Finite Group Databasebeta

← #19140376

Subgroups — #19140376

Order 5504.

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

normal subgroups only

This group has 526 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
1C2×#13063310C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#14582840C212yesmaximal, complemented
4#14582834C212yesmaximal, complemented
5#14582829C211yesmaximal, characteristic, complemented
6#14582826C211yesmaximal, characteristic, complemented
7#14582825C211yesmaximal, characteristic, complemented
8#14582777C212yesmaximal
9#14582770C212yesmaximal, complemented
10#14582761C211yesmaximal, characteristic, complemented
11C43×#398C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2212yes—
15#13063310—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2212yes—
20C4⋊C4×D43—24no—
21C2×(C2×D43)⋊C4C2211yescharacteristic
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C43⋊#95C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C23×D43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2312yes—
46C22×Dic43C2312yes—
47C22×Dic43C2311yescharacteristic
48C2×D172—22no—
49C2×D172—24no—
50C2×C4×D43—24no—
51C2×C4×D43—24no—
52C2×C4×D43—42no—
53C2×C4×D43—42no—
54C2×C4×D43D414yes—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43—42no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—24no—
62(C2×D43)⋊C4—42no—
63(C2×D43)⋊C4—42no—
64C4⋊Dic43—22no—
65Dic43⋊C4—24no—
66Dic43⋊C4—22no—
67Dic43⋊C4—42no—
68C23×C43C2411yescharacteristic
69C22×D43—21no—
70C22×D43—21no—
71C22×D43—22no—
72C22×D43—21no—
73C22×D43—22no—
74C22×D43—21no—
75C22×D43—21no—
76C22×D43—22no—
77C22×D43C2×D412yes—
78C22×D43#4114yes—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43C2×D412yes—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43C2×D412yes—
102D172—44no—
103C4×D43—28no—
104C4×D43—48no—
105C22×C43C22×D411yescharacteristic
106C22×C43C2×#4112yes—
107C22×C43H(5,𝔽2)11yescharacteristic
108C22×C43H(5,𝔽2)11yescharacteristic
109C22×C432−1+412yes—
110C2×D43—22no—
111C2×D43—22no—
112C2×D43—24no—
113C2×D43—24no—
114C2×D43—41no—
115C2×D43—41no—
116C2×D43—41no—
117C2×D43—42no—
118C2×D43—42no—
119C2×D43#12314yes—
120C4×C43—22no—
121C4×C43—41no—
122C4×C43—42no—
123C4×C43—41no—
124C4×C43—42no—
125Dic43—22no—
126Dic43—42no—
127Dic43—41no—
128Dic43—42no—
129#2623—431nomaximal, Sylow
130C2×C43C2×#12311yescharacteristic
131C2×C43#53511yescharacteristic
132C2×C43#53611yescharacteristic
133C2×C43#53912yes—
134C2×C43#53912yes—
135D43—24no—
136D43—81no—
137C2×#123—431no—
138C22×C4⋊C4—431no—
139#400—432no—
140#399—432no—
141#398—431no—
142#398D4311yescharacteristic, complemented
143#397—431no—
144#397—431no—
145#386—432no—
146#385—432no—
147#381—431no—
148C43#262311yescharacteristic, complemented, Sylow
149C22×D4—431no—
150C23×C4—431no—
151C23×C4—432no—
152#123—864no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—431no—
155C2×C4⋊C4—431no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4—864no—
158C2×C4⋊C4C2×D4311yescharacteristic
159C2×C4⋊C4C2×D4311yescharacteristic
160C2×C4⋊C4C2×D4312yes—
161C2×C22⋊C4—431no—
162C2×C22⋊C4—431no—
163C2×C22⋊C4—431no—
164C2×C22⋊C4—432no—
165C2×C22⋊C4—432no—
166C2×C22⋊C4—432no—
167#95—431no—
168#95—432no—
169#95—432no—
170#95—432no—
171#95—432no—
172#95C2×D4311yescharacteristic
173#95C2×D4312yes—
174C24—431no—
175C24—431no—
176C2×D4—862no—
177C2×D4—864no—
178C22×C4—431no—
179C22×C4—434no—
180C22×C4—431no—
181C22×C4—432no—
182C22×C4—432no—
183C22×C4—864no—
184C22×C4—864no—
185C22×C4—1722no—
186C22×C4—1722no—
187C22×C4C22×D4312yes—
188C22×C4C22×D4311yescharacteristic
189C22×C4C22×D4312yes—
190C22×C4C22×D4311yescharacteristic
191C22×C4C22×D4311yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—864no—
196C4⋊C4—862no—
197C4⋊C4—862no—
198C4⋊C4—1722no—
199C22⋊C4—862no—
200C22⋊C4—862no—
201C22⋊C4—864no—
202C22⋊C4—862no—
203C22⋊C4—1722no—
204C22⋊C4—1722no—
205C23—432no—
206C23—434no—
207C23—861no—
208C23—861no—
209C23—862no—
210C23—861no—
211C23—862no—
212C23—861no—
213C23—861no—
214C23—862no—
215C23C23×D4311yescharacteristic
216D4—1724no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—432no—
230C2×C4—868no—
231C2×C4—862no—
232C2×C4—861no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4—1728no—
241C2×C4D4×D4312yes—
242C22—434no—
243C22—862no—
244C22—862no—
245C22—864no—
246C22—864no—
247C22—1721no—
248C22—1721no—
249C22—1721no—
250C22—1722no—
251C22—1722no—
252C22C2×D4×D4311yescharacteristic
253C22#41×D4312yes—
254C22#1306337011yescharacteristic
255C22#1306337111yescharacteristic
256C22#1306337312yes—
257C4—22no—
258C4—41no—
259C4—42no—
260C4—41no—
261C4—42no—
262C4—862no—
263C4—1722no—
264C4—1721no—
265C4—1722no—
266C2—864no—
267C2—3441no—
268C2#123×D4311yescharacteristic
269C2#1458346511yescharacteristic
270C2#1458347411yescharacteristic
271C2#1458349512yes—
272C2#1458349712yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2623
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D43C2semidirect
3. #14582840C2semidirect
4. #14582834C2semidirect
5. #14582829C2semidirect
6. #14582826C2semidirect
7. #14582825C2semidirect
9. #14582770C2semidirect
10. #14582761C2semidirect
11. C43×#398C2semidirect
142. #398D43semidirect
148. C43#2623semidirect