Finite Group Databasebeta

← #28365608

Subgroups — #28365608

Order 13952.

1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C23×C22⋊D109C211yesmaximal, characteristic
2C2×C22⋊C4×D109C212yesmaximal, complemented
3#20294902C218yesmaximal, complemented
4#20294887C212yesmaximal, complemented
5#20294882C211yesmaximal, characteristic, complemented
6#379×C109C211yesmaximal, characteristic, complemented
7C24×D109C2211yescharacteristic
8C22×C22⋊D109—28no—
9C22×C22⋊D109C418yescomplemented
10C22×C22⋊D109C2214yes—
11C23×Dic109C2211yescharacteristic
12C22×C4×D109C2214yescomplemented
13C2×C22⋊Dic109C2212yes—
14C2×C22⋊Dic109C2214yescomplemented
15C2×#13182006C2214yescomplemented
16C22⋊C4×D109—28no—
17#16812606C2218yescomplemented
18C25×C109C2211yescharacteristic
19C2×C22⋊C4×C109C2212yes—
20C2×C22⋊C4×C109C2214yescomplemented
21C23×D109—44no—
22C23×D109C2×C414yes—
23C23×D109D418yes—
24C23×D109C2312yes—
25C2×C22⋊D109—232no—
26C2×C22⋊D109—28no—
27C2×C22⋊D109—28no—
28C2×C22⋊D109C2×C4116yescomplemented
29C22×Dic109—24no—
30C22×Dic109C2×C414yescomplemented
31C22×Dic109C2314yes—
32C22×Dic109C2312yes—
33C2×C4×D109—28no—
34C2×C4×D109—48no—
35C22⋊Dic109—24no—
36C22⋊Dic109—44no—
37#13182006—28no—
38C24×C109—24no—
39C24×C109—44no—
40C24×C109C2×C414yescomplemented
41C24×C109C2312yes—
42C24×C109C2311yescharacteristic
43C22×C4×C109C2314yes—
44C22⋊C4×C109—24no—
45C22⋊C4×C109—44no—
46C23×C109—24no—
47C23×C109—28no—
48C23×C109—24no—
49C23×C109—24no—
50C23×C109—24no—
51C23×C109—48no—
52C23×C109—416no—
53C23×C109C22×C414yes—
54C23×C109C22×C412yes—
55C23×C109C2×D414yes—
56C23×C109C2411yescharacteristic
57C22×D109—28no—
58C22×D109—48no—
59C22×D109—416no—
60C22×D109C22⋊C4116yescomplemented
61C22×D109C22×C414yes—
62C22×D109C2×D414yes—
63C22×D109C2×D414yes—
64C2×C4×C109—24no—
65C2×C4×C109—28no—
66C22⋊D109—232no—
67C2×Dic109—28no—
68C2×Dic109—24no—
69C2×Dic109—24no—
70C2×Dic109—28no—
71C2×Dic109C22×C414yes—
72C4×D109—416no—
73C22×C109—24no—
74C22×C109—28no—
75C22×C109—24no—
76C22×C109—24no—
77C22×C109—24no—
78C22×C109—416no—
79C22×C109—48no—
80C22×C109C2×C22⋊C414yes—
81C22×C109C23×C411yescharacteristic
82C22×C109C22×D412yes—
83C22×C109H(5,𝔽2)14yes—
84C2×D109—28no—
85C2×D109—28no—
86C2×D109—28no—
87C2×D109—416no—
88C2×D109C2×C22⋊C418yes—
89C4×C109—44no—
90Dic109—24no—
91Dic109—44no—
92C2×C109—24no—
93C2×C109—44no—
94C2×C109C22×C22⋊C411yescharacteristic
95C2×C109#51812yes—
96C2×C109#53414yes—
97D109—28no—
98#2308—1091nomaximal, Sylow
99C109#230811yescharacteristic, complemented, Sylow
100C23×D4—1091no—
101C22×C22⋊C4—1092no—
102#386—1098no—
103#381—1092no—
104#379—1091no—
105#379D10911yescharacteristic, complemented
106C25—1091no—
107C25C2×D10911yescharacteristic
108C22×D4—1098no—
109C22×D4—1094no—
110C22×D4—2188no—
111C23×C4—1091no—
112C23×C4—1094no—
113C2×C22⋊C4—1094no—
114C2×C22⋊C4—1092no—
115C2×C22⋊C4—1094no—
116C2×C22⋊C4—2188no—
117C2×C22⋊C4C2×D10912yes—
118C2×C22⋊C4C2×D10914yescomplemented
119#95—1098no—
120C24—24no—
121C24—44no—
122C24—1094no—
123C24—1098no—
124C24—1092no—
125C24—4364no—
126C24C4×D10914yescomplemented
127C24C22×D10912yes—
128C24C22×D10911yescharacteristic
129C2×D4—10916no—
130C2×D4—21832no—
131C2×D4—2188no—
132C2×D4—2188no—
133C22×C4—1094no—
134C22×C4—1092no—
135C22×C4—1094no—
136C22×C4—4368no—
137C22×C4—2188no—
138C22×C4—2184no—
139C22×C4C22×D10914yes—
140C22⋊C4—24no—
141C22⋊C4—44no—
142C22⋊C4—4364no—
143C22⋊C4—2188no—
144C22⋊C4—2184no—
145C23—24no—
146C23—28no—
147C23—24no—
148C23—24no—
149C23—24no—
150C23—48no—
151C23—416no—
152C23—10916no—
153C23—1094no—
154C23—1094no—
155C23—1094no—
156C23—4368no—
157C23—43616no—
158C23—2188no—
159C23C2×C4×D10914yes—
160C23C2×C4×D10912yes—
161C23D4×D10914yes—
162C23C23×D10911yescharacteristic
163D4—21832no—
164C2×C4—24no—
165C2×C4—28no—
166C2×C4—1094no—
167C2×C4—43616no—
168C2×C4—2184no—
169C2×C4—2188no—
170C2×C4—2188no—
171C2×C4—2184no—
172C22—24no—
173C22—28no—
174C22—24no—
175C22—24no—
176C22—24no—
177C22—416no—
178C22—48no—
179C22—1098no—
180C22—43616no—
181C22—2188no—
182C22—2188no—
183C22—2188no—
184C22C22⋊C4×D10914yes—
185C22C22×C4×D10911yescharacteristic
186C22C2×D4×D10912yes—
187C22#1681274414yes—
188C4—44no—
189C4—4364no—
190C4—2184no—
191C2—24no—
192C2—44no—
193C2—2188no—
194C2C2×C22⋊C4×D10911yescharacteristic
195C2#2029549912yes—
196C2#2029558614yes—
subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
Fitting#379×C109C2
socle, cosocleC23×C109C24
prime radicalC23×C22⋊D109C2
hypercenter#379D109
hypocenterC109#2308
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D109C2semidirect
3. #20294902C2semidirect
4. #20294887C2semidirect
5. #20294882C2semidirect
6. #379×C109C2semidirect
9. C22×C22⋊D109C4semidirect
12. C22×C4×D109C22semidirect
14. C2×C22⋊Dic109C22semidirect
15. C2×#13182006C22semidirect
17. #16812606C22semidirect
20. C2×C22⋊C4×C109C22semidirect
28. C2×C22⋊D109C2×C4semidirect
30. C22×Dic109C2×C4semidirect
40. C24×C109C2×C4semidirect
60. C22×D109C22⋊C4semidirect
99. C109#2308semidirect
105. #379D109semidirect
118. C2×C22⋊C4C2×D109semidirect
126. C24C4×D109semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D1092
C2×C22⋊C4×D1092
#202949022
#202948872
#202948822
#379×C1092
#2308109