Finite Group Databasebeta

← #19144435

Subgroups — #19144435

Order 5504.

362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 133 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#14583376C211yesmaximal, characteristic
3#14583209C212yesmaximal, complemented
4#14583205C212yesmaximal, complemented
5#14583193C212yesmaximal, complemented
6#14583183C212yesmaximal, complemented
7#14582935C211yesmaximal, characteristic
8#14582927C211yesmaximal, characteristic
9#14582909C211yesmaximal, characteristic
10C2×#13063248C211yesmaximal, characteristic
11C43×#428C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13C22×C43⋊C8C2211yescharacteristic
14#13063324—21no—
15#13063324C2212yes—
16#13063316—21no—
17#13063316C2212yes—
18#13063304—22no—
19C4×Dic86—21no—
20C4×Dic86—21no—
21#13063290C2212yes—
22#13063290C2212yes—
23#13063284C2211yescharacteristic
24#13063284C2211yescharacteristic
25#13063281—22no—
26#13063258C2211yescharacteristic
27#13063258C2211yescharacteristic
28#13063256C2211yescharacteristic
29#13063256C2211yescharacteristic
30Dic43⋊C8C2212yes—
31Dic43⋊C8C2212yes—
32#13063250C2212yes—
33#13063250C2212yes—
34#13063248C2212yes—
35#13063248C2212yes—
36C2×M16×C43C2211yescharacteristic
37#117×C43C2211yescharacteristic
38C2×C4⋊C4×C43C2211yescharacteristic
39#107×C43C2212yes—
40#106×C43C2212yes—
41C22×C4×C43—21no—
42C22×C4×C43C2311yescharacteristic
43C22×Dic43—21no—
44C2×Dic86—21no—
45C2×Dic86—22no—
46C2×Dic86—22no—
47C2×Dic86Q814yescomplemented
48C2×Dic86C2312yes—
49M16×C43—22no—
50C2×C8×C43C2312yes—
51C4⋊C4×C43—21no—
52C4⋊C4×C43C2311yescharacteristic
53C4⋊C4×C43C2312yes—
54C4⋊C4×C43C2311yescharacteristic
55C22⋊C4×C43—21no—
56C42×C43—21no—
57C22⋊Dic43—21no—
58C22⋊Dic43D412yes—
59C4⋊Dic43—22no—
60C4⋊Dic43D411yescharacteristic
61C4⋊Dic43D411yescharacteristic
62C4⋊Dic43C2311yescharacteristic
63C4⋊Dic43C2311yescharacteristic
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68C4×Dic43—21no—
69C4×Dic43—22no—
70C4×Dic43—22no—
71C4×Dic43C2312yes—
72C2×C43⋊C8—22no—
73C2×C43⋊C8C2311yescharacteristic
74C2×C43⋊C8C2311yescharacteristic
75C23×C43C2×D411yescharacteristic
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—81no—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×Q812yes—
82C2×C4×C43#4112yes—
83C2×C4×C43C2411yescharacteristic
84C2×Dic43—24no—
85C2×Dic43—22no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43C2×D412yes—
89C2×Dic43C2×D412yes—
90Dic86—24no—
91Dic86—22no—
92Dic86—82no—
93Dic86C2×Q814yes—
94C8×C43—22no—
95C43⋊C8—21no—
96C43⋊C8—21no—
97C22×C43—21no—
98C22×C43—21no—
99C22×C43C22⋊Q812yes—
100C22×C43C22×D411yescharacteristic
101C4×C43—42no—
102C4×C43—41no—
103C4×C43—41no—
104C4×C43C22⋊Q812yes—
105C4×C43C22×Q811yescharacteristic
106C4×C43C2×#4111yescharacteristic
107Dic43—24no—
108Dic43—22no—
109Dic43—22no—
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#428D4311yescharacteristic
124#427—431no—
125#424—431no—
126#419—431no—
127C2×#103—431no—
128C43#308211yescharacteristic, complemented, Sylow
129C22×Q8—431no—
130C2×M16C2×D4311yescharacteristic
131C22×C8—431no—
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—862no—
144#117C2×D4311yescharacteristic
145C2×C4⋊C4C2×D4311yescharacteristic
146#107—431no—
147#107—431no—
148#107C2×D4312yes—
149#106—431no—
150#106—431no—
151#106C2×D4312yes—
152C4⋊C8—432no—
153C4⋊C8—432no—
154#103—432no—
155#103—432no—
156#103—432no—
157#103—432no—
158C2×Q8—434no—
159C2×Q8—432no—
160C2×Q8—862no—
161C2×Q8—862no—
162C2×Q8—861no—
163C22×C4—21no—
164C22×C4—861no—
165C22×C4C22×D4311yescharacteristic
166M16—22no—
167C2×C8—431no—
168C2×C8—431no—
169C2×C8—862no—
170C2×C8C22×D4312yes—
171C4⋊C4—21no—
172C4⋊C4—431no—
173C4⋊C4—431no—
174C4⋊C4—431no—
175C4⋊C4—431no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4C22×D4312yes—
182C4⋊C4C22×D4311yescharacteristic
183C4⋊C4C22×D4311yescharacteristic
184C22⋊C4—21no—
185C22⋊C4—432no—
186C22⋊C4—861no—
187C42—21no—
188C42—432no—
189C42—862no—
190C42—862no—
191C42—861no—
192C23D4×D4311yescharacteristic
193Q8—434no—
194Q8—864no—
195Q8—862no—
196Q8—3442no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—81no—
201C2×C4—432no—
202C2×C4—432no—
203C2×C4—864no—
204C2×C4—862no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4#1062189812yes—
208C2×C4D4×D4311yescharacteristic
209C2×C4Q8×D4312yes—
210C2×C4C23×D4311yescharacteristic
211C8—22no—
212C8—861no—
213C8—861no—
214C22—21no—
215C22—21no—
216C22#1306330312yes—
217C22C2×D4×D4311yescharacteristic
218C4—42no—
219C4—41no—
220C4—41no—
221C4—864no—
222C4—862no—
223C4—862no—
224C4—1721no—
225C4—1721no—
226C4#1306330312yes—
227C4C2×Q8×D4311yescharacteristic
228C4C2×#1062189811yescharacteristic
229C2—22no—
230C2C2×#1306330311yescharacteristic
231C2#1458370911yescharacteristic
232C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#428C2
socleC22×C43C22×D4
hypercenter#428D43
hypocenterC43#3082
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #14583209C2semidirect
4. #14583205C2semidirect
5. #14583193C2semidirect
6. #14583183C2semidirect
47. C2×Dic86Q8semidirect
128. C43#3082semidirect