Finite Group Databasebeta

← #28366217

Subgroups — #28366217

Order 13952.

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×#16812691C211yesmaximal, characteristic
2#20294923C212yesmaximal
3#20294921C212yesmaximal
4#20294913C212yesmaximal
5#20294911C212yesmaximal
6#20294909C212yesmaximal
7#20294907C212yesmaximal
8#20294892C211yesmaximal, characteristic
9#382×C109C211yesmaximal, characteristic
10#16812691C418yescomplemented
11C2×C4⋊Dic109C2211yescharacteristic
12C2×C4⋊Dic109C2211yescharacteristic
13C2×C4⋊Dic109C2211yescharacteristic
14C2×C4⋊Dic109C2211yescharacteristic
15C2×#13182008C2212yes—
16C2×#13182008C2212yes—
17C2×#13182008C2212yes—
18C2×#13182008C2212yes—
19C2×C4×Dic109C2212yes—
20C2×C4×Dic109C2212yes—
21#16812606C2212yes—
22#16812606C2212yes—
23#16812606C2212yes—
24#16812606C2212yes—
25#16812606C2212yes—
26#16812606C2212yes—
27C2×C4⋊C4×C109C2211yescharacteristic
28C2×C4⋊C4×C109C2211yescharacteristic
29C2×C42×C109C2211yescharacteristic
30#95×C109C2212yes—
31#95×C109C2212yes—
32C22×Dic109C2312yes—
33C22×Dic109C2312yes—
34C22×Dic109C2312yes—
35C22×Dic109C2312yes—
36C4⋊Dic109—41no—
37C4⋊Dic109—41no—
38C4⋊Dic109C2×C414yes—
39C4⋊Dic109C2×C414yes—
40#13182008—42no—
41#13182008—42no—
42#13182008C2×C418yes—
43#13182008C2×C418yes—
44C4×Dic109—42no—
45C4×Dic109—42no—
46C22×C4×C109C2312yes—
47C22×C4×C109C2312yes—
48C22×C4×C109C2311yescharacteristic
49C22×C4×C109C2311yescharacteristic
50C22×C4×C109C2311yescharacteristic
51C4⋊C4×C109—41no—
52C4⋊C4×C109—41no—
53C42×C109C2×C414yes—
54C23×C109C2411yescharacteristic
55C2×C4×C109—21no—
56C2×C4×C109—21no—
57C2×C4×C109—21no—
58C2×C4×C109—21no—
59C2×C4×C109—21no—
60C2×C4×C109—21no—
61C2×C4×C109—22no—
62C2×C4×C109—22no—
63C2×C4×C109—22no—
64C2×C4×C109—22no—
65C2×C4×C109—22no—
66C2×C4×C109—22no—
67C2×C4×C109C22×C412yes—
68C2×C4×C109C22×C412yes—
69C2×C4×C109C22×C412yes—
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—22no—
79C2×Dic109—22no—
80C2×Dic109C22×C414yes—
81C2×Dic109C22×C414yes—
82C22×C109C23×C411yescharacteristic
83C22×C109H(5,𝔽2)11yescharacteristic
84C22×C109H(5,𝔽2)11yescharacteristic
85C22×C1092−1+411yescharacteristic
86C22×C1092−1+411yescharacteristic
87C22×C1092−1+411yescharacteristic
88C22×C1092−1+411yescharacteristic
89C4×C109—22no—
90C4×C109—22no—
91C4×C109—22no—
92C4×C109—42no—
93C4×C109—42no—
94Dic109—24no—
95Dic109—24no—
96Dic109—42no—
97Dic109—42no—
98C2×C109#51911yescharacteristic
99C2×C109#52011yescharacteristic
100C2×C109#52011yescharacteristic
101C2×C109#56211yescharacteristic
102C2×C109#56311yescharacteristic
103C2×C109#56311yescharacteristic
104C2×C109#56411yescharacteristic
105#2382—1091nomaximal, Sylow
106C109#238211yescharacteristic, complemented, Sylow
107C2×#125—1091no—
108#389—1092no—
109#389—1092no—
110#387—1092no—
111#387—1092no—
112#387—1092no—
113#387—1092no—
114#382—1091no—
115#382D10911yescharacteristic
116#125—1098no—
117C2×C4⋊C4—1092no—
118C2×C4⋊C4—1092no—
119C2×C4⋊C4—1091no—
120C2×C4⋊C4—1091no—
121C2×C4⋊C4—1092no—
122C2×C4⋊C4—1092no—
123C2×C4⋊C4—1091no—
124C2×C4⋊C4—1091no—
125C2×C4⋊C4C2×D10911yescharacteristic
126C2×C4⋊C4C2×D10911yescharacteristic
127C2×C42—1092no—
128C2×C42—1092no—
129C2×C42C2×D10911yescharacteristic
130#95—1092no—
131#95—1092no—
132#95—1092no—
133#95—1092no—
134#95—1092no—
135#95—1092no—
136#95C2×D10912yes—
137#95C2×D10912yes—
138C22×C4—1092no—
139C22×C4—1092no—
140C22×C4—1092no—
141C22×C4—1092no—
142C22×C4C22×D10912yes—
143C22×C4C22×D10912yes—
144C22×C4C22×D10911yescharacteristic
145C22×C4C22×D10911yescharacteristic
146C22×C4C22×D10911yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—1098no—
150C4⋊C4—1098no—
151C4⋊C4—1094no—
152C4⋊C4—1094no—
153C4⋊C4—4362no—
154C4⋊C4—4362no—
155C4⋊C4—4361no—
156C4⋊C4—4361no—
157C42—4362no—
158C42—4362no—
159C42C4×D10914yes—
160C23C23×D10911yescharacteristic
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—1094no—
174C2×C4—1094no—
175C2×C4—2182no—
176C2×C4—2182no—
177C2×C4—2182no—
178C2×C4—2182no—
179C2×C4—2182no—
180C2×C4—2182no—
181C2×C4—2182no—
182C2×C4—2182no—
183C2×C4—2182no—
184C2×C4—2182no—
185C2×C4C2×C4×D10912yes—
186C2×C4C2×C4×D10912yes—
187C2×C4C2×C4×D10912yes—
188C22C22×C4×D10911yescharacteristic
189C22#1681274411yescharacteristic
190C22#1681274511yescharacteristic
191C22#1681274611yescharacteristic
192C22#1681274611yescharacteristic
193C22#1681274611yescharacteristic
194C22#1681274711yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—4362no—
201C4—4362no—
202C4—2184no—
203C4—2184no—
204C2#2029550311yescharacteristic
205C2#2029550611yescharacteristic
206C2#2029550711yescharacteristic
207C2#2029577011yescharacteristic
208C2#2029577611yescharacteristic
209C2#2029578011yescharacteristic
210C2C109⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
Fitting#382×C109C2
socle, prime radical, cosocleC23×C109C24
hypercenter#382D109
hypocenterC109#2382
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #16812691C4semidirect
106. C109#2382semidirect

Maximal subgroups

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

subgroupindex
C2×#168126912
#202949232
#202949212
#202949132
#202949112
#202949092
#202949072
#202948922
#382×C1092
#2382109