Finite Group Databasebeta

← #28361369

Subgroups — #28361369

Order 13952.

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

normal subgroups only

This group has 316 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×#16812661C211yesmaximal, characteristic
2#20294988C212yesmaximal, complemented
3#20294752C211yesmaximal, characteristic, complemented
4#20294749C212yesmaximal, complemented
5#324×C109C211yesmaximal, characteristic, complemented
6C22×D436C411yescharacteristic
7C22×C4×D109C411yescharacteristic
8C22×C4×D109C2211yescharacteristic
9C2×#13182012—22no—
10#16812661—22no—
11#16812661—22no—
12C2×#13182006C411yescharacteristic
13C2×#13182006C2211yescharacteristic
14C2×C4×Dic109C411yescharacteristic
15C22⋊#11724784C2212yes—
16#16812611—22no—
17C2×C4⋊C4×C109C2211yescharacteristic
18C22⋊C8×C109C2212yes—
19C23×D109C2×C411yescharacteristic
20C23×D109C2×C411yescharacteristic
21C2×D436—22no—
22C2×D436—22no—
23C2×D436—22no—
24C22×Dic109C2×C411yescharacteristic
25C22×Dic109C2×C411yescharacteristic
26C2×C4×D109—21no—
27C2×C4×D109—21no—
28C2×C4×D109—42no—
29C2×C4×D109—42no—
30C2×C4×D109D412yes—
31C2×C4×D109D412yes—
32#13182012—44no—
33C2×#11724784—22no—
34#13182006—22no—
35#13182006—22no—
36C4×Dic109—21no—
37C4×Dic109—21no—
38C22×C4×C109C2×C411yescharacteristic
39C22×C4×C109C2×C411yescharacteristic
40C22×C4×C109C2311yescharacteristic
41C2×C8×C109—22no—
42C4⋊C4×C109—22no—
43C23×C109C22×C411yescharacteristic
44C22×D109—21no—
45C22×D109—21no—
46C22×D109—21no—
47C22×D109—21no—
48C22×D109—41no—
49C22×D109—41no—
50C22×D109—41no—
51C22×D109—41no—
52C22×D109C22⋊C412yes—
53C22×D109M1612yescomplemented
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109—21no—
57C2×C4×C109—41no—
58C2×C4×C109—41no—
59C2×C4×C109M1612yescomplemented
60C2×C4×C109C2×D412yes—
61C2×Dic109—22no—
62C2×Dic109—21no—
63C2×Dic109—41no—
64C2×Dic109C22⋊C411yescharacteristic
65C2×Dic109C22⋊C411yescharacteristic
66D436—28no—
67C4×D109—24no—
68C4×D109—42no—
69C4×D109—42no—
70C4×D109—42no—
71C8×C109—42no—
72#11724784—42no—
73C22×C109—21no—
74C22×C109—21no—
75C22×C109C2×C22⋊C411yescharacteristic
76C22×C109C2×M1611yescharacteristic
77C22×C109C2×M1611yescharacteristic
78C2×D109—22no—
79C2×D109—22no—
80C2×D109—22no—
81C2×D109—22no—
82C2×D109—42no—
83C2×D109—42no—
84C2×D109—42no—
85C2×D109—41no—
86C2×D109—41no—
87C2×D109—42no—
88C4×C109—22no—
89C4×C109—22no—
90C4×C109—41no—
91Dic109—21no—
92Dic109—41no—
93Dic109#9912yes—
94C2×C109—21no—
95C2×C109—21no—
96C2×C109#40711yescharacteristic
97C2×C109C2×#9911yescharacteristic
98C2×C109#41311yescharacteristic
99D109—42no—
100D109—42no—
101#1465—1091nomaximal, Sylow
102C109#146511yescharacteristic, complemented, Sylow
103C2×C4×D4—1091no—
104#407—1092no—
105#324—1091no—
106#324D10911yescharacteristic, complemented
107#323—1092no—
108C22×D4—1091no—
109C23×C4—1091no—
110C23×C4—1091no—
111C2×M16—2182no—
112C4×D4—2182no—
113C4×D4—2182no—
114C2×C4⋊C4C2×D10911yescharacteristic
115C2×C22⋊C4—1091no—
116C2×C22⋊C4—1091no—
117C2×C42—1091no—
118C22⋊C8—1092no—
119C22⋊C8—2182no—
120C22⋊C8C2×D10912yes—
121C24—1091no—
122C24—1091no—
123C2×D4—2182no—
124C2×D4—2182no—
125C2×D4—2182no—
126C22×C4—1091no—
127C22×C4—1092no—
128C22×C4—1092no—
129C22×C4—1091no—
130C22×C4—4362no—
131C22×C4—4362no—
132C22×C4—2181no—
133C22×C4—2181no—
134C22×C4C4×D10911yescharacteristic
135C22×C4C4×D10911yescharacteristic
136C22×C4C22×D10911yescharacteristic
137M16—4364no—
138C2×C8—22no—
139C2×C8—2182no—
140C4⋊C4—22no—
141C22⋊C4—2182no—
142C22⋊C4—2182no—
143C42—2181no—
144C42—2181no—
145C23—1092no—
146C23—1092no—
147C23—4361no—
148C23—4361no—
149C23—4361no—
150C23—4361no—
151C23—2181no—
152C23—2181no—
153C23—2181no—
154C23—2181no—
155C23C2×C4×D10911yescharacteristic
156D4—2188no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—1091no—
163C2×C4—1091no—
164C2×C4—4362no—
165C2×C4—4362no—
166C2×C4—4362no—
167C2×C4—4361no—
168C2×C4—2184no—
169C2×C4—2182no—
170C2×C4—2181no—
171C2×C4#1318201212yescomplemented
172C2×C4D4×D10912yes—
173C8—42no—
174C8—4362no—
175C22—21no—
176C22—21no—
177C22—4362no—
178C22—4362no—
179C22—4362no—
180C22—4362no—
181C22—4361no—
182C22—4361no—
183C22—2182no—
184C22—2182no—
185C22—2182no—
186C22—2182no—
187C22C22⋊C4×D10911yescharacteristic
188C22M16×D10911yescharacteristic
189C22C2×#1318201211yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—1092no—
194C4—4361no—
195C4—2181no—
196C2—21no—
197C2—21no—
198C2—4362no—
199C2—4362no—
200C2#2029498811yescharacteristic
201C2#99×D10911yescharacteristic
202C2#2029500911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D109
commutatorC23×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#324×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC22×D436C4
cosocleC22×C4×C109C23
hypercenter#324D109
hypocenterC109#1465
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20294988C2semidirect
3. #20294752C2semidirect
4. #20294749C2semidirect
5. #324×C109C2semidirect
53. C22×D109M16semidirect
59. C2×C4×C109M16semidirect
102. C109#1465semidirect
106. #324D109semidirect
171. C2×C4#13182012semidirect

Maximal subgroups

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

subgroupindex
C2×#168126612
#202949882
#202947522
#202947492
#324×C1092
#1465109