Finite Group Databasebeta

← #19133511

Subgroups — #19133511

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#14583033C211yesmaximal, characteristic, complemented
3#14582807C211yesmaximal, characteristic, complemented
4#14582634C211yesmaximal, characteristic, complemented
5#14582633C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic, complemented
7C43×#447C211yesmaximal, characteristic, complemented
8C22×C22⋊D43—21no—
9C2×D4×D43—21no—
10C2×#10621882—21no—
11#13063310—21no—
12#13063307—21no—
13#13063299C2211yescharacteristic
14#13063297—21no—
15#13063295—21no—
16#13063293—21no—
17C2×C22⋊Dic43—21no—
18C2×(C2×D43)⋊C4C2211yescharacteristic
19#13063246—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic, complemented
21C43⋊#95C2211yescharacteristic, complemented
22C22×D4×C43C2211yescharacteristic, complemented
23C2×D8×C43—21no—
24#121×C43C2211yescharacteristic
25#102×C43—21no—
26C22⋊C8×C43C2211yescharacteristic, complemented
27C24×C43—21no—
28C23×D43—21no—
29C23×D43D411yescharacteristic
30C2×D4×C43—21no—
31C2×D4×C43—21no—
32C2×D4×C43—21no—
33C2×D4×C43—42no—
34C2×D4×C43D411yescharacteristic, complemented
35C22×C4×C43C2311yescharacteristic
36C2×C22⋊D43—21no—
37C2×C22⋊D43—21no—
38C2×C22⋊D43—21no—
39C2×C22⋊D43—42no—
40C2×C22⋊D43—42no—
41C2×C22⋊D43—42no—
42C22×Dic43—21no—
43C22×Dic43D411yescharacteristic
44D4×D43—42no—
45D4×D43—42no—
46C2×D172—21no—
47C2×D172D411yescharacteristic, complemented
48C2×C4×D43—21no—
49D8×C43—42no—
50C2×C8×C43—21no—
51C4⋊C4×C43D411yescharacteristic, complemented
52C22⋊C4×C43—21no—
53C22⋊Dic43—21no—
54C22⋊Dic43—42no—
55#10621882—42no—
56(C2×D43)⋊C4—21no—
57(C2×D43)⋊C4—21no—
58(C2×D43)⋊C4—21no—
59(C2×D43)⋊C4—21no—
60C4⋊Dic43D411yescharacteristic, complemented
61Dic43⋊C4—21no—
62C2×C43⋊C8—21no—
63C23×C43—22no—
64C23×C43—21no—
65C23×C43—41no—
66C23×C43—41no—
67C23×C43—41no—
68C23×C43—41no—
69C23×C43—41no—
70C23×C43—41no—
71C23×C43C2×D411yescharacteristic
72C22×D43—21no—
73C22×D43—21no—
74C22×D43—21no—
75C22×D43—42no—
76C22×D43—41no—
77C22×D43—41no—
78C22×D43—81no—
79C22×D43—81no—
80C22×D43D812yescomplemented
81D4×C43—22no—
82D4×C43—22no—
83D4×C43—41no—
84D4×C43—41no—
85D4×C43—41no—
86D4×C43—41no—
87D4×C43—41no—
88C2×C4×C43—21no—
89C2×C4×C43—41no—
90C2×C4×C43C2×D411yescharacteristic
91C2×C4×C43C2×D411yescharacteristic
92C22⋊D43—42no—
93C22⋊D43—48no—
94C22⋊D43—41no—
95C22⋊D43—41no—
96C22⋊D43—81no—
97C2×Dic43—22no—
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—41no—
101C2×Dic43—41no—
102C2×Dic43—41no—
103D172—41no—
104D172—42no—
105C4×D43—42no—
106C8×C43—41no—
107C43⋊C8—41no—
108C22×C43—21no—
109C22×C43—21no—
110C22×C43—42no—
111C22×C43—42no—
112C22×C43—41no—
113C22×C43—41no—
114C22×C43—41no—
115C22×C43—42no—
116C22×C43—81no—
117C22×C43—81no—
118C22×C43—81no—
119C22×C43—81no—
120C22×C43#12011yescharacteristic
121C22×C43C2×D811yescharacteristic
122C22×C43AGL(1,ℤ/8)11yescharacteristic
123C2×D43—22no—
124C2×D43—41no—
125C2×D43—41no—
126C2×D43—42no—
127C2×D43—41no—
128C2×D43—41no—
129C2×D43—41no—
130C2×D43—81no—
131C2×D43—84no—
132C4×C43—21no—
133C4×C43—21no—
134C4×C43—41no—
135Dic43—42no—
136Dic43—41no—
137Dic43—41no—
138#1595—431nomaximal, Sylow
139C2×C43—21no—
140C2×C43—21no—
141C2×C43—81no—
142C2×C43—82no—
143C2×C43#44711yescharacteristic
144C2×C43#45311yescharacteristic
145C2×C43B(4,𝔽2)11yescharacteristic
146D43—42no—
147D43—81no—
148#534—431no—
149#447—431no—
150#447D4311yescharacteristic, complemented
151#392—431no—
152#327—431no—
153#327—431no—
154#323—431no—
155C43#159511yescharacteristic, complemented, Sylow
156C22×D4—861no—
157C22×D4—861no—
158C22×D4C2×D4311yescharacteristic, complemented
159C2×D8—21no—
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—21no—
171#102—861no—
172C22⋊C8—431no—
173C22⋊C8C2×D4311yescharacteristic, complemented
174#95—431no—
175C24—21no—
176C24—431no—
177C24—861no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—42no—
182C2×D4—431no—
183C2×D4—861no—
184C2×D4—861no—
185C2×D4—861no—
186C2×D4—861no—
187C2×D4—1722no—
188C2×D4—1722no—
189C2×D4—1722no—
190C2×D4—1722no—
191C2×D4—1722no—
192C2×D4C22⋊D4311yescharacteristic, complemented
193C22×C4—431no—
194C22×C4—861no—
195C22×C4—861no—
196C22×C4C22×D4311yescharacteristic
197D8—42no—
198D8—1722no—
199C2×C8—21no—
200C2×C8—861no—
201C4⋊C4—431no—
202C4⋊C4—861no—
203C4⋊C4C22⋊D4311yescharacteristic, complemented
204C22⋊C4—21no—
205C22⋊C4—861no—
206C22⋊C4—861no—
207C22⋊C4—861no—
208C22⋊C4—861no—
209C22⋊C4—861no—
210C22⋊C4—1722no—
211C23—22no—
212C23—21no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—41no—
219C23—432no—
220C23—861no—
221C23—861no—
222C23—861no—
223C23—3441no—
224C23—3441no—
225C23—1721no—
226C23—1721no—
227C23—1722no—
228C23D4×D4311yescharacteristic
229D4—22no—
230D4—22no—
231D4—41no—
232D4—41no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—3441no—
237D4—1721no—
238D4—1722no—
239D4—1722no—
240D4—1728no—
241D4—1721no—
242D4—1721no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—862no—
246C2×C4—861no—
247C2×C4—861no—
248C2×C4—1722no—
249C2×C4—1721no—
250C2×C4—1721no—
251C2×C4—1721no—
252C2×C4D4×D4311yescharacteristic
253C2×C4C2×C22⋊D4311yescharacteristic
254C8—41no—
255C8—1721no—
256C22—21no—
257C22—21no—
258C22—42no—
259C22—42no—
260C22—41no—
261C22—42no—
262C22—41no—
263C22—41no—
264C22—81no—
265C22—81no—
266C22—81no—
267C22—81no—
268C22—862no—
269C22—3441no—
270C22—3444no—
271C22—1722no—
272C22—1721no—
273C22—1721no—
274C22—1721no—
275C22—1721no—
276C22—1721no—
277C22#1306329311yescharacteristic
278C22D8×D4311yescharacteristic
279C22#1306334911yescharacteristic
280C4—21no—
281C4—21no—
282C4—41no—
283C4—1722no—
284C4—1721no—
285C4—1721no—
286C2—21no—
287C2—21no—
288C2—82no—
289C2—81no—
290C2—3441no—
291C2—1722no—
292C2#1458303111yescharacteristic
293C2#1458306511yescharacteristic
294C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#447C2
socleC22×C43#120
hypercenter#447D43
hypocenterC43#1595
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14583457C2semidirect
2. #14583033C2semidirect
3. #14582807C2semidirect
4. #14582634C2semidirect
5. #14582633C2semidirect
6. #14582622C2semidirect
7. C43×#447C2semidirect
20. C22⋊(C43⋊C8)C22semidirect
21. C43⋊#95C22semidirect
22. C22×D4×C43C22semidirect
26. C22⋊C8×C43C22semidirect
34. C2×D4×C43D4semidirect
47. C2×D172D4semidirect
51. C4⋊C4×C43D4semidirect
60. C4⋊Dic43D4semidirect
80. C22×D43D8semidirect
150. #447D43semidirect
155. C43#1595semidirect
158. C22×D4C2×D43semidirect
173. C22⋊C8C2×D43semidirect
192. C2×D4C22⋊D43semidirect
203. C4⋊C4C22⋊D43semidirect