Finite Group Databasebeta

← #19133514

Subgroups — #19133514

Order 5504.

368 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 51 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#14583457C211yesmaximal, characteristic, complemented
2#14583035C211yesmaximal, characteristic, complemented
3#14583032C211yesmaximal, characteristic, complemented
4#14582809C211yesmaximal, characteristic, complemented
5#14582632C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C22×D172—21no—
9C22×D172C2211yescharacteristic, complemented
10C2×D4×D43—21no—
11C2×D344—21no—
12C2×#10621882—21no—
13#13063310—21no—
14#13063307—21no—
15#13063299C2211yescharacteristic
16#13063297—21no—
17#13063295—21no—
18#13063293—21no—
19C2×(C2×D43)⋊C4—21no—
20C2×(C2×D43)⋊C4C2211yescharacteristic
21#13063247—21no—
22#13063245—21no—
23C22⋊(C43⋊C8)C2211yescharacteristic, complemented
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic, complemented
26#95×C43C2211yescharacteristic, complemented
27C23×D43—21no—
28C23×D43—21no—
29C23×D43D411yescharacteristic
30C2×D4×C43—21no—
31C2×D4×C43D411yescharacteristic, complemented
32C22×C4×C43—21no—
33C22×C4×C43C2311yescharacteristic
34C2×C22⋊D43—21no—
35C2×C22⋊D43—21no—
36C2×C22⋊D43—21no—
37C22×Dic43D411yescharacteristic
38D4×D43—42no—
39D4×D43—42no—
40C2×D172—21no—
41C2×D172—21no—
42C2×D172—21no—
43C2×D172—42no—
44C2×D172—42no—
45C2×D172—42no—
46C2×D172—42no—
47C2×D172D411yescharacteristic, complemented
48C2×C4×D43—21no—
49C2×C8×C43—21no—
50C4⋊C4×C43D411yescharacteristic, complemented
51C22⋊C4×C43—21no—
52C22⋊Dic43—21no—
53#10621882—42no—
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—21no—
56(C2×D43)⋊C4—21no—
57(C2×D43)⋊C4—21no—
58(C2×D43)⋊C4—42no—
59C4⋊Dic43D411yescharacteristic, complemented
60Dic43⋊C4—21no—
61C2×C43⋊C8—21no—
62D344—42no—
63C23×C43—21no—
64C23×C43C2×D411yescharacteristic
65C22×D43—21no—
66C22×D43—21no—
67C22×D43—22no—
68C22×D43—21no—
69C22×D43—42no—
70C22×D43—41no—
71C22×D43—41no—
72C22×D43—41no—
73C22×D43—41no—
74C22×D43—41no—
75C22×D43—41no—
76C22×D43—41no—
77C22×D43—41no—
78C22×D43—81no—
79C22×D43—81no—
80C22×D43D812yescomplemented
81D4×C43—41no—
82D4×C43—41no—
83D4×C43—41no—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43C2×D411yescharacteristic
90C2×C4×C43C2×D411yescharacteristic
91C22⋊D43—42no—
92C22⋊D43—41no—
93C22⋊D43—41no—
94C22⋊D43—81no—
95C2×Dic43—21no—
96C2×Dic43—21no—
97C2×Dic43—41no—
98D172—22no—
99D172—22no—
100D172—41no—
101D172—41no—
102D172—41no—
103D172—42no—
104D172—48no—
105C4×D43—42no—
106C8×C43—41no—
107C43⋊C8—41no—
108C22×C43—21no—
109C22×C43—21no—
110C22×C43—41no—
111C22×C43—41no—
112C22×C43—41no—
113C22×C43#12011yescharacteristic
114C22×C43C2×D811yescharacteristic
115C22×C43AGL(1,ℤ/8)11yescharacteristic
116C2×D43—22no—
117C2×D43—41no—
118C2×D43—41no—
119C2×D43—42no—
120C2×D43—42no—
121C2×D43—42no—
122C2×D43—41no—
123C2×D43—41no—
124C2×D43—42no—
125C2×D43—41no—
126C2×D43—81no—
127C2×D43—84no—
128C2×D43—81no—
129C2×D43—81no—
130C2×D43—81no—
131C2×D43—81no—
132C4×C43—21no—
133C4×C43—21no—
134C4×C43—42no—
135C4×C43—41no—
136Dic43—41no—
137Dic43—41no—
138#1595—431nomaximal, Sylow
139C2×C43—21no—
140C2×C43—21no—
141C2×C43—81no—
142C2×C43#44711yescharacteristic
143C2×C43#45311yescharacteristic
144C2×C43B(4,𝔽2)11yescharacteristic
145D43—42no—
146D43—82no—
147D43—81no—
148#534—431no—
149#447—431no—
150#447—431no—
151#392—431no—
152#327—431no—
153#327D4311yescharacteristic, complemented
154#323—431no—
155C43#159511yescharacteristic, complemented, Sylow
156C22×D4—431no—
157C22×D4—861no—
158C22×D4—861no—
159C2×D8—861no—
160C2×D8—861no—
161#123—861no—
162#123—861no—
163#121—431no—
164#121—861no—
165#121C2×D4311yescharacteristic
166#120—861no—
167#120—861no—
168C2×C22⋊C4—431no—
169C2×C22⋊C4—861no—
170#102—861no—
171#102—861no—
172C22⋊C8—431no—
173C22⋊C8C2×D4311yescharacteristic, complemented
174#95C2×D4311yescharacteristic, complemented
175C24—431no—
176C24—861no—
177C24—861no—
178C2×D4—21no—
179C2×D4—431no—
180C2×D4—861no—
181C2×D4—861no—
182C2×D4—861no—
183C2×D4—861no—
184C2×D4—861no—
185C2×D4—861no—
186C2×D4—1722no—
187C2×D4—1722no—
188C2×D4—1722no—
189C2×D4—1722no—
190C2×D4—1722no—
191C2×D4—1722no—
192C2×D4D17211yescharacteristic, complemented
193C22×C4—21no—
194C22×C4—431no—
195C22×C4—861no—
196C22×C4C22×D4311yescharacteristic
197D8—1722no—
198D8—1722no—
199C2×C8—21no—
200C2×C8—861no—
201C4⋊C4—431no—
202C4⋊C4—861no—
203C4⋊C4D17211yescharacteristic, complemented
204C22⋊C4—21no—
205C22⋊C4—861no—
206C22⋊C4—861no—
207C22⋊C4—861no—
208C22⋊C4—861no—
209C22⋊C4—861no—
210C22⋊C4—1722no—
211C23—21no—
212C23—432no—
213C23—862no—
214C23—861no—
215C23—861no—
216C23—861no—
217C23—3441no—
218C23—3441no—
219C23—1721no—
220C23—1721no—
221C23—1721no—
222C23—1721no—
223C23—1721no—
224C23—1722no—
225C23—1721no—
226C23—1721no—
227C23—1721no—
228C23D4×D4311yescharacteristic
229D4—41no—
230D4—41no—
231D4—41no—
232D4—862no—
233D4—862no—
234D4—3441no—
235D4—1721no—
236D4—1721no—
237D4—1721no—
238D4—1722no—
239D4—1728no—
240D4—1722no—
241D4—1721no—
242D4—1721no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—861no—
249C2×C4—861no—
250C2×C4—1722no—
251C2×C4—1721no—
252C2×C4C2×D17211yescharacteristic
253C2×C4D4×D4311yescharacteristic
254C8—41no—
255C8—1721no—
256C22—21no—
257C22—21no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—862no—
262C22—3441no—
263C22—3441no—
264C22—3441no—
265C22—3444no—
266C22—3441no—
267C22—3441no—
268C22—1722no—
269C22—1722no—
270C22—1722no—
271C22—1721no—
272C22—1722no—
273C22—1721no—
274C22—1721no—
275C22—1721no—
276C22—1721no—
277C22#1306329511yescharacteristic
278C22D8×D4311yescharacteristic
279C22#1306335211yescharacteristic
280C4—21no—
281C4—21no—
282C4—42no—
283C4—41no—
284C4—1721no—
285C4—1721no—
286C2—21no—
287C2—21no—
288C2—81no—
289C2—3442no—
290C2—3441no—
291C2—1722no—
292C2#1458303411yescharacteristic
293C2#1458306811yescharacteristic
294C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43#120
hypercenter#327D43
hypocenterC43#1595
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
1. #14583457C2semidirect
2. #14583035C2semidirect
3. #14583032C2semidirect
4. #14582809C2semidirect
5. #14582632C2semidirect
6. #14582622C2semidirect
7. C43×#327C2semidirect
9. C22×D172C22semidirect
23. C22⋊(C43⋊C8)C22semidirect
25. C22⋊C8×C43C22semidirect
26. #95×C43C22semidirect
31. C2×D4×C43D4semidirect
47. C2×D172D4semidirect
50. C4⋊C4×C43D4semidirect
59. C4⋊Dic43D4semidirect
80. C22×D43D8semidirect
153. #327D43semidirect
155. C43#1595semidirect
173. C22⋊C8C2×D43semidirect
174. #95C2×D43semidirect
192. C2×D4D172semidirect
203. C4⋊C4D172semidirect