Finite Group Databasebeta

← #19147381

Subgroups — #19147381

Order 5504.

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

normal subgroups only

This group has 340 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#14583624C211yesmaximal, characteristic, complemented
2#14583610C211yesmaximal, characteristic
3#14583266C212yesmaximal, complemented
4#14583204C212yesmaximal, complemented
5#14583191C211yesmaximal, characteristic, complemented
6#14583103C212yesmaximal
7#14583101C211yesmaximal, characteristic
8#14583029C211yesmaximal, characteristic, complemented
9#14583002C212yesmaximal
10C4×#10621873C211yesmaximal, characteristic
11C43×#487C211yesmaximal, characteristic, complemented
12C2×#10621873C2211yescharacteristic
13C2×#10621884C2212yes—
14#13063323C2212yes—
15#13063316—21no—
16#13063316C2212yes—
17#13063315—22no—
18#13063305—21no—
19#13063301—22no—
20Q8×Dic43C2212yes—
21C4×Dic86C2211yescharacteristic
22C4×Dic86C2211yescharacteristic
23#13063290—21no—
24C4×D172C2211yescharacteristic
25#13063287C2212yes—
26C4⋊C4×D43—21no—
27#13063258C2212yes—
28#13063257C2211yescharacteristic
29C4⋊(C43⋊C8)C2211yescharacteristic
30Dic43⋊C8C2212yes—
31#13063250C2211yescharacteristic
32#13063249C2212yes—
33#13063248C2212yes—
34#13063247C2211yescharacteristic
35#13063235C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37C4⋊Q8×C43C2211yescharacteristic
38#103×C43C2212yes—
39#103×C43C2212yes—
40C4×C8×C43C2211yescharacteristic
41C2×Q8×C43—21no—
42C2×Q8×C43C2312yes—
43C2×D172C2311yescharacteristic
44C2×C4×D43—21no—
45C2×C4×D43—22no—
46C2×Dic86D411yescharacteristic
47C2×Dic86C2311yescharacteristic
48C2×C8×C43C2311yescharacteristic
49C2×C8×C43C2311yescharacteristic
50C4⋊C4×C43—21no—
51C4⋊C4×C43—21no—
52C4⋊C4×C43—21no—
53C4⋊C4×C43C2312yes—
54C42×C43C2311yescharacteristic
55#10621884—24no—
56(C2×D43)⋊C4—21no—
57(C2×D43)⋊C4—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43—22no—
60C4⋊Dic43D411yescharacteristic
61C4⋊Dic43C2311yescharacteristic
62C4⋊Dic43C2311yescharacteristic
63Dic43⋊C4—21no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4—22no—
67Dic43⋊C4D412yes—
68C4×Dic43—21no—
69C4×Dic43—22no—
70C4×Dic43C2312yes—
71C2×C43⋊C8C2312yes—
72#10621873—22no—
73C22×D43—21no—
74Q8×C43—22no—
75Q8×C43—22no—
76Q8×C43—81no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2411yescharacteristic
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43C2×D412yes—
86C2×Dic43C2×D412yes—
87D172—21no—
88D172#4112yes—
89C4×D43—42no—
90C4×D43—82no—
91Dic86—22no—
92Dic86—21no—
93Dic86—21no—
94C8×C43—21no—
95C8×C43—21no—
96C43⋊C8—22no—
97C22×C43C22×D411yescharacteristic
98C2×D43—22no—
99C2×D43—41no—
100C2×D43—41no—
101C4×C43—21no—
102C4×C43—42no—
103C4×C43—42no—
104C4×C43#13712yes—
105C4×C43C2×#4111yescharacteristic
106C4×C432−1+411yescharacteristic
107Dic43—22no—
108Dic43—22no—
109Dic43—41no—
110Dic43—41no—
111Dic43—41no—
112#3372—431nomaximal, Sylow
113C2×C43#54811yescharacteristic
114C2×C43C2×#13711yescharacteristic
115C2×C43#57711yescharacteristic
116D43—42no—
117#557—431no—
118#554—431no—
119#491—432no—
120#487D4311yescharacteristic, complemented
121#479—432no—
122#477—431no—
123#461—431no—
124#461—432no—
125#446—431no—
126#440—432no—
127C4×SD16—431no—
128C43#337211yescharacteristic, complemented, Sylow
129C2×SD16—432no—
130C2×SD16—431no—
131C4⋊Q8—432no—
132C4⋊Q8C2×D4311yescharacteristic
133C4⋊Q8C2×D4311yescharacteristic
134#125—432no—
135#125—862no—
136#125—861no—
137C22⋊Q8—861no—
138C22⋊Q8—862no—
139C4×Q8—431no—
140C4×Q8—432no—
141C4×Q8—431no—
142C4×Q8—861no—
143C4×D4—432no—
144C4×D4—431no—
145C2×C4⋊C4—861no—
146#107—432no—
147#106—431no—
148C4⋊C8—432no—
149C4⋊C8—431no—
150#103—432no—
151#103—431no—
152#103—432no—
153#103C2×D4312yes—
154#103C2×D4312yes—
155#102—431no—
156#97—432no—
157C4×C8C2×D4311yescharacteristic
158C2×Q8—21no—
159C2×Q8—431no—
160C2×Q8—431no—
161C2×Q8C22×D4312yes—
162C2×D4—431no—
163C22×C4—862no—
164C22×C4—861no—
165SD16—862no—
166SD16—864no—
167C2×C8—432no—
168C2×C8C22×D4311yescharacteristic
169C2×C8C22×D4311yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—431no—
174C4⋊C4—432no—
175C4⋊C4—431no—
176C4⋊C4—431no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4—862no—
182C4⋊C4—861no—
183C4⋊C4C22×D4312yes—
184C22⋊C4—862no—
185C22⋊C4—861no—
186C42—432no—
187C42—862no—
188C42—861no—
189C42C22×D4311yescharacteristic
190C23—861no—
191Q8—22no—
192Q8—22no—
193Q8—81no—
194Q8—862no—
195Q8—861no—
196Q8—861no—
197D4—432no—
198D4—861no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—432no—
202C2×C4—432no—
203C2×C4—861no—
204C2×C4—861no—
205C2×C4—861no—
206C2×C4—3442no—
207C2×C4—1722no—
208C2×C4D4×D4311yescharacteristic
209C2×C4D4×D4311yescharacteristic
210C2×C4C23×D4311yescharacteristic
211C8—21no—
212C8—21no—
213C8—862no—
214C22—862no—
215C22—1721no—
216C22—1721no—
217C22C2×D4×D4311yescharacteristic
218C4—21no—
219C4—42no—
220C4—42no—
221C4—862no—
222C4—862no—
223C4—1721no—
224C4—1721no—
225C4—1721no—
226C4#1306335712yes—
227C4#41×D4311yescharacteristic
228C4#1306337211yescharacteristic
229C2—1722no—
230C2#1458355711yescharacteristic
231C2C2×#1306335711yescharacteristic
232C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#487C2
socleC22×C43C22×D4
hypercenter#487D43
hypocenterC43#3372
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #14583624C2semidirect
3. #14583266C2semidirect
4. #14583204C2semidirect
5. #14583191C2semidirect
8. #14583029C2semidirect
11. C43×#487C2semidirect
120. #487D43semidirect
128. C43#3372semidirect