Finite Group Databasebeta

← #19145678

Subgroups — #19145678

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#14583511C211yesmaximal, characteristic, complemented
2#14583294C211yesmaximal, characteristic, complemented
3#14583278C211yesmaximal, characteristic, complemented
4#14583267C211yesmaximal, characteristic, complemented
5#14583253C211yesmaximal, characteristic, complemented
6#14583118C212yesmaximal, complemented
7#14583106C212yesmaximal, complemented
8#14583061C212yesmaximal
9#14583055C212yesmaximal, complemented
10#14582960C211yesmaximal, characteristic, complemented
11C43×#536C211yesmaximal, characteristic
12C2×#10621885C2212yes—
13C2×#10621885C2212yes—
14C2×#10621885C2212yes—
15C2×#10621883C2212yes—
16#13063325C2211yescharacteristic
17#13063318—22no—
18#13063317C2211yescharacteristic
19#13063315—22no—
20#13063304C2212yes—
21C4×Dic86C2212yes—
22C4⋊(C43⋊C8)C2212yes—
23#13063249C2212yes—
24#13063249C2212yes—
25#13063249C2212yes—
26#13063246C2212yes—
27C22⋊(C43⋊C8)C2212yes—
28#13063236C2211yescharacteristic
29C4×C43⋊C8C2211yescharacteristic
30C2×#41×C43C2211yescharacteristic
31C22×Q8×C43C2211yescharacteristic
32C4⋊Q8×C43C2211yescharacteristic
33C4⋊Q8×C43C2211yescharacteristic
34#124×C43C2211yescharacteristic
35#124×C43C2211yescharacteristic
36#123×C43—22no—
37C22⋊Q8×C43—22no—
38#117×C43C2211yescharacteristic
39#41×C43—42no—
40C2×Q8×C43—21no—
41C2×Q8×C43—42no—
42C2×Q8×C43C2311yescharacteristic
43C2×Q8×C43C2311yescharacteristic
44C2×Q8×C43C2311yescharacteristic
45C2×D4×C43—21no—
46C2×D4×C43C2311yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43C2311yescharacteristic
50C2×Dic86C2312yes—
51C4⋊C4×C43—22no—
52C4⋊C4×C43—22no—
53C4⋊C4×C43D412yes—
54C22⋊C4×C43—22no—
55C22⋊C4×C43—22no—
56C22⋊C4×C43D412yes—
57C42×C43C2311yescharacteristic
58C42×C43C2311yescharacteristic
59C22⋊Dic43—22no—
60#10621885—42no—
61#10621885—42no—
62#10621885—42no—
63#10621883—42no—
64C4⋊Dic43—22no—
65C4⋊Dic43C2312yes—
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68Dic43⋊C4—22no—
69C4×Dic43—22no—
70C2×C43⋊C8C2312yes—
71C2×C43⋊C8C2312yes—
72C23×C43—21no—
73C23×C43C2×D411yescharacteristic
74Q8×C43—22no—
75Q8×C43—22no—
76Q8×C43—22no—
77Q8×C43—42no—
78D4×C43—22no—
79D4×C43—42no—
80C2×C4×C43—22no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43C2×D412yes—
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2×D412yes—
89C2×C4×C43C2411yescharacteristic
90C2×Dic43—22no—
91C2×Dic43—22no—
92Dic86—22no—
93Dic86—22no—
94C43⋊C8—22no—
95C43⋊C8—22no—
96C22×C43—21no—
97C22×C43—22no—
98C22×C43—41no—
99C22×C43—42no—
100C22×C43C22×D411yescharacteristic
101C4×C43—21no—
102C4×C43—22no—
103C4×C43—22no—
104C4×C43—41no—
105C4×C43—41no—
106C4×C43—41no—
107C4×C43H(5,𝔽2)12yes—
108Dic43—42no—
109Dic43—42no—
110#3223—431nomaximal, Sylow
111C2×C43—41no—
112C2×C43—81no—
113C2×C43#53511yescharacteristic
114C2×C43#57812yes—
115#541—431no—
116#536D4311yescharacteristic
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×#41C2×D4311yescharacteristic
128C22×Q8C2×D4311yescharacteristic
129C2×Q16—432no—
130C2×Q16—432no—
131C2×Q16—432no—
132C2×SD16—432no—
133C4⋊Q8—431no—
134C4⋊Q8C2×D4311yescharacteristic
135C4⋊Q8C2×D4311yescharacteristic
136#126—862no—
137#125—431no—
138#125—862no—
139#124C2×D4311yescharacteristic
140#124C2×D4311yescharacteristic
141#123—22no—
142C22⋊Q8—22no—
143C22⋊Q8—432no—
144C4×Q8—432no—
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—42no—
155C2×Q8—21no—
156C2×Q8—42no—
157C2×Q8—432no—
158C2×Q8C22×D4311yescharacteristic
159C2×Q8C22×D4311yescharacteristic
160C2×Q8C22×D4311yescharacteristic
161C2×D4—21no—
162C2×D4C22×D4311yescharacteristic
163C22×C4—21no—
164C22×C4—21no—
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—432no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4C22⋊D4312yes—
180C22⋊C4—22no—
181C22⋊C4—22no—
182C22⋊C4—862no—
183C22⋊C4C22⋊D4312yes—
184C42—862no—
185C42C22×D4311yescharacteristic
186C42C22×D4311yescharacteristic
187C23—21no—
188C23C2×C22⋊D4311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—862no—
194Q8—862no—
195D4—22no—
196D4—42no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—862no—
204C2×C4—862no—
205C2×C4C2×C22⋊D4312yes—
206C2×C4C2×C22⋊D4312yes—
207C2×C4C2×C22⋊D4311yescharacteristic
208C2×C4C23×D4311yescharacteristic
209C8—862no—
210C8—862no—
211C22—22no—
212C22—21no—
213C22—42no—
214C22—41no—
215C22C22×C22⋊D4311yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—1722no—
223C4—1722no—
224C4#1306337012yes—
225C2—41no—
226C2—81no—
227C2#1458346611yescharacteristic
228C2#1458371412yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#536C2
socleC22×C43C22×D4
hypercenter#536D43
hypocenterC43#3223
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #14583511C2semidirect
2. #14583294C2semidirect
3. #14583278C2semidirect
4. #14583267C2semidirect
5. #14583253C2semidirect
6. #14583118C2semidirect
7. #14583106C2semidirect
9. #14583055C2semidirect
10. #14582960C2semidirect
126. C43#3223semidirect