Finite Group Databasebeta

← C47×#7797 #26047495

Subgroups — C47×#7797 #26047495

Order 12032.

478 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C47×#2683C211yesmaximal, characteristic
2C47×#2093C211yesmaximal, characteristic
3C47×#2083C212yesmaximal, complemented
4C47×#1271C212yesmaximal, complemented
5C47×#1270C211yesmaximal, characteristic
6C2×C22⋊Q8×C47—22no—
7C2×#107×C47—22no—
8C2×#107×C47—21no—
9C2×#102×C47—21no—
10C47×#396—22no—
11C47×#395—21no—
12C47×#390C2211yescharacteristic
13C47×#389C2212yes—
14C47×#386—21no—
15C47×#384C2211yescharacteristic
16C47×#340—22no—
17C47×#336C2212yes—
18C47×#336C2211yescharacteristic
19C22×Q8×C47—21no—
20C22×D4×C47D411yescharacteristic
21C23×C4×C47—21no—
22C22×C8×C47—22no—
23C22×C8×C47—21no—
24C22⋊Q8×C47—44no—
25C22⋊Q8×C47—44no—
26C2×C4⋊C4×C47—22no—
27C2×C4⋊C4×C47—22no—
28C2×C4⋊C4×C47—22no—
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47D412yes—
31C2×C4⋊C4×C47D412yes—
32C2×C4⋊C4×C47D411yescharacteristic
33C2×C22⋊C4×C47—22no—
34C2×C22⋊C4×C47—22no—
35C2×C22⋊C4×C47—21no—
36C2×C42×C47C2311yescharacteristic
37#107×C47—42no—
38#107×C47—44no—
39#102×C47—42no—
40#95×C47—21no—
41#95×C47—22no—
42C24×C47—21no—
43C2×Q8×C47—44no—
44C2×Q8×C47—81no—
45C2×D4×C47—21no—
46C2×D4×C47—41no—
47C2×D4×C47—41no—
48C2×D4×C47Q1612yes—
49C22×C4×C47—22no—
50C22×C4×C47—21no—
51C22×C4×C47—22no—
52C22×C4×C47—44no—
53C22×C4×C47—41no—
54C22×C4×C47—81no—
55C22×C4×C47C2×D412yes—
56C22×C4×C47C2×D411yescharacteristic
57C2×C8×C47—22no—
58C2×C8×C47—24no—
59C2×C8×C47—42no—
60C2×C8×C47—41no—
61C2×C8×C47—42no—
62C2×C8×C47—41no—
63C4⋊C4×C47—22no—
64C4⋊C4×C47—44no—
65C4⋊C4×C47—41no—
66C4⋊C4×C47—42no—
67C4⋊C4×C47—41no—
68C4⋊C4×C47—41no—
69C4⋊C4×C47—42no—
70C4⋊C4×C47—42no—
71C4⋊C4×C47—42no—
72C4⋊C4×C47—42no—
73C4⋊C4×C47D814yes—
74C22⋊C4×C47—44no—
75C22⋊C4×C47—42no—
76C22⋊C4×C47—42no—
77C22⋊C4×C47—81no—
78C42×C47—41no—
79C23×C47—22no—
80C23×C47—42no—
81C23×C47—41no—
82C23×C47—42no—
83C23×C47—41no—
84C23×C47#12011yescharacteristic
85Q8×C47—84no—
86D4×C47—42no—
87D4×C47—81no—
88C2×C4×C47—21no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47—24no—
93C2×C4×C47—42no—
94C2×C4×C47—42no—
95C2×C4×C47—42no—
96C2×C4×C47—42no—
97C2×C4×C47—41no—
98C2×C4×C47—42no—
99C2×C4×C47—42no—
100C2×C4×C47—84no—
101C2×C4×C47—82no—
102C2×C4×C47—81no—
103C2×C4×C47C2×D812yes—
104C2×C4×C47C2×Q1611yescharacteristic
105C2×C4×C47AGL(1,ℤ/8)12yes—
106C2×C4×C47#13711yescharacteristic
107C8×C47—44no—
108C8×C47—42no—
109#7797C4711yesmaximal, characteristic, direct product factor, Sylow
110C22×C47—42no—
111C22×C47—44no—
112C22×C47—82no—
113C22×C47—81no—
114C22×C47—81no—
115C22×C47#44712yes—
116C22×C47#45111yescharacteristic
117C22×C47#45311yescharacteristic
118C22×C47#45612yes—
119C22×C47#45811yescharacteristic
120C4×C47—22no—
121C4×C47—22no—
122C4×C47—21no—
123C4×C47—21no—
124C4×C47—44no—
125C4×C47—82no—
126C4×C47—81no—
127C4×C47—161no—
128#2683C2×C4711yescharacteristic
129#2093C2×C4711yescharacteristic
130#2083C2×C4712yescomplemented
131#1271C2×C4712yescomplemented
132#1270C2×C4711yescharacteristic
133C2×C47—82no—
134C2×C47#161012yes—
135C2×C47#161411yescharacteristic
136C2×C47#161911yescharacteristic
137C2×C47#164912yes—
138C2×C47#166011yescharacteristic
139C2×C22⋊Q8—22no—
140C2×#107—22no—
141C2×#107—21no—
142C2×#102—21no—
143#396—22no—
144#395—21no—
145#390C22×C4711yescharacteristic
146#389C22×C4712yes—
147#386—21no—
148#384C22×C4711yescharacteristic
149#340—22no—
150#336C22×C4712yes—
151#336C22×C4711yescharacteristic
152C47#779711yescharacteristic, direct product factor, Sylow
153C22×Q8—21no—
154C22×D4D4×C4711yescharacteristic
155C23×C4—21no—
156C22×C8—22no—
157C22×C8—21no—
158C22⋊Q8—44no—
159C22⋊Q8—44no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4D4×C4712yes—
165C2×C4⋊C4D4×C4712yes—
166C2×C4⋊C4D4×C4711yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—21no—
170C2×C42C23×C4711yescharacteristic
171#107—42no—
172#107—44no—
173#102—42no—
174#95—21no—
175#95—22no—
176C24—21no—
177C2×Q8—44no—
178C2×Q8—81no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4Q16×C4712yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—44no—
187C22×C4—41no—
188C22×C4—81no—
189C22×C4C2×D4×C4712yes—
190C22×C4C2×D4×C4711yescharacteristic
191C2×C8—22no—
192C2×C8—24no—
193C2×C8—42no—
194C2×C8—41no—
195C2×C8—42no—
196C2×C8—41no—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—44no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4D8×C4714yes—
208C22⋊C4—44no—
209C22⋊C4—42no—
210C22⋊C4—42no—
211C22⋊C4—81no—
212C42—41no—
213C23—22no—
214C23—41no—
215C23—42no—
216C23—41no—
217C23—42no—
218C23#120×C4711yescharacteristic
219Q8—84no—
220D4—42no—
221D4—81no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4—81no—
236C2×C4—82no—
237C2×C4C2×D8×C4712yes—
238C2×C4C2×Q16×C4711yescharacteristic
239C2×C4AGL(1,ℤ/8)×C4712yes—
240C2×C4#137×C4711yescharacteristic
241C8—44no—
242C8—42no—
243C22—42no—
244C22—44no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22C47×#44712yes—
249C22C47×#45111yescharacteristic
250C22C47×#45311yescharacteristic
251C22C47×#45612yes—
252C22C47×#45811yescharacteristic
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—44no—
258C4—82no—
259C4—81no—
260C4—161no—
261C2—82no—
262C2C47×#161012yes—
263C2C47×#161411yescharacteristic
264C2C47×#161911yescharacteristic
265C2C47×#164912yes—
266C2C47×#166011yescharacteristic
subgroupG/H
center, socleC23×C47#120
commutator, Frattini, cosocleC2×C42C23×C47
prime radicalC22×D4×C47D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#2083C2semidirect
4. C47×#1271C2semidirect
109. #7797C47direct (N × H)
130. #2083C2×C47semidirect
131. #1271C2×C47semidirect
152. C47#7797direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#26832
C47×#20932
C47×#20832
C47×#12712
C47×#12702
#779747