Finite Group Databasebeta

← #27194277

Subgroups — #27194277

Order 13184.

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

normal subgroups only

This group has 214 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#20268501C211yesmaximal, characteristic
2#20268170C211yesmaximal, characteristic, complemented
3#20268078C211yesmaximal, characteristic
4#20267539C211yesmaximal, characteristic, complemented
5Q8⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6#20267518C211yesmaximal, characteristic
7#477×C103C211yesmaximal, characteristic, complemented
8C2×#13110095—22no—
9#15693021C2211yescharacteristic
10#15693013—21no—
11#15692999—22no—
12#15692997—21no—
13C4×D412—21no—
14C4×D412C2211yescharacteristic
15C4⋊C4×D103—21no—
16#15692952—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18#15692941—21no—
19C4×C103⋊C8C2211yescharacteristic
20C4⋊Q8×C103C2211yescharacteristic
21C4×Q8×C103C2211yescharacteristic
22#107×C103—21no—
23C4⋊C8×C103C2211yescharacteristic
24#103×C103—21no—
25C2×Dic206D412yes—
26C2×D412D411yescharacteristic
27C2×C4×D103—21no—
28C2×C4×D103—22no—
29#13110095—44no—
30C2×C103⋊C8—21no—
31C2×C103⋊C8—21no—
32C4⋊Dic103—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103D411yescharacteristic
35Dic103⋊C4—22no—
36Dic103⋊C4—22no—
37(C2×D103)⋊C4—22no—
38(C2×D103)⋊C4—21no—
39C2×Q8×C103—21no—
40C2×Q8×C103D411yescharacteristic
41C2×C8×C103—21no—
42C4⋊C4×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103D411yescharacteristic
46C42×C103—21no—
47C42×C103C2311yescharacteristic
48C22×D103—21no—
49Q8×C103—21no—
50Q8×C103—21no—
51Q8×C103—42no—
52C2×C4×C103—21no—
53C2×C4×C103—21no—
54C2×C4×C103—41no—
55C2×C4×C103C2×D411yescharacteristic
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×Dic103—21no—
59C2×Dic103—22no—
60D412—21no—
61D412Q1612yescomplemented
62C4×D103—41no—
63C4×D103—41no—
64C4×D103—82no—
65Dic206—42no—
66C8×C103—41no—
67C103⋊C8—22no—
68C103⋊C8—41no—
69C22×C103#12011yescharacteristic
70C2×D103—22no—
71C2×D103—41no—
72C2×D103—41no—
73C4×C103—21no—
74C4×C103—41no—
75C4×C103—41no—
76C4×C103—81no—
77C4×C103C2×Q1611yescharacteristic
78C4×C103#13511yescharacteristic
79C4×C103#13711yescharacteristic
80C4×C103#13711yescharacteristic
81Dic103—41no—
82Dic103—42no—
83C2×C103#45111yescharacteristic
84C2×C103#45211yescharacteristic
85C2×C103#45311yescharacteristic
86D103—42no—
87#1632—1031nomaximal, Sylow
88C103#163211yescharacteristic, complemented, Sylow
89#554—1031no—
90#494—1031no—
91#477D10311yescharacteristic, complemented
92#476—1031no—
93#333—1031no—
94Q8⋊C8—1031no—
95D4⋊C8—1031no—
96C2×Q16—2062no—
97C4⋊Q8—1031no—
98C4⋊Q8C2×D10311yescharacteristic
99#125—2061no—
100C22⋊Q8—2062no—
101C22⋊Q8—2061no—
102C4×Q8C2×D10311yescharacteristic
103C4×D4—1031no—
104C4×D4—2061no—
105C2×C4⋊C4—2061no—
106#107—21no—
107#106—2061no—
108C4⋊C8—1031no—
109C4⋊C8C2×D10311yescharacteristic
110#103—21no—
111#102—2061no—
112C4×C8—1031no—
113C2×Q8—21no—
114C2×Q8—1032no—
115C2×Q8C22⋊D10311yescharacteristic
116C2×D4—1031no—
117C22×C4—2062no—
118C22×C4—2061no—
119Q16—4124no—
120C2×C8—21no—
121C2×C8—2061no—
122C2×C8—2061no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—1031no—
127C4⋊C4—2062no—
128C4⋊C4—2062no—
129C4⋊C4—2061no—
130C4⋊C4—2061no—
131C4⋊C4C22⋊D10311yescharacteristic
132C22⋊C4—2062no—
133C22⋊C4—2061no—
134C42—21no—
135C42C22×D10311yescharacteristic
136C23—2061no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—4122no—
141D4—1032no—
142D4—2061no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—8242no—
147C2×C4—4121no—
148C2×C4—4121no—
149C2×C4—2061no—
150C2×C4—2062no—
151C2×C4D4×D10311yescharacteristic
152C2×C4D4×D10311yescharacteristic
153C2×C4C2×C22⋊D10311yescharacteristic
154C8—41no—
155C8—4121no—
156C8—2062no—
157C22—4121no—
158C22—4121no—
159C22—2062no—
160C22#1569298911yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—4121no—
166C4—4122no—
167C4Q16×D10311yescharacteristic
168C4#1569304111yescharacteristic
169C4#1569305211yescharacteristic
170C4#1569305311yescharacteristic
171C2—4122no—
172C2#2026794511yescharacteristic
173C2#2026795111yescharacteristic
174C2#2026795711yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#477×C103C2
socleC22×C103#120
prime radicalC2×D412D4
hypercenter#477D103
hypocenterC103#1632
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #20268170C2semidirect
4. #20267539C2semidirect
5. Q8⋊(C103⋊C8)C2semidirect
7. #477×C103C2semidirect
61. D412Q16semidirect
88. C103#1632semidirect
91. #477D103semidirect

Maximal subgroups

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

subgroupindex
#202685012
#202681702
#202680782
#202675392
Q8⋊(C103⋊C8)2
#202675182
#477×C1032
#1632103