Finite Group Databasebeta

← #27194175

Subgroups — #27194175

Order 13184.

208 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 53 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#20268124C211yesmaximal, characteristic, complemented
2#20268107C211yesmaximal, characteristic
3#20267730C211yesmaximal, characteristic, complemented
4#20267528C211yesmaximal, characteristic, complemented
5#20267525C211yesmaximal, characteristic
6#20267517C211yesmaximal, characteristic, complemented
7#539×C103C211yesmaximal, characteristic
8C2×C4⋊Dic103C2211yescharacteristic
9#15692954—21no—
10#15692952—21no—
11#15692945—21no—
12#15692942—21no—
13C22⋊(C103⋊C8)C2211yescharacteristic
14C22⋊(C103⋊C8)C2211yescharacteristic
15C103⋊#95—21no—
16C103⋊#95—21no—
17C103⋊#95C2211yescharacteristic
18#126×C103—21no—
19#125×C103—21no—
20#123×C103—21no—
21#123×C103—21no—
22C22⋊Q8×C103—21no—
23C22⋊Q8×C103C2211yescharacteristic
24#121×C103C2211yescharacteristic
25C4×D4×C103—21no—
26C2×C4⋊C4×C103C2211yescharacteristic
27C22×Dic103—21no—
28C22×Dic103—21no—
29C2×C103⋊C8—21no—
30C2×C103⋊C8—21no—
31C4⋊Dic103—21no—
32C4⋊Dic103—21no—
33C2×Q8×C103D411yescharacteristic
34C2×D4×C103—21no—
35C2×D4×C103D411yescharacteristic
36C22×C4×C103—21no—
37C22×C4×C103D411yescharacteristic
38C22×C4×C103D411yescharacteristic
39C22×C4×C103C2311yescharacteristic
40C4⋊C4×C103—21no—
41C4⋊C4×C103—21no—
42C4⋊C4×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103D411yescharacteristic
47C4⋊C4×C103D411yescharacteristic
48C22⋊C4×C103—21no—
49C22⋊C4×C103—21no—
50C22⋊C4×C103—21no—
51C22⋊C4×C103—21no—
52C22⋊C4×C103—21no—
53C42×C103—21no—
54C23×C103—21no—
55C23×C103C2×D411yescharacteristic
56Q8×C103—41no—
57D4×C103—41no—
58D4×C103—41no—
59D4×C103—41no—
60C2×C4×C103—21no—
61C2×C4×C103—21no—
62C2×C4×C103—21no—
63C2×C4×C103—21no—
64C2×C4×C103—21no—
65C2×C4×C103—21no—
66C2×C4×C103—21no—
67C2×C4×C103—41no—
68C2×C4×C103—41no—
69C2×C4×C103—81no—
70C2×C4×C103C2×D411yescharacteristic
71C2×C4×C103C2×D411yescharacteristic
72C2×Dic103—41no—
73C2×Dic103—41no—
74C2×Dic103—42no—
75C2×Dic103—41no—
76C2×Dic103—41no—
77C103⋊C8—41no—
78C103⋊C8—41no—
79C22×C103—21no—
80C22×C103—21no—
81C22×C103—41no—
82C22×C103—41no—
83C22×C103—41no—
84C22×C103#12011yescharacteristic
85C22×C103#13511yescharacteristic
86C22×C103#13711yescharacteristic
87C4×C103—21no—
88C4×C103—21no—
89C4×C103—41no—
90C4×C103—41no—
91C4×C103—41no—
92C4×C103—41no—
93C4×C103—41no—
94Dic103—81no—
95Dic103—81no—
96C2×C103—21no—
97C2×C103—21no—
98C2×C103—81no—
99C2×C103#45211yescharacteristic
100C2×C103#45411yescharacteristic
101C2×C103#45811yescharacteristic
102#1615—1031nomaximal, Sylow
103C103#161511yescharacteristic, complemented, Sylow
104#539D10311yescharacteristic
105#484—1031no—
106#481—1031no—
107#400—1031no—
108#328—1031no—
109#327—1031no—
110#324—1031no—
111#126—21no—
112#125—21no—
113#123—21no—
114#123—21no—
115C22⋊Q8—21no—
116C22⋊Q8C2×D10311yescharacteristic
117#121C2×D10311yescharacteristic
118C4×D4—21no—
119C2×C4⋊C4—1031no—
120C2×C4⋊C4C2×D10311yescharacteristic
121#107—2061no—
122#106—2061no—
123#103—2061no—
124#102—2061no—
125C22⋊C8—1031no—
126C22⋊C8—1031no—
127#95—1031no—
128#95—2061no—
129#95—2061no—
130C2×Q8C22⋊D10311yescharacteristic
131C2×D4—21no—
132C2×D4C22⋊D10311yescharacteristic
133C22×C4—21no—
134C22×C4—2061no—
135C22×C4—2061no—
136C22×C4C22⋊D10311yescharacteristic
137C22×C4C22⋊D10311yescharacteristic
138C22×C4C22×D10311yescharacteristic
139C2×C8—2061no—
140C2×C8—2061no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—2061no—
148C4⋊C4—2061no—
149C4⋊C4C22⋊D10311yescharacteristic
150C4⋊C4C22⋊D10311yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—21no—
156C42—21no—
157C23—21no—
158C23C2×C22⋊D10311yescharacteristic
159Q8—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—4121no—
174C2×C4—4121no—
175C2×C4—4122no—
176C2×C4—4121no—
177C2×C4—4121no—
178C2×C4C2×C22⋊D10311yescharacteristic
179C2×C4C2×C22⋊D10311yescharacteristic
180C8—4121no—
181C8—4121no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1569299011yescharacteristic
188C22#1569304111yescharacteristic
189C22#1569305111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—41no—
195C4—41no—
196C4—41no—
197C4—8241no—
198C4—8241no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#2026795311yescharacteristic
203C2#2026796411yescharacteristic
204C2#2026798111yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#539×C103C2
socleC22×C103#120
prime radical#121×C103C22
hypercenter#539D103
hypocenterC103#1615
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #20268124C2semidirect
3. #20267730C2semidirect
4. #20267528C2semidirect
6. #20267517C2semidirect
103. C103#1615semidirect

Maximal subgroups

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

subgroupindex
#202681242
#202681072
#202677302
#202675282
#202675252
#202675172
#539×C1032
#1615103