Finite Group Databasebeta

← #20254525

Subgroups — #20254525

Order 6016.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689678C211yesmaximal, characteristic, complemented
2#15689674C211yesmaximal, characteristic
3#15689526C211yesmaximal, characteristic, complemented
4#15689471C211yesmaximal, characteristic, complemented
5#15689470C211yesmaximal, characteristic, complemented
6#15689449C214yesmaximal, complemented
7#15689422C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic, complemented
9C47×#498C211yesmaximal, characteristic, complemented
10C2×#10625354—21no—
11#13094024C2211yescharacteristic
12#13094021C2211yescharacteristic
13#13094015C2212yes—
14#13094013—21no—
15#13094004—21no—
16#13094000—21no—
17#13093999—21no—
18#13093999C2212yes—
19Q8×Dic47—21no—
20#13093989—21no—
21#13093986—21no—
22#13093986C2212yes—
23#13093982C2212yes—
24C42×D47C2211yescharacteristic
25#13093957C2214yes—
26Dic47⋊C8C2212yes—
27#13093946C2214yes—
28#13093944C2214yes—
29(C2×D47)⋊C8C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C4⋊Q8×C47C2211yescharacteristic
32C4⋊Q8×C47C2211yescharacteristic
33#106×C47C2214yes—
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47—21no—
36C2×Q8×C47—21no—
37#10625354—44no—
38C2×D188—22no—
39C2×D188—21no—
40C2×D188—21no—
41C2×D188C2312yes—
42C2×C4×D47—22no—
43C2×C4×D47D411yescharacteristic
44C2×C4×D47D411yescharacteristic
45C2×C4×D47C2311yescharacteristic
46C2×Dic94—21no—
47C2×C8×C47C2312yes—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47C2312yes—
51C4⋊C4×C47C2312yes—
52C42×C47C2311yescharacteristic
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—21no—
57C4⋊Dic47—22no—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60C4×Dic47—22no—
61C4×Dic47D411yescharacteristic
62C4×Dic47D411yescharacteristic
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2312yes—
65C22×D47—22no—
66C22×D47C2×D411yescharacteristic
67Q8×C47—42no—
68Q8×C47—42no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2411yescharacteristic
74C2×Dic47—22no—
75C2×Dic47C2×D411yescharacteristic
76C2×Dic47C2×D411yescharacteristic
77C2×Dic47C2×D411yescharacteristic
78D188—24no—
79D188—44no—
80D188—42no—
81D188—42no—
82C4×D47—22no—
83C4×D47—22no—
84C4×D47—22no—
85C4×D47—44no—
86Dic94—42no—
87C8×C47—22no—
88C47⋊C8—22no—
89C22×C47C22×D411yescharacteristic
90C2×D47—21no—
91C2×D47—21no—
92C2×D47—21no—
93C2×D47—42no—
94C2×D47—42no—
95C2×D47—42no—
96C4×C47—42no—
97C4×C47—42no—
98C4×C47#13512yes—
99C4×C47AGL(1,ℤ/8)12yes—
100C4×C472−1+412yes—
101Dic47—21no—
102Dic47—21no—
103Dic47—21no—
104Dic47—42no—
105#3228—471nomaximal, Sylow
106C2×C47#53611yescharacteristic
107C2×C47C2×#13511yescharacteristic
108C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
109D47—41no—
110D47—82no—
111#533—471no—
112#532—471no—
113#500—471no—
114#498D4711yescharacteristic, complemented
115#486—471no—
116#486—471no—
117#482—474no—
118#478—474no—
119#431—471no—
120C47#322811yescharacteristic, complemented, Sylow
121C2×#41—941no—
122C4⋊Q8—471no—
123C4⋊Q8C2×D4711yescharacteristic
124C4⋊Q8C2×D4711yescharacteristic
125#127—471no—
126#125—472no—
127#124—941no—
128C22⋊Q8—941no—
129C22⋊Q8—941no—
130#121—472no—
131#121—941no—
132C4×Q8—941no—
133C4×Q8—941no—
134C4×D4—472no—
135C4×D4—941no—
136#117—472no—
137C2×C42—471no—
138#107—474no—
139#106C2×D4714yes—
140C4⋊C8—472no—
141#102—474no—
142#102—474no—
143C22⋊C8—472no—
144C4×C8—471no—
145C4×C8C2×D4711yescharacteristic
146#41—1884no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—941no—
150C2×D4—472no—
151C2×D4—942no—
152C2×D4—941no—
153C2×D4—941no—
154C22×C4—471no—
155C22×C4—471no—
156C22×C4—471no—
157C22×C4—942no—
158C2×C8—472no—
159C2×C8C22×D4712yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—472no—
163C4⋊C4—942no—
164C4⋊C4—942no—
165C4⋊C4—941no—
166C4⋊C4C22×D4712yes—
167C4⋊C4C22×D4712yes—
168C22⋊C4—942no—
169C22⋊C4—942no—
170C22⋊C4—942no—
171C42—471no—
172C42—471no—
173C42—471no—
174C42—942no—
175C42C22×D4711yescharacteristic
176C23—471no—
177C23—942no—
178Q8—42no—
179Q8—42no—
180Q8—1882no—
181D4—944no—
182D4—1884no—
183D4—1882no—
184D4—1882no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—471no—
188C2×C4—471no—
189C2×C4—471no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—1884no—
195C2×C4D4×D4711yescharacteristic
196C2×C4D4×D4711yescharacteristic
197C2×C4C23×D4711yescharacteristic
198C8—22no—
199C8—942no—
200C22—941no—
201C22—941no—
202C22—941no—
203C22—1882no—
204C22—1882no—
205C22—1882no—
206C22C2×D4×D4711yescharacteristic
207C4—42no—
208C4—42no—
209C4—941no—
210C4—941no—
211C4—941no—
212C4—1882no—
213C4#1309404512yes—
214C4#1309405112yes—
215C4#1309407212yes—
216C2—3762no—
217C2—1881no—
218C2#1568969811yescharacteristic
219C2C2×#1309404511yescharacteristic
220C2C2×#1309405111yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#498C2
socleC22×C47C22×D4
hypercenter#498D47
hypocenterC47#3228
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689526C2semidirect
4. #15689471C2semidirect
5. #15689470C2semidirect
6. #15689449C2semidirect
7. #15689422C2semidirect
8. #15689174C2semidirect
9. C47×#498C2semidirect
114. #498D47semidirect
120. C47#3228semidirect