Finite Group Databasebeta

← #19140556

Subgroups — #19140556

Order 5504.

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

normal subgroups only

This group has 420 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
1#14582827C212yesmaximal, complemented
2#14582827C212yesmaximal, complemented
3#14582824C212yesmaximal, complemented
4#14582822C212yesmaximal, complemented
5#14582802C211yesmaximal, characteristic
6#14582802C211yesmaximal, characteristic
7#14582798C211yesmaximal, characteristic, complemented
8#14582797C211yesmaximal, characteristic, complemented
9#14582795C211yesmaximal, characteristic, complemented
10#14582745C211yesmaximal, characteristic, complemented
11C43×#390C211yesmaximal, characteristic
12C2×C4⋊Dic43C2211yescharacteristic
13C2×C4⋊Dic43C2211yescharacteristic
14C2×C4⋊Dic43C2212yes—
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×C22⋊Dic43C2212yes—
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×C22⋊Dic43C2212yes—
21C2×C4×Dic43C2211yescharacteristic
22C2×C4×Dic43C2211yescharacteristic
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2211yescharacteristic
27C43⋊#95C2211yescharacteristic
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2211yescharacteristic
30C22×D4×C43C2211yescharacteristic
31C2×C4⋊C4×C43C2211yescharacteristic
32C2×C22⋊C4×C43C2212yes—
33C2×C22⋊C4×C43C2212yes—
34C2×C42×C43C2211yescharacteristic
35C24×C43C2312yes—
36C2×D4×C43—22no—
37C2×D4×C43—22no—
38C2×D4×C43—22no—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×Dic43C2311yescharacteristic
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2312yes—
48C22×Dic43C2312yes—
49C4⋊C4×C43—22no—
50C22⋊C4×C43—42no—
51C22⋊C4×C43—42no—
52C42×C43—22no—
53C22⋊Dic43—42no—
54C22⋊Dic43—42no—
55C22⋊Dic43—42no—
56C22⋊Dic43—42no—
57C4⋊Dic43—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43—42no—
60Dic43⋊C4—42no—
61Dic43⋊C4—42no—
62C4×Dic43—22no—
63C4×Dic43—22no—
64C23×C43—22no—
65C23×C43—22no—
66C23×C43—22no—
67C23×C43—22no—
68C23×C43—22no—
69C23×C43—22no—
70C23×C43—22no—
71C23×C43C2411yescharacteristic
72D4×C43—44no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43#4112yes—
83C2×C4×C43#4112yes—
84C2×C4×C43#4112yes—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—21no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—21no—
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—21no—
102C2×Dic43—21no—
103C22×C43—42no—
104C22×C43—42no—
105C22×C43—42no—
106C22×C43—42no—
107C22×C43—42no—
108C22×C43—42no—
109C22×C43—42no—
110C22×C43C2×#4111yescharacteristic
111C22×C43C2×#4111yescharacteristic
112C22×C43C2×#4111yescharacteristic
113C22×C43H(5,𝔽2)11yescharacteristic
114C22×C43H(5,𝔽2)11yescharacteristic
115C22×C43H(5,𝔽2)11yescharacteristic
116C22×C432−1+411yescharacteristic
117C4×C43—41no—
118C4×C43—42no—
119C4×C43—41no—
120C4×C43#12614yes—
121Dic43—41no—
122Dic43—42no—
123Dic43—42no—
124Dic43—41no—
125Dic43—41no—
126Dic43—41no—
127#2644—431nomaximal, Sylow
128C2×C43—82no—
129C2×C43C2×#12611yescharacteristic
130C2×C43#54011yescharacteristic
131C2×C43#54011yescharacteristic
132C2×C43#54011yescharacteristic
133C2×C43#54211yescharacteristic
134C2×C43#54211yescharacteristic
135C2×C43#54211yescharacteristic
136#397—432no—
137#397—432no—
138#397—432no—
139#396—432no—
140#390—431no—
141#390—431no—
142#390D4311yescharacteristic
143#389—431no—
144#389—431no—
145#389—431no—
146#376—431no—
147C43#264411yescharacteristic, complemented, Sylow
148C22×D4C2×D4311yescharacteristic
149C2×C4⋊C4—431no—
150C2×C4⋊C4—431no—
151C2×C4⋊C4—432no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4C2×D4311yescharacteristic
155C2×C22⋊C4—432no—
156C2×C22⋊C4—432no—
157C2×C22⋊C4—432no—
158C2×C22⋊C4—432no—
159C2×C22⋊C4C2×D4312yes—
160C2×C22⋊C4C2×D4312yes—
161C2×C42—431no—
162C2×C42—431no—
163C2×C42C2×D4311yescharacteristic
164#95—431no—
165#95—431no—
166#95—431no—
167#95—431no—
168#95—432no—
169#95—432no—
170#95—432no—
171C24C22×D4312yes—
172C2×D4—22no—
173C2×D4—22no—
174C2×D4—22no—
175C22×C4—431no—
176C22×C4—431no—
177C22×C4—431no—
178C22×C4—431no—
179C22×C4—432no—
180C22×C4—432no—
181C22×C4C22×D4311yescharacteristic
182C22×C4C22×D4311yescharacteristic
183C22×C4C22×D4312yes—
184C22×C4C22×D4311yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—862no—
187C4⋊C4—862no—
188C4⋊C4—1722no—
189C4⋊C4—1722no—
190C4⋊C4—1722no—
191C22⋊C4—42no—
192C22⋊C4—42no—
193C22⋊C4—1722no—
194C22⋊C4—1722no—
195C22⋊C4—1722no—
196C22⋊C4—1722no—
197C42—22no—
198C42—862no—
199C42—862no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23C23×D4311yescharacteristic
208D4—44no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—861no—
219C2×C4—861no—
220C2×C4—862no—
221C2×C4—861no—
222C2×C4—861no—
223C2×C4—862no—
224C2×C4—861no—
225C2×C4—861no—
226C2×C4—862no—
227C2×C4—862no—
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#1062189812yes—
237C2×C4#1062190012yes—
238C2×C4#1062190012yes—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22C2×#1062190011yescharacteristic
247C22C2×#1062190011yescharacteristic
248C22C2×#1062189811yescharacteristic
249C22#1306337011yescharacteristic
250C22#1306337011yescharacteristic
251C22#1306337111yescharacteristic
252C22#1306337211yescharacteristic
253C4—41no—
254C4—42no—
255C4—41no—
256C4—1721no—
257C4—1722no—
258C4—1722no—
259C4—1721no—
260C4—1721no—
261C4—1721no—
262C4#1306331814yes—
263C2—82no—
264C2C2×#1306331811yescharacteristic
265C2#1458350011yescharacteristic
266C2#1458350211yescharacteristic
267C2#1458350311yescharacteristic
268C2#1458351411yescharacteristic
269C2#1458351611yescharacteristic
270C2#1458351811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#390C2
hypercenter#390D43
hypocenterC43#2644
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #14582827C2semidirect
2. #14582827C2semidirect
3. #14582824C2semidirect
4. #14582822C2semidirect
7. #14582798C2semidirect
8. #14582797C2semidirect
9. #14582795C2semidirect
10. #14582745C2semidirect
147. C43#2644semidirect