Finite Group Databasebeta

← #27194268

Subgroups — #27194268

Order 13184.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#20268461C211yesmaximal, characteristic
2#20268083C211yesmaximal, characteristic, complemented
3#20268078C211yesmaximal, characteristic, complemented
4#20267535C211yesmaximal, characteristic, complemented
5#20267523C211yesmaximal, characteristic, complemented
6#20267520C211yesmaximal, characteristic, complemented
7#492×C103C211yesmaximal, characteristic, complemented
8C2×#13110104—21no—
9#15693017—21no—
10#15692993—22no—
11#15692992—21no—
12C4×Dic206C2211yescharacteristic
13C4×D412C2211yescharacteristic
14D4×Dic103—21no—
15#15692954—21no—
16#15692952—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692944—21no—
20#15692941—21no—
21C2×SD16×C103—22no—
22C4⋊Q8×C103C2211yescharacteristic
23#127×C103C2211yescharacteristic
24C4×C8×C103C2211yescharacteristic
25#13110104—42no—
26#13110104—42no—
27C2×Dic206D411yescharacteristic
28C2×D412D411yescharacteristic
29C2×C22⋊D103—22no—
30C2×C22⋊D103—22no—
31C22×Dic103—22no—
32C2×C4×D103—21no—
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C4⋊Dic103D411yescharacteristic
36C4⋊Dic103D411yescharacteristic
37Dic103⋊C4—21no—
38C22⋊Dic103—22no—
39(C2×D103)⋊C4—21no—
40C4×Dic103—21no—
41C2×Q8×C103—21no—
42C2×D4×C103—21no—
43C2×D4×C103—21no—
44C2×D4×C103D412yes—
45SD16×C103—44no—
46C2×C8×C103—21no—
47C4⋊C4×C103—21no—
48C4⋊C4×C103—21no—
49C42×C103C2311yescharacteristic
50C23×C103—22no—
51C22×D103—21no—
52Q8×C103—42no—
53D4×C103—42no—
54D4×C103—41no—
55D4×C103—41no—
56D4×C103—41no—
57D4×C103—41no—
58C2×C4×C103—41no—
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103C2×D411yescharacteristic
62C22⋊D103—44no—
63C22⋊D103—82no—
64C2×Dic103—21no—
65C2×Dic103—21no—
66C2×Dic103—21no—
67C2×Dic103—44no—
68D412—21no—
69D412—21no—
70C4×D103—41no—
71C4×D103—41no—
72Dic206—21no—
73Dic206SD1612yescomplemented
74C8×C103—22no—
75C103⋊C8—41no—
76C103⋊C8—41no—
77C22×C103—42no—
78C22×C103—42no—
79C22×C103—42no—
80C22×C103#12011yescharacteristic
81C2×D103—41no—
82C2×D103—41no—
83C2×D103—41no—
84C4×C103—21no—
85C4×C103—81no—
86C4×C103C2×SD1611yescharacteristic
87C4×C103#13511yescharacteristic
88C4×C103AGL(1,ℤ/8)11yescharacteristic
89C4×C103#13711yescharacteristic
90Dic103—22no—
91Dic103—41no—
92Dic103—41no—
93C2×C103—82no—
94C2×C103#45011yescharacteristic
95C2×C103#45211yescharacteristic
96C2×C103#45311yescharacteristic
97D103—81no—
98#1631—1031nomaximal, Sylow
99C103#163111yescharacteristic, complemented, Sylow
100#550—1031no—
101#492D10311yescharacteristic, complemented
102#477—1031no—
103#476—1031no—
104#331—1031no—
105Q8⋊C8—1031no—
106D4⋊C8—1031no—
107C2×#41—2061no—
108C2×SD16—22no—
109C4⋊Q8C2×D10311yescharacteristic
110#127—2061no—
111#127C2×D10311yescharacteristic
112#121—2061no—
113#121—2062no—
114C4×Q8—1031no—
115C4×D4—1031no—
116C4×D4—2061no—
117#107—2061no—
118#106—2061no—
119C4⋊C8—1031no—
120C4⋊C8—1031no—
121#103—2061no—
122#102—2061no—
123C4×C8C2×D10311yescharacteristic
124#41—4122no—
125#41—4122no—
126C2×Q8—21no—
127C2×Q8—1031no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—1031no—
131C2×D4—2062no—
132C2×D4—2062no—
133C2×D4C22⋊D10312yes—
134C22×C4—2062no—
135C22×C4—2061no—
136SD16—44no—
137C2×C8—21no—
138C2×C8—2061no—
139C2×C8—2061no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—1031no—
143C4⋊C4—1031no—
144C4⋊C4—2061no—
145C22⋊C4—2062no—
146C22⋊C4—2061no—
147C42—2061no—
148C42C22×D10311yescharacteristic
149C23—22no—
150C23—2061no—
151Q8—42no—
152Q8—1032no—
153Q8—2061no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—8242no—
160D4—4124no—
161D4—2061no—
162D4—2061no—
163C2×C4—41no—
164C2×C4—4124no—
165C2×C4—4121no—
166C2×C4—4121no—
167C2×C4—2061no—
168C2×C4—2061no—
169C2×C4—2061no—
170C2×C4D4×D10311yescharacteristic
171C2×C4D4×D10311yescharacteristic
172C2×C4C2×C22⋊D10311yescharacteristic
173C8—22no—
174C8—4121no—
175C8—4121no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—4121no—
180C22—4121no—
181C22—4121no—
182C22#1569298911yescharacteristic
183C4—21no—
184C4—81no—
185C4—4121no—
186C4—4121no—
187C4—2062no—
188C4SD16×D10311yescharacteristic
189C4#1569304211yescharacteristic
190C4#1569304811yescharacteristic
191C4#1569305011yescharacteristic
192C2—82no—
193C2—8241no—
194C2#2026794011yescharacteristic
195C2#2026795011yescharacteristic
196C2#2026795811yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#492×C103C2
socleC22×C103#120
prime radical#20268461C2
hypercenter#492D103
hypocenterC103#1631
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #20268083C2semidirect
3. #20268078C2semidirect
4. #20267535C2semidirect
5. #20267523C2semidirect
6. #20267520C2semidirect
7. #492×C103C2semidirect
73. Dic206SD16semidirect
99. C103#1631semidirect
101. #492D103semidirect

Maximal subgroups

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

subgroupindex
#202684612
#202680832
#202680782
#202675352
#202675232
#202675202
#492×C1032
#1631103