Finite Group Databasebeta

← #19139033

Subgroups — #19139033

Order 5504.

546 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13063308C211yesmaximal, characteristic
2#14582837C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic, complemented
4#14582830C211yesmaximal, characteristic, complemented
5#14582825C211yesmaximal, characteristic, complemented
6#14582790C212yesmaximal, complemented
7#14582783C212yesmaximal, complemented
8#14582776C212yesmaximal
9#14582757C212yesmaximal, complemented
10C2×C43⋊#95C211yesmaximal, characteristic, complemented
11C2×#117×C43C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2211yescharacteristic
13C23×Dic43C2212yes—
14#13063308—24no—
15C2×Dic43⋊C4C2211yescharacteristic
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×C22⋊Dic43C2211yescharacteristic
20C2×(C2×D43)⋊C4C2211yescharacteristic
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2211yescharacteristic
27C43⋊#95C2212yes—
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C23×C4×C43C2211yescharacteristic
32#117×C43—24no—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36C2×C42×C43C2212yes—
37C24×C43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C22×C4×C43—24no—
40C22×C4×C43D414yes—
41C22×C4×C43C2312yes—
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—22no—
46C2×C22⋊D43—24no—
47C22×Dic43—24no—
48C22×Dic43—24no—
49C22×Dic43—42no—
50C22×Dic43C2312yes—
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C22×Dic43C2311yescharacteristic
54C22×Dic43C2312yes—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—22no—
57C22⋊C4×C43—24no—
58C42×C43—24no—
59C22⋊Dic43—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—42no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4—24no—
67Dic43⋊C4—42no—
68C23×C43—22no—
69C23×C43—21no—
70C23×C43—21no—
71C23×C43C2×D412yes—
72C23×C43#4114yes—
73C23×C43C2411yescharacteristic
74C22×D43—21no—
75C22×D43—22no—
76C22×D43—22no—
77C22×D43—21no—
78C22×D43—21no—
79C2×C4×C43—28no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43C2×D412yes—
89C2×C4×C43C2×D412yes—
90C22⋊D43—44no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—21no—
94C2×Dic43—21no—
95C2×Dic43—21no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—21no—
103C2×Dic43—48no—
104C2×Dic43#4114yes—
105C22×C43—22no—
106C22×C43—22no—
107C22×C43—24no—
108C22×C43—24no—
109C22×C43#12314yes—
110C22×C43C22×D411yescharacteristic
111C22×C43C2×#4112yes—
112C22×C43C2×#4112yes—
113C22×C43H(5,𝔽2)11yescharacteristic
114C22×C432−1+411yescharacteristic
115C2×D43—41no—
116C2×D43—41no—
117C2×D43—41no—
118C2×D43—42no—
119C2×D43—42no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—42no—
123C4×C43—42no—
124Dic43—24no—
125Dic43—41no—
126Dic43—41no—
127Dic43—41no—
128Dic43—42no—
129#2498—431nomaximal, Sylow
130C2×C43—24no—
131C2×C43C2×#12311yescharacteristic
132C2×C43#53211yescharacteristic
133C2×C43#53711yescharacteristic
134C2×C43#55112yes—
135C2×C43#55212yes—
136D43—81no—
137C2×#123—431no—
138C2×#117D4311yescharacteristic, complemented
139#400—431no—
140#399—431no—
141#398—431no—
142#397—431no—
143#388—432no—
144#387—432no—
145#386—432no—
146#380—432no—
147C2×#95—431no—
148C43#249811yescharacteristic, complemented, Sylow
149C22×D4—431no—
150C23×C4—432no—
151C23×C4C2×D4311yescharacteristic
152#123—864no—
153#117—24no—
154C2×C4⋊C4—431no—
155C2×C4⋊C4—431no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4C2×D4311yescharacteristic
159C2×C4⋊C4C2×D4311yescharacteristic
160C2×C22⋊C4—431no—
161C2×C22⋊C4—431no—
162C2×C22⋊C4—431no—
163C2×C22⋊C4—432no—
164C2×C22⋊C4—432no—
165C2×C22⋊C4C2×D4312yes—
166C2×C42C2×D4312yes—
167#95—432no—
168#95—431no—
169#95—431no—
170#95—432no—
171#95—432no—
172#95—432no—
173#95—432no—
174C24—431no—
175C24C22×D4311yescharacteristic
176C2×D4—864no—
177C2×D4—862no—
178C22×C4—24no—
179C22×C4—432no—
180C22×C4—432no—
181C22×C4—431no—
182C22×C4—431no—
183C22×C4—431no—
184C22×C4—864no—
185C22×C4—864no—
186C22×C4—1722no—
187C22×C4C22⋊D4314yes—
188C22×C4C22×D4312yes—
189C22×C4C22×D4312yes—
190C22×C4C22×D4311yescharacteristic
191C22×C4C22×D4311yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—864no—
195C4⋊C4—862no—
196C4⋊C4—862no—
197C4⋊C4—1722no—
198C22⋊C4—24no—
199C22⋊C4—864no—
200C22⋊C4—862no—
201C22⋊C4—862no—
202C22⋊C4—862no—
203C22⋊C4—1722no—
204C42—24no—
205C23—22no—
206C23—21no—
207C23—21no—
208C23—861no—
209C23—862no—
210C23—862no—
211C23—861no—
212C23—861no—
213C23#1062189814yes—
214C23C2×C22⋊D4312yes—
215C23C23×D4311yescharacteristic
216D4—1724no—
217C2×C4—28no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—434no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4—861no—
230C2×C4—861no—
231C2×C4—861no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—861no—
238C2×C4—861no—
239C2×C4—1728no—
240C2×C4C2×C22⋊D4312yes—
241C2×C4C2×C22⋊D4312yes—
242C22—24no—
243C22—24no—
244C22—22no—
245C22—22no—
246C22—1722no—
247C22—1722no—
248C22—1721no—
249C22—1721no—
250C22—1721no—
251C22#1306330814yes—
252C22C22×C22⋊D4311yescharacteristic
253C22#41×D4312yes—
254C22C2×#1062189812yes—
255C22#1306337111yescharacteristic
256C22#1306337211yescharacteristic
257C4—22no—
258C4—22no—
259C4—42no—
260C4—42no—
261C4—864no—
262C4—1722no—
263C4—1721no—
264C4—1721no—
265C4—1721no—
266C2—24no—
267C2—3441no—
268C2C2×#1306330811yescharacteristic
269C2#1458344511yescharacteristic
270C2#1458347711yescharacteristic
271C2#1458357312yes—
272C2#1458358212yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#117×C43C2
hypercenterC2×#117D43
hypocenterC43#2498
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14582837C2semidirect
3. #14582834C2semidirect
4. #14582830C2semidirect
5. #14582825C2semidirect
6. #14582790C2semidirect
7. #14582783C2semidirect
9. #14582757C2semidirect
10. C2×C43⋊#95C2semidirect
11. C2×#117×C43C2semidirect
138. C2×#117D43semidirect
148. C43#2498semidirect