Finite Group Databasebeta

← C47×#11665 #26051363

Subgroups — C47×#11665 #26051363

Order 12032.

360 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#135×C47C211yesmaximal, characteristic
2C47×#2163C211yesmaximal, characteristic, complemented
3C47×#1568C211yesmaximal, characteristic, complemented
4C47×#1334C212yesmaximal, complemented
5C47×#1333C212yesmaximal, complemented
6C2×#135×C47C411yescharacteristic
7C4×#41×C47—21no—
8C4×Q16×C47C411yescharacteristic
9C4×Q16×C47C2211yescharacteristic
10C4×SD16×C47—21no—
11C4×SD16×C47—21no—
12C4×D8×C47C411yescharacteristic
13C4×D8×C47C2211yescharacteristic
14C47×#432—21no—
15C47×#427C411yescharacteristic
16C47×#416—21no—
17C2×C4×C8×C47C2211yescharacteristic
18C47×C4⋊C16—21no—
19C47×C22⋊C16—21no—
20C47×#346C2212yes—
21C47×#335—21no—
22C47×#334C2212yes—
23C2×#41×C47—21no—
24#135×C47—22no—
25#135×C47—22no—
26C2×Q16×C47C2×C411yescharacteristic
27C2×SD16×C47—21no—
28C2×D8×C47C2×C411yescharacteristic
29C22×C8×C47C2×C411yescharacteristic
30C22×C8×C47D411yescharacteristic
31C4×Q8×C47—21no—
32C4×Q8×C47—21no—
33C4×D4×C47—21no—
34C4×D4×C47—21no—
35C4×D4×C47—41no—
36C4×D4×C47—41no—
37#117×C47—21no—
38#117×C47—41no—
39C2×C42×C47—41no—
40C2×C42×C47D411yescharacteristic
41C2×C16×C47—22no—
42#107×C47C2×C411yescharacteristic
43#107×C47C2×C411yescharacteristic
44#106×C47—21no—
45C4⋊C8×C47—22no—
46#103×C47—21no—
47#103×C47—21no—
48#102×C47—21no—
49#102×C47—21no—
50C22⋊C8×C47—41no—
51#97×C47—41no—
52C4×C8×C47C2×C411yescharacteristic
53C4×C8×C47D411yescharacteristic
54C4×C8×C47D411yescharacteristic
55C4×C8×C47C2311yescharacteristic
56#41×C47—24no—
57#41×C47—42no—
58C2×Q8×C47—21no—
59C2×D4×C47—21no—
60C2×D4×C47—41no—
61C22×C4×C47—41no—
62C22×C4×C47—41no—
63C22×C4×C47—41no—
64C22×C4×C47C22⋊C411yescharacteristic
65C22×C4×C47D811yescharacteristic
66C22×C4×C47SD1611yescharacteristic
67Q16×C47—21no—
68Q16×C47M1612yes—
69SD16×C47—24no—
70D8×C47—21no—
71D8×C47M1612yes—
72C2×C8×C47—21no—
73C2×C8×C47—21no—
74C2×C8×C47—41no—
75C2×C8×C47—42no—
76C2×C8×C47C22⋊C411yescharacteristic
77C2×C8×C47C22⋊C411yescharacteristic
78C2×C8×C47C22×C411yescharacteristic
79C2×C8×C47C2×D411yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C22⋊C4×C47—41no—
85C22⋊C4×C47—41no—
86C22⋊C4×C47—41no—
87C42×C47—41no—
88C42×C47—41no—
89C42×C47—41no—
90C42×C47C22⋊C411yescharacteristic
91C42×C47D811yescharacteristic
92C42×C47SD1611yescharacteristic
93C42×C47C2×D411yescharacteristic
94C16×C47—42no—
95C23×C47—41no—
96C23×C47#10211yescharacteristic
97Q8×C47—22no—
98Q8×C47—41no—
99D4×C47—22no—
100D4×C47—44no—
101D4×C47—41no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—44no—
107C2×C4×C47—41no—
108C2×C4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47—82no—
111C2×C4×C47—82no—
112C2×C4×C47#10211yescharacteristic
113C2×C4×C47#10211yescharacteristic
114C2×C4×C47#10211yescharacteristic
115C2×C4×C47C2×C22⋊C411yescharacteristic
116C2×C4×C47C2×D811yescharacteristic
117C2×C4×C47C2×SD1611yescharacteristic
118C8×C47—21no—
119C8×C47—21no—
120C8×C47—21no—
121C8×C47—82no—
122C8×C47C2×M1611yescharacteristic
123C8×C47C2×M1611yescharacteristic
124#11665C4711yesmaximal, characteristic, direct product factor, Sylow
125C22×C47—21no—
126C22×C47—21no—
127C22×C47—21no—
128C22×C47—42no—
129C22×C47—81no—
130C22×C47—81no—
131C22×C47C2×#10211yescharacteristic
132C4×C47—21no—
133C4×C47—21no—
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—21no—
137C4×C47—42no—
138C4×C47—81no—
139C4×C47—81no—
140C4×C47#40711yescharacteristic
141C4×C47#42111yescharacteristic
142C4×#135C2×C4711yescharacteristic
143#2163C2×C4711yescharacteristic, complemented
144#1568C2×C4711yescharacteristic, complemented
145#1334C2×C4712yescomplemented
146#1333C2×C4712yescomplemented
147C2×C47—41no—
148C2×C47—82no—
149C2×C47#148611yescharacteristic
150C2×C47#214511yescharacteristic
151C2×C47#214811yescharacteristic
152C2×#135C4×C4711yescharacteristic
153C4×#41—21no—
154C4×Q16C4×C4711yescharacteristic
155C4×Q16C22×C4711yescharacteristic
156C4×SD16—21no—
157C4×SD16—21no—
158C4×D8C4×C4711yescharacteristic
159C4×D8C22×C4711yescharacteristic
160#432—21no—
161#427C4×C4711yescharacteristic
162#416—21no—
163C2×C4×C8C22×C4711yescharacteristic
164C4⋊C16—21no—
165C22⋊C16—21no—
166#346C22×C4712yes—
167#335—21no—
168#334C22×C4712yes—
169C47#1166511yescharacteristic, direct product factor, Sylow
170C2×#41—21no—
171#135—22no—
172#135—22no—
173C2×Q16C2×C4×C4711yescharacteristic
174C2×SD16—21no—
175C2×D8C2×C4×C4711yescharacteristic
176C22×C8C2×C4×C4711yescharacteristic
177C22×C8D4×C4711yescharacteristic
178C4×Q8—21no—
179C4×Q8—21no—
180C4×D4—21no—
181C4×D4—21no—
182C4×D4—41no—
183C4×D4—41no—
184#117—21no—
185#117—41no—
186C2×C42—41no—
187C2×C42D4×C4711yescharacteristic
188C2×C16—22no—
189#107C2×C4×C4711yescharacteristic
190#107C2×C4×C4711yescharacteristic
191#106—21no—
192C4⋊C8—22no—
193#103—21no—
194#103—21no—
195#102—21no—
196#102—21no—
197C22⋊C8—41no—
198#97—41no—
199C4×C8C2×C4×C4711yescharacteristic
200C4×C8D4×C4711yescharacteristic
201C4×C8D4×C4711yescharacteristic
202C4×C8C23×C4711yescharacteristic
203#41—24no—
204#41—42no—
205C2×Q8—21no—
206C2×D4—21no—
207C2×D4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4C22⋊C4×C4711yescharacteristic
212C22×C4D8×C4711yescharacteristic
213C22×C4SD16×C4711yescharacteristic
214Q16—21no—
215Q16M16×C4712yes—
216SD16—24no—
217D8—21no—
218D8M16×C4712yes—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—41no—
222C2×C8—42no—
223C2×C8C22⋊C4×C4711yescharacteristic
224C2×C8C22⋊C4×C4711yescharacteristic
225C2×C8C22×C4×C4711yescharacteristic
226C2×C8C2×D4×C4711yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C42—41no—
235C42—41no—
236C42—41no—
237C42C22⋊C4×C4711yescharacteristic
238C42D8×C4711yescharacteristic
239C42SD16×C4711yescharacteristic
240C42C2×D4×C4711yescharacteristic
241C16—42no—
242C23—41no—
243C23#102×C4711yescharacteristic
244Q8—22no—
245Q8—41no—
246D4—22no—
247D4—44no—
248D4—41no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—44no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4#102×C4711yescharacteristic
260C2×C4#102×C4711yescharacteristic
261C2×C4#102×C4711yescharacteristic
262C2×C4C2×C22⋊C4×C4711yescharacteristic
263C2×C4C2×D8×C4711yescharacteristic
264C2×C4C2×SD16×C4711yescharacteristic
265C8—21no—
266C8—21no—
267C8—21no—
268C8—82no—
269C8C2×M16×C4711yescharacteristic
270C8C2×M16×C4711yescharacteristic
271C22—21no—
272C22—21no—
273C22—21no—
274C22—42no—
275C22—81no—
276C22—81no—
277C22C2×#102×C4711yescharacteristic
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—42no—
284C4—81no—
285C4—81no—
286C4C47×#40711yescharacteristic
287C4C47×#42111yescharacteristic
288C2—41no—
289C2—82no—
290C2C47×#148611yescharacteristic
291C2C47×#214511yescharacteristic
292C2C47×#214811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#102
commutatorC2×C8C22×C4×C47
Frattini, cosocleC4×C8C23×C47
prime radicalC2×#135×C47C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ C2×C4×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2163C2semidirect
3. C47×#1568C2semidirect
4. C47×#1334C2semidirect
5. C47×#1333C2semidirect
124. #11665C47direct (N × H)
143. #2163C2×C47semidirect
144. #1568C2×C47semidirect
145. #1334C2×C47semidirect
146. #1333C2×C47semidirect
169. C47#11665direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#135×C472
C47×#21632
C47×#15682
C47×#13342
C47×#13332
#1166547