Finite Group Databasebeta

← #27194314

Subgroups — #27194314

Order 13184.

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

normal subgroups only

This group has 194 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#20268511C211yesmaximal, characteristic
2#20268141C211yesmaximal, characteristic, complemented
3#20268083C211yesmaximal, characteristic, complemented
4#20267538C211yesmaximal, characteristic, complemented
5#20267521C211yesmaximal, characteristic, complemented
6D4⋊(C103⋊C8)C211yesmaximal, characteristic
7#476×C103C211yesmaximal, characteristic
8#15693021C2211yescharacteristic
9#15693014—22no—
10#15693008—21no—
11#15693000—21no—
12C4×Dic206C2211yescharacteristic
13#15692986—21no—
14#15692980—21no—
15#15692954—21no—
16C4⋊(C103⋊C8)C2211yescharacteristic
17#15692945—22no—
18#15692944—21no—
19C4×C103⋊C8C2211yescharacteristic
20C4⋊Q8×C103C2211yescharacteristic
21C4×D4×C103C2211yescharacteristic
22#106×C103—21no—
23C4⋊C8×C103C2211yescharacteristic
24#102×C103—21no—
25C2×Dic206—21no—
26C2×Dic206D411yescharacteristic
27C2×C103⋊C8—21no—
28C2×C103⋊C8—21no—
29C4⋊Dic103—21no—
30C4⋊Dic103D412yes—
31C4⋊Dic103D411yescharacteristic
32Dic103⋊C4—22no—
33Dic103⋊C4—21no—
34C22⋊Dic103—22no—
35C22⋊Dic103—22no—
36C4×Dic103—22no—
37C4×Dic103—21no—
38C2×Q8×C103—21no—
39C2×D4×C103D411yescharacteristic
40C22×C4×C103—21no—
41C2×C8×C103—21no—
42C4⋊C4×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103D411yescharacteristic
45C22⋊C4×C103—21no—
46C42×C103C2311yescharacteristic
47C23×C103—21no—
48Q8×C103—42no—
49D4×C103—21no—
50D4×C103—21no—
51C2×C4×C103—21no—
52C2×C4×C103—41no—
53C2×C4×C103—41no—
54C2×C4×C103—41no—
55C2×C4×C103C2×D411yescharacteristic
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×Dic103—21no—
59C2×Dic103—21no—
60C2×Dic103—22no—
61Dic206—21no—
62Dic206—21no—
63Dic206—41no—
64Dic206—41no—
65C8×C103—41no—
66C103⋊C8—41no—
67C103⋊C8—41no—
68C22×C103—41no—
69C22×C103—41no—
70C22×C103—41no—
71C22×C103#12011yescharacteristic
72C4×C103—21no—
73C4×C103—41no—
74C4×C103—81no—
75C4×C103#13511yescharacteristic
76C4×C103#13511yescharacteristic
77C4×C103#13711yescharacteristic
78C4×C103#13711yescharacteristic
79Dic103—41no—
80Dic103—42no—
81Dic103—41no—
82C2×C103—81no—
83C2×C103#45211yescharacteristic
84C2×C103#45211yescharacteristic
85C2×C103#45411yescharacteristic
86#1638—1031nomaximal, Sylow
87C103#163811yescharacteristic, complemented, Sylow
88#556—1031no—
89#487—1031no—
90#477—1031no—
91#476D10311yescharacteristic
92#332—1031no—
93Q8⋊C8—1031no—
94D4⋊C8—1031no—
95C4⋊Q8—1031no—
96C4⋊Q8C2×D10311yescharacteristic
97#126—2062no—
98#124—2061no—
99C22⋊Q8—2061no—
100C4×Q8—1031no—
101C4×Q8—2061no—
102C4×D4C2×D10311yescharacteristic
103#117—2061no—
104#107—2061no—
105#106—21no—
106C4⋊C8—1031no—
107C4⋊C8C2×D10311yescharacteristic
108#103—2061no—
109#103—2062no—
110#102—21no—
111C4×C8—1031no—
112C2×Q8—21no—
113C2×Q8—1031no—
114C2×Q8—2061no—
115C2×D4C22⋊D10311yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—2061no—
119C2×C8—2061no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—1032no—
123C4⋊C4—1031no—
124C4⋊C4—2062no—
125C4⋊C4—2061no—
126C4⋊C4—2061no—
127C4⋊C4C22⋊D10311yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2062no—
130C22⋊C4—2062no—
131C42—2062no—
132C42—2061no—
133C42C22×D10311yescharacteristic
134C23—21no—
135Q8—42no—
136Q8—4121no—
137Q8—4121no—
138Q8—2061no—
139Q8—2061no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—2061no—
147C2×C4—2062no—
148C2×C4—2061no—
149C2×C4D4×D10311yescharacteristic
150C2×C4D4×D10311yescharacteristic
151C2×C4C2×C22⋊D10311yescharacteristic
152C8—41no—
153C8—4121no—
154C8—4121no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1569298911yescharacteristic
159C4—21no—
160C4—41no—
161C4—81no—
162C4—4121no—
163C4—4122no—
164C4—4121no—
165C4#1569304111yescharacteristic
166C4#1569304211yescharacteristic
167C4#1569305011yescharacteristic
168C4#1569305211yescharacteristic
169C2—81no—
170C2#2026795011yescharacteristic
171C2#2026795111yescharacteristic
172C2#2026796211yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#476×C103C2
socleC22×C103#120
prime radicalC2×D4×C103D4
hypercenter#476D103
hypocenterC103#1638
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #20268141C2semidirect
3. #20268083C2semidirect
4. #20267538C2semidirect
5. #20267521C2semidirect
87. C103#1638semidirect

Maximal subgroups

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

subgroupindex
#202685112
#202681412
#202680832
#202675382
#202675212
D4⋊(C103⋊C8)2
#476×C1032
#1638103