Finite Group Databasebeta

← #19144433

Subgroups — #19144433

Order 5504.

362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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#14583530C211yesmaximal, characteristic
2#14583377C211yesmaximal, characteristic
3#14583208C212yesmaximal, complemented
4#14583204C212yesmaximal, complemented
5#14583192C212yesmaximal, complemented
6#14583182C212yesmaximal, complemented
7#14582939C211yesmaximal, characteristic
8#14582937C211yesmaximal, characteristic
9#14582925C211yesmaximal, characteristic
10#14582908C211yesmaximal, characteristic
11C2×#103×C43C211yesmaximal, characteristic
12C2×#10621877C2211yescharacteristic
13#13063324—21no—
14#13063324C2212yes—
15#13063316—21no—
16#13063316C2212yes—
17#13063304—22no—
18Q8×Dic43—21no—
19Q8×Dic43—21no—
20Q8×Dic43C2212yes—
21Q8×Dic43C2212yes—
22#13063284—22no—
23#13063284C2211yescharacteristic
24#13063284C2211yescharacteristic
25#13063284C2211yescharacteristic
26#13063259C2211yescharacteristic
27#13063259C2211yescharacteristic
28#13063258C2212yes—
29#13063257C2211yescharacteristic
30#13063257C2211yescharacteristic
31#13063256C2212yes—
32Dic43⋊C8C2212yes—
33Dic43⋊C8C2212yes—
34#13063249C2212yes—
35#13063249C2212yes—
36C22×Q8×C43C2211yescharacteristic
37C22×C8×C43C2211yescharacteristic
38C2×C4⋊C4×C43C2211yescharacteristic
39#103×C43C2212yes—
40#103×C43C2212yes—
41C2×Q8×C43—21no—
42C2×Q8×C43—22no—
43C2×Q8×C43Q814yescomplemented
44C2×Q8×C43C2312yes—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43C2311yescharacteristic
48C2×Dic86—22no—
49C2×C8×C43—22no—
50C2×C8×C43C2311yescharacteristic
51C2×C8×C43C2311yescharacteristic
52C4⋊C4×C43—21no—
53C4⋊C4×C43C2312yes—
54C22⋊Dic43—21no—
55C22⋊Dic43—21no—
56C22⋊Dic43D412yes—
57C4⋊Dic43—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43—22no—
60C4⋊Dic43D411yescharacteristic
61C4⋊Dic43D411yescharacteristic
62C4⋊Dic43C2311yescharacteristic
63C4⋊Dic43C2311yescharacteristic
64C4⋊Dic43C2311yescharacteristic
65C4⋊Dic43C2311yescharacteristic
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68C4×Dic43—21no—
69C4×Dic43—21no—
70C4×Dic43—22no—
71C4×Dic43—22no—
72C4×Dic43C2312yes—
73#10621877—22no—
74C2×C43⋊C8C2312yes—
75C23×C43C2×D411yescharacteristic
76Q8×C43—24no—
77Q8×C43—22no—
78Q8×C43C2×Q814yes—
79C2×C4×C43—24no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—81no—
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×Q812yes—
85C2×C4×C43#4112yes—
86C2×C4×C43C2411yescharacteristic
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43C2×D412yes—
92C2×Dic43C2×D412yes—
93Dic86—82no—
94C8×C43—21no—
95C8×C43—21no—
96C43⋊C8—22no—
97C22×C43—21no—
98C22×C43—21no—
99C22×C43C22⋊Q812yes—
100C22×C43C22×D411yescharacteristic
101C4×C43—24no—
102C4×C43—42no—
103C4×C43C22⋊Q812yes—
104C4×C43C22×Q811yescharacteristic
105C4×C43C2×#4111yescharacteristic
106Dic43—22no—
107Dic43—22no—
108Dic43—41no—
109Dic43—41no—
110Dic43—41no—
111Dic43—41no—
112#3082—431nomaximal, Sylow
113C2×C43—22no—
114C2×C43C2×C22⋊Q811yescharacteristic
115C2×C43#57711yescharacteristic
116C2×C43#57811yescharacteristic
117#544—431no—
118#519—431no—
119#479—432no—
120#479—432no—
121#477—432no—
122#475—432no—
123#428—431no—
124#427—431no—
125#424—431no—
126#419—431no—
127C2×#103D4311yescharacteristic
128C43#308211yescharacteristic, complemented, Sylow
129C22×Q8C2×D4311yescharacteristic
130C2×M16—431no—
131C22×C8C2×D4311yescharacteristic
132C4⋊Q8—432no—
133C4⋊Q8—861no—
134#125—432no—
135#125—861no—
136C22⋊Q8—862no—
137C4×Q8—432no—
138C4×Q8—432no—
139C4×Q8—861no—
140C4×Q8—861no—
141#117—431no—
142#117—431no—
143#117—431no—
144#117—862no—
145C2×C4⋊C4C2×D4311yescharacteristic
146#107—431no—
147#107—431no—
148#107—432no—
149#106—431no—
150#106—431no—
151#106—432no—
152C4⋊C8—432no—
153C4⋊C8—432no—
154#103—432no—
155#103—432no—
156#103C2×D4312yes—
157#103C2×D4312yes—
158C2×Q8—21no—
159C2×Q8—22no—
160C2×Q8—862no—
161C2×Q8Dic8614yescomplemented
162C2×Q8C22×D4312yes—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C22×D4311yescharacteristic
166M16—862no—
167C2×C8—22no—
168C2×C8—432no—
169C2×C8C22×D4311yescharacteristic
170C2×C8C22×D4311yescharacteristic
171C4⋊C4—21no—
172C4⋊C4—431no—
173C4⋊C4—431no—
174C4⋊C4—431no—
175C4⋊C4—431no—
176C4⋊C4—431no—
177C4⋊C4—431no—
178C4⋊C4—862no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4—862no—
182C4⋊C4—862no—
183C4⋊C4C22×D4312yes—
184C22⋊C4—432no—
185C22⋊C4—861no—
186C22⋊C4—861no—
187C42—432no—
188C42—862no—
189C42—862no—
190C42—861no—
191C42—861no—
192C23D4×D4311yescharacteristic
193Q8—24no—
194Q8—22no—
195Q8—3442no—
196Q8C2×Dic8614yes—
197C2×C4—24no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—81no—
201C2×C4—432no—
202C2×C4—432no—
203C2×C4—861no—
204C2×C4—861no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4C2×Dic8612yes—
208C2×C4D4×D4311yescharacteristic
209C2×C4#1062190012yes—
210C2×C4C23×D4311yescharacteristic
211C8—21no—
212C8—21no—
213C8—862no—
214C22—21no—
215C22—21no—
216C22#1306330212yes—
217C22C2×D4×D4311yescharacteristic
218C4—24no—
219C4—42no—
220C4—862no—
221C4—862no—
222C4—1721no—
223C4—1721no—
224C4—1721no—
225C4—1721no—
226C4#1306330212yes—
227C4C22×Dic8611yescharacteristic
228C4C2×#1062190011yescharacteristic
229C2—22no—
230C2C2×#1306330211yescharacteristic
231C2#1458370511yescharacteristic
232C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#103×C43C2
socleC22×C43C22×D4
hypercenterC2×#103D43
hypocenterC43#3082
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #14583208C2semidirect
4. #14583204C2semidirect
5. #14583192C2semidirect
6. #14583182C2semidirect
43. C2×Q8×C43Q8semidirect
128. C43#3082semidirect
161. C2×Q8Dic86semidirect