Finite Group Databasebeta

← #20244737

Subgroups — #20244737

Order 6016.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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#15689751C211yesmaximal, characteristic
2#15689166C211yesmaximal, characteristic
3#15689165C211yesmaximal, characteristic
4#15688989C211yesmaximal, characteristic
5#15688891C211yesmaximal, characteristic
6#15688883C211yesmaximal, characteristic
7C47×#339C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9#13094024—21no—
10#13094023—21no—
11#13094016—21no—
12#13094015—21no—
13#13094001—22no—
14#13093983C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17#13093958—21no—
18#13093957—21no—
19#13093956—21no—
20#13093955—21no—
21C47⋊#95—22no—
22C2×M16×C47C2211yescharacteristic
23#117×C47C2211yescharacteristic
24C2×C42×C47C2211yescharacteristic
25C22×C4×C47—21no—
26C22×C4×C47C2311yescharacteristic
27C22×Dic47—21no—
28C22×Dic47D412yes—
29C2×Dic94—22no—
30M16×C47—21no—
31M16×C47Q812yescomplemented
32C2×C8×C47—21no—
33C4⋊C4×C47D411yescharacteristic
34C4⋊C4×C47D411yescharacteristic
35C22⋊C4×C47—21no—
36C42×C47—21no—
37C42×C47—21no—
38C42×C47Q812yescomplemented
39C22⋊Dic47—21no—
40C4⋊Dic47—22no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47D411yescharacteristic
46C4⋊Dic47D411yescharacteristic
47Dic47⋊C4—22no—
48Dic47⋊C4—22no—
49C4×Dic47—21no—
50#10625329—21no—
51#10625329Q812yescomplemented
52C2×C47⋊C8—21no—
53C23×C47C2×D411yescharacteristic
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—22no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×Q811yescharacteristic
62C2×C4×C47C2×Q811yescharacteristic
63C2×C4×C47C2×Q811yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—22no—
68C2×Dic47—42no—
69C2×Dic47—42no—
70C2×Dic47—41no—
71Dic94—82no—
72C8×C47—22no—
73C47⋊C8—22no—
74C22×C47—21no—
75C22×C47—21no—
76C22×C47#12011yescharacteristic
77C22×C47C22⋊Q811yescharacteristic
78C22×C47C4⋊Q811yescharacteristic
79C4×C47—42no—
80C4×C47—41no—
81C4×C47—41no—
82C4×C47C22⋊Q811yescharacteristic
83C4×C47C22⋊Q811yescharacteristic
84C4×C47C4⋊Q811yescharacteristic
85C4×C47C4⋊Q811yescharacteristic
86Dic47—41no—
87Dic47—41no—
88Dic47—42no—
89Dic47—81no—
90#2061—471nomaximal, Sylow
91C2×C47—21no—
92C2×C47—21no—
93C2×C47#39511yescharacteristic
94C2×C47#45411yescharacteristic
95C2×C47#45511yescharacteristic
96#544—471no—
97#428—471no—
98#428—471no—
99#382—471no—
100#343—471no—
101#339—471no—
102#339D4711yescharacteristic
103C47#206111yescharacteristic, complemented, Sylow
104C2×M16—471no—
105C2×M16C2×D4711yescharacteristic
106C4⋊Q8—941no—
107C4⋊Q8—941no—
108#125—941no—
109#125—941no—
110C22⋊Q8—942no—
111#117—471no—
112#117C2×D4711yescharacteristic
113C2×C4⋊C4—471no—
114C2×C4⋊C4—471no—
115C2×C42C2×D4711yescharacteristic
116#107—941no—
117#107—941no—
118#106—941no—
119#106—941no—
120#95—942no—
121C2×Q8—942no—
122C22×C4—21no—
123C22×C4—472no—
124C22×C4—941no—
125C22×C4C22×D4711yescharacteristic
126M16—21no—
127M16—472no—
128M16—941no—
129M16Dic9412yescomplemented
130C2×C8—21no—
131C2×C8—941no—
132C4⋊C4—471no—
133C4⋊C4—471no—
134C4⋊C4—942no—
135C4⋊C4—942no—
136C4⋊C4—942no—
137C4⋊C4—941no—
138C4⋊C4—941no—
139C4⋊C4—941no—
140C4⋊C4—941no—
141C4⋊C4D18811yescharacteristic
142C4⋊C4D18811yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—941no—
145C42—21no—
146C42—21no—
147C42—941no—
148C42Dic9412yescomplemented
149C23D4×D4711yescharacteristic
150Q8—3762no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—941no—
157C2×C4—941no—
158C2×C4—942no—
159C2×C4—1882no—
160C2×C4—1881no—
161C2×C4—1882no—
162C2×C4C2×Dic9411yescharacteristic
163C2×C4C2×Dic9411yescharacteristic
164C2×C4C2×D18811yescharacteristic
165C2×C4D4×D4711yescharacteristic
166C2×C4#1062535211yescharacteristic
167C2×C4Q8×D4711yescharacteristic
168C8—22no—
169C8—942no—
170C22—21no—
171C22—21no—
172C22#1309399411yescharacteristic
173C22#1309400111yescharacteristic
174C22#1309402311yescharacteristic
175C4—42no—
176C4—41no—
177C4—41no—
178C4—3761no—
179C4—1881no—
180C4—1882no—
181C4—1881no—
182C4#1309400111yescharacteristic
183C4#1309400411yescharacteristic
184C4#1309402311yescharacteristic
185C4#1309402411yescharacteristic
186C2—21no—
187C2—21no—
188C2#1568904411yescharacteristic
189C2#1568929711yescharacteristic
190C2#1568930211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47#120
hypercenter#339D47
hypocenterC47#2061
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
31. M16×C47Q8semidirect
38. C42×C47Q8semidirect
51. #10625329Q8semidirect
103. C47#2061semidirect
129. M16Dic94semidirect
148. C42Dic94semidirect