Finite Group Databasebeta

← #20256353

Subgroups — #20256353

Order 6016.

320 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 129 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#15689849C212yesmaximal
2#15689531C212yesmaximal
3#15689525C211yesmaximal, characteristic
4#15689432C212yesmaximal
5#15689430C212yesmaximal
6#15689416C212yesmaximal
7#15689253C211yesmaximal, characteristic
8#15689230C212yesmaximal
9C4×Q16×C47C211yesmaximal, characteristic
10#13094023—22no—
11#13094023C2212yes—
12#13094016—22no—
13#13094016C2212yes—
14#13094015—22no—
15#13094015C2212yes—
16Q8×Dic47C2212yes—
17Q8×Dic47C2212yes—
18C4×Dic94—22no—
19C4×Dic94C2211yescharacteristic
20#13093958C2211yescharacteristic
21#13093958C2211yescharacteristic
22#13093957C2212yes—
23#13093956C2212yes—
24#13093955C2212yes—
25C4⋊(C47⋊C8)C2211yescharacteristic
26Dic47⋊C8C2212yes—
27#13093948C2212yes—
28#13093948C2212yes—
29#13093934C2212yes—
30C2×Q16×C47C2211yescharacteristic
31C4×Q8×C47C2212yes—
32#107×C47C2211yescharacteristic
33#103×C47C2212yes—
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47C2312yes—
36C2×Dic94—22no—
37C2×Dic94D411yescharacteristic
38Q16×C47Q814yescomplemented
39C2×C8×C47C2311yescharacteristic
40C2×C8×C47C2311yescharacteristic
41C4⋊C4×C47—22no—
42C4⋊C4×C47C2312yes—
43C42×C47—22no—
44C42×C47C2311yescharacteristic
45C4⋊Dic47—22no—
46C4⋊Dic47—22no—
47C4⋊Dic47—22no—
48C4⋊Dic47D411yescharacteristic
49C4⋊Dic47C2312yes—
50C4⋊Dic47C2312yes—
51Dic47⋊C4—22no—
52Dic47⋊C4—22no—
53Dic47⋊C4—22no—
54Dic47⋊C4—22no—
55Dic47⋊C4D412yes—
56C4×Dic47—22no—
57C4×Dic47—22no—
58C4×Dic47C2312yes—
59C2×C47⋊C8C2312yes—
60Q8×C47—22no—
61Q8×C47C2×Q814yes—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2411yescharacteristic
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47C2×D412yes—
70C2×Dic47C2×D412yes—
71Dic94—41no—
72Dic94—44no—
73C8×C47—21no—
74C8×C47C2×Q812yes—
75C47⋊C8—22no—
76C22×C47C22×D411yescharacteristic
77C4×C47—24no—
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—42no—
81C4×C47C22×Q811yescharacteristic
82C4×C472−1+411yescharacteristic
83Dic47—22no—
84Dic47—22no—
85Dic47—42no—
86Dic47—42no—
87#3390—471nomaximal, Sylow
88C2×C47D4×Q811yescharacteristic
89C2×C47#57511yescharacteristic
90C2×C47#57811yescharacteristic
91#557—472no—
92#501—472no—
93#499—471no—
94#479—472no—
95#479—472no—
96#477—472no—
97#446—471no—
98#441—472no—
99C4×Q16D4711yescharacteristic
100C47#339011yescharacteristic, complemented, Sylow
101C2×Q16C2×D4711yescharacteristic
102C4⋊Q8—472no—
103C4⋊Q8—942no—
104#125—472no—
105#125—472no—
106#125—942no—
107#125—942no—
108C4×Q8—471no—
109C4×Q8—472no—
110C4×Q8—472no—
111C4×Q8—942no—
112C4×Q8C2×D4712yes—
113#107—471no—
114#107—471no—
115#107—472no—
116#107C2×D4711yescharacteristic
117#106—472no—
118#106—472no—
119C4⋊C8—472no—
120C4⋊C8—471no—
121#103—472no—
122#103—472no—
123#103C2×D4712yes—
124#97—472no—
125C4×C8C2×D4711yescharacteristic
126C2×Q8—471no—
127C2×Q8—942no—
128C2×Q8C22×D4712yes—
129Q16Dic9414yescomplemented
130C2×C8—472no—
131C2×C8C22×D4711yescharacteristic
132C2×C8C22×D4711yescharacteristic
133C4⋊C4—22no—
134C4⋊C4—472no—
135C4⋊C4—471no—
136C4⋊C4—472no—
137C4⋊C4—472no—
138C4⋊C4—942no—
139C4⋊C4—942no—
140C4⋊C4—942no—
141C4⋊C4—942no—
142C4⋊C4—942no—
143C4⋊C4—942no—
144C4⋊C4—942no—
145C4⋊C4C22×D4712yes—
146C42—22no—
147C42—472no—
148C42—942no—
149C42—942no—
150C42C22×D4711yescharacteristic
151Q8—22no—
152Q8—1881no—
153Q8—1884no—
154Q8C2×Dic9414yes—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—472no—
158C2×C4—472no—
159C2×C4—942no—
160C2×C4—942no—
161C2×C4D4×D4711yescharacteristic
162C2×C4D4×D4711yescharacteristic
163C2×C4C23×D4711yescharacteristic
164C8—21no—
165C8—942no—
166C8C2×Dic9412yes—
167C22C2×D4×D4711yescharacteristic
168C4—24no—
169C4—21no—
170C4—21no—
171C4—42no—
172C4—942no—
173C4—942no—
174C4—1882no—
175C4—1882no—
176C4C22×Dic9411yescharacteristic
177C4#1309407111yescharacteristic
178C2D4×Dic9411yescharacteristic
179C2#1568992011yescharacteristic
180C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×Q16×C47C2
socleC22×C47C22×D4
hypercenterC4×Q16D47
hypocenterC47#3390
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
38. Q16×C47Q8semidirect
100. C47#3390semidirect
129. Q16Dic94semidirect