Finite Group Databasebeta

← #20248864

Subgroups — #20248864

Order 6016.

596 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 139 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×#13093999C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
3#15689061C211yesmaximal, characteristic, complemented
4#15689041C211yesmaximal, characteristic, complemented
5#15689040C211yesmaximal, characteristic, complemented
6#15689015C212yesmaximal, complemented
7#15689012C212yesmaximal, complemented
8#15689001C212yesmaximal, complemented
9#15689001C212yesmaximal, complemented
10#15688970C211yesmaximal, characteristic, complemented
11C47×#400C211yesmaximal, characteristic, complemented
12C22×D188C2212yes—
13C22×D188C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15C22×C4×D47C2211yescharacteristic
16C22×C4×D47C2211yescharacteristic
17#13093999—24no—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C4⋊C4×D47—24no—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×C4×Dic47C2212yes—
29C47⋊#95C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34#95×C47C2211yescharacteristic
35#95×C47C2212yes—
36#95×C47C2212yes—
37C23×D47C2312yes—
38C23×D47C2311yescharacteristic
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×Dic47C2312yes—
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C2×D188—24no—
49C2×D188—24no—
50C2×D188—24no—
51C2×D188—22no—
52C2×D188—42no—
53C2×C4×D47—22no—
54C2×C4×D47—22no—
55C2×C4×D47—22no—
56C2×C4×D47—22no—
57C2×C4×D47—42no—
58C2×C4×D47—42no—
59C2×C4×D47D414yes—
60C4⋊C4×C47—22no—
61C4⋊C4×C47—22no—
62(C2×D47)⋊C4—24no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—24no—
65(C2×D47)⋊C4—24no—
66(C2×D47)⋊C4—42no—
67(C2×D47)⋊C4—42no—
68C4⋊Dic47—22no—
69Dic47⋊C4—22no—
70Dic47⋊C4—22no—
71C4×Dic47—42no—
72C23×C47C2411yescharacteristic
73C22×D47—21no—
74C22×D47—21no—
75C22×D47—22no—
76C22×D47—22no—
77C22×D47—22no—
78C22×D47—22no—
79C22×D47—22no—
80C22×D47—22no—
81C22×D47—22no—
82C22×D47—22no—
83C22×D47C2×D412yes—
84C22×D47#4114yes—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
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—
97C2×C4×C47#4112yes—
98C2×Dic47—21no—
99C2×Dic47—21no—
100C2×Dic47—22no—
101C2×Dic47—21no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47C2×D412yes—
107C2×Dic47#4112yes—
108D188—44no—
109D188—48no—
110C4×D47—28no—
111C4×D47—44no—
112C4×D47—44no—
113C22×C47C22×D411yescharacteristic
114C22×C47C2×#4111yescharacteristic
115C22×C47C2×#4112yes—
116C22×C47C2×#4111yescharacteristic
117C22×C47H(5,𝔽2)12yes—
118C2×D47—22no—
119C2×D47—22no—
120C2×D47—24no—
121C2×D47—24no—
122C2×D47—42no—
123C2×D47—42no—
124C2×D47—42no—
125C2×D47—42no—
126C2×D47—42no—
127C2×D47—42no—
128C2×D47—42no—
129C2×D47#12414yes—
130C4×C47—22no—
131C4×C47—22no—
132C4×C47—42no—
133C4×C47—41no—
134C4×C47—42no—
135Dic47—22no—
136Dic47—22no—
137Dic47—41no—
138Dic47—42no—
139#2591—471nomaximal, Sylow
140C2×C47#52511yescharacteristic
141C2×C47C2×#12411yescharacteristic
142C2×C47#53411yescharacteristic
143C2×C47#55312yes—
144C2×C47#55312yes—
145D47—24no—
146D47—82no—
147C2×#121—471no—
148C22×C4⋊C4—471no—
149#400—471no—
150#400D4711yescharacteristic, complemented
151#394—471no—
152#394—471no—
153#388—472no—
154#388—472no—
155#386—472no—
156#386—472no—
157C4×C22⋊C4—471no—
158C47#259111yescharacteristic, complemented, Sylow
159C22×D4—472no—
160C22×D4—471no—
161C23×C4—471no—
162C23×C4—471no—
163C23×C4—471no—
164#121—944no—
165C2×C4⋊C4—471no—
166C2×C4⋊C4—471no—
167C2×C4⋊C4—471no—
168C2×C4⋊C4—944no—
169C2×C4⋊C4C2×D4711yescharacteristic
170C2×C4⋊C4C2×D4711yescharacteristic
171C2×C22⋊C4—472no—
172C2×C22⋊C4—472no—
173C2×C22⋊C4—472no—
174C2×C22⋊C4—472no—
175C2×C22⋊C4—472no—
176C2×C22⋊C4—472no—
177C2×C42—472no—
178#95—471no—
179#95—472no—
180#95—472no—
181#95C2×D4711yescharacteristic
182#95C2×D4712yes—
183#95C2×D4712yes—
184C24—471no—
185C24—472no—
186C2×D4—944no—
187C2×D4—944no—
188C2×D4—944no—
189C2×D4—942no—
190C2×D4—1882no—
191C22×C4—471no—
192C22×C4—471no—
193C22×C4—474no—
194C22×C4—472no—
195C22×C4—471no—
196C22×C4—942no—
197C22×C4—942no—
198C22×C4—942no—
199C22×C4—942no—
200C22×C4—1882no—
201C22×C4—1882no—
202C22×C4C22×D4712yes—
203C22×C4C22×D4712yes—
204C22×C4C22×D4711yescharacteristic
205C22×C4C22×D4711yescharacteristic
206C22×C4C22×D4711yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—942no—
210C4⋊C4—942no—
211C4⋊C4—942no—
212C22⋊C4—944no—
213C22⋊C4—944no—
214C22⋊C4—944no—
215C22⋊C4—944no—
216C22⋊C4—1882no—
217C22⋊C4—1882no—
218C42—1882no—
219C23—472no—
220C23—474no—
221C23—941no—
222C23—941no—
223C23—942no—
224C23—942no—
225C23—942no—
226C23—942no—
227C23—942no—
228C23—942no—
229C23—942no—
230C23—942no—
231C23C23×D4711yescharacteristic
232D4—1884no—
233D4—1888no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—472no—
246C2×C4—472no—
247C2×C4—948no—
248C2×C4—941no—
249C2×C4—941no—
250C2×C4—942no—
251C2×C4—941no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—1884no—
257C2×C4—1884no—
258C2×C4D4×D4712yes—
259C2×C4#1062535412yes—
260C22—474no—
261C22—944no—
262C22—944no—
263C22—942no—
264C22—942no—
265C22—1882no—
266C22—1882no—
267C22—1882no—
268C22—1882no—
269C22—1882no—
270C22—1882no—
271C22—1882no—
272C22C2×D4×D4711yescharacteristic
273C22#41×D4711yescharacteristic
274C22#41×D4712yes—
275C22C2×#1062535411yescharacteristic
276C22#1309407012yes—
277C4—22no—
278C4—22no—
279C4—42no—
280C4—42no—
281C4—41no—
282C4—942no—
283C4—942no—
284C4—1882no—
285C4—1881no—
286C2—944no—
287C2—3762no—
288C2#1568963611yescharacteristic
289C2#124×D4711yescharacteristic
290C2#1568968411yescharacteristic
291C2#1568982412yes—
292C2#1568982612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2591
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. #15689061C2semidirect
4. #15689041C2semidirect
5. #15689040C2semidirect
6. #15689015C2semidirect
7. #15689012C2semidirect
8. #15689001C2semidirect
9. #15689001C2semidirect
10. #15688970C2semidirect
11. C47×#400C2semidirect
150. #400D47semidirect
158. C47#2591semidirect