Finite Group Databasebeta

← #28378428

Subgroups — #28378428

Order 13952.

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

normal subgroups only

This group has 346 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#20295997C211yesmaximal, characteristic, complemented
2C4×C22⋊#89137C211yesmaximal, characteristic, complemented
3#20295877C214yesmaximal, complemented
4C2×#16812670C211yesmaximal, characteristic
5C2×#13182039—21no—
6C2×C22⋊#89137—21no—
7C2×C4×#89137—21no—
8#16812756C2212yescomplemented
9C22⋊#11724786—21no—
10(C2×#89137)⋊C4C2212yescomplemented
11C22×C22⋊D109—21no—
12C22×C4×D109C2211yescharacteristic
13#16812670—21no—
14#16812670—21no—
15#16812670C412yescomplemented
16#16812670C2212yes—
17C2×C4⋊Dic109C411yescharacteristic, complemented
18C2×C22⋊Dic109—21no—
19C22×D4×C109C411yescharacteristic, complemented
20C22×#89137—22no—
21#13182039—42no—
22C2×#11724786—22no—
23C22⋊#89137—24no—
24C4×#89137—42no—
25C23×D109D411yescharacteristic
26C2×C22⋊D109—22no—
27C2×C22⋊D109—22no—
28C2×C22⋊D109—44no—
29C22×Dic109—21no—
30C22×Dic109D411yescharacteristic
31C2×C4×D109—42no—
32C2×C4×D109C2×C411yescharacteristic
33C2×C4×D109D411yescharacteristic
34C2×C4×D109D411yescharacteristic
35C2×C4×D109C2311yescharacteristic
36C4⋊Dic109—21no—
37C4⋊Dic109C2×C412yes—
38C22⋊Dic109—22no—
39C22⋊Dic109—22no—
40C24×C109—21no—
41C2×D4×C109—21no—
42C2×D4×C109—42no—
43C2×D4×C109C2×C412yes—
44C22×C4×C109C2×C411yescharacteristic
45C23×C109—22no—
46C23×C109—42no—
47C23×C109—42no—
48C23×C109—42no—
49C23×C109C22⋊C411yescharacteristic
50C22×D109—22no—
51C22×D109—22no—
52C22×D109—41no—
53C22×D109C22⋊C411yescharacteristic
54C22×D109C2×D411yescharacteristic
55C2×#89137—24no—
56C2×#89137—42no—
57C2×#89137—42no—
58D4×C109—42no—
59D4×C109—42no—
60C2×C4×C109—22no—
61C2×C4×C109C22⋊C411yescharacteristic
62C2×C4×C109C22×C411yescharacteristic
63C22⋊D109—44no—
64C22⋊D109—44no—
65C2×Dic109—22no—
66C2×Dic109—41no—
67C2×Dic109—42no—
68C2×Dic109C22⋊C411yescharacteristic
69C2×Dic109C2×D411yescharacteristic
70C4×D109—22no—
71C4×D109—22no—
72C4×D109—41no—
73C4×D109—41no—
74#11724786—42no—
75C22×C109—21no—
76C22×C109—21no—
77C22×C109—42no—
78C22×C109—42no—
79C22×C109—42no—
80C22×C109—84no—
81C22×C109#10412yes—
82C22×C109C2×C22⋊C411yescharacteristic
83C2×D109—21no—
84C2×D109—21no—
85C2×D109—21no—
86C2×D109—21no—
87C2×D109—21no—
88C2×D109—44no—
89C2×D109AGL(1,ℤ/8)12yes—
90#89137—44no—
91C4×C109—21no—
92C4×C109#9912yes—
93Dic109—21no—
94Dic109—21no—
95Dic109—42no—
96C2×C109—22no—
97C2×C109—82no—
98C2×C109C2×#9911yescharacteristic
99C2×C109#41811yescharacteristic
100C2×C109C2×#10411yescharacteristic
101D109—22no—
102D109—41no—
103#1507—1091nomaximal, Sylow
104C109#150711yescharacteristic, complemented, Sylow
105C2×#121—1091no—
106#407—1091no—
107C4×C22⋊C4—1091no—
108#327—1094no—
109C22×D4—2181no—
110C22×D4#8913711yescharacteristic, complemented
111C23×C4—1091no—
112C2×M16—2181no—
113#121—1092no—
114#121—1092no—
115#121—2181no—
116#121—2181no—
117C2×C4⋊C4—1091no—
118C2×C22⋊C4—2181no—
119C2×C22⋊C4—2181no—
120C2×C42—2181no—
121C22⋊C8—1092no—
122C22⋊C8—2181no—
123#95—1092no—
124C24—21no—
125C24—1091no—
126C2×D4—21no—
127C2×D4—42no—
128C2×D4—4364no—
129C2×D4—2182no—
130C2×D4—2182no—
131C2×D4C2×#8913712yes—
132C22×C4—1091no—
133C22×C4—1091no—
134C22×C4—1091no—
135C22×C4—1091no—
136C22×C4—1091no—
137C22×C4—4362no—
138C22×C4—2182no—
139C22×C4—2181no—
140C22×C4C2×#8913711yescharacteristic
141M16—4362no—
142C2×C8—2182no—
143C4⋊C4—1092no—
144C4⋊C4—2181no—
145C22⋊C4—2182no—
146C22⋊C4—2182no—
147C22⋊C4—2184no—
148C42—4362no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—42no—
153C23—1091no—
154C23—1091no—
155C23—4361no—
156C23—2182no—
157C23—2182no—
158C23C22⋊#8913711yescharacteristic
159D4—42no—
160D4—42no—
161D4—4364no—
162D4—4364no—
163C2×C4—22no—
164C2×C4—1091no—
165C2×C4—1091no—
166C2×C4—4361no—
167C2×C4—4361no—
168C2×C4—4362no—
169C2×C4—4362no—
170C2×C4—4362no—
171C2×C4—4361no—
172C2×C4—2184no—
173C2×C4—2182no—
174C2×C4—2182no—
175C2×C4—2182no—
176C2×C4C22⋊#8913711yescharacteristic
177C2×C4C22×#8913711yescharacteristic
178C8—4362no—
179C22—21no—
180C22—21no—
181C22—42no—
182C22—42no—
183C22—42no—
184C22—84no—
185C22—1092no—
186C22—4364no—
187C22—2181no—
188C22—2181no—
189C22—2181no—
190C22—2181no—
191C22—2181no—
192C22#1681276312yes—
193C22C2×C22⋊#8913711yescharacteristic
194C4—21no—
195C4—4364no—
196C4—4362no—
197C4—2181no—
198C4—2181no—
199C4#1681275712yes—
200C2—22no—
201C2—82no—
202C2—4361no—
203C2—2182no—
204C2C2×#1681275711yescharacteristic
205C2#2029601811yescharacteristic
206C2C2×#1681276311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC22×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×#16812670C2
cosocleC2×C4×D109C23
hypercenterC22×D4#89137
hypocenterC109#1507
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #20295997C2semidirect
2. C4×C22⋊#89137C2semidirect
3. #20295877C2semidirect
8. #16812756C22semidirect
10. (C2×#89137)⋊C4C22semidirect
15. #16812670C4semidirect
17. C2×C4⋊Dic109C4semidirect
19. C22×D4×C109C4semidirect
104. C109#1507semidirect
110. C22×D4#89137semidirect

Maximal subgroups

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

subgroupindex
#202959972
C4×C22⋊#891372
#202958772
C2×#168126702
#1507109