Finite Group Databasebeta

← #20241799

Subgroups — #20241799

Order 6016.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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#15689657C211yesmaximal, characteristic
2C4×#10625329C211yesmaximal, characteristic, complemented
3#15688853C212yesmaximal, complemented
4#15688850C212yesmaximal, complemented
5C2×C4⋊C8×C47C211yesmaximal, characteristic, complemented
6C2×#10625329—21no—
7#13094018—21no—
8#13094016C411yescharacteristic
9#13094012C411yescharacteristic
10#13094007—21no—
11#13094003C411yescharacteristic
12#13093998C411yescharacteristic
13C4×Dic94C2211yescharacteristic
14C4×D188C2211yescharacteristic
15C4×C22⋊D47—21no—
16#13093981—21no—
17#13093935—21no—
18C4×C47⋊C8C2212yes—
19C22×C8×C47—21no—
20C2×C42×C47C2211yescharacteristic
21C4⋊C8×C47—21no—
22C4⋊C8×C47C2212yes—
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C2×C22⋊D47—21no—
27C2×D188C2×C411yescharacteristic
28C2×C4×D47—21no—
29C2×Dic94C2×C411yescharacteristic
30C2×C8×C47—22no—
31C2×C8×C47—42no—
32C42×C47C2×C411yescharacteristic
33C42×C47D411yescharacteristic
34C42×C47D411yescharacteristic
35C42×C47C2311yescharacteristic
36C22⋊Dic47—21no—
37(C2×D47)⋊C4—21no—
38(C2×D47)⋊C4—21no—
39(C2×D47)⋊C4—21no—
40(C2×D47)⋊C4—21no—
41C4⋊Dic47C2×C411yescharacteristic
42C4⋊Dic47C2×C411yescharacteristic
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48#10625329—24no—
49C2×C47⋊C8—22no—
50C23×C47C22⋊C411yescharacteristic
51C22×D47—21no—
52C2×C4×C47—22no—
53C2×C4×C47—22no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22⋊C411yescharacteristic
58C2×C4×C47C22⋊C411yescharacteristic
59C2×C4×C47C22×C411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C22⋊D47—42no—
63C2×Dic47—21no—
64C2×Dic47—21no—
65C2×Dic47—21no—
66D188—22no—
67C4×D47—41no—
68C4×D47—41no—
69Dic94—22no—
70C8×C47—42no—
71C47⋊C8—24no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47#10412yes—
75C22×C47C2×C22⋊C411yescharacteristic
76C2×D47—41no—
77C2×D47—41no—
78C2×D47—41no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—21no—
83C4×C47#13112yes—
84C4×C47AGL(1,ℤ/8)11yescharacteristic
85C4×C47#13711yescharacteristic
86Dic47—41no—
87Dic47—41no—
88Dic47—41no—
89#1483—471nomaximal, Sylow
90C2×C47—22no—
91C2×C47#40811yescharacteristic
92C2×C47#41711yescharacteristic
93C2×C47C2×#10411yescharacteristic
94D47—81no—
95#529—471no—
96C2×C4⋊C8D4711yescharacteristic, complemented
97C4×M16—471no—
98Q8⋊C8—472no—
99D4⋊C8—472no—
100C47#148311yescharacteristic, complemented, Sylow
101C2×M16—941no—
102C22×C8—21no—
103#126—941no—
104#125—471no—
105#124—471no—
106#123—941no—
107C22⋊Q8—471no—
108#121—471no—
109C4×Q8—471no—
110C4×D4—471no—
111C4×D4—941no—
112#117—941no—
113C2×C42C2×D4711yescharacteristic
114C4⋊C8—21no—
115C4⋊C8C2×D4712yes—
116#97—941no—
117C4×C8—472no—
118C2×Q8—471no—
119C2×D4—471no—
120C2×D4—941no—
121C22×C4—941no—
122C22×C4C4×D4711yescharacteristic
123C22×C4D18811yescharacteristic
124C22×C4C22⋊D4711yescharacteristic
125M16—944no—
126C2×C8—22no—
127C2×C8—42no—
128C2×C8—942no—
129C4⋊C4—471no—
130C4⋊C4—471no—
131C4⋊C4—941no—
132C4⋊C4—941no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C22⋊C4—941no—
136C22⋊C4—941no—
137C22⋊C4—941no—
138C22⋊C4—941no—
139C22⋊C4—941no—
140C42—941no—
141C42C4×D4711yescharacteristic
142C42D18811yescharacteristic
143C42C22⋊D4711yescharacteristic
144C42C22×D4711yescharacteristic
145C23—941no—
146C23(C2×D47)⋊C411yescharacteristic
147Q8—942no—
148D4—942no—
149D4—1882no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—941no—
155C2×C4—941no—
156C2×C4—941no—
157C2×C4—1881no—
158C2×C4—1881no—
159C2×C4(C2×D47)⋊C411yescharacteristic
160C2×C4(C2×D47)⋊C411yescharacteristic
161C2×C4(C2×D47)⋊C411yescharacteristic
162C2×C4C2×C4×D4711yescharacteristic
163C2×C4C2×D18811yescharacteristic
164C2×C4C2×C22⋊D4711yescharacteristic
165C8—42no—
166C8—944no—
167C22—21no—
168C22—21no—
169C22—1881no—
170C22—1881no—
171C22—1881no—
172C22#1309395012yes—
173C22C2×(C2×D47)⋊C411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—1881no—
179C4—1881no—
180C4—1881no—
181C4#1309403012yes—
182C4#1309405011yescharacteristic
183C4#1309405511yescharacteristic
184C2—22no—
185C2—3761no—
186C2#1568908911yescharacteristic
187C2#1568912211yescharacteristic
188C2C2×#1309395011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC2×C4⋊C8×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×C4⋊C8D47
hypocenterC47#1483
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#10625329C2semidirect
3. #15688853C2semidirect
4. #15688850C2semidirect
5. C2×C4⋊C8×C47C2semidirect
96. C2×C4⋊C8D47semidirect
100. C47#1483semidirect