Finite Group Databasebeta

← C47×#2197 #20239807

Subgroups — C47×#2197 #20239807

Order 6016.

258 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 56 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×#551C211yesmaximal, characteristic, complemented
2C47×#458C211yesmaximal, characteristic, complemented
3C47×B(4,𝔽2)C211yesmaximal, characteristic
4C47×#455C211yesmaximal, characteristic, complemented
5C47×#354C211yesmaximal, characteristic, complemented
6C47×#352C211yesmaximal, characteristic, complemented
7C47×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8H(5,𝔽2)×C47C2211yescharacteristic
9#137×C47—21no—
10#126×C47—21no—
11#124×C47C2211yescharacteristic
12#123×C47—21no—
13#123×C47—21no—
14#123×C47C2211yescharacteristic
15C22⋊Q8×C47—21no—
16#120×C47—21no—
17#120×C47C2211yescharacteristic
18C4×D4×C47—21no—
19#117×C47—21no—
20C2×C22⋊C4×C47—21no—
21#104×C47—21no—
22#100×C47C2211yescharacteristic
23#99×C47—21no—
24#99×C47—21no—
25#99×C47C2211yescharacteristic
26#99×C47C2211yescharacteristic
27C24×C47D411yescharacteristic
28#41×C47—21no—
29#41×C47—41no—
30C2×Q8×C47D411yescharacteristic, complemented
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—41no—
35C2×D4×C47—41no—
36C2×D4×C47C2311yescharacteristic
37C22×C4×C47—21no—
38C22×C4×C47—21no—
39C22×C4×C47D411yescharacteristic, complemented
40Q16×C47—41no—
41SD16×C47—41no—
42M16×C47—21no—
43C4⋊C4×C47—21no—
44C4⋊C4×C47—21no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47—21no—
47C4⋊C4×C47—41no—
48C22⋊C4×C47—21no—
49C22⋊C4×C47—21no—
50C22⋊C4×C47—21no—
51C22⋊C4×C47—21no—
52C22⋊C4×C47—21no—
53C22⋊C4×C47—21no—
54C22⋊C4×C47—21no—
55C22⋊C4×C47—21no—
56C22⋊C4×C47—41no—
57C22⋊C4×C47—41no—
58C22⋊C4×C47D411yescharacteristic
59C22⋊C4×C47D411yescharacteristic, complemented
60C42×C47—21no—
61C42×C47D411yescharacteristic, complemented
62C23×C47—21no—
63C23×C47—21no—
64C23×C47—21no—
65C23×C47—41no—
66C23×C47—42no—
67C23×C47C2×D411yescharacteristic
68C23×C47C2×D411yescharacteristic
69Q8×C47—21no—
70Q8×C47—41no—
71D4×C47—21no—
72D4×C47—41no—
73D4×C47—42no—
74D4×C47—41no—
75D4×C47—41no—
76D4×C47—41no—
77D4×C47—82no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—41no—
86C2×C4×C47—42no—
87C2×C4×C47—41no—
88C2×C4×C47—41no—
89C2×C4×C47—41no—
90C2×C4×C47—81no—
91C2×C4×C47C2×D411yescharacteristic
92C8×C47—41no—
93C22×C47—22no—
94C22×C47—21no—
95C22×C47—21no—
96C22×C47—41no—
97C22×C47—41no—
98C22×C47—41no—
99C22×C47—42no—
100C22×C47—41no—
101C22×C47—41no—
102C22×C47—81no—
103C22×C47—81no—
104C22×C47—81no—
105C22×C47#12011yescharacteristic
106C4×C47—21no—
107C4×C47—41no—
108C4×C47—41no—
109C4×C47—41no—
110C4×C47—41no—
111C4×C47—41no—
112C4×C47—41no—
113C4×C47—81no—
114C4×C47—81no—
115#2197C4711yesmaximal, characteristic, direct product factor, Sylow
116C2×C47—21no—
117C2×C47—41no—
118C2×C47—41no—
119C2×C47—42no—
120C2×C47—81no—
121C2×C47B(4,𝔽2)11yescharacteristic
122#551C2×C4711yescharacteristic, complemented
123#458C2×C4711yescharacteristic, complemented
124B(4,𝔽2)C2×C4711yescharacteristic
125#455C2×C4711yescharacteristic, complemented
126#354C2×C4711yescharacteristic, complemented
127#352C2×C4711yescharacteristic, complemented
128AΣL(1,𝔽16)C2×C4711yescharacteristic, complemented
129C47#219711yescharacteristic, direct product factor, Sylow
130H(5,𝔽2)C22×C4711yescharacteristic
131#137—21no—
132#126—21no—
133#124C22×C4711yescharacteristic
134#123—21no—
135#123—21no—
136#123C22×C4711yescharacteristic
137C22⋊Q8—21no—
138#120—21no—
139#120C22×C4711yescharacteristic
140C4×D4—21no—
141#117—21no—
142C2×C22⋊C4—21no—
143#104—21no—
144#100C22×C4711yescharacteristic
145#99—21no—
146#99—21no—
147#99C22×C4711yescharacteristic
148#99C22×C4711yescharacteristic
149C24D4×C4711yescharacteristic
150#41—21no—
151#41—41no—
152C2×Q8D4×C4711yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4C23×C4711yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4D4×C4711yescharacteristic, complemented
162Q16—41no—
163SD16—41no—
164M16—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—41no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4D4×C4711yescharacteristic
181C22⋊C4D4×C4711yescharacteristic, complemented
182C42—21no—
183C42D4×C4711yescharacteristic, complemented
184C23—21no—
185C23—21no—
186C23—21no—
187C23—41no—
188C23—42no—
189C23C2×D4×C4711yescharacteristic
190C23C2×D4×C4711yescharacteristic
191Q8—21no—
192Q8—41no—
193D4—21no—
194D4—41no—
195D4—42no—
196D4—41no—
197D4—41no—
198D4—41no—
199D4—82no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4C2×D4×C4711yescharacteristic
214C8—41no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22—81no—
227C22#120×C4711yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—41no—
235C4—81no—
236C4—81no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—42no—
241C2—81no—
242C2C47×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C47B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C23×C47
prime radicalC47×B(4,𝔽2)C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C47 ◁ C2×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#551C2semidirect
2. C47×#458C2semidirect
4. C47×#455C2semidirect
5. C47×#354C2semidirect
6. C47×#352C2semidirect
7. C47×AΣL(1,𝔽16)C2semidirect
30. C2×Q8×C47D4semidirect
39. C22×C4×C47D4semidirect
59. C22⋊C4×C47D4semidirect
61. C42×C47D4semidirect
115. #2197C47direct (N × H)
122. #551C2×C47semidirect
123. #458C2×C47semidirect
125. #455C2×C47semidirect
126. #354C2×C47semidirect
127. #352C2×C47semidirect
128. AΣL(1,𝔽16)C2×C47semidirect
129. C47#2197direct (N × H)
152. C2×Q8D4×C47semidirect
161. C22×C4D4×C47semidirect
181. C22⋊C4D4×C47semidirect
183. C42D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#5512
C47×#4582
C47×B(4,𝔽2)2
C47×#4552
C47×#3542
C47×#3522
C47×AΣL(1,𝔽16)2
#219747