Finite Group Databasebeta

← #19133577

Subgroups — #19133577

Order 5504.

260 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 49 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#14583487C211yesmaximal, characteristic
2#14583057C211yesmaximal, characteristic, complemented
3#14583040C211yesmaximal, characteristic, complemented
4#14582811C211yesmaximal, characteristic, complemented
5#14582637C211yesmaximal, characteristic, complemented
6#14582634C211yesmaximal, characteristic, complemented
7C43×#323C211yesmaximal, characteristic, complemented
8C22×Dic86C2211yescharacteristic
9C2×Dic172—21no—
10C2×#10621873—21no—
11#13063318—21no—
12#13063311—21no—
13#13063307—21no—
14#13063304C2211yescharacteristic
15#13063299C2211yescharacteristic
16#13063298—21no—
17#13063294—21no—
18C4×C22⋊D43—21no—
19C2×C22⋊Dic43—21no—
20#13063250—21no—
21#13063250—21no—
22C43⋊#95—21no—
23C43⋊#95C2211yescharacteristic
24C2×C22⋊C4×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26C22⋊C8×C43C2211yescharacteristic
27C24×C43D411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×C4×C43C2311yescharacteristic
30C2×C22⋊D43—21no—
31C2×C22⋊D43—21no—
32C2×C22⋊D43—21no—
33C22×Dic43—21no—
34C22×Dic43—21no—
35C2×D172D411yescharacteristic
36C2×C4×D43—21no—
37C2×Dic86—21no—
38C2×Dic86—21no—
39C2×Dic86—42no—
40C2×Dic86D411yescharacteristic
41C2×C8×C43—21no—
42C2×C8×C43—21no—
43C22⋊C4×C43—21no—
44C22⋊C4×C43—21no—
45C22⋊Dic43—21no—
46C22⋊Dic43—21no—
47C22⋊Dic43—21no—
48C22⋊Dic43—42no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51C4⋊Dic43D411yescharacteristic
52C4⋊Dic43D411yescharacteristic
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55C4×Dic43—21no—
56Dic172—42no—
57#10621873—42no—
58C23×C43—21no—
59C23×C43—21no—
60C23×C43—21no—
61C23×C43—41no—
62C23×C43—41no—
63C23×C43C2×D411yescharacteristic
64C22×D43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C22⋊D43—41no—
71C22⋊D43—41no—
72C22⋊D43—81no—
73C22⋊D43—81no—
74C2×Dic43—22no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—41no—
79C2×Dic43—41no—
80C2×Dic43—41no—
81C2×Dic43—41no—
82C2×Dic43—41no—
83D172—41no—
84C4×D43—81no—
85Dic86—22no—
86Dic86—22no—
87Dic86—41no—
88Dic86—41no—
89Dic86—41no—
90C8×C43—41no—
91C8×C43—41no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—42no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—81no—
99C22×C43#12011yescharacteristic
100C22×C43#13511yescharacteristic
101C22×C43#13711yescharacteristic
102C2×D43—41no—
103C2×D43—41no—
104C2×D43—41no—
105C4×C43—21no—
106C4×C43—21no—
107C4×C43—41no—
108Dic43—41no—
109Dic43—41no—
110Dic43—42no—
111Dic43—41no—
112Dic43—81no—
113#1606—431nomaximal, Sylow
114C2×C43—21no—
115C2×C43—21no—
116C2×C43—81no—
117C2×C43#45211yescharacteristic
118C2×C43#45511yescharacteristic
119C2×C43B(4,𝔽2)11yescharacteristic
120D43—81no—
121#538—431no—
122#451—431no—
123#448—431no—
124#393—431no—
125#328—431no—
126#327—431no—
127#323D4311yescharacteristic, complemented
128C43#160611yescharacteristic, complemented, Sylow
129C22×Q8—431no—
130C2×Q16—861no—
131C2×SD16—861no—
132#126—861no—
133#124—861no—
134#123—861no—
135C22⋊Q8—431no—
136#121—431no—
137#121—861no—
138#120—861no—
139C4×D4—861no—
140C2×C22⋊C4—861no—
141C2×C22⋊C4C2×D4311yescharacteristic
142#103—861no—
143#103—861no—
144C22⋊C8C2×D4311yescharacteristic
145C22⋊C8C2×D4311yescharacteristic
146#95—431no—
147#95—861no—
148C24D17211yescharacteristic
149C2×Q8—431no—
150C2×Q8—861no—
151C2×Q8—861no—
152C2×Q8—1722no—
153C2×D4—431no—
154C2×D4—861no—
155C2×D4—861no—
156C2×D4—861no—
157C22×C4—861no—
158C22×C4—861no—
159C22×C4—861no—
160C22×C4D17211yescharacteristic
161C22×C4C22×D4311yescharacteristic
162Q16—1722no—
163SD16—1722no—
164C2×C8—21no—
165C2×C8—21no—
166C4⋊C4—431no—
167C4⋊C4—431no—
168C4⋊C4—861no—
169C4⋊C4—861no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—861no—
173C22⋊C4—861no—
174C22⋊C4—861no—
175C22⋊C4—861no—
176C22⋊C4—861no—
177C22⋊C4—1722no—
178C42—861no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23—861no—
185C23C2×D17211yescharacteristic
186Q8—862no—
187Q8—862no—
188Q8—1721no—
189Q8—1721no—
190Q8—1721no—
191D4—3441no—
192D4—3441no—
193D4—1721no—
194D4—1721no—
195D4—1721no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—862no—
200C2×C4—861no—
201C2×C4—861no—
202C2×C4—861no—
203C2×C4—3441no—
204C2×C4—1721no—
205C2×C4—1721no—
206C2×C4—1721no—
207C2×C4—1721no—
208C2×C4—1721no—
209C2×C4D4×D4311yescharacteristic
210C2×C4D4×D4311yescharacteristic
211C8—41no—
212C8—41no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—1721no—
221C22—1721no—
222C22—1721no—
223C22#1306329511yescharacteristic
224C22#1306334711yescharacteristic
225C22#1306335811yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—3441no—
230C4—1721no—
231C4—1721no—
232C4—1722no—
233C4—1721no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—3441no—
238C2#1458306311yescharacteristic
239C2#1458307911yescharacteristic
240C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#323C2
socleC22×C43#120
hypercenter#323D43
hypocenterC43#1606
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14583057C2semidirect
3. #14583040C2semidirect
4. #14582811C2semidirect
5. #14582637C2semidirect
6. #14582634C2semidirect
7. C43×#323C2semidirect
127. #323D43semidirect
128. C43#1606semidirect