Finite Group Databasebeta

← #28361371

Subgroups — #28361371

Order 13952.

300 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#16812659C211yesmaximal, characteristic
2#20295080C212yesmaximal, complemented
3#20294750C211yesmaximal, characteristic, complemented
4#20294749C212yesmaximal, complemented
5#323×C109C211yesmaximal, characteristic, complemented
6C22×C22⋊D109C411yescharacteristic
7C23×Dic109C411yescharacteristic
8C22×C4×D109C411yescharacteristic
9#16812659—22no—
10#16812659—22no—
11C2×#13182008C411yescharacteristic
12C2×#13182006C2211yescharacteristic
13C2×C4×Dic109C2211yescharacteristic
14#16812628—22no—
15C22⋊#11724784C2212yes—
16#16812609—22no—
17C2×C22⋊C4×C109C2211yescharacteristic
18C22⋊C8×C109C2212yes—
19C23×D109C2×C411yescharacteristic
20C2×C22⋊D109—22no—
21C2×C22⋊D109—22no—
22C2×C22⋊D109—22no—
23C22×Dic109—21no—
24C22×Dic109—21no—
25C22×Dic109—42no—
26C22×Dic109C2×C411yescharacteristic
27C22×Dic109C2×C411yescharacteristic
28C22×Dic109C2×C411yescharacteristic
29C2×C4×D109—21no—
30C2×C4×D109—21no—
31C2×C4×D109—42no—
32C2×#11724784—22no—
33#13182008—22no—
34#13182006—22no—
35C4×Dic109D412yes—
36C4×Dic109D412yes—
37C24×C109C2×C411yescharacteristic
38C22×C4×C109C2×C411yescharacteristic
39C22×C4×C109C2311yescharacteristic
40C2×C8×C109—22no—
41C22⋊C4×C109—22no—
42C23×C109—21no—
43C23×C109—21no—
44C23×C109—41no—
45C23×C109—41no—
46C23×C109M1612yes—
47C23×C109C22×C411yescharacteristic
48C22×D109—21no—
49C22×D109—21no—
50C22×D109—41no—
51C22×D109—41no—
52C22×D109M1612yes—
53C2×C4×C109—21no—
54C2×C4×C109—41no—
55C2×C4×C109—41no—
56C2×C4×C109C2×D412yes—
57C22⋊D109—28no—
58C2×Dic109—21no—
59C2×Dic109—21no—
60C2×Dic109—22no—
61C2×Dic109—21no—
62C2×Dic109—42no—
63C2×Dic109—42no—
64C2×Dic109—41no—
65C2×Dic109C22⋊C412yes—
66C2×Dic109C22⋊C411yescharacteristic
67C2×Dic109C22⋊C411yescharacteristic
68C4×D109—42no—
69C4×D109—42no—
70C8×C109—42no—
71#11724784—42no—
72C22×C109—21no—
73C22×C109—21no—
74C22×C109—22no—
75C22×C109—42no—
76C22×C109—42no—
77C22×C109—41no—
78C22×C109—41no—
79C22×C109C2×C22⋊C411yescharacteristic
80C22×C109C2×M1611yescharacteristic
81C22×C109C2×M1611yescharacteristic
82C2×D109—22no—
83C2×D109—42no—
84C2×D109—41no—
85C2×D109—41no—
86C2×D109—42no—
87C4×C109—22no—
88C4×C109—41no—
89Dic109—22no—
90Dic109—21no—
91Dic109—41no—
92Dic109#10012yes—
93C2×C109—21no—
94C2×C109—21no—
95C2×C109—42no—
96C2×C109#40711yescharacteristic
97C2×C109#41011yescharacteristic
98C2×C109C2×#10011yescharacteristic
99D109—42no—
100#1466—1091nomaximal, Sylow
101C109#146611yescharacteristic, complemented, Sylow
102C2×C4×D4—1091no—
103#432—1092no—
104#323—1091no—
105#323—1092no—
106#323D10911yescharacteristic, complemented
107C22×D4—1091no—
108C23×C4—1091no—
109C23×C4—1091no—
110C4×D4—2182no—
111C4×D4—2182no—
112C2×C4⋊C4—1091no—
113C2×C22⋊C4—1091no—
114C2×C22⋊C4C2×D10911yescharacteristic
115C2×C42—1091no—
116C4⋊C8—2182no—
117C22⋊C8—1092no—
118C22⋊C8C2×D10912yes—
119#97—2182no—
120C24—1091no—
121C24C4×D10911yescharacteristic
122C2×D4—2182no—
123C2×D4—2182no—
124C2×D4—2182no—
125C22×C4—1091no—
126C22×C4—1091no—
127C22×C4—1091no—
128C22×C4—4362no—
129C22×C4—4362no—
130C22×C4—2181no—
131C22×C4—2181no—
132C22×C4—2181no—
133C22×C4—2181no—
134C22×C4C4×D10911yescharacteristic
135C22×C4C22×D10911yescharacteristic
136C2×C8—22no—
137C2×C8—2182no—
138C4⋊C4—2182no—
139C22⋊C4—22no—
140C22⋊C4—2182no—
141C42—1092no—
142C42—1092no—
143C23—21no—
144C23—21no—
145C23—41no—
146C23—41no—
147C23—1092no—
148C23—4361no—
149C23—4361no—
150C23—2181no—
151C23—2181no—
152C23#1318201212yes—
153C23C2×C4×D10911yescharacteristic
154D4—2188no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—1091no—
159C2×C4—1092no—
160C2×C4—1091no—
161C2×C4—4362no—
162C2×C4—4362no—
163C2×C4—4362no—
164C2×C4—4362no—
165C2×C4—4361no—
166C2×C4—2182no—
167C2×C4—2181no—
168C2×C4—2181no—
169C2×C4—2181no—
170C2×C4D4×D10912yes—
171C8—42no—
172C8—4362no—
173C22—21no—
174C22—21no—
175C22—22no—
176C22—42no—
177C22—42no—
178C22—41no—
179C22—41no—
180C22—4362no—
181C22—4362no—
182C22—4361no—
183C22—4361no—
184C22—2182no—
185C22C22⋊C4×D10911yescharacteristic
186C22M16×D10911yescharacteristic
187C22C2×#1318201211yescharacteristic
188C4—22no—
189C4—41no—
190C4—1092no—
191C4—4361no—
192C4—2182no—
193C4—2181no—
194C2—21no—
195C2—21no—
196C2—42no—
197C2—4362no—
198C2#2029498811yescharacteristic
199C2#2029499811yescharacteristic
200C2#100×D10911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D109
commutatorC23×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#323×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC22×C22⋊D109C4
cosocleC22×C4×C109C23
hypercenter#323D109
hypocenterC109#1466
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #20295080C2semidirect
3. #20294750C2semidirect
4. #20294749C2semidirect
5. #323×C109C2semidirect
101. C109#1466semidirect
106. #323D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168126592
#202950802
#202947502
#202947492
#323×C1092
#1466109