Finite Group Databasebeta

← #20247700

Subgroups — #20247700

Order 6016.

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×#13093986C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
3#15689062C211yesmaximal, characteristic, complemented
4#15689060C211yesmaximal, characteristic, complemented
5#15689058C211yesmaximal, characteristic, complemented
6#15689020C212yesmaximal, complemented
7#15689001C212yesmaximal
8#15688997C212yesmaximal, complemented
9#15688982C212yesmaximal, complemented
10#15688982C211yesmaximal, characteristic, complemented
11C47×#400C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15C22×C4×D47C2212yes—
16#13093986—24no—
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2212yes—
22C4⋊C4×D47—24no—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×C4×Dic47C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34#95×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C23×D47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C2×D188—22no—
49C2×D188—22no—
50C2×D188Q814yes—
51C2×C4×D47—24no—
52C2×C4×D47—24no—
53C2×C4×D47—22no—
54C2×C4×D47—24no—
55C2×C4×D47—42no—
56C2×C4×D47—42no—
57C2×C4×D47D414yes—
58C4⋊C4×C47—22no—
59C4⋊C4×C47—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—24no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—42no—
64(C2×D47)⋊C4—42no—
65C4⋊Dic47—22no—
66C4⋊Dic47—42no—
67Dic47⋊C4—24no—
68Dic47⋊C4—24no—
69Dic47⋊C4—42no—
70C4×Dic47—22no—
71C23×C47C2411yescharacteristic
72C22×D47—22no—
73C22×D47—22no—
74C22×D47—21no—
75C22×D47—22no—
76C22×D47—21no—
77C22×D47—22no—
78C22×D47C2×D412yes—
79C22×D47C2×Q812yes—
80C22×D47C2×Q812yes—
81C22×D47#4112yes—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—22no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47C2×D412yes—
94C2×C4×C47C2×Q812yes—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47C2×D412yes—
104C2×Dic47#4114yes—
105D188—28no—
106C4×D47—28no—
107C4×D47—48no—
108C4×D47—44no—
109C22×C47C22×D411yescharacteristic
110C22×C47C22×Q811yescharacteristic
111C22×C47C2×#4111yescharacteristic
112C22×C47C2×#4112yes—
113C22×C47H(5,𝔽2)12yes—
114C2×D47—22no—
115C2×D47—22no—
116C2×D47—24no—
117C2×D47—24no—
118C2×D47—22no—
119C2×D47—24no—
120C2×D47—41no—
121C2×D47—41no—
122C2×D47—42no—
123C2×D47C22⋊Q814yes—
124C4×C47—22no—
125C4×C47—22no—
126C4×C47—41no—
127C4×C47—42no—
128C4×C47—42no—
129Dic47—42no—
130Dic47—41no—
131Dic47—42no—
132Dic47#12314yes—
133#2487—471nomaximal, Sylow
134C2×C47C2×C22⋊Q811yescharacteristic
135C2×C47C2×#12311yescharacteristic
136C2×C47#53511yescharacteristic
137C2×C47#55312yes—
138C2×C47#55412yes—
139D47—24no—
140D47—42no—
141C2×C4×D4—471no—
142C22×C4⋊C4—471no—
143#400—471no—
144#400D4711yescharacteristic, complemented
145#399—471no—
146#399—471no—
147#389—472no—
148#386—472no—
149#385—472no—
150#380—472no—
151#380—471no—
152C47#248711yescharacteristic, complemented, Sylow
153C22×D4—471no—
154C23×C4—471no—
155C23×C4—471no—
156C23×C4—472no—
157C4×D4—944no—
158C2×C4⋊C4—472no—
159C2×C4⋊C4—471no—
160C2×C4⋊C4—472no—
161C2×C4⋊C4—472no—
162C2×C4⋊C4—472no—
163C2×C4⋊C4—944no—
164C2×C4⋊C4C2×D4711yescharacteristic
165C2×C4⋊C4C2×D4711yescharacteristic
166C2×C22⋊C4—471no—
167C2×C22⋊C4—471no—
168C2×C22⋊C4—472no—
169C2×C22⋊C4—472no—
170C2×C22⋊C4—472no—
171C2×C42—471no—
172#95—472no—
173#95—471no—
174#95—472no—
175#95C2×D4712yes—
176#95C2×D4711yescharacteristic
177#95C2×D4712yes—
178C24—471no—
179C24—471no—
180C2×D4—474no—
181C2×D4—942no—
182C2×D4—942no—
183C22×C4—471no—
184C22×C4—474no—
185C22×C4—472no—
186C22×C4—472no—
187C22×C4—471no—
188C22×C4—944no—
189C22×C4—942no—
190C22×C4—944no—
191C22×C4—944no—
192C22×C4—1882no—
193C22×C4—1882no—
194C22×C4C22×D4711yescharacteristic
195C22×C4C22×D4712yes—
196C22×C4C22×D4712yes—
197C22×C4C22×D4711yescharacteristic
198C22×C4C22×D4711yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—944no—
202C4⋊C4—944no—
203C4⋊C4—942no—
204C4⋊C4—1882no—
205C4⋊C4—1882no—
206C22⋊C4—944no—
207C22⋊C4—942no—
208C22⋊C4—942no—
209C22⋊C4—1882no—
210C22⋊C4—1882no—
211C42—942no—
212C23—472no—
213C23—472no—
214C23—472no—
215C23—472no—
216C23—942no—
217C23—942no—
218C23—941no—
219C23—942no—
220C23—941no—
221C23—942no—
222C23C23×D4711yescharacteristic
223D4—948no—
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—472no—
236C2×C4—474no—
237C2×C4—948no—
238C2×C4—941no—
239C2×C4—942no—
240C2×C4—942no—
241C2×C4—942no—
242C2×C4—942no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—1884no—
247C2×C4—1888no—
248C2×C4D4×D4712yes—
249C2×C4Q8×D4712yes—
250C22—474no—
251C22—944no—
252C22—944no—
253C22—942no—
254C22—942no—
255C22—944no—
256C22—942no—
257C22—1882no—
258C22—1881no—
259C22—1881no—
260C22C2×D4×D4711yescharacteristic
261C22C2×Q8×D4711yescharacteristic
262C22#41×D4711yescharacteristic
263C22#41×D4712yes—
264C22#1309407012yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—41no—
269C4—42no—
270C4—474no—
271C4—1882no—
272C4—1882no—
273C4—1881no—
274C2—944no—
275C2—1882no—
276C2C22⋊Q8×D4711yescharacteristic
277C2#123×D4711yescharacteristic
278C2#1568969111yescharacteristic
279C2#1568982412yes—
280C2#1568982912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2487
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D47C2semidirect
3. #15689062C2semidirect
4. #15689060C2semidirect
5. #15689058C2semidirect
6. #15689020C2semidirect
8. #15688997C2semidirect
9. #15688982C2semidirect
10. #15688982C2semidirect
11. C47×#400C2semidirect
144. #400D47semidirect
152. C47#2487semidirect