Finite Group Databasebeta

← #28371326

Subgroups — #28371326

Order 13952.

1102 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 197 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
1C24×Dic109C211yesmaximal, characteristic, complemented
2C2×#16812683C212yesmaximal, complemented
3C2×#16812668C211yesmaximal, characteristic
4#20294903C214yesmaximal, complemented
5#20294901C214yesmaximal, complemented
6#20294887C212yesmaximal, complemented
7#379×C109C211yesmaximal, characteristic, complemented
8C22×C22⋊D109C2211yescharacteristic
9C22×C22⋊D109C2212yes—
10C23×Dic109—28no—
11C23×Dic109—24no—
12C23×Dic109C2214yes—
13C23×Dic109C2212yes—
14#16812683—28no—
15#16812668—24no—
16C2×C4⋊Dic109C2214yescomplemented
17C2×C22⋊Dic109C2211yescharacteristic
18C2×C22⋊Dic109C2212yes—
19C2×#13182006C2214yescomplemented
20#16812606C2218yescomplemented
21C25×C109C2211yescharacteristic
22C2×C22⋊C4×C109C2212yes—
23C2×C22⋊C4×C109C2214yes—
24C23×D109C2311yescharacteristic
25C2×C22⋊D109—22no—
26C2×C22⋊D109—24no—
27C2×C22⋊D109—24no—
28C2×C22⋊D109—28no—
29C22×Dic109—232no—
30C22×Dic109—24no—
31C22×Dic109—28no—
32C22×Dic109—24no—
33C22×Dic109—216no—
34C22×Dic109D418yescomplemented
35C22×Dic109C2312yes—
36C22×Dic109C2311yescharacteristic
37C22×Dic109C2314yes—
38C4⋊Dic109—28no—
39C22⋊Dic109—22no—
40C22⋊Dic109—24no—
41#13182006—28no—
42C24×C109—24no—
43C24×C109—28no—
44C24×C109D414yes—
45C24×C109C2311yescharacteristic
46C24×C109C2312yes—
47C22×C4×C109C2314yes—
48C22⋊C4×C109—24no—
49C22⋊C4×C109—28no—
50C23×C109—232no—
51C23×C109—28no—
52C23×C109—216no—
53C23×C109—24no—
54C23×C109—24no—
55C23×C109—24no—
56C23×C109C2×D414yes—
57C23×C109C2×D412yes—
58C23×C109C2×D414yes—
59C23×C109#4118yes—
60C23×C109C2411yescharacteristic
61C22×D109—22no—
62C22×D109—21no—
63C22×D109—24no—
64C2×C4×C109—24no—
65C2×C4×C109—28no—
66C22⋊D109—44no—
67C22⋊D109—48no—
68C2×Dic109—232no—
69C2×Dic109—216no—
70C2×Dic109—24no—
71C2×Dic109—24no—
72C2×Dic109—21no—
73C2×Dic109—22no—
74C2×Dic109—22no—
75C2×Dic109—24no—
76C2×Dic109C2×D418yes—
77C22×C109—232no—
78C22×C109—24no—
79C22×C109—24no—
80C22×C109—24no—
81C22×C109—28no—
82C22×C109—216no—
83C22×C109#12014yes—
84C22×C109#12318yescomplemented
85C22×C109C22×D412yes—
86C22×C109C22×D411yescharacteristic
87C22×C109C2×#4114yes—
88C2×D109—41no—
89C2×D109—42no—
90C2×D109—44no—
91C4×C109—44no—
92Dic109—28no—
93Dic109—41no—
94Dic109—42no—
95C2×C109—24no—
96C2×C109—28no—
97C2×C109C2×#12011yescharacteristic
98C2×C109C2×#12312yes—
99C2×C109#52514yes—
100D109—81no—
101#2849—1091nomaximal, Sylow
102C109#284911yescharacteristic, complemented, Sylow
103C24×C4—1091no—
104C2×#123—1092no—
105C2×#120—1091no—
106#386—1094no—
107#385—1094no—
108#381—1092no—
109#379D10911yescharacteristic, complemented
110C25C2×D10911yescharacteristic
111C22×D4—1091no—
112C22×D4—1092no—
113C23×C4—1092no—
114C23×C4—1094no—
115C23×C4—2188no—
116C23×C4—2184no—
117#123—2188no—
118#120—2184no—
119C2×C4⋊C4—1094no—
120C2×C22⋊C4—1091no—
121C2×C22⋊C4—1092no—
122C2×C22⋊C4—1094no—
123C2×C22⋊C4C2×D10912yes—
124C2×C22⋊C4C2×D10914yes—
125#95—1098no—
126C24—24no—
127C24—28no—
128C24—1091no—
129C24D43614yes—
130C24C22×D10911yescharacteristic
131C24C22×D10912yes—
132C2×D4—2184no—
133C2×D4—2182no—
134C2×D4—2184no—
135C2×D4—2188no—
136C22×C4—1098no—
137C22×C4—1094no—
138C22×C4—1092no—
139C22×C4—1091no—
140C22×C4—21816no—
141C22×C4—21832no—
142C22×C4—2184no—
143C22×C4—2188no—
144C22×C4—2184no—
145C22×C4C22×D10914yes—
146C4⋊C4—2188no—
147C22⋊C4—24no—
148C22⋊C4—28no—
149C22⋊C4—2188no—
150C22⋊C4—2182no—
151C22⋊C4—2184no—
152C23—232no—
153C23—28no—
154C23—216no—
155C23—24no—
156C23—24no—
157C23—24no—
158C23—2182no—
159C23—2181no—
160C23—2184no—
161C23D4×D10914yes—
162C23C2×D43612yes—
163C23C2×D43614yes—
164C23#1318202818yes—
165C23C23×D10911yescharacteristic
166D4—4364no—
167D4—4368no—
168C2×C4—24no—
169C2×C4—28no—
170C2×C4—1098no—
171C2×C4—2182no—
172C2×C4—2181no—
173C2×C4—2182no—
174C2×C4—2184no—
175C2×C4—21832no—
176C2×C4—21816no—
177C2×C4—2184no—
178C2×C4—2184no—
179C22—232no—
180C22—24no—
181C22—24no—
182C22—24no—
183C22—28no—
184C22—216no—
185C22—4361no—
186C22—4362no—
187C22—4364no—
188C22#1681266914yes—
189C22#1681268318yescomplemented
190C22C2×D4×D10912yes—
191C22C22×D43611yescharacteristic
192C22C2×#1318202814yes—
193C4—44no—
194C4—4361no—
195C4—4362no—
196C4—2188no—
197C2—24no—
198C2—28no—
199C2—8721no—
200C2C2×#1681266911yescharacteristic
201C2C2×#1681268312yes—
202C2#2029553214yes—
subgroupG/H
center, FrattiniC23C23×D109
commutator, socle, cosocleC23×C109C24
Fitting#379×C109C2
prime radicalC2×#16812668C2
hypercenter#379D109
hypocenterC109#2849
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C24×Dic109C2semidirect
2. C2×#16812683C2semidirect
4. #20294903C2semidirect
5. #20294901C2semidirect
6. #20294887C2semidirect
7. #379×C109C2semidirect
16. C2×C4⋊Dic109C22semidirect
19. C2×#13182006C22semidirect
20. #16812606C22semidirect
34. C22×Dic109D4semidirect
84. C22×C109#123semidirect
102. C109#2849semidirect
109. #379D109semidirect
189. C22#16812683semidirect

Maximal subgroups

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

subgroupindex
C24×Dic1092
C2×#168126832
C2×#168126682
#202949032
#202949012
#202948872
#379×C1092
#2849109