Finite Group Databasebeta

← #19132940

Subgroups — #19132940

Order 5504.

280 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 63 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×#13063307C211yesmaximal, characteristic
2#14582861C211yesmaximal, characteristic, complemented
3C22⋊C8×D43C211yesmaximal, characteristic, complemented
4#14582624C211yesmaximal, characteristic, complemented
5#14582624C211yesmaximal, characteristic, complemented
6#14582623C211yesmaximal, characteristic, complemented
7C43×#323C211yesmaximal, characteristic, complemented
8C22×C22⋊D43C411yescharacteristic
9C22×C4×D43C2211yescharacteristic
10C2×#10621872—21no—
11C2×C8×D43—21no—
12#13063307—21no—
13#13063307—21no—
14#13063307—21no—
15#13063307—21no—
16C2×C4⋊Dic43C411yescharacteristic
17C2×Dic43⋊C4C2211yescharacteristic
18C2×C22⋊Dic43C411yescharacteristic
19C2×(C2×D43)⋊C4C411yescharacteristic
20C22⋊(C43⋊C8)C2211yescharacteristic
21C22⋊(C43⋊C8)C2211yescharacteristic
22(C2×D43)⋊C8—21no—
23(C2×D43)⋊C8—21no—
24C2×C22⋊C4×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26C22⋊C8×C43C2211yescharacteristic
27C24×C43C2×C411yescharacteristic
28C23×D43C2×C411yescharacteristic
29C22×C4×C43C2×C411yescharacteristic
30C22×C4×C43C2311yescharacteristic
31C2×C22⋊D43—21no—
32C2×C22⋊D43—21no—
33C2×C22⋊D43—42no—
34C22×Dic43C2×C411yescharacteristic
35C22×Dic43C2×C411yescharacteristic
36C22×Dic43C2×C411yescharacteristic
37C2×C4×D43—42no—
38C2×C4×D43D411yescharacteristic
39C2×C4×D43D411yescharacteristic
40C2×C4×D43D411yescharacteristic
41C2×C4×D43D411yescharacteristic
42C2×C8×C43—21no—
43C2×C8×C43—21no—
44C22⋊C4×C43—21no—
45C22⋊C4×C43—21no—
46C22⋊Dic43—21no—
47C22⋊Dic43—21no—
48(C2×D43)⋊C4—21no—
49(C2×D43)⋊C4—21no—
50C4⋊Dic43—21no—
51C4⋊Dic43—21no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54C2×C43⋊C8—21no—
55C2×C43⋊C8—21no—
56#10621872—42no—
57C8×D43—42no—
58C23×C43—21no—
59C23×C43—21no—
60C23×C43—21no—
61C23×C43—41no—
62C23×C43—41no—
63C23×C43C22×C411yescharacteristic
64C22×D43—21no—
65C22×D43—21no—
66C22×D43—22no—
67C22×D43—41no—
68C22×D43C22⋊C411yescharacteristic
69C22×D43C22⋊C411yescharacteristic
70C2×C4×C43—21no—
71C2×C4×C43—41no—
72C2×C4×C43—41no—
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C22⋊D43—42no—
76C22⋊D43—42no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—41no—
82C2×Dic43—41no—
83C2×Dic43C22⋊C411yescharacteristic
84C2×Dic43C22⋊C411yescharacteristic
85C4×D43—22no—
86C4×D43—22no—
87C4×D43—41no—
88C4×D43—41no—
89C8×C43—41no—
90C8×C43—41no—
91C43⋊C8—41no—
92C43⋊C8—41no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—81no—
99C22×C43—81no—
100C22×C43C2×C22⋊C411yescharacteristic
101C22×C43#13111yescharacteristic
102C22×C43#13111yescharacteristic
103C2×D43—21no—
104C2×D43—21no—
105C2×D43—21no—
106C2×D43—21no—
107C2×D43—21no—
108C2×D43—42no—
109C2×D43—42no—
110C2×D43#9912yes—
111C4×C43—21no—
112C4×C43—21no—
113C4×C43—41no—
114Dic43—21no—
115Dic43—21no—
116Dic43—41no—
117Dic43—41no—
118#1468—431nomaximal, Sylow
119C2×C43—21no—
120C2×C43—21no—
121C2×C43—81no—
122C2×C43#40811yescharacteristic
123C2×C43C2×#9911yescharacteristic
124C2×C43#41311yescharacteristic
125D43—22no—
126D43—41no—
127C2×#123—431no—
128#407—431no—
129C2×C22⋊C8—431no—
130#324—431no—
131#324—431no—
132#323—431no—
133#323D4311yescharacteristic, complemented
134C43#146811yescharacteristic, complemented, Sylow
135C22×D4—431no—
136C23×C4—431no—
137C2×M16—861no—
138C22×C8—861no—
139#123—861no—
140#123—861no—
141#123—861no—
142#123—861no—
143C2×C4⋊C4—431no—
144C2×C4⋊C4—431no—
145C2×C22⋊C4—431no—
146C2×C22⋊C4—431no—
147C2×C22⋊C4C2×D4311yescharacteristic
148C22⋊C8—431no—
149C22⋊C8—431no—
150C22⋊C8—861no—
151C22⋊C8—861no—
152C22⋊C8C2×D4311yescharacteristic
153C22⋊C8C2×D4311yescharacteristic
154C24—431no—
155C24C4×D4311yescharacteristic
156C2×D4—861no—
157C2×D4—861no—
158C2×D4—1722no—
159C22×C4—431no—
160C22×C4—431no—
161C22×C4—431no—
162C22×C4—431no—
163C22×C4—431no—
164C22×C4—431no—
165C22×C4—431no—
166C22×C4—1722no—
167C22×C4C4×D4311yescharacteristic
168C22×C4C22×D4311yescharacteristic
169M16—1722no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—861no—
173C2×C8—861no—
174C2×C8—1722no—
175C4⋊C4—861no—
176C4⋊C4—861no—
177C4⋊C4—861no—
178C4⋊C4—861no—
179C22⋊C4—21no—
180C22⋊C4—21no—
181C22⋊C4—861no—
182C22⋊C4—861no—
183C22⋊C4—861no—
184C22⋊C4—861no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—41no—
189C23—41no—
190C23—431no—
191C23—431no—
192C23—862no—
193C23—861no—
194C23—861no—
195C23—1721no—
196C23C2×C4×D4311yescharacteristic
197D4—1722no—
198D4—1722no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—431no—
203C2×C4—431no—
204C2×C4—862no—
205C2×C4—862no—
206C2×C4—861no—
207C2×C4—861no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—1721no—
211C2×C4—1721no—
212C2×C4—1721no—
213C2×C4—1721no—
214C2×C4D4×D4311yescharacteristic
215C2×C4D4×D4311yescharacteristic
216C8—41no—
217C8—41no—
218C8—1721no—
219C8—1721no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22—432no—
228C22—861no—
229C22—861no—
230C22—861no—
231C22—861no—
232C22—861no—
233C22—1722no—
234C22—1722no—
235C22C22⋊C4×D4311yescharacteristic
236C22#1306333111yescharacteristic
237C22#1306333311yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—861no—
242C4—861no—
243C4—1721no—
244C4—1721no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—862no—
249C2—1721no—
250C2#1458286411yescharacteristic
251C2#99×D4311yescharacteristic
252C2#1458288011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#323C2
socleC22×C43C2×C22⋊C4
hypercenter#323D43
hypocenterC43#1468
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14582861C2semidirect
3. C22⋊C8×D43C2semidirect
4. #14582624C2semidirect
5. #14582624C2semidirect
6. #14582623C2semidirect
7. C43×#323C2semidirect
133. #323D43semidirect
134. C43#1468semidirect