Finite Group Databasebeta

← #19136246

Subgroups — #19136246

Order 5504.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#14583463C211yesmaximal, characteristic
2#14582873C211yesmaximal, characteristic, complemented
3#14582687C214yesmaximal, complemented
4C43×#413C211yesmaximal, characteristic, complemented
5C22×D172C411yescharacteristic, complemented
6#13063321—21no—
7#13063314—21no—
8#13063299—21no—
9#13063299—21no—
10#13063293C412yescomplemented
11#13063293C2212yes—
12#13063284—21no—
13#13063284C411yescharacteristic, complemented
14#13063240—21no—
15#13063240C2212yes—
16C2×#41×C43C2211yescharacteristic
17C2×M16×C43—21no—
18#101×C43—21no—
19#100×C43C2212yes—
20C23×D43C2×C412yes—
21#41×C43—41no—
22#41×C43—41no—
23C2×Q8×C43D411yescharacteristic
24C2×D4×C43C2×C411yescharacteristic
25C2×D4×C43D411yescharacteristic
26C2×D4×C43C2311yescharacteristic
27C22×C4×C43C2×C411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×C4×C43D411yescharacteristic
30C2×C22⋊D43—22no—
31C2×C22⋊D43—22no—
32C2×D172—21no—
33C2×D172—21no—
34C2×D172—41no—
35C2×D172—41no—
36M16×C43—22no—
37M16×C43—41no—
38C2×C8×C43—41no—
39C22⋊Dic43—22no—
40C22⋊Dic43C2×C412yes—
41(C2×D43)⋊C4—22no—
42(C2×D43)⋊C4—22no—
43C4⋊Dic43—21no—
44C4⋊Dic43—41no—
45C4×Dic43—21no—
46C4×Dic43—41no—
47C23×C43C22⋊C411yescharacteristic
48C23×C43C22×C411yescharacteristic
49C23×C43C2×D411yescharacteristic
50C22×D43—22no—
51C22×D43—42no—
52C22×D43—82no—
53Q8×C43—41no—
54D4×C43—41no—
55D4×C43—41no—
56D4×C43—41no—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43—21no—
61C2×C4×C43—21no—
62C2×C4×C43—21no—
63C2×C4×C43C22⋊C411yescharacteristic
64C2×C4×C43C22⋊C411yescharacteristic
65C2×C4×C43C22⋊C411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C22⋊D43—82no—
68C22⋊D43—82no—
69C2×Dic43—22no—
70C2×Dic43—42no—
71D172—42no—
72D172—41no—
73D172—41no—
74C8×C43—42no—
75C22×C43—21no—
76C22×C43—21no—
77C22×C43—21no—
78C22×C43—41no—
79C22×C43—41no—
80C22×C43—41no—
81C22×C43C2×C22⋊C411yescharacteristic
82C2×D43—42no—
83C2×D43—42no—
84C2×D43—42no—
85C2×D43—84no—
86C4×C43—21no—
87C4×C43—21no—
88C4×C43—21no—
89C4×C43#9911yescharacteristic
90C4×C43#9911yescharacteristic
91Dic43—42no—
92Dic43—82no—
93#2122—431nomaximal, Sylow
94C2×C43—21no—
95C2×C43—41no—
96C2×C43—41no—
97C2×C43—41no—
98C2×C43C2×#9911yescharacteristic
99D43—82no—
100#535—431no—
101#413D4311yescharacteristic, complemented
102#410—431no—
103AΣL(1,𝔽16)—434no—
104C43#212211yescharacteristic, complemented, Sylow
105C2×#41C2×D4311yescharacteristic
106C22×D4—431no—
107C2×M16—21no—
108#127—861no—
109#124—861no—
110#121—861no—
111#121—861no—
112#120—432no—
113#120—432no—
114#117—431no—
115#117—861no—
116#101—21no—
117#100C2×D4312yes—
118#99—432no—
119#99—861no—
120C24—432no—
121#41—41no—
122#41—41no—
123C2×Q8C22⋊D4311yescharacteristic
124C2×D4—862no—
125C2×D4—862no—
126C2×D4—861no—
127C2×D4—861no—
128C2×D4—1721no—
129C2×D4—1721no—
130C2×D4C4×D4311yescharacteristic
131C2×D4D17211yescharacteristic
132C2×D4C22×D4311yescharacteristic
133C22×C4C4×D4311yescharacteristic
134C22×C4D17211yescharacteristic
135C22×C4C22⋊D4311yescharacteristic
136M16—22no—
137M16—41no—
138C2×C8—41no—
139C4⋊C4—861no—
140C4⋊C4—1721no—
141C22⋊C4—432no—
142C22⋊C4—862no—
143C22⋊C4—862no—
144C22⋊C4—862no—
145C42—861no—
146C42—1721no—
147C23—862no—
148C23—3442no—
149C23—1722no—
150C23(C2×D43)⋊C411yescharacteristic
151C23C2×C4×D4311yescharacteristic
152C23C2×D17211yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—3442no—
158D4—3442no—
159D4—1722no—
160D4—1721no—
161D4—1721no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—862no—
169C2×C4—1722no—
170C2×C4(C2×D43)⋊C411yescharacteristic
171C2×C4(C2×D43)⋊C411yescharacteristic
172C2×C4(C2×D43)⋊C411yescharacteristic
173C2×C4C2×C22⋊D4311yescharacteristic
174C8—42no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—3444no—
182C22—1722no—
183C22—1722no—
184C22—1722no—
185C22C2×(C2×D43)⋊C411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—3442no—
190C4—1722no—
191C4#1306323911yescharacteristic
192C4#1306323911yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—3442no—
198C2C2×#1306323911yescharacteristic
subgroupG/H
centerC2C2×#13063239
commutatorC23×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#413C2
socleC2×C43C2×#99
hypercenter#413D43
hypocenterC43#2122
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #14582873C2semidirect
3. #14582687C2semidirect
4. C43×#413C2semidirect
5. C22×D172C4semidirect
10. #13063293C4semidirect
13. #13063284C4semidirect
101. #413D43semidirect
104. C43#2122semidirect