Finite Group Databasebeta

← #20242634

Subgroups — #20242634

Order 6016.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689788C211yesmaximal, characteristic
2#15689400C211yesmaximal, characteristic
3#15689330C211yesmaximal, characteristic, complemented
4#15688869C211yesmaximal, characteristic, complemented
5#15688855C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic
7C47×#500C211yesmaximal, characteristic, complemented
8C2×Q8×D47—21no—
9C2×#10625337—21no—
10#13094023—21no—
11#13094002—22no—
12#13094000—21no—
13C4×Dic94C2211yescharacteristic
14C4×D188C2211yescharacteristic
15#13093986—21no—
16#13093957—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093948—21no—
20#13093944—21no—
21C4⋊Q8×C47C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23#107×C47—22no—
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27Q8×D47—42no—
28Q8×D47—42no—
29C2×D188D411yescharacteristic
30C2×C4×D47—22no—
31C2×C4×D47—21no—
32C2×Dic94—22no—
33C2×Dic94D411yescharacteristic
34C2×C8×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47D412yes—
39C42×C47C2311yescharacteristic
40#10625337—42no—
41(C2×D47)⋊C4—22no—
42(C2×D47)⋊C4—21no—
43C4⋊Dic47D411yescharacteristic
44C4⋊Dic47D411yescharacteristic
45Dic47⋊C4—22no—
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C22×D47—21no—
51Q8×C47—41no—
52Q8×C47—41no—
53Q8×C47—41no—
54Q8×C47—41no—
55C2×C4×C47—22no—
56C2×C4×C47—41no—
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×Dic47—21no—
61C2×Dic47—21no—
62C2×Dic47—21no—
63D188—21no—
64D188Q1612yescomplemented
65C4×D47—44no—
66C4×D47—41no—
67C4×D47—41no—
68Dic94—21no—
69Dic94—44no—
70Dic94D812yes—
71C8×C47—22no—
72C47⋊C8—41no—
73C47⋊C8—41no—
74C22×C47#12011yescharacteristic
75C2×D47—22no—
76C2×D47—41no—
77C2×D47—41no—
78C4×C47—21no—
79C4×C47—42no—
80C4×C47—81no—
81C4×C47C2×D811yescharacteristic
82C4×C47C2×Q1611yescharacteristic
83C4×C47AGL(1,ℤ/8)11yescharacteristic
84C4×C47#13711yescharacteristic
85Dic47—22no—
86Dic47—41no—
87Dic47—41no—
88#1649—471nomaximal, Sylow
89C2×C47#44711yescharacteristic
90C2×C47#45111yescharacteristic
91C2×C47#45611yescharacteristic
92D47—42no—
93D4×Q8—471no—
94#500D4711yescharacteristic, complemented
95#474—471no—
96#462—471no—
97#332—471no—
98Q8⋊C8—471no—
99D4⋊C8—471no—
100C47#164911yescharacteristic, complemented, Sylow
101C22×Q8—941no—
102C2×Q16—941no—
103C4⋊Q8—941no—
104C4⋊Q8C2×D4711yescharacteristic
105C4⋊Q8C2×D4711yescharacteristic
106C22⋊Q8—941no—
107C22⋊Q8—942no—
108C4×Q8—471no—
109C4×D4—471no—
110C4×D4—941no—
111#107—22no—
112#107—941no—
113C4⋊C8—471no—
114C4⋊C8—471no—
115#103—941no—
116#102—941no—
117C4×C8C2×D4711yescharacteristic
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—471no—
121C2×Q8—942no—
122C2×Q8—1882no—
123C2×Q8—1882no—
124C2×D4—471no—
125C22×C4—942no—
126C22×C4—941no—
127Q16—1882no—
128C2×C8—21no—
129C2×C8—941no—
130C2×C8—941no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—471no—
135C4⋊C4—471no—
136C4⋊C4—942no—
137C4⋊C4—941no—
138C4⋊C4C22⋊D4712yes—
139C22⋊C4—942no—
140C22⋊C4—941no—
141C42—941no—
142C42C22×D4711yescharacteristic
143C23—941no—
144Q8—41no—
145Q8—41no—
146Q8—41no—
147Q8—41no—
148Q8—472no—
149Q8—941no—
150Q8—1884no—
151D4—472no—
152D4—941no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—941no—
156C2×C4—941no—
157C2×C4—941no—
158C2×C4—1884no—
159C2×C4—1881no—
160C2×C4—1881no—
161C2×C4D4×D4711yescharacteristic
162C2×C4D4×D4711yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C8—22no—
165C8—1881no—
166C8—1881no—
167C22—942no—
168C22—1881no—
169C22—1881no—
170C22#1309399211yescharacteristic
171C4—21no—
172C4—42no—
173C4—81no—
174C4—942no—
175C4—1881no—
176C4—1881no—
177C4D8×D4711yescharacteristic
178C4Q16×D4711yescharacteristic
179C4#1309404811yescharacteristic
180C4#1309405611yescharacteristic
181C2—1882no—
182C2#1568925511yescharacteristic
183C2#1568927711yescharacteristic
184C2#1568930511yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#500C2
socleC22×C47#120
hypercenter#500D47
hypocenterC47#1649
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #15689330C2semidirect
4. #15688869C2semidirect
5. #15688855C2semidirect
7. C47×#500C2semidirect
64. D188Q16semidirect
94. #500D47semidirect
100. C47#1649semidirect