Finite Group Databasebeta

← #19136248

Subgroups — #19136248

Order 5504.

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

normal subgroups only

This group has 234 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#14583470C211yesmaximal, characteristic
2#14582883C211yesmaximal, characteristic
3#14582688C214yesmaximal, complemented
4C43×#410C211yesmaximal, characteristic
5C22×Dic86C411yescharacteristic, complemented
6C2×#10621877—21no—
7#13063323—21no—
8#13063312—21no—
9#13063306C412yescomplemented
10#13063306C2212yes—
11#13063304—21no—
12#13063304—21no—
13#13063284C411yescharacteristic, complemented
14#13063244—21no—
15#13063242C2212yes—
16C2×#41×C43C2211yescharacteristic
17#117×C43—21no—
18#99×C43—21no—
19#99×C43C2212yes—
20#41×C43—41no—
21#41×C43—41no—
22C2×Q8×C43D411yescharacteristic
23C2×D4×C43C2×C411yescharacteristic
24C2×D4×C43D411yescharacteristic
25C2×D4×C43C2311yescharacteristic
26C22×C4×C43C2×C411yescharacteristic
27C22×C4×C43D411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×Dic43C2×C412yes—
30C2×Dic86—21no—
31C2×Dic86—21no—
32C2×Dic86—41no—
33C2×Dic86—41no—
34C4⋊C4×C43—41no—
35C22⋊C4×C43—22no—
36C42×C43—41no—
37C22⋊Dic43—22no—
38C22⋊Dic43—22no—
39C22⋊Dic43C2×C412yes—
40C4⋊Dic43—21no—
41Dic43⋊C4—22no—
42Dic43⋊C4—22no—
43C4×Dic43—21no—
44#10621877—22no—
45#10621877—41no—
46C2×C43⋊C8—41no—
47C23×C43C22⋊C411yescharacteristic
48C23×C43C22×C411yescharacteristic
49C23×C43C2×D411yescharacteristic
50Q8×C43—41no—
51D4×C43—41no—
52D4×C43—41no—
53D4×C43—41no—
54C2×C4×C43—21no—
55C2×C4×C43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43—42no—
61C2×C4×C43C22⋊C411yescharacteristic
62C2×C4×C43C22⋊C411yescharacteristic
63C2×C4×C43C22⋊C411yescharacteristic
64C2×C4×C43C2×D411yescharacteristic
65C2×Dic43—22no—
66C2×Dic43—22no—
67C2×Dic43—42no—
68Dic86—42no—
69Dic86—41no—
70Dic86—41no—
71C43⋊C8—42no—
72C22×C43—21no—
73C22×C43—21no—
74C22×C43—21no—
75C22×C43—41no—
76C22×C43—41no—
77C22×C43—41no—
78C22×C43C2×C22⋊C411yescharacteristic
79C4×C43—21no—
80C4×C43—21no—
81C4×C43—21no—
82C4×C43—82no—
83C4×C43#9911yescharacteristic
84C4×C43#9911yescharacteristic
85Dic43—42no—
86Dic43—42no—
87#2123—431nomaximal, Sylow
88C2×C43—21no—
89C2×C43—41no—
90C2×C43—41no—
91C2×C43—41no—
92C2×C43C2×#9911yescharacteristic
93#536—431no—
94#413—431no—
95#410D4311yescharacteristic
96#352—434no—
97C43#212311yescharacteristic, complemented, Sylow
98C2×#41C2×D4311yescharacteristic
99C22×Q8—431no—
100C2×M16—861no—
101C4⋊Q8—861no—
102#124—861no—
103#123—432no—
104#123—432no—
105C22⋊Q8—861no—
106C22⋊Q8—861no—
107#117—21no—
108#117—431no—
109#101—861no—
110#100—432no—
111#99—21no—
112#99C2×D4312yes—
113#41—41no—
114#41—41no—
115C2×Q8—861no—
116C2×Q8—861no—
117C2×Q8—1721no—
118C2×Q8—1721no—
119C2×Q8D17211yescharacteristic
120C2×D4C4×D4311yescharacteristic
121C2×D4C22⋊D4311yescharacteristic
122C2×D4C22×D4311yescharacteristic
123C22×C4—432no—
124C22×C4C4×D4311yescharacteristic
125C22×C4D17211yescharacteristic
126C22×C4C22⋊D4311yescharacteristic
127M16—862no—
128M16—1721no—
129C2×C8—1721no—
130C4⋊C4—41no—
131C4⋊C4—862no—
132C4⋊C4—861no—
133C4⋊C4—862no—
134C22⋊C4—22no—
135C22⋊C4—432no—
136C22⋊C4—862no—
137C22⋊C4—862no—
138C42—41no—
139C42—861no—
140C23(C2×D43)⋊C411yescharacteristic
141C23C2×C4×D4311yescharacteristic
142C23C2×C22⋊D4311yescharacteristic
143Q8—41no—
144Q8—1722no—
145Q8—1721no—
146Q8—1721no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—862no—
158C2×C4—862no—
159C2×C4—1722no—
160C2×C4(C2×D43)⋊C411yescharacteristic
161C2×C4(C2×D43)⋊C411yescharacteristic
162C2×C4(C2×D43)⋊C411yescharacteristic
163C2×C4C2×D17211yescharacteristic
164C8—1722no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×(C2×D43)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—82no—
176C4—1722no—
177C4—1722no—
178C4#1306323911yescharacteristic
179C4#1306323911yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1306323911yescharacteristic
subgroupG/H
centerC2C2×#13063239
commutatorC23×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#410C2
socleC2×C43C2×#99
hypercenter#410D43
hypocenterC43#2123
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #14582688C2semidirect
5. C22×Dic86C4semidirect
9. #13063306C4semidirect
13. #13063284C4semidirect
97. C43#2123semidirect