Finite Group Databasebeta

← #19139971

Subgroups — #19139971

Order 5504.

544 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 159 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×#13063301C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic
3#14582831C211yesmaximal, characteristic, complemented
4#14582829C211yesmaximal, characteristic, complemented
5#14582818C211yesmaximal, characteristic, complemented
6#14582796C212yesmaximal, complemented
7#14582795C212yesmaximal, complemented
8#14582773C212yesmaximal
9#14582770C212yesmaximal
10#14582746C211yesmaximal, characteristic
11C43×#395C211yesmaximal, characteristic, complemented
12C22×C4×D43C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15#13063301—24no—
16C2×C4⋊Dic43C2212yes—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×C4⋊Dic43C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2212yes—
22C2×Dic43⋊C4C2211yescharacteristic
23C2×Dic43⋊C4C2212yes—
24C4⋊C4×D43—24no—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×C4×Dic43C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C22×Q8×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C23×D43C2311yescharacteristic
38C2×Q8×C43—22no—
39C2×Q8×C43—42no—
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2312yes—
44C22×C4×C43C2311yescharacteristic
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C22×Dic43C2312yes—
49C22×Dic43C2311yescharacteristic
50C2×C4×D43—22no—
51C2×C4×D43—22no—
52C2×C4×D43—22no—
53C2×C4×D43—22no—
54C2×C4×D43—42no—
55C2×C4×D43—42no—
56C2×C4×D43D414yes—
57C4⋊C4×C43—22no—
58C4⋊C4×C43—42no—
59(C2×D43)⋊C4—24no—
60(C2×D43)⋊C4Q818yescomplemented
61C4⋊Dic43—22no—
62C4⋊Dic43—22no—
63C4⋊Dic43—24no—
64Dic43⋊C4—22no—
65Dic43⋊C4—24no—
66Dic43⋊C4—22no—
67Dic43⋊C4—24no—
68Dic43⋊C4—42no—
69C4×Dic43—42no—
70C23×C43C2411yescharacteristic
71C22×D43—21no—
72C22×D43—21no—
73C22×D43—22no—
74C22×D43C2×D412yes—
75C22×D43C2×Q814yes—
76Q8×C43—44no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43C2×D412yes—
88C2×C4×C43C2×Q814yes—
89C2×C4×C43#4112yes—
90C2×Dic43—21no—
91C2×Dic43—22no—
92C2×Dic43—21no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—21no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43C2×D412yes—
101C2×Dic43C2×Q814yes—
102C2×Dic43#4112yes—
103C4×D43—28no—
104C4×D43—44no—
105C4×D43—44no—
106C22×C43C22×D411yescharacteristic
107C22×C43C22×Q812yes—
108C22×C43C2×#4111yescharacteristic
109C22×C43C2×#4111yescharacteristic
110C22×C43H(5,𝔽2)12yes—
111C2×D43—22no—
112C2×D43—22no—
113C2×D43—24no—
114C2×D43—24no—
115C2×D43C4⋊Q814yes—
116C4×C43—22no—
117C4×C43—22no—
118C4×C43—24no—
119C4×C43—41no—
120C4×C43—42no—
121Dic43—22no—
122Dic43—22no—
123Dic43—24no—
124Dic43—42no—
125Dic43—41no—
126#2583—431nomaximal, Sylow
127C2×C43#52511yescharacteristic
128C2×C43C2×C4⋊Q811yescharacteristic
129C2×C43#53411yescharacteristic
130C2×C43#55412yes—
131C2×C43#55412yes—
132D43—24no—
133C2×C22⋊Q8—431no—
134C22×C4⋊C4—431no—
135#398—431no—
136#398—431no—
137#395—431no—
138#395D4311yescharacteristic, complemented
139#389—432no—
140#389—432no—
141#385—432no—
142#385—432no—
143C4×C22⋊C4—431no—
144C43#258311yescharacteristic, complemented, Sylow
145C22×Q8C2×D4311yescharacteristic
146C23×C4—431no—
147C23×C4—431no—
148C23×C4—431no—
149C22⋊Q8—864no—
150C2×C4⋊C4—431no—
151C2×C4⋊C4—431no—
152C2×C4⋊C4—431no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—431no—
155C2×C4⋊C4—432no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4—432no—
158C2×C4⋊C4—864no—
159C2×C4⋊C4C2×D4311yescharacteristic
160C2×C4⋊C4C2×D4312yes—
161C2×C22⋊C4—432no—
162C2×C22⋊C4—432no—
163C2×C42—432no—
164#95—431no—
165#95—432no—
166#95—432no—
167#95—432no—
168#95C2×D4311yescharacteristic
169#95C2×D4312yes—
170C24—431no—
171C2×Q8—22no—
172C2×Q8—42no—
173C22×C4—432no—
174C22×C4—431no—
175C22×C4—431no—
176C22×C4—434no—
177C22×C4—432no—
178C22×C4—431no—
179C22×C4—862no—
180C22×C4—862no—
181C22×C4—862no—
182C22×C4—862no—
183C22×C4—1722no—
184C22×C4—1722no—
185C22×C4C22×D4311yescharacteristic
186C22×C4C22×D4312yes—
187C22×C4C22×D4311yescharacteristic
188C22×C4C22×D4312yes—
189C22×C4C22×D4311yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—862no—
193C4⋊C4—862no—
194C4⋊C4—864no—
195C4⋊C4—864no—
196C4⋊C4—862no—
197C4⋊C4—862no—
198C4⋊C4—864no—
199C4⋊C4—1722no—
200C22⋊C4—438no—
201C22⋊C4—864no—
202C42—1722no—
203C23—432no—
204C23—434no—
205C23—861no—
206C23—861no—
207C23—862no—
208C23C23×D4311yescharacteristic
209Q8—44no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—432no—
221C2×C4—434no—
222C2×C4—432no—
223C2×C4—868no—
224C2×C4—861no—
225C2×C4—862no—
226C2×C4—861no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4—862no—
230C2×C4—861no—
231C2×C4—862no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—1724no—
235C2×C4—1724no—
236C2×C4D4×D4312yes—
237C2×C4Q8×D4314yes—
238C2×C4#1062190212yes—
239C22—434no—
240C22—864no—
241C22—864no—
242C22—862no—
243C22—862no—
244C22C2×D4×D4311yescharacteristic
245C22C2×Q8×D4312yes—
246C22#41×D4311yescharacteristic
247C22C2×#1062190211yescharacteristic
248C22#1306337012yes—
249C4—24no—
250C4—22no—
251C4—22no—
252C4—41no—
253C4—42no—
254C4—864no—
255C4—862no—
256C4—862no—
257C4—1722no—
258C4—1721no—
259C2—864no—
260C2#1458341211yescharacteristic
261C2C4⋊Q8×D4311yescharacteristic
262C2#1458345911yescharacteristic
263C2#1458360312yes—
264C2#1458361012yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2583
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. #14582831C2semidirect
4. #14582829C2semidirect
5. #14582818C2semidirect
6. #14582796C2semidirect
7. #14582795C2semidirect
11. C43×#395C2semidirect
60. (C2×D43)⋊C4Q8semidirect
138. #395D43semidirect
144. C43#2583semidirect