Finite Group Databasebeta

← #28371305

Subgroups — #28371305

Order 13952.

356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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#20294967C212yesmaximal
2#20294966C212yesmaximal
3#20294965C211yesmaximal, characteristic
4#20294947C212yesmaximal
5#20294947C212yesmaximal
6#20294946C212yesmaximal
7#20294891C211yesmaximal, characteristic
8#20294890C212yesmaximal
9#400×C109C211yesmaximal, characteristic
10C22×Dic218C2212yes—
11C2×C4⋊Dic109C2211yescharacteristic
12C2×C4⋊Dic109C2212yes—
13C2×C4⋊Dic109C2211yescharacteristic
14C2×#13182008C2212yes—
15C2×#13182008C2212yes—
16C2×#13182008C2212yes—
17C2×C4×Dic109C2211yescharacteristic
18#16812606C2212yes—
19#16812606C2212yes—
20#16812606C2212yes—
21#16812606C2212yes—
22#16812606C2212yes—
23#16812606C2212yes—
24#16812606C2212yes—
25#16812606C2211yescharacteristic
26C2×C4⋊C4×C109C2211yescharacteristic
27C2×C4⋊C4×C109C2211yescharacteristic
28#95×C109C2212yes—
29#95×C109C2212yes—
30#95×C109C2211yescharacteristic
31C2×Dic218—42no—
32C2×Dic218—42no—
33C2×Dic218—42no—
34C22×Dic109C2312yes—
35C22×Dic109C2312yes—
36C22×Dic109C2312yes—
37C22×Dic109C2312yes—
38C4⋊Dic109—41no—
39C4⋊Dic109—41no—
40C4⋊Dic109—42no—
41#13182008—42no—
42#13182008—42no—
43#13182008—42no—
44C4×Dic109Q814yescomplemented
45C22×C4×C109C2312yes—
46C22×C4×C109C2311yescharacteristic
47C22×C4×C109C2312yes—
48C22×C4×C109C2311yescharacteristic
49C22×C4×C109C2311yescharacteristic
50C4⋊C4×C109—41no—
51C4⋊C4×C109—41no—
52C23×C109C2411yescharacteristic
53C2×C4×C109—21no—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109—21no—
57C2×C4×C109—22no—
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×C109—22no—
65C2×C4×C109C2×Q812yes—
66C2×Dic109—22no—
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×Dic109C2×Q814yes—
78Dic218—48no—
79C22×C109C22×Q811yescharacteristic
80C22×C109H(5,𝔽2)11yescharacteristic
81C22×C109H(5,𝔽2)12yes—
82C22×C1092−1+411yescharacteristic
83C22×C1092−1+412yes—
84C4×C109—22no—
85C4×C109—42no—
86C4×C109—42no—
87C4×C109—41no—
88C4×C109—41no—
89Dic109—24no—
90Dic109—42no—
91Dic109—42no—
92Dic109—42no—
93C2×C109#54411yescharacteristic
94C2×C109#54412yes—
95C2×C109H(3,𝔽4)11yescharacteristic
96C2×C109#56312yes—
97C2×C109#56311yescharacteristic
98#2844—1091nomaximal, Sylow
99C109#284411yescharacteristic, complemented, Sylow
100#400—1091no—
101#400—1092no—
102#400—1092no—
103#400D10911yescharacteristic
104#395—1092no—
105#395—1092no—
106#395—1092no—
107#382—1091no—
108#382—1092no—
109C22×Q8—1092no—
110C2×C4⋊C4—1092no—
111C2×C4⋊C4—1092no—
112C2×C4⋊C4—1092no—
113C2×C4⋊C4—1091no—
114C2×C4⋊C4—1091no—
115C2×C4⋊C4—1092no—
116C2×C4⋊C4C2×D10911yescharacteristic
117C2×C4⋊C4C2×D10911yescharacteristic
118C2×C42—1091no—
119#95—1092no—
120#95—1092no—
121#95—1092no—
122#95—1092no—
123#95—1092no—
124#95—1092no—
125#95—1092no—
126#95—1091no—
127#95C2×D10912yes—
128#95C2×D10912yes—
129#95C2×D10911yescharacteristic
130C2×Q8—4362no—
131C2×Q8—4362no—
132C2×Q8—4362no—
133C22×C4—1092no—
134C22×C4—1092no—
135C22×C4—1092no—
136C22×C4—1092no—
137C22×C4C22×D10911yescharacteristic
138C22×C4C22×D10911yescharacteristic
139C22×C4C22×D10912yes—
140C22×C4C22×D10912yes—
141C22×C4C22×D10911yescharacteristic
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—4362no—
145C4⋊C4—4362no—
146C4⋊C4—4362no—
147C4⋊C4—4361no—
148C4⋊C4—4361no—
149C4⋊C4—4362no—
150C42—1094no—
151C23C23×D10911yescharacteristic
152Q8—4368no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
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×C4—2182no—
176C2×C4—2182no—
177C2×C4Q8×D10912yes—
178C22C2×Q8×D10911yescharacteristic
179C22#1681274411yescharacteristic
180C22#1681274512yes—
181C22#1681274611yescharacteristic
182C22#1681274612yes—
183C4—22no—
184C4—42no—
185C4—42no—
186C4—41no—
187C4—41no—
188C4—4362no—
189C4—4362no—
190C4—4362no—
191C4—2184no—
192C2#2029565511yescharacteristic
193C2#2029565612yes—
194C2#2029576811yescharacteristic
195C2#2029577812yes—
196C2#2029577911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D109
commutator, socle, prime radical, cosocleC23×C109C24
Fitting#400×C109C2
hypercenter#400D109
hypocenterC109#2844
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic109Q8semidirect
99. C109#2844semidirect

Maximal subgroups

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

subgroupindex
#202949672
#202949662
#202949652
#202949472
#202949462
#202948912
#202948902
#400×C1092
#2844109