Finite Group Databasebeta

← #19140069

Subgroups — #19140069

Order 5504.

596 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 139 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×#13063296C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#14582839C211yesmaximal, characteristic, complemented
4#14582838C211yesmaximal, characteristic, complemented
5#14582813C211yesmaximal, characteristic, complemented
6#14582792C212yesmaximal, complemented
7#14582787C212yesmaximal, complemented
8#14582775C212yesmaximal, complemented
9#14582775C212yesmaximal, complemented
10#14582746C211yesmaximal, characteristic, complemented
11C43×#394C211yesmaximal, characteristic, complemented
12C22×C22⋊D43C2212yes—
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15C22×C4×D43C2211yescharacteristic
16#13063296—24no—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×C4⋊Dic43C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C4⋊C4×D43—24no—
22C2×C22⋊Dic43C2212yes—
23C2×C22⋊Dic43C2212yes—
24C2×C22⋊Dic43C2212yes—
25C2×(C2×D43)⋊C4C2212yes—
26C2×C4×Dic43C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C22×D4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2212yes—
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2312yes—
38C23×D43C2311yescharacteristic
39C2×D4×C43—22no—
40C2×D4×C43—42no—
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—24no—
46C2×C22⋊D43—24no—
47C2×C22⋊D43—24no—
48C22×Dic43C2312yes—
49C22×Dic43C2312yes—
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C2×C4×D43—22no—
54C2×C4×D43—22no—
55C2×C4×D43—22no—
56C2×C4×D43—22no—
57C2×C4×D43—42no—
58C2×C4×D43—42no—
59C2×C4×D43D414yes—
60C4⋊C4×C43—22no—
61C22⋊C4×C43—24no—
62C22⋊C4×C43—42no—
63C22⋊Dic43—24no—
64C22⋊Dic43—24no—
65C22⋊Dic43—42no—
66(C2×D43)⋊C4—24no—
67C4⋊Dic43—22no—
68C4⋊Dic43—22no—
69Dic43⋊C4—22no—
70Dic43⋊C4—22no—
71C4×Dic43—42no—
72C23×C43—22no—
73C23×C43—22no—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43—22no—
77C23×C43—22no—
78C23×C43—22no—
79C23×C43C2411yescharacteristic
80C22×D43—21no—
81C22×D43—21no—
82C22×D43—22no—
83C22×D43C2×D412yes—
84C22×D43#4114yes—
85D4×C43—44no—
86C2×C4×C43—21no—
87C2×C4×C43—21no—
88C2×C4×C43—22no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43C2×D412yes—
95C2×C4×C43#4112yes—
96C22⋊D43—48no—
97C2×Dic43—21no—
98C2×Dic43—21no—
99C2×Dic43—22no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43C2×D412yes—
109C2×Dic43#4112yes—
110C4×D43—28no—
111C4×D43—44no—
112C4×D43—44no—
113C22×C43—42no—
114C22×C43—42no—
115C22×C43—42no—
116C22×C43—42no—
117C22×C43—42no—
118C22×C43—42no—
119C22×C43—42no—
120C22×C43C22×D411yescharacteristic
121C22×C43C2×#4111yescharacteristic
122C22×C43C2×#4112yes—
123C22×C43C2×#4111yescharacteristic
124C22×C43H(5,𝔽2)12yes—
125C2×D43—22no—
126C2×D43—22no—
127C2×D43—24no—
128C2×D43—24no—
129C2×D43#12414yes—
130C4×C43—22no—
131C4×C43—22no—
132C4×C43—41no—
133C4×C43—42no—
134Dic43—22no—
135Dic43—22no—
136Dic43—42no—
137Dic43—41no—
138Dic43—42no—
139#2591—431nomaximal, Sylow
140C2×C43—82no—
141C2×C43#52511yescharacteristic
142C2×C43C2×#12411yescharacteristic
143C2×C43#53411yescharacteristic
144C2×C43#55312yes—
145C2×C43#55312yes—
146D43—24no—
147C2×#121—431no—
148C22×C4⋊C4—431no—
149#400—431no—
150#400—431no—
151#394—431no—
152#394D4311yescharacteristic, complemented
153#388—432no—
154#388—432no—
155#386—432no—
156#386—432no—
157C4×C22⋊C4—431no—
158C43#259111yescharacteristic, complemented, Sylow
159C22×D4—432no—
160C22×D4C2×D4311yescharacteristic
161C23×C4—431no—
162C23×C4—431no—
163C23×C4—431no—
164#121—864no—
165C2×C4⋊C4—431no—
166C2×C4⋊C4—431no—
167C2×C4⋊C4—431no—
168C2×C4⋊C4—431no—
169C2×C4⋊C4—864no—
170C2×C4⋊C4C2×D4311yescharacteristic
171C2×C22⋊C4—432no—
172C2×C22⋊C4—432no—
173C2×C22⋊C4—432no—
174C2×C22⋊C4—432no—
175C2×C22⋊C4C2×D4312yes—
176C2×C22⋊C4C2×D4312yes—
177C2×C42—432no—
178#95—431no—
179#95—432no—
180#95—432no—
181#95—432no—
182#95—432no—
183#95C2×D4311yescharacteristic
184C24—431no—
185C24C22×D4312yes—
186C2×D4—22no—
187C2×D4—42no—
188C2×D4—864no—
189C2×D4—864no—
190C2×D4—864no—
191C22×C4—431no—
192C22×C4—431no—
193C22×C4—434no—
194C22×C4—432no—
195C22×C4—432no—
196C22×C4—431no—
197C22×C4—862no—
198C22×C4—862no—
199C22×C4—862no—
200C22×C4—862no—
201C22×C4—1722no—
202C22×C4—1722no—
203C22×C4C22×D4312yes—
204C22×C4C22×D4311yescharacteristic
205C22×C4C22×D4311yescharacteristic
206C22×C4C22×D4311yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—862no—
209C4⋊C4—862no—
210C4⋊C4—862no—
211C4⋊C4—862no—
212C22⋊C4—24no—
213C22⋊C4—42no—
214C22⋊C4—864no—
215C22⋊C4—864no—
216C22⋊C4—864no—
217C22⋊C4—1722no—
218C42—1722no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—432no—
227C23—434no—
228C23—861no—
229C23—861no—
230C23—862no—
231C23C23×D4311yescharacteristic
232D4—44no—
233D4—1728no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—432no—
243C2×C4—432no—
244C2×C4—868no—
245C2×C4—861no—
246C2×C4—861no—
247C2×C4—862no—
248C2×C4—862no—
249C2×C4—861no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—862no—
254C2×C4—862no—
255C2×C4—862no—
256C2×C4—1724no—
257C2×C4—1724no—
258C2×C4D4×D4312yes—
259C2×C4#1062190012yes—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—434no—
268C22—864no—
269C22—864no—
270C22—862no—
271C22—862no—
272C22C2×D4×D4311yescharacteristic
273C22#41×D4311yescharacteristic
274C22#41×D4312yes—
275C22C2×#1062190011yescharacteristic
276C22#1306337012yes—
277C4—22no—
278C4—22no—
279C4—42no—
280C4—41no—
281C4—862no—
282C4—862no—
283C4—1722no—
284C4—1722no—
285C4—1721no—
286C2—82no—
287C2—864no—
288C2#1458340911yescharacteristic
289C2#124×D4311yescharacteristic
290C2#1458345911yescharacteristic
291C2#1458359412yes—
292C2#1458359612yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2591
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D43C2semidirect
3. #14582839C2semidirect
4. #14582838C2semidirect
5. #14582813C2semidirect
6. #14582792C2semidirect
7. #14582787C2semidirect
8. #14582775C2semidirect
9. #14582775C2semidirect
10. #14582746C2semidirect
11. C43×#394C2semidirect
152. #394D43semidirect
158. C43#2591semidirect