Finite Group Databasebeta

← #19140515

Subgroups — #19140515

Order 5504.

520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13063304C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D43C211yesmaximal, characteristic
3#14582831C211yesmaximal, characteristic, complemented
4#14582826C211yesmaximal, characteristic, complemented
5#14582824C212yesmaximal, complemented
6#14582820C211yesmaximal, characteristic, complemented
7#14582815C212yesmaximal
8#14582812C211yesmaximal, characteristic, complemented
9#14582784C212yesmaximal, complemented
10#14582773C212yesmaximal, complemented
11C43×#381C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×C22⋊D43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15#13063304—24no—
16C4×C22⋊D43—24no—
17C2×C4⋊Dic43C2212yes—
18C2×C4⋊Dic43C2211yescharacteristic
19C2×C4⋊Dic43C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2211yescharacteristic
22C2×C22⋊Dic43C2212yes—
23C2×C22⋊Dic43C2211yescharacteristic
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C23×C4×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2212yes—
34#95×C43C2212yes—
35#95×C43C2211yescharacteristic
36#95×C43C2211yescharacteristic
37C24×C43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C22×C4×C43—42no—
40C22×C4×C43D414yes—
41C22×C4×C43C2312yes—
42C22×C4×C43C2312yes—
43C22×C4×C43C2311yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—22no—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—22no—
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2312yes—
50C22×Dic43C2312yes—
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C2×C4×D43—22no—
54C2×C4×D43—42no—
55C2×Dic86—22no—
56C2×Dic86—42no—
57C22⋊C4×C43—42no—
58C22⋊Dic43—22no—
59C22⋊Dic43—24no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—24no—
62(C2×D43)⋊C4—42no—
63C4⋊Dic43—22no—
64C4⋊Dic43—24no—
65C4⋊Dic43—42no—
66Dic43⋊C4—22no—
67Dic43⋊C4—24no—
68C4×Dic43—22no—
69C23×C43—21no—
70C23×C43—21no—
71C23×C43—22no—
72C23×C43—22no—
73C23×C43C2×D412yes—
74C23×C43C2411yescharacteristic
75C22×D43—21no—
76C22×D43—21no—
77C22×D43—22no—
78C22×D43—22no—
79C22×D43#4112yes—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—44no—
89C2×C4×C43C2×D412yes—
90C2×C4×C43C2×D412yes—
91C22⋊D43—28no—
92C2×Dic43—21no—
93C2×Dic43—21no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43#4112yes—
105C4×D43—44no—
106Dic86—44no—
107C22×C43—22no—
108C22×C43—22no—
109C22×C43—22no—
110C22×C43—42no—
111C22×C43—42no—
112C22×C43C22×D411yescharacteristic
113C22×C43C2×#4111yescharacteristic
114C22×C43C2×#4111yescharacteristic
115C22×C43H(5,𝔽2)12yes—
116C22×C432−1+412yes—
117C2×D43—22no—
118C2×D43—24no—
119C2×D43—41no—
120C2×D43—41no—
121C2×D43—42no—
122C4×C43—22no—
123C4×C43—22no—
124C4×C43—42no—
125C4×C43—42no—
126Dic43—22no—
127Dic43—42no—
128Dic43—42no—
129Dic43—41no—
130Dic43—41no—
131#2638—431nomaximal, Sylow
132C2×C43—42no—
133C2×C43#52511yescharacteristic
134C2×C43#53411yescharacteristic
135C2×C43#53611yescharacteristic
136C2×C43#53912yes—
137C2×C43#54212yes—
138D43—42no—
139C2×C22⋊Q8—431no—
140C2×C4×D4—431no—
141#398—431no—
142#397—432no—
143#397—431no—
144#395—431no—
145#394—432no—
146#393—431no—
147#387—432no—
148#385—432no—
149#381D4311yescharacteristic, complemented
150C43#263811yescharacteristic, complemented, Sylow
151C22×Q8—431no—
152C22×D4—431no—
153C23×C4—431no—
154C23×C4C2×D4311yescharacteristic
155C22⋊Q8—864no—
156C4×D4—864no—
157C2×C4⋊C4—431no—
158C2×C4⋊C4—432no—
159C2×C4⋊C4—431no—
160C2×C4⋊C4—432no—
161C2×C4⋊C4—432no—
162C2×C22⋊C4—431no—
163C2×C22⋊C4—432no—
164C2×C22⋊C4—431no—
165C2×C22⋊C4—432no—
166C2×C22⋊C4—432no—
167C2×C22⋊C4C2×D4312yes—
168C2×C42—431no—
169#95—432no—
170#95—432no—
171#95—432no—
172#95—432no—
173#95C2×D4312yes—
174#95C2×D4311yescharacteristic
175#95C2×D4311yescharacteristic
176C24—431no—
177C24C22×D4311yescharacteristic
178C2×Q8—862no—
179C2×Q8—1722no—
180C2×D4—862no—
181C2×D4—862no—
182C2×D4—862no—
183C22×C4—42no—
184C22×C4—431no—
185C22×C4—431no—
186C22×C4—432no—
187C22×C4—432no—
188C22×C4—431no—
189C22×C4—862no—
190C22×C4—1722no—
191C22×C4D17214yes—
192C22×C4C22×D4312yes—
193C22×C4C22×D4312yes—
194C22×C4C22×D4311yescharacteristic
195C22×C4C22×D4311yescharacteristic
196C4⋊C4—864no—
197C4⋊C4—862no—
198C4⋊C4—864no—
199C4⋊C4—862no—
200C4⋊C4—1722no—
201C22⋊C4—42no—
202C22⋊C4—864no—
203C22⋊C4—862no—
204C22⋊C4—864no—
205C22⋊C4—862no—
206C22⋊C4—1722no—
207C42—862no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—22no—
212C23—432no—
213C23—861no—
214C23—861no—
215C23—862no—
216C23—862no—
217C23C2×D17212yes—
218C23C23×D4311yescharacteristic
219Q8—1724no—
220D4—868no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—44no—
230C2×C4—432no—
231C2×C4—861no—
232C2×C4—861no—
233C2×C4—861no—
234C2×C4—862no—
235C2×C4—861no—
236C2×C4—862no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4—862no—
241C2×C4—862no—
242C2×C4—862no—
243C2×C4—1724no—
244C2×C4C2×D17212yes—
245C2×C4C2×D17212yes—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—42no—
250C22—42no—
251C22—862no—
252C22—864no—
253C22—1721no—
254C22—1721no—
255C22—1722no—
256C22C22×D17211yescharacteristic
257C22#41×D4311yescharacteristic
258C22#41×D4311yescharacteristic
259C22#1306337012yes—
260C22#1306337212yes—
261C4—22no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—862no—
266C4—1722no—
267C4—1721no—
268C4—1722no—
269C4—1721no—
270C2—42no—
271C2—1722no—
272C2#1458341111yescharacteristic
273C2#1458346111yescharacteristic
274C2#1458347511yescharacteristic
275C2#1458349212yes—
276C2#1458351712yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#381C2
hypercenter#381D43
hypocenterC43#2638
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#13063304C2semidirect
3. #14582831C2semidirect
4. #14582826C2semidirect
5. #14582824C2semidirect
6. #14582820C2semidirect
8. #14582812C2semidirect
9. #14582784C2semidirect
10. #14582773C2semidirect
11. C43×#381C2semidirect
149. #381D43semidirect
150. C43#2638semidirect