Finite Group Databasebeta

← #20256191

Subgroups — #20256191

Order 6016.

326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689852C211yesmaximal, characteristic
2#15689493C212yesmaximal
3#15689475C211yesmaximal, characteristic
4#15689427C212yesmaximal
5#15689405C211yesmaximal, characteristic
6#15689333C211yesmaximal, characteristic
7#15689333C212yesmaximal
8#15689254C211yesmaximal, characteristic
9#15689228C212yesmaximal
10C4×#10625337C211yesmaximal, characteristic
11C47×#557C211yesmaximal, characteristic
12C2×#10625337C2211yescharacteristic
13C2×#10625337C2212yes—
14#13094024C2211yescharacteristic
15#13094024C2212yes—
16#13094015—21no—
17#13094015—22no—
18Q8×Dic47—21no—
19C4×Dic94C2211yescharacteristic
20C4×Dic94C2212yes—
21#13093957C2211yescharacteristic
22#13093955C2212yes—
23C4⋊(C47⋊C8)C2211yescharacteristic
24C4⋊(C47⋊C8)C2212yes—
25#13093948C2211yescharacteristic
26#13093947C2211yescharacteristic
27#13093947C2212yes—
28#13093947C2212yes—
29#13093947C2212yes—
30#13093947C2212yes—
31#13093935C2212yes—
32C4×C47⋊C8C2211yescharacteristic
33C4⋊Q8×C47—21no—
34C4⋊Q8×C47C2211yescharacteristic
35#125×C47—22no—
36#125×C47C2212yes—
37C4×Q8×C47—21no—
38C4×Q8×C47C2211yescharacteristic
39C4×Q8×C47C2212yes—
40C4×Q8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47D411yescharacteristic
43C2×Q8×C47C2311yescharacteristic
44C2×Dic94C2311yescharacteristic
45C2×Dic94C2312yes—
46C4⋊C4×C47—22no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—22no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47D411yescharacteristic
52C4⋊C4×C47D412yes—
53C4⋊C4×C47C2311yescharacteristic
54C4⋊C4×C47C2312yes—
55C42×C47—22no—
56C42×C47—21no—
57C42×C47C2312yes—
58C42×C47C2311yescharacteristic
59#10625337—22no—
60#10625337—24no—
61C4⋊Dic47—22no—
62C4⋊Dic47—21no—
63C4⋊Dic47—22no—
64C4⋊Dic47—21no—
65C4⋊Dic47C2311yescharacteristic
66Dic47⋊C4—22no—
67Dic47⋊C4—21no—
68C4×Dic47—22no—
69C4×Dic47—21no—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72C2×C47⋊C8C2312yes—
73Q8×C47—22no—
74Q8×C47—21no—
75Q8×C47—42no—
76Q8×C47#4112yes—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2×D412yes—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2411yescharacteristic
85C2×Dic47—21no—
86C2×Dic47—22no—
87C2×Dic47—21no—
88Dic94—21no—
89Dic94—22no—
90Dic94—21no—
91Dic94—22no—
92C47⋊C8—21no—
93C47⋊C8—22no—
94C47⋊C8—21no—
95C22×C47C22×D411yescharacteristic
96C4×C47—22no—
97C4×C47—22no—
98C4×C47—22no—
99C4×C47—21no—
100C4×C47—42no—
101C4×C47—41no—
102C4×C47#13712yes—
103C4×C47C2×#4111yescharacteristic
104C4×C472−1+411yescharacteristic
105Dic47—41no—
106Dic47—42no—
107Dic47—41no—
108#3374—471nomaximal, Sylow
109C2×C47#54811yescharacteristic
110C2×C47C2×#13711yescharacteristic
111C2×C47#57811yescharacteristic
112#557—471no—
113#557D4711yescharacteristic
114#491—472no—
115#487—471no—
116#479—472no—
117#475—471no—
118#462—472no—
119#462—471no—
120#446—471no—
121#441—472no—
122C4×Q16—471no—
123C47#337411yescharacteristic, complemented, Sylow
124C2×Q16—471no—
125C2×Q16—472no—
126C4⋊Q8—21no—
127C4⋊Q8—471no—
128C4⋊Q8—472no—
129C4⋊Q8C2×D4711yescharacteristic
130#125—22no—
131#125—941no—
132#125—942no—
133#125C2×D4712yes—
134C4×Q8—21no—
135C4×Q8—471no—
136C4×Q8—472no—
137C4×Q8—941no—
138C4×Q8C2×D4711yescharacteristic
139C4×Q8C2×D4712yes—
140C4×Q8C2×D4711yescharacteristic
141#107—471no—
142#106—472no—
143C4⋊C8—471no—
144C4⋊C8—472no—
145#103—471no—
146#103—471no—
147#103—472no—
148#103—472no—
149#103—472no—
150#103—472no—
151#97—472no—
152C4×C8—471no—
153C2×Q8—21no—
154C2×Q8—471no—
155C2×Q8—472no—
156C2×Q8C22⋊D4711yescharacteristic
157C2×Q8C22×D4711yescharacteristic
158Q16—942no—
159Q16—944no—
160C2×C8—471no—
161C2×C8—471no—
162C2×C8—472no—
163C4⋊C4—22no—
164C4⋊C4—21no—
165C4⋊C4—22no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—471no—
169C4⋊C4—942no—
170C4⋊C4—941no—
171C4⋊C4—942no—
172C4⋊C4—941no—
173C4⋊C4—942no—
174C4⋊C4—941no—
175C4⋊C4C22⋊D4711yescharacteristic
176C4⋊C4C22⋊D4712yes—
177C4⋊C4C22×D4712yes—
178C4⋊C4C22×D4711yescharacteristic
179C42—22no—
180C42—21no—
181C42—942no—
182C42—941no—
183C42C22×D4711yescharacteristic
184C42C22×D4712yes—
185Q8—22no—
186Q8—21no—
187Q8—42no—
188Q8—941no—
189Q8—942no—
190Q8—941no—
191Q8—942no—
192Q8#1062535412yes—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—941no—
197C2×C4—942no—
198C2×C4—941no—
199C2×C4C2×C22⋊D4712yes—
200C2×C4C2×C22⋊D4712yes—
201C2×C4C2×C22⋊D4711yescharacteristic
202C2×C4C2×C22⋊D4711yescharacteristic
203C2×C4C23×D4711yescharacteristic
204C8—941no—
205C8—942no—
206C8—941no—
207C22C22×C22⋊D4711yescharacteristic
208C4—22no—
209C4—22no—
210C4—22no—
211C4—21no—
212C4—42no—
213C4—41no—
214C4—1882no—
215C4—1881no—
216C4—1881no—
217C4#1309405412yes—
218C4C2×#1062535411yescharacteristic
219C4#1309407211yescharacteristic
220C2#1568978411yescharacteristic
221C2C2×#1309405411yescharacteristic
222C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#557C2
socleC22×C47C22×D4
hypercenter#557D47
hypocenterC47#3374
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
123. C47#3374semidirect