Finite Group Databasebeta

← #20244908

Subgroups — #20244908

Order 6016.

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

normal subgroups only

This group has 274 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×#13093958C211yesmaximal, characteristic, complemented
2C2×#13093956C211yesmaximal, characteristic, complemented
3C2×#13093946C211yesmaximal, characteristic
4C2×#13093946C211yesmaximal, characteristic
5#15689025C211yesmaximal, characteristic
6#15688989C211yesmaximal, characteristic, complemented
7C47×#336C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×(C2×D47)⋊C4—22no—
13#13093958—22no—
14#13093956—22no—
15#13093946—22no—
16#13093946—22no—
17C47⋊#95—22no—
18C22×C8×C47C2211yescharacteristic
19C22×C8×C47C2211yescharacteristic
20C2×C42×C47C2211yescharacteristic
21C23×D47—21no—
22C22×C4×C47D412yes—
23C22×C4×C47C2311yescharacteristic
24C22×Dic47—21no—
25C22×Dic47—21no—
26C22×Dic47—21no—
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×C47—21no—
36C2×C8×C47—21no—
37C2×C8×C47D412yes—
38C2×C8×C47D412yes—
39C42×C47—21no—
40C42×C47—21no—
41(C2×D47)⋊C4—44no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48C23×C47C2×D411yescharacteristic
49C22×D47—22no—
50C22×D47—41no—
51C22×D47—41no—
52C22×D47—42no—
53C22×D47—42no—
54C2×C4×C47—22no—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×Q811yescharacteristic
60C2×C4×C47#4111yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×Dic47—41no—
64C2×Dic47—41no—
65C2×Dic47—41no—
66C2×Dic47—42no—
67C2×Dic47—42no—
68C2×Dic47—42no—
69D188—22no—
70D188—22no—
71D188—41no—
72D188—41no—
73C8×C47—22no—
74C8×C47—22no—
75C22×C47C22⋊Q811yescharacteristic
76C22×C47#12311yescharacteristic
77C22×C47#12711yescharacteristic
78C22×C47#13512yes—
79C22×C47AGL(1,ℤ/8)12yes—
80C2×D47—42no—
81C2×D47—44no—
82C2×D47—82no—
83C2×D47—81no—
84C2×D47—81no—
85C4×C47—42no—
86C4×C47C22⋊Q811yescharacteristic
87C4×C47C22⋊Q811yescharacteristic
88C4×C47#12311yescharacteristic
89C4×C47#12311yescharacteristic
90Dic47—81no—
91Dic47—81no—
92Dic47—81no—
93#2092—471nomaximal, Sylow
94C2×C47#39911yescharacteristic
95C2×C47#47812yes—
96C2×C47#48212yes—
97C2×C47#49511yescharacteristic
98C2×C47#49611yescharacteristic
99D47—82no—
100C2×#107—471no—
101C2×#106—471no—
102C2×#102—471no—
103C2×#102—471no—
104#390—471no—
105#382—471no—
106#336D4711yescharacteristic, complemented
107C47#209211yescharacteristic, complemented, Sylow
108C22×D4—471no—
109C22×C8C2×D4711yescharacteristic
110C22×C8C2×D4711yescharacteristic
111C2×C4⋊C4—471no—
112C2×C4⋊C4—471no—
113C2×C4⋊C4—471no—
114C2×C22⋊C4—942no—
115C2×C42C2×D4711yescharacteristic
116#107—942no—
117#106—942no—
118#102—942no—
119#102—942no—
120#95—942no—
121C24—941no—
122C2×D4—472no—
123C2×D4—941no—
124C2×D4—941no—
125C2×D4—941no—
126C2×D4—941no—
127C2×D4—941no—
128C22×C4—941no—
129C22×C4—941no—
130C22×C4—941no—
131C22×C4D18812yes—
132C22×C4C22×D4711yescharacteristic
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8D18812yes—
138C2×C8D18812yes—
139C4⋊C4—941no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C22⋊C4—1884no—
146C42—21no—
147C42—21no—
148C23—942no—
149C23—1881no—
150C23—1881no—
151C23—1882no—
152C23—1882no—
153C23C2×D18811yescharacteristic
154D4—942no—
155D4—942no—
156D4—1881no—
157D4—1881no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—1881no—
162C2×C4—1881no—
163C2×C4—1881no—
164C2×C4—1882no—
165C2×C4—1882no—
166C2×C4—1882no—
167C2×C4C2×D18811yescharacteristic
168C2×C4C2×D18811yescharacteristic
169C2×C4#1062535211yescharacteristic
170C2×C4#1062535211yescharacteristic
171C2×C4#1062535211yescharacteristic
172C2×C4Q8×D4711yescharacteristic
173C8—22no—
174C8—22no—
175C22—3761no—
176C22—3761no—
177C22—3762no—
178C22—1882no—
179C22—1884no—
180C22#1309400411yescharacteristic
181C22#1309400811yescharacteristic
182C22#1309402111yescharacteristic
183C22#1309404612yes—
184C22#1309405212yes—
185C4—42no—
186C4—3761no—
187C4—3761no—
188C4—3761no—
189C4#1309400411yescharacteristic
190C4#1309400411yescharacteristic
191C4#1309400811yescharacteristic
192C4#1309400811yescharacteristic
193C2—3762no—
194C2#1568906011yescharacteristic
195C2#1568942412yes—
196C2#1568944812yes—
197C2#1568950711yescharacteristic
198C2#1568951211yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#336C2
socleC23×C47C2×D4
hypercenter#336D47
hypocenterC47#2092
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
1. C2×#13093958C2semidirect
2. C2×#13093956C2semidirect
6. #15688989C2semidirect
7. C47×#336C2semidirect
106. #336D47semidirect
107. C47#2092semidirect