Finite Group Databasebeta

← #19136286

Subgroups — #19136286

Order 5504.

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

normal subgroups only

This group has 262 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#14582883C211yesmaximal, characteristic, complemented
3#14582695C214yesmaximal, complemented
4C43×#413C211yesmaximal, characteristic, complemented
5C22×D172C411yescharacteristic
6C2×#10621877—21no—
7#13063321C412yes—
8#13063314C2212yes—
9#13063299—21no—
10#13063299—21no—
11#13063293—21no—
12#13063293—21no—
13#13063284C411yescharacteristic
14#13063244C2212yescomplemented
15#13063242—21no—
16C2×#41×C43C2211yescharacteristic
17C2×M16×C43—21no—
18#101×C43C2212yescomplemented
19#100×C43—21no—
20C23×D43—21no—
21#41×C43—41no—
22#41×C43—41no—
23C2×Q8×C43C2311yescharacteristic
24C2×D4×C43C2×C411yescharacteristic
25C2×D4×C43D411yescharacteristic
26C2×D4×C43D411yescharacteristic
27C22×C4×C43C2×C411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×C4×C43D411yescharacteristic
30C2×C22⋊D43—22no—
31C2×C22⋊D43—22no—
32C2×D172—21no—
33C2×D172—41no—
34C2×D172—41no—
35C2×D172C2×C412yes—
36M16×C43—22no—
37M16×C43—41no—
38C2×C8×C43—41no—
39C22⋊Dic43—21no—
40(C2×D43)⋊C4—22no—
41(C2×D43)⋊C4—22no—
42C4⋊Dic43—21no—
43C4×Dic43C2×C412yes—
44#10621877—22no—
45#10621877—41no—
46C2×C43⋊C8—41no—
47C23×C43C22⋊C411yescharacteristic
48C23×C43C22⋊C411yescharacteristic
49C23×C43C22⋊C411yescharacteristic
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×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C22⋊D43—82no—
68C22⋊D43—82no—
69C2×Dic43—22no—
70D172—42no—
71D172—41no—
72D172—41no—
73C8×C43—42no—
74C43⋊C8—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—
92#2134—431nomaximal, Sylow
93C2×C43—21no—
94C2×C43—41no—
95C2×C43—41no—
96C2×C43—41no—
97C2×C43C2×#9911yescharacteristic
98D43—82no—
99#535—431no—
100#413—431no—
101#413D4311yescharacteristic, complemented
102#355—434no—
103C43#213411yescharacteristic, complemented, Sylow
104C2×#41C2×D4311yescharacteristic
105C22×D4—431no—
106C2×M16—21no—
107C2×M16—861no—
108#127—432no—
109#124—432no—
110#121—861no—
111#121—861no—
112#120—861no—
113#120—861no—
114#117—431no—
115#101—432no—
116#101C2×D4312yescomplemented
117#100—21no—
118#100—861no—
119C24—861no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D4311yescharacteristic
123C2×D4—432no—
124C2×D4—862no—
125C2×D4—862no—
126C2×D4—861no—
127C2×D4—1721no—
128C2×D4—1721no—
129C2×D4C4×D4311yescharacteristic
130C2×D4D17211yescharacteristic
131C2×D4C22⋊D4311yescharacteristic
132C22×C4C4×D4311yescharacteristic
133C22×C4D17211yescharacteristic
134C22×C4C22⋊D4311yescharacteristic
135M16—22no—
136M16—41no—
137M16—862no—
138M16—1721no—
139C2×C8—41no—
140C2×C8—1721no—
141C4⋊C4—861no—
142C22⋊C4—861no—
143C22⋊C4—862no—
144C22⋊C4—862no—
145C42—432no—
146C23—862no—
147C23—3442no—
148C23—1722no—
149C23(C2×D43)⋊C411yescharacteristic
150C23(C2×D43)⋊C411yescharacteristic
151C23(C2×D43)⋊C411yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—3442no—
157D4—3442no—
158D4—1722no—
159D4—1721no—
160D4—1721no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—862no—
168C2×C4(C2×D43)⋊C411yescharacteristic
169C2×C4C2×C4×D4311yescharacteristic
170C2×C4C2×D17211yescharacteristic
171C2×C4C2×C22⋊D4311yescharacteristic
172C8—42no—
173C8—1722no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—3444no—
181C22—1722no—
182C22—1722no—
183C22—1722no—
184C22C2×(C2×D43)⋊C411yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—1722no—
189C4#1306323911yescharacteristic
190C4#1306323911yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—3442no—
196C2C2×#1306323911yescharacteristic
subgroupG/H
centerC2C2×#13063239
commutatorC2×C4×C43C22×C4
FrattiniC2×Q8C22×D43
FittingC43×#413C2
socleC2×C43C2×#99
hypercenter#413D43
hypocenterC43#2134
LCSG ▷ C2×C4×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. #14582883C2semidirect
3. #14582695C2semidirect
4. C43×#413C2semidirect
14. #13063244C22semidirect
18. #101×C43C22semidirect
101. #413D43semidirect
103. C43#2134semidirect
116. #101C2×D43semidirect