Finite Group Databasebeta

← #19134693

Subgroups — #19134693

Order 5504.

306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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#117×D43C211yesmaximal, characteristic
2#14582862C211yesmaximal, characteristic
3C4×(C2×D43)⋊C4C211yesmaximal, characteristic
4#14582660C211yesmaximal, characteristic, complemented
5#14582659C211yesmaximal, characteristic, complemented
6#14582658C211yesmaximal, characteristic, complemented
7C43×#339C211yesmaximal, characteristic, complemented
8C22×C4×D43C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10#13063284C2211yescharacteristic
11#13063283C411yescharacteristic, complemented
12#13063283C411yescharacteristic, complemented
13#13063282—21no—
14#13063281—21no—
15C4⋊C4×D43C411yescharacteristic, complemented
16C4⋊C4×D43C411yescharacteristic, complemented
17C2×(C2×D43)⋊C4—21no—
18C22⋊C4×D43—21no—
19C2×C4×Dic43C2211yescharacteristic
20C42×D43—21no—
21(C2×D43)⋊C8—21no—
22(C2×D43)⋊C8—21no—
23C43⋊#95—21no—
24C2×M16×C43C2211yescharacteristic
25#117×C43C2211yescharacteristic
26C2×C42×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43C2311yescharacteristic
30C22×Dic43—21no—
31C22×Dic43D411yescharacteristic
32C2×C4×D43—21no—
33C2×C4×D43—21no—
34C2×C4×D43—21no—
35C2×C4×D43—21no—
36C2×C4×D43—21no—
37C2×C4×D43—21no—
38C2×C4×D43C2×C411yescharacteristic
39C2×C4×D43C2×C411yescharacteristic
40C2×C4×D43D411yescharacteristic
41C2×C4×D43D411yescharacteristic
42M16×C43—21no—
43M16×C43—21no—
44C2×C8×C43—21no—
45C4⋊C4×C43C2×C411yescharacteristic
46C4⋊C4×C43C2×C411yescharacteristic
47C22⋊C4×C43—21no—
48C42×C43—21no—
49C42×C43—21no—
50C42×C43—21no—
51C22⋊Dic43—21no—
52(C2×D43)⋊C4—24no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55C4⋊Dic43C2×C411yescharacteristic
56C4⋊Dic43C2×C411yescharacteristic
57Dic43⋊C4—21no—
58Dic43⋊C4—21no—
59C4×Dic43—21no—
60C4×Dic43—21no—
61C4×Dic43—21no—
62C4×Dic43—21no—
63C4×Dic43—21no—
64#10621877—21no—
65#10621877—21no—
66C2×C43⋊C8—21no—
67C23×C43C2×D411yescharacteristic
68C22×D43—21no—
69C22×D43—21no—
70C22×D43—22no—
71C22×D43—41no—
72C22×D43C22⋊C411yescharacteristic
73C22×D43C22⋊C411yescharacteristic
74C2×C4×C43—22no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43C22×C411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43#4111yescharacteristic
82C2×C4×C43#4111yescharacteristic
83C2×C4×C43#4111yescharacteristic
84C2×C4×C43#4111yescharacteristic
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—22no—
88C2×Dic43—21no—
89C2×Dic43—21no—
90C2×Dic43—41no—
91C2×Dic43—41no—
92C2×Dic43C22⋊C411yescharacteristic
93C2×Dic43C22⋊C411yescharacteristic
94C4×D43—21no—
95C4×D43—21no—
96C4×D43—21no—
97C4×D43—21no—
98C4×D43—21no—
99C4×D43—21no—
100C4×D43—21no—
101C4×D43—21no—
102C4×D43—42no—
103C4×D43—42no—
104C8×C43—41no—
105C43⋊C8—41no—
106C22×C43—21no—
107C22×C43—21no—
108C22×C43C2×C22⋊C411yescharacteristic
109C22×C43#12311yescharacteristic
110C22×C43#12311yescharacteristic
111C2×D43—21no—
112C2×D43—21no—
113C2×D43—21no—
114C2×D43—21no—
115C2×D43—21no—
116C2×D43—42no—
117C2×D43—42no—
118C2×D43#10412yes—
119C4×C43—42no—
120C4×C43—41no—
121C4×C43—41no—
122C4×C43#11711yescharacteristic
123C4×C43#11711yescharacteristic
124C4×C43#12311yescharacteristic
125C4×C43#12311yescharacteristic
126Dic43—21no—
127Dic43—21no—
128Dic43—42no—
129Dic43—41no—
130Dic43—41no—
131#1826—431nomaximal, Sylow
132C2×C43—21no—
133C2×C43—21no—
134C2×C43#38111yescharacteristic
135C2×C43C2×#10411yescharacteristic
136C2×C43#42111yescharacteristic
137D43—22no—
138D43—41no—
139C2×#117—431no—
140#407—431no—
141C4×C22⋊C4—431no—
142#339—431no—
143#339—431no—
144#339—431no—
145#339D4311yescharacteristic, complemented
146C43#182611yescharacteristic, complemented, Sylow
147C23×C4—431no—
148C2×M16—431no—
149C2×M16C2×D4311yescharacteristic
150#117—431no—
151#117—431no—
152#117—431no—
153#117—861no—
154#117—861no—
155#117C2×D4311yescharacteristic
156C2×C4⋊C4—431no—
157C2×C4⋊C4—431no—
158C2×C22⋊C4—861no—
159C2×C22⋊C4—861no—
160C2×C42—431no—
161C2×C42—861no—
162C2×C42C2×D4311yescharacteristic
163C22⋊C8—861no—
164C22⋊C8—861no—
165#95—861no—
166C24—431no—
167C22×C4—21no—
168C22×C4—431no—
169C22×C4—431no—
170C22×C4—431no—
171C22×C4—431no—
172C22×C4—431no—
173C22×C4—861no—
174C22×C4—861no—
175C22×C4—861no—
176C22×C4—861no—
177C22×C4—861no—
178C22×C4—861no—
179C22×C4—861no—
180C22×C4C22×D4311yescharacteristic
181M16—21no—
182M16—21no—
183M16—861no—
184M16—861no—
185C2×C8—21no—
186C2×C8—861no—
187C4⋊C4—431no—
188C4⋊C4—431no—
189C4⋊C4—861no—
190C4⋊C4—861no—
191C4⋊C4C4×D4311yescharacteristic
192C4⋊C4C4×D4311yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—861no—
195C22⋊C4—861no—
196C22⋊C4—864no—
197C22⋊C4—861no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—861no—
202C42—861no—
203C42—861no—
204C42—861no—
205C42—861no—
206C23—431no—
207C23—431no—
208C23—862no—
209C23—861no—
210C23—861no—
211C23—1721no—
212C23D4×D4311yescharacteristic
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—431no—
219C2×C4—431no—
220C2×C4—861no—
221C2×C4—861no—
222C2×C4—861no—
223C2×C4—861no—
224C2×C4—861no—
225C2×C4—861no—
226C2×C4—861no—
227C2×C4—861no—
228C2×C4—861no—
229C2×C4—861no—
230C2×C4—862no—
231C2×C4—861no—
232C2×C4—861no—
233C2×C4—1722no—
234C2×C4—1722no—
235C2×C4—1721no—
236C2×C4—1721no—
237C2×C4C2×C4×D4311yescharacteristic
238C2×C4#1062189811yescharacteristic
239C2×C4#1062189811yescharacteristic
240C2×C4D4×D4311yescharacteristic
241C2×C4#1062190011yescharacteristic
242C2×C4#1062190211yescharacteristic
243C8—41no—
244C8—1721no—
245C22—21no—
246C22—21no—
247C22—432no—
248C22—861no—
249C22—861no—
250C22—861no—
251C22—861no—
252C22—861no—
253C22—1722no—
254C22—1722no—
255C22C22⋊C4×D4311yescharacteristic
256C22#1306330711yescharacteristic
257C22#1306331011yescharacteristic
258C4—42no—
259C4—41no—
260C4—41no—
261C4—861no—
262C4—861no—
263C4—1722no—
264C4—1721no—
265C4—1721no—
266C4#1306328211yescharacteristic
267C4#1306328311yescharacteristic
268C4#1306330711yescharacteristic
269C4#1306331011yescharacteristic
270C2—21no—
271C2—21no—
272C2—862no—
273C2—1721no—
274C2#1458276111yescharacteristic
275C2#104×D4311yescharacteristic
276C2#1458291411yescharacteristic
subgroupG/H
centerC2×C4D4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#339C2
socleC22×C43C2×C22⋊C4
hypercenter#339D43
hypocenterC43#1826
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. #14582660C2semidirect
5. #14582659C2semidirect
6. #14582658C2semidirect
7. C43×#339C2semidirect
11. #13063283C4semidirect
12. #13063283C4semidirect
15. C4⋊C4×D43C4semidirect
16. C4⋊C4×D43C4semidirect
145. #339D43semidirect
146. C43#1826semidirect