Finite Group Databasebeta

← #28378897

Subgroups — #28378897

Order 13952.

336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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#20296029C212yesmaximal, complemented
2C2×#16812759C212yesmaximal
3#20295906C212yesmaximal, complemented
4C2×#16812659C211yesmaximal, characteristic
5C2×#13182038C2214yes—
6#16812766—22no—
7C4⋊#11724786—22no—
8#16812759—24no—
9C22×C22⋊D109C2211yescharacteristic
10C23×Dic109C411yescharacteristic
11C22×C4×D109C411yescharacteristic
12#16812659—22no—
13#16812659—22no—
14C2×#13182008C2211yescharacteristic
15C2×#13182006C411yescharacteristic
16C2×C4×Dic109C2211yescharacteristic
17C2×C22⋊C4×C109C411yescharacteristic
18#13182038—24no—
19#13182038—24no—
20C2×#11724786—24no—
21C23×D109C2×C411yescharacteristic
22C2×C22⋊D109—22no—
23C2×C22⋊D109—22no—
24C2×C22⋊D109D412yes—
25C2×C22⋊D109Q812yes—
26C22×Dic109—21no—
27C22×Dic109—21no—
28C22×Dic109—42no—
29C22×Dic109C2×C411yescharacteristic
30C22×Dic109C2×C411yescharacteristic
31C22×Dic109C2311yescharacteristic
32C2×C4×D109—21no—
33C2×C4×D109—21no—
34C2×C4×D109—42no—
35#13182008—22no—
36#13182006—22no—
37C4×Dic109D412yes—
38C4×Dic109D412yes—
39C24×C109C2×C411yescharacteristic
40C22×C4×C109C2×C411yescharacteristic
41C22×C4×C109C2×C411yescharacteristic
42C22⋊C4×C109—22no—
43C23×C109—21no—
44C23×C109—21no—
45C23×C109—41no—
46C23×C109—41no—
47C23×C109C4⋊C412yes—
48C23×C109C22×C411yescharacteristic
49C22×D109—21no—
50C22×D109—21no—
51C22×D109—41no—
52C22×D109—41no—
53C22×D109C4⋊C412yes—
54C2×C4×C109—21no—
55C2×C4×C109—41no—
56C2×C4×C109—41no—
57C2×C4×C109C22⋊C412yes—
58C22⋊D109—24no—
59C22⋊D109—24no—
60C2×Dic109—22no—
61C2×Dic109—21no—
62C2×Dic109—42no—
63C2×Dic109—42no—
64C2×Dic109—41no—
65C2×Dic109C22⋊C411yescharacteristic
66C2×Dic109C22⋊C411yescharacteristic
67C2×Dic109C2×D411yescharacteristic
68C2×Dic109C2×D412yes—
69C2×Dic109C2×Q811yescharacteristic
70C2×Dic109#4112yes—
71C4×D109—42no—
72C4×D109—42no—
73#11724786—44no—
74C22×C109—21no—
75C22×C109—21no—
76C22×C109—22no—
77C22×C109—42no—
78C22×C109—42no—
79C22×C109—41no—
80C22×C109—41no—
81C22×C109C2×C22⋊C411yescharacteristic
82C22×C109C2×C4⋊C411yescharacteristic
83C22×C109#11711yescharacteristic
84C2×D109—22no—
85C2×D109—42no—
86C2×D109—41no—
87C2×D109—41no—
88C2×D109—42no—
89C4×C109—22no—
90C4×C109—41no—
91Dic109—21no—
92Dic109—41no—
93Dic109#10012yescomplemented
94Dic109#12112yes—
95Dic109C22⋊Q812yes—
96C2×C109—21no—
97C2×C109—21no—
98C2×C109—42no—
99C2×C109#38011yescharacteristic
100C2×C109C2×#10011yescharacteristic
101C2×C109#41311yescharacteristic
102D109—42no—
103#1800—1091nomaximal, Sylow
104C109#180011yescharacteristic, complemented, Sylow
105C2×C4×D4—1091no—
106#423—1092no—
107C2×#100—1092no—
108#343—1092no—
109C22×D4—1091no—
110C23×C4—1091no—
111C23×C4—1091no—
112C2×M16—1094no—
113C4×D4—2182no—
114C4×D4—2182no—
115C2×C4⋊C4—1091no—
116C2×C22⋊C4—1091no—
117C2×C22⋊C4#8913711yescharacteristic
118C2×C42—1091no—
119C4⋊C8—2182no—
120C4⋊C8—2182no—
121#100—2184no—
122C24—1091no—
123C24C2×#8913711yescharacteristic
124C2×D4—1092no—
125C2×D4—1092no—
126C2×D4—2182no—
127C2×D4—2182no—
128C22×C4—1091no—
129C22×C4—1091no—
130C22×C4—1091no—
131C22×C4—4362no—
132C22×C4—4362no—
133C22×C4—2181no—
134C22×C4—2181no—
135C22×C4—2181no—
136C22×C4—2181no—
137C22×C4C2×#8913711yescharacteristic
138C22×C4C2×#8913711yescharacteristic
139M16—2184no—
140M16—2184no—
141C2×C8—2184no—
142C4⋊C4—2182no—
143C22⋊C4—22no—
144C22⋊C4—2182no—
145C42—1092no—
146C42—1092no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—1092no—
152C23—4361no—
153C23—4361no—
154C23—2181no—
155C23—2181no—
156C23C4⋊#8913712yes—
157C23C22×#8913711yescharacteristic
158D4—2184no—
159D4—2184no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—1092no—
164C2×C4—1091no—
165C2×C4—1091no—
166C2×C4—1091no—
167C2×C4—1092no—
168C2×C4—1091no—
169C2×C4—4362no—
170C2×C4—4362no—
171C2×C4—4362no—
172C2×C4—4362no—
173C2×C4—4361no—
174C2×C4—2182no—
175C2×C4—2181no—
176C2×C4C22⋊#8913712yes—
177C8—4364no—
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—4362no—
186C22—4362no—
187C22—4361no—
188C22—4361no—
189C22—2182no—
190C22C2×C22⋊#8913711yescharacteristic
191C22C2×C4⋊#8913711yescharacteristic
192C22#1681277811yescharacteristic
193C4—22no—
194C4—41no—
195C4—1092no—
196C4—1092no—
197C4—1092no—
198C4—4361no—
199C4—2181no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2—4362no—
204C2#2029596811yescharacteristic
205C2D109⋊#10011yescharacteristic
206C2#2029601311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
FittingC2×C22⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×C22⋊D109C22
cosocleC22×Dic109C23
hypercenterC2×C22⋊C4#89137
hypocenterC109#1800
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. #20296029C2semidirect
3. #20295906C2semidirect
93. Dic109#100semidirect
104. C109#1800semidirect

Maximal subgroups

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

subgroupindex
#202960292
C2×#168127592
#202959062
C2×#168126592
#1800109