Finite Group Databasebeta

← C47×#7833 #26047531

Subgroups — C47×#7833 #26047531

Order 12032.

438 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2804C211yesmaximal, characteristic
2C47×#2095C212yesmaximal, complemented
3C47×#2094C211yesmaximal, characteristic
4C47×#1272C212yesmaximal, complemented
5C47×#1270C211yesmaximal, characteristic
6C2×#107×C47—22no—
7C2×#106×C47—21no—
8C2×#103×C47—22no—
9C2×#102×C47—21no—
10C47×#400—21no—
11C47×#393—22no—
12C47×#391C2212yes—
13C47×#390C2211yescharacteristic
14C47×#386—21no—
15C47×#385—22no—
16C47×#384C2211yescharacteristic
17C47×#336C2212yes—
18C47×#336C2211yescharacteristic
19C22×Q8×C47D412yes—
20C22×D4×C47D411yescharacteristic
21C23×C4×C47—21no—
22C22×C8×C47—21no—
23C22×C8×C47—22no—
24C2×C4⋊C4×C47—21no—
25C2×C4⋊C4×C47—22no—
26C2×C4⋊C4×C47—21no—
27C2×C4⋊C4×C47D412yes—
28C2×C4⋊C4×C47D411yescharacteristic
29C2×C22⋊C4×C47—22no—
30C2×C22⋊C4×C47—22no—
31C2×C22⋊C4×C47—21no—
32C2×C42×C47C2311yescharacteristic
33#107×C47—44no—
34#106×C47—42no—
35#103×C47—44no—
36#102×C47—42no—
37#95×C47—22no—
38#95×C47—21no—
39#95×C47—22no—
40#95×C47—22no—
41C24×C47—21no—
42C2×Q8×C47—22no—
43C2×Q8×C47—22no—
44C2×Q8×C47—42no—
45C2×Q8×C47—42no—
46C2×D4×C47—21no—
47C2×D4×C47—41no—
48C2×D4×C47—41no—
49C2×D4×C47Q1612yes—
50C22×C4×C47—21no—
51C22×C4×C47—22no—
52C22×C4×C47—22no—
53C22×C4×C47—41no—
54C22×C4×C47—82no—
55C22×C4×C47—81no—
56C22×C4×C47C2×D411yescharacteristic
57C22×C4×C47C2×D412yes—
58C2×C8×C47—24no—
59C2×C8×C47—22no—
60C2×C8×C47—41no—
61C2×C8×C47—42no—
62C2×C8×C47—42no—
63C2×C8×C47—41no—
64C4⋊C4×C47—41no—
65C4⋊C4×C47—42no—
66C4⋊C4×C47—42no—
67C4⋊C4×C47—41no—
68C4⋊C4×C47—42no—
69C4⋊C4×C47—41no—
70C4⋊C4×C47—81no—
71C22⋊C4×C47—42no—
72C22⋊C4×C47—42no—
73C22⋊C4×C47—82no—
74C22⋊C4×C47—81no—
75C42×C47—41no—
76C23×C47—22no—
77C23×C47—42no—
78C23×C47—42no—
79C23×C47—41no—
80C23×C47—41no—
81C23×C47#12011yescharacteristic
82Q8×C47—44no—
83Q8×C47—82no—
84D4×C47—42no—
85D4×C47—81no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—22no—
90C2×C4×C47—42no—
91C2×C4×C47—42no—
92C2×C4×C47—42no—
93C2×C4×C47—42no—
94C2×C4×C47—41no—
95C2×C4×C47—42no—
96C2×C4×C47—42no—
97C2×C4×C47—42no—
98C2×C4×C47—84no—
99C2×C4×C47—81no—
100C2×C4×C47—82no—
101C2×C4×C47C2×Q1611yescharacteristic
102C2×C4×C47#13512yes—
103C2×C4×C47#13711yescharacteristic
104C2×C4×C47#13712yes—
105C8×C47—42no—
106C8×C47—44no—
107#7833C4711yesmaximal, characteristic, direct product factor, Sylow
108C22×C47—42no—
109C22×C47—44no—
110C22×C47—82no—
111C22×C47—81no—
112C22×C47—81no—
113C22×C47#45111yescharacteristic
114C22×C47#45212yes—
115C22×C47#45311yescharacteristic
116C22×C47#45312yes—
117C22×C47#45811yescharacteristic
118C4×C47—21no—
119C4×C47—21no—
120C4×C47—22no—
121C4×C47—22no—
122C4×C47—82no—
123C4×C47—81no—
124C4×C47—82no—
125C4×C47—161no—
126#2804C2×C4711yescharacteristic
127#2095C2×C4712yescomplemented
128#2094C2×C4711yescharacteristic
129#1272C2×C4712yescomplemented
130#1270C2×C4711yescharacteristic
131C2×C47—82no—
132C2×C47#161411yescharacteristic
133C2×C47#161812yes—
134C2×C47#163011yescharacteristic
135C2×C47#163212yes—
136C2×C47#165511yescharacteristic
137C2×#107—22no—
138C2×#106—21no—
139C2×#103—22no—
140C2×#102—21no—
141#400—21no—
142#393—22no—
143#391C22×C4712yes—
144#390C22×C4711yescharacteristic
145#386—21no—
146#385—22no—
147#384C22×C4711yescharacteristic
148#336C22×C4711yescharacteristic
149#336C22×C4712yes—
150C47#783311yescharacteristic, direct product factor, Sylow
151C22×Q8D4×C4712yes—
152C22×D4D4×C4711yescharacteristic
153C23×C4—21no—
154C22×C8—21no—
155C22×C8—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4D4×C4712yes—
160C2×C4⋊C4D4×C4711yescharacteristic
161C2×C22⋊C4—22no—
162C2×C22⋊C4—22no—
163C2×C22⋊C4—21no—
164C2×C42C23×C4711yescharacteristic
165#107—44no—
166#106—42no—
167#103—44no—
168#102—42no—
169#95—22no—
170#95—21no—
171#95—22no—
172#95—22no—
173C24—21no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—42no—
177C2×Q8—42no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4Q16×C4712yes—
182C22×C4—22no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—41no—
186C22×C4—82no—
187C22×C4—81no—
188C22×C4C2×D4×C4711yescharacteristic
189C22×C4C2×D4×C4712yes—
190C2×C8—22no—
191C2×C8—24no—
192C2×C8—41no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—81no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—82no—
206C22⋊C4—81no—
207C42—41no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23—41no—
212C23—41no—
213C23#120×C4711yescharacteristic
214Q8—44no—
215Q8—82no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4C2×Q16×C4711yescharacteristic
234C2×C4#135×C4712yes—
235C2×C4#137×C4711yescharacteristic
236C2×C4#137×C4712yes—
237C8—42no—
238C8—44no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22C47×#45111yescharacteristic
245C22C47×#45212yes—
246C22C47×#45311yescharacteristic
247C22C47×#45312yes—
248C22C47×#45811yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—81no—
255C4—82no—
256C4—161no—
257C2—82no—
258C2C47×#161411yescharacteristic
259C2C47×#161812yes—
260C2C47×#163011yescharacteristic
261C2C47×#163212yes—
262C2C47×#165511yescharacteristic
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
2. C47×#2095C2semidirect
4. C47×#1272C2semidirect
107. #7833C47direct (N × H)
127. #2095C2×C47semidirect
129. #1272C2×C47semidirect
150. C47#7833direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#28042
C47×#20952
C47×#20942
C47×#12722
C47×#12702
#783347