Finite Group Databasebeta

← #19147339

Subgroups — #19147339

Order 5504.

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

normal subgroups only

This group has 338 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
1Q8×Dic86C211yesmaximal, characteristic, complemented
2#14583623C211yesmaximal, characteristic
3#14583260C212yesmaximal
4#14583249C211yesmaximal, characteristic, complemented
5#14583190C211yesmaximal, characteristic
6#14583182C212yesmaximal, complemented
7#14583123C212yesmaximal
8#14583026C211yesmaximal, characteristic, complemented
9#14583006C212yesmaximal, complemented
10C4×#10621884C211yesmaximal, characteristic
11C43×#462C211yesmaximal, characteristic, complemented
12C2×#10621884C2211yescharacteristic
13#13063325—21no—
14#13063325C2211yescharacteristic
15#13063324—22no—
16#13063324C2212yes—
17#13063320—22no—
18#13063314C2212yes—
19#13063305—21no—
20Q8×Dic43C2212yes—
21Q8×Dic43C2212yes—
22C4×Dic86—21no—
23C4×Dic86C2211yescharacteristic
24C4×D172C2211yescharacteristic
25#13063283—21no—
26#13063257C2212yes—
27#13063256C2211yescharacteristic
28Dic43⋊C8C2212yes—
29#13063249C2212yes—
30#13063249C2211yescharacteristic
31#13063249C2212yes—
32#13063247C2212yes—
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×Dic86—21no—
46C2×Dic86—22no—
47C2×Dic86D411yescharacteristic
48Q16×C43—24no—
49C2×C8×C43C2312yes—
50C4⋊C4×C43—21no—
51C4⋊C4×C43—21no—
52C4⋊C4×C43—21no—
53C4⋊C4×C43C2311yescharacteristic
54C42×C43—21no—
55C42×C43C2311yescharacteristic
56#10621884—22no—
57(C2×D43)⋊C4—21no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60C4⋊Dic43—21no—
61C4⋊Dic43—22no—
62C4⋊Dic43—22no—
63C4⋊Dic43D411yescharacteristic
64C4⋊Dic43C2312yes—
65C4⋊Dic43C2311yescharacteristic
66Dic43⋊C4—22no—
67Dic43⋊C4D412yes—
68C4×Dic43—22no—
69C4×Dic43—22no—
70C4×Dic43C2312yes—
71C2×C43⋊C8C2311yescharacteristic
72C2×C43⋊C8C2311yescharacteristic
73C22×D43—21no—
74Q8×C43—21no—
75Q8×C43—22no—
76Q8×C43—22no—
77Q8×C43#4112yes—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2411yescharacteristic
84C2×Dic43—21no—
85C2×Dic43—22no—
86C2×Dic43C2×D412yes—
87C2×Dic43C2×D412yes—
88D172—21no—
89D172—21no—
90C4×D43—42no—
91Dic86—22no—
92Dic86—82no—
93Dic86—81no—
94C8×C43—22no—
95C43⋊C8—21no—
96C43⋊C8—21no—
97C22×C43C22×D411yescharacteristic
98C2×D43—41no—
99C2×D43—41no—
100C2×D43—41no—
101C4×C43—22no—
102C4×C43—21no—
103C4×C43—42no—
104C4×C43—41no—
105C4×C43#13712yes—
106C4×C43C2×#4111yescharacteristic
107C4×C432−1+411yescharacteristic
108Dic43—22no—
109Dic43—22no—
110Dic43—41no—
111Dic43—42no—
112#3369—431nomaximal, Sylow
113C2×C43#54811yescharacteristic
114C2×C43C2×#13711yescharacteristic
115C2×C43#57711yescharacteristic
116D43—81no—
117Q82—431no—
118#556—431no—
119#489—432no—
120#487—431no—
121#476—431no—
122#475—432no—
123#464—432no—
124#462D4311yescharacteristic, complemented
125#446—431no—
126#441—432no—
127C4×SD16—431no—
128C43#336911yescharacteristic, complemented, Sylow
129C2×Q16C2×D4312yes—
130C2×SD16—431no—
131C4⋊Q8—432no—
132C4⋊Q8—431no—
133C4⋊Q8—861no—
134C4⋊Q8—862no—
135C4⋊Q8C2×D4311yescharacteristic
136#126—862no—
137#124—432no—
138C22⋊Q8—861no—
139C4×Q8—431no—
140C4×Q8—432no—
141C4×Q8—432no—
142C4×Q8—861no—
143C4×Q8C2×D4311yescharacteristic
144C4×D4—431no—
145#117—861no—
146#106—432no—
147#106—431no—
148C4⋊C8—432no—
149C4⋊C8C2×D4311yescharacteristic
150#103—431no—
151#103—432no—
152#103—432no—
153#103C2×D4312yes—
154#102—432no—
155#102—431no—
156#97—432no—
157C4×C8—431no—
158C2×Q8—431no—
159C2×Q8—862no—
160C2×Q8—861no—
161C2×Q8C22×D4312yes—
162C2×Q8C22×D4311yescharacteristic
163C2×D4—431no—
164C22×C4—861no—
165Q16—24no—
166SD16—862no—
167C2×C8—431no—
168C2×C8—431no—
169C2×C8C22×D4312yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—431no—
174C4⋊C4—432no—
175C4⋊C4—432no—
176C4⋊C4—431no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—862no—
180C4⋊C4—861no—
181C4⋊C4C22×D4311yescharacteristic
182C22⋊C4—862no—
183C22⋊C4—862no—
184C22⋊C4—861no—
185C42—21no—
186C42—432no—
187C42—862no—
188C42—862no—
189C42C22×D4311yescharacteristic
190C23—861no—
191Q8—21no—
192Q8—22no—
193Q8—22no—
194Q8—862no—
195Q8—3441no—
196Q8—3442no—
197Q8#1062190012yes—
198D4—861no—
199D4—861no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—432no—
204C2×C4—432no—
205C2×C4—861no—
206C2×C4—862no—
207C2×C4—1722no—
208C2×C4D4×D4311yescharacteristic
209C2×C4D4×D4311yescharacteristic
210C2×C4C23×D4311yescharacteristic
211C8—22no—
212C8—861no—
213C8—861no—
214C22—1721no—
215C22—1721no—
216C22—1721no—
217C22C2×D4×D4311yescharacteristic
218C4—22no—
219C4—21no—
220C4—42no—
221C4—41no—
222C4—862no—
223C4—862no—
224C4—1721no—
225C4—1722no—
226C4#1306335712yes—
227C4C2×#1062190011yescharacteristic
228C4#1306337211yescharacteristic
229C2—3441no—
230C2#1458355511yescharacteristic
231C2C2×#1306335711yescharacteristic
232C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#462C2
socleC22×C43C22×D4
hypercenter#462D43
hypocenterC43#3369
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. Q8×Dic86C2semidirect
4. #14583249C2semidirect
6. #14583182C2semidirect
8. #14583026C2semidirect
9. #14583006C2semidirect
11. C43×#462C2semidirect
124. #462D43semidirect
128. C43#3369semidirect