Finite Group Databasebeta

← #28378301

Subgroups — #28378301

Order 13952.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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#20296046C211yesmaximal, characteristic, complemented
2#20296042C211yesmaximal, characteristic, complemented
3#20295870C212yesmaximal, complemented
4#20295869C212yesmaximal, complemented
5C2×#16812685C211yesmaximal, characteristic
6#16812766—21no—
7C4⋊#11724786—21no—
8C22⋊#11724786C2212yes—
9C22⋊#11724786C2212yes—
10#16812754—21no—
11C4×#11724786—21no—
12C22×Dic218C411yescharacteristic
13C22×C22⋊D109C411yescharacteristic
14#16812685—21no—
15#16812685—21no—
16#16812685—21no—
17#16812685—21no—
18C2×C22⋊Dic109C2211yescharacteristic
19C2×#13182006C411yescharacteristic
20C2×#13182006C2211yescharacteristic
21C2×C4×Dic109C2211yescharacteristic
22C2×C22⋊C4×C109C411yescharacteristic
23C2×#11724786—22no—
24C2×#11724786—22no—
25C23×D109C2×C411yescharacteristic
26C2×Dic218—21no—
27C2×Dic218—21no—
28C2×Dic218—42no—
29C2×C22⋊D109—21no—
30C2×C22⋊D109—21no—
31C2×C22⋊D109—42no—
32C22×Dic109C2×C411yescharacteristic
33C22×Dic109C2×C411yescharacteristic
34C22×Dic109C2311yescharacteristic
35C22⋊Dic109—21no—
36C22⋊Dic109—21no—
37#13182006—21no—
38#13182006—21no—
39#13182006—21no—
40#13182006—21no—
41C4×Dic109D411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109D411yescharacteristic
45C24×C109C2×C411yescharacteristic
46C22×C4×C109C2×C411yescharacteristic
47C22×C4×C109C2×C411yescharacteristic
48C22⋊C4×C109—21no—
49C22⋊C4×C109—21no—
50C23×C109—21no—
51C23×C109—22no—
52C23×C109—41no—
53C23×C109—41no—
54C23×C109C22×C411yescharacteristic
55C22×D109—21no—
56C22×D109—22no—
57C22×D109—41no—
58C22×D109—41no—
59C2×C4×C109—22no—
60C2×C4×C109—21no—
61C2×C4×C109—41no—
62C2×C4×C109C22⋊C411yescharacteristic
63C2×C4×C109C22⋊C411yescharacteristic
64C22⋊D109—42no—
65C22⋊D109—42no—
66C2×Dic109—22no—
67C2×Dic109—21no—
68C2×Dic109—41no—
69C2×Dic109—41no—
70C2×Dic109C22⋊C411yescharacteristic
71C2×Dic109C22⋊C411yescharacteristic
72C2×Dic109C2×D411yescharacteristic
73C2×Dic109C2×D411yescharacteristic
74Dic218—42no—
75Dic218—42no—
76#11724786—42no—
77#11724786—42no—
78C22×C109—21no—
79C22×C109—21no—
80C22×C109—41no—
81C22×C109—41no—
82C22×C109—41no—
83C22×C109—82no—
84C22×C109C2×C22⋊C411yescharacteristic
85C22×C109#13112yes—
86C2×D109—41no—
87C2×D109—41no—
88C2×D109—41no—
89C2×D109—82no—
90C4×C109—21no—
91C4×C109—21no—
92C4×C109—41no—
93Dic109—21no—
94Dic109—21no—
95Dic109—21no—
96Dic109—41no—
97Dic109#10012yes—
98C2×C109—22no—
99C2×C109—81no—
100C2×C109#40811yescharacteristic
101C2×C109#41011yescharacteristic
102C2×C109C2×#10011yescharacteristic
103D109—81no—
104#1469—1091nomaximal, Sylow
105C109#146911yescharacteristic, complemented, Sylow
106C2×#124—1091no—
107#432—1091no—
108#431—1091no—
109#323—1092no—
110#323—1092no—
111C22×Q8—1091no—
112C22×D4—1091no—
113#124—2181no—
114#124—2181no—
115#124—2181no—
116#124—2181no—
117C2×C22⋊C4—1091no—
118C2×C22⋊C4—1091no—
119C2×C22⋊C4—1091no—
120C2×C22⋊C4#8913711yescharacteristic
121C2×C42—1091no—
122C4⋊C8—2181no—
123C4⋊C8—2181no—
124C22⋊C8—1092no—
125C22⋊C8—1092no—
126#97—2181no—
127C4×C8—2181no—
128C24—1091no—
129C24C2×#8913711yescharacteristic
130C2×Q8—4362no—
131C2×Q8—2181no—
132C2×Q8—2181no—
133C2×D4—4362no—
134C2×D4—2181no—
135C2×D4—2181no—
136C22×C4—1091no—
137C22×C4—1091no—
138C22×C4—1091no—
139C22×C4C2×#8913711yescharacteristic
140C22×C4C2×#8913711yescharacteristic
141C2×C8—2182no—
142C2×C8—2182no—
143C22⋊C4—21no—
144C22⋊C4—21no—
145C22⋊C4—2181no—
146C22⋊C4—2181no—
147C22⋊C4—2181no—
148C22⋊C4—2181no—
149C22⋊C4—2181no—
150C22⋊C4—2181no—
151C42—1091no—
152C42—1091no—
153C42—1091no—
154C42—1091no—
155C23—21no—
156C23—22no—
157C23—41no—
158C23—41no—
159C23—4361no—
160C23—4361no—
161C23—2182no—
162C23—2181no—
163C23C22×#8913711yescharacteristic
164Q8—4362no—
165Q8—4362no—
166D4—4362no—
167D4—4362no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—1091no—
172C2×C4—1091no—
173C2×C4—1091no—
174C2×C4—1091no—
175C2×C4—4361no—
176C2×C4—4361no—
177C2×C4—2182no—
178C2×C4—2181no—
179C2×C4C22⋊#8913711yescharacteristic
180C2×C4C22⋊#8913711yescharacteristic
181C8—4362no—
182C8—4362no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—82no—
189C22—8722no—
190C22—4361no—
191C22—4361no—
192C22—4361no—
193C22C2×C22⋊#8913711yescharacteristic
194C22#1681278612yes—
195C4—21no—
196C4—21no—
197C4—41no—
198C4—1092no—
199C4—4361no—
200C4—2181no—
201C4—2181no—
202C4—2181no—
203C2—22no—
204C2—81no—
205C2—8721no—
206C2#2029599911yescharacteristic
207C2#2029600511yescharacteristic
208C2D109⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
FittingC2×C22⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×C22⋊D109C4
cosocleC22×Dic109C23
hypercenterC2×C22⋊C4#89137
hypocenterC109#1469
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20296046C2semidirect
2. #20296042C2semidirect
3. #20295870C2semidirect
4. #20295869C2semidirect
105. C109#1469semidirect

Maximal subgroups

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

subgroupindex
#202960462
#202960422
#202958702
#202958692
C2×#168126852
#1469109