Finite Group Databasebeta

← #19147625

Subgroups — #19147625

Order 5504.

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

normal subgroups only

This group has 350 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#14583627C211yesmaximal, characteristic, complemented
2#14583623C211yesmaximal, characteristic
3#14583292C212yesmaximal
4#14583278C211yesmaximal, characteristic, complemented
5#14583124C212yesmaximal
6#14583107C212yesmaximal, complemented
7#14583105C211yesmaximal, characteristic
8#14583026C211yesmaximal, characteristic, complemented
9#14583003C212yesmaximal, complemented
10C4×#10621884C211yesmaximal, characteristic
11C43×#462C211yesmaximal, characteristic, complemented
12C2×#10621885C2212yes—
13C2×#10621885C2212yes—
14C2×#10621873C2212yes—
15C2×#10621884C2211yescharacteristic
16#13063325C2211yescharacteristic
17#13063323C2212yes—
18#13063320—22no—
19#13063317—21no—
20#13063315—22no—
21#13063314C2212yes—
22#13063305—21no—
23Q8×Dic43C2212yes—
24C4×Dic86—21no—
25C4×Dic86C2211yescharacteristic
26#13063290C2212yes—
27C4×D172C2211yescharacteristic
28#13063283—21no—
29#13063256C2211yescharacteristic
30Dic43⋊C8C2212yes—
31#13063250C2212yes—
32#13063249C2211yescharacteristic
33#13063245C2211yescharacteristic
34#13063235C2212yes—
35C4×C43⋊C8C2211yescharacteristic
36C2×Q16×C43C2212yes—
37C4⋊Q8×C43C2211yescharacteristic
38C4×Q8×C43C2211yescharacteristic
39C4⋊C8×C43C2211yescharacteristic
40#103×C43C2212yes—
41C2×Q8×C43C2312yes—
42C2×Q8×C43C2311yescharacteristic
43C2×D172C2311yescharacteristic
44C2×C4×D43—21no—
45C2×Dic86D411yescharacteristic
46C2×Dic86C2312yes—
47Q16×C43—42no—
48C2×C8×C43C2312yes—
49C4⋊C4×C43—21no—
50C4⋊C4×C43—21no—
51C4⋊C4×C43—21no—
52C4⋊C4×C43C2311yescharacteristic
53C42×C43—21no—
54C42×C43C2311yescharacteristic
55#10621885—24no—
56#10621885—42no—
57#10621884—22no—
58(C2×D43)⋊C4—21no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61C4⋊Dic43—21no—
62C4⋊Dic43—21no—
63C4⋊Dic43—22no—
64C4⋊Dic43D411yescharacteristic
65C4⋊Dic43C2311yescharacteristic
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68Dic43⋊C4—22no—
69Dic43⋊C4D412yes—
70C4×Dic43—22no—
71C4×Dic43—22no—
72C4×Dic43C2312yes—
73C2×C43⋊C8C2311yescharacteristic
74C2×C43⋊C8C2311yescharacteristic
75#10621873—42no—
76C22×D43—21no—
77Q8×C43—21no—
78Q8×C43—22no—
79Q8×C43—22no—
80Q8×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2×D411yescharacteristic
86C2×C4×C43C2411yescharacteristic
87C2×Dic43—21no—
88C2×Dic43—22no—
89C2×Dic43C2×D412yes—
90C2×Dic43C2×D412yes—
91D172—21no—
92D172—21no—
93C4×D43—42no—
94Dic86—22no—
95Dic86—22no—
96Dic86—22no—
97C8×C43—22no—
98C43⋊C8—21no—
99C43⋊C8#4112yes—
100C22×C43C22×D411yescharacteristic
101C2×D43—41no—
102C2×D43—41no—
103C2×D43—41no—
104C4×C43—21no—
105C4×C43—42no—
106C4×C43—41no—
107C4×C43—41no—
108C4×C43#13712yes—
109C4×C43C2×#4111yescharacteristic
110C4×C43H(5,𝔽2)11yescharacteristic
111Dic43—22no—
112Dic43—22no—
113Dic43—42no—
114Dic43—41no—
115#3398—431nomaximal, Sylow
116C2×C43#55011yescharacteristic
117C2×C43C2×#13711yescharacteristic
118C2×C43#57811yescharacteristic
119D43—81no—
120#557—431no—
121#556—431no—
122#497—432no—
123#494—431no—
124#464—432no—
125#462—432no—
126#462D4311yescharacteristic, complemented
127#461—431no—
128#446—431no—
129#441—432no—
130C4×SD16—431no—
131C43#339811yescharacteristic, complemented, Sylow
132C2×Q16—432no—
133C2×Q16—432no—
134C2×Q16C2×D4312yes—
135C2×SD16—431no—
136C2×SD16—432no—
137C4⋊Q8—432no—
138C4⋊Q8—431no—
139C4⋊Q8C2×D4311yescharacteristic
140#126—862no—
141#125—861no—
142#125—862no—
143#124—432no—
144C22⋊Q8—861no—
145C4×Q8—431no—
146C4×Q8—432no—
147C4×Q8—432no—
148C4×Q8—861no—
149C4×Q8C2×D4311yescharacteristic
150C4×D4—431no—
151#117—861no—
152#106—431no—
153C4⋊C8—432no—
154C4⋊C8C2×D4311yescharacteristic
155#103—431no—
156#103—432no—
157#103C2×D4312yes—
158#102—431no—
159#97—432no—
160C4×C8—431no—
161C2×Q8—431no—
162C2×Q8—432no—
163C2×Q8C22×D4311yescharacteristic
164C2×Q8C22×D4312yes—
165C2×D4—431no—
166C22×C4—861no—
167Q16—42no—
168Q16—864no—
169Q16—1722no—
170SD16—862no—
171SD16—1722no—
172C2×C8—431no—
173C2×C8—431no—
174C2×C8C22×D4312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—431no—
179C4⋊C4—432no—
180C4⋊C4—431no—
181C4⋊C4—862no—
182C4⋊C4—862no—
183C4⋊C4—862no—
184C4⋊C4—862no—
185C4⋊C4—861no—
186C4⋊C4—861no—
187C4⋊C4C22×D4311yescharacteristic
188C22⋊C4—862no—
189C22⋊C4—862no—
190C22⋊C4—861no—
191C42—21no—
192C42—432no—
193C42—862no—
194C42—862no—
195C42C22×D4311yescharacteristic
196C23—861no—
197Q8—21no—
198Q8—22no—
199Q8—21no—
200Q8—22no—
201Q8—862no—
202Q8—862no—
203Q8—862no—
204D4—861no—
205D4—861no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—432no—
210C2×C4—432no—
211C2×C4—861no—
212C2×C4—862no—
213C2×C4—1722no—
214C2×C4D4×D4311yescharacteristic
215C2×C4D4×D4311yescharacteristic
216C2×C4C23×D4311yescharacteristic
217C8—22no—
218C8—432no—
219C8—861no—
220C22—1721no—
221C22—1721no—
222C22—1721no—
223C22C2×D4×D4311yescharacteristic
224C4—21no—
225C4—41no—
226C4—42no—
227C4—41no—
228C4—862no—
229C4—862no—
230C4—1722no—
231C4—1721no—
232C4#1306335712yes—
233C4#41×D4311yescharacteristic
234C4#1306337011yescharacteristic
235C2—3441no—
236C2#1458356711yescharacteristic
237C2C2×#1306335711yescharacteristic
238C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#462C2
socleC22×C43C22×D4
hypercenter#462D43
hypocenterC43#3398
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #14583627C2semidirect
4. #14583278C2semidirect
6. #14583107C2semidirect
8. #14583026C2semidirect
9. #14583003C2semidirect
11. C43×#462C2semidirect
126. #462D43semidirect
131. C43#3398semidirect