Finite Group Databasebeta

← #20243441

Subgroups — #20243441

Order 6016.

256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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×#13094032C211yesmaximal, characteristic
2C2×#13093959C211yesmaximal, characteristic, complemented
3#15689159C211yesmaximal, characteristic, complemented
4#15689141C211yesmaximal, characteristic
5#15689139C211yesmaximal, characteristic
6#15688895C211yesmaximal, characteristic, complemented
7C47×#344C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094032—21no—
10#13094032—21no—
11#13094032C412yescomplemented
12#13094032C412yescomplemented
13C2×#10625329C2211yescharacteristic
14C2×#10625324—21no—
15C22×C47⋊C8C2211yescharacteristic
16C2×C8×D47—21no—
17#13093983C2211yescharacteristic
18#13093959—21no—
19#13093959—21no—
20#13093957—21no—
21#13093955—21no—
22#13093952—22no—
23#13093950—22no—
24C2×M16×C47C2211yescharacteristic
25C2×M16×C47C2211yescharacteristic
26#117×C47C2211yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—21no—
29#10625350—21no—
30#10625350—21no—
31#10625350C2×C412yes—
32#10625350D412yes—
33C2×D188Q811yescharacteristic
34C2×C4×D47—21no—
35C2×Dic94Q811yescharacteristic
36M16×C47—21no—
37M16×C47—21no—
38M16×C47—21no—
39M16×C47C2×C412yes—
40C2×C8×C47—21no—
41C2×C8×C47—21no—
42C4⋊C4×C47—21no—
43C22⋊C4×C47—21no—
44C42×C47—21no—
45C22⋊Dic47—21no—
46C4⋊Dic47—21no—
47C4×Dic47—21no—
48#10625329—21no—
49#10625329—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8C2×C411yescharacteristic
52C2×C47⋊C8C2×C411yescharacteristic
53C2×C47⋊C8D411yescharacteristic
54C2×C47⋊C8D411yescharacteristic
55C2×C47⋊C8D411yescharacteristic
56C2×C47⋊C8D411yescharacteristic
57#10625324—22no—
58#10625324—22no—
59C8×D47—22no—
60C8×D47—22no—
61C23×C47#4111yescharacteristic
62C22×D47—21no—
63C2×C4×C47—41no—
64C2×C4×C47C22×C411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×Q811yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C22⋊D47—22no—
71C22⋊D47—22no—
72C2×Dic47—21no—
73C2×Dic47—41no—
74D188—21no—
75D188C4⋊C412yes—
76C4×D47—22no—
77C4×D47—22no—
78Dic94—21no—
79Dic94C4⋊C412yes—
80C8×C47—22no—
81C8×C47—41no—
82C47⋊C8—41no—
83C47⋊C8C22⋊C411yescharacteristic
84C47⋊C8C22⋊C411yescharacteristic
85C47⋊C8C22⋊C411yescharacteristic
86C47⋊C8C22⋊C411yescharacteristic
87C22×C47—41no—
88C22×C47#11711yescharacteristic
89C22×C47#12111yescharacteristic
90C22×C47C22⋊Q811yescharacteristic
91C2×D47—22no—
92C2×D47—42no—
93C4×C47—81no—
94C4×C47C2×C22⋊C411yescharacteristic
95C4×C47C2×C4⋊C411yescharacteristic
96C4×C47#12111yescharacteristic
97C4×C47C22⋊Q811yescharacteristic
98Dic47—22no—
99Dic47—81no—
100#1814—471nomaximal, Sylow
101C2×C47—21no—
102C2×C47—21no—
103C2×C47—21no—
104C2×C47#38011yescharacteristic
105D47—42no—
106C2×#131—471no—
107C2×#108—471no—
108#427—471no—
109#421—471no—
110#421—471no—
111#344—471no—
112#344D4711yescharacteristic, complemented
113C47#181411yescharacteristic, complemented, Sylow
114C2×#41—471no—
115#131—472no—
116#131—472no—
117#131—941no—
118#131—941no—
119C2×M16—471no—
120C2×M16—941no—
121C2×M16C2×D4711yescharacteristic
122C2×M16C2×D4711yescharacteristic
123C22×C8—471no—
124C22×C8—941no—
125#117—471no—
126#117C2×D4711yescharacteristic
127#108—941no—
128#108—941no—
129#107—941no—
130#106—941no—
131#104—942no—
132#104—942no—
133#41—472no—
134#41—472no—
135#41—941no—
136#41—941no—
137C2×Q8—471no—
138C2×D4—471no—
139C2×D4—941no—
140C22×C4—941no—
141C22×C4C22×D4711yescharacteristic
142M16—21no—
143M16—21no—
144M16—21no—
145M16—942no—
146M16—942no—
147M16—941no—
148M16—941no—
149M16C4×D4712yes—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—471no—
153C2×C8—471no—
154C2×C8—471no—
155C2×C8—471no—
156C2×C8—471no—
157C2×C8—471no—
158C2×C8—942no—
159C2×C8—942no—
160C2×C8—941no—
161C4⋊C4—21no—
162C4⋊C4—941no—
163C22⋊C4—21no—
164C22⋊C4—941no—
165C42—21no—
166C42—941no—
167C23—941no—
168C23#1062535011yescharacteristic
169Q8—472no—
170Q8—941no—
171D4—472no—
172D4—942no—
173D4—942no—
174D4—941no—
175C2×C4—41no—
176C2×C4—941no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—1881no—
180C2×C4C2×C4×D4711yescharacteristic
181C2×C4#1062535011yescharacteristic
182C2×C4D4×D4711yescharacteristic
183C2×C4D4×D4711yescharacteristic
184C2×C4D4×D4711yescharacteristic
185C2×C4Q8×D4711yescharacteristic
186C8—22no—
187C8—41no—
188C8—471no—
189C8—471no—
190C8—471no—
191C8—471no—
192C8—1881no—
193C22—41no—
194C22—942no—
195C22—1882no—
196C22#1309398111yescharacteristic
197C22#1309399711yescharacteristic
198C22#1309400211yescharacteristic
199C4—81no—
200C4—942no—
201C4—3761no—
202C4C22⋊C4×D4711yescharacteristic
203C4C4⋊C4×D4711yescharacteristic
204C4#1309399711yescharacteristic
205C4#1309400211yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—1882no—
210C2#1568898211yescharacteristic
subgroupG/H
centerC4#13093997
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#344C2
socleC2×C47#380
hypercenter#344D47
hypocenterC47#1814
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. C2×#13093959C2semidirect
3. #15689159C2semidirect
6. #15688895C2semidirect
7. C47×#344C2semidirect
11. #13094032C4semidirect
12. #13094032C4semidirect
112. #344D47semidirect
113. C47#1814semidirect