Finite Group Databasebeta

← #19133084

Subgroups — #19133084

Order 5504.

304 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 77 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#14583410C211yesmaximal, characteristic
2C2×C22⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
3#14582635C212yesmaximal, complemented
4#14582632C212yesmaximal, complemented
5C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
6C2×#10621898C411yescharacteristic, complemented
7C22×C43⋊C8—21no—
8#13063308—21no—
9#13063304C411yescharacteristic, complemented
10#13063304C2211yescharacteristic
11#13063299C411yescharacteristic, complemented
12#13063299C2211yescharacteristic
13#13063294—21no—
14C4×C22⋊D43—21no—
15C4×C22⋊D43—21no—
16#13063284C411yescharacteristic, complemented
17C22⋊(C43⋊C8)—21no—
18C22⋊(C43⋊C8)C2212yes—
19C23×C4×C43C2211yescharacteristic
20C2×C22⋊C4×C43—21no—
21C2×C42×C43—21no—
22#95×C43C2212yes—
23C24×C43D411yescharacteristic
24C22×C4×C43—22no—
25C22×C4×C43—42no—
26C22×C4×C43C2×C411yescharacteristic
27C22×C4×C43C2×C411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×C4×C43D411yescharacteristic
30C22×C4×C43D411yescharacteristic
31C22×C4×C43C2311yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35#10621898—42no—
36C2×D172C2×C411yescharacteristic
37C2×C4×D43—21no—
38C2×Dic86C2×C411yescharacteristic
39C22⋊C4×C43—24no—
40C42×C43—42no—
41C22⋊Dic43—21no—
42C22⋊Dic43—21no—
43C22⋊Dic43—21no—
44(C2×D43)⋊C4—21no—
45(C2×D43)⋊C4—21no—
46C4⋊Dic43C2×C411yescharacteristic
47C4⋊Dic43C2×C411yescharacteristic
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50C4×Dic43—21no—
51C2×C43⋊C8—22no—
52C2×C43⋊C8—42no—
53C23×C43—22no—
54C23×C43—22no—
55C23×C43—41no—
56C23×C43C22⋊C411yescharacteristic
57C23×C43C22⋊C411yescharacteristic
58C23×C43C2×D411yescharacteristic
59C22×D43—21no—
60C2×C4×C43—22no—
61C2×C4×C43—22no—
62C2×C4×C43—22no—
63C2×C4×C43—24no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—42no—
68C2×C4×C43—42no—
69C2×C4×C43C22⋊C411yescharacteristic
70C2×C4×C43C22⋊C411yescharacteristic
71C2×C4×C43C22×C411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C22⋊D43—42no—
74C22⋊D43—42no—
75C22⋊D43—42no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79D172—41no—
80C4×D43—42no—
81Dic86—41no—
82C43⋊C8—42no—
83C22×C43—21no—
84C22×C43—21no—
85C22×C43—21no—
86C22×C43—21no—
87C22×C43—21no—
88C22×C43—21no—
89C22×C43—21no—
90C22×C43—44no—
91C22×C43#10412yes—
92C22×C43C2×C22⋊C411yescharacteristic
93C22×C43#13512yes—
94C2×D43—41no—
95C2×D43—41no—
96C2×D43—41no—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—44no—
101C4×C43#9912yes—
102Dic43—41no—
103Dic43—41no—
104Dic43—41no—
105#1501—431nomaximal, Sylow
106C2×C43—22no—
107C2×C43—22no—
108C2×C43—41no—
109C2×C43C2×#9911yescharacteristic
110C2×C43#41611yescharacteristic
111C2×C43C2×#10411yescharacteristic
112D43—81no—
113#525—431no—
114C2×C22⋊C8—431no—
115C4×C22⋊C4D4311yescharacteristic, complemented
116#328—432no—
117#327—432no—
118C43#150111yescharacteristic, complemented, Sylow
119C2×#41—431no—
120C23×C4C2×D4311yescharacteristic
121C22×C8—861no—
122#123—861no—
123C22⋊Q8—431no—
124C22⋊Q8—431no—
125#121—431no—
126#121—431no—
127#120—861no—
128C4×D4—861no—
129C4×D4—861no—
130#117—431no—
131C2×C22⋊C4—21no—
132C2×C42—21no—
133C22⋊C8—432no—
134C22⋊C8—861no—
135#95C2×D4312yes—
136C24C22⋊D4311yescharacteristic
137#41—1722no—
138C2×Q8—431no—
139C2×D4—431no—
140C2×D4—861no—
141C2×D4—861no—
142C2×D4—861no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—861no—
146C22×C4C4×D4311yescharacteristic
147C22×C4C4×D4311yescharacteristic
148C22×C4D17211yescharacteristic
149C22×C4D17211yescharacteristic
150C22×C4C22⋊D4311yescharacteristic
151C22×C4C22×D4311yescharacteristic
152C2×C8—862no—
153C2×C8—1722no—
154C4⋊C4—431no—
155C4⋊C4—431no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C22⋊C4—24no—
159C22⋊C4—861no—
160C22⋊C4—861no—
161C22⋊C4—861no—
162C22⋊C4—861no—
163C22⋊C4—861no—
164C42—42no—
165C42—861no—
166C23—22no—
167C23—22no—
168C23—41no—
169C23—861no—
170C23(C2×D43)⋊C411yescharacteristic
171C23(C2×D43)⋊C411yescharacteristic
172C23C2×C22⋊D4311yescharacteristic
173Q8—1721no—
174D4—1721no—
175D4—1722no—
176D4—1722no—
177D4—1722no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—861no—
188C2×C4—861no—
189C2×C4—861no—
190C2×C4—1722no—
191C2×C4(C2×D43)⋊C411yescharacteristic
192C2×C4(C2×D43)⋊C411yescharacteristic
193C2×C4C2×C4×D4311yescharacteristic
194C2×C4C2×D17211yescharacteristic
195C8—1722no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—44no—
204C22—1721no—
205C22—1721no—
206C22—1721no—
207C22#1306325312yes—
208C22C2×(C2×D43)⋊C411yescharacteristic
209C22#1306334512yes—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—44no—
214C4—1721no—
215C4—1721no—
216C4—1721no—
217C4#1306323912yes—
218C2—22no—
219C2—22no—
220C2—41no—
221C2—3441no—
222C2C2×#1306323911yescharacteristic
223C2#1458289311yescharacteristic
224C2C2×#1306325311yescharacteristic
subgroupG/H
centerC2×C4(C2×D43)⋊C4
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC4×C22⋊C4×C43C2
socleC22×C43C2×C22⋊C4
hypercenterC4×C22⋊C4D43
hypocenterC43#1501
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C43⋊C8)C2semidirect
3. #14582635C2semidirect
4. #14582632C2semidirect
5. C4×C22⋊C4×C43C2semidirect
6. C2×#10621898C4semidirect
9. #13063304C4semidirect
11. #13063299C4semidirect
16. #13063284C4semidirect
115. C4×C22⋊C4D43semidirect
118. C43#1501semidirect