Finite Group Databasebeta

← #20244744

Subgroups — #20244744

Order 6016.

228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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×#13093959C211yesmaximal, characteristic, complemented
2#15689165C211yesmaximal, characteristic, complemented
3#15689151C211yesmaximal, characteristic, complemented
4#15689128C211yesmaximal, characteristic
5C2×#13093945C211yesmaximal, characteristic
6#15688891C211yesmaximal, characteristic, complemented
7C2×#100×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13093983C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12#13093959—22no—
13#13093958—21no—
14#13093956—21no—
15Dic47⋊C8—22no—
16#13093945—21no—
17#13093945—21no—
18#13093945—22no—
19C22×D4×C47C2211yescharacteristic
20C2×M16×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22#100×C47—22no—
23C24×C47—21no—
24C2×D4×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47Q812yes—
30C22×C4×C47C2311yescharacteristic
31C22×Dic47—21no—
32M16×C47—21no—
33M16×C47—21no—
34M16×C47—21no—
35M16×C47D412yes—
36C2×C8×C47—21no—
37C2×C8×C47—21no—
38C22⋊Dic47—21no—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47D411yescharacteristic
42C4⋊Dic47D411yescharacteristic
43C4×Dic47—21no—
44#10625329—21no—
45#10625329—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8D412yes—
50C23×C47—22no—
51C23×C47—41no—
52C23×C47—41no—
53C23×C47—81no—
54C23×C47—81no—
55C23×C47#4111yescharacteristic
56D4×C47—22no—
57D4×C47—22no—
58D4×C47—41no—
59D4×C47—41no—
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×Q811yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—41no—
69C2×Dic47—81no—
70C8×C47—22no—
71C8×C47—41no—
72C47⋊C8—22no—
73C47⋊C8—41no—
74C22×C47—21no—
75C22×C47—21no—
76C22×C47—42no—
77C22×C47—82no—
78C22×C47—82no—
79C22×C47—81no—
80C22×C47—81no—
81C22×C47#12111yescharacteristic
82C22×C47C22⋊Q811yescharacteristic
83C22×C47#12611yescharacteristic
84C4×C47#12111yescharacteristic
85C4×C47#12111yescharacteristic
86C4×C47C22⋊Q811yescharacteristic
87C4×C47C22⋊Q811yescharacteristic
88Dic47—41no—
89Dic47—41no—
90Dic47—81no—
91#2063—471nomaximal, Sylow
92C2×C47—21no—
93C2×C47—21no—
94C2×C47—82no—
95C2×C47#39611yescharacteristic
96C2×C47#47111yescharacteristic
97C2×C47#47211yescharacteristic
98C2×#108—471no—
99#428—471no—
100#424—471no—
101#418—471no—
102C2×#102—471no—
103C2×#100D4711yescharacteristic
104#343—471no—
105C47#206311yescharacteristic, complemented, Sylow
106C22×D4C2×D4711yescharacteristic
107C2×M16—471no—
108C2×M16C2×D4711yescharacteristic
109C2×M16C2×D4711yescharacteristic
110C22×C8—471no—
111#117—471no—
112C2×C4⋊C4—471no—
113#108—942no—
114#107—941no—
115#106—941no—
116C4⋊C8—942no—
117#102—941no—
118#102—941no—
119#102—942no—
120#100—22no—
121C24—21no—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4Dic9412yes—
128C22×C4—941no—
129C22×C4C22×D4711yescharacteristic
130M16—21no—
131M16—21no—
132M16—21no—
133M16—941no—
134M16—941no—
135M16C22⋊D4712yes—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—472no—
139C2×C8—941no—
140C2×C8—941no—
141C2×C8—941no—
142C4⋊C4—471no—
143C4⋊C4—471no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C22⋊C4—941no—
147C42—941no—
148C23—22no—
149C23—41no—
150C23—41no—
151C23—81no—
152C23—81no—
153C23#1062535011yescharacteristic
154D4—22no—
155D4—22no—
156D4—41no—
157D4—41no—
158C2×C4—941no—
159C2×C4—941no—
160C2×C4—3761no—
161C2×C4—1881no—
162C2×C4C2×Dic9411yescharacteristic
163C2×C4D4×D4711yescharacteristic
164C2×C4D4×D4711yescharacteristic
165C2×C4#1062535211yescharacteristic
166C2×C4#1062535211yescharacteristic
167C2×C4C2×C22⋊D4711yescharacteristic
168C8—22no—
169C8—41no—
170C8—942no—
171C8—1881no—
172C22—21no—
173C22—21no—
174C22—42no—
175C22—82no—
176C22—82no—
177C22—81no—
178C22—81no—
179C22#1309399711yescharacteristic
180C22#1309400311yescharacteristic
181C22#1309401711yescharacteristic
182C4—3761no—
183C4—1881no—
184C4—1881no—
185C4#1309399511yescharacteristic
186C4#1309399611yescharacteristic
187C4#1309400111yescharacteristic
188C4#1309400111yescharacteristic
189C2—21no—
190C2—21no—
191C2—82no—
192C2#1568904611yescharacteristic
193C2#1568938511yescharacteristic
194C2#1568939211yescharacteristic
subgroupG/H
centerC22#13093997
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#100×C47C2
socleC22×C47#121
hypercenterC2×#100D47
hypocenterC47#2063
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#13093959C2semidirect
2. #15689165C2semidirect
3. #15689151C2semidirect
6. #15688891C2semidirect
105. C47#2063semidirect