Finite Group Databasebeta

← #20256268

Subgroups — #20256268

Order 6016.

338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689848C211yesmaximal, characteristic, complemented
2#15689834C211yesmaximal, characteristic
3#15689523C212yesmaximal, complemented
4#15689433C212yesmaximal, complemented
5#15689422C212yesmaximal
6#15689415C211yesmaximal, characteristic, complemented
7#15689400C211yesmaximal, characteristic
8C8×Dic94C211yesmaximal, characteristic, complemented
9C4×#10625325C211yesmaximal, characteristic
10#15689210C212yesmaximal
11C47×#498C211yesmaximal, characteristic, complemented
12C2×#10625325C2211yescharacteristic
13#13094022—21no—
14#13094015C2212yes—
15#13094015C2212yes—
16#13094014—22no—
17#13094004—21no—
18#13094000—22no—
19Q8×Dic47—21no—
20C4×Dic94C2211yescharacteristic
21C4×Dic94C2211yescharacteristic
22#13093989C2212yes—
23C4×D188C2211yescharacteristic
24#13093986C2212yes—
25C4⋊C4×D47—21no—
26#13093957C2212yes—
27#13093957C2212yes—
28#13093956C2211yescharacteristic
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2211yescharacteristic
32#13093947C2212yes—
33#13093946C2211yescharacteristic
34#13093944C2212yes—
35C8×Dic47C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4⋊Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39#106×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47—21no—
43C2×D188C2311yescharacteristic
44C2×C4×D47—21no—
45C2×C4×D47—22no—
46C2×Dic94D411yescharacteristic
47C2×Dic94C2311yescharacteristic
48C2×C8×C47C2311yescharacteristic
49C2×C8×C47C2311yescharacteristic
50C4⋊C4×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2312yes—
53C4⋊C4×C47C2312yes—
54C42×C47C2311yescharacteristic
55(C2×D47)⋊C4—21no—
56(C2×D47)⋊C4—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47D411yescharacteristic
60C4⋊Dic47C2311yescharacteristic
61C4⋊Dic47C2311yescharacteristic
62Dic47⋊C4—21no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4D412yes—
67C4×Dic47—21no—
68C4×Dic47—22no—
69C4×Dic47C2312yes—
70C2×C47⋊C8C2312yes—
71#10625325Q814yescomplemented
72C22×D47—21no—
73Q8×C47—42no—
74Q8×C47—81no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2411yescharacteristic
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47C2×D412yes—
84C2×Dic47C2×D412yes—
85D188—21no—
86D188C2×Q812yes—
87C4×D47—42no—
88C4×D47—82no—
89Dic94—22no—
90Dic94—21no—
91Dic94C2×Q812yes—
92C8×C47—21no—
93C8×C47C2×Q812yes—
94C47⋊C8—22no—
95C22×C47C22×D411yescharacteristic
96C2×D47—22no—
97C2×D47—41no—
98C2×D47—41no—
99C4×C47—21no—
100C4×C47—42no—
101C4×C47—42no—
102C4×C47#13512yes—
103C4×C47C22×Q811yescharacteristic
104C4×C472−1+411yescharacteristic
105Dic47—22no—
106Dic47—22no—
107Dic47—22no—
108Dic47—41no—
109Dic47—41no—
110#3381—471nomaximal, Sylow
111C2×C47D4×Q811yescharacteristic
112C2×C47C2×#13511yescharacteristic
113C2×C47#57711yescharacteristic
114D47—42no—
115#557—471no—
116#554—471no—
117#499—472no—
118#498D4711yescharacteristic, complemented
119#479—472no—
120#478—472no—
121#477—471no—
122#474—471no—
123C8×Q8—471no—
124C4×SD16—472no—
125C4×SD16—471no—
126C47#338111yescharacteristic, complemented, Sylow
127C2×SD16—471no—
128C4⋊Q8—941no—
129C4⋊Q8C2×D4711yescharacteristic
130C4⋊Q8C2×D4711yescharacteristic
131#125—472no—
132#125—472no—
133#125—942no—
134C22⋊Q8—941no—
135C22⋊Q8—942no—
136C4×Q8—471no—
137C4×Q8—472no—
138C4×Q8—471no—
139C4×Q8—941no—
140C4×D4—472no—
141C4×D4—471no—
142C2×C4⋊C4—941no—
143#107—472no—
144#107—472no—
145#106—471no—
146#106C2×D4712yes—
147#106C2×D4712yes—
148C4⋊C8—472no—
149C4⋊C8—471no—
150#103—471no—
151#103—472no—
152#102—471no—
153#102—472no—
154C4×C8—472no—
155C4×C8C2×D4711yescharacteristic
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—471no—
159C2×Q8—471no—
160C2×D4—471no—
161C22×C4—942no—
162C22×C4—941no—
163SD16—474no—
164C2×C8—472no—
165C2×C8C22×D4711yescharacteristic
166C2×C8C22×D4711yescharacteristic
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—472no—
170C4⋊C4—471no—
171C4⋊C4—471no—
172C4⋊C4—471no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—941no—
179C4⋊C4C22×D4712yes—
180C4⋊C4C22×D4712yes—
181C22⋊C4—942no—
182C22⋊C4—941no—
183C42—472no—
184C42—942no—
185C42—941no—
186C42C22×D4711yescharacteristic
187C23—941no—
188Q8—42no—
189Q8—81no—
190Q8—472no—
191Q8—942no—
192Q8—941no—
193D4—472no—
194D4—941no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—472no—
198C2×C4—472no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—3762no—
203C2×C4—1882no—
204C2×C4D4×D4711yescharacteristic
205C2×C4D4×D4711yescharacteristic
206C2×C4C23×D4711yescharacteristic
207C8—21no—
208C8—942no—
209C8Q8×D4712yes—
210C22—942no—
211C22—1881no—
212C22—1881no—
213C22C2×D4×D4711yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—942no—
218C4—942no—
219C4—942no—
220C4—1881no—
221C4—1881no—
222C4#1309404512yes—
223C4C2×Q8×D4711yescharacteristic
224C4#1309407211yescharacteristic
225C2—1882no—
226C2#1568978811yescharacteristic
227C2C2×#1309404511yescharacteristic
228C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#498C2
socleC22×C47C22×D4
hypercenter#498D47
hypocenterC47#3381
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. #15689848C2semidirect
3. #15689523C2semidirect
4. #15689433C2semidirect
6. #15689415C2semidirect
8. C8×Dic94C2semidirect
11. C47×#498C2semidirect
71. #10625325Q8semidirect
118. #498D47semidirect
126. C47#3381semidirect