Finite Group Databasebeta

← #28371298

Subgroups — #28371298

Order 13952.

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

normal subgroups only

This group has 348 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#20294965C211yesmaximal, characteristic
3#20294960C212yesmaximal
4#20294959C212yesmaximal
5#20294957C212yesmaximal
6#20294945C212yesmaximal
7#20294895C211yesmaximal, characteristic
8#20294893C212yesmaximal
9#395×C109C211yesmaximal, characteristic
10C2×C4⋊Dic109C2211yescharacteristic
11C2×C4⋊Dic109C2211yescharacteristic
12C2×#13182008C2212yes—
13C2×#13182008C2212yes—
14C2×#13182008C2212yes—
15C2×#13182008C2212yes—
16C2×#13182008C2212yes—
17C2×C4×Dic109C2211yescharacteristic
18#16812606C2212yes—
19#16812606C2212yes—
20#16812606C2212yes—
21#16812606C2211yescharacteristic
22#16812606C2212yes—
23#16812606C2212yes—
24#16812606C2212yes—
25#16812606C2212yes—
26C22×Q8×C109C2211yescharacteristic
27C2×C4⋊C4×C109C2212yes—
28C2×C4⋊C4×C109C2211yescharacteristic
29#95×C109C2212yes—
30#95×C109C2211yescharacteristic
31C22×Dic109C2312yes—
32C22×Dic109C2312yes—
33C22×Dic109C2312yes—
34C22×Dic109C2312yes—
35C4⋊Dic109—41no—
36C4⋊Dic109—41no—
37#13182008—42no—
38#13182008—42no—
39#13182008—42no—
40#13182008—42no—
41#13182008—42no—
42C4×Dic109Q814yescomplemented
43C2×Q8×C109—41no—
44C2×Q8×C109—42no—
45C22×C4×C109C2312yes—
46C22×C4×C109C2312yes—
47C22×C4×C109C2311yescharacteristic
48C22×C4×C109C2311yescharacteristic
49C22×C4×C109C2311yescharacteristic
50C4⋊C4×C109—41no—
51C4⋊C4×C109—42no—
52C23×C109C2411yescharacteristic
53Q8×C109—44no—
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—21no—
61C2×C4×C109—22no—
62C2×C4×C109—22no—
63C2×C4×C109—22no—
64C2×C4×C109—22no—
65C2×C4×C109—22no—
66C2×C4×C109C2×Q812yes—
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—24no—
77C2×Dic109C2×Q814yes—
78C22×C109C22×Q811yescharacteristic
79C22×C109H(5,𝔽2)11yescharacteristic
80C22×C109H(5,𝔽2)12yes—
81C22×C1092−1+411yescharacteristic
82C22×C1092−1+412yes—
83C4×C109—22no—
84C4×C109—41no—
85C4×C109—41no—
86C4×C109—42no—
87C4×C109—42no—
88Dic109—24no—
89Dic109—42no—
90Dic109—42no—
91Dic109—42no—
92C2×C109#54412yes—
93C2×C109#54411yescharacteristic
94C2×C109#56011yescharacteristic
95C2×C109#56311yescharacteristic
96C2×C109#56312yes—
97#2843—1091nomaximal, Sylow
98C109#284311yescharacteristic, complemented, Sylow
99#400—1091no—
100#400—1092no—
101#398—1092no—
102#398—1092no—
103#398—1092no—
104#395—1092no—
105#395D10911yescharacteristic
106#384—1091no—
107#383—1092no—
108C22×Q8C2×D10911yescharacteristic
109C2×C4⋊C4—1092no—
110C2×C4⋊C4—1092no—
111C2×C4⋊C4—1092no—
112C2×C4⋊C4—1092no—
113C2×C4⋊C4—1092no—
114C2×C4⋊C4—1091no—
115C2×C4⋊C4—1091no—
116C2×C4⋊C4C2×D10911yescharacteristic
117C2×C4⋊C4C2×D10912yes—
118C2×C42—1091no—
119#95—1092no—
120#95—1092no—
121#95—1092no—
122#95—1092no—
123#95—1092no—
124#95—1092no—
125#95—1091no—
126#95—1092no—
127#95C2×D10912yes—
128#95C2×D10911yescharacteristic
129C2×Q8—41no—
130C2×Q8—42no—
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—41no—
141C4⋊C4—42no—
142C4⋊C4—4362no—
143C4⋊C4—4362no—
144C4⋊C4—4362no—
145C4⋊C4—4362no—
146C4⋊C4—4362no—
147C4⋊C4—4361no—
148C4⋊C4—4361no—
149C42—1094no—
150C23C23×D10911yescharacteristic
151Q8—44no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—1094no—
165C2×C4—2182no—
166C2×C4—2182no—
167C2×C4—2182no—
168C2×C4—2182no—
169C2×C4—2182no—
170C2×C4—2182no—
171C2×C4—2184no—
172C2×C4—2182no—
173C2×C4—2182no—
174C2×C4—2182no—
175C2×C4Q8×D10912yes—
176C22C2×Q8×D10911yescharacteristic
177C22#1681274411yescharacteristic
178C22#1681274412yes—
179C22#1681274611yescharacteristic
180C22#1681274712yes—
181C4—22no—
182C4—41no—
183C4—42no—
184C4—41no—
185C4—42no—
186C4—4362no—
187C4—4362no—
188C4—4362no—
189C4—2184no—
190C2#2029565312yes—
191C2#2029565511yescharacteristic
192C2#2029576511yescharacteristic
193C2#2029577511yescharacteristic
194C2#2029577712yes—
subgroupG/H
center, FrattiniC23C23×D109
commutator, socle, prime radical, cosocleC23×C109C24
Fitting#395×C109C2
hypercenter#395D109
hypocenterC109#2843
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
42. C4×Dic109Q8semidirect
98. C109#2843semidirect

Maximal subgroups

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

subgroupindex
#202949672
#202949652
#202949602
#202949592
#202949572
#202949452
#202948952
#202948932
#395×C1092
#2843109