Finite Group Databasebeta

← #20244784

Subgroups — #20244784

Order 6016.

248 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#13093957C211yesmaximal, characteristic
2C2×Dic47⋊C8C211yesmaximal, characteristic
3C2×#13093949C211yesmaximal, characteristic
4C2×#13093947C211yesmaximal, characteristic
5#15689028C211yesmaximal, characteristic
6#15689019C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—21no—
12C2×C4×Dic47C2211yescharacteristic
13#13093957—22no—
14Dic47⋊C8—22no—
15#13093949—22no—
16#13093947—22no—
17C47⋊#95—21no—
18C47⋊#95—21no—
19C47⋊#95—21no—
20C22×C8×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47C2311yescharacteristic
26C22×Dic47—21no—
27C22×Dic47—21no—
28C22×Dic47D411yescharacteristic
29C22×Dic47D411yescharacteristic
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×Dic94—21no—
33C2×Dic94—21no—
34C2×Dic94—21no—
35C2×Dic94Q812yes—
36C2×C8×C47—21no—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47D412yes—
45Dic47⋊C4—42no—
46C4×Dic47—21no—
47C4×Dic47—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8D412yes—
51C23×C47C2×D411yescharacteristic
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×Q811yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×Dic47—21no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—21no—
70C2×Dic47—21no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75C2×Dic47Q1612yes—
76Dic94—22no—
77Dic94—22no—
78Dic94—41no—
79Dic94—41no—
80C8×C47—41no—
81C47⋊C8—22no—
82C22×C47#12111yescharacteristic
83C22×C47#12111yescharacteristic
84C22×C47C22⋊Q811yescharacteristic
85C22×C47C2×Q1611yescharacteristic
86C22×C47#13511yescharacteristic
87C22×C47AGL(1,ℤ/8)11yescharacteristic
88C22×C47#13711yescharacteristic
89C4×C47—81no—
90C4×C47—81no—
91C4×C47#12111yescharacteristic
92C4×C47C22⋊Q811yescharacteristic
93C4×C47C22⋊Q811yescharacteristic
94C4×C47#12611yescharacteristic
95Dic47—22no—
96Dic47—42no—
97Dic47—42no—
98Dic47—41no—
99#2068—471nomaximal, Sylow
100C2×C47#39611yescharacteristic
101C2×C47#46211yescharacteristic
102C2×C47#46311yescharacteristic
103C2×C47#46711yescharacteristic
104C2×C47#46811yescharacteristic
105C2×C47#47711yescharacteristic
106C2×C47#47911yescharacteristic
107C2×#107—471no—
108C2×C4⋊C8—471no—
109C2×#103—471no—
110C2×#103—471no—
111#391—471no—
112#389—471no—
113#340D4711yescharacteristic
114C47#206811yescharacteristic, complemented, Sylow
115C22×Q8—471no—
116C22×C8—471no—
117C22×C8C2×D4711yescharacteristic
118C2×C4⋊C4—471no—
119C2×C4⋊C4—941no—
120C2×C4⋊C4C2×D4711yescharacteristic
121C2×C4⋊C4C2×D4711yescharacteristic
122C2×C42—471no—
123#107—942no—
124C4⋊C8—942no—
125#103—942no—
126#103—942no—
127#95—941no—
128#95—941no—
129#95—941no—
130C2×Q8—472no—
131C2×Q8—941no—
132C2×Q8—941no—
133C2×Q8—941no—
134C2×Q8—941no—
135C2×Q8—941no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—471no—
139C22×C4—471no—
140C22×C4—941no—
141C22×C4—941no—
142C22×C4C22×D4711yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—472no—
147C2×C8—941no—
148C2×C8—941no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—472no—
154C4⋊C4—941no—
155C4⋊C4—1882no—
156C42—941no—
157C42—941no—
158C23D4×D4711yescharacteristic
159Q8—942no—
160Q8—942no—
161Q8—1881no—
162Q8—1881no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—472no—
170C2×C4—941no—
171C2×C4—941no—
172C2×C4—941no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4—941no—
176C2×C4—941no—
177C2×C4—1881no—
178C2×C4—1881no—
179C2×C4—1881no—
180C2×C4—1881no—
181C2×C4#1062535011yescharacteristic
182C2×C4#1062535011yescharacteristic
183C2×C4#1062535011yescharacteristic
184C2×C4D4×D4711yescharacteristic
185C2×C4D4×D4711yescharacteristic
186C2×C4Q8×D4711yescharacteristic
187C8—41no—
188C8—942no—
189C22#1309399711yescharacteristic
190C22#1309399711yescharacteristic
191C22#1309400211yescharacteristic
192C22Q16×D4711yescharacteristic
193C22#1309404511yescharacteristic
194C22#1309404811yescharacteristic
195C22#1309405311yescharacteristic
196C4—81no—
197C4—81no—
198C4—942no—
199C4—1882no—
200C4—1882no—
201C4—1881no—
202C4#1309399711yescharacteristic
203C4#1309400211yescharacteristic
204C4#1309400211yescharacteristic
205C4#1309401811yescharacteristic
206C2#1568904711yescharacteristic
207C2#1568933211yescharacteristic
208C2#1568933711yescharacteristic
209C2#1568936311yescharacteristic
210C2#1568936811yescharacteristic
211C2#1568941711yescharacteristic
212C2#1568943311yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2068
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
114. C47#2068semidirect