Finite Group Databasebeta

← #19137576

Subgroups — #19137576

Order 5504.

928 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 209 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×#13063293C211yesmaximal, characteristic
2C2×(C22⋊D43)⋊C4C212yesmaximal, complemented
3C2×C22⋊C4×D43C212yesmaximal, complemented
4#14582787C212yesmaximal, complemented
5#14582779C211yesmaximal, characteristic, complemented
6#14582775C212yesmaximal, complemented
7#14582770C212yesmaximal, complemented
8C4×(C2×D43)⋊C4C212yesmaximal, complemented
9C43×#390C211yesmaximal, characteristic, complemented
10C24×D43C2211yescharacteristic
11C22×C22⋊D43C2212yes—
12C23×Dic43C2211yescharacteristic, complemented
13C22×C4×D43C2212yes—
14C22×C4×D43C2212yes—
15#13063293C418yescomplemented
16(C22⋊D43)⋊C4—28no—
17C2×Dic43⋊C4C2212yescomplemented
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2211yescharacteristic
20C2×C22⋊Dic43C2211yescharacteristic, complemented
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2212yes—
24C22⋊C4×D43—28no—
25C2×C4×Dic43C2212yescomplemented
26C43⋊#95C2212yescomplemented
27C43⋊#95C2212yescomplemented
28C43⋊#95C2212yescomplemented
29C22×D4×C43C2211yescharacteristic
30C2×C4⋊C4×C43C2211yescharacteristic, complemented
31C2×C22⋊C4×C43C2212yes—
32C2×C22⋊C4×C43C2212yescomplemented
33C2×C42×C43C2211yescharacteristic, complemented
34C24×C43C2311yescharacteristic
35C24×C43C2311yescharacteristic
36C23×D43—24no—
37C23×D43—24no—
38C23×D43—41no—
39C23×D43—41no—
40C23×D43C2×C414yescomplemented
41C23×D43C2312yes—
42C2×D4×C43—41no—
43C2×D4×C43—41no—
44C2×D4×C43C2×C414yescomplemented
45C22×C4×C43C2312yes—
46C22×C4×C43C2311yescharacteristic
47C22×C4×C43C2312yes—
48C2×C22⋊D43—24no—
49C2×C22⋊D43—24no—
50C2×C22⋊D43C2×C418yescomplemented
51C22×Dic43—24no—
52C22×Dic43—41no—
53C22×Dic43C2312yes—
54C22×Dic43C2312yes—
55C22×Dic43C2312yes—
56C2×C4×D43—24no—
57C2×C4×D43—24no—
58C2×C4×D43—24no—
59C2×C4×D43—24no—
60C2×C4×D43—42no—
61C2×C4×D43—42no—
62C4⋊C4×C43—41no—
63C22⋊C4×C43—24no—
64C22⋊C4×C43—24no—
65C42×C43—41no—
66C22⋊Dic43—24no—
67C22⋊Dic43—41no—
68C22⋊Dic43C2×C414yescomplemented
69(C2×D43)⋊C4—24no—
70(C2×D43)⋊C4C2×C418yescomplemented
71(C2×D43)⋊C4D418yescomplemented
72Dic43⋊C4—24no—
73C4×Dic43—24no—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43—22no—
77C23×C43—22no—
78C23×C43—21no—
79C23×C43—21no—
80C23×C43—21no—
81C23×C43—21no—
82C23×C43C22×C412yes—
83C23×C43C22×C412yes—
84C23×C43C2411yescharacteristic
85C22×D43—22no—
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—22no—
89C22×D43—216no—
90C22×D43—44no—
91C22×D43—44no—
92C22×D43—48no—
93C22×D43—44no—
94C22×D43C22×C414yes—
95C22×D43C2×D414yes—
96C22×D43#4114yes—
97D4×C43—44no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43C22×C412yes—
106C2×C4×C43C2×D414yes—
107C22⋊D43—216no—
108C2×Dic43—22no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43—44no—
116C2×Dic43C22×C414yes—
117C2×Dic43C2×D414yes—
118C4×D43—48no—
119C4×D43—48no—
120C22×C43—24no—
121C22×C43—24no—
122C22×C43—22no—
123C22×C43—22no—
124C22×C43—41no—
125C22×C43—41no—
126C22×C43—42no—
127C22×C43—42no—
128C22×C43—41no—
129C22×C43—41no—
130C22×C43C23×C411yescharacteristic
131C22×C43C22×D412yes—
132C22×C43C2×#4112yes—
133C22×C43H(5,𝔽2)11yescharacteristic
134C22×C43H(5,𝔽2)11yescharacteristic
135C2×D43—24no—
136C2×D43—24no—
137C2×D43—24no—
138C2×D43—24no—
139C2×D43—24no—
140C2×D43—24no—
141C2×D43—416no—
142C2×D43C4×D418yescomplemented
143C4×C43—22no—
144C4×C43—24no—
145C4×C43—42no—
146Dic43—24no—
147Dic43—24no—
148Dic43—42no—
149#2358—431nomaximal, Sylow
150C2×C43—42no—
151C2×C43—42no—
152C2×C43C2×C4×D412yes—
153C2×C43#51811yescharacteristic
154C2×C43D4211yescharacteristic
155C2×C43#54612yes—
156C2×C43#55111yescharacteristic
157D43—28no—
158C2×#120—431no—
159C2×C4×D4—432no—
160C22×C22⋊C4—432no—
161#390D4311yescharacteristic, complemented
162#388—432no—
163#386—431no—
164#386—432no—
165#385—432no—
166C4×C22⋊C4—432no—
167C43#235811yescharacteristic, complemented, Sylow
168C25—431no—
169C22×D4—432no—
170C22×D4C2×D4311yescharacteristic
171C23×C4—431no—
172C23×C4—432no—
173C23×C4—432no—
174#120—438no—
175C4×D4—868no—
176C2×C4⋊C4—432no—
177C2×C4⋊C4C2×D4311yescharacteristic, complemented
178C2×C22⋊C4—431no—
179C2×C22⋊C4—432no—
180C2×C22⋊C4—432no—
181C2×C22⋊C4—432no—
182C2×C22⋊C4—432no—
183C2×C22⋊C4—431no—
184C2×C22⋊C4—868no—
185C2×C22⋊C4C2×D4312yes—
186C2×C22⋊C4C2×D4312yescomplemented
187C2×C42—432no—
188C2×C42C2×D4311yescharacteristic, complemented
189#95—432no—
190#95—432no—
191#95—432no—
192C24—432no—
193C24—434no—
194C24—864no—
195C24—864no—
196C24—1721no—
197C24—1721no—
198C24C22×D4311yescharacteristic
199C24C22×D4311yescharacteristic
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—438no—
203C2×D4—864no—
204C2×D4—864no—
205C2×D4C4×D4314yescomplemented
206C22×C4—432no—
207C22×C4—432no—
208C22×C4—432no—
209C22×C4—864no—
210C22×C4—864no—
211C22×C4—864no—
212C22×C4—864no—
213C22×C4—864no—
214C22×C4—1722no—
215C22×C4—1722no—
216C22×C4—1721no—
217C22×C4C22×D4312yes—
218C22×C4C22×D4311yescharacteristic
219C22×C4C22×D4312yes—
220C4⋊C4—41no—
221C4⋊C4—864no—
222C22⋊C4—24no—
223C22⋊C4—24no—
224C22⋊C4—434no—
225C22⋊C4—438no—
226C22⋊C4—438no—
227C22⋊C4—864no—
228C22⋊C4—864no—
229C22⋊C4—1721no—
230C42—41no—
231C42—864no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—434no—
241C23—434no—
242C23—434no—
243C23—8616no—
244C23—862no—
245C23—862no—
246C23—862no—
247C23—862no—
248C23—1724no—
249C23—1724no—
250C23—1724no—
251C23—1728no—
252C23C2×C4×D4312yes—
253C23C2×C4×D4312yes—
254C23C23×D4311yescharacteristic
255D4—44no—
256D4—8616no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—434no—
265C2×C4—434no—
266C2×C4—862no—
267C2×C4—862no—
268C2×C4—862no—
269C2×C4—862no—
270C2×C4—862no—
271C2×C4—862no—
272C2×C4—862no—
273C2×C4—1728no—
274C2×C4—1728no—
275C2×C4—1724no—
276C2×C4C2×C4×D4312yes—
277C2×C4D4×D4314yes—
278C22—24no—
279C22—24no—
280C22—22no—
281C22—22no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—42no—
287C22—42no—
288C22—438no—
289C22—864no—
290C22—864no—
291C22—864no—
292C22—864no—
293C22—864no—
294C22—864no—
295C22—17216no—
296C22C22×C4×D4311yescharacteristic
297C22C2×D4×D4312yes—
298C22#41×D4312yes—
299C22#1306337011yescharacteristic
300C22#1306337011yescharacteristic
301C4—22no—
302C4—24no—
303C4—42no—
304C4—864no—
305C4—864no—
306C4—1722no—
307C2—42no—
308C2—42no—
309C2—868no—
310C2C4×D4×D4312yes—
311C2#1458337211yescharacteristic
312C2#1458353411yescharacteristic
313C2#1458353812yes—
314C2#1458357911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#390C2
socleC23×C43C24
hypercenter#390D43
hypocenterC43#2358
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D43)⋊C4C2semidirect
3. C2×C22⋊C4×D43C2semidirect
4. #14582787C2semidirect
5. #14582779C2semidirect
6. #14582775C2semidirect
7. #14582770C2semidirect
8. C4×(C2×D43)⋊C4C2semidirect
9. C43×#390C2semidirect
12. C23×Dic43C22semidirect
15. #13063293C4semidirect
17. C2×Dic43⋊C4C22semidirect
20. C2×C22⋊Dic43C22semidirect
25. C2×C4×Dic43C22semidirect
26. C43⋊#95C22semidirect
27. C43⋊#95C22semidirect
28. C43⋊#95C22semidirect
30. C2×C4⋊C4×C43C22semidirect
32. C2×C22⋊C4×C43C22semidirect
33. C2×C42×C43C22semidirect
40. C23×D43C2×C4semidirect
44. C2×D4×C43C2×C4semidirect
50. C2×C22⋊D43C2×C4semidirect
68. C22⋊Dic43C2×C4semidirect
70. (C2×D43)⋊C4C2×C4semidirect
71. (C2×D43)⋊C4D4semidirect
142. C2×D43C4×D4semidirect
161. #390D43semidirect
167. C43#2358semidirect
177. C2×C4⋊C4C2×D43semidirect
186. C2×C22⋊C4C2×D43semidirect
188. C2×C42C2×D43semidirect
205. C2×D4C4×D43semidirect