Finite Group Databasebeta

← C47×#10393 #26050091

Subgroups — C47×#10393 #26050091

Order 12032.

526 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2842C211yesmaximal, characteristic
2C47×#1819C212yesmaximal
3C47×#1819C211yesmaximal, characteristic
4C47×#1304C211yesmaximal, characteristic
5C47×#1304C212yesmaximal
6C22×C22⋊C4×C47C2211yescharacteristic
7C47×#399—22no—
8C47×#396—24no—
9C47×#379C2212yes—
10C47×#379C2211yescharacteristic
11C47×#379C2211yescharacteristic
12C47×#379C2212yes—
13C47×#342—24no—
14C47×#342—22no—
15C25×C47C2311yescharacteristic
16C23×C4×C47Q812yes—
17C2×C4⋊C4×C47—24no—
18C2×C4⋊C4×C47—22no—
19C2×C22⋊C4×C47—22no—
20C2×C22⋊C4×C47—21no—
21C2×C22⋊C4×C47—21no—
22C2×C22⋊C4×C47—22no—
23C2×C22⋊C4×C47—22no—
24C2×C22⋊C4×C47—21no—
25C2×C22⋊C4×C47—22no—
26C2×C22⋊C4×C47—22no—
27C2×C22⋊C4×C47—22no—
28C2×C22⋊C4×C47—22no—
29C2×C22⋊C4×C47—22no—
30C2×C22⋊C4×C47—22no—
31C2×C22⋊C4×C47D414yes—
32C2×C22⋊C4×C47D412yes—
33#95×C47—22no—
34C24×C47—42no—
35C24×C47—82no—
36C24×C47C2×D412yes—
37C24×C47C2×D411yescharacteristic
38C24×C47C2×Q811yescharacteristic
39C24×C47#4112yes—
40C24×C47#4111yescharacteristic
41C22×C4×C47—22no—
42C22×C4×C47—24no—
43C22×C4×C47—22no—
44C22×C4×C47—22no—
45C22×C4×C47—22no—
46C22×C4×C47—42no—
47C22×C4×C47—41no—
48C22×C4×C47—82no—
49C4⋊C4×C47—84no—
50C4⋊C4×C47—82no—
51C22⋊C4×C47—41no—
52C22⋊C4×C47—42no—
53C22⋊C4×C47—41no—
54C22⋊C4×C47—44no—
55C22⋊C4×C47—42no—
56C22⋊C4×C47—44no—
57C22⋊C4×C47—42no—
58C22⋊C4×C47—82no—
59C22⋊C4×C47—82no—
60C22⋊C4×C47—82no—
61C22⋊C4×C47—82no—
62C22⋊C4×C47—82no—
63C22⋊C4×C47—82no—
64C23×C47—24no—
65C23×C47—22no—
66C23×C47—42no—
67C23×C47—41no—
68C23×C47—42no—
69C23×C47—42no—
70C23×C47—42no—
71C23×C47—42no—
72C23×C47—42no—
73C23×C47—42no—
74C23×C47—41no—
75C23×C47—42no—
76C23×C47—88no—
77C23×C47#12011yescharacteristic
78C23×C47C22⋊Q812yes—
79C23×C47C22⋊Q811yescharacteristic
80C23×C47#12412yes—
81C23×C47#12411yescharacteristic
82C2×C4×C47—44no—
83C2×C4×C47—44no—
84C2×C4×C47—44no—
85C2×C4×C47—42no—
86C2×C4×C47—44no—
87C2×C4×C47—42no—
88C2×C4×C47—82no—
89C2×C4×C47—82no—
90C2×C4×C47—82no—
91C2×C4×C47—82no—
92C2×C4×C47—81no—
93C2×C4×C47—82no—
94C2×C4×C47—82no—
95C2×C4×C47—82no—
96#10393C4711yesmaximal, characteristic, direct product factor, Sylow
97C22×C47—22no—
98C22×C47—22no—
99C22×C47—21no—
100C22×C47—22no—
101C22×C47—21no—
102C22×C47—22no—
103C22×C47—22no—
104C22×C47—22no—
105C22×C47—22no—
106C22×C47—22no—
107C22×C47—22no—
108C22×C47—44no—
109C22×C47—84no—
110C22×C47—82no—
111C22×C47—82no—
112C22×C47—84no—
113C22×C47#39311yescharacteristic
114C22×C47#45812yes—
115C4×C47—82no—
116C4×C47—84no—
117C4×C47—82no—
118C4×C47—162no—
119C4×C47—161no—
120#2842C2×C4711yescharacteristic
121#1819C2×C4712yes—
122#1819C2×C4711yescharacteristic
123#1304C2×C4711yescharacteristic
124#1304C2×C4712yes—
125C2×C47—22no—
126C2×C47—42no—
127C2×C47—41no—
128C2×C47—42no—
129C2×C47—41no—
130C2×C47#203011yescharacteristic
131C2×C47#203212yes—
132C22×C22⋊C4C22×C4711yescharacteristic
133#399—22no—
134#396—24no—
135#379C22×C4712yes—
136#379C22×C4711yescharacteristic
137#379C22×C4711yescharacteristic
138#379C22×C4712yes—
139#342—24no—
140#342—22no—
141C47#1039311yescharacteristic, direct product factor, Sylow
142C25C23×C4711yescharacteristic
143C23×C4Q8×C4712yes—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—22no—
146C2×C22⋊C4—22no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—22no—
153C2×C22⋊C4—22no—
154C2×C22⋊C4—22no—
155C2×C22⋊C4—22no—
156C2×C22⋊C4—22no—
157C2×C22⋊C4—22no—
158C2×C22⋊C4D4×C4714yes—
159C2×C22⋊C4D4×C4712yes—
160#95—22no—
161C24—42no—
162C24—82no—
163C24C2×D4×C4712yes—
164C24C2×D4×C4711yescharacteristic
165C24C2×Q8×C4711yescharacteristic
166C24#41×C4712yes—
167C24#41×C4711yescharacteristic
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—41no—
175C22×C4—82no—
176C4⋊C4—84no—
177C4⋊C4—82no—
178C22⋊C4—41no—
179C22⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—44no—
182C22⋊C4—42no—
183C22⋊C4—44no—
184C22⋊C4—42no—
185C22⋊C4—82no—
186C22⋊C4—82no—
187C22⋊C4—82no—
188C22⋊C4—82no—
189C22⋊C4—82no—
190C22⋊C4—82no—
191C23—24no—
192C23—22no—
193C23—42no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—42no—
201C23—41no—
202C23—42no—
203C23—88no—
204C23#120×C4711yescharacteristic
205C23C22⋊Q8×C4712yes—
206C23C22⋊Q8×C4711yescharacteristic
207C23#124×C4712yes—
208C23#124×C4711yescharacteristic
209C2×C4—44no—
210C2×C4—44no—
211C2×C4—44no—
212C2×C4—44no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—82no—
216C2×C4—82no—
217C2×C4—82no—
218C2×C4—82no—
219C2×C4—81no—
220C2×C4—82no—
221C2×C4—82no—
222C2×C4—82no—
223C22—22no—
224C22—22no—
225C22—21no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—84no—
236C22—82no—
237C22—82no—
238C22—84no—
239C22C47×#39311yescharacteristic
240C22C47×#45812yes—
241C4—82no—
242C4—84no—
243C4—82no—
244C4—162no—
245C4—161no—
246C2—22no—
247C2—42no—
248C2—41no—
249C2—42no—
250C2—41no—
251C2C47×#203011yescharacteristic
252C2C47×#203212yes—
subgroupG/H
center, socleC22×C47#393
commutator, Frattini, cosocleC25C23×C47
prime radicalC25×C47C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
96. #10393C47direct (N × H)
141. C47#10393direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#28422
C47×#18192
C47×#13042
#1039347