Finite Group Databasebeta

← #19134542

Subgroups — #19134542

Order 5504.

670 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#13063370C211yesmaximal, characteristic
2C2×#13063240C211yesmaximal, characteristic, complemented
3C2×#13063239C212yesmaximal, complemented
4#14582778C212yesmaximal, complemented
5C43×#386C211yesmaximal, characteristic, complemented
6#13063370—22no—
7#13063370—24no—
8#13063370C414yescomplemented
9C2×#10621898—21no—
10C2×#10621900—22no—
11C22×C22⋊D43—21no—
12C22×C22⋊D43C2212yes—
13C2×D4×D43—22no—
14C2×C22⋊Dic43C2212yescomplemented
15C2×(C2×D43)⋊C4—22no—
16#13063240—22no—
17#13063239—24no—
18C43⋊#95—22no—
19C22×D4×C43C2211yescharacteristic
20C23×C4×C43C2211yescharacteristic, complemented
21C2×C22⋊C4×C43—21no—
22C2×C22⋊C4×C43C2211yescharacteristic, complemented
23#95×C43—21no—
24C24×C43D411yescharacteristic
25C24×C43C2311yescharacteristic
26C23×D43—21no—
27C23×D43D412yes—
28C2×D4×C43—22no—
29C2×D4×C43—22no—
30C2×D4×C43C2×C412yes—
31C2×D4×C43D412yes—
32C22×C4×C43—21no—
33C22×C4×C43—22no—
34C22×C4×C43—21no—
35C22×C4×C43—42no—
36C22×C4×C43D411yescharacteristic
37C2×C22⋊D43—22no—
38C2×C22⋊D43—24no—
39C2×C22⋊D43—24no—
40C2×C22⋊D43—22no—
41C2×C22⋊D43—22no—
42C2×C22⋊D43—22no—
43C2×C22⋊D43—22no—
44C2×C22⋊D43C2×C414yes—
45C2×C22⋊D43D414yes—
46C22×Dic43—21no—
47C22×Dic43—22no—
48C22×Dic43D412yes—
49#10621900—28no—
50#10621900—28no—
51D4×D43—28no—
52D4×D43—28no—
53#10621898—24no—
54#10621898—24no—
55C2×D172—21no—
56C2×C4×D43—22no—
57C2×Dic86—21no—
58C22⋊C4×C43—22no—
59C22⋊C4×C43—42no—
60C22⋊Dic43—22no—
61C22⋊Dic43—22no—
62(C2×D43)⋊C4—44no—
63C23×C43—21no—
64C23×C43—21no—
65C23×C43—41no—
66C23×C43—41no—
67C23×C43—41no—
68C23×C43—41no—
69C23×C43C22⋊C412yescomplemented
70C23×C43C22×C411yescharacteristic
71C23×C43C2×D411yescharacteristic
72C23×C43C2×D412yes—
73C23×C43C2×D412yes—
74C23×C43C2×D411yescharacteristic
75C22×D43—22no—
76C22×D43—24no—
77C22×D43—22no—
78C22×D43—42no—
79C22×D43—42no—
80C22×D43—81no—
81C22×D43—81no—
82C22×D43C22⋊C414yescomplemented
83D4×C43—24no—
84D4×C43—24no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—24no—
88C2×C4×C43—22no—
89C2×C4×C43—42no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43C22⋊C412yescomplemented
96C22⋊D43—28no—
97C22⋊D43—24no—
98C22⋊D43—24no—
99C22⋊D43—24no—
100C22⋊D43—24no—
101C2×Dic43—24no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—42no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43C22⋊C414yescomplemented
108D172—24no—
109C4×D43—28no—
110Dic86—24no—
111C22×C43—22no—
112C22×C43—21no—
113C22×C43—22no—
114C22×C43—21no—
115C22×C43—22no—
116C22×C43—41no—
117C22×C43—41no—
118C22×C43—42no—
119C22×C43—42no—
120C22×C43—41no—
121C22×C43—41no—
122C22×C43—81no—
123C22×C43C2×C22⋊C412yes—
124C22×C43C2×C22⋊C411yescharacteristic
125C22×C43#12011yescharacteristic
126C22×C43#12011yescharacteristic
127C22×C43#12012yes—
128C2×D43—24no—
129C2×D43—42no—
130C2×D43—42no—
131C2×D43—44no—
132C2×D43—82no—
133C2×D43—84no—
134C4×C43—22no—
135C4×C43—42no—
136C4×C43—81no—
137Dic43—24no—
138Dic43—82no—
139#1790—431nomaximal, Sylow
140C2×C43—22no—
141C2×C43—21no—
142C2×C43—22no—
143C2×C43—21no—
144C2×C43—42no—
145C2×C43#37911yescharacteristic
146C2×C43B(4,𝔽2)11yescharacteristic
147C2×C43#45811yescharacteristic
148D43—44no—
149C2×H(5,𝔽2)—431no—
150C2×#99—431no—
151C2×#99—432no—
152#386—432no—
153#386D4311yescharacteristic, complemented
154C43#179011yescharacteristic, complemented, Sylow
155H(5,𝔽2)—434no—
156H(5,𝔽2)—864no—
157H(5,𝔽2)—862no—
158C2×#41—862no—
159C2×#41—861no—
160C22×D4—432no—
161C22×D4—862no—
162C22×D4—861no—
163C22×D4C2×D4311yescharacteristic
164C23×C4C2×D4311yescharacteristic, complemented
165C2×C22⋊C4—21no—
166C2×C22⋊C4—432no—
167C2×C22⋊C4—862no—
168C2×C22⋊C4C2×D4311yescharacteristic, complemented
169#99—864no—
170#99—862no—
171#95—21no—
172#95—862no—
173C24—432no—
174C24—861no—
175C24C22⋊D4311yescharacteristic
176C24C22×D4311yescharacteristic
177#41—864no—
178#41—868no—
179#41—868no—
180#41—864no—
181C2×Q8—861no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—434no—
185C2×D4—434no—
186C2×D4—861no—
187C2×D4—868no—
188C2×D4—868no—
189C2×D4—862no—
190C2×D4—864no—
191C2×D4—864no—
192C2×D4—862no—
193C2×D4—862no—
194C2×D4—862no—
195C2×D4—862no—
196C2×D4C4×D4312yes—
197C2×D4D17212yes—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—42no—
202C22×C4—432no—
203C22×C4—862no—
204C22×C4—861no—
205C22×C4—862no—
206C22×C4C22⋊D4311yescharacteristic
207C22⋊C4—22no—
208C22⋊C4—42no—
209C22⋊C4—862no—
210C22⋊C4—862no—
211C22⋊C4—1724no—
212C23—21no—
213C23—21no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—434no—
219C23—864no—
220C23—862no—
221C23—862no—
222C23—3441no—
223C23—3441no—
224C23—1722no—
225C23—1722no—
226C23(C2×D43)⋊C412yescomplemented
227C23C2×C4×D4311yescharacteristic
228C23C2×D17211yescharacteristic
229C23D4×D4312yes—
230C23D4×D4312yes—
231C23C2×C22⋊D4311yescharacteristic
232Q8—864no—
233D4—24no—
234D4—24no—
235D4—864no—
236D4—868no—
237D4—864no—
238D4—864no—
239D4—864no—
240D4—864no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—24no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—434no—
252C2×C4—868no—
253C2×C4—864no—
254C2×C4—862no—
255C2×C4—862no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4(C2×D43)⋊C412yescomplemented
260C22—21no—
261C22—22no—
262C22—21no—
263C22—22no—
264C22—22no—
265C22—41no—
266C22—41no—
267C22—42no—
268C22—42no—
269C22—41no—
270C22—41no—
271C22—81no—
272C22—864no—
273C22—3442no—
274C22—3444no—
275C22—1724no—
276C22—1722no—
277C22—1722no—
278C22C22⋊C4×D4312yes—
279C22C2×(C2×D43)⋊C411yescharacteristic
280C22#1306329311yescharacteristic
281C22#1306329311yescharacteristic
282C22#1306329512yes—
283C4—22no—
284C4—42no—
285C4—81no—
286C4—864no—
287C4—3442no—
288C2—21no—
289C2—22no—
290C2—21no—
291C2—22no—
292C2—42no—
293C2—1724no—
294C2#1458275411yescharacteristic
295C2#1458308511yescharacteristic
296C2#1458308811yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC43×#386C2
socleC22×C43#120
hypercenter#386D43
hypocenterC43#1790
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#13063240C2semidirect
3. C2×#13063239C2semidirect
4. #14582778C2semidirect
5. C43×#386C2semidirect
8. #13063370C4semidirect
14. C2×C22⋊Dic43C22semidirect
20. C23×C4×C43C22semidirect
22. C2×C22⋊C4×C43C22semidirect
69. C23×C43C22⋊C4semidirect
82. C22×D43C22⋊C4semidirect
95. C2×C4×C43C22⋊C4semidirect
107. C2×Dic43C22⋊C4semidirect
153. #386D43semidirect
154. C43#1790semidirect
164. C23×C4C2×D43semidirect
168. C2×C22⋊C4C2×D43semidirect
226. C23(C2×D43)⋊C4semidirect
259. C2×C4(C2×D43)⋊C4semidirect