Finite Group Databasebeta

← #19145672

Subgroups — #19145672

Order 5504.

364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583475C211yesmaximal, characteristic
2#14583291C211yesmaximal, characteristic, complemented
3#14583278C211yesmaximal, characteristic, complemented
4#14583269C211yesmaximal, characteristic, complemented
5#14583256C211yesmaximal, characteristic, complemented
6#14583121C212yesmaximal, complemented
7#14583109C212yesmaximal, complemented
8#14583059C212yesmaximal
9#14583054C212yesmaximal, complemented
10#14582960C211yesmaximal, characteristic, complemented
11C43×#541C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×Dic86C2211yescharacteristic
14C2×#10621885C2212yes—
15C2×#10621885C2212yes—
16C2×#10621885C2212yes—
17C2×#10621884C2212yes—
18#13063325C2211yescharacteristic
19#13063325C2211yescharacteristic
20#13063313C2211yescharacteristic
21#13063313C2211yescharacteristic
22#13063309—22no—
23#13063305—22no—
24C4⋊(C43⋊C8)C2212yes—
25#13063248C2212yes—
26#13063248C2212yes—
27#13063248C2212yes—
28#13063245C2212yes—
29C22⋊(C43⋊C8)C2212yes—
30#13063236C2211yescharacteristic
31C4×C43⋊C8C2211yescharacteristic
32C4⋊Q8×C43C2211yescharacteristic
33#126×C43—22no—
34#125×C43—22no—
35#125×C43C2211yescharacteristic
36C22⋊Q8×C43C2212yes—
37C4×Q8×C43C2212yes—
38#117×C43C2211yescharacteristic
39C2×Q8×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C2×C22⋊D43—21no—
42C22×Dic43—21no—
43#10621898—42no—
44C2×D172C2311yescharacteristic
45C2×C4×D43—21no—
46C2×Dic86—21no—
47C2×Dic86—42no—
48C2×Dic86C2311yescharacteristic
49C2×Dic86C2311yescharacteristic
50C2×Dic86C2311yescharacteristic
51C4⋊C4×C43—22no—
52C4⋊C4×C43—22no—
53C4⋊C4×C43—22no—
54C4⋊C4×C43—22no—
55C4⋊C4×C43D412yes—
56C4⋊C4×C43C2312yes—
57C22⋊C4×C43—22no—
58C22⋊C4×C43D412yes—
59C42×C43—22no—
60C42×C43C2311yescharacteristic
61C42×C43C2311yescharacteristic
62#10621885—42no—
63#10621885—42no—
64#10621885—42no—
65#10621884—42no—
66(C2×D43)⋊C4—22no—
67(C2×D43)⋊C4—22no—
68C4⋊Dic43—22no—
69C4⋊Dic43—22no—
70C2×C43⋊C8C2312yes—
71C2×C43⋊C8C2312yes—
72C23×C43C2×D411yescharacteristic
73C22×D43—21no—
74Q8×C43—22no—
75Q8×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43C2×D412yes—
80C2×C4×C43C2×D412yes—
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2411yescharacteristic
83C22⋊D43—42no—
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—42no—
88D172—22no—
89C4×D43—42no—
90Dic86—22no—
91Dic86—22no—
92Dic86—22no—
93Dic86—42no—
94C43⋊C8—22no—
95C43⋊C8—22no—
96C22×C43—21no—
97C22×C43—22no—
98C22×C43C22×D411yescharacteristic
99C2×D43—41no—
100C2×D43—42no—
101C4×C43—21no—
102C4×C43—22no—
103C4×C43—22no—
104C4×C43—42no—
105C4×C43—42no—
106C4×C43H(5,𝔽2)12yes—
107Dic43—41no—
108Dic43—41no—
109Dic43—41no—
110#3223—431nomaximal, Sylow
111C2×C43—41no—
112C2×C43#53511yescharacteristic
113C2×C43#57812yes—
114D43—81no—
115#541D4311yescharacteristic, complemented
116#536—431no—
117#497—431no—
118#494—431no—
119#491—431no—
120#488—431no—
121#464—432no—
122#462—432no—
123#452—432no—
124#451—432no—
125#433—431no—
126C43#322311yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C22×Q8—431no—
129C2×Q16—432no—
130C2×Q16—432no—
131C2×Q16—432no—
132C2×SD16—432no—
133C4⋊Q8—431no—
134C4⋊Q8—431no—
135C4⋊Q8C2×D4311yescharacteristic
136#126—22no—
137#125—22no—
138#125C2×D4311yescharacteristic
139#124—431no—
140#124—431no—
141#123—862no—
142C22⋊Q8—862no—
143C22⋊Q8C2×D4312yes—
144C4×Q8C2×D4312yes—
145#117C2×D4311yescharacteristic
146C4⋊C8—432no—
147#103—432no—
148#103—432no—
149#103—432no—
150#102—432no—
151C22⋊C8—432no—
152#97—431no—
153C4×C8—431no—
154#41—1722no—
155C2×Q8—431no—
156C2×Q8—431no—
157C2×Q8—431no—
158C2×Q8—861no—
159C2×Q8—1722no—
160C2×Q8C22×D4312yes—
161C2×D4—431no—
162C2×D4—861no—
163C22×C4—861no—
164C22×C4—861no—
165C22×C4C22×D4311yescharacteristic
166Q16—1722no—
167Q16—1722no—
168Q16—1722no—
169SD16—1722no—
170C2×C8—432no—
171C2×C8—432no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4C22⋊D4312yes—
179C4⋊C4C22×D4312yes—
180C22⋊C4—22no—
181C22⋊C4—862no—
182C22⋊C4—862no—
183C22⋊C4C22⋊D4312yes—
184C42—22no—
185C42C22×D4311yescharacteristic
186C42C22×D4311yescharacteristic
187C23—861no—
188C23C2×C22⋊D4311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—862no—
192Q8—862no—
193Q8—862no—
194Q8—1722no—
195D4—862no—
196D4—1722no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—861no—
201C2×C4—861no—
202C2×C4—861no—
203C2×C4—1722no—
204C2×C4—1722no—
205C2×C4C2×C22⋊D4312yes—
206C2×C4C2×C22⋊D4312yes—
207C2×C4C2×C22⋊D4311yescharacteristic
208C2×C4C23×D4311yescharacteristic
209C8—862no—
210C8—862no—
211C22—22no—
212C22—21no—
213C22—1722no—
214C22—1721no—
215C22C22×C22⋊D4311yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—1721no—
222C4—1721no—
223C4—1721no—
224C4#1306337112yes—
225C2—41no—
226C2—3441no—
227C2#1458346311yescharacteristic
228C2#1458371412yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#541C2
socleC22×C43C22×D4
hypercenter#541D43
hypocenterC43#3223
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #14583291C2semidirect
3. #14583278C2semidirect
4. #14583269C2semidirect
5. #14583256C2semidirect
6. #14583121C2semidirect
7. #14583109C2semidirect
9. #14583054C2semidirect
10. #14582960C2semidirect
11. C43×#541C2semidirect
115. #541D43semidirect
126. C43#3223semidirect