Finite Group Databasebeta

← #20244913

Subgroups — #20244913

Order 6016.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13093957C211yesmaximal, characteristic, complemented
2C2×#13093946C211yesmaximal, characteristic
3C2×#13093944C211yesmaximal, characteristic
4#15689024C211yesmaximal, characteristic
5#15688992C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#107×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—22no—
12C2×(C2×D47)⋊C4—22no—
13C2×C4×Dic47C2211yescharacteristic
14#13093957—22no—
15#13093946—22no—
16#13093944—22no—
17C22×C8×C47C2211yescharacteristic
18C2×C4⋊C4×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20#107×C47—22no—
21C23×D47—21no—
22C22×C4×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—21no—
26C22×Dic47D412yes—
27C2×D188—21no—
28C2×D188—21no—
29C2×D188—21no—
30C2×D188—21no—
31C2×D188—21no—
32C2×D188Q812yes—
33C2×C8×C47—21no—
34C2×C8×C47—21no—
35C2×C8×C47D412yes—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40(C2×D47)⋊C4—44no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43Dic47⋊C4—44no—
44C4×Dic47—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8D412yes—
49C23×C47C2×D411yescharacteristic
50C22×D47—22no—
51C22×D47—41no—
52C22×D47—41no—
53C22×D47—42no—
54C22×D47—42no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—42no—
58C2×C4×C47—42no—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×Q811yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×Dic47—22no—
66C2×Dic47—22no—
67C2×Dic47—41no—
68C2×Dic47—42no—
69C2×Dic47D814yes—
70D188—22no—
71D188—22no—
72D188—41no—
73D188—41no—
74C8×C47—22no—
75C47⋊C8—22no—
76C22×C47C22⋊Q811yescharacteristic
77C22×C47#12311yescharacteristic
78C22×C47#12711yescharacteristic
79C22×C47C2×D812yes—
80C22×C47#13712yes—
81C2×D47—42no—
82C2×D47—44no—
83C2×D47—82no—
84C2×D47—81no—
85C2×D47—81no—
86C4×C47—81no—
87C4×C47—81no—
88C4×C47C22⋊Q811yescharacteristic
89C4×C47C22⋊Q811yescharacteristic
90C4×C47#12311yescharacteristic
91C4×C47#12311yescharacteristic
92Dic47—24no—
93Dic47—81no—
94#2093—471nomaximal, Sylow
95C2×C47#39911yescharacteristic
96C2×C47#47412yes—
97C2×C47#48012yes—
98C2×C47#49311yescharacteristic
99C2×C47#49711yescharacteristic
100D47—82no—
101C2×#107—471no—
102C2×#107D4711yescharacteristic, complemented
103C2×#102—471no—
104C2×#102—471no—
105#390—471no—
106#384—471no—
107#336—471no—
108C47#209311yescharacteristic, complemented, Sylow
109C22×D4—471no—
110C22×C8—471no—
111C22×C8C2×D4711yescharacteristic
112C2×C4⋊C4—471no—
113C2×C4⋊C4—942no—
114C2×C4⋊C4C2×D4711yescharacteristic
115C2×C4⋊C4C2×D4711yescharacteristic
116C2×C22⋊C4—942no—
117C2×C42—471no—
118#107—22no—
119#107—942no—
120#102—942no—
121#102—942no—
122C24—941no—
123C2×D4—472no—
124C2×D4—941no—
125C2×D4—941no—
126C2×D4—941no—
127C2×D4—941no—
128C2×D4—941no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—472no—
132C22×C4—941no—
133C22×C4C22×D4711yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—472no—
137C2×C8—941no—
138C2×C8—941no—
139C2×C8C22⋊D4712yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C4⋊C4—1884no—
147C22⋊C4—1884no—
148C42—941no—
149C42—941no—
150C23—942no—
151C23—1881no—
152C23—1881no—
153C23—1882no—
154C23—1882no—
155C23D4×D4711yescharacteristic
156D4—942no—
157D4—942no—
158D4—1881no—
159D4—1881no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—474no—
165C2×C4—942no—
166C2×C4—942no—
167C2×C4—1881no—
168C2×C4—1882no—
169C2×C4#1062535011yescharacteristic
170C2×C4#1062535011yescharacteristic
171C2×C4D4×D4711yescharacteristic
172C2×C4Q8×D4711yescharacteristic
173C2×C4#1062535411yescharacteristic
174C2×C4C2×C22⋊D4711yescharacteristic
175C8—22no—
176C8—942no—
177C22—3761no—
178C22—3761no—
179C22—3762no—
180C22—1882no—
181C22—1884no—
182C22#1309400211yescharacteristic
183C22#1309400911yescharacteristic
184C22#1309402011yescharacteristic
185C22D8×D4712yes—
186C22#1309405612yes—
187C4—81no—
188C4—81no—
189C4—944no—
190C4—3761no—
191C4#1309400011yescharacteristic
192C4#1309400211yescharacteristic
193C4#1309400711yescharacteristic
194C4#1309400911yescharacteristic
195C2—3762no—
196C2#1568905811yescharacteristic
197C2#1568940212yes—
198C2#1568943812yes—
199C2#1568949811yescharacteristic
200C2#1568951611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#107×C47C2
socleC23×C47C2×D4
hypercenterC2×#107D47
hypocenterC47#2093
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#13093957C2semidirect
5. #15688992C2semidirect
6. #15688877C2semidirect
7. C2×#107×C47C2semidirect
102. C2×#107D47semidirect
108. C47#2093semidirect