Finite Group Databasebeta

← #19145978

Subgroups — #19145978

Order 5504.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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
2#14583194C212yesmaximal, complemented
3#14583176C212yesmaximal, complemented
4#14583147C214yesmaximal, complemented
5#14583101C212yesmaximal, complemented
6#14583099C212yesmaximal, complemented
7#14582923C211yesmaximal, characteristic, complemented
8C43×#533C211yesmaximal, characteristic, complemented
9C2×#10621898—21no—
10C2×#10621884C2214yes—
11C2×#10621877C2212yes—
12#13063325C2211yescharacteristic
13#13063322C2211yescharacteristic
14#13063313—21no—
15#13063299—21no—
16#13063299C2212yes—
17C4×D172—21no—
18C4×D172C2212yes—
19#13063258C2214yes—
20C4⋊(C43⋊C8)C2212yes—
21C4⋊(C43⋊C8)C2212yes—
22#13063249C2214yes—
23#13063245C2214yes—
24C4⋊Q8×C43C2211yescharacteristic
25C4⋊Q8×C43C2211yescharacteristic
26#125×C43—21no—
27C22⋊Q8×C43—21no—
28C22⋊Q8×C43C2212yes—
29C4×Q8×C43—21no—
30C4×Q8×C43C2212yes—
31#117×C43—21no—
32C2×C42×C43C2211yescharacteristic
33C2×Q8×C43—21no—
34C2×Q8×C43C2312yes—
35C22×C4×C43D411yescharacteristic
36C22×C4×C43D411yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—22no—
39#10621898—44no—
40C2×D172—21no—
41C2×D172—21no—
42C2×D172C2312yes—
43C2×C4×D43—22no—
44C2×Dic86—21no—
45C4⋊C4×C43—21no—
46C4⋊C4×C43—21no—
47C4⋊C4×C43—21no—
48C4⋊C4×C43—22no—
49C4⋊C4×C43—22no—
50C4⋊C4×C43C2312yes—
51C22⋊C4×C43—22no—
52C42×C43—22no—
53C42×C43D411yescharacteristic
54C42×C43D411yescharacteristic
55C42×C43C2311yescharacteristic
56C42×C43C2311yescharacteristic
57#10621884—44no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60C4⋊Dic43—21no—
61C4⋊Dic43C2312yes—
62#10621877—42no—
63C2×C43⋊C8C2314yes—
64C23×C43C2×D411yescharacteristic
65C22×D43—22no—
66Q8×C43—22no—
67Q8×C43—22no—
68Q8×C43—42no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2411yescharacteristic
81C22⋊D43—44no—
82C2×Dic43—22no—
83D172—22no—
84D172—22no—
85D172—42no—
86D172—42no—
87C4×D43—44no—
88Dic86—42no—
89C43⋊C8—24no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43C22×D411yescharacteristic
94C2×D43—42no—
95C2×D43—42no—
96C2×D43—42no—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—42no—
101C4×C43—42no—
102C4×C43AGL(1,ℤ/8)12yes—
103C4×C43#13712yes—
104C4×C43H(5,𝔽2)11yescharacteristic
105C4×C432−1+411yescharacteristic
106Dic43—42no—
107#3254—431nomaximal, Sylow
108C2×C43—41no—
109C2×C43#53711yescharacteristic
110C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C43C2×#13711yescharacteristic
112D43—82no—
113#533D4311yescharacteristic, complemented
114#532—431no—
115#477—432no—
116#474—432no—
117#468—434no—
118#461—432no—
119#460—432no—
120#423—431no—
121C43#325411yescharacteristic, complemented, Sylow
122C2×#41—861no—
123C2×SD16—434no—
124C2×M16—432no—
125C4⋊Q8—431no—
126C4⋊Q8C2×D4311yescharacteristic
127C4⋊Q8C2×D4311yescharacteristic
128#127—431no—
129#125—21no—
130#124—861no—
131C22⋊Q8—21no—
132C22⋊Q8C2×D4312yes—
133#121—432no—
134#121—861no—
135C4×Q8—21no—
136C4×Q8C2×D4312yes—
137C4×D4—432no—
138C4×D4—861no—
139#117—21no—
140C2×C42C2×D4311yescharacteristic
141#107—434no—
142C4⋊C8—432no—
143C4⋊C8—432no—
144#103—434no—
145#102—434no—
146#41—1724no—
147C2×Q8—21no—
148C2×Q8—861no—
149C2×Q8C22×D4312yes—
150C2×D4—432no—
151C2×D4—862no—
152C2×D4—861no—
153C2×D4—861no—
154C22×C4—862no—
155C22×C4C22⋊D4311yescharacteristic
156C22×C4C22⋊D4311yescharacteristic
157C22×C4C22×D4311yescharacteristic
158SD16—1724no—
159M16—1722no—
160C2×C8—434no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—432no—
167C4⋊C4—861no—
168C4⋊C4C22×D4312yes—
169C22⋊C4—22no—
170C22⋊C4—862no—
171C22⋊C4—862no—
172C42—22no—
173C42C22⋊D4311yescharacteristic
174C42C22⋊D4311yescharacteristic
175C42C22×D4311yescharacteristic
176C42C22×D4311yescharacteristic
177C23—862no—
178C23C2×C22⋊D4311yescharacteristic
179Q8—22no—
180Q8—22no—
181Q8—42no—
182Q8—1722no—
183D4—862no—
184D4—862no—
185D4—1722no—
186D4—1724no—
187D4—1722no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—862no—
195C2×C4—1724no—
196C2×C4C2×C22⋊D4311yescharacteristic
197C2×C4C2×C22⋊D4311yescharacteristic
198C2×C4C2×C22⋊D4311yescharacteristic
199C2×C4C2×C22⋊D4311yescharacteristic
200C2×C4C2×C22⋊D4311yescharacteristic
201C2×C4C23×D4311yescharacteristic
202C8—864no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—1722no—
207C22—1722no—
208C22—1722no—
209C22C22×C22⋊D4311yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—42no—
214C4—42no—
215C4—1722no—
216C4#1306335012yes—
217C4#1306335612yes—
218C4#1306337111yescharacteristic
219C4#1306337211yescharacteristic
220C2—41no—
221C2—3442no—
222C2#1458347711yescharacteristic
223C2C2×#1306335011yescharacteristic
224C2C2×#1306335611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#533C2
socleC22×C43C22×D4
hypercenter#533D43
hypocenterC43#3254
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #14583194C2semidirect
3. #14583176C2semidirect
4. #14583147C2semidirect
5. #14583101C2semidirect
6. #14583099C2semidirect
7. #14582923C2semidirect
8. C43×#533C2semidirect
113. #533D43semidirect
121. C43#3254semidirect