Finite Group Databasebeta

← #19142608

Subgroups — #19142608

Order 5504.

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

normal subgroups only

This group has 478 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×#13063304C211yesmaximal, characteristic, complemented
2#14582832C212yesmaximal, complemented
3#14582829C211yesmaximal, characteristic, complemented
4#14582827C212yesmaximal, complemented
5#14582824C211yesmaximal, characteristic, complemented
6#14582822C212yesmaximal, complemented
7#14582819C211yesmaximal, characteristic, complemented
8#14582813C212yesmaximal
9#14582811C211yesmaximal, characteristic, complemented
10#14582759C211yesmaximal, characteristic, complemented
11C2×#123×C43C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13#13063304—24no—
14C2×C4⋊Dic43C2211yescharacteristic
15C2×C4⋊Dic43C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×C22⋊Dic43C2212yes—
21C2×C22⋊Dic43C2212yes—
22C2×C22⋊Dic43C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2211yescharacteristic
28C43⋊#95C2212yes—
29C22×D4×C43C2211yescharacteristic
30C23×C4×C43C2211yescharacteristic
31#123×C43—24no—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2211yescharacteristic
36C2×C22⋊C4×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C24×C43C2311yescharacteristic
39C2×D4×C43—22no—
40C2×D4×C43—42no—
41C22×C4×C43—42no—
42C22×C4×C43D414yes—
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C22×C4×C43C2311yescharacteristic
46C22×C4×C43C2311yescharacteristic
47C22×C4×C43C2311yescharacteristic
48C22×Dic43C2312yes—
49C22×Dic43C2312yes—
50C22×Dic43C2312yes—
51C22×Dic43C2312yes—
52C2×Dic86—22no—
53C2×Dic86—42no—
54C4⋊C4×C43—22no—
55C4⋊C4×C43—22no—
56C22⋊C4×C43—22no—
57C22⋊C4×C43—22no—
58C22⋊C4×C43—22no—
59C22⋊Dic43—24no—
60C22⋊Dic43—42no—
61C22⋊Dic43—42no—
62C22⋊Dic43—42no—
63C4⋊Dic43—22no—
64C4⋊Dic43—42no—
65Dic43⋊C4—24no—
66Dic43⋊C4—42no—
67Dic43⋊C4—42no—
68C23×C43—21no—
69C23×C43—22no—
70C23×C43—22no—
71C23×C43—21no—
72C23×C43—21no—
73C23×C43—21no—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43—21no—
77C23×C43C2×D412yes—
78C23×C43C2411yescharacteristic
79D4×C43—44no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—44no—
90C2×C4×C43C2×D412yes—
91C2×C4×C43C2×D412yes—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104Dic86—44no—
105C22×C43—22no—
106C22×C43—22no—
107C22×C43—22no—
108C22×C43—42no—
109C22×C43—42no—
110C22×C43—41no—
111C22×C43—41no—
112C22×C43—41no—
113C22×C43—42no—
114C22×C43—42no—
115C22×C43C22×D411yescharacteristic
116C22×C43H(5,𝔽2)12yes—
117C22×C43H(5,𝔽2)11yescharacteristic
118C22×C432−1+412yes—
119C22×C432−1+411yescharacteristic
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—41no—
123C4×C43—41no—
124C4×C43—41no—
125Dic43—42no—
126Dic43—42no—
127Dic43—42no—
128Dic43—42no—
129#2814—431nomaximal, Sylow
130C2×C43—42no—
131C2×C43—81no—
132C2×C43#53411yescharacteristic
133C2×C43#53611yescharacteristic
134C2×C43#53711yescharacteristic
135C2×C43#56212yes—
136C2×C43#56312yes—
137C2×#123D4311yescharacteristic
138C2×C22⋊Q8—431no—
139#398—431no—
140#398—432no—
141#397—431no—
142#397—432no—
143#396—432no—
144#395—431no—
145#394—432no—
146#393—431no—
147#380—431no—
148C43#281411yescharacteristic, complemented, Sylow
149C22×Q8—431no—
150C22×D4C2×D4311yescharacteristic
151C23×C4C2×D4311yescharacteristic
152#123—24no—
153C22⋊Q8—864no—
154C2×C4⋊C4—432no—
155C2×C4⋊C4—431no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4—432no—
159C2×C4⋊C4C2×D4311yescharacteristic
160C2×C4⋊C4C2×D4311yescharacteristic
161C2×C22⋊C4—432no—
162C2×C22⋊C4—432no—
163C2×C22⋊C4—432no—
164C2×C22⋊C4—432no—
165C2×C22⋊C4C2×D4311yescharacteristic
166C2×C22⋊C4C2×D4311yescharacteristic
167C2×C22⋊C4C2×D4311yescharacteristic
168#95—431no—
169#95—431no—
170#95—432no—
171#95—432no—
172#95—432no—
173#95—432no—
174C24C22×D4311yescharacteristic
175C24C22×D4311yescharacteristic
176C2×Q8—862no—
177C2×Q8—1722no—
178C2×D4—22no—
179C2×D4—42no—
180C22×C4—42no—
181C22×C4—432no—
182C22×C4—432no—
183C22×C4—432no—
184C22×C4—432no—
185C22×C4C22⋊D4314yes—
186C22×C4C22×D4311yescharacteristic
187C22×C4C22×D4311yescharacteristic
188C22×C4C22×D4311yescharacteristic
189C22×C4C22×D4311yescharacteristic
190C22×C4C22×D4311yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—864no—
194C4⋊C4—862no—
195C4⋊C4—1722no—
196C4⋊C4—1722no—
197C4⋊C4—1722no—
198C22⋊C4—22no—
199C22⋊C4—22no—
200C22⋊C4—22no—
201C22⋊C4—864no—
202C22⋊C4—1722no—
203C22⋊C4—1722no—
204C22⋊C4—1722no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—21no—
212C23—22no—
213C23—21no—
214C23C2×C22⋊D4312yes—
215C23C23×D4311yescharacteristic
216Q8—1724no—
217D4—44no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—44no—
228C2×C4—862no—
229C2×C4—862no—
230C2×C4—862no—
231C2×C4—862no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4C2×C22⋊D4312yes—
241C2×C4C2×C22⋊D4312yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22C22×C22⋊D4311yescharacteristic
253C22#1306337012yes—
254C22#1306337111yescharacteristic
255C22#1306337212yes—
256C22#1306337211yescharacteristic
257C4—22no—
258C4—22no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—1722no—
263C4—1722no—
264C4—1722no—
265C4—1722no—
266C2—42no—
267C2—81no—
268C2#1458345811yescharacteristic
269C2#1458347011yescharacteristic
270C2#1458347711yescharacteristic
271C2#1458364612yes—
272C2#1458365212yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#123×C43C2
hypercenterC2×#123D43
hypocenterC43#2814
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#13063304C2semidirect
2. #14582832C2semidirect
3. #14582829C2semidirect
4. #14582827C2semidirect
5. #14582824C2semidirect
6. #14582822C2semidirect
7. #14582819C2semidirect
9. #14582811C2semidirect
10. #14582759C2semidirect
148. C43#2814semidirect