Finite Group Databasebeta

← #28378308

Subgroups — #28378308

Order 13952.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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#20295870C212yesmaximal, complemented
4#20295869C212yesmaximal, complemented
5C2×#16812671C211yesmaximal, characteristic
6C2×#13182038—21no—
7C22×#11724786—21no—
8C22⋊#11724786—21no—
9C22⋊#11724786—21no—
10C22⋊#11724786C2212yes—
11C22⋊#11724786C2212yes—
12C22×C22⋊D109C411yescharacteristic
13C22×C22⋊D109C411yescharacteristic
14C23×Dic109C2211yescharacteristic
15#16812671—21no—
16#16812671—21no—
17#16812671—21no—
18#16812671—21no—
19C2×#13182008C411yescharacteristic
20C2×C22⋊Dic109C2211yescharacteristic
21C2×#13182006C2211yescharacteristic
22C22×D4×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—21no—
31C2×C22⋊D109—21no—
32C2×C22⋊D109—42no—
33C2×C22⋊D109—42no—
34C22×Dic109—42no—
35C22×Dic109C2×C411yescharacteristic
36C22×Dic109C2×C411yescharacteristic
37C22×Dic109D411yescharacteristic
38C22×Dic109D411yescharacteristic
39C22×Dic109D411yescharacteristic
40C22×Dic109D411yescharacteristic
41C22×Dic109C2311yescharacteristic
42#13182008—21no—
43#13182008—21no—
44C22⋊Dic109—21no—
45C22⋊Dic109—21no—
46#13182006—21no—
47#13182006—21no—
48C24×C109C2×C411yescharacteristic
49C24×C109C2×C411yescharacteristic
50C2×D4×C109—21no—
51C2×D4×C109—21no—
52C2×D4×C109—42no—
53C22×C4×C109C2×C411yescharacteristic
54C23×C109—22no—
55C23×C109—22no—
56C23×C109—21no—
57C23×C109—22no—
58C23×C109—41no—
59C23×C109—41no—
60C23×C109—41no—
61C23×C109C22⋊C411yescharacteristic
62C23×C109C22⋊C411yescharacteristic
63C23×C109C22×C411yescharacteristic
64C22×D109—21no—
65C22×D109—22no—
66C22×D109—41no—
67C22×D109—41no—
68D4×C109—42no—
69D4×C109—42no—
70C2×C4×C109—21no—
71C2×C4×C109—41no—
72C22⋊D109—42no—
73C22⋊D109—42no—
74C22⋊D109—42no—
75C22⋊D109—42no—
76C2×Dic109—22no—
77C2×Dic109—22no—
78C2×Dic109—22no—
79C2×Dic109—21no—
80C2×Dic109—41no—
81C2×Dic109—41no—
82C2×Dic109—41no—
83C2×Dic109—41no—
84C2×Dic109C22⋊C411yescharacteristic
85C2×Dic109C22⋊C411yescharacteristic
86C2×Dic109C2×D411yescharacteristic
87C2×Dic109C2×D411yescharacteristic
88#11724786—42no—
89#11724786—42no—
90C22×C109—21no—
91C22×C109—21no—
92C22×C109—21no—
93C22×C109—21no—
94C22×C109—21no—
95C22×C109—21no—
96C22×C109—21no—
97C22×C109—44no—
98C22×C109—41no—
99C22×C109—41no—
100C22×C109—41no—
101C22×C109—82no—
102C22×C109#10012yes—
103C22×C109C2×C22⋊C411yescharacteristic
104C22×C109#13112yes—
105C2×D109—41no—
106C2×D109—41no—
107C2×D109—41no—
108C2×D109—82no—
109C4×C109—41no—
110Dic109—21no—
111Dic109—21no—
112Dic109—21no—
113Dic109—41no—
114Dic109#9912yes—
115C2×C109—22no—
116C2×C109—22no—
117C2×C109—41no—
118C2×C109—81no—
119C2×C109#40811yescharacteristic
120C2×C109C2×#9911yescharacteristic
121C2×C109C2×#10011yescharacteristic
122D109—81no—
123#1471—1091nomaximal, Sylow
124C109#147111yescharacteristic, complemented, Sylow
125C2×#121—1091no—
126#407—1091no—
127C2×C22⋊C8—1091no—
128#323—1092no—
129#323—1092no—
130C22×D4—1091no—
131C22×D4—1091no—
132C22×D4#8913711yescharacteristic
133C23×C4—1091no—
134C2×M16—2181no—
135C22×C8—2181no—
136#121—2181no—
137#121—2181no—
138#121—2181no—
139#121—2181no—
140C2×C4⋊C4—1091no—
141C2×C22⋊C4—1091no—
142C2×C22⋊C4—1091no—
143C22⋊C8—1092no—
144C22⋊C8—1092no—
145C22⋊C8—2181no—
146C22⋊C8—2181no—
147C24—1091no—
148C24C2×#8913711yescharacteristic
149C24C2×#8913711yescharacteristic
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—42no—
153C2×D4—4362no—
154C2×D4—4362no—
155C2×D4—2181no—
156C2×D4—2181no—
157C2×D4—2181no—
158C2×D4—2181no—
159C22×C4—1091no—
160C22×C4—1091no—
161C22×C4—1091no—
162C22×C4—1091no—
163C22×C4—1091no—
164C22×C4—1091no—
165C22×C4—1091no—
166C22×C4—4362no—
167C22×C4C2×#8913711yescharacteristic
168M16—4362no—
169C2×C8—4362no—
170C2×C8—2182no—
171C2×C8—2182no—
172C4⋊C4—2181no—
173C4⋊C4—2181no—
174C22⋊C4—2181no—
175C22⋊C4—2181no—
176C22⋊C4—2181no—
177C22⋊C4—2181no—
178C23—22no—
179C23—22no—
180C23—21no—
181C23—22no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23—4361no—
186C23—4361no—
187C23—2182no—
188C23—2181no—
189C23C22⋊#8913711yescharacteristic
190C23C22⋊#8913711yescharacteristic
191C23C22×#8913711yescharacteristic
192D4—42no—
193D4—42no—
194D4—4362no—
195D4—4362no—
196D4—4362no—
197D4—4362no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—1091no—
201C2×C4—1091no—
202C2×C4—1091no—
203C2×C4—1091no—
204C2×C4—4361no—
205C2×C4—4361no—
206C2×C4—4361no—
207C2×C4—4361no—
208C2×C4—2182no—
209C2×C4—2182no—
210C2×C4—2182no—
211C2×C4—2181no—
212C8—4362no—
213C8—4362no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—44no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—82no—
226C22—8722no—
227C22—4361no—
228C22—4361no—
229C22—4361no—
230C22#1681275912yes—
231C22C2×C22⋊#8913711yescharacteristic
232C22#1681278612yes—
233C4—41no—
234C4—1092no—
235C4—4361no—
236C4—2181no—
237C4—2181no—
238C4—2181no—
239C2—22no—
240C2—22no—
241C2—41no—
242C2—81no—
243C2—8721no—
244C2#2029599911yescharacteristic
245C2D109⋊#9911yescharacteristic
246C2C2×#1681275911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
FittingC22×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×#16812671C2
cosocleC22×Dic109C23
hypercenterC22×D4#89137
hypocenterC109#1471
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #20295996C2semidirect
2. C2×C22⋊#11724786C2semidirect
3. #20295870C2semidirect
4. #20295869C2semidirect
124. C109#1471semidirect

Maximal subgroups

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

subgroupindex
#202959962
C2×C22⋊#117247862
#202958702
#202958692
C2×#168126712
#1471109