Finite Group Databasebeta

← #19147290

Subgroups — #19147290

Order 5504.

348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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#14583634C211yesmaximal, characteristic
2#14583624C211yesmaximal, characteristic, complemented
3#14583255C212yesmaximal, complemented
4#14583247C211yesmaximal, characteristic
5#14583198C212yesmaximal, complemented
6#14583124C212yesmaximal, complemented
7#14583100C211yesmaximal, characteristic
8#14583023C211yesmaximal, characteristic, complemented
9C4×#10621885C211yesmaximal, characteristic, complemented
10#14582986C212yesmaximal, complemented
11C43×#475C211yesmaximal, characteristic, complemented
12C2×#10621885C2211yescharacteristic
13C2×#10621873C2212yes—
14#13063323—21no—
15#13063322C2211yescharacteristic
16#13063316C2212yes—
17#13063315—22no—
18#13063314C2212yes—
19#13063313—21no—
20#13063310—22no—
21Q8×Dic43—21no—
22C4×Dic86C2211yescharacteristic
23C4×Dic86C2211yescharacteristic
24#13063290C2212yes—
25C4×D172—21no—
26#13063287C2212yes—
27#13063258C2211yescharacteristic
28Dic43⋊C8C2212yes—
29#13063249C2211yescharacteristic
30#13063248C2211yescharacteristic
31#13063247C2212yes—
32#13063245C2212yes—
33#13063245C2212yes—
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
43C2×D172—21no—
44C2×D172—21no—
45C2×D172C2312yes—
46C2×C4×D43—22no—
47C2×Dic86D411yescharacteristic
48C2×Dic86C2311yescharacteristic
49C2×C8×C43C2312yes—
50C4⋊C4×C43—21no—
51C4⋊C4×C43—21no—
52C4⋊C4×C43C2312yes—
53C4⋊C4×C43C2311yescharacteristic
54C42×C43—21no—
55C42×C43C2311yescharacteristic
56#10621885—22no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60C4⋊Dic43—22no—
61C4⋊Dic43D411yescharacteristic
62C4⋊Dic43C2311yescharacteristic
63Dic43⋊C4—21no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4D412yes—
67C4×Dic43—21no—
68C4×Dic43—22no—
69C4×Dic43C2312yes—
70C2×C43⋊C8C2311yescharacteristic
71C2×C43⋊C8C2311yescharacteristic
72#10621873—24no—
73C22×D43—22no—
74Q8×C43—21no—
75Q8×C43—21no—
76Q8×C43—42no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2411yescharacteristic
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43C2×D412yes—
86C2×Dic43C2×D412yes—
87D172—22no—
88D172—22no—
89D172—42no—
90D172—81no—
91C4×D43—82no—
92Dic86—22no—
93Dic86—21no—
94Dic86#4112yes—
95C8×C43—22no—
96C43⋊C8—21no—
97C43⋊C8—21no—
98C22×C43C22×D411yescharacteristic
99C2×D43—42no—
100C2×D43—42no—
101C2×D43—42no—
102C4×C43—21no—
103C4×C43—41no—
104C4×C43—42no—
105C4×C43—41no—
106C4×C43#13512yes—
107C4×C43C2×#4111yescharacteristic
108C4×C432−1+411yescharacteristic
109Dic43—22no—
110Dic43—22no—
111Dic43—22no—
112Dic43—41no—
113#3365—431nomaximal, Sylow
114C2×C43#54811yescharacteristic
115C2×C43C2×#13511yescharacteristic
116C2×C43#57711yescharacteristic
117D43—82no—
118#559—431no—
119#557—431no—
120#488—432no—
121#486—431no—
122#478—432no—
123#475D4311yescharacteristic, complemented
124#464—432no—
125#460—431no—
126C8×Q8—431no—
127C4×Q16—431no—
128C4×SD16—432no—
129C43#336511yescharacteristic, complemented, Sylow
130C2×Q16—431no—
131C2×SD16—432no—
132C4⋊Q8—861no—
133C4⋊Q8C2×D4311yescharacteristic
134#127—431no—
135#125—432no—
136#125—862no—
137#124—432no—
138#124—861no—
139#123—862no—
140C4×Q8—431no—
141C4×Q8—432no—
142C4×Q8—431no—
143C4×Q8—861no—
144C4×Q8C2×D4311yescharacteristic
145C4×D4—432no—
146C4×D4—861no—
147#107—431no—
148#106C2×D4312yes—
149C4⋊C8—432no—
150C4⋊C8C2×D4311yescharacteristic
151#103—431no—
152#103—431no—
153#103C2×D4312yes—
154#102—432no—
155#102—432no—
156#102—432no—
157C4×C8—432no—
158C4×C8—431no—
159C2×Q8—21no—
160C2×Q8—431no—
161C2×Q8—431no—
162C2×Q8C22×D4311yescharacteristic
163C2×D4—432no—
164C2×D4—861no—
165C2×D4—861no—
166C22×C4—862no—
167Q16—862no—
168SD16—864no—
169C2×C8—431no—
170C2×C8—431no—
171C2×C8C22×D4312yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—431no—
175C4⋊C4—432no—
176C4⋊C4—431no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—862no—
180C4⋊C4—861no—
181C4⋊C4C22×D4312yes—
182C4⋊C4C22×D4311yescharacteristic
183C22⋊C4—862no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C42—21no—
187C42—432no—
188C42—862no—
189C42—861no—
190C42C22×D4311yescharacteristic
191C23—862no—
192Q8—21no—
193Q8—21no—
194Q8—42no—
195Q8—432no—
196Q8—862no—
197Q8—861no—
198D4—862no—
199D4—862no—
200D4—3441no—
201D4—1722no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—432no—
206C2×C4—432no—
207C2×C4—861no—
208C2×C4—861no—
209C2×C4—3442no—
210C2×C4D4×D4311yescharacteristic
211C2×C4D4×D4311yescharacteristic
212C2×C4C23×D4311yescharacteristic
213C8—22no—
214C8—861no—
215C8—861no—
216C22—1722no—
217C22—1722no—
218C22—1722no—
219C22C2×D4×D4311yescharacteristic
220C4—21no—
221C4—41no—
222C4—42no—
223C4—41no—
224C4—862no—
225C4—862no—
226C4—862no—
227C4—1721no—
228C4#1306334612yes—
229C4#41×D4311yescharacteristic
230C4#1306337311yescharacteristic
231C2—3442no—
232C2#1458355911yescharacteristic
233C2C2×#1306334611yescharacteristic
234C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#475C2
socleC22×C43C22×D4
hypercenter#475D43
hypocenterC43#3365
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
2. #14583624C2semidirect
3. #14583255C2semidirect
5. #14583198C2semidirect
6. #14583124C2semidirect
8. #14583023C2semidirect
9. C4×#10621885C2semidirect
10. #14582986C2semidirect
11. C43×#475C2semidirect
123. #475D43semidirect
129. C43#3365semidirect