Finite Group Databasebeta

← C47×#12215 #26051913

Subgroups — C47×#12215 #26051913

Order 12032.

400 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2607C211yesmaximal, characteristic
2C47×#2030C211yesmaximal, characteristic
3C47×#1602C212yesmaximal
4C47×#1351C212yesmaximal
5C47×#1317C211yesmaximal, characteristic
6C47×#543C2211yescharacteristic
7C47×#451—22no—
8C47×#399—21no—
9C47×#393C2212yes—
10C47×#391—22no—
11C47×#387—22no—
12C47×#381—21no—
13C47×#381C2211yescharacteristic
14C4×C22⋊C4×C47—21no—
15C47×#342—21no—
16C47×#342C2211yescharacteristic
17C47×#328—22no—
18C47×#323C2212yes—
19C22×Q8×C47D412yes—
20C23×C4×C47D411yescharacteristic
21C2×Q16×C47—42no—
22C22⋊Q8×C47—22no—
23C22⋊Q8×C47—42no—
24C2×C4⋊C4×C47—22no—
25C2×C4⋊C4×C47—21no—
26C2×C22⋊C4×C47—21no—
27C2×C22⋊C4×C47—22no—
28C2×C22⋊C4×C47—21no—
29C2×C22⋊C4×C47D411yescharacteristic
30C2×C22⋊C4×C47C2311yescharacteristic
31C2×C42×C47—21no—
32C2×C42×C47—21no—
33#103×C47—42no—
34C22⋊C8×C47—22no—
35#95×C47—22no—
36#95×C47—21no—
37#95×C47—22no—
38#95×C47—22no—
39#95×C47—42no—
40#95×C47D412yes—
41C24×C47C2×D411yescharacteristic
42C2×Q8×C47—22no—
43C2×Q8×C47—44no—
44C2×Q8×C47—42no—
45C22×C4×C47—21no—
46C22×C4×C47—22no—
47C22×C4×C47—21no—
48C22×C4×C47—22no—
49C22×C4×C47—21no—
50C22×C4×C47—22no—
51C22×C4×C47—41no—
52C22×C4×C47—41no—
53C22×C4×C47—41no—
54C22×C4×C47Q1612yescomplemented
55C22×C4×C47C2×D412yes—
56Q16×C47—84no—
57C2×C8×C47—42no—
58C4⋊C4×C47—22no—
59C4⋊C4×C47—44no—
60C4⋊C4×C47—42no—
61C4⋊C4×C47—81no—
62C22⋊C4×C47—41no—
63C22⋊C4×C47—44no—
64C22⋊C4×C47—41no—
65C22⋊C4×C47—41no—
66C22⋊C4×C47—41no—
67C22⋊C4×C47—41no—
68C22⋊C4×C47—41no—
69C42×C47—81no—
70C42×C47—81no—
71C23×C47—21no—
72C23×C47—21no—
73C23×C47—42no—
74C23×C47#12011yescharacteristic
75C23×C47C2×Q1611yescharacteristic
76C23×C47#13711yescharacteristic
77Q8×C47—44no—
78Q8×C47—82no—
79Q8×C47—82no—
80C2×C4×C47—24no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—42no—
84C2×C4×C47—41no—
85C2×C4×C47—41no—
86C2×C4×C47—42no—
87C2×C4×C47—42no—
88C2×C4×C47—42no—
89C2×C4×C47—42no—
90C2×C4×C47—42no—
91C2×C4×C47—42no—
92C2×C4×C47—42no—
93C2×C4×C47—41no—
94C2×C4×C47—42no—
95C2×C4×C47—81no—
96C2×C4×C47—82no—
97C2×C4×C47—81no—
98C2×C4×C47—82no—
99C8×C47—82no—
100#12215C4711yesmaximal, characteristic, direct product factor, Sylow
101C22×C47—22no—
102C22×C47—21no—
103C22×C47—21no—
104C22×C47—41no—
105C22×C47—41no—
106C22×C47—42no—
107C22×C47—81no—
108C22×C47#45111yescharacteristic
109C22×C47#45511yescharacteristic
110C22×C47B(4,𝔽2)11yescharacteristic
111C4×C47—42no—
112C4×C47—42no—
113C4×C47—44no—
114C4×C47—82no—
115C4×C47—81no—
116C4×C47—82no—
117C4×C47—161no—
118#2607C2×C4711yescharacteristic
119#2030C2×C4711yescharacteristic
120#1602C2×C4712yes—
121#1351C2×C4712yes—
122#1317C2×C4711yescharacteristic
123C2×C47—21no—
124C2×C47—21no—
125C2×C47—41no—
126C2×C47—41no—
127C2×C47#160211yescharacteristic
128C2×C47#219712yes—
129#543C22×C4711yescharacteristic
130#451—22no—
131#399—21no—
132#393C22×C4712yes—
133#391—22no—
134#387—22no—
135#381—21no—
136#381C22×C4711yescharacteristic
137C4×C22⋊C4—21no—
138#342—21no—
139#342C22×C4711yescharacteristic
140#328—22no—
141#323C22×C4712yes—
142C47#1221511yescharacteristic, direct product factor, Sylow
143C22×Q8D4×C4712yes—
144C23×C4D4×C4711yescharacteristic
145C2×Q16—42no—
146C22⋊Q8—22no—
147C22⋊Q8—42no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C22⋊C4—21no—
151C2×C22⋊C4—22no—
152C2×C22⋊C4—21no—
153C2×C22⋊C4D4×C4711yescharacteristic
154C2×C22⋊C4C23×C4711yescharacteristic
155C2×C42—21no—
156C2×C42—21no—
157#103—42no—
158C22⋊C8—22no—
159#95—22no—
160#95—21no—
161#95—22no—
162#95—22no—
163#95—42no—
164#95D4×C4712yes—
165C24C2×D4×C4711yescharacteristic
166C2×Q8—22no—
167C2×Q8—44no—
168C2×Q8—42no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4Q16×C4712yescomplemented
179C22×C4C2×D4×C4712yes—
180Q16—84no—
181C2×C8—42no—
182C4⋊C4—22no—
183C4⋊C4—44no—
184C4⋊C4—42no—
185C4⋊C4—81no—
186C22⋊C4—41no—
187C22⋊C4—44no—
188C22⋊C4—41no—
189C22⋊C4—41no—
190C22⋊C4—41no—
191C22⋊C4—41no—
192C22⋊C4—41no—
193C42—81no—
194C42—81no—
195C23—21no—
196C23—21no—
197C23—42no—
198C23#120×C4711yescharacteristic
199C23C2×Q16×C4711yescharacteristic
200C23#137×C4711yescharacteristic
201Q8—44no—
202Q8—82no—
203Q8—82no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—81no—
220C2×C4—82no—
221C2×C4—81no—
222C2×C4—82no—
223C8—82no—
224C22—22no—
225C22—21no—
226C22—21no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22—81no—
231C22C47×#45111yescharacteristic
232C22C47×#45511yescharacteristic
233C22C47×B(4,𝔽2)11yescharacteristic
234C4—42no—
235C4—42no—
236C4—44no—
237C4—82no—
238C4—81no—
239C4—82no—
240C4—161no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2C47×#160211yescharacteristic
246C2C47×#219712yes—
subgroupG/H
center, socleC22×C47B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C47
prime radicalC24×C47C2×D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C47 ◁ C2×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
54. C22×C4×C47Q16semidirect
100. #12215C47direct (N × H)
142. C47#12215direct (N × H)
178. C22×C4Q16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#26072
C47×#20302
C47×#16022
C47×#13512
C47×#13172
#1221547