Finite Group Databasebeta

← #27194246

Subgroups — #27194246

Order 13184.

250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic206C211yesmaximal, characteristic, complemented
2#20268137C211yesmaximal, characteristic, complemented
3#20267988C211yesmaximal, characteristic, complemented
4#20267536C211yesmaximal, characteristic, complemented
5#20267521C211yesmaximal, characteristic, complemented
6D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
7#459×C103C211yesmaximal, characteristic
8C22×Dic206—21no—
9C2×#13110093—21no—
10#15693021C2211yescharacteristic
11#15693020—21no—
12#15693000—21no—
13#15692998—22no—
14C4×Dic206C2211yescharacteristic
15D4×Dic103—21no—
16C4⋊(C103⋊C8)C2211yescharacteristic
17#15692942—22no—
18#15692942—21no—
19C4×C103⋊C8C2211yescharacteristic
20C2×D8×C103—21no—
21#127×C103C2211yescharacteristic
22C4×D4×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24#102×C103—21no—
25C2×Dic206—22no—
26C2×Dic206—21no—
27C2×Dic206—42no—
28C2×Dic206—42no—
29C2×Dic206D411yescharacteristic
30C22×Dic103—22no—
31#13110093—42no—
32C2×C103⋊C8—21no—
33C2×C103⋊C8—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103D411yescharacteristic
36C4⋊Dic103D412yes—
37Dic103⋊C4—22no—
38Dic103⋊C4—21no—
39C22⋊Dic103—22no—
40C4×Dic103—21no—
41C2×D4×C103—21no—
42C2×D4×C103—21no—
43C2×D4×C103—21no—
44C2×D4×C103D411yescharacteristic
45C22×C4×C103—21no—
46D8×C103—42no—
47C2×C8×C103—21no—
48C4⋊C4×C103D411yescharacteristic
49C22⋊C4×C103—21no—
50C42×C103C2311yescharacteristic
51C23×C103—21no—
52C23×C103—41no—
53D4×C103—21no—
54D4×C103—42no—
55D4×C103—41no—
56D4×C103—41no—
57D4×C103—41no—
58D4×C103—41no—
59D4×C103SD1612yescomplemented
60C2×C4×C103—21no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C2×Dic103—21no—
67C2×Dic103—21no—
68C2×Dic103—22no—
69C2×Dic103—44no—
70Dic206—21no—
71Dic206—44no—
72Dic206—41no—
73Dic206—41no—
74Dic206D812yescomplemented
75C8×C103—41no—
76C103⋊C8—41no—
77C103⋊C8—41no—
78C22×C103—22no—
79C22×C103—41no—
80C22×C103—41no—
81C22×C103—81no—
82C22×C103—81no—
83C22×C103—81no—
84C22×C103#12011yescharacteristic
85C4×C103—21no—
86C4×C103—41no—
87C4×C103C2×D811yescharacteristic
88C4×C103C2×SD1611yescharacteristic
89C4×C103AGL(1,ℤ/8)11yescharacteristic
90C4×C103#13711yescharacteristic
91Dic103—22no—
92Dic103—42no—
93Dic103—41no—
94C2×C103—42no—
95C2×C103—161no—
96C2×C103#44711yescharacteristic
97C2×C103#44811yescharacteristic
98C2×C103#45411yescharacteristic
99#1627—1031nomaximal, Sylow
100C103#162711yescharacteristic, complemented, Sylow
101D4×Q8—1031no—
102#486—1031no—
103#460—1031no—
104#459D10311yescharacteristic
105#332—1031no—
106Q8⋊C8—1031no—
107D4⋊C8—1031no—
108C22×Q8—2061no—
109C2×SD16—2061no—
110C2×D8—21no—
111C4⋊Q8—1031no—
112C4⋊Q8—2061no—
113#127C2×D10311yescharacteristic
114C22⋊Q8—2062no—
115C22⋊Q8—2061no—
116C4×Q8—1031no—
117C4×D4—2061no—
118C4×D4C2×D10311yescharacteristic
119C4⋊C8—1031no—
120C4⋊C8C2×D10311yescharacteristic
121#102—21no—
122#102—2061no—
123#102—2062no—
124C4×C8—1031no—
125C2×Q8—1031no—
126C2×Q8—4122no—
127C2×Q8—4122no—
128C2×Q8—2062no—
129C2×Q8—2061no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4C22⋊D10311yescharacteristic
134C22×C4—21no—
135C22×C4—2062no—
136SD16—4122no—
137D8—42no—
138C2×C8—21no—
139C2×C8—2061no—
140C2×C8—2061no—
141C4⋊C4—1031no—
142C4⋊C4—1032no—
143C4⋊C4—2062no—
144C4⋊C4—2061no—
145C4⋊C4—2061no—
146C4⋊C4C22⋊D10311yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—2062no—
149C42—2061no—
150C42C22×D10311yescharacteristic
151C23—21no—
152C23—41no—
153Q8—1032no—
154Q8—4124no—
155Q8—4121no—
156Q8—4121no—
157Q8—2061no—
158D4—21no—
159D4—42no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4#1311009312yescomplemented
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—4124no—
169C2×C4—2061no—
170C2×C4—2062no—
171C2×C4—2061no—
172C2×C4D4×D10311yescharacteristic
173C2×C4D4×D10311yescharacteristic
174C2×C4C2×C22⋊D10311yescharacteristic
175C8—41no—
176C8—4121no—
177C8—4121no—
178C22—22no—
179C22—41no—
180C22—41no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22#1569298911yescharacteristic
185C4—21no—
186C4—41no—
187C4—4122no—
188C4—4121no—
189C4—2062no—
190C4D8×D10311yescharacteristic
191C4C2×#1311009311yescharacteristic
192C4#1569304511yescharacteristic
193C4#1569305111yescharacteristic
194C2—42no—
195C2—161no—
196C2#2026792311yescharacteristic
197C2#2026792911yescharacteristic
198C2#2026796211yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting, prime radical#459×C103C2
socleC22×C103#120
hypercenter#459D103
hypocenterC103#1627
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. D4×Dic206C2semidirect
2. #20268137C2semidirect
3. #20267988C2semidirect
4. #20267536C2semidirect
5. #20267521C2semidirect
6. D4⋊(C103⋊C8)C2semidirect
59. D4×C103SD16semidirect
74. Dic206D8semidirect
100. C103#1627semidirect
164. D4#13110093semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2062
#202681372
#202679882
#202675362
#202675212
D4⋊(C103⋊C8)2
#459×C1032
#1627103