Finite Group Databasebeta

← #27194251

Subgroups — #27194251

Order 13184.

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

normal subgroups only

This group has 216 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#20268515C211yesmaximal, 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×#13110093—21no—
9C2×#13110090—21no—
10#15693016—22no—
11#15693010—21no—
12#15693001—21no—
13Q8×Dic103—21no—
14C4×Dic206C2211yescharacteristic
15C4×D412C2211yescharacteristic
16#15692979—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×Dic206D411yescharacteristic
26C2×D412D411yescharacteristic
27C2×C4×D103—21no—
28#13110093—42no—
29#13110090—42no—
30C2×C103⋊C8—21no—
31C2×C103⋊C8—21no—
32C4⋊Dic103—22no—
33C4⋊Dic103D411yescharacteristic
34C4⋊Dic103D411yescharacteristic
35Dic103⋊C4—21no—
36(C2×D103)⋊C4—22no—
37(C2×D103)⋊C4—22no—
38(C2×D103)⋊C4—21no—
39C4×Dic103—22no—
40C4×Dic103—21no—
41C2×Q8×C103—21no—
42C2×D4×C103—21no—
43C2×D4×C103—21no—
44C2×D4×C103—21no—
45C2×C8×C103—21no—
46C4⋊C4×C103—21no—
47C4⋊C4×C103D412yes—
48C42×C103C2311yescharacteristic
49C23×C103—41no—
50C22×D103—21no—
51Q8×C103—41no—
52Q8×C103—41no—
53D4×C103—42no—
54D4×C103—41no—
55D4×C103—41no—
56D4×C103—41no—
57D4×C103—41no—
58C2×C4×C103—22no—
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103C2×D411yescharacteristic
62C2×Dic103—21no—
63C2×Dic103—21no—
64C2×Dic103—21no—
65D412—21no—
66D412—21no—
67C4×D103—41no—
68C4×D103—41no—
69Dic206—21no—
70Dic206—21no—
71C8×C103—41no—
72C103⋊C8—41no—
73C103⋊C8—41no—
74C22×C103—81no—
75C22×C103—81no—
76C22×C103—81no—
77C22×C103#12011yescharacteristic
78C2×D103—41no—
79C2×D103—41no—
80C2×D103—41no—
81C4×C103—21no—
82C4×C103—42no—
83C4×C103#13511yescharacteristic
84C4×C103#13511yescharacteristic
85C4×C103AGL(1,ℤ/8)11yescharacteristic
86C4×C103AGL(1,ℤ/8)11yescharacteristic
87Dic103—41no—
88Dic103—41no—
89Dic103—41no—
90C2×C103—161no—
91C2×C103#44911yescharacteristic
92C2×C103#44911yescharacteristic
93C2×C103#45411yescharacteristic
94D103—81no—
95#1628—1031nomaximal, Sylow
96C103#162811yescharacteristic, complemented, Sylow
97#556—1031no—
98#486D10311yescharacteristic, complemented
99#460—1031no—
100#459—1031no—
101#332—1031no—
102Q8⋊C8—1031no—
103D4⋊C8—1031no—
104C2×SD16—2061no—
105C2×D8—2061no—
106C4⋊Q8C2×D10311yescharacteristic
107#127C2×D10311yescharacteristic
108#126—2062no—
109#124—2061no—
110C22⋊Q8—2061no—
111C4×Q8—1031no—
112C4×Q8—2061no—
113C4×D4—1031no—
114#117—2061no—
115C4⋊C8—1031no—
116C4⋊C8—1031no—
117#102—22no—
118#102—2061no—
119#102—2061no—
120C4×C8C2×D10311yescharacteristic
121C2×Q8—21no—
122C2×Q8—1031no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—1031no—
127C22×C4—2061no—
128SD16—4122no—
129D8—4122no—
130C2×C8—21no—
131C2×C8—2061no—
132C2×C8—2061no—
133C4⋊C4—21no—
134C4⋊C4—1031no—
135C4⋊C4—1031no—
136C4⋊C4—2062no—
137C4⋊C4—2061no—
138C4⋊C4C22⋊D10312yes—
139C22⋊C4—2062no—
140C22⋊C4—2062no—
141C22⋊C4—2061no—
142C42—2062no—
143C42—2061no—
144C42C22×D10311yescharacteristic
145C23—41no—
146C23—2061no—
147Q8—41no—
148Q8—41no—
149Q8—2061no—
150Q8—2061no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—2061no—
157D4—2061no—
158C2×C4—22no—
159C2×C4—4121no—
160C2×C4—4121no—
161C2×C4—2061no—
162C2×C4—2061no—
163C2×C4—2061no—
164C2×C4D4×D10311yescharacteristic
165C2×C4D4×D10311yescharacteristic
166C2×C4C2×C22⋊D10311yescharacteristic
167C8—41no—
168C8—4121no—
169C8—4121no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—4121no—
174C22—4121no—
175C22—4121no—
176C22#1569298911yescharacteristic
177C4—21no—
178C4—42no—
179C4—4121no—
180C4—4121no—
181C4—4121no—
182C4#1569304011yescharacteristic
183C4#1569304211yescharacteristic
184C4#1569304511yescharacteristic
185C4#1569304811yescharacteristic
186C2—161no—
187C2—8241no—
188C2#2026793311yescharacteristic
189C2#2026793511yescharacteristic
190C2#2026796311yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#486×C103C2
socleC22×C103#120
prime radical#20267983C2
hypercenter#486D103
hypocenterC103#1628
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. #20268515C2semidirect
2. #20267988C2semidirect
4. #20267537C2semidirect
5. #20267523C2semidirect
6. #20267520C2semidirect
7. #486×C103C2semidirect
96. C103#1628semidirect
98. #486D103semidirect

Maximal subgroups

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

subgroupindex
#202685152
#202679882
#202679832
#202675372
#202675232
#202675202
#486×C1032
#1628103