Finite Group Databasebeta

← #19133161

Subgroups — #19133161

Order 5504.

340 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 71 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#121×D43C211yesmaximal, characteristic
2C22⋊C8×D43C211yesmaximal, characteristic, complemented
3#14582758C211yesmaximal, characteristic, complemented
4#14582634C211yesmaximal, characteristic, complemented
5#14582633C211yesmaximal, characteristic, complemented
6#14582632C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C2×D4×D43—21no—
9C2×D4×D43C411yescharacteristic, complemented
10C22×C4×D43C2211yescharacteristic
11C2×C8×D43—21no—
12#13063300C411yescharacteristic, complemented
13#13063299C2211yescharacteristic
14#13063298—21no—
15#13063297—21no—
16#13063296C411yescharacteristic, complemented
17C2×Dic43⋊C4—21no—
18C4⋊C4×D43C411yescharacteristic, complemented
19C2×(C2×D43)⋊C4—21no—
20C22⋊C4×D43—21no—
21C22⋊(C43⋊C8)C2211yescharacteristic, complemented
22(C2×D43)⋊C8—21no—
23C43⋊#95C2211yescharacteristic, complemented
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic, complemented
26#95×C43C2211yescharacteristic, complemented
27C23×D43—21no—
28C23×D43D411yescharacteristic
29C2×D4×C43—21no—
30C2×D4×C43C2×C411yescharacteristic
31C22×C4×C43—21no—
32C22×C4×C43C2311yescharacteristic
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C2×C22⋊D43—21no—
36C22×Dic43—21no—
37C22×Dic43D411yescharacteristic
38D4×D43—42no—
39D4×D43—42no—
40D4×D43—42no—
41C2×D172—21no—
42C2×D172C2×C411yescharacteristic
43C2×C4×D43—21no—
44C2×C4×D43—42no—
45C2×C4×D43C2×C411yescharacteristic
46C2×C4×D43C2×C411yescharacteristic
47C2×C4×D43D411yescharacteristic
48C2×C4×D43D411yescharacteristic
49C2×C8×C43—21no—
50C4⋊C4×C43C2×C411yescharacteristic
51C22⋊C4×C43—21no—
52C22⋊Dic43—21no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—42no—
56C4⋊Dic43C2×C411yescharacteristic
57Dic43⋊C4—21no—
58Dic43⋊C4—42no—
59C2×C43⋊C8—21no—
60C8×D43—42no—
61C23×C43—21no—
62C23×C43C2×D411yescharacteristic
63C22×D43—21no—
64C22×D43—41no—
65C22×D43—41no—
66C22×D43—42no—
67C22×D43—42no—
68C22×D43—42no—
69C22×D43C22⋊C411yescharacteristic
70C22×D43C22⋊C411yescharacteristic
71C22×D43D812yes—
72C22×D43SD1612yes—
73D4×C43—41no—
74D4×C43—41no—
75D4×C43—41no—
76C2×C4×C43—21no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43C22×C411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C22⋊D43—41no—
84C22⋊D43—41no—
85C22⋊D43—42no—
86C22⋊D43—42no—
87C2×Dic43—22no—
88C2×Dic43—21no—
89C2×Dic43—41no—
90C2×Dic43—41no—
91C2×Dic43—41no—
92C2×Dic43C22⋊C411yescharacteristic
93C2×Dic43C22⋊C411yescharacteristic
94D172—41no—
95D172—42no—
96C4×D43—22no—
97C4×D43—22no—
98C4×D43—41no—
99C4×D43—41no—
100C4×D43—42no—
101C8×C43—41no—
102C43⋊C8—41no—
103C22×C43—21no—
104C22×C43—21no—
105C22×C43—41no—
106C22×C43—41no—
107C22×C43—41no—
108C22×C43C2×C22⋊C411yescharacteristic
109C22×C43C2×D811yescharacteristic
110C22×C43C2×SD1611yescharacteristic
111C2×D43—21no—
112C2×D43—21no—
113C2×D43—21no—
114C2×D43—21no—
115C2×D43—42no—
116C2×D43—42no—
117C2×D43—41no—
118C2×D43—41no—
119C2×D43—41no—
120C2×D43—84no—
121C2×D43#10212yes—
122C2×D43#10212yes—
123C4×C43—21no—
124C4×C43—21no—
125C4×C43—41no—
126C4×C43—81no—
127Dic43—21no—
128Dic43—41no—
129Dic43—81no—
130Dic43#9912yes—
131#1519—431nomaximal, Sylow
132C2×C43—21no—
133C2×C43—21no—
134C2×C43—81no—
135C2×C43C2×#9911yescharacteristic
136C2×C43C2×#10211yescharacteristic
137C2×C43#42111yescharacteristic
138D43—22no—
139D43—22no—
140D43—81no—
141C2×#121—431no—
142C2×C22⋊C8—431no—
143#380—431no—
144#327—431no—
145#327—431no—
146#327—431no—
147#327D4311yescharacteristic, complemented
148C43#151911yescharacteristic, complemented, Sylow
149C22×D4—431no—
150C22×D4—861no—
151C23×C4—431no—
152C22×C8—861no—
153#121—431no—
154#121—431no—
155#121—431no—
156#121—861no—
157#121—861no—
158#121C2×D4311yescharacteristic
159C2×C4⋊C4—431no—
160C2×C4⋊C4—861no—
161C2×C22⋊C4—861no—
162C2×C22⋊C4—861no—
163C22⋊C8—431no—
164C22⋊C8—861no—
165C22⋊C8C2×D4311yescharacteristic, complemented
166#95—431no—
167#95C2×D4311yescharacteristic, complemented
168C24—431no—
169C24—861no—
170C2×D4—21no—
171C2×D4—431no—
172C2×D4—861no—
173C2×D4—861no—
174C2×D4—861no—
175C2×D4—861no—
176C2×D4—1722no—
177C2×D4—1722no—
178C2×D4—1722no—
179C2×D4C4×D4311yescharacteristic
180C22×C4—21no—
181C22×C4—431no—
182C22×C4—431no—
183C22×C4—431no—
184C22×C4—431no—
185C22×C4—431no—
186C22×C4—861no—
187C22×C4—861no—
188C22×C4—1722no—
189C22×C4C22×D4311yescharacteristic
190C2×C8—21no—
191C2×C8—861no—
192C2×C8—1722no—
193C4⋊C4—431no—
194C4⋊C4—861no—
195C4⋊C4—1722no—
196C4⋊C4C4×D4311yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—861no—
199C22⋊C4—861no—
200C22⋊C4—861no—
201C22⋊C4—1722no—
202C23—21no—
203C23—431no—
204C23—431no—
205C23—432no—
206C23—432no—
207C23—861no—
208C23—1721no—
209C23—1721no—
210C23—1722no—
211C23—1722no—
212C23—1722no—
213C23D4×D4311yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—1721no—
218D4—1722no—
219D4—1722no—
220D4—1722no—
221D4—1721no—
222D4—1721no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—431no—
229C2×C4—431no—
230C2×C4—862no—
231C2×C4—862no—
232C2×C4—862no—
233C2×C4—861no—
234C2×C4—1721no—
235C2×C4—1721no—
236C2×C4—1722no—
237C2×C4—1721no—
238C2×C4—1721no—
239C2×C4—1721no—
240C2×C4C2×C4×D4311yescharacteristic
241C2×C4D4×D4311yescharacteristic
242C8—41no—
243C8—1721no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—432no—
250C22—432no—
251C22—861no—
252C22—861no—
253C22—861no—
254C22—861no—
255C22—3444no—
256C22—1722no—
257C22—1722no—
258C22—1721no—
259C22—1721no—
260C22—1721no—
261C22C22⋊C4×D4311yescharacteristic
262C22D8×D4311yescharacteristic
263C22SD16×D4311yescharacteristic
264C4—21no—
265C4—21no—
266C4—41no—
267C4—81no—
268C4—432no—
269C4—861no—
270C4—3441no—
271C4—1721no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—862no—
276C2—862no—
277C2—3441no—
278C2#99×D4311yescharacteristic
279C2#102×D4311yescharacteristic
280C2#1458291411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43C2×C22⋊C4
hypercenter#327D43
hypocenterC43#1519
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D43C2semidirect
3. #14582758C2semidirect
4. #14582634C2semidirect
5. #14582633C2semidirect
6. #14582632C2semidirect
7. C43×#327C2semidirect
9. C2×D4×D43C4semidirect
12. #13063300C4semidirect
16. #13063296C4semidirect
18. C4⋊C4×D43C4semidirect
21. C22⋊(C43⋊C8)C22semidirect
23. C43⋊#95C22semidirect
25. C22⋊C8×C43C22semidirect
26. #95×C43C22semidirect
147. #327D43semidirect
148. C43#1519semidirect
165. C22⋊C8C2×D43semidirect
167. #95C2×D43semidirect