Finite Group Databasebeta

← #20244665

Subgroups — #20244665

Order 6016.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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#15689171C211yesmaximal, characteristic, complemented
2#15689140C211yesmaximal, characteristic
3#15689132C211yesmaximal, characteristic, complemented
4#15689107C211yesmaximal, characteristic
5C2×#13093943C211yesmaximal, characteristic, complemented
6#15688895C211yesmaximal, characteristic, complemented
7C2×#137×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13093983C2211yescharacteristic
12#13093959—22no—
13#13093951—22no—
14#13093948—22no—
15#13093943—21no—
16#13093943—22no—
17#13093941—21no—
18C2×#41×C47C2211yescharacteristic
19C22×Q8×C47C2211yescharacteristic
20#137×C47—22no—
21#137×C47—22no—
22C2×Q16×C47—21no—
23C2×SD16×C47—21no—
24C2×M16×C47C2211yescharacteristic
25#41×C47—21no—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47D411yescharacteristic
35C2×Q8×C47D412yes—
36C2×D4×C47—21no—
37C2×D4×C47D411yescharacteristic
38C22×C4×C47—21no—
39C22×C4×C47—21no—
40C22×C4×C47C2311yescharacteristic
41Q16×C47—24no—
42SD16×C47—24no—
43M16×C47—21no—
44M16×C47D412yes—
45C2×C8×C47—21no—
46C22⋊Dic47—21no—
47C4⋊Dic47—21no—
48C4×Dic47—21no—
49#10625329—21no—
50#10625329—21no—
51#10625329—21no—
52#10625329—21no—
53#10625329—21no—
54#10625329D412yes—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C23×C47—21no—
59C23×C47#4111yescharacteristic
60Q8×C47—22no—
61Q8×C47—21no—
62Q8×C47—21no—
63Q8×C47—22no—
64Q8×C47—41no—
65Q8×C47—41no—
66D4×C47—21no—
67D4×C47—21no—
68D4×C47—41no—
69D4×C47—41no—
70C2×C4×C47—22no—
71C2×C4×C47—21no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×Dic47—41no—
83C8×C47—22no—
84C47⋊C8—22no—
85C47⋊C8—41no—
86C47⋊C8—41no—
87C22×C47—41no—
88C22×C47—41no—
89C22×C47—81no—
90C22×C47#12111yescharacteristic
91C22×C47#12311yescharacteristic
92C22×C47#12411yescharacteristic
93C4×C47—41no—
94C4×C47—42no—
95C4×C47#12011yescharacteristic
96C4×C47#12111yescharacteristic
97C4×C47#12111yescharacteristic
98C4×C47#12311yescharacteristic
99Dic47—81no—
100#2049—471nomaximal, Sylow
101C2×C47—21no—
102C2×C47—21no—
103C2×C47—21no—
104C2×C47—81no—
105C2×C47#39411yescharacteristic
106C2×#137D4711yescharacteristic
107#430—471no—
108#421—471no—
109#419—471no—
110#413—471no—
111C2×#101—471no—
112#344—471no—
113C47#204911yescharacteristic, complemented, Sylow
114C2×#41C2×D4711yescharacteristic
115C22×Q8C2×D4711yescharacteristic
116#137—22no—
117#137—22no—
118C2×Q16—21no—
119C2×SD16—21no—
120C2×M16—471no—
121C2×M16—471no—
122C2×M16—471no—
123C2×M16C2×D4711yescharacteristic
124#117—471no—
125#108—942no—
126#104—942no—
127#103—942no—
128#101—942no—
129#101—941no—
130#100—941no—
131#41—21no—
132#41—21no—
133#41—21no—
134#41—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8C22⋊D4711yescharacteristic
141C2×Q8C22⋊D4712yes—
142C2×D4—21no—
143C2×D4C22⋊D4711yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4C22×D4711yescharacteristic
147Q16—24no—
148SD16—24no—
149M16—21no—
150M16—472no—
151M16—941no—
152M16—941no—
153M16—941no—
154M16—941no—
155M16—941no—
156M16C22⋊D4712yes—
157C2×C8—21no—
158C2×C8—941no—
159C2×C8—941no—
160C2×C8—941no—
161C4⋊C4—941no—
162C22⋊C4—941no—
163C42—941no—
164C23—21no—
165C23#1062535211yescharacteristic
166Q8—22no—
167Q8—21no—
168Q8—21no—
169Q8—22no—
170Q8—41no—
171Q8—41no—
172D4—21no—
173D4—21no—
174D4—41no—
175D4—41no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—1881no—
183C2×C4D4×D4711yescharacteristic
184C2×C4#1062535211yescharacteristic
185C2×C4#1062535211yescharacteristic
186C2×C4C2×C22⋊D4711yescharacteristic
187C2×C4C2×C22⋊D4711yescharacteristic
188C2×C4C2×C22⋊D4711yescharacteristic
189C8—22no—
190C8—942no—
191C8—1881no—
192C8—1881no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22#1309399611yescharacteristic
197C22#1309400511yescharacteristic
198C22#1309401111yescharacteristic
199C4—41no—
200C4—42no—
201C4—3761no—
202C4#1309399311yescharacteristic
203C4#1309399511yescharacteristic
204C4#1309399611yescharacteristic
205C4#1309400511yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—81no—
210C2#1568903711yescharacteristic
subgroupG/H
centerC2#15689037
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#137×C47C2
socleC2×C47#394
hypercenterC2×#137D47
hypocenterC47#2049
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. #15689171C2semidirect
3. #15689132C2semidirect
5. C2×#13093943C2semidirect
6. #15688895C2semidirect
113. C47#2049semidirect