Finite Group Databasebeta

← #19138874

Subgroups — #19138874

Order 5504.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×(C2×D43)⋊C4C211yesmaximal, characteristic
2C2×C22⋊C4×D43C211yesmaximal, characteristic
3#14582828C212yesmaximal, complemented
4#14582826C212yesmaximal, complemented
5#14582774C211yesmaximal, characteristic, complemented
6#14582773C212yesmaximal, complemented
7#14582771C211yesmaximal, characteristic, complemented
8#14582762C211yesmaximal, characteristic, complemented
9#14582761C212yesmaximal, complemented
10#14582754C211yesmaximal, characteristic
11C43×#381C211yesmaximal, characteristic, complemented
12C24×D43C2211yescharacteristic
13C23×Dic43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15C22×C4×D43C2211yescharacteristic
16C2×C4⋊Dic43C2212yescomplemented
17C2×Dic43⋊C4C2212yescomplemented
18C2×C22⋊Dic43C2211yescharacteristic
19C2×C22⋊Dic43C2211yescharacteristic
20C2×(C2×D43)⋊C4—24no—
21C2×(C2×D43)⋊C4C2211yescharacteristic
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C22⋊C4×D43—24no—
28C43⋊#95C2212yescomplemented
29C43⋊#95C2212yescomplemented
30C43⋊#95C2212yescomplemented
31C43⋊#95C2212yescomplemented
32C23×C4×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2211yescharacteristic
35#95×C43C2212yescomplemented
36#95×C43C2212yescomplemented
37C24×C43C2311yescharacteristic
38C23×D43—22no—
39C23×D43—22no—
40C23×D43—24no—
41C23×D43—42no—
42C23×D43D414yes—
43C23×D43C2311yescharacteristic
44C23×D43C2311yescharacteristic
45C22×C4×C43—22no—
46C22×C4×C43—22no—
47C22×C4×C43—22no—
48C22×C4×C43C2311yescharacteristic
49C22×C4×C43C2312yes—
50C22×C4×C43C2311yescharacteristic
51C22×C4×C43C2312yes—
52C22×Dic43—22no—
53C22×Dic43—42no—
54C22×Dic43C2311yescharacteristic
55C22×Dic43C2312yes—
56C22×Dic43C2312yes—
57C22×Dic43C2311yescharacteristic
58C2×C4×D43—22no—
59C2×C4×D43—22no—
60C2×C4×D43—24no—
61C2×C4×D43—42no—
62C22⋊C4×C43—22no—
63C22⋊C4×C43—22no—
64C22⋊Dic43—22no—
65C22⋊Dic43—22no—
66(C2×D43)⋊C4—22no—
67(C2×D43)⋊C4—22no—
68(C2×D43)⋊C4—24no—
69(C2×D43)⋊C4—24no—
70(C2×D43)⋊C4—24no—
71(C2×D43)⋊C4—42no—
72C4⋊Dic43—42no—
73Dic43⋊C4—42no—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43C2×D412yes—
77C23×C43#4112yes—
78C23×C43#4112yes—
79C23×C43C2411yescharacteristic
80C22×D43—21no—
81C22×D43—21no—
82C22×D43—22no—
83C22×D43—28no—
84C22×D43—22no—
85C22×D43—21no—
86C22×D43—21no—
87C22×D43—22no—
88C22×D43—28no—
89C22×D43—44no—
90C22×D43—48no—
91C22×D43—48no—
92C22×D43C2×D412yes—
93C22×D43C2×D412yes—
94C22×D43#4114yes—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—44no—
106C2×Dic43—22no—
107C2×Dic43—21no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43—22no—
116C2×Dic43—44no—
117C4×D43—44no—
118C4×D43—44no—
119C22×C43—22no—
120C22×C43—22no—
121C22×C43—24no—
122C22×C43—24no—
123C22×C43#12314yes—
124C22×C43C22×D411yescharacteristic
125C22×C43C2×#4112yes—
126C22×C43C2×#4111yescharacteristic
127C22×C43C2×#4111yescharacteristic
128C22×C43H(5,𝔽2)12yes—
129C2×D43—22no—
130C2×D43—22no—
131C2×D43—24no—
132C2×D43—24no—
133C2×D43—22no—
134C2×D43—22no—
135C2×D43—22no—
136C2×D43—416no—
137C2×D43—42no—
138C2×D43—42no—
139C2×D43#12314yes—
140C4×C43—41no—
141C4×C43—42no—
142C4×C43—41no—
143C4×C43—42no—
144Dic43—41no—
145Dic43—41no—
146Dic43—42no—
147Dic43—42no—
148#2483—431nomaximal, Sylow
149C2×C43—24no—
150C2×C43C2×#12311yescharacteristic
151C2×C43C2×#12311yescharacteristic
152C2×C43#53411yescharacteristic
153C2×C43#55112yes—
154C2×C43#55112yes—
155D43—24no—
156D43—42no—
157C22×C22⋊C4—431no—
158C22×C22⋊C4—431no—
159#397—432no—
160#397—432no—
161#385—431no—
162#385—431no—
163#385—432no—
164#381—431no—
165#381—432no—
166#381D4311yescharacteristic, complemented
167#379—431no—
168C43#248311yescharacteristic, complemented, Sylow
169C25—431no—
170C23×C4—431no—
171C23×C4—431no—
172C23×C4—431no—
173C23×C4C2×D4311yescharacteristic
174C2×C4⋊C4—432no—
175C2×C4⋊C4—432no—
176C2×C22⋊C4—431no—
177C2×C22⋊C4—431no—
178C2×C22⋊C4—432no—
179C2×C22⋊C4—431no—
180C2×C22⋊C4—432no—
181C2×C22⋊C4—431no—
182C2×C22⋊C4—432no—
183C2×C22⋊C4—432no—
184C2×C22⋊C4—864no—
185C2×C22⋊C4—864no—
186C2×C22⋊C4C2×D4311yescharacteristic
187C2×C22⋊C4C2×D4311yescharacteristic
188#95—432no—
189#95—432no—
190#95—432no—
191#95—432no—
192#95C2×D4312yescomplemented
193#95C2×D4312yescomplemented
194C24—431no—
195C24—431no—
196C24—434no—
197C24—864no—
198C24—862no—
199C24—862no—
200C24—1722no—
201C24C22×D4311yescharacteristic
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—431no—
206C22×C4—432no—
207C22×C4—431no—
208C22×C4—432no—
209C22×C4—862no—
210C22×C4—862no—
211C22×C4—864no—
212C22×C4—862no—
213C22×C4—1722no—
214C22×C4—1722no—
215C22×C4C22×D4312yes—
216C22×C4C22×D4311yescharacteristic
217C22×C4C22×D4312yes—
218C22×C4C22×D4311yescharacteristic
219C4⋊C4—1722no—
220C4⋊C4—1722no—
221C22⋊C4—22no—
222C22⋊C4—22no—
223C22⋊C4—862no—
224C22⋊C4—862no—
225C22⋊C4—864no—
226C22⋊C4—864no—
227C22⋊C4—864no—
228C22⋊C4—862no—
229C22⋊C4—862no—
230C22⋊C4—1722no—
231C23—22no—
232C23—22no—
233C23—432no—
234C23—434no—
235C23—432no—
236C23—868no—
237C23—861no—
238C23—861no—
239C23—862no—
240C23—868no—
241C23—862no—
242C23—861no—
243C23—861no—
244C23—862no—
245C23—1724no—
246C23—1728no—
247C23—1728no—
248C23#1062189812yes—
249C23D4×D4312yes—
250C23#1062190012yes—
251C23C23×D4311yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—44no—
263C2×C4—861no—
264C2×C4—862no—
265C2×C4—861no—
266C2×C4—862no—
267C2×C4—862no—
268C2×C4—862no—
269C2×C4—862no—
270C2×C4—862no—
271C2×C4—862no—
272C2×C4—862no—
273C2×C4—1724no—
274C2×C4—1724no—
275C2×C4—1724no—
276C22—24no—
277C22—24no—
278C22—22no—
279C22—22no—
280C22—434no—
281C22—864no—
282C22—864no—
283C22—862no—
284C22—862no—
285C22—862no—
286C22—862no—
287C22—862no—
288C22—17216no—
289C22—1722no—
290C22—1722no—
291C22#1306330714yes—
292C22C2×D4×D4311yescharacteristic
293C22#41×D4312yes—
294C22C2×#1062190011yescharacteristic
295C22C2×#1062189811yescharacteristic
296C22#1306337112yes—
297C4—42no—
298C4—41no—
299C4—42no—
300C4—41no—
301C4—1722no—
302C4—1721no—
303C4—1721no—
304C4—1722no—
305C2—24no—
306C2—864no—
307C2—1722no—
308C2#123×D4311yescharacteristic
309C2C2×#1306330711yescharacteristic
310C2#1458346011yescharacteristic
311C2#1458357212yes—
312C2#1458357312yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#381C2
hypercenter#381D43
hypocenterC43#2483
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #14582828C2semidirect
4. #14582826C2semidirect
5. #14582774C2semidirect
6. #14582773C2semidirect
7. #14582771C2semidirect
8. #14582762C2semidirect
9. #14582761C2semidirect
11. C43×#381C2semidirect
16. C2×C4⋊Dic43C22semidirect
17. C2×Dic43⋊C4C22semidirect
28. C43⋊#95C22semidirect
29. C43⋊#95C22semidirect
30. C43⋊#95C22semidirect
31. C43⋊#95C22semidirect
35. #95×C43C22semidirect
36. #95×C43C22semidirect
166. #381D43semidirect
168. C43#2483semidirect
192. #95C2×D43semidirect
193. #95C2×D43semidirect