Finite Group Databasebeta

← #20242584

Subgroups — #20242584

Order 6016.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689794C211yesmaximal, characteristic
2#15689470C211yesmaximal, characteristic, complemented
3#15689403C211yesmaximal, characteristic, complemented
4#15689334C211yesmaximal, characteristic, complemented
5#15688866C211yesmaximal, characteristic, complemented
6#15688855C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625350—21no—
9C2×Dic188—21no—
10#13094024C2211yescharacteristic
11#13094021C2211yescharacteristic
12#13094020—21no—
13#13093998—21no—
14#13093997—22no—
15C4×Dic94C2211yescharacteristic
16#13093986—21no—
17#13093957—21no—
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093949—21no—
20#13093946—22no—
21#13093945—21no—
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×D4×C47D411yescharacteristic
26C22×C4×C47—21no—
27C2×C22⋊D47—22no—
28C2×C22⋊D47—22no—
29#10625350—42no—
30#10625350—42no—
31C2×D188—21no—
32C2×D188—21no—
33C2×D188D412yes—
34C2×C4×D47—22no—
35C2×Dic94—21no—
36C2×Dic94D411yescharacteristic
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C4⋊C4×C47D411yescharacteristic
40C22⋊C4×C47—21no—
41C42×C47C2311yescharacteristic
42(C2×D47)⋊C4—22no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47D411yescharacteristic
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C2×C47⋊C8—21no—
49Dic188—42no—
50C23×C47—21no—
51C22×D47—22no—
52D4×C47—21no—
53D4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C22⋊D47—44no—
61C22⋊D47—82no—
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—41no—
65D188—42no—
66D188—41no—
67D188—41no—
68D188—41no—
69D188—41no—
70C4×D47—44no—
71Dic94—21no—
72Dic94—41no—
73Dic94—41no—
74Dic94D812yes—
75C8×C47—41no—
76C8×C47—41no—
77C47⋊C8—41no—
78C22×C47—41no—
79C22×C47—41no—
80C22×C47—41no—
81C22×C47#12011yescharacteristic
82C2×D47—42no—
83C2×D47—42no—
84C2×D47—42no—
85C4×C47—21no—
86C4×C47—41no—
87C4×C47C2×D811yescharacteristic
88C4×C47#13511yescharacteristic
89C4×C47AGL(1,ℤ/8)11yescharacteristic
90C4×C47#13711yescharacteristic
91Dic47—22no—
92Dic47—41no—
93Dic47—81no—
94#1641—471nomaximal, Sylow
95C2×C47—81no—
96C2×C47#44711yescharacteristic
97C2×C47#45211yescharacteristic
98C2×C47#45511yescharacteristic
99D47—82no—
100#550—471no—
101#486—471no—
102#474—471no—
103#462—471no—
104#331—471no—
105Q8⋊C8—471no—
106D4⋊C8D4711yescharacteristic, complemented
107C47#164111yescharacteristic, complemented, Sylow
108C2×#41—941no—
109C2×Q16—941no—
110C4⋊Q8—471no—
111#127—471no—
112#127—941no—
113#121—942no—
114#121—941no—
115C4×Q8—471no—
116C4×D4—941no—
117C4×D4C2×D4711yescharacteristic
118#107—941no—
119C4⋊C8—471no—
120C4⋊C8C2×D4711yescharacteristic
121#103—941no—
122#102—942no—
123#102—941no—
124C4×C8C2×D4711yescharacteristic
125#41—1882no—
126#41—1882no—
127C2×Q8—471no—
128C2×Q8—941no—
129C2×D4—472no—
130C2×D4—942no—
131C2×D4—942no—
132C2×D4—941no—
133C2×D4—941no—
134C2×D4D18811yescharacteristic
135C22×C4—21no—
136C22×C4—942no—
137Q16—1882no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—941no—
141C4⋊C4—471no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C4⋊C4D18811yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—942no—
148C42—941no—
149C42C22×D4711yescharacteristic
150C23—21no—
151C23—942no—
152Q8—472no—
153Q8—941no—
154Q8—1881no—
155Q8—1881no—
156D4—21no—
157D4—21no—
158D4—3762no—
159D4—1882no—
160D4—1884no—
161D4—1881no—
162D4—1881no—
163D4—1881no—
164D4—1881no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—941no—
169C2×C4—941no—
170C2×C4—1884no—
171C2×C4—1881no—
172C2×C4C2×D18811yescharacteristic
173C2×C4D4×D4711yescharacteristic
174C2×C4D4×D4711yescharacteristic
175C8—41no—
176C8—41no—
177C8—1881no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—1882no—
182C22—1882no—
183C22—1882no—
184C22#1309399411yescharacteristic
185C4—21no—
186C4—41no—
187C4—942no—
188C4—3761no—
189C4—1881no—
190C4D8×D4711yescharacteristic
191C4#1309404611yescharacteristic
192C4#1309405111yescharacteristic
193C4#1309405711yescharacteristic
194C2—81no—
195C2—3762no—
196C2#1568925811yescharacteristic
197C2#1568928711yescharacteristic
198C2#1568930211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47#120
hypercenterD4⋊C8D47
hypocenterC47#1641
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #15689470C2semidirect
3. #15689403C2semidirect
4. #15689334C2semidirect
5. #15688866C2semidirect
6. #15688855C2semidirect
7. C47×D4⋊C8C2semidirect
106. D4⋊C8D47semidirect
107. C47#1641semidirect