Finite Group Databasebeta

← #20256196

Subgroups — #20256196

Order 6016.

326 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689848C211yesmaximal, characteristic
2#15689848C211yesmaximal, characteristic
3#15689490C212yesmaximal
4#15689432C212yesmaximal
5#15689405C211yesmaximal, characteristic
6#15689332C212yesmaximal
7#15689330C211yesmaximal, characteristic
8#15689253C211yesmaximal, characteristic
9#15689227C212yesmaximal
10C4×Dic188C211yesmaximal, characteristic
11C47×#487C211yesmaximal, characteristic
12C2×Dic188C2211yescharacteristic
13C2×#10625337C2212yes—
14#13094022—21no—
15#13094022C2212yes—
16#13094015—21no—
17#13094015C2212yes—
18#13094014—22no—
19#13094014—22no—
20Q8×Dic47—21no—
21Q8×Dic47C2212yes—
22C4×Dic94C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24C4×Dic94C2211yescharacteristic
25#13093989—21no—
26#13093989C2212yes—
27#13093958C2211yescharacteristic
28#13093955C2212yes—
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2211yescharacteristic
32#13093949C2211yescharacteristic
33#13093948C2212yes—
34#13093947C2212yes—
35#13093934C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4⋊Q8×C47C2211yescharacteristic
38#103×C47C2212yes—
39#103×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47C2312yes—
43C2×Dic94D411yescharacteristic
44C2×Dic94C2311yescharacteristic
45C2×Dic94C2311yescharacteristic
46C2×C8×C47C2311yescharacteristic
47C2×C8×C47C2311yescharacteristic
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47C2312yes—
52C42×C47C2311yescharacteristic
53#10625337—24no—
54C4⋊Dic47—22no—
55C4⋊Dic47—22no—
56C4⋊Dic47D411yescharacteristic
57C4⋊Dic47C2311yescharacteristic
58C4⋊Dic47C2311yescharacteristic
59Dic47⋊C4—21no—
60Dic47⋊C4—21no—
61Dic47⋊C4—22no—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4D412yes—
66C4×Dic47—21no—
67C4×Dic47—21no—
68C4×Dic47—22no—
69C4×Dic47—22no—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2312yes—
72Dic188—22no—
73Q8×C47—22no—
74Q8×C47—22no—
75Q8×C47—42no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2411yescharacteristic
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47C2×D412yes—
86C2×Dic47C2×D412yes—
87Dic94—22no—
88Dic94—21no—
89Dic94—21no—
90Dic94—21no—
91Dic94#4112yes—
92C8×C47—21no—
93C8×C47—21no—
94C47⋊C8—22no—
95C22×C47C22×D411yescharacteristic
96C4×C47—21no—
97C4×C47—42no—
98C4×C47—42no—
99C4×C47#13712yes—
100C4×C47C2×#4111yescharacteristic
101C4×C472−1+411yescharacteristic
102Dic47—22no—
103Dic47—22no—
104Dic47—22no—
105Dic47—41no—
106Dic47—41no—
107Dic47—41no—
108#3374—471nomaximal, Sylow
109C2×C47#54811yescharacteristic
110C2×C47C2×#13711yescharacteristic
111C2×C47#57811yescharacteristic
112#557—471no—
113#557—471no—
114#491—472no—
115#487D4711yescharacteristic
116#479—472no—
117#475—471no—
118#462—471no—
119#462—472no—
120#446—471no—
121#441—472no—
122C4×Q16—471no—
123C47#337411yescharacteristic, complemented, Sylow
124C2×Q16—472no—
125C2×Q16—471no—
126C4⋊Q8—472no—
127C4⋊Q8—941no—
128C4⋊Q8C2×D4711yescharacteristic
129C4⋊Q8C2×D4711yescharacteristic
130#125—472no—
131#125—942no—
132#125—942no—
133#125—941no—
134C4×Q8—471no—
135C4×Q8—472no—
136C4×Q8—472no—
137C4×Q8—471no—
138C4×Q8—471no—
139C4×Q8—941no—
140C4×Q8—941no—
141#107—471no—
142#106—472no—
143C4⋊C8—472no—
144C4⋊C8—471no—
145#103—472no—
146#103—471no—
147#103—471no—
148#103—472no—
149#103C2×D4712yes—
150#103C2×D4712yes—
151#97—472no—
152C4×C8C2×D4711yescharacteristic
153C2×Q8—21no—
154C2×Q8—471no—
155C2×Q8—471no—
156C2×Q8—471no—
157C2×Q8C22×D4712yes—
158Q16—942no—
159Q16—944no—
160C2×C8—472no—
161C2×C8C22×D4711yescharacteristic
162C2×C8C22×D4711yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—472no—
167C4⋊C4—471no—
168C4⋊C4—471no—
169C4⋊C4—471no—
170C4⋊C4—942no—
171C4⋊C4—942no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—941no—
177C4⋊C4—941no—
178C4⋊C4C22×D4712yes—
179C42—472no—
180C42—942no—
181C42—942no—
182C42—941no—
183C42—941no—
184C42C22×D4711yescharacteristic
185Q8—22no—
186Q8—22no—
187Q8—42no—
188Q8—472no—
189Q8—942no—
190Q8—941no—
191Q8—941no—
192Q8—941no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—472no—
196C2×C4—472no—
197C2×C4—941no—
198C2×C4—941no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4D4×D4711yescharacteristic
202C2×C4D4×D4711yescharacteristic
203C2×C4C23×D4711yescharacteristic
204C8—21no—
205C8—21no—
206C8—942no—
207C22C2×D4×D4711yescharacteristic
208C4—21no—
209C4—42no—
210C4—42no—
211C4—942no—
212C4—942no—
213C4—942no—
214C4—1881no—
215C4—1881no—
216C4—1881no—
217C4#1309405312yes—
218C4#41×D4711yescharacteristic
219C4#1309407111yescharacteristic
220C2#1568978111yescharacteristic
221C2C2×#1309405311yescharacteristic
222C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#487C2
socleC22×C47C22×D4
hypercenter#487D47
hypocenterC47#3374
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
123. C47#3374semidirect