Finite Group Databasebeta

← #28365833

Subgroups — #28365833

Order 13952.

428 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 177 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#20294913C212yesmaximal
4#20294911C212yesmaximal
5#20294909C212yesmaximal
6#20294908C212yesmaximal
7C4×C4⋊Dic109C211yesmaximal, characteristic
8#20294877C212yesmaximal
9#383×C109C211yesmaximal, characteristic
10#16812691C418yescomplemented
11C2×C4⋊Dic109C2212yes—
12C2×C4⋊Dic109C2211yescharacteristic
13C2×C4⋊Dic109C2211yescharacteristic
14C2×#13182008C2212yes—
15C2×#13182008C2212yes—
16C2×#13182008C2212yes—
17C2×#13182008C2212yes—
18C2×C4×Dic109C2212yes—
19C2×C4×Dic109C2212yes—
20C2×C4×Dic109C2211yescharacteristic
21C2×C4×Dic109C2211yescharacteristic
22#16812606C2212yes—
23#16812606C2212yes—
24#16812606C2212yes—
25#16812606C2212yes—
26#16812606C2212yes—
27C2×C42×C109C2211yescharacteristic
28#95×C109C2211yescharacteristic
29#95×C109C2211yescharacteristic
30#95×C109C2212yes—
31#95×C109C2212yes—
32C22×Dic109C2312yes—
33C22×Dic109C2312yes—
34C22×Dic109C2312yes—
35C22×Dic109C2312yes—
36C4⋊Dic109—24no—
37C4⋊Dic109C2×C414yes—
38C4⋊Dic109C2×C414yes—
39#13182008—24no—
40#13182008—42no—
41#13182008C2×C418yes—
42#13182008C2×C418yes—
43C4×Dic109—24no—
44C4×Dic109—41no—
45C4×Dic109—42no—
46C4×Dic109—41no—
47C22×C4×C109C2312yes—
48C22×C4×C109C2312yes—
49C22×C4×C109C2311yescharacteristic
50C22×C4×C109C2311yescharacteristic
51C22×C4×C109C2311yescharacteristic
52C42×C109C2×C414yes—
53C23×C109C2411yescharacteristic
54C2×C4×C109—22no—
55C2×C4×C109—21no—
56C2×C4×C109—22no—
57C2×C4×C109—21no—
58C2×C4×C109—22no—
59C2×C4×C109—22no—
60C2×C4×C109—22no—
61C2×C4×C109—22no—
62C2×C4×C109—22no—
63C2×C4×C109—22no—
64C2×C4×C109C22×C412yes—
65C2×C4×C109C22×C412yes—
66C2×C4×C109C22×C412yes—
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×Dic109C22×C414yes—
77C2×Dic109C22×C414yes—
78C2×Dic109#4114yes—
79C22×C109C23×C411yescharacteristic
80C22×C109C2×#4112yes—
81C22×C109H(5,𝔽2)11yescharacteristic
82C22×C1092−1+412yes—
83C22×C1092−1+411yescharacteristic
84C4×C109—22no—
85C4×C109—22no—
86C4×C109—22no—
87C4×C109—42no—
88C4×C109—42no—
89Dic109—24no—
90Dic109—24no—
91Dic109—24no—
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×#125—1091no—
101#389—1092no—
102#387—1092no—
103#387—1092no—
104#387—1092no—
105#387—1092no—
106#383D10911yescharacteristic
107C4×C4⋊C4—1091no—
108C4×C4⋊C4—1092no—
109#125—1098no—
110C2×C4⋊C4—1092no—
111C2×C4⋊C4—1092no—
112C2×C4⋊C4—1091no—
113C2×C4⋊C4—1091no—
114C2×C4⋊C4—1092no—
115C2×C4⋊C4—1092no—
116C2×C4⋊C4—1092no—
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—1092no—
126#95—1092no—
127#95C2×D10912yes—
128#95C2×D10911yescharacteristic
129#95C2×D10912yes—
130#95C2×D10911yescharacteristic
131C22×C4—1092no—
132C22×C4—1092no—
133C22×C4—1092no—
134C22×C4—1092no—
135C22×C4C22×D10912yes—
136C22×C4C22×D10912yes—
137C22×C4C22×D10911yescharacteristic
138C22×C4C22×D10911yescharacteristic
139C22×C4C22×D10911yescharacteristic
140C4⋊C4—1098no—
141C4⋊C4—1098no—
142C4⋊C4—1094no—
143C4⋊C4—1094no—
144C4⋊C4—4362no—
145C4⋊C4—2184no—
146C4⋊C4—2184no—
147C42—4361no—
148C42—4361no—
149C42—4362no—
150C42—2184no—
151C42C4×D10914yes—
152C23C23×D10911yescharacteristic
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—1094no—
164C2×C4—1094no—
165C2×C4—1094no—
166C2×C4—2182no—
167C2×C4—2182no—
168C2×C4—2182no—
169C2×C4—2182no—
170C2×C4—2182no—
171C2×C4—2182no—
172C2×C4—2182no—
173C2×C4—2182no—
174C2×C4—2182no—
175C2×C4C2×C4×D10912yes—
176C2×C4C2×C4×D10912yes—
177C2×C4C2×C4×D10912yes—
178C22C22×C4×D10911yescharacteristic
179C22#41×D10912yes—
180C22#1681274511yescharacteristic
181C22#1681274612yes—
182C22#1681274611yescharacteristic
183C4—22no—
184C4—22no—
185C4—22no—
186C4—42no—
187C4—42no—
188C4—4362no—
189C4—2184no—
190C4—2184no—
191C4—2184no—
192C2#2029549411yescharacteristic
193C2#2029550311yescharacteristic
194C2#2029550611yescharacteristic
195C2#2029561712yes—
196C2#2029563312yes—
subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
Fitting#383×C109C2
socle, prime radical, cosocleC23×C109C24
hypercenter#383D109
hypocenterC109#2336
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
10. #16812691C4semidirect
99. C109#2336semidirect

Maximal subgroups

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

subgroupindex
C2×#168126912
#202949232
#202949132
#202949112
#202949092
#202949082
C4×C4⋊Dic1092
#202948772
#383×C1092
#2336109