Finite Group Databasebeta

← #19139188

Subgroups — #19139188

Order 5504.

440 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 137 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#14582828C212yesmaximal, complemented
2#14582826C212yesmaximal, complemented
3#14582801C211yesmaximal, characteristic
4#14582800C211yesmaximal, characteristic
5#14582800C211yesmaximal, characteristic
6#14582798C211yesmaximal, characteristic, complemented
7#14582791C212yesmaximal, complemented
8#14582788C212yesmaximal, complemented
9C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
10C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
11C43×#382C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C2×C4⋊Dic43C2211yescharacteristic
14C2×C4⋊Dic43C2212yes—
15C2×Dic43⋊C4C2211yescharacteristic
16C2×Dic43⋊C4C2211yescharacteristic
17C2×(C2×D43)⋊C4C2212yes—
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×C4×Dic43C2211yescharacteristic
24C2×C4×Dic43C2211yescharacteristic
25C2×C4×Dic43C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2211yescharacteristic
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2212yes—
30C2×C4⋊C4×C43C2211yescharacteristic
31C2×C4⋊C4×C43C2211yescharacteristic
32C2×C42×C43C2211yescharacteristic
33#95×C43C2212yes—
34#95×C43C2212yes—
35C23×D43C2312yes—
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2312yes—
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×Dic43C2311yescharacteristic
42C22×Dic43C2311yescharacteristic
43C22×Dic43C2312yes—
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2311yescharacteristic
46C2×D172—22no—
47C2×D172—22no—
48C2×D172—22no—
49C4⋊C4×C43—22no—
50C4⋊C4×C43—22no—
51C42×C43—22no—
52(C2×D43)⋊C4—24no—
53(C2×D43)⋊C4—24no—
54(C2×D43)⋊C4—42no—
55(C2×D43)⋊C4—42no—
56(C2×D43)⋊C4—42no—
57(C2×D43)⋊C4—42no—
58C4⋊Dic43—22no—
59C4⋊Dic43—42no—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62C4×Dic43—22no—
63C4×Dic43—22no—
64C4×Dic43—42no—
65C23×C43C2411yescharacteristic
66C22×D43—22no—
67C22×D43—22no—
68C22×D43—22no—
69C22×D43—22no—
70C22×D43—22no—
71C22×D43—22no—
72C22×D43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43#4112yes—
86C2×C4×C43#4112yes—
87C2×C4×C43#4112yes—
88C2×Dic43—21no—
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43—21no—
92C2×Dic43—21no—
93C2×Dic43—21no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—22no—
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43#4112yes—
102C2×Dic43#4112yes—
103D172—44no—
104C22×C43C2×#4111yescharacteristic
105C22×C43C2×#4111yescharacteristic
106C22×C43C2×#4111yescharacteristic
107C22×C43C2×#4111yescharacteristic
108C22×C43C2×#4111yescharacteristic
109C22×C43H(5,𝔽2)11yescharacteristic
110C22×C43H(5,𝔽2)11yescharacteristic
111C2×D43—42no—
112C2×D43—42no—
113C2×D43—42no—
114C2×D43—42no—
115C2×D43—42no—
116C2×D43—42no—
117C2×D43—42no—
118C4×C43—41no—
119C4×C43—41no—
120C4×C43—42no—
121C4×C43—42no—
122C4×C43#12614yes—
123Dic43—22no—
124Dic43—22no—
125Dic43—41no—
126Dic43—42no—
127Dic43—41no—
128#2513—431nomaximal, Sylow
129C2×C43C2×#12611yescharacteristic
130C2×C43#52911yescharacteristic
131C2×C43#54011yescharacteristic
132C2×C43#55311yescharacteristic
133C2×C43#55511yescharacteristic
134C2×C43#55911yescharacteristic
135C2×C43#55911yescharacteristic
136D43—82no—
137#397—432no—
138#397—432no—
139#390—431no—
140#390—431no—
141#390—431no—
142#389—431no—
143#388—432no—
144#388—432no—
145#382D4311yescharacteristic, complemented
146C4×C4⋊C4—431no—
147C4×C4⋊C4—431no—
148C43#251311yescharacteristic, complemented, Sylow
149C22×D4—431no—
150C2×C4⋊C4—431no—
151C2×C4⋊C4—431no—
152C2×C4⋊C4—431no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4C2×D4311yescharacteristic
155C2×C4⋊C4C2×D4311yescharacteristic
156C2×C22⋊C4—432no—
157C2×C22⋊C4—432no—
158C2×C22⋊C4—432no—
159C2×C22⋊C4—432no—
160C2×C22⋊C4—432no—
161C2×C22⋊C4—432no—
162C2×C42—431no—
163C2×C42—431no—
164C2×C42—432no—
165C2×C42C2×D4311yescharacteristic
166#95—431no—
167#95—432no—
168#95—431no—
169#95—432no—
170#95C2×D4312yes—
171#95C2×D4312yes—
172C24—432no—
173C2×D4—862no—
174C2×D4—862no—
175C2×D4—862no—
176C22×C4—431no—
177C22×C4—431no—
178C22×C4—431no—
179C22×C4—431no—
180C22×C4—432no—
181C22×C4C22×D4312yes—
182C22×C4C22×D4311yescharacteristic
183C22×C4C22×D4311yescharacteristic
184C22×C4C22×D4312yes—
185C22×C4C22×D4311yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—862no—
189C4⋊C4—862no—
190C4⋊C4—862no—
191C4⋊C4—1722no—
192C22⋊C4—864no—
193C22⋊C4—864no—
194C22⋊C4—1722no—
195C22⋊C4—1722no—
196C22⋊C4—1722no—
197C22⋊C4—1722no—
198C42—22no—
199C42—862no—
200C42—862no—
201C42—1722no—
202C23—862no—
203C23—862no—
204C23—862no—
205C23—862no—
206C23—862no—
207C23—862no—
208C23—862no—
209C23C23×D4311yescharacteristic
210D4—1724no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—432no—
224C2×C4—432no—
225C2×C4—861no—
226C2×C4—861no—
227C2×C4—861no—
228C2×C4—861no—
229C2×C4—861no—
230C2×C4—861no—
231C2×C4—861no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—861no—
235C2×C4—861no—
236C2×C4—862no—
237C2×C4—861no—
238C2×C4#1062189812yes—
239C2×C4#1062190012yes—
240C2×C4#1062190212yes—
241C22—1722no—
242C22—1722no—
243C22—1722no—
244C22—1722no—
245C22—1722no—
246C22—1722no—
247C22—1722no—
248C22#41×D4311yescharacteristic
249C22#41×D4311yescharacteristic
250C22C2×#1062190011yescharacteristic
251C22C2×#1062189811yescharacteristic
252C22C2×#1062190211yescharacteristic
253C22#1306337111yescharacteristic
254C22#1306337111yescharacteristic
255C4—41no—
256C4—41no—
257C4—42no—
258C4—42no—
259C4—862no—
260C4—862no—
261C4—1721no—
262C4—1721no—
263C4—1722no—
264C4#1306332014yes—
265C2—3442no—
266C2C2×#1306332011yescharacteristic
267C2#1458343411yescharacteristic
268C2#1458350511yescharacteristic
269C2#1458359311yescharacteristic
270C2#1458361211yescharacteristic
271C2#1458363111yescharacteristic
272C2#1458363111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#382C2
hypercenter#382D43
hypocenterC43#2513
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #14582828C2semidirect
2. #14582826C2semidirect
6. #14582798C2semidirect
7. #14582791C2semidirect
8. #14582788C2semidirect
9. C4⋊C4×Dic43C2semidirect
10. C4×Dic43⋊C4C2semidirect
11. C43×#382C2semidirect
145. #382D43semidirect
148. C43#2513semidirect