Finite Group Databasebeta

← #19138907

Subgroups — #19138907

Order 5504.

584 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 151 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×#13063287C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#14582838C211yesmaximal, characteristic, complemented
4#14582836C211yesmaximal, characteristic, complemented
5#14582834C211yesmaximal, characteristic, complemented
6#14582796C212yesmaximal, complemented
7#14582777C212yesmaximal
8#14582773C212yesmaximal, complemented
9#14582758C211yesmaximal, characteristic, complemented
10#14582758C212yesmaximal, complemented
11C43×#400C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15C22×C4×D43C2212yes—
16#13063287—24no—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×C4⋊Dic43C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2212yes—
22C4⋊C4×D43—24no—
23C2×(C2×D43)⋊C4C2211yescharacteristic
24C2×(C2×D43)⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C2×C4×Dic43C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34#95×C43C2212yes—
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C23×D43C2311yescharacteristic
38C23×D43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×Dic43C2312yes—
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×D172—22no—
49C2×D172—22no—
50C2×D172Q814yes—
51C2×C4×D43—24no—
52C2×C4×D43—22no—
53C2×C4×D43—24no—
54C2×C4×D43—24no—
55C2×C4×D43—42no—
56C2×C4×D43—42no—
57C2×C4×D43D414yes—
58C4⋊C4×C43—22no—
59C4⋊C4×C43—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—24no—
63(C2×D43)⋊C4—42no—
64(C2×D43)⋊C4—42no—
65C4⋊Dic43—22no—
66C4⋊Dic43—42no—
67Dic43⋊C4—24no—
68Dic43⋊C4—24no—
69Dic43⋊C4—42no—
70C4×Dic43—22no—
71C23×C43C2411yescharacteristic
72C22×D43—22no—
73C22×D43—22no—
74C22×D43—21no—
75C22×D43—22no—
76C22×D43—21no—
77C22×D43—22no—
78C22×D43C2×D412yes—
79C22×D43C2×Q812yes—
80C22×D43C2×Q812yes—
81C22×D43#4112yes—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43C2×D412yes—
94C2×C4×C43C2×Q812yes—
95C2×Dic43—21no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43C2×D412yes—
104C2×Dic43#4114yes—
105D172—28no—
106C4×D43—28no—
107C4×D43—48no—
108C4×D43—44no—
109C22×C43C22×D411yescharacteristic
110C22×C43C22×Q811yescharacteristic
111C22×C43C2×#4111yescharacteristic
112C22×C43C2×#4112yes—
113C22×C43H(5,𝔽2)12yes—
114C2×D43—22no—
115C2×D43—22no—
116C2×D43—24no—
117C2×D43—24no—
118C2×D43—22no—
119C2×D43—24no—
120C2×D43—41no—
121C2×D43—41no—
122C2×D43—42no—
123C2×D43C22⋊Q814yes—
124C4×C43—22no—
125C4×C43—22no—
126C4×C43—41no—
127C4×C43—42no—
128C4×C43—42no—
129Dic43—42no—
130Dic43—41no—
131Dic43—42no—
132Dic43#12314yes—
133#2487—431nomaximal, Sylow
134C2×C43C2×C22⋊Q811yescharacteristic
135C2×C43C2×#12311yescharacteristic
136C2×C43#53511yescharacteristic
137C2×C43#55312yes—
138C2×C43#55412yes—
139D43—24no—
140D43—42no—
141C2×C4×D4—431no—
142C22×C4⋊C4—431no—
143#400—431no—
144#400D4311yescharacteristic, complemented
145#399—431no—
146#399—431no—
147#389—432no—
148#386—432no—
149#385—432no—
150#380—432no—
151#380—431no—
152C43#248711yescharacteristic, complemented, Sylow
153C22×D4—431no—
154C23×C4—431no—
155C23×C4—431no—
156C23×C4—432no—
157C4×D4—864no—
158C2×C4⋊C4—432no—
159C2×C4⋊C4—431no—
160C2×C4⋊C4—432no—
161C2×C4⋊C4—432no—
162C2×C4⋊C4—432no—
163C2×C4⋊C4—864no—
164C2×C4⋊C4C2×D4311yescharacteristic
165C2×C4⋊C4C2×D4311yescharacteristic
166C2×C22⋊C4—431no—
167C2×C22⋊C4—431no—
168C2×C22⋊C4—432no—
169C2×C22⋊C4—432no—
170C2×C22⋊C4—432no—
171C2×C42—431no—
172#95—432no—
173#95—431no—
174#95—432no—
175#95C2×D4312yes—
176#95C2×D4311yescharacteristic
177#95C2×D4312yes—
178C24—431no—
179C24—431no—
180C2×D4—434no—
181C2×D4—862no—
182C2×D4—862no—
183C22×C4—431no—
184C22×C4—434no—
185C22×C4—432no—
186C22×C4—432no—
187C22×C4—431no—
188C22×C4—864no—
189C22×C4—862no—
190C22×C4—864no—
191C22×C4—864no—
192C22×C4—1722no—
193C22×C4—1722no—
194C22×C4C22×D4311yescharacteristic
195C22×C4C22×D4312yes—
196C22×C4C22×D4312yes—
197C22×C4C22×D4311yescharacteristic
198C22×C4C22×D4311yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—864no—
202C4⋊C4—864no—
203C4⋊C4—862no—
204C4⋊C4—1722no—
205C4⋊C4—1722no—
206C22⋊C4—862no—
207C22⋊C4—864no—
208C22⋊C4—862no—
209C22⋊C4—1722no—
210C22⋊C4—1722no—
211C42—862no—
212C23—432no—
213C23—432no—
214C23—432no—
215C23—432no—
216C23—862no—
217C23—862no—
218C23—861no—
219C23—862no—
220C23—861no—
221C23—862no—
222C23C23×D4311yescharacteristic
223D4—868no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—432no—
236C2×C4—434no—
237C2×C4—868no—
238C2×C4—861no—
239C2×C4—862no—
240C2×C4—862no—
241C2×C4—862no—
242C2×C4—862no—
243C2×C4—862no—
244C2×C4—862no—
245C2×C4—862no—
246C2×C4—1724no—
247C2×C4—1728no—
248C2×C4D4×D4312yes—
249C2×C4Q8×D4312yes—
250C22—434no—
251C22—864no—
252C22—864no—
253C22—862no—
254C22—862no—
255C22—864no—
256C22—862no—
257C22—1722no—
258C22—1721no—
259C22—1721no—
260C22C2×D4×D4311yescharacteristic
261C22C2×Q8×D4311yescharacteristic
262C22#41×D4311yescharacteristic
263C22#41×D4312yes—
264C22#1306337112yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—41no—
269C4—42no—
270C4—434no—
271C4—1722no—
272C4—1722no—
273C4—1721no—
274C2—864no—
275C2—1722no—
276C2C22⋊Q8×D4311yescharacteristic
277C2#123×D4311yescharacteristic
278C2#1458346711yescharacteristic
279C2#1458360012yes—
280C2#1458360512yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2487
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D43C2semidirect
3. #14582838C2semidirect
4. #14582836C2semidirect
5. #14582834C2semidirect
6. #14582796C2semidirect
8. #14582773C2semidirect
9. #14582758C2semidirect
10. #14582758C2semidirect
11. C43×#400C2semidirect
144. #400D43semidirect
152. C43#2487semidirect