Finite Group Databasebeta

← #27194350

Subgroups — #27194350

Order 13184.

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

normal subgroups only

This group has 208 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#20268143C211yesmaximal, characteristic, complemented
3#20267993C211yesmaximal, characteristic
4#20267539C211yesmaximal, characteristic, complemented
5Q8⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6#20267518C211yesmaximal, characteristic
7#475×C103C211yesmaximal, characteristic, complemented
8C2×#13110092—21no—
9#15693021C2211yescharacteristic
10#15693013—21no—
11#15692999—22no—
12#15692997—21no—
13C4×D412—21no—
14C4×D412C2211yescharacteristic
15C4⋊C4×D103—21no—
16C4⋊(C103⋊C8)C2211yescharacteristic
17#15692945—21no—
18#15692944—22no—
19C4×C103⋊C8C2211yescharacteristic
20C4⋊Q8×C103C2211yescharacteristic
21C4×Q8×C103C2211yescharacteristic
22#106×C103—21no—
23C4⋊C8×C103C2211yescharacteristic
24#103×C103—21no—
25C2×Dic206D412yes—
26C2×D412D411yescharacteristic
27C2×C4×D103—21no—
28C2×C4×D103—22no—
29#13110092—42no—
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—41no—
52Q8×C103—41no—
53C2×C4×C103—21no—
54C2×C4×C103—21no—
55C2×C4×C103—41no—
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×Dic103—21no—
60C2×Dic103—22no—
61D412—21no—
62D412SD1612yes—
63C4×D103—41no—
64C4×D103—41no—
65C4×D103—82no—
66Dic206—42no—
67C8×C103—41no—
68C103⋊C8—41no—
69C103⋊C8—41no—
70C22×C103#12011yescharacteristic
71C2×D103—22no—
72C2×D103—41no—
73C2×D103—41no—
74C4×C103—21no—
75C4×C103—41no—
76C4×C103—41no—
77C4×C103—81no—
78C4×C103C2×SD1611yescharacteristic
79C4×C103#13511yescharacteristic
80C4×C103#13711yescharacteristic
81C4×C103#13711yescharacteristic
82Dic103—41no—
83Dic103—42no—
84C2×C103#44811yescharacteristic
85C2×C103#45211yescharacteristic
86C2×C103#45511yescharacteristic
87D103—42no—
88#1643—1031nomaximal, Sylow
89C103#164311yescharacteristic, complemented, Sylow
90#554—1031no—
91#487—1031no—
92#475D10311yescharacteristic, complemented
93#461—1031no—
94#333—1031no—
95Q8⋊C8—1031no—
96D4⋊C8—1031no—
97C2×SD16—2061no—
98C4⋊Q8—1031no—
99C4⋊Q8C2×D10311yescharacteristic
100#125—2061no—
101C22⋊Q8—2062no—
102C22⋊Q8—2061no—
103C4×Q8C2×D10311yescharacteristic
104C4×D4—1031no—
105C4×D4—2061no—
106C2×C4⋊C4—2061no—
107#106—21no—
108C4⋊C8—1031no—
109C4⋊C8C2×D10311yescharacteristic
110#103—21no—
111#103—2062no—
112#103—2061no—
113C4×C8—1031no—
114C2×Q8—21no—
115C2×Q8—1032no—
116C2×Q8C22⋊D10311yescharacteristic
117C2×D4—1031no—
118C22×C4—2062no—
119C22×C4—2061no—
120SD16—4122no—
121C2×C8—21no—
122C2×C8—2061no—
123C2×C8—2061no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1031no—
128C4⋊C4—2062no—
129C4⋊C4—2062no—
130C4⋊C4—2061no—
131C4⋊C4—2061no—
132C4⋊C4C22⋊D10311yescharacteristic
133C22⋊C4—2062no—
134C22⋊C4—2061no—
135C42—21no—
136C42C22×D10311yescharacteristic
137C23—2061no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—4122no—
143D4—1032no—
144D4—2061no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—8242no—
149C2×C4—4121no—
150C2×C4—4121no—
151C2×C4—2061no—
152C2×C4—2062no—
153C2×C4D4×D10311yescharacteristic
154C2×C4D4×D10311yescharacteristic
155C2×C4C2×C22⋊D10311yescharacteristic
156C8—41no—
157C8—4121no—
158C8—4121no—
159C22—4121no—
160C22—4121no—
161C22—2062no—
162C22#1569298911yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—4121no—
168C4—4122no—
169C4SD16×D10311yescharacteristic
170C4#1569304111yescharacteristic
171C4#1569305011yescharacteristic
172C4#1569305211yescharacteristic
173C2—4122no—
174C2#2026792811yescharacteristic
175C2#2026795111yescharacteristic
176C2#2026796711yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#475×C103C2
socleC22×C103#120
prime radicalC2×D412D4
hypercenter#475D103
hypocenterC103#1643
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #20268143C2semidirect
4. #20267539C2semidirect
5. Q8⋊(C103⋊C8)C2semidirect
7. #475×C103C2semidirect
89. C103#1643semidirect
92. #475D103semidirect

Maximal subgroups

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

subgroupindex
#202685012
#202681432
#202679932
#202675392
Q8⋊(C103⋊C8)2
#202675182
#475×C1032
#1643103