Finite Group Databasebeta

← #20244293

Subgroups — #20244293

Order 6016.

296 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#13093960C211yesmaximal, characteristic, complemented
2#15689132C211yesmaximal, characteristic, complemented
3#15689128C211yesmaximal, characteristic
4C2×#13093943C211yesmaximal, characteristic, complemented
5C2×#13093941C211yesmaximal, characteristic
6#15689078C211yesmaximal, characteristic, complemented
7C22×SD16×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13093983C2211yescharacteristic
12#13093960—22no—
13#13093948—22no—
14#13093945—22no—
15#13093943—22no—
16#13093941—22no—
17#13093934—21no—
18C8×Dic47—21no—
19C22×Q8×C47C2211yescharacteristic
20C22×D4×C47C2211yescharacteristic
21C2×SD16×C47—21no—
22C2×SD16×C47—21no—
23C2×SD16×C47—22no—
24C2×SD16×C47C414yescomplemented
25C22×C8×C47C2211yescharacteristic
26C24×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47C2×C412yes—
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47—21no—
36C2×D4×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47C2×C412yes—
39C22×C4×C47—21no—
40C22×C4×C47C2311yescharacteristic
41SD16×C47—24no—
42SD16×C47—24no—
43C2×C8×C47C2×C412yes—
44C2×C8×C47D411yescharacteristic
45C2×C8×C47D411yescharacteristic
46C2×C8×C47D412yes—
47C22⋊Dic47—21no—
48C4⋊Dic47D412yes—
49C4×Dic47—21no—
50#10625329—21no—
51#10625329—21no—
52#10625329—21no—
53#10625329—21no—
54#10625329—21no—
55#10625329D412yes—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C23×C47—22no—
60C23×C47—41no—
61C23×C47—41no—
62C23×C47—82no—
63C23×C47#4111yescharacteristic
64Q8×C47—22no—
65Q8×C47—22no—
66Q8×C47—41no—
67Q8×C47—41no—
68D4×C47—22no—
69D4×C47—22no—
70D4×C47—41no—
71D4×C47—41no—
72C2×C4×C47—22no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47C22×C411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×Dic47—22no—
82C8×C47C22⋊C412yes—
83C8×C47C22⋊C412yes—
84C47⋊C8—22no—
85C47⋊C8—41no—
86C47⋊C8—41no—
87C22×C47—22no—
88C22×C47—42no—
89C22×C47—82no—
90C22×C47—82no—
91C22×C47—82no—
92C22×C47C4×D411yescharacteristic
93C22×C47#12111yescharacteristic
94C22×C47#12411yescharacteristic
95C4×C47—42no—
96C4×C47C2×C22⋊C411yescharacteristic
97C4×C47C4×D411yescharacteristic
98C4×C47#12111yescharacteristic
99C4×C47#12711yescharacteristic
100Dic47—42no—
101#1977—471nomaximal, Sylow
102C2×C47—21no—
103C2×C47—21no—
104C2×C47—82no—
105C2×C47#39011yescharacteristic
106C2×C47#47112yes—
107C22×SD16D4711yescharacteristic
108C2×#108—471no—
109#419—471no—
110#418—471no—
111C2×#101—471no—
112C2×#100—471no—
113#405—471no—
114C47#197711yescharacteristic, complemented, Sylow
115C22×Q8C2×D4711yescharacteristic
116C22×D4C2×D4711yescharacteristic
117C2×SD16—21no—
118C2×SD16—21no—
119C2×SD16—22no—
120C2×SD16Dic4714yescomplemented
121C2×M16—471no—
122C2×M16—471no—
123C2×M16—471no—
124C22×C8C2×D4711yescharacteristic
125#117—471no—
126#108—942no—
127#103—942no—
128#102—942no—
129#101—942no—
130#100—942no—
131#97—941no—
132C4×C8—941no—
133C24—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8C2×Dic4712yes—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4C2×Dic4712yes—
146C22×C4—21no—
147C22×C4C22×D4711yescharacteristic
148SD16—24no—
149SD16—24no—
150M16—472no—
151M16—941no—
152M16—941no—
153M16—941no—
154M16—941no—
155M16—941no—
156C2×C8—941no—
157C2×C8—941no—
158C2×C8—941no—
159C2×C8C2×Dic4712yes—
160C2×C8C22⋊D4711yescharacteristic
161C2×C8C22⋊D4711yescharacteristic
162C2×C8C22⋊D4712yes—
163C4⋊C4—472no—
164C22⋊C4—941no—
165C42—941no—
166C23—22no—
167C23—41no—
168C23—41no—
169C23—82no—
170C23#1062535211yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—41no—
174Q8—41no—
175D4—22no—
176D4—22no—
177D4—41no—
178D4—41no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—942no—
183C2×C4D4×D4711yescharacteristic
184C2×C4D4×D4711yescharacteristic
185C2×C4#1062535211yescharacteristic
186C2×C4C22×Dic4711yescharacteristic
187C2×C4C2×C22⋊D4711yescharacteristic
188C2×C4C2×C22⋊D4711yescharacteristic
189C8—942no—
190C8—1881no—
191C8—1881no—
192C8C22⋊Dic4712yes—
193C8C22⋊Dic4712yes—
194C22—22no—
195C22—42no—
196C22—82no—
197C22—82no—
198C22—82no—
199C22D4×Dic4711yescharacteristic
200C22#1309399511yescharacteristic
201C22#1309401111yescharacteristic
202C4—42no—
203C4—1882no—
204C4C2×C22⋊Dic4711yescharacteristic
205C4D4×Dic4711yescharacteristic
206C4#1309399511yescharacteristic
207C4#1309402011yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#1568902611yescharacteristic
212C2#1568938312yes—
subgroupG/H
centerC22#13093995
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×SD16×C47C2
socleC22×C47#121
hypercenterC22×SD16D47
hypocenterC47#1977
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13093960C2semidirect
2. #15689132C2semidirect
4. C2×#13093943C2semidirect
6. #15689078C2semidirect
24. C2×SD16×C47C4semidirect
114. C47#1977semidirect
120. C2×SD16Dic47semidirect