Finite Group Databasebeta

← #19147236

Subgroups — #19147236

Order 5504.

370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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#14583627C211yesmaximal, characteristic, complemented
2#14583564C211yesmaximal, characteristic
3#14583251C211yesmaximal, characteristic, complemented
4#14583248C212yesmaximal, complemented
5#14583183C212yesmaximal, complemented
6#14583105C211yesmaximal, characteristic
7#14583103C212yesmaximal
8#14583023C211yesmaximal, characteristic, complemented
9C4×#10621884C211yesmaximal, characteristic
10#14582986C212yesmaximal
11C43×#475C211yesmaximal, characteristic, complemented
12C2×Q8×D43—21no—
13C2×#10621873C2212yes—
14C2×#10621884C2211yescharacteristic
15#13063325C2211yescharacteristic
16#13063324C2212yes—
17#13063323C2212yes—
18#13063317—21no—
19#13063315—22no—
20#13063303—22no—
21#13063301—21no—
22C4×Dic86—21no—
23C4×Dic86C2211yescharacteristic
24#13063290C2212yes—
25C4×D172C2211yescharacteristic
26#13063287C2212yes—
27#13063256C2211yescharacteristic
28Dic43⋊C8C2212yes—
29#13063250C2212yes—
30#13063249C2211yescharacteristic
31#13063248C2212yes—
32#13063248C2212yes—
33#13063245C2211yescharacteristic
34C4×C43⋊C8C2211yescharacteristic
35C8×Dic43C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37C4×Q8×C43C2211yescharacteristic
38#106×C43C2212yes—
39C4⋊C8×C43C2211yescharacteristic
40#103×C43C2212yes—
41C2×Q8×C43—21no—
42C2×Q8×C43C2311yescharacteristic
43Q8×D43—44no—
44C2×D172C2311yescharacteristic
45C2×C4×D43—21no—
46C2×C4×D43—22no—
47C2×Dic86—22no—
48C2×Dic86D411yescharacteristic
49C2×Dic86C2312yes—
50C2×C8×C43C2312yes—
51C4⋊C4×C43—21no—
52C4⋊C4×C43—21no—
53C4⋊C4×C43C2312yes—
54C4⋊C4×C43C2311yescharacteristic
55C42×C43—21no—
56C42×C43C2311yescharacteristic
57#10621884—22no—
58(C2×D43)⋊C4—21no—
59(C2×D43)⋊C4—22no—
60C4⋊Dic43—21no—
61C4⋊Dic43—21no—
62C4⋊Dic43D411yescharacteristic
63C4⋊Dic43C2311yescharacteristic
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68Dic43⋊C4D412yes—
69C4×Dic43—22no—
70C4×Dic43C2312yes—
71C2×C43⋊C8C2311yescharacteristic
72C2×C43⋊C8C2311yescharacteristic
73#10621873—24no—
74C22×D43—21no—
75Q8×C43—21no—
76Q8×C43—21no—
77Q8×C43—42no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2411yescharacteristic
84C2×Dic43—22no—
85C2×Dic43—21no—
86C2×Dic43C2×D412yes—
87C2×Dic43C2×D412yes—
88D172—21no—
89D172#4112yes—
90C4×D43—42no—
91C4×D43—44no—
92Dic86—22no—
93Dic86—22no—
94Dic86—44no—
95Dic86SD1614yescomplemented
96C8×C43—22no—
97C43⋊C8—21no—
98C43⋊C8—21no—
99C22×C43C22×D411yescharacteristic
100C2×D43—22no—
101C2×D43—41no—
102C2×D43—41no—
103C4×C43—21no—
104C4×C43—41no—
105C4×C43—42no—
106C4×C43—41no—
107C4×C43C2×SD1612yes—
108C4×C43C2×#4111yescharacteristic
109C4×C432−1+411yescharacteristic
110Dic43—22no—
111Dic43—42no—
112Dic43—41no—
113Dic43C2×SD1614yes—
114#3359—431nomaximal, Sylow
115C2×C43#54811yescharacteristic
116C2×C43C22×SD1611yescharacteristic
117C2×C43#57811yescharacteristic
118D43—42no—
119#557—431no—
120D4×Q8—431no—
121#487—431no—
122#487—432no—
123#475—432no—
124#475D4311yescharacteristic, complemented
125#461—431no—
126#461—432no—
127C8×Q8—431no—
128C4×SD16—431no—
129C4×SD16—432no—
130C43#335911yescharacteristic, complemented, Sylow
131C22×Q8—861no—
132C2×SD16—431no—
133C2×SD16—432no—
134C4⋊Q8—432no—
135C4⋊Q8—432no—
136C4⋊Q8—431no—
137C4⋊Q8C2×D4311yescharacteristic
138#125—861no—
139#125—862no—
140C22⋊Q8—862no—
141C22⋊Q8—861no—
142C4×Q8—431no—
143C4×Q8—432no—
144C4×Q8—861no—
145C4×Q8C2×D4311yescharacteristic
146C4×D4—432no—
147C4×D4—431no—
148#106—431no—
149#106C2×D4312yes—
150C4⋊C8—432no—
151C4⋊C8C2×D4311yescharacteristic
152#103—431no—
153#103—432no—
154#103—432no—
155#103—432no—
156#103C2×D4312yes—
157#102—431no—
158C4×C8—432no—
159C4×C8—431no—
160C2×Q8—21no—
161C2×Q8—431no—
162C2×Q8—432no—
163C2×Q8—862no—
164C2×Q8—1724no—
165C2×Q8C22×D4311yescharacteristic
166C2×D4—431no—
167C22×C4—862no—
168C22×C4—861no—
169SD16—864no—
170SD16—862no—
171C2×C8—431no—
172C2×C8—431no—
173C2×C8C22×D4312yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—432no—
177C4⋊C4—431no—
178C4⋊C4—431no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4—862no—
182C4⋊C4—862no—
183C4⋊C4—861no—
184C4⋊C4—861no—
185C4⋊C4C22×D4311yescharacteristic
186C4⋊C4C22×D4312yes—
187C22⋊C4—862no—
188C22⋊C4—861no—
189C42—21no—
190C42—432no—
191C42—862no—
192C42C22×D4311yescharacteristic
193C23—861no—
194Q8—21no—
195Q8—21no—
196Q8—42no—
197Q8—434no—
198Q8—862no—
199Q8—862no—
200Q8—1724no—
201D4—432no—
202D4—861no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—432no—
207C2×C4—432no—
208C2×C4—862no—
209C2×C4—861no—
210C2×C4—1724no—
211C2×C4—1722no—
212C2×C4D4×D4311yescharacteristic
213C2×C4D4×D4311yescharacteristic
214C2×C4C23×D4311yescharacteristic
215C8—22no—
216C8—861no—
217C8—861no—
218C22—862no—
219C22—1721no—
220C22—1721no—
221C22C2×D4×D4311yescharacteristic
222C4—21no—
223C4—41no—
224C4—42no—
225C4—41no—
226C4—434no—
227C4—862no—
228C4—1722no—
229C4—1721no—
230C4SD16×D4312yes—
231C4#41×D4311yescharacteristic
232C4#1306337311yescharacteristic
233C2—1722no—
234C2#1458355911yescharacteristic
235C2C2×SD16×D4311yescharacteristic
236C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#475C2
socleC22×C43C22×D4
hypercenter#475D43
hypocenterC43#3359
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #14583627C2semidirect
3. #14583251C2semidirect
4. #14583248C2semidirect
5. #14583183C2semidirect
8. #14583023C2semidirect
11. C43×#475C2semidirect
95. Dic86SD16semidirect
124. #475D43semidirect
130. C43#3359semidirect