Finite Group Databasebeta

← #28378940

Subgroups — #28378940

Order 13952.

306 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 68 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
2C4×C22⋊#89137C211yesmaximal, characteristic
3#20295896C212yesmaximal, complemented
4#20295896C212yesmaximal, complemented
5#117×D109C211yesmaximal, characteristic
6C2×#13182039C2212yes—
7C2×C22⋊#89137—21no—
8C2×C4×#89137C2212yes—
9#16812756—21no—
10C22⋊#11724786—21no—
11(C2×#89137)⋊C4—21no—
12C22×C4×D109C2211yescharacteristic
13#16812658C411yescharacteristic, complemented
14#16812657C2211yescharacteristic
15#16812657C2211yescharacteristic
16#16812656—21no—
17#16812655—21no—
18C4⋊C4×D109C411yescharacteristic, complemented
19C4⋊C4×D109C411yescharacteristic, complemented
20C22⋊C4×D109—21no—
21C42×D109—21no—
22#117×C109C411yescharacteristic, complemented
23C22×#89137—22no—
24#13182039—24no—
25C2×#11724786—22no—
26C22⋊#89137—24no—
27C4×#89137—24no—
28C23×D109D411yescharacteristic
29C22×Dic109D411yescharacteristic
30C2×C4×D109—24no—
31C2×C4×D109—21no—
32C2×C4×D109—21no—
33C2×C4×D109C2×C411yescharacteristic
34C2×C4×D109D411yescharacteristic
35C2×C4×D109D411yescharacteristic
36C2×C4×D109C2311yescharacteristic
37C4⋊Dic109C2×C411yescharacteristic
38C4⋊Dic109C2×C411yescharacteristic
39#13182008—21no—
40#13182008—21no—
41C22⋊Dic109—21no—
42#13182006—21no—
43#13182006—21no—
44C4×Dic109—21no—
45C4×Dic109—21no—
46C4×Dic109—21no—
47C22×C4×C109C2×C411yescharacteristic
48C4⋊C4×C109C2×C411yescharacteristic
49C4⋊C4×C109C2×C411yescharacteristic
50C22⋊C4×C109—21no—
51C42×C109—21no—
52C23×C109C22⋊C411yescharacteristic
53C22×D109—22no—
54C22×D109—22no—
55C22×D109—41no—
56C22×D109C22⋊C411yescharacteristic
57C22×D109C2×D411yescharacteristic
58C2×#89137—24no—
59C2×#89137—42no—
60C2×#89137—42no—
61C2×C4×C109—22no—
62C2×C4×C109—21no—
63C2×C4×C109—21no—
64C2×C4×C109C22⋊C411yescharacteristic
65C2×C4×C109C22×C411yescharacteristic
66C2×Dic109—22no—
67C2×Dic109—21no—
68C2×Dic109—21no—
69C2×Dic109C22⋊C411yescharacteristic
70C2×Dic109C2×D411yescharacteristic
71C4×D109—22no—
72C4×D109—22no—
73C4×D109—22no—
74C4×D109—42no—
75C4×D109—42no—
76C4×D109#4114yes—
77#11724786—42no—
78C22×C109—21no—
79C22×C109—21no—
80C22×C109—21no—
81C22×C109C2×C22⋊C411yescharacteristic
82C2×D109—21no—
83C2×D109—21no—
84C2×D109—21no—
85C2×D109—21no—
86C2×D109—44no—
87C2×D109#10412yes—
88C2×D109#12312yes—
89#89137—44no—
90C4×C109—21no—
91C4×C109—41no—
92C4×C109—41no—
93C4×C109#11712yes—
94Dic109—21no—
95Dic109—41no—
96Dic109—41no—
97Dic109#12312yes—
98C2×C109—41no—
99C2×C109#38111yescharacteristic
100C2×C109C2×#10411yescharacteristic
101C2×C109#42111yescharacteristic
102D109—22no—
103D109—22no—
104#1826—1091nomaximal, Sylow
105C109#182611yescharacteristic, complemented, Sylow
106C2×#117—1091no—
107#407—1091no—
108C4×C22⋊C4—1091no—
109#339—1092no—
110#339—1092no—
111C23×C4—1091no—
112C2×M16—1092no—
113#117—1091no—
114#117—1091no—
115#117—1091no—
116#117—2181no—
117#117—2181no—
118#117#8913711yescharacteristic, complemented
119C2×C4⋊C4—1091no—
120C2×C4⋊C4—1091no—
121C2×C22⋊C4—2181no—
122C2×C22⋊C4—2181no—
123C2×C42—1092no—
124C2×C42—2181no—
125C22⋊C8—2181no—
126C22⋊C8—2181no—
127#95—2181no—
128C24—1091no—
129C22×C4—1091no—
130C22×C4—1091no—
131C22×C4—1091no—
132C22×C4—1091no—
133C22×C4—1091no—
134C22×C4—2184no—
135C22×C4—2181no—
136C22×C4—2181no—
137C22×C4—2182no—
138C22×C4C2×#8913711yescharacteristic
139M16—2184no—
140C2×C8—2182no—
141C4⋊C4—1091no—
142C4⋊C4—1091no—
143C4⋊C4—2181no—
144C4⋊C4—2181no—
145C4⋊C4C2×#8913711yescharacteristic
146C4⋊C4C2×#8913711yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—2181no—
149C22⋊C4—2181no—
150C22⋊C4—2184no—
151C22⋊C4—2181no—
152C42—21no—
153C42—2181no—
154C42—2181no—
155C42—2184no—
156C42—2181no—
157C23—1091no—
158C23—1091no—
159C23—4361no—
160C23—2182no—
161C23—2182no—
162C23C22⋊#8913711yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—1091no—
167C2×C4—1094no—
168C2×C4—1091no—
169C2×C4—4362no—
170C2×C4—4362no—
171C2×C4—4362no—
172C2×C4—4362no—
173C2×C4—2182no—
174C2×C4—2182no—
175C2×C4—2182no—
176C2×C4—2184no—
177C2×C4—2181no—
178C2×C4—2181no—
179C2×C4—2182no—
180C2×C4C22⋊#8913711yescharacteristic
181C2×C4C22×#8913711yescharacteristic
182C8—4362no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—1092no—
187C22—1092no—
188C22—4364no—
189C22—2181no—
190C22—2181no—
191C22—2181no—
192C22—2181no—
193C22C2×C22⋊#8913711yescharacteristic
194C4—21no—
195C4—41no—
196C4—41no—
197C4—1092no—
198C4—4364no—
199C4—4361no—
200C4—4361no—
201C4—2181no—
202C4#1681277812yes—
203C2—41no—
204C2—2182no—
205C2—2182no—
206C2#2029596911yescharacteristic
207C2D109⋊#10411yescharacteristic
208C2#2029602311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#117×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC23×D109D4
cosocleC2×C4×D109C23
hypercenter#117#89137
hypocenterC109#1826
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #20295896C2semidirect
4. #20295896C2semidirect
13. #16812658C4semidirect
18. C4⋊C4×D109C4semidirect
19. C4⋊C4×D109C4semidirect
22. #117×C109C4semidirect
105. C109#1826semidirect
118. #117#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
#202958962
#117×D1092
#1826109