⋊C4—1031no—
119C2×C4⋊C4—1032no—
120C2×C4⋊C4—1032no—
121C2×C4⋊C4—1031no—
122C2×C4⋊C4—1031no—
123C2×C4⋊C4—1032no—
124C2×C4⋊C4—1032no—
125C2×C4⋊C4C2×D10311yescharacteristic
126C2×C4⋊C4C2×D10311yescharacteristic
127C2×C42—1032no—
128C2×C42—1032no—
129C2×C42C2×D10311yescharacteristic
130#95—1032no—
131#95—1032no—
132#95—1032no—
133#95—1032no—
134#95—1032no—
135#95—1032no—
136#95C2×D10312yes—
137#95C2×D10312yes—
138C22×C4—1032no—
139C22×C4—1032no—
140C22×C4—1032no—
141C22×C4—1032no—
142C22×C4C22×D10312yes—
143C22×C4C22×D10312yes—
144C22×C4C22×D10311yescharacteristic
145C22×C4C22×D10311yescharacteristic
146C22×C4C22×D10311yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—1038no—
150C4⋊C4—1038no—
151C4⋊C4—1034no—
152C4⋊C4—1034no—
153C4⋊C4—4122no—
154C4⋊C4—4122no—
155C4⋊C4—4121no—
156C4⋊C4—4121no—
157C42—4122no—
158C42—4122no—
159C42C4×D10314yes—
160C23C23×D10311yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—1034no—
174C2×C4—1034no—
175C2×C4—2062no—
176C2×C4—2062no—
177C2×C4—2062no—
178C2×C4—2062no—
179C2×C4—2062no—
180C2×C4—2062no—
181C2×C4—2062no—
182C2×C4—2062no—
183C2×C4—2062no—
184C2×C4—2062no—
185C2×C4C2×C4×D10312yes—
186C2×C4C2×C4×D10312yes—
187C2×C4C2×C4×D10312yes—
188C22C22×C4×D10311yescharacteristic
189C22#1569306611yescharacteristic
190C22#1569306711yescharacteristic
191C22#1569306811yescharacteristic
192C22#1569306811yescharacteristic
193C22#1569306811yescharacteristic
194C22#1569306911yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—4122no—
201C4—4122no—
202C4—2064no—
203C4—2064no—
204C2#2026826811yescharacteristic
205C2#2026827111yescharacteristic
206C2#2026827211yescharacteristic
207C2#2026853511yescharacteristic
208C2#2026854111yescharacteristic
209C2#2026854511yescharacteristic
210C2C103⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#382×C103C2
socle, prime radical, cosocleC23×C103C24
hypercenter#382D103
hypocenterC103#2382
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #15693013C4semidirect
106. C103#2382semidirect

Maximal subgroups

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

subgroupindex
C2×#156930132
#202676882
#202676862
#202676782
#202676762
#202676742
#202676722
#202676572
#382×C1032
#2382103