Finite Group Databasebeta

← #20253917

Subgroups — #20253917

Order 6016.

340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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#15689753C212yesmaximal
2#15689533C212yesmaximal, complemented
3#15689531C212yesmaximal, complemented
4#15689523C211yesmaximal, characteristic, complemented
5#15689521C211yesmaximal, characteristic, complemented
6#15689520C211yesmaximal, characteristic, complemented
7#15689164C212yesmaximal
8#15689158C211yesmaximal, characteristic
9#106×D47C211yesmaximal, characteristic
10#15689077C211yesmaximal, characteristic
11C47×#499C211yesmaximal, characteristic, complemented
12C2×#10625324C2211yescharacteristic
13C2×C8×D47C2211yescharacteristic
14#13094024C2212yes—
15#13094023—22no—
16#13094023C2212yes—
17#13094015C2212yes—
18#13094014—22no—
19#13094004—22no—
20#13094002—22no—
21#13093982C2212yes—
22#13093981C2211yescharacteristic
23C4⋊C4×D47C2212yes—
24#13093957C2212yes—
25#13093957C2212yes—
26#13093956C2211yescharacteristic
27#13093956C2211yescharacteristic
28#13093956C2212yes—
29#13093955C2212yes—
30#13093955C2212yes—
31#13093935C2211yescharacteristic
32#13093934C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34#125×C47C2212yes—
35#107×C47C2212yes—
36#106×C47C2211yescharacteristic
37#106×C47C2211yescharacteristic
38C4×C8×C47C2211yescharacteristic
39C2×C4×D47—22no—
40C2×C4×D47C2311yescharacteristic
41C2×Dic94—22no—
42C2×Dic94—22no—
43C2×C8×C47C2311yescharacteristic
44C2×C8×C47C2311yescharacteristic
45C4⋊C4×C47—22no—
46C4⋊C4×C47—22no—
47C4⋊C4×C47C2312yes—
48C4⋊C4×C47C2312yes—
49C42×C47C2311yescharacteristic
50(C2×D47)⋊C4—22no—
51(C2×D47)⋊C4D412yes—
52C4⋊Dic47—22no—
53C4⋊Dic47—22no—
54C4⋊Dic47C2312yes—
55C4⋊Dic47C2312yes—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59Dic47⋊C4D412yes—
60C4×Dic47—22no—
61C4×Dic47C2311yescharacteristic
62C2×C47⋊C8C2311yescharacteristic
63C2×C47⋊C8C2311yescharacteristic
64#10625324Q814yescomplemented
65C8×D47Q814yescomplemented
66C22×D47C2×D411yescharacteristic
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2411yescharacteristic
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47C2×D412yes—
74C2×Dic47C2×D411yescharacteristic
75C4×D47—82no—
76C4×D47C2×Q812yes—
77C4×D47C2×Q812yes—
78Dic94—82no—
79Dic94—82no—
80C8×C47C2×Q812yes—
81C8×C47C2×Q812yes—
82C47⋊C8C2×Q812yes—
83C47⋊C8C2×Q812yes—
84C22×C47C22×D411yescharacteristic
85C2×D47—22no—
86C2×D47C4⋊Q812yes—
87C4×C47—22no—
88C4×C47—42no—
89C4×C47—42no—
90C4×C47C22×Q811yescharacteristic
91C4×C47C22×Q811yescharacteristic
92Dic47—22no—
93Dic47—42no—
94Dic47—42no—
95Dic47C4⋊Q812yes—
96#3163—471nomaximal, Sylow
97C2×C47C2×C4⋊Q811yescharacteristic
98C2×C47#57712yes—
99D47—22no—
100#544—472no—
101#501—472no—
102#501—472no—
103#499—471no—
104#499D4711yescharacteristic, complemented
105#498—471no—
106#498—471no—
107#428—472no—
108#427—471no—
109C2×#106—471no—
110#405—471no—
111C47#316311yescharacteristic, complemented, Sylow
112C2×M16—471no—
113C22×C8—471no—
114C4⋊Q8—472no—
115C4⋊Q8—472no—
116C4⋊Q8—942no—
117#125—472no—
118#125—942no—
119#125C2×D4712yes—
120C22⋊Q8—942no—
121C22⋊Q8—942no—
122#117—471no—
123#117—472no—
124C2×C4⋊C4—472no—
125#107—472no—
126#107—472no—
127#107C2×D4712yes—
128#106—471no—
129#106—471no—
130#106—472no—
131#106—472no—
132#106—472no—
133#106C2×D4711yescharacteristic
134#106C2×D4711yescharacteristic
135#97—471no—
136#97—471no—
137C4×C8—471no—
138C4×C8C2×D4711yescharacteristic
139C2×Q8—942no—
140C2×Q8—942no—
141C22×C4—471no—
142C22×C4—942no—
143M16—474no—
144C2×C8—471no—
145C2×C8—471no—
146C2×C8—474no—
147C2×C8C22×D4711yescharacteristic
148C2×C8C22×D4711yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—472no—
152C4⋊C4—472no—
153C4⋊C4—472no—
154C4⋊C4—942no—
155C4⋊C4—942no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C4⋊C4—942no—
159C4⋊C4C22×D4712yes—
160C4⋊C4C22×D4712yes—
161C22⋊C4—472no—
162C22⋊C4—942no—
163C42—471no—
164C42—942no—
165C42C22×D4711yescharacteristic
166C23—471no—
167Q8—3762no—
168Q8—3762no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—471no—
172C2×C4—472no—
173C2×C4—472no—
174C2×C4—472no—
175C2×C4—942no—
176C2×C4—942no—
177C2×C4—3762no—
178C2×C4D4×D4712yes—
179C2×C4C23×D4711yescharacteristic
180C8—472no—
181C8—472no—
182C8Q8×D4712yes—
183C8Q8×D4712yes—
184C22—472no—
185C22—942no—
186C22C2×D4×D4711yescharacteristic
187C4—22no—
188C4—42no—
189C4—42no—
190C4—472no—
191C4—942no—
192C4—1882no—
193C4—1882no—
194C4C2×Q8×D4711yescharacteristic
195C4C2×Q8×D4711yescharacteristic
196C2—942no—
197C2C4⋊Q8×D4711yescharacteristic
198C2#1568993012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#499C2
socleC22×C47C22×D4
hypercenter#499D47
hypocenterC47#3163
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
2. #15689533C2semidirect
3. #15689531C2semidirect
4. #15689523C2semidirect
5. #15689521C2semidirect
6. #15689520C2semidirect
11. C47×#499C2semidirect
64. #10625324Q8semidirect
65. C8×D47Q8semidirect
104. #499D47semidirect
111. C47#3163semidirect