Finite Group Databasebeta

← #20253766

Subgroups — #20253766

Order 6016.

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

normal subgroups only

This group has 380 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#15689676C211yesmaximal, characteristic
2C2×#13094022C211yesmaximal, characteristic
3#15689490C214yesmaximal, complemented
4#15689472C214yesmaximal, complemented
5#15689133C211yesmaximal, characteristic
6#15689132C211yesmaximal, characteristic
7#15689131C211yesmaximal, characteristic
8M16×Dic47C211yesmaximal, characteristic
9C47×#419C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C2×#10625329C2211yescharacteristic
12#13094023C2212yes—
13#13094022—22no—
14#13094022C2212yes—
15#13094022C2212yes—
16#13094015C2212yes—
17#13094001—22no—
18C4×Dic94—22no—
19#13093983C2211yescharacteristic
20C2×Dic47⋊C4—22no—
21C2×C4×Dic47C2211yescharacteristic
22#13093949C2214yes—
23#13093948C2214yes—
24#13093947C2214yes—
25#13093934C2212yes—
26C8×Dic47C2212yes—
27C22×Q8×C47C2211yescharacteristic
28C2×M16×C47C2211yescharacteristic
29#117×C47C2211yescharacteristic
30#103×C47C2214yes—
31C2×Q8×C47—21no—
32C2×Q8×C47—22no—
33C2×Q8×C47—22no—
34C2×Q8×C47C2312yes—
35C22×C4×C47—21no—
36C22×C4×C47C2311yescharacteristic
37C22×Dic47—21no—
38C22×Dic47D412yes—
39C2×Dic94—22no—
40C2×Dic94—22no—
41C2×Dic94—21no—
42C2×Dic94—22no—
43C2×Dic94C2312yes—
44M16×C47—22no—
45C2×C8×C47C2312yes—
46C4⋊C4×C47C2312yes—
47C22⋊C4×C47—21no—
48C42×C47—21no—
49C22⋊Dic47—21no—
50C4⋊Dic47—22no—
51C4⋊Dic47C2312yes—
52Dic47⋊C4—24no—
53Dic47⋊C4—24no—
54Dic47⋊C4—22no—
55Dic47⋊C4—22no—
56C4×Dic47—21no—
57C4×Dic47D412yes—
58C4×Dic47C2311yescharacteristic
59C4×Dic47C2311yescharacteristic
60#10625329—22no—
61C2×C47⋊C8C2312yes—
62C23×C47C2×D411yescharacteristic
63Q8×C47—22no—
64Q8×C47—22no—
65Q8×C47—42no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—42no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47#4112yes—
71C2×C4×C47#4112yes—
72C2×C4×C47C2411yescharacteristic
73C2×Dic47—24no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—42no—
77C2×Dic47C2×D412yes—
78C2×Dic47C2×D412yes—
79Dic94—22no—
80Dic94—22no—
81Dic94—42no—
82Dic94—44no—
83C8×C47—22no—
84C47⋊C8—22no—
85C22×C47—22no—
86C22×C47#12412yes—
87C22×C47C22×D411yescharacteristic
88C4×C47—42no—
89C4×C47—42no—
90C4×C47#12412yes—
91C4×C47C2×#4111yescharacteristic
92C4×C47C2×#4111yescharacteristic
93Dic47—22no—
94Dic47—42no—
95Dic47—42no—
96Dic47#13714yes—
97#3139—471nomaximal, Sylow
98C2×C47—22no—
99C2×C47C2×#12411yescharacteristic
100C2×C47C2×#13712yes—
101#533—471no—
102C2×C4⋊Q8—471no—
103#491—474no—
104#487—474no—
105#419—471no—
106#419—471no—
107#419—471no—
108#419D4711yescharacteristic
109C4×M16—471no—
110C47#313911yescharacteristic, complemented, Sylow
111C22×Q8—471no—
112C22×Q8C2×D4711yescharacteristic
113C2×M16—471no—
114C2×M16C2×D4711yescharacteristic
115C4⋊Q8—472no—
116C4⋊Q8—472no—
117C4⋊Q8—472no—
118C4⋊Q8—942no—
119#125—472no—
120C22⋊Q8—942no—
121C4×Q8—942no—
122#117—471no—
123#117C2×D4711yescharacteristic
124C2×C4⋊C4—942no—
125C2×C42—471no—
126#103—474no—
127#103—474no—
128#103—474no—
129#103C2×D4714yes—
130#97—472no—
131C4×C8—472no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—472no—
136C2×Q8—942no—
137C2×Q8—941no—
138C2×Q8—942no—
139C2×Q8—942no—
140C2×Q8C22×D4712yes—
141C22×C4—21no—
142C22×C4—472no—
143C22×C4—941no—
144C22×C4C22×D4711yescharacteristic
145M16—22no—
146M16—942no—
147C2×C8—472no—
148C2×C8C22×D4712yes—
149C4⋊C4—472no—
150C4⋊C4—944no—
151C4⋊C4—944no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—942no—
155C4⋊C4C22×D4712yes—
156C22⋊C4—21no—
157C22⋊C4—941no—
158C42—21no—
159C42—472no—
160C42—471no—
161C42—471no—
162C42—941no—
163C23D4×D4711yescharacteristic
164Q8—22no—
165Q8—22no—
166Q8—42no—
167Q8—942no—
168Q8—942no—
169Q8—1884no—
170Q8—1882no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—472no—
175C2×C4—472no—
176C2×C4—944no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—1882no—
180C2×C4#1062535012yes—
181C2×C4D4×D4711yescharacteristic
182C2×C4#1062535212yes—
183C2×C4C23×D4711yescharacteristic
184C8—22no—
185C8—942no—
186C22—22no—
187C22#1309401012yes—
188C22C2×D4×D4711yescharacteristic
189C4—42no—
190C4—42no—
191C4—474no—
192C4—942no—
193C4—1882no—
194C4—1882no—
195C4#1309401012yes—
196C4C2×#1062535211yescharacteristic
197C4C2×#1062535011yescharacteristic
198C2—22no—
199C2C2×#1309401011yescharacteristic
200C2#137×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#419C2
socleC22×C47C22×D4
hypercenter#419D47
hypocenterC47#3139
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #15689490C2semidirect
4. #15689472C2semidirect
110. C47#3139semidirect