Finite Group Databasebeta

← #27194244

Subgroups — #27194244

Order 13184.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#20268456C211yesmaximal, characteristic, complemented
2#20267988C211yesmaximal, characteristic, complemented
3#20267983C211yesmaximal, characteristic
4#20267537C211yesmaximal, characteristic, complemented
5#20267523C211yesmaximal, characteristic, complemented
6#20267520C211yesmaximal, characteristic, complemented
7#486×C103C211yesmaximal, characteristic, complemented
8C2×Q8×D103—21no—
9C2×#13110093—21no—
10C2×#13110090—21no—
11#15693020—21no—
12#15692999—22no—
13#15692997—21no—
14C4×Dic206C2211yescharacteristic
15C4×D412C2211yescharacteristic
16#15692983—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692942—21no—
20#15692942—21no—
21C4⋊Q8×C103C2211yescharacteristic
22#127×C103C2211yescharacteristic
23#102×C103—22no—
24C4×C8×C103C2211yescharacteristic
25C2×Dic206—22no—
26C2×Dic206D411yescharacteristic
27Q8×D103—42no—
28Q8×D103—42no—
29C2×D412D411yescharacteristic
30C2×C4×D103—22no—
31C2×C4×D103—21no—
32#13110093—42no—
33#13110090—42no—
34C2×C103⋊C8—21no—
35C2×C103⋊C8—21no—
36C4⋊Dic103D411yescharacteristic
37C4⋊Dic103D411yescharacteristic
38Dic103⋊C4—22no—
39Dic103⋊C4—21no—
40(C2×D103)⋊C4—22no—
41(C2×D103)⋊C4—21no—
42C4×Dic103—21no—
43C2×Q8×C103—21no—
44C2×D4×C103—21no—
45C2×D4×C103—21no—
46C2×D4×C103—21no—
47C2×C8×C103—21no—
48C4⋊C4×C103—21no—
49C4⋊C4×C103D412yes—
50C42×C103C2311yescharacteristic
51C23×C103—41no—
52C22×D103—21no—
53Q8×C103—41no—
54Q8×C103—41no—
55D4×C103—42no—
56D4×C103—41no—
57D4×C103—41no—
58D4×C103—41no—
59D4×C103—41no—
60C2×C4×C103—22no—
61C2×C4×C103C2×D411yescharacteristic
62C2×C4×C103C2×D411yescharacteristic
63C2×C4×C103C2×D411yescharacteristic
64C2×Dic103—21no—
65C2×Dic103—21no—
66C2×Dic103—21no—
67D412—21no—
68D412SD1612yescomplemented
69C4×D103—44no—
70C4×D103—41no—
71C4×D103—41no—
72Dic206—21no—
73Dic206—44no—
74Dic206D812yescomplemented
75C8×C103—41no—
76C103⋊C8—41no—
77C103⋊C8—41no—
78C22×C103—81no—
79C22×C103—81no—
80C22×C103—81no—
81C22×C103#12011yescharacteristic
82C2×D103—22no—
83C2×D103—41no—
84C2×D103—41no—
85C4×C103—21no—
86C4×C103—42no—
87C4×C103C2×D811yescharacteristic
88C4×C103C2×SD1611yescharacteristic
89C4×C103AGL(1,ℤ/8)11yescharacteristic
90C4×C103#13711yescharacteristic
91Dic103—22no—
92Dic103—41no—
93Dic103—41no—
94C2×C103—161no—
95C2×C103#44711yescharacteristic
96C2×C103#44811yescharacteristic
97C2×C103#45411yescharacteristic
98D103—42no—
99#1627—1031nomaximal, Sylow
100C103#162711yescharacteristic, complemented, Sylow
101D4×Q8—1031no—
102#486D10311yescharacteristic, complemented
103#460—1031no—
104#459—1031no—
105#332—1031no—
106Q8⋊C8—1031no—
107D4⋊C8—1031no—
108C22×Q8—2061no—
109C2×SD16—2061no—
110C2×D8—2061no—
111C4⋊Q8—2061no—
112C4⋊Q8C2×D10311yescharacteristic
113#127C2×D10311yescharacteristic
114C22⋊Q8—2061no—
115C22⋊Q8—2062no—
116C4×Q8—1031no—
117C4×D4—1031no—
118C4×D4—2061no—
119C4⋊C8—1031no—
120C4⋊C8—1031no—
121#102—22no—
122#102—2061no—
123#102—2061no—
124C4×C8C2×D10311yescharacteristic
125C2×Q8—21no—
126C2×Q8—1031no—
127C2×Q8—4122no—
128C2×Q8—4122no—
129C2×Q8—2062no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—1031no—
134C22×C4—2062no—
135C22×C4—2061no—
136SD16—4122no—
137D8—4122no—
138C2×C8—21no—
139C2×C8—2061no—
140C2×C8—2061no—
141C4⋊C4—21no—
142C4⋊C4—1031no—
143C4⋊C4—1031no—
144C4⋊C4—2062no—
145C4⋊C4—2061no—
146C4⋊C4C22⋊D10312yes—
147C22⋊C4—2062no—
148C22⋊C4—2061no—
149C42—2061no—
150C42C22×D10311yescharacteristic
151C23—41no—
152C23—2061no—
153Q8—41no—
154Q8—41no—
155Q8—1032no—
156Q8—4124no—
157Q8—2061no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—1032no—
164D4—2061no—
165C2×C4—22no—
166C2×C4—4124no—
167C2×C4—4121no—
168C2×C4—4121no—
169C2×C4—2061no—
170C2×C4—2061no—
171C2×C4—2061no—
172C2×C4D4×D10311yescharacteristic
173C2×C4D4×D10311yescharacteristic
174C2×C4C2×C22⋊D10311yescharacteristic
175C8—41no—
176C8—4121no—
177C8—4121no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—4121no—
182C22—4121no—
183C22—2062no—
184C22#1569298911yescharacteristic
185C4—21no—
186C4—42no—
187C4—4121no—
188C4—4121no—
189C4—2062no—
190C4D8×D10311yescharacteristic
191C4SD16×D10311yescharacteristic
192C4#1569304511yescharacteristic
193C4#1569305011yescharacteristic
194C2—161no—
195C2—4122no—
196C2#2026792311yescharacteristic
197C2#2026792811yescharacteristic
198C2#2026796311yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#486×C103C2
socleC22×C103#120
prime radical#20267983C2
hypercenter#486D103
hypocenterC103#1627
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20268456C2semidirect
2. #20267988C2semidirect
4. #20267537C2semidirect
5. #20267523C2semidirect
6. #20267520C2semidirect
7. #486×C103C2semidirect
68. D412SD16semidirect
74. Dic206D8semidirect
100. C103#1627semidirect
102. #486D103semidirect

Maximal subgroups

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

subgroupindex
#202684562
#202679882
#202679832
#202675372
#202675232
#202675202
#486×C1032
#1627103