Finite Group Databasebeta

← #19145252

Subgroups — #19145252

Order 5504.

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

normal subgroups only

This group has 338 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#14583507C212yesmaximal
2#14583299C211yesmaximal, characteristic, complemented
3#14583277C211yesmaximal, characteristic, complemented
4#14583266C212yesmaximal, complemented
5#14583158C211yesmaximal, characteristic
6#14583154C211yesmaximal, characteristic
7#14583139C212yesmaximal
8#14583007C211yesmaximal, characteristic, complemented
9C4×#10621885C212yesmaximal, complemented
10#14582856C211yesmaximal, characteristic
11C43×#441C211yesmaximal, characteristic, complemented
12C2×Dic172C2211yescharacteristic
13C2×#10621885C2212yes—
14C2×#10621872C2211yescharacteristic
15C2×C8×D43C2211yescharacteristic
16#13063323C2212yes—
17#13063320—22no—
18#13063319—22no—
19#13063317—22no—
20#13063316C2212yes—
21#13063315—22no—
22#13063305C2212yes—
23#13063301C2212yes—
24C4×Dic86C2212yes—
25#13063282C2211yescharacteristic
26#13063258C2212yes—
27#13063257C2211yescharacteristic
28#13063250C2212yes—
29#13063249C2212yes—
30#13063248C2212yes—
31#13063235C2211yescharacteristic
32C4×C43⋊C8C2211yescharacteristic
33C8×Dic43C2211yescharacteristic
34C2×Q16×C43C2211yescharacteristic
35C4×Q8×C43C2212yes—
36#106×C43C2211yescharacteristic
37#103×C43C2212yes—
38#97×C43C2211yescharacteristic
39C2×Q8×C43C2312yes—
40C2×C4×D43C2311yescharacteristic
41C2×Dic86C2312yes—
42Q16×C43—22no—
43C2×C8×C43C2311yescharacteristic
44C2×C8×C43C2311yescharacteristic
45C4⋊C4×C43—22no—
46C4⋊C4×C43C2312yes—
47C42×C43—22no—
48C42×C43C2311yescharacteristic
49#10621885—24no—
50(C2×D43)⋊C4—22no—
51(C2×D43)⋊C4—22no—
52(C2×D43)⋊C4D412yes—
53C4⋊Dic43—22no—
54C4⋊Dic43—22no—
55C4⋊Dic43C2312yes—
56Dic43⋊C4—22no—
57Dic43⋊C4—22no—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60Dic43⋊C4—22no—
61Dic43⋊C4D412yes—
62C4×Dic43—22no—
63C4×Dic43C2311yescharacteristic
64C2×C43⋊C8C2311yescharacteristic
65C2×C43⋊C8C2311yescharacteristic
66Dic172—22no—
67#10621872—22no—
68C8×D43—22no—
69C22×D43C2×D411yescharacteristic
70Q8×C43—22no—
71Q8×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43C2×D412yes—
75C2×C4×C43C2411yescharacteristic
76C2×Dic43—22no—
77C2×Dic43—22no—
78C2×Dic43C2×D412yes—
79C2×Dic43C2×D411yescharacteristic
80C4×D43—21no—
81C4×D43—21no—
82Dic86—22no—
83Dic86—22no—
84C8×C43—21no—
85C8×C43#4112yes—
86C43⋊C8—21no—
87C43⋊C8#4112yes—
88C22×C43C22×D411yescharacteristic
89C2×D43—21no—
90C2×D43—22no—
91C4×C43—22no—
92C4×C43—42no—
93C4×C43—42no—
94C4×C43C2×#4111yescharacteristic
95C4×C43C2×#4111yescharacteristic
96Dic43—21no—
97Dic43—22no—
98Dic43—42no—
99Dic43—42no—
100#3177—431nomaximal, Sylow
101C2×C43#53211yescharacteristic
102C2×C43#57812yes—
103D43—41no—
104#541—432no—
105#499—431no—
106#494—431no—
107#491—432no—
108#470—431no—
109#470—431no—
110#467—432no—
111#441—431no—
112#441D4311yescharacteristic, complemented
113C4×Q16—432no—
114#405—431no—
115C43#317711yescharacteristic, complemented, Sylow
116C2×Q16—432no—
117C2×Q16—431no—
118C2×Q16C2×D4311yescharacteristic
119C2×M16—431no—
120C22×C8—431no—
121C4⋊Q8—432no—
122#126—862no—
123#126—862no—
124#125—432no—
125#125—862no—
126#125—862no—
127C22⋊Q8—432no—
128C22⋊Q8—432no—
129C4×Q8—432no—
130C4×Q8C2×D4312yes—
131#117—431no—
132#107—432no—
133#106—431no—
134#106C2×D4311yescharacteristic
135#103—432no—
136#103—432no—
137#103—432no—
138#103C2×D4312yes—
139#97—431no—
140#97C2×D4311yescharacteristic
141C4×C8—431no—
142C4×C8—431no—
143C2×Q8—432no—
144C2×Q8C22×D4312yes—
145C22×C4—431no—
146Q16—22no—
147Q16—864no—
148Q16—862no—
149M16—862no—
150C2×C8—431no—
151C2×C8—431no—
152C2×C8—862no—
153C2×C8C22×D4311yescharacteristic
154C2×C8C22×D4311yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—432no—
157C4⋊C4—432no—
158C4⋊C4—862no—
159C4⋊C4—862no—
160C4⋊C4—862no—
161C4⋊C4—862no—
162C4⋊C4—862no—
163C4⋊C4—862no—
164C4⋊C4—862no—
165C4⋊C4C22×D4312yes—
166C22⋊C4—432no—
167C22⋊C4—862no—
168C22⋊C4—862no—
169C42—22no—
170C42—431no—
171C42—862no—
172C42C22×D4311yescharacteristic
173C23—431no—
174Q8—22no—
175Q8—22no—
176Q8—862no—
177Q8—862no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—432no—
181C2×C4—431no—
182C2×C4—861no—
183C2×C4—861no—
184C2×C4—862no—
185C2×C4—862no—
186C2×C4D4×D4312yes—
187C2×C4C23×D4311yescharacteristic
188C8—21no—
189C8—432no—
190C8—861no—
191C8#1062189812yes—
192C22—861no—
193C22—862no—
194C22C2×D4×D4311yescharacteristic
195C4—22no—
196C4—42no—
197C4—42no—
198C4—861no—
199C4—862no—
200C4—1722no—
201C4—1722no—
202C4#41×D4311yescharacteristic
203C4C2×#1062189811yescharacteristic
204C2—1721no—
205C2#1458344611yescharacteristic
206C2#1458371512yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#441C2
socleC22×C43C22×D4
hypercenter#441D43
hypocenterC43#3177
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #14583299C2semidirect
3. #14583277C2semidirect
4. #14583266C2semidirect
8. #14583007C2semidirect
9. C4×#10621885C2semidirect
11. C43×#441C2semidirect
112. #441D43semidirect
115. C43#3177semidirect