Finite Group Databasebeta

← #27194357

Subgroups — #27194357

Order 13184.

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

normal subgroups only

This group has 208 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#20268498C211yesmaximal, characteristic
2#20268143C211yesmaximal, characteristic, complemented
3#20267998C211yesmaximal, characteristic, complemented
4#20267539C211yesmaximal, characteristic, complemented
5#20267521C211yesmaximal, characteristic, complemented
6D4⋊(C103⋊C8)C211yesmaximal, characteristic
7#474×C103C211yesmaximal, characteristic
8C2×#13110095—21no—
9#15693021C2211yescharacteristic
10#15693012—21no—
11#15693000—21no—
12#15692998—22no—
13C4×Dic206C2211yescharacteristic
14D4×Dic103—21no—
15C2×C4⋊Dic103—21no—
16C4⋊(C103⋊C8)C2211yescharacteristic
17#15692945—21no—
18#15692944—22no—
19C4×C103⋊C8C2211yescharacteristic
20C4⋊Q8×C103C2211yescharacteristic
21C4×D4×C103C2211yescharacteristic
22#107×C103—21no—
23C4⋊C8×C103C2211yescharacteristic
24#102×C103—21no—
25C2×Dic206D411yescharacteristic
26C2×Dic206D412yes—
27C22×Dic103—22no—
28#13110095—42no—
29C2×C103⋊C8—21no—
30C2×C103⋊C8—21no—
31C4⋊Dic103—22no—
32C4⋊Dic103—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103D411yescharacteristic
35Dic103⋊C4—22no—
36Dic103⋊C4—21no—
37C22⋊Dic103—22no—
38C4×Dic103—21no—
39C2×Q8×C103—21no—
40C2×D4×C103D411yescharacteristic
41C22×C4×C103—21no—
42C2×C8×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103D411yescharacteristic
46C22⋊C4×C103—21no—
47C42×C103C2311yescharacteristic
48C23×C103—21no—
49Q8×C103—41no—
50Q8×C103—41no—
51D4×C103—21no—
52D4×C103Q1612yescomplemented
53C2×C4×C103—21no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×Dic103—21no—
61C2×Dic103—21no—
62C2×Dic103—22no—
63C2×Dic103—82no—
64Dic206—21no—
65Dic206—21no—
66Dic206—42no—
67C8×C103—41no—
68C103⋊C8—41no—
69C103⋊C8—41no—
70C22×C103—22no—
71C22×C103—41no—
72C22×C103—41no—
73C22×C103#12011yescharacteristic
74C4×C103—21no—
75C4×C103—41no—
76C4×C103—81no—
77C4×C103C2×Q1611yescharacteristic
78C4×C103#13511yescharacteristic
79C4×C103AGL(1,ℤ/8)11yescharacteristic
80C4×C103#13711yescharacteristic
81Dic103—41no—
82Dic103—42no—
83Dic103—41no—
84C2×C103—42no—
85C2×C103#44911yescharacteristic
86C2×C103#45111yescharacteristic
87C2×C103#45511yescharacteristic
88#1644—1031nomaximal, Sylow
89C103#164411yescharacteristic, complemented, Sylow
90#554—1031no—
91#487—1031no—
92#474D10311yescharacteristic
93#462—1031no—
94#333—1031no—
95Q8⋊C8—1031no—
96D4⋊C8—1031no—
97C2×Q16—2061no—
98C4⋊Q8—1031no—
99C4⋊Q8C2×D10311yescharacteristic
100#125—2061no—
101C22⋊Q8—2062no—
102C22⋊Q8—2061no—
103C4×Q8—1031no—
104C4×D4—2061no—
105C4×D4C2×D10311yescharacteristic
106C2×C4⋊C4—2061no—
107#107—21no—
108C4⋊C8—1031no—
109C4⋊C8C2×D10311yescharacteristic
110#103—2062no—
111#103—2061no—
112#102—21no—
113C4×C8—1031no—
114C2×Q8—21no—
115C2×Q8—1032no—
116C2×Q8—1031no—
117C2×D4C22⋊D10311yescharacteristic
118C22×C4—21no—
119C22×C4—2062no—
120Q16—4122no—
121C2×C8—21no—
122C2×C8—2061no—
123C2×C8—2061no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—1031no—
127C4⋊C4—2062no—
128C4⋊C4—2062no—
129C4⋊C4—2061no—
130C4⋊C4—2061no—
131C4⋊C4—2061no—
132C4⋊C4C22⋊D10311yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—2062no—
135C42—2061no—
136C42C22×D10311yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—4122no—
141Q8—2061no—
142Q8—2061no—
143D4—21no—
144D4#1311009512yescomplemented
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—8242no—
150C2×C4—2061no—
151C2×C4—2061no—
152C2×C4—2062no—
153C2×C4D4×D10311yescharacteristic
154C2×C4D4×D10311yescharacteristic
155C2×C4C2×C22⋊D10311yescharacteristic
156C8—41no—
157C8—4121no—
158C8—4121no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#1569298911yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—4121no—
167C4—4121no—
168C4—4122no—
169C4C2×#1311009511yescharacteristic
170C4#1569304011yescharacteristic
171C4#1569304511yescharacteristic
172C4#1569305111yescharacteristic
173C2—42no—
174C2#2026793311yescharacteristic
175C2#2026794611yescharacteristic
176C2#2026796711yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#474×C103C2
socleC22×C103#120
prime radicalC2×D4×C103D4
hypercenter#474D103
hypocenterC103#1644
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #20268143C2semidirect
3. #20267998C2semidirect
4. #20267539C2semidirect
5. #20267521C2semidirect
52. D4×C103Q16semidirect
89. C103#1644semidirect
144. D4#13110095semidirect

Maximal subgroups

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

subgroupindex
#202684982
#202681432
#202679982
#202675392
#202675212
D4⋊(C103⋊C8)2
#474×C1032
#1644103