Finite Group Databasebeta

← D47×#2030 #26243676

Subgroups — D47×#2030 #26243676

Order 12032.

1482 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 217 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
1#543×D47C211yesmaximal, characteristic
2#381×D47C213yesmaximal
3#20244556C213yesmaximal, complemented
4#20244555C213yesmaximal, complemented
5#20244554C211yesmaximal, characteristic, complemented
6#342×D47C213yesmaximal
7C47×#2030C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9#15689749C2213yes—
10#15689748—26no—
11C22⋊Q8×D47—26no—
12C2×C22⋊C4×D47C2213yes—
13C2×C22⋊C4×D47C2213yes—
14#15688986C2213yes—
15#15688985—26no—
16#15688984C2213yes—
17#15688984C2213yes—
18#95×D47—26no—
19#15688890C2213yes—
20#15688889C2216yes—
21C47×#543C2211yescharacteristic
22C47×#381C2213yes—
23C47×#342C2213yes—
24C24×D47C2311yescharacteristic
25C2×Q8×D47—22no—
26C23×Dic47C2311yescharacteristic
27C22×C4×D47—23no—
28C22×C4×D47—23no—
29C22×C4×D47—26no—
30C22×C4×D47—23no—
31C22×C4×D47D416yes—
32C22×C4×D47Q814yescomplemented
33#13094004—26no—
34#13094003—26no—
35#13094002—212no—
36#13094001—212no—
37#13094000—26no—
38C4⋊C4×D47—26no—
39C2×C22⋊Dic47C2313yes—
40C2×C22⋊Dic47C2313yes—
41C2×(C2×D47)⋊C4—23no—
42C2×(C2×D47)⋊C4D416yes—
43C22⋊C4×D47—26no—
44C22⋊C4×D47—26no—
45C22⋊C4×D47—212no—
46C47⋊#95—26no—
47C47⋊#95—26no—
48C47⋊#95—26no—
49C23×C4×C47C2311yescharacteristic
50C22⋊Q8×C47—26no—
51C2×C22⋊C4×C47C2313yes—
52C2×C22⋊C4×C47C2313yes—
53#95×C47—26no—
54C24×C47C2411yescharacteristic
55C23×D47—44no—
56C23×D47C2×D413yes—
57C23×D47C2×D413yes—
58C23×D47C2×Q812yes—
59C23×D47#4116yes—
60C2×Q8×C47—22no—
61C22×C4×C47—23no—
62C22×C4×C47—23no—
63C22×C4×C47—23no—
64C22×C4×C47C2×D416yes—
65C22×C4×C47C2×Q812yescomplemented
66C22×Dic47—23no—
67C22×Dic47—23no—
68C22×Dic47—23no—
69C22×Dic47C2×D416yes—
70C22×Dic47C2×Q812yescomplemented
71Q8×D47—84no—
72C2×C4×D47—26no—
73C2×C4×D47—212no—
74C2×C4×D47—212no—
75C2×C4×D47—26no—
76C2×C4×D47—43no—
77C2×C4×D47—41no—
78C2×C4×D47—46no—
79C2×C4×D47—46no—
80C2×C4×D47—412no—
81C2×C4×D47—412no—
82C2×C4×D47—46no—
83C2×Dic94—26no—
84C4⋊C4×C47—26no—
85C22⋊C4×C47—26no—
86C22⋊C4×C47—26no—
87C22⋊Dic47—26no—
88C22⋊Dic47—26no—
89(C2×D47)⋊C4—212no—
90(C2×D47)⋊C4—46no—
91C4⋊Dic47—26no—
92Dic47⋊C4—212no—
93C23×C47—42no—
94C23×C47C22×D413yes—
95C23×C47C22×Q811yescharacteristic
96C23×C47C2×#4113yes—
97C22×D47—212no—
98C22×D47—44no—
99C22×D47—412no—
100C22×D47—46no—
101C22×D47#12013yes—
102C22×D47#12011yescharacteristic
103C22×D47C22⋊Q816yes—
104C22×D47C22⋊Q816yes—
105C22×D47#12416yes—
106C22×D47#12416yes—
107Q8×C47—82no—
108C2×C4×C47—26no—
109C2×C4×C47—26no—
110C2×C4×C47—41no—
111C2×C4×C47—43no—
112C2×C4×C47—46no—
113C2×C4×C47—46no—
114C2×C4×C47—43no—
115C2×Dic47—26no—
116C2×Dic47—26no—
117C2×Dic47—41no—
118C2×Dic47—43no—
119C2×Dic47—46no—
120C2×Dic47—46no—
121C2×Dic47—43no—
122C4×D47—412no—
123C4×D47—44no—
124C4×D47—412no—
125C4×D47—86no—
126C4×D47—812no—
127Dic94—86no—
128C2×#2030—471nomaximal, Sylow
129C22×C47—26no—
130C22×C47—41no—
131C22×C47—43no—
132C22×C47C2×#12011yescharacteristic
133C22×C47C2×C22⋊Q813yes—
134C22×C47C2×#12413yes—
135C2×D47—26no—
136C2×D47—212no—
137C2×D47—212no—
138C2×D47—46no—
139C2×D47—46no—
140C2×D47#39316yes—
141C2×D47#39312yes—
142C2×D47#45814yes—
143C4×C47—42no—
144C4×C47—46no—
145C4×C47—83no—
146Dic47—42no—
147Dic47—46no—
148Dic47—83no—
149C2×#543—471no—
150C2×#381—473no—
151#2030—473no—
152#2030—473no—
153#2030—471no—
154#2030D4711yescharacteristic, direct product factor
155C2×#342—473no—
156C2×C47—23no—
157C2×C47—23no—
158C2×C47C2×#39311yescharacteristic
159C2×C47C2×#45812yes—
160D47—26no—
161D47#203014yesdirect product factor
162C24×C4—471no—
163#543—473no—
164#543—946no—
165#543C2×D4711yescharacteristic
166C2×C22⋊Q8—946no—
167C22×C22⋊C4—473no—
168C22×C22⋊C4—473no—
169#381—473no—
170#381—473no—
171#381—473no—
172#381—946no—
173#381C2×D4713yes—
174C2×#95—946no—
175#342—476no—
176#342—473no—
177#342C2×D4713yes—
178C47C2×#203011yescharacteristic, complemented, Sylow
179C25—471no—
180C22×Q8—942no—
181C23×C4—471no—
182C23×C4—474no—
183C23×C4—476no—
184C23×C4—943no—
185C23×C4—943no—
186C23×C4—946no—
187C23×C4—943no—
188C23×C4C22×D4711yescharacteristic
189C22⋊Q8—26no—
190C22⋊Q8—9412no—
191C22⋊Q8—9412no—
192C22⋊Q8—946no—
193C22⋊Q8—946no—
194C22⋊Q8—946no—
195C2×C4⋊C4—946no—
196C2×C22⋊C4—473no—
197C2×C22⋊C4—476no—
198C2×C22⋊C4—473no—
199C2×C22⋊C4—946no—
200C2×C22⋊C4—946no—
201C2×C22⋊C4—9412no—
202C2×C22⋊C4—943no—
203C2×C22⋊C4C22×D4713yes—
204C2×C22⋊C4C22×D4713yes—
205#95—26no—
206#95—946no—
207#95—946no—
208#95—946no—
209C24—473no—
210C24—473no—
211C24—472no—
212C24—476no—
213C24—1884no—
214C24C23×D4711yescharacteristic
215C2×Q8—22no—
216C2×Q8—946no—
217C2×Q8—3764no—
218C22×C4—23no—
219C22×C4—23no—
220C22×C4—23no—
221C22×C4—472no—
222C22×C4—476no—
223C22×C4—946no—
224C22×C4—946no—
225C22×C4—9412no—
226C22×C4—9412no—
227C22×C4—943no—
228C22×C4—943no—
229C22×C4—943no—
230C22×C4—1886no—
231C22×C4—18812no—
232C22×C4—18812no—
233C22×C4—1881no—
234C22×C4—1883no—
235C22×C4—1886no—
236C22×C4—1886no—
237C22×C4D4×D4716yes—
238C22×C4Q8×D4712yescomplemented
239C4⋊C4—26no—
240C4⋊C4—9412no—
241C4⋊C4—946no—
242C22⋊C4—26no—
243C22⋊C4—26no—
244C22⋊C4—9412no—
245C22⋊C4—946no—
246C22⋊C4—946no—
247C22⋊C4—1886no—
248C23—42no—
249C23—471no—
250C23—473no—
251C23—476no—
252C23—476no—
253C23—476no—
254C23—476no—
255C23—9412no—
256C23—1886no—
257C23—1884no—
258C23—18812no—
259C23C2×D4×D4713yes—
260C23C2×Q8×D4711yescharacteristic
261C23#41×D4713yes—
262Q8—82no—
263Q8—3766no—
264C2×C4—26no—
265C2×C4—26no—
266C2×C4—41no—
267C2×C4—43no—
268C2×C4—46no—
269C2×C4—46no—
270C2×C4—43no—
271C2×C4—946no—
272C2×C4—946no—
273C2×C4—3766no—
274C2×C4—37612no—
275C2×C4—1884no—
276C2×C4—18812no—
277C2×C4—18812no—
278C2×C4—1886no—
279C2×C4—1883no—
280C2×C4—1881no—
281C2×C4—1883no—
282C2×C4—1886no—
283C22—26no—
284C22—41no—
285C22—43no—
286C22—472no—
287C22—474no—
288C22—476no—
289C22—9412no—
290C22—9412no—
291C22—946no—
292C22—1886no—
293C22—1886no—
294C22#120×D4711yescharacteristic
295C22C22⋊Q8×D4713yes—
296C22#124×D4713yes—
297C4—42no—
298C4—46no—
299C4—83no—
300C4—3763no—
301C4—1882no—
302C4—1886no—
303C2—23no—
304C2—23no—
305C2—474no—
306C2—946no—
307C2#393×D4711yescharacteristic
308C2#458×D4712yes—
subgroupG/H
centerC22#120×D47
commutator, cosocleC24×C47C24
FrattiniC24C23×D47
FittingC47×#2030C2
socleC22×C47C2×#120
prime radicalC24×D47C23
hypercenter#2030D47
hypocenterC47C2×#2030
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #2030

Complements

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

NH ≅ G/Ntype
3. #20244556C2semidirect
4. #20244555C2semidirect
5. #20244554C2semidirect
7. C47×#2030C2semidirect
32. C22×C4×D47Q8semidirect
65. C22×C4×C47C2×Q8semidirect
70. C22×Dic47C2×Q8semidirect
154. #2030D47direct (N × H)
161. D47#2030direct (N × H)
178. C47C2×#2030semidirect
238. C22×C4Q8×D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#543×D472
#381×D472
#202445562
#202445552
#202445542
#342×D472
C47×#20302
C2×#203047