Finite Group Databasebeta

← #19133782

Subgroups — #19133782

Order 5504.

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

normal subgroups only

This group has 212 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#14583635C211yesmaximal, characteristic
2#14583245C211yesmaximal, characteristic
3#14583185C211yesmaximal, characteristic, complemented
4#14583110C211yesmaximal, characteristic, complemented
5#14582629C211yesmaximal, characteristic, complemented
6#14582629C211yesmaximal, characteristic, complemented
7C43×#331C211yesmaximal, characteristic
8C2×Dic172—21no—
9#13063325C2211yescharacteristic
10#13063312—21no—
11#13063312—21no—
12#13063306—22no—
13C4×Dic86C2211yescharacteristic
14C4×Dic86C2211yescharacteristic
15D4×Dic43—21no—
16D4×Dic43—21no—
17#13063257—21no—
18#13063250—21no—
19#13063250—21no—
20#13063246—22no—
21C4×C43⋊C8C2211yescharacteristic
22#127×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4⋊C8×C43C2211yescharacteristic
25C2×D4×C43—21no—
26C2×D4×C43—21no—
27C2×D4×C43D412yes—
28C22×Dic43—22no—
29C2×Dic86—21no—
30C2×Dic86D411yescharacteristic
31C2×Dic86D411yescharacteristic
32C2×C8×C43—21no—
33C2×C8×C43—21no—
34C42×C43C2311yescharacteristic
35C22⋊Dic43—22no—
36C22⋊Dic43—22no—
37C22⋊Dic43—22no—
38C4⋊Dic43—21no—
39C4⋊Dic43—21no—
40C4⋊Dic43D411yescharacteristic
41C4⋊Dic43D411yescharacteristic
42Dic43⋊C4—21no—
43Dic43⋊C4—21no—
44C4×Dic43—21no—
45C4×Dic43—21no—
46C2×C43⋊C8—21no—
47Dic172—42no—
48C23×C43—22no—
49D4×C43—42no—
50D4×C43—41no—
51D4×C43—41no—
52D4×C43—41no—
53D4×C43—41no—
54C2×C4×C43C2×D411yescharacteristic
55C2×C4×C43C2×D411yescharacteristic
56C2×C4×C43C2×D411yescharacteristic
57C2×Dic43—21no—
58C2×Dic43—21no—
59C2×Dic43—21no—
60C2×Dic43—21no—
61C2×Dic43—41no—
62C2×Dic43—82no—
63Dic86—21no—
64Dic86—21no—
65Dic86—21no—
66Dic86—21no—
67Dic86—41no—
68Dic86—41no—
69C8×C43—41no—
70C8×C43—41no—
71C43⋊C8—41no—
72C22×C43—42no—
73C22×C43—42no—
74C22×C43—42no—
75C22×C43#12011yescharacteristic
76C4×C43—21no—
77C4×C43#13511yescharacteristic
78C4×C43#13511yescharacteristic
79C4×C43AGL(1,ℤ/8)11yescharacteristic
80C4×C43#13711yescharacteristic
81Dic43—41no—
82Dic43—41no—
83Dic43—41no—
84Dic43—41no—
85Dic43—81no—
86#1640—431nomaximal, Sylow
87C2×C43—82no—
88C2×C43#44911yescharacteristic
89C2×C43#45211yescharacteristic
90C2×C43#45511yescharacteristic
91#559—431no—
92#486—431no—
93#475—431no—
94#462—431no—
95#331D4311yescharacteristic
96Q8⋊C8—431no—
97Q8⋊C8—431no—
98C43#164011yescharacteristic, complemented, Sylow
99C2×Q16—861no—
100C4⋊Q8—431no—
101#127C2×D4311yescharacteristic
102#124—861no—
103#124—861no—
104#123—862no—
105C4×Q8—431no—
106C4×Q8—431no—
107C4×D4—861no—
108C4×D4—861no—
109#106—861no—
110C4⋊C8C2×D4311yescharacteristic
111C4⋊C8C2×D4311yescharacteristic
112#103—861no—
113#103—861no—
114#102—862no—
115C4×C8—431no—
116C2×Q8—431no—
117C2×Q8—431no—
118C2×Q8—861no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4D17212yes—
122C22×C4—862no—
123Q16—1722no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—861no—
127C4⋊C4—431no—
128C4⋊C4—431no—
129C4⋊C4—861no—
130C4⋊C4—861no—
131C4⋊C4—861no—
132C4⋊C4—861no—
133C22⋊C4—862no—
134C22⋊C4—862no—
135C22⋊C4—862no—
136C42—861no—
137C42—861no—
138C42C22×D4311yescharacteristic
139C23—22no—
140Q8—861no—
141Q8—861no—
142Q8—861no—
143Q8—861no—
144Q8—1721no—
145Q8—1721no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—861no—
152C2×C4—861no—
153C2×C4—861no—
154C2×C4—861no—
155C2×C4—3442no—
156C2×C4—1721no—
157C2×C4C2×D17211yescharacteristic
158C2×C4D4×D4311yescharacteristic
159C2×C4D4×D4311yescharacteristic
160C8—41no—
161C8—41no—
162C8—1721no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1306329511yescharacteristic
167C4—21no—
168C4—3441no—
169C4—1721no—
170C4—1721no—
171C4—1721no—
172C4—1721no—
173C4#1306334411yescharacteristic
174C4#1306334611yescharacteristic
175C4#1306334911yescharacteristic
176C4#1306335411yescharacteristic
177C2—82no—
178C2#1458304511yescharacteristic
179C2#1458306211yescharacteristic
180C2#1458307911yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#331C2
socleC22×C43#120
hypercenter#331D43
hypocenterC43#1640
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #14583185C2semidirect
4. #14583110C2semidirect
5. #14582629C2semidirect
6. #14582629C2semidirect
98. C43#1640semidirect