Finite Group Databasebeta

← #19145787

Subgroups — #19145787

Order 5504.

368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583449C211yesmaximal, characteristic
2C2×#13063317C211yesmaximal, characteristic, complemented
3#14583308C212yesmaximal, complemented
4#14583264C212yesmaximal, complemented
5#14583218C212yesmaximal, complemented
6#14583213C212yesmaximal, complemented
7#14583200C214yesmaximal, complemented
8C43×#432C211yesmaximal, characteristic, complemented
9C2×#10621898—21no—
10#13063325C2211yescharacteristic
11#13063322C2211yescharacteristic
12#13063317—21no—
13#13063317—21no—
14#13063317C2212yes—
15#13063317C2212yes—
16#13063313—21no—
17#13063299—21no—
18#13063299C2212yes—
19C4×D172—21no—
20C4×D172C2212yes—
21C2×C4⋊Dic43C2211yescharacteristic
22C2×C4⋊Dic43C2211yescharacteristic
23C2×Dic43⋊C4—21no—
24C2×Dic43⋊C4—21no—
25#13063259C2214yes—
26#13063257C2214yes—
27#13063247C2214yes—
28#13063247C2214yes—
29C2×C42×C43C2211yescharacteristic
30C4⋊C8×C43C2212yes—
31C22⋊C8×C43C2212yes—
32#97×C43C2212yes—
33C22×C4×C43D411yescharacteristic
34C22×C4×C43D411yescharacteristic
35C22×C4×C43C2311yescharacteristic
36C2×C22⋊D43—22no—
37C22×Dic43—21no—
38C22×Dic43—21no—
39#10621898—44no—
40C2×D172—21no—
41C2×D172—21no—
42C2×D172C2312yes—
43C2×C4×D43—22no—
44C2×Dic86—21no—
45C2×C8×C43C2314yes—
46C42×C43D411yescharacteristic
47C42×C43D411yescharacteristic
48C42×C43C2311yescharacteristic
49C42×C43C2311yescharacteristic
50(C2×D43)⋊C4—22no—
51(C2×D43)⋊C4—22no—
52C4⋊Dic43—21no—
53C4⋊Dic43—21no—
54C4⋊Dic43—21no—
55C4⋊Dic43C2312yes—
56C4⋊Dic43C2312yes—
57C4⋊Dic43C2312yes—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62C23×C43C2×D411yescharacteristic
63C22×D43—22no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—41no—
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2411yescharacteristic
73C22⋊D43—44no—
74C2×Dic43—22no—
75C2×Dic43—22no—
76C2×Dic43—22no—
77C2×Dic43—42no—
78C2×Dic43—42no—
79D172—24no—
80D172—42no—
81D172—42no—
82C4×D43—44no—
83Dic86—42no—
84C8×C43—24no—
85C22×C43—21no—
86C22×C43—21no—
87C22×C43AGL(1,ℤ/8)12yes—
88C22×C43C22×D411yescharacteristic
89C2×D43—42no—
90C2×D43—42no—
91C2×D43—42no—
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—21no—
95C4×C43—21no—
96C4×C43—21no—
97C4×C432−1+412yes—
98Dic43—42no—
99Dic43—42no—
100Dic43—42no—
101#3234—431nomaximal, Sylow
102C2×C43—22no—
103C2×C43#53611yescharacteristic
104C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
105C2×C43#57511yescharacteristic
106D43—82no—
107#532—431no—
108C2×#125—431no—
109#501—432no—
110#490—432no—
111#481—432no—
112#480—432no—
113#478—434no—
114#432D4311yescharacteristic, complemented
115C43#323411yescharacteristic, complemented, Sylow
116C2×#41—861no—
117C4⋊Q8—431no—
118#127—431no—
119#125—432no—
120#125—432no—
121#125—861no—
122#125—861no—
123#124—861no—
124#121—432no—
125#121—861no—
126C4×D4—432no—
127C4×D4—861no—
128C2×C4⋊C4—431no—
129C2×C4⋊C4—431no—
130C2×C4⋊C4—861no—
131C2×C4⋊C4—861no—
132C2×C42C2×D4311yescharacteristic
133#107—434no—
134#106—434no—
135C4⋊C8C2×D4312yes—
136#102—434no—
137#102—434no—
138C22⋊C8C2×D4312yes—
139#97C2×D4312yes—
140#41—1724no—
141C2×Q8—861no—
142C2×D4—432no—
143C2×D4—862no—
144C2×D4—861no—
145C2×D4—861no—
146C22×C4—861no—
147C22×C4—861no—
148C22×C4—862no—
149C22×C4D17211yescharacteristic
150C22×C4D17211yescharacteristic
151C22×C4C22×D4311yescharacteristic
152C2×C8C22×D4314yes—
153C4⋊C4—432no—
154C4⋊C4—432no—
155C4⋊C4—432no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C4⋊C4—862no—
159C4⋊C4—862no—
160C4⋊C4—862no—
161C4⋊C4—862no—
162C4⋊C4—861no—
163C22⋊C4—862no—
164C22⋊C4—862no—
165C42D17211yescharacteristic
166C42D17211yescharacteristic
167C42C22×D4311yescharacteristic
168C42C22×D4311yescharacteristic
169C23—862no—
170C23C2×D17211yescharacteristic
171Q8—1722no—
172D4—864no—
173D4—1722no—
174D4—1722no—
175D4—1724no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—862no—
180C2×C4—862no—
181C2×C4—862no—
182C2×C4—1724no—
183C2×C4—1722no—
184C2×C4—1722no—
185C2×C4C2×D17211yescharacteristic
186C2×C4C2×D17211yescharacteristic
187C2×C4C2×D17211yescharacteristic
188C2×C4C2×D17211yescharacteristic
189C2×C4C2×D17211yescharacteristic
190C2×C4C23×D4311yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—1722no—
195C22—1722no—
196C22—1722no—
197C22#1306335312yes—
198C22C22×D17211yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—21no—
204C4—1722no—
205C4—1722no—
206C4—1722no—
207C4#1306337212yes—
208C2—22no—
209C2—3442no—
210C2#1458347511yescharacteristic
211C2C2×#1306335311yescharacteristic
212C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#432C2
socleC22×C43C22×D4
hypercenter#432D43
hypocenterC43#3234
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×#13063317C2semidirect
3. #14583308C2semidirect
4. #14583264C2semidirect
5. #14583218C2semidirect
6. #14583213C2semidirect
7. #14583200C2semidirect
8. C43×#432C2semidirect
114. #432D43semidirect
115. C43#3234semidirect