Finite Group Databasebeta

← #19147631

Subgroups — #19147631

Order 5504.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 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#14583624C211yesmaximal, characteristic, complemented
2#14583623C211yesmaximal, characteristic
3#14583292C212yesmaximal
4#14583123C212yesmaximal
5#14583107C212yesmaximal, complemented
6#14583106C211yesmaximal, characteristic, complemented
7#14583101C211yesmaximal, characteristic
8#14583029C211yesmaximal, characteristic, complemented
9#14583006C212yesmaximal, complemented
10C4×#10621873C211yesmaximal, characteristic
11C43×#494C211yesmaximal, characteristic, complemented
12C2×#10621885C2212yes—
13C2×#10621873C2211yescharacteristic
14C2×#10621884C2212yes—
15#13063323C2212yes—
16#13063320—22no—
17#13063316—21no—
18#13063315—22no—
19#13063314C2212yes—
20#13063305—21no—
21Q8×Dic43C2212yes—
22Q8×Dic43C2212yes—
23C4×Dic86C2211yescharacteristic
24C4×Dic86C2211yescharacteristic
25#13063290—21no—
26C4×D172C2211yescharacteristic
27#13063283—21no—
28#13063257C2211yescharacteristic
29C4⋊(C43⋊C8)C2211yescharacteristic
30Dic43⋊C8C2212yes—
31#13063250C2211yescharacteristic
32#13063249C2212yes—
33#13063249C2212yes—
34#13063247C2211yescharacteristic
35#13063235C2212yes—
36C2×Q16×C43C2212yes—
37C2×Q16×C43C2212yes—
38C4⋊Q8×C43C2211yescharacteristic
39C4⋊Q8×C43C2211yescharacteristic
40C4×C8×C43C2211yescharacteristic
41C2×Q8×C43C2312yes—
42C2×Q8×C43C2312yes—
43C2×D172C2311yescharacteristic
44C2×C4×D43—21no—
45C2×Dic86D411yescharacteristic
46C2×Dic86C2311yescharacteristic
47Q16×C43—24no—
48Q16×C43—42no—
49C2×C8×C43C2311yescharacteristic
50C2×C8×C43C2311yescharacteristic
51C4⋊C4×C43—21no—
52C4⋊C4×C43—21no—
53C4⋊C4×C43—21no—
54C4⋊C4×C43—21no—
55C42×C43C2311yescharacteristic
56#10621885—42no—
57#10621884—42no—
58(C2×D43)⋊C4—21no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61C4⋊Dic43—22no—
62C4⋊Dic43—22no—
63C4⋊Dic43D411yescharacteristic
64C4⋊Dic43C2311yescharacteristic
65C4⋊Dic43C2311yescharacteristic
66Dic43⋊C4—21no—
67Dic43⋊C4—22no—
68Dic43⋊C4—22no—
69Dic43⋊C4D412yes—
70C4×Dic43—21no—
71C4×Dic43—22no—
72C4×Dic43—22no—
73C4×Dic43C2312yes—
74C2×C43⋊C8C2312yes—
75#10621873—22no—
76C22×D43—21no—
77Q8×C43—22no—
78Q8×C43—22no—
79Q8×C43—22no—
80Q8×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2411yescharacteristic
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43C2×D412yes—
90C2×Dic43C2×D412yes—
91D172—21no—
92D172—21no—
93C4×D43—42no—
94Dic86—22no—
95Dic86—21no—
96Dic86—21no—
97C8×C43—21no—
98C8×C43#4112yes—
99C43⋊C8—22no—
100C22×C43C22×D411yescharacteristic
101C2×D43—41no—
102C2×D43—41no—
103C2×D43—41no—
104C4×C43—21no—
105C4×C43—42no—
106C4×C43—42no—
107C4×C43#13712yes—
108C4×C43C2×#4111yescharacteristic
109C4×C43H(5,𝔽2)11yescharacteristic
110Dic43—22no—
111Dic43—22no—
112Dic43—41no—
113Dic43—41no—
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#494D4311yescharacteristic, complemented
124#464—432no—
125#462—432no—
126#462—431no—
127#461—431no—
128#446—431no—
129#441—432no—
130C4×SD16—431no—
131C43#339811yescharacteristic, complemented, Sylow
132C2×Q16—432no—
133C2×Q16C2×D4312yes—
134C2×Q16C2×D4312yes—
135C2×SD16—432no—
136C2×SD16—431no—
137C4⋊Q8—432no—
138C4⋊Q8C2×D4311yescharacteristic
139C4⋊Q8C2×D4311yescharacteristic
140#126—862no—
141#125—862no—
142#125—861no—
143#124—432no—
144C22⋊Q8—861no—
145C4×Q8—431no—
146C4×Q8—432no—
147C4×Q8—432no—
148C4×Q8—431no—
149C4×Q8—861no—
150C4×D4—431no—
151#117—861no—
152#106—431no—
153C4⋊C8—432no—
154C4⋊C8—431no—
155#103—432no—
156#103—432no—
157#103—431no—
158#102—431no—
159#97—432no—
160C4×C8C2×D4311yescharacteristic
161C2×Q8—431no—
162C2×Q8—431no—
163C2×Q8C22×D4312yes—
164C2×Q8C22×D4312yes—
165C2×D4—431no—
166C22×C4—861no—
167Q16—24no—
168Q16—42no—
169Q16—1722no—
170SD16—862no—
171SD16—1722no—
172C2×C8—432no—
173C2×C8C22×D4311yescharacteristic
174C2×C8C22×D4311yescharacteristic
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—431no—
180C4⋊C4—432no—
181C4⋊C4—431no—
182C4⋊C4—431no—
183C4⋊C4—862no—
184C4⋊C4—862no—
185C4⋊C4—862no—
186C4⋊C4—862no—
187C4⋊C4—861no—
188C22⋊C4—862no—
189C22⋊C4—862no—
190C22⋊C4—861no—
191C42—432no—
192C42—862no—
193C42—862no—
194C42—861no—
195C42C22×D4311yescharacteristic
196C23—861no—
197Q8—22no—
198Q8—22no—
199Q8—22no—
200Q8—22no—
201Q8—862no—
202Q8—861no—
203Q8—861no—
204D4—861no—
205D4—861no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—432no—
209C2×C4—432no—
210C2×C4—861no—
211C2×C4—861no—
212C2×C4—861no—
213C2×C4—1722no—
214C2×C4D4×D4311yescharacteristic
215C2×C4D4×D4311yescharacteristic
216C2×C4C23×D4311yescharacteristic
217C8—21no—
218C8—862no—
219C8#1062190012yes—
220C22—1721no—
221C22—1721no—
222C22—1721no—
223C22C2×D4×D4311yescharacteristic
224C4—21no—
225C4—42no—
226C4—42no—
227C4—862no—
228C4—862no—
229C4—1721no—
230C4—1721no—
231C4—1721no—
232C4#1306335712yes—
233C4C2×#1062190011yescharacteristic
234C4#1306337011yescharacteristic
235C2—3441no—
236C2#1458356911yescharacteristic
237C2C2×#1306335711yescharacteristic
238C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#494C2
socleC22×C43C22×D4
hypercenter#494D43
hypocenterC43#3398
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #14583624C2semidirect
5. #14583107C2semidirect
6. #14583106C2semidirect
8. #14583029C2semidirect
9. #14583006C2semidirect
11. C43×#494C2semidirect
123. #494D43semidirect
131. C43#3398semidirect