Finite Group Databasebeta

← #28366211

Subgroups — #28366211

Order 13952.

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

normal subgroups only

This group has 424 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×#16812697C211yesmaximal, characteristic
2#20294933C211yesmaximal, characteristic
3#20294930C212yesmaximal
4#20294913C212yesmaximal
5#20294910C212yesmaximal
6#20294908C212yesmaximal
7#20294907C212yesmaximal
8#20294893C212yesmaximal
9#391×C109C211yesmaximal, characteristic
10C22×Dic218C2211yescharacteristic
11#16812697C418yescomplemented
12C2×C4⋊Dic109C2211yescharacteristic
13C2×#13182008C2212yes—
14C2×#13182008C2212yes—
15C2×#13182008C2212yes—
16C2×C4×Dic109C2212yes—
17C2×C4×Dic109C2211yescharacteristic
18C2×C4×Dic109C2211yescharacteristic
19#16812606C2212yes—
20#16812606C2212yes—
21#16812606C2212yes—
22#16812606C2212yes—
23#16812606C2212yes—
24#16812606C2212yes—
25#16812606C2212yes—
26#16812606C2212yes—
27C22×Q8×C109C2211yescharacteristic
28C2×C4⋊C4×C109C2211yescharacteristic
29C2×C42×C109C2211yescharacteristic
30#95×C109C2212yes—
31#95×C109C2212yes—
32C2×Dic218—41no—
33C2×Dic218—41no—
34C2×Dic218C2×C414yes—
35C22×Dic109C2312yes—
36C22×Dic109C2312yes—
37C22×Dic109C2312yes—
38C22×Dic109C2312yes—
39C4⋊Dic109—41no—
40#13182008—42no—
41#13182008C2×C418yes—
42#13182008C2×C418yes—
43C4×Dic109—42no—
44C4×Dic109—41no—
45C4×Dic109C2×C414yes—
46C2×Q8×C109—41no—
47C2×Q8×C109—41no—
48C2×Q8×C109C2×C414yes—
49C22×C4×C109C2312yes—
50C22×C4×C109C2312yes—
51C22×C4×C109C2311yescharacteristic
52C22×C4×C109C2311yescharacteristic
53C22×C4×C109C2311yescharacteristic
54C4⋊C4×C109—41no—
55C42×C109—41no—
56C23×C109C2411yescharacteristic
57Q8×C109—44no—
58C2×C4×C109—21no—
59C2×C4×C109—21no—
60C2×C4×C109—21no—
61C2×C4×C109—21no—
62C2×C4×C109—21no—
63C2×C4×C109—21no—
64C2×C4×C109—22no—
65C2×C4×C109—22no—
66C2×C4×C109—22no—
67C2×C4×C109—24no—
68C2×C4×C109—22no—
69C2×C4×C109C22×C412yes—
70C2×C4×C109C22×C412yes—
71C2×C4×C109C22×C412yes—
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×Dic109—24no—
81C2×Dic109C22×C414yes—
82C2×Dic109C22×C414yes—
83Dic218—44no—
84C22×C109C23×C411yescharacteristic
85C22×C109H(5,𝔽2)11yescharacteristic
86C22×C109H(5,𝔽2)11yescharacteristic
87C22×C1092−1+412yes—
88C22×C1092−1+412yes—
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#51811yescharacteristic
99C2×C109#51912yes—
100C2×C109#56311yescharacteristic
101C2×C109#56311yescharacteristic
102C2×C109#56312yes—
103#2381—1091nomaximal, Sylow
104C109#238111yescharacteristic, complemented, Sylow
105C2×C4⋊Q8—1091no—
106#391—1091no—
107#391—1092no—
108#391D10911yescharacteristic
109#387—1092no—
110#387—1092no—
111#387—1092no—
112#387—1092no—
113#383—1092no—
114C22×Q8—1091no—
115C22×Q8C2×D10911yescharacteristic
116C4⋊Q8—1098no—
117C2×C4⋊C4—1092no—
118C2×C4⋊C4—1092no—
119C2×C4⋊C4—1092no—
120C2×C4⋊C4—1091no—
121C2×C4⋊C4C2×D10911yescharacteristic
122C2×C42—1091no—
123C2×C42—1092no—
124C2×C42—1091no—
125C2×C42C2×D10911yescharacteristic
126#95—1092no—
127#95—1092no—
128#95—1092no—
129#95—1092no—
130#95—1092no—
131#95—1092no—
132#95—1092no—
133#95—1092no—
134#95C2×D10912yes—
135#95C2×D10912yes—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—1094no—
139C2×Q8—4361no—
140C2×Q8—4361no—
141C2×Q8C4×D10914yes—
142C22×C4—1092no—
143C22×C4—1092no—
144C22×C4—1092no—
145C22×C4—1092no—
146C22×C4C22×D10912yes—
147C22×C4C22×D10912yes—
148C22×C4C22×D10911yescharacteristic
149C22×C4C22×D10911yescharacteristic
150C22×C4C22×D10911yescharacteristic
151C4⋊C4—41no—
152C4⋊C4—1098no—
153C4⋊C4—1098no—
154C4⋊C4—4362no—
155C4⋊C4—4361no—
156C42—41no—
157C42—1094no—
158C42—4361no—
159C42—4362no—
160C23C23×D10911yescharacteristic
161Q8—44no—
162Q8—4364no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—1094no—
175C2×C4—1094no—
176C2×C4—2182no—
177C2×C4—2182no—
178C2×C4—2182no—
179C2×C4—2184no—
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#1681274411yescharacteristic
191C22#1681274612yes—
192C22#1681274712yes—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—4362no—
199C4—4362no—
200C4—2184no—
201C4—2184no—
202C2#2029549911yescharacteristic
203C2#2029550212yes—
204C2#2029577511yescharacteristic
205C2#2029577611yescharacteristic
206C2#2029577712yes—
subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
Fitting#391×C109C2
socle, prime radical, cosocleC23×C109C24
hypercenter#391D109
hypocenterC109#2381
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #16812697C4semidirect
104. C109#2381semidirect

Maximal subgroups

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

subgroupindex
C2×#168126972
#202949332
#202949302
#202949132
#202949102
#202949082
#202949072
#202948932
#391×C1092
#2381109