Finite Group Databasebeta

← #26119411

Subgroups — #26119411

Order 12032.

416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#20246681C211yesmaximal, characteristic
2#20241887C212yesmaximal
3#20241289C212yesmaximal
4#20241217C211yesmaximal, characteristic
5C47×#1995C211yesmaximal, characteristic
6C2×C4×Dic94—21no—
7#15689176C2212yes—
8#15689055—22no—
9#15689044—22no—
10C4×C4⋊Dic47—21no—
11C4×C4⋊Dic47C2212yes—
12#15688860—22no—
13#15688860—22no—
14C47×#533C2211yescharacteristic
15C47×#423C2211yescharacteristic
16C47×#376C2211yescharacteristic
17C47×#339—21no—
18C47×#339—21no—
19C22×Dic94—21no—
20C4×Dic94—42no—
21C4×Dic94—42no—
22C2×C4⋊Dic47—22no—
23C2×C4⋊Dic47—21no—
24C2×C4⋊Dic47—22no—
25C2×Dic47⋊C4—22no—
26C2×C4×Dic47—22no—
27C4⋊(C47⋊C8)—22no—
28C22⋊(C47⋊C8)—22no—
29C4×C47⋊C8—22no—
30C47⋊#95—21no—
31C47⋊#95—21no—
32C47⋊#95D412yes—
33C47⋊#95D412yes—
34C2×M16×C47—21no—
35C4⋊Q8×C47Q812yescomplemented
36#125×C47—21no—
37C22⋊Q8×C47—22no—
38C4×Q8×C47—22no—
39#117×C47—21no—
40C2×C42×C47D411yescharacteristic
41C2×C42×C47D411yescharacteristic
42C2×C42×C47C2311yescharacteristic
43C4⋊C8×C47—22no—
44#95×C47—22no—
45C2×Q8×C47—22no—
46C22×C4×C47—21no—
47C22×C4×C47—21no—
48C22×C4×C47C2×D412yes—
49C22×C4×C47C2×D411yescharacteristic
50C22×Dic47—22no—
51C22×Dic47—22no—
52C2×Dic94—44no—
53C2×Dic94—42no—
54M16×C47—41no—
55M16×C47—41no—
56C2×C8×C47—41no—
57C4⋊C4×C47—22no—
58C4⋊C4×C47—22no—
59C4⋊C4×C47—42no—
60C22⋊C4×C47—41no—
61C42×C47—21no—
62C42×C47—21no—
63C42×C47—41no—
64C42×C47SD1612yes—
65C42×C47Q1612yes—
66C42×C47C2×Q811yescharacteristic
67C42×C47#4111yescharacteristic
68C42×C47#4112yes—
69C4⋊Dic47—44no—
70C4⋊Dic47—44no—
71C4⋊Dic47—42no—
72Dic47⋊C4—44no—
73C4×Dic47—42no—
74C4×Dic47—42no—
75C2×C47⋊C8—42no—
76C23×C47#12011yescharacteristic
77Q8×C47—82no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—42no—
81C2×C4×C47—42no—
82C2×C4×C47—42no—
83C2×C4×C47—42no—
84C2×C4×C47C22⋊Q812yes—
85C2×C4×C47C22⋊Q811yescharacteristic
86C2×C4×C47#12412yes—
87C2×C4×C47#12411yescharacteristic
88C2×C4×C47C2×SD1611yescharacteristic
89C2×C4×C47C2×Q1611yescharacteristic
90C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
91C2×C4×C47#13711yescharacteristic
92C2×Dic47—24no—
93C2×Dic47—42no—
94C2×Dic47—42no—
95C2×Dic47—42no—
96C2×Dic47—42no—
97C2×Dic47—42no—
98Dic94—48no—
99C8×C47—81no—
100C47⋊C8—82no—
101#10371—471nomaximal, Sylow
102C22×C47—22no—
103C22×C47#39311yescharacteristic
104C22×C47#45011yescharacteristic
105C22×C47#45111yescharacteristic
106C4×C47—22no—
107C4×C47—22no—
108C4×C47—42no—
109C4×C47—42no—
110C4×C47—82no—
111C4×C47#47511yescharacteristic
112C4×C47#47711yescharacteristic
113C4×C47#48711yescharacteristic
114C4×C47#48911yescharacteristic
115Dic47—44no—
116Dic47—82no—
117#2399—471no—
118#1995D4711yescharacteristic
119#1503—472no—
120#1303—472no—
121#1274—471no—
122C2×C47—21no—
123C2×C47—21no—
124C2×C47#202411yescharacteristic
125C2×C47#203112yes—
126#533C2×D4711yescharacteristic
127C2×C4×Q8—941no—
128#431—472no—
129#423C2×D4711yescharacteristic
130#398—942no—
131#395—942no—
132C4×C4⋊C4—472no—
133C4×C4⋊C4—941no—
134#376C2×D4711yescharacteristic
135#339—21no—
136#339—21no—
137#328—942no—
138#328—942no—
139C47#1037111yescharacteristic, complemented, Sylow
140C22×Q8—941no—
141C2×M16—21no—
142C4⋊Q8Dic9412yescomplemented
143#125—21no—
144C22⋊Q8—22no—
145C4×Q8—22no—
146C4×Q8—1882no—
147C4×Q8—1882no—
148#117—21no—
149C2×C4⋊C4—942no—
150C2×C4⋊C4—941no—
151C2×C4⋊C4—942no—
152C2×C4⋊C4—942no—
153C2×C42—942no—
154C2×C42C22⋊D4711yescharacteristic
155C2×C42C22⋊D4711yescharacteristic
156C2×C42C22×D4711yescharacteristic
157C4⋊C8—22no—
158C4⋊C8—942no—
159C22⋊C8—942no—
160C4×C8—942no—
161#95—22no—
162#95—472no—
163#95—472no—
164#95—941no—
165#95—941no—
166C2×Q8—22no—
167C2×Q8—1882no—
168C2×Q8—1884no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—942no—
172C22×C4—942no—
173C22×C4D4×D4712yes—
174C22×C4C2×C22⋊D4711yescharacteristic
175M16—41no—
176M16—41no—
177C2×C8—41no—
178C2×C8—1882no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—42no—
182C4⋊C4—1884no—
183C4⋊C4—1882no—
184C4⋊C4—1884no—
185C4⋊C4—1884no—
186C22⋊C4—41no—
187C42—21no—
188C42—21no—
189C42—41no—
190C42—1882no—
191C42—1882no—
192C42#1062533612yes—
193C42#1062533712yes—
194C42C2×Dic9411yescharacteristic
195C42#1062535011yescharacteristic
196C42#1062535212yes—
197C23#1309399211yescharacteristic
198Q8—82no—
199Q8—1888no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—944no—
207C2×C4—1882no—
208C2×C4—1882no—
209C2×C4—1882no—
210C2×C4—1882no—
211C2×C4—1882no—
212C2×C4#1309400112yes—
213C2×C4#1309400311yescharacteristic
214C2×C4#1309401012yes—
215C2×C4#1309401111yescharacteristic
216C2×C4C2×#1062533611yescharacteristic
217C2×C4C2×#1062533711yescharacteristic
218C2×C4#1309404911yescharacteristic
219C2×C4#1309405411yescharacteristic
220C8—81no—
221C8—3762no—
222C22—22no—
223C22#1568903511yescharacteristic
224C22#1568927311yescharacteristic
225C22#1568927811yescharacteristic
226C4—22no—
227C4—22no—
228C4—42no—
229C4—42no—
230C4—82no—
231C4—3762no—
232C4—1884no—
233C4#1568940811yescharacteristic
234C4#1568941811yescharacteristic
235C4#1568947311yescharacteristic
236C4#1568948211yescharacteristic
237C2—21no—
238C2—21no—
239C2#2024452911yescharacteristic
240C2#2024455812yes—
subgroupG/H
centerC2×C4#13094011
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1995C2
socleC22×C47#393
prime radicalC23×C47#120
hypercenter#1995D47
hypocenterC47#10371
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
35. C4⋊Q8×C47Q8semidirect
139. C47#10371semidirect
142. C4⋊Q8Dic94semidirect

Maximal subgroups

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

subgroupindex
#202466812
#202418872
#202412892
#202412172
C47×#19952
#1037147