Finite Group Databasebeta

← #19144081

Subgroups — #19144081

Order 5504.

480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#13063358C211yesmaximal, characteristic
2C2×#13063356C211yesmaximal, characteristic
3C2×#13063323C211yesmaximal, characteristic, complemented
4#14583367C211yesmaximal, characteristic
5#14583108C214yesmaximal, complemented
6#14583103C214yesmaximal, complemented
7#14582922C211yesmaximal, characteristic, complemented
8#14582907C211yesmaximal, characteristic, complemented
9C43×#419C211yesmaximal, characteristic, complemented
10C2×#10621898C2211yescharacteristic
11C22×Dic86C2211yescharacteristic
12#13063358—24no—
13#13063356—24no—
14C2×Dic172C2212yes—
15C2×#10621885C2212yes—
16C2×#10621873C2212yes—
17C2×#10621884C2212yes—
18C2×#10621877C2211yescharacteristic
19#13063323—21no—
20#13063323—21no—
21#13063323C2214yes—
22#13063290C2212yes—
23#13063287C2212yes—
24(C22⋊D43)⋊C4—22no—
25#13063282—21no—
26C2×Dic43⋊C4—22no—
27C2×C4×Dic43C2211yescharacteristic
28C42×D43—21no—
29Dic43⋊C8C2214yes—
30#13063248C2214yes—
31C22×Q8×C43C2211yescharacteristic
32C2×M16×C43C2211yescharacteristic
33#117×C43C2211yescharacteristic
34#103×C43C2214yes—
35C2×Q8×C43—21no—
36C2×Q8×C43—22no—
37C2×Q8×C43—22no—
38C2×Q8×C43C2312yes—
39C22×C4×C43—21no—
40C22×C4×C43C2311yescharacteristic
41C2×C22⋊D43—21no—
42C22×Dic43—21no—
43C22×Dic43D412yes—
44#10621898—22no—
45#10621898D414yes—
46C2×D172C2311yescharacteristic
47C2×C4×D43—21no—
48C2×C4×D43—22no—
49C2×Dic86—22no—
50C2×Dic86—22no—
51C2×Dic86—21no—
52C2×Dic86C2312yes—
53C2×Dic86C2311yescharacteristic
54M16×C43—22no—
55C2×C8×C43C2312yes—
56C4⋊C4×C43C2312yes—
57C22⋊C4×C43—21no—
58C42×C43—21no—
59#10621885—24no—
60#10621884—24no—
61(C2×D43)⋊C4—22no—
62Dic43⋊C4—24no—
63Dic43⋊C4—24no—
64Dic43⋊C4—22no—
65C4×Dic43—22no—
66C4×Dic43D411yescharacteristic
67C4×Dic43D411yescharacteristic
68C4×Dic43C2312yes—
69#10621877—22no—
70C2×C43⋊C8C2312yes—
71Dic172—24no—
72#10621873—24no—
73C23×C43C2×D411yescharacteristic
74C22×D43—21no—
75Q8×C43—22no—
76Q8×C43—22no—
77Q8×C43—42no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—42no—
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D412yes—
83C2×C4×C43#4112yes—
84C2×C4×C43C2411yescharacteristic
85C22⋊D43—24no—
86C2×Dic43—21no—
87C2×Dic43—24no—
88C2×Dic43—22no—
89C2×Dic43—42no—
90C2×Dic43C2×D412yes—
91C2×Dic43C2×D412yes—
92D172—21no—
93D172C2×D412yes—
94C4×D43—24no—
95C4×D43—44no—
96Dic86—21no—
97Dic86—22no—
98Dic86—22no—
99Dic86—42no—
100Dic86C2×D412yes—
101C8×C43—22no—
102C43⋊C8—22no—
103C22×C43—22no—
104C22×C43#12112yes—
105C22×C43C22×D411yescharacteristic
106C2×D43—22no—
107C2×D43—42no—
108C4×C43—42no—
109C4×C43—42no—
110C4×C43#12112yes—
111C4×C43C22×D411yescharacteristic
112C4×C43C2×#4111yescharacteristic
113Dic43—22no—
114Dic43—22no—
115Dic43—42no—
116Dic43#13714yescomplemented
117#3039—431nomaximal, Sylow
118C2×C43—22no—
119C2×C43C2×#12111yescharacteristic
120C2×C43C2×#13712yes—
121D43—42no—
122C2×#137—431no—
123C2×#137—431no—
124C2×C4⋊Q8—431no—
125C4×#41—431no—
126#462—434no—
127#461—434no—
128#423—431no—
129#419—431no—
130#419D4311yescharacteristic, complemented
131C43#303911yescharacteristic, complemented, Sylow
132C2×#41—431no—
133C22×Q8—431no—
134C22×Q8C2×D4311yescharacteristic
135#137—864no—
136#137—864no—
137C2×Q16—432no—
138C2×Q16—432no—
139C2×SD16—432no—
140C2×SD16—432no—
141C2×M16—431no—
142C2×M16C2×D4311yescharacteristic
143C4⋊Q8—434no—
144C4⋊Q8—861no—
145C4⋊Q8—861no—
146C4×Q8—432no—
147C4×D4—432no—
148C4×D4—862no—
149#117—861no—
150#117C2×D4311yescharacteristic
151C2×C4⋊C4—862no—
152C2×C42—431no—
153C2×C42—861no—
154C4⋊C8—434no—
155#103—434no—
156#103C2×D4314yes—
157#41—434no—
158#41—862no—
159C2×Q8—21no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—431no—
163C2×Q8—432no—
164C2×Q8—861no—
165C2×Q8—862no—
166C2×Q8—862no—
167C2×Q8C22×D4312yes—
168C2×D4—431no—
169C2×D4—861no—
170C22×C4—21no—
171C22×C4—432no—
172C22×C4—862no—
173C22×C4—861no—
174C22×C4—861no—
175C22×C4C22×D4311yescharacteristic
176Q16—864no—
177Q16—864no—
178SD16—864no—
179SD16—864no—
180M16—22no—
181M16—862no—
182C2×C8—432no—
183C2×C8C22×D4312yes—
184C4⋊C4—864no—
185C4⋊C4—864no—
186C4⋊C4—862no—
187C4⋊C4C22×D4312yes—
188C22⋊C4—21no—
189C22⋊C4—862no—
190C42—21no—
191C42—431no—
192C42—431no—
193C42—432no—
194C42—862no—
195C23—861no—
196C23D4×D4311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—42no—
200Q8—432no—
201Q8—861no—
202Q8—862no—
203Q8—862no—
204Q8—1722no—
205D4—432no—
206D4—864no—
207D4—861no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—432no—
212C2×C4—432no—
213C2×C4—864no—
214C2×C4—861no—
215C2×C4—864no—
216C2×C4—862no—
217C2×C4—1724no—
218C2×C4—1722no—
219C2×C4#1062189812yes—
220C2×C4D4×D4311yescharacteristic
221C2×C4D4×D4312yes—
222C2×C4C23×D4311yescharacteristic
223C8—22no—
224C8—862no—
225C22—22no—
226C22—862no—
227C22—1722no—
228C22#1306329812yes—
229C22C2×D4×D4311yescharacteristic
230C4—42no—
231C4—42no—
232C4—434no—
233C4—862no—
234C4—862no—
235C4—1722no—
236C4#1306329812yes—
237C4C2×D4×D4311yescharacteristic
238C4C2×#1062189811yescharacteristic
239C2—22no—
240C2—1722no—
241C2C2×#1306329811yescharacteristic
242C2#137×D4312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#419C2
socleC22×C43C22×D4
hypercenter#419D43
hypocenterC43#3039
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. C2×#13063323C2semidirect
5. #14583108C2semidirect
6. #14583103C2semidirect
7. #14582922C2semidirect
8. #14582907C2semidirect
9. C43×#419C2semidirect
116. Dic43#137semidirect
130. #419D43semidirect
131. C43#3039semidirect