Finite Group Databasebeta

← #20247875

Subgroups — #20247875

Order 6016.

596 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13093997C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
3#15689050C211yesmaximal, characteristic, complemented
4#15689049C211yesmaximal, characteristic, complemented
5#15689048C211yesmaximal, characteristic, complemented
6#15689023C212yesmaximal, complemented
7#15689001C212yesmaximal, complemented
8#15688999C212yesmaximal, complemented
9#15688987C212yesmaximal, complemented
10#15688970C211yesmaximal, characteristic, complemented
11C47×#397C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C22⋊D47C2211yescharacteristic
14C22×C22⋊D47C2211yescharacteristic
15C22×C4×D47C2211yescharacteristic
16C22×C4×D47C2212yes—
17#13093997—24no—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2212yes—
21C4⋊C4×D47—24no—
22C2×C22⋊Dic47C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×C4×Dic47C2212yes—
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C23×D47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—22no—
45C2×C22⋊D47—24no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—24no—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51C22×Dic47C2311yescharacteristic
52C2×D188—22no—
53C2×D188—24no—
54C2×C4×D47—24no—
55C2×C4×D47—24no—
56C2×C4×D47—42no—
57C2×C4×D47—42no—
58C2×C4×D47D414yes—
59C4⋊C4×C47—22no—
60C22⋊C4×C47—22no—
61C22⋊C4×C47—42no—
62C22⋊Dic47—42no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—42no—
66(C2×D47)⋊C4—42no—
67C4⋊Dic47—22no—
68Dic47⋊C4—24no—
69Dic47⋊C4—22no—
70C4×Dic47—24no—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—21no—
75C23×C47—21no—
76C23×C47C2411yescharacteristic
77C22×D47—22no—
78C22×D47—21no—
79C22×D47—21no—
80C22×D47—21no—
81C22×D47—22no—
82C22×D47—22no—
83C22×D47—21no—
84C22×D47—21no—
85C22×D47C2×D412yes—
86C22×D47#4114yes—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47C2×D412yes—
97C22⋊D47—44no—
98C22⋊D47—44no—
99C2×Dic47—22no—
100C2×Dic47—21no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47C2×D412yes—
108C2×Dic47#4114yes—
109D188—44no—
110C4×D47—28no—
111C4×D47—48no—
112C22×C47—41no—
113C22×C47—41no—
114C22×C47—41no—
115C22×C47—42no—
116C22×C47—42no—
117C22×C47C22×D411yescharacteristic
118C22×C47C2×#4112yes—
119C22×C47C2×#4112yes—
120C22×C47H(5,𝔽2)11yescharacteristic
121C22×C47H(5,𝔽2)11yescharacteristic
122C2×D47—22no—
123C2×D47—22no—
124C2×D47—24no—
125C2×D47—24no—
126C2×D47—41no—
127C2×D47—41no—
128C2×D47—41no—
129C2×D47—42no—
130C2×D47—42no—
131C2×D47#12414yes—
132C4×C47—22no—
133C4×C47—41no—
134C4×C47—42no—
135C4×C47—42no—
136Dic47—41no—
137Dic47—42no—
138Dic47—42no—
139Dic47#12314yes—
140#2504—471nomaximal, Sylow
141C2×C47—81no—
142C2×C47C2×#12311yescharacteristic
143C2×C47C2×#12411yescharacteristic
144C2×C47#53511yescharacteristic
145C2×C47#55312yes—
146C2×C47#55312yes—
147D47—24no—
148D47—81no—
149C2×#121—471no—
150C22×C4⋊C4—471no—
151#397—471no—
152#397—471no—
153#397—471no—
154#397D4711yescharacteristic, complemented
155#390—472no—
156#386—472no—
157#386—472no—
158#382—472no—
159C4×C22⋊C4—471no—
160C47#250411yescharacteristic, complemented, Sylow
161C22×D4—471no—
162C22×D4—471no—
163C22×D4—471no—
164C23×C4—471no—
165C23×C4—472no—
166#121—944no—
167C2×C4⋊C4—472no—
168C2×C4⋊C4—471no—
169C2×C4⋊C4—471no—
170C2×C4⋊C4—944no—
171C2×C4⋊C4C2×D4711yescharacteristic
172C2×C22⋊C4—471no—
173C2×C22⋊C4—472no—
174C2×C22⋊C4—472no—
175C2×C22⋊C4—472no—
176C2×C22⋊C4—472no—
177C2×C22⋊C4C2×D4711yescharacteristic
178C2×C22⋊C4C2×D4712yes—
179C2×C42—472no—
180#95—471no—
181#95—472no—
182#95—472no—
183#95—472no—
184#95C2×D4711yescharacteristic
185#95C2×D4712yes—
186C24—471no—
187C24—471no—
188C24C22×D4711yescharacteristic
189C2×D4—942no—
190C2×D4—944no—
191C2×D4—942no—
192C2×D4—944no—
193C2×D4—942no—
194C2×D4—944no—
195C22×C4—471no—
196C22×C4—474no—
197C22×C4—471no—
198C22×C4—472no—
199C22×C4—472no—
200C22×C4—944no—
201C22×C4—944no—
202C22×C4—1882no—
203C22×C4—1882no—
204C22×C4C22×D4711yescharacteristic
205C22×C4C22×D4712yes—
206C22×C4C22×D4712yes—
207C22×C4C22×D4711yescharacteristic
208C4⋊C4—22no—
209C4⋊C4—944no—
210C4⋊C4—942no—
211C4⋊C4—942no—
212C22⋊C4—22no—
213C22⋊C4—42no—
214C22⋊C4—944no—
215C22⋊C4—942no—
216C22⋊C4—1882no—
217C22⋊C4—1882no—
218C22⋊C4—1882no—
219C42—944no—
220C23—21no—
221C23—22no—
222C23—22no—
223C23—21no—
224C23—21no—
225C23—472no—
226C23—474no—
227C23—942no—
228C23—941no—
229C23—941no—
230C23—941no—
231C23—942no—
232C23—942no—
233C23—941no—
234C23—941no—
235C23C23×D4711yescharacteristic
236D4—1884no—
237D4—1884no—
238D4—1884no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—472no—
249C2×C4—474no—
250C2×C4—948no—
251C2×C4—941no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—1888no—
260C2×C4D4×D4712yes—
261C22—42no—
262C22—42no—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—474no—
267C22—944no—
268C22—944no—
269C22—942no—
270C22—942no—
271C22—1882no—
272C22—1882no—
273C22—1881no—
274C22—1881no—
275C22—1881no—
276C22C2×D4×D4711yescharacteristic
277C22#41×D4712yes—
278C22#41×D4712yes—
279C22#1309406911yescharacteristic
280C22#1309407011yescharacteristic
281C4—22no—
282C4—42no—
283C4—41no—
284C4—42no—
285C4—474no—
286C4—1882no—
287C4—1881no—
288C4—1882no—
289C2—81no—
290C2—944no—
291C2—3761no—
292C2#123×D4711yescharacteristic
293C2#124×D4711yescharacteristic
294C2#1568968911yescharacteristic
295C2#1568981812yes—
296C2#1568982412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2504
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D47C2semidirect
3. #15689050C2semidirect
4. #15689049C2semidirect
5. #15689048C2semidirect
6. #15689023C2semidirect
7. #15689001C2semidirect
8. #15688999C2semidirect
9. #15688987C2semidirect
10. #15688970C2semidirect
11. C47×#397C2semidirect
154. #397D47semidirect
160. C47#2504semidirect