Finite Group Databasebeta

← #28365838

Subgroups — #28365838

Order 13952.

428 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 217 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#20294925C212yesmaximal
2#20294912C212yesmaximal
3#20294912C212yesmaximal
4#20294912C212yesmaximal
5#20294912C212yesmaximal
6#20294894C211yesmaximal, characteristic
7C4⋊C4×Dic109C212yesmaximal
8C4×C4⋊Dic109C211yesmaximal, characteristic
9C2×#125×C109C211yesmaximal, characteristic
10C2×C4⋊Dic109C2212yes—
11C2×C4⋊Dic109C2212yes—
12C2×C4⋊Dic109C2212yes—
13C2×C4×Dic109C2212yes—
14C2×C4×Dic109C2211yescharacteristic
15C2×C4×Dic109C2212yes—
16C2×C4×Dic109C2211yescharacteristic
17#16812606C2212yes—
18#16812606C2212yes—
19#16812606C2212yes—
20#16812606C2212yes—
21#16812606C2212yes—
22#16812606C2212yes—
23#16812606C2211yescharacteristic
24#16812606C2212yes—
25#16812606C2211yescharacteristic
26#125×C109C418yescomplemented
27C2×C4⋊C4×C109C2211yescharacteristic
28C2×C4⋊C4×C109C2211yescharacteristic
29C2×C4⋊C4×C109C2212yes—
30C2×C4⋊C4×C109C2212yes—
31C2×C42×C109C2211yescharacteristic
32C22×Dic109C2312yes—
33C22×Dic109C2312yes—
34C22×Dic109C2312yes—
35C22×Dic109C2312yes—
36C4⋊Dic109—24no—
37C4⋊Dic109—24no—
38C4⋊Dic109—42no—
39C4×Dic109—24no—
40C4×Dic109—41no—
41C4×Dic109—42no—
42C4×Dic109—41no—
43C22×C4×C109C2311yescharacteristic
44C22×C4×C109C2311yescharacteristic
45C22×C4×C109C2311yescharacteristic
46C22×C4×C109C2312yes—
47C22×C4×C109C2312yes—
48C4⋊C4×C109C2×C414yes—
49C4⋊C4×C109C2×C414yes—
50C4⋊C4×C109C2×C418yes—
51C4⋊C4×C109C2×C418yes—
52C42×C109C2×C414yes—
53C23×C109C2411yescharacteristic
54C2×C4×C109—22no—
55C2×C4×C109—22no—
56C2×C4×C109—22no—
57C2×C4×C109—21no—
58C2×C4×C109—22no—
59C2×C4×C109—21no—
60C2×C4×C109—22no—
61C2×C4×C109—22no—
62C2×C4×C109C22×C412yes—
63C2×C4×C109C22×C412yes—
64C2×C4×C109C22×C412yes—
65C2×C4×C109C22×C414yes—
66C2×C4×C109C22×C414yes—
67C2×Dic109—22no—
68C2×Dic109—22no—
69C2×Dic109—22no—
70C2×Dic109—22no—
71C2×Dic109—22no—
72C2×Dic109—22no—
73C2×Dic109—22no—
74C2×Dic109—22no—
75C2×Dic109—22no—
76C2×Dic109—22no—
77C2×Dic109—22no—
78C2×Dic109#4114yes—
79C22×C109C23×C411yescharacteristic
80C22×C109C2×#4112yes—
81C22×C109H(5,𝔽2)11yescharacteristic
82C22×C1092−1+411yescharacteristic
83C22×C1092−1+412yes—
84C4×C109—24no—
85C4×C109—22no—
86C4×C109—22no—
87C4×C109—22no—
88C4×C109—24no—
89Dic109—24no—
90Dic109—42no—
91Dic109—42no—
92Dic109—42no—
93C2×C109C4×#4111yescharacteristic
94C2×C109#51911yescharacteristic
95C2×C109#52011yescharacteristic
96C2×C109#53912yes—
97C2×C109#54112yes—
98#2336—1091nomaximal, Sylow
99C109#233611yescharacteristic, complemented, Sylow
100C2×#125D10911yescharacteristic
101#389—1092no—
102#387—1092no—
103#387—1092no—
104#387—1092no—
105#387—1092no—
106#383—1091no—
107C4×C4⋊C4—1092no—
108C4×C4⋊C4—1091no—
109#125Dic10918yescomplemented
110C2×C4⋊C4—1092no—
111C2×C4⋊C4—1092no—
112C2×C4⋊C4—1092no—
113C2×C4⋊C4C2×D10912yes—
114C2×C4⋊C4C2×D10911yescharacteristic
115C2×C4⋊C4C2×D10911yescharacteristic
116C2×C4⋊C4C2×D10912yes—
117C2×C42—1091no—
118C2×C42—1091no—
119C2×C42—1092no—
120C2×C42—1092no—
121C2×C42C2×D10911yescharacteristic
122#95—1092no—
123#95—1092no—
124#95—1092no—
125#95—1091no—
126#95—1092no—
127#95—1091no—
128#95—1092no—
129#95—1092no—
130#95—1092no—
131C22×C4—1092no—
132C22×C4—1092no—
133C22×C4—1092no—
134C22×C4—1092no—
135C22×C4C22×D10911yescharacteristic
136C22×C4C22×D10911yescharacteristic
137C22×C4C22×D10912yes—
138C22×C4C22×D10912yes—
139C22×C4C22×D10911yescharacteristic
140C4⋊C4—4362no—
141C4⋊C4—2184no—
142C4⋊C4—2184no—
143C4⋊C4C2×Dic10918yes—
144C4⋊C4C2×Dic10914yes—
145C4⋊C4C2×Dic10914yes—
146C4⋊C4C2×Dic10918yes—
147C42—4361no—
148C42—4361no—
149C42—4362no—
150C42—2184no—
151C42C2×Dic10914yes—
152C23C23×D10911yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—1094no—
162C2×C4—2182no—
163C2×C4—2182no—
164C2×C4—2182no—
165C2×C4—2182no—
166C2×C4—2182no—
167C2×C4—2182no—
168C2×C4—2182no—
169C2×C4—2182no—
170C2×C4—2182no—
171C2×C4—2182no—
172C2×C4—2182no—
173C2×C4C22×Dic10912yes—
174C2×C4C22×Dic10912yes—
175C2×C4C22×Dic10912yes—
176C2×C4C22×Dic10914yes—
177C2×C4C22×Dic10914yes—
178C22C23×Dic10911yescharacteristic
179C22#41×D10912yes—
180C22#1681274511yescharacteristic
181C22#1681274611yescharacteristic
182C22#1681274712yes—
183C4—24no—
184C4—22no—
185C4—22no—
186C4—22no—
187C4—24no—
188C4—4362no—
189C4—4362no—
190C4—4362no—
191C4—2184no—
192C2#41×Dic10911yescharacteristic
193C2#2029550411yescharacteristic
194C2#2029550911yescharacteristic
195C2#2029562412yes—
196C2#2029563512yes—
subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
FittingC2×#125×C109C2
socle, prime radical, cosocleC23×C109C24
hypercenterC2×#125D109
hypocenterC109#2336
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
26. #125×C109C4semidirect
99. C109#2336semidirect
109. #125Dic109semidirect

Maximal subgroups

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

subgroupindex
#202949252
#202949122
#202948942
C4⋊C4×Dic1092
C4×C4⋊Dic1092
C2×#125×C1092
#2336109