Finite Group Databasebeta

← #28378299

Subgroups — #28378299

Order 13952.

280 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 62 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#20295996C211yesmaximal, characteristic, complemented
2C2×C22⋊#11724786C211yesmaximal, characteristic, complemented
3#20295871C212yesmaximal, complemented
4#20295870C212yesmaximal, complemented
5C2×#16812683C211yesmaximal, characteristic
6C2×#13182038—21no—
7C22×#11724786—21no—
8C22⋊#11724786—21no—
9C22⋊#11724786—21no—
10C22⋊#11724786C2212yes—
11C22⋊#11724786C2212yes—
12C22×C22⋊D109C411yescharacteristic
13C23×Dic109C2211yescharacteristic
14#16812683—21no—
15#16812683—21no—
16#16812683—21no—
17#16812683—21no—
18C2×C4⋊Dic109C411yescharacteristic
19C2×C4⋊Dic109C2211yescharacteristic
20C2×#13182006C411yescharacteristic
21C2×#13182006C2211yescharacteristic
22C2×C22⋊C4×C109C411yescharacteristic
23#13182038—42no—
24C2×#11724786—22no—
25C2×#11724786—22no—
26C2×#11724786—42no—
27C23×D109C2×C411yescharacteristic
28C2×C22⋊D109—21no—
29C2×C22⋊D109—21no—
30C2×C22⋊D109—42no—
31C22×Dic109—42no—
32C22×Dic109C2×C411yescharacteristic
33C22×Dic109C2×C411yescharacteristic
34C22×Dic109D411yescharacteristic
35C22×Dic109D411yescharacteristic
36C22×Dic109D411yescharacteristic
37C22×Dic109D411yescharacteristic
38C22×Dic109C2311yescharacteristic
39C4⋊Dic109—21no—
40C4⋊Dic109—21no—
41C4⋊Dic109—21no—
42C4⋊Dic109—21no—
43#13182006—21no—
44#13182006—21no—
45#13182006—21no—
46#13182006—21no—
47C24×C109C2×C411yescharacteristic
48C22×C4×C109C2×C411yescharacteristic
49C22×C4×C109C2×C411yescharacteristic
50C22⋊C4×C109—21no—
51C22⋊C4×C109—21no—
52C23×C109—22no—
53C23×C109—22no—
54C23×C109—41no—
55C23×C109C22⋊C411yescharacteristic
56C23×C109C22⋊C411yescharacteristic
57C23×C109C22×C411yescharacteristic
58C22×D109—21no—
59C22×D109—22no—
60C22×D109—41no—
61C22×D109—41no—
62C2×C4×C109—21no—
63C2×C4×C109—21no—
64C2×C4×C109—22no—
65C2×C4×C109—41no—
66C22⋊D109—42no—
67C22⋊D109—42no—
68C2×Dic109—22no—
69C2×Dic109—22no—
70C2×Dic109—21no—
71C2×Dic109—41no—
72C2×Dic109—41no—
73C2×Dic109—41no—
74C2×Dic109—41no—
75C2×Dic109—41no—
76C2×Dic109C22⋊C411yescharacteristic
77C2×Dic109C22⋊C411yescharacteristic
78C2×Dic109C2×D411yescharacteristic
79C2×Dic109C2×D411yescharacteristic
80#11724786—42no—
81#11724786—42no—
82C22×C109—21no—
83C22×C109—21no—
84C22×C109—21no—
85C22×C109—21no—
86C22×C109—21no—
87C22×C109—21no—
88C22×C109—21no—
89C22×C109—44no—
90C22×C109#9912yes—
91C22×C109C2×C22⋊C411yescharacteristic
92C22×C109#13112yes—
93C2×D109—41no—
94C2×D109—41no—
95C2×D109—41no—
96C2×D109—82no—
97C4×C109—41no—
98C4×C109—41no—
99Dic109—21no—
100Dic109—21no—
101Dic109—21no—
102Dic109—21no—
103Dic109—41no—
104C2×C109—22no—
105C2×C109—22no—
106C2×C109—41no—
107C2×C109#40811yescharacteristic
108C2×C109C2×#9911yescharacteristic
109C2×C109#41311yescharacteristic
110D109—81no—
111#1468—1091nomaximal, Sylow
112C109#146811yescharacteristic, complemented, Sylow
113C2×#123—1091no—
114#407—1091no—
115C2×C22⋊C8—1091no—
116#324—1092no—
117#323—1092no—
118C22×D4—1091no—
119C23×C4—1091no—
120C2×M16—2181no—
121C22×C8—2181no—
122#123—2181no—
123#123—2181no—
124#123—2181no—
125#123—2181no—
126C2×C4⋊C4—1091no—
127C2×C4⋊C4—1091no—
128C2×C22⋊C4—1091no—
129C2×C22⋊C4—1091no—
130C2×C22⋊C4#8913711yescharacteristic
131C22⋊C8—1092no—
132C22⋊C8—1092no—
133C22⋊C8—2181no—
134C22⋊C8—2181no—
135C24—1091no—
136C24C2×#8913711yescharacteristic
137C2×D4—4362no—
138C2×D4—2181no—
139C2×D4—2181no—
140C22×C4—1091no—
141C22×C4—1091no—
142C22×C4—1091no—
143C22×C4—1091no—
144C22×C4—1091no—
145C22×C4—1091no—
146C22×C4—1091no—
147C22×C4—4362no—
148C22×C4C2×#8913711yescharacteristic
149C22×C4C2×#8913711yescharacteristic
150M16—4362no—
151C2×C8—4362no—
152C2×C8—2182no—
153C2×C8—2182no—
154C4⋊C4—2181no—
155C4⋊C4—2181no—
156C4⋊C4—2181no—
157C4⋊C4—2181no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—2181no—
161C22⋊C4—2181no—
162C22⋊C4—2181no—
163C22⋊C4—2181no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—4361no—
168C23—4361no—
169C23—2182no—
170C23—2181no—
171C23C22⋊#8913711yescharacteristic
172C23C22⋊#8913711yescharacteristic
173C23C22×#8913711yescharacteristic
174D4—4362no—
175D4—4362no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—41no—
180C2×C4—1091no—
181C2×C4—1091no—
182C2×C4—1091no—
183C2×C4—1091no—
184C2×C4—4361no—
185C2×C4—4361no—
186C2×C4—4361no—
187C2×C4—4361no—
188C2×C4—4361no—
189C2×C4—2181no—
190C2×C4—2182no—
191C2×C4—2182no—
192C8—4362no—
193C8—4362no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—8722no—
203C22—4361no—
204C22—4361no—
205C22—4361no—
206C22#1681275812yes—
207C22C2×C22⋊#8913711yescharacteristic
208C22#1681278612yes—
209C4—41no—
210C4—41no—
211C4—4361no—
212C4—2181no—
213C4—2181no—
214C4—2181no—
215C4—2181no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—8721no—
220C2#2029599911yescharacteristic
221C2C2×#1681275811yescharacteristic
222C2#2029601311yescharacteristic
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#1468
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20295996C2semidirect
2. C2×C22⋊#11724786C2semidirect
3. #20295871C2semidirect
4. #20295870C2semidirect
112. C109#1468semidirect

Maximal subgroups

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

subgroupindex
#202959962
C2×C22⋊#117247862
#202958712
#202958702
C2×#168126832
#1468109