Finite Group Databasebeta

← #27194412

Subgroups — #27194412

Order 13184.

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

normal subgroups only

This group has 200 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#20268514C211yesmaximal, characteristic
2#20268187C211yesmaximal, characteristic, complemented
3#20268068C211yesmaximal, characteristic
4#20267536C211yesmaximal, characteristic, complemented
5Q8⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6#20267518C211yesmaximal, characteristic
7#462×C103C211yesmaximal, characteristic, complemented
8#15693021C2211yescharacteristic
9#15693016—22no—
10#15693009—21no—
11#15692997—21no—
12C4×Dic206—21no—
13C4×D412C2211yescharacteristic
14#15692979—21no—
15#15692954—21no—
16#15692952—22no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18#15692941—21no—
19C4×C103⋊C8C2211yescharacteristic
20C2×Q16×C103—21no—
21C4⋊Q8×C103C2211yescharacteristic
22C4×Q8×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24#103×C103—21no—
25C2×Dic206—21no—
26C2×D412D411yescharacteristic
27C2×C4×D103—21no—
28C2×C103⋊C8—21no—
29C2×C103⋊C8—21no—
30C4⋊Dic103—21no—
31C4⋊Dic103D412yes—
32C4⋊Dic103D411yescharacteristic
33Dic103⋊C4—22no—
34(C2×D103)⋊C4—22no—
35(C2×D103)⋊C4—22no—
36(C2×D103)⋊C4—21no—
37C4×Dic103—22no—
38C2×Q8×C103—21no—
39C2×Q8×C103D411yescharacteristic
40Q16×C103—42no—
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—
62D412—21no—
63C4×D103—41no—
64C4×D103—41no—
65Dic206—41no—
66Dic206—41no—
67C8×C103—41no—
68C103⋊C8—22no—
69C103⋊C8—41no—
70C22×C103#12011yescharacteristic
71C2×D103—41no—
72C2×D103—41no—
73C2×D103—41no—
74C4×C103—21no—
75C4×C103—41no—
76C4×C103—41no—
77C4×C103—81no—
78C4×C103#13511yescharacteristic
79C4×C103#13511yescharacteristic
80C4×C103AGL(1,ℤ/8)11yescharacteristic
81C4×C103#13711yescharacteristic
82Dic103—41no—
83Dic103—42no—
84C2×C103#44911yescharacteristic
85C2×C103#45211yescharacteristic
86C2×C103#45611yescharacteristic
87D103—81no—
88#1652—1031nomaximal, Sylow
89C103#165211yescharacteristic, complemented, Sylow
90#556—1031no—
91#498—1031no—
92#474—1031no—
93#462D10311yescharacteristic, complemented
94#332—1031no—
95Q8⋊C8—1031no—
96D4⋊C8—1031no—
97C2×Q16—21no—
98C4⋊Q8—1031no—
99C4⋊Q8C2×D10311yescharacteristic
100#126—2062no—
101#124—2061no—
102C22⋊Q8—2061no—
103C4×Q8—2061no—
104C4×Q8C2×D10311yescharacteristic
105C4×D4—1031no—
106#117—2061no—
107#107—2061no—
108#106—2062no—
109C4⋊C8—1031no—
110C4⋊C8C2×D10311yescharacteristic
111#103—21no—
112#102—2061no—
113C4×C8—1031no—
114C2×Q8—21no—
115C2×Q8—2061no—
116C2×Q8C22⋊D10311yescharacteristic
117C2×D4—1031no—
118C22×C4—2061no—
119Q16—42no—
120C2×C8—21no—
121C2×C8—2061no—
122C2×C8—2061no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—1032no—
127C4⋊C4—1031no—
128C4⋊C4—2062no—
129C4⋊C4—2061no—
130C4⋊C4C22⋊D10311yescharacteristic
131C22⋊C4—2062no—
132C22⋊C4—2062no—
133C22⋊C4—2061no—
134C42—21no—
135C42—2062no—
136C42C22×D10311yescharacteristic
137C23—2061no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—4121no—
143Q8—4121no—
144D4—2061no—
145D4—2061no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
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—2062no—
159C22—4121no—
160C22—4121no—
161C22—4121no—
162C22#1569298911yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—4121no—
168C4—4122no—
169C4#1569304111yescharacteristic
170C4#1569304411yescharacteristic
171C4#1569304711yescharacteristic
172C4#1569305311yescharacteristic
173C2—8241no—
174C2#2026793411yescharacteristic
175C2#2026795211yescharacteristic
176C2#2026797211yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#462×C103C2
socleC22×C103#120
prime radicalC2×D412D4
hypercenter#462D103
hypocenterC103#1652
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #20268187C2semidirect
4. #20267536C2semidirect
5. Q8⋊(C103⋊C8)C2semidirect
7. #462×C103C2semidirect
89. C103#1652semidirect
93. #462D103semidirect

Maximal subgroups

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

subgroupindex
#202685142
#202681872
#202680682
#202675362
Q8⋊(C103⋊C8)2
#202675182
#462×C1032
#1652103