Finite Group Databasebeta

← #20254300

Subgroups — #20254300

Order 6016.

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

normal subgroups only

This group has 402 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#15689701C212yesmaximal, complemented
2#15689454C212yesmaximal, complemented
3#15689442C212yesmaximal, complemented
4#15689381C211yesmaximal, characteristic, complemented
5#15689376C211yesmaximal, characteristic, complemented
6#15689352C212yesmaximal, complemented
7#15689287C212yesmaximal, complemented
8#15689270C212yesmaximal, complemented
9C47×#408C211yesmaximal, characteristic, complemented
10C2×#10625350C2212yes—
11C2×Dic188C2211yescharacteristic
12C2×#10625325C2212yes—
13C2×D376C2211yescharacteristic
14#13094003C2212yes—
15#13094003C2212yes—
16#13094000—22no—
17#13093998C2212yes—
18#13093998C2212yes—
19#13093996—22no—
20#13093996—22no—
21#13093995—22no—
22C2×C4⋊Dic47C2212yes—
23#13093956C2212yes—
24#13093956C2211yescharacteristic
25#13093956C2211yescharacteristic
26#13093949C2212yes—
27#13093949C2212yes—
28#13093946C2212yes—
29#13093946C2212yes—
30C2×#41×C47C2211yescharacteristic
31C2×M16×C47C2211yescharacteristic
32C22×C8×C47C2211yescharacteristic
33C22⋊C8×C47C2212yes—
34C22⋊C8×C47C2212yes—
35#41×C47—41no—
36#41×C47—41no—
37C2×Q8×C47D411yescharacteristic
38C2×D4×C47D412yes—
39C2×D4×C47D411yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C2×C22⋊D47—22no—
43C2×C22⋊D47—22no—
44C2×C22⋊D47—22no—
45C22×Dic47—22no—
46#10625350—42no—
47#10625350—42no—
48C2×D188C2312yes—
49C2×C4×D47—22no—
50C2×Dic94C2312yes—
51M16×C47—41no—
52C2×C8×C47—41no—
53C2×C8×C47C2312yes—
54C2×C8×C47C2311yescharacteristic
55C2×C8×C47C2311yescharacteristic
56C22⋊Dic47—22no—
57C22⋊Dic47—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47C2312yes—
62C4⋊Dic47C2312yes—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic188—41no—
66D376—41no—
67#10625325—42no—
68C23×C47C2×D411yescharacteristic
69C23×C47C2×D412yes—
70C22×D47—22no—
71Q8×C47—41no—
72D4×C47—42no—
73D4×C47—41no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2411yescharacteristic
81C22⋊D47—44no—
82C22⋊D47—82no—
83C22⋊D47—82no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—82no—
88D188—22no—
89D188—22no—
90C4×D47—44no—
91Dic94—22no—
92Dic94—22no—
93C8×C47—22no—
94C8×C47—21no—
95C8×C47—21no—
96C22×C47—22no—
97C22×C47—21no—
98C22×C47—22no—
99C22×C47—22no—
100C22×C47—22no—
101C22×C47C22×D411yescharacteristic
102C2×D47—42no—
103C2×D47—42no—
104C2×D47—42no—
105C4×C47—22no—
106C4×C47—21no—
107C4×C47H(5,𝔽2)11yescharacteristic
108C4×C47H(5,𝔽2)11yescharacteristic
109Dic47—42no—
110Dic47—42no—
111Dic47—42no—
112#3204—471nomaximal, Sylow
113C2×C47—42no—
114C2×C47—41no—
115C2×C47#53411yescharacteristic
116C2×C47#57712yes—
117D47—82no—
118#537—472no—
119#483—472no—
120#481—472no—
121#470—471no—
122#469—471no—
123#465—472no—
124#452—472no—
125#449—472no—
126#408D4711yescharacteristic, complemented
127C47#320411yescharacteristic, complemented, Sylow
128C2×#41—472no—
129C2×#41C2×D4711yescharacteristic
130C2×Q16—471no—
131C2×SD16—472no—
132C2×D8—471no—
133C2×M16C2×D4711yescharacteristic
134C22×C8C2×D4711yescharacteristic
135C22⋊Q8—472no—
136C22⋊Q8—472no—
137C22⋊Q8—942no—
138#121—472no—
139#121—472no—
140#121—942no—
141#121—942no—
142#121—942no—
143C2×C4⋊C4—472no—
144#106—472no—
145#106—471no—
146#106—471no—
147#103—472no—
148#103—472no—
149#102—472no—
150#102—472no—
151C22⋊C8C2×D4712yes—
152C22⋊C8C2×D4712yes—
153#41—41no—
154#41—41no—
155#41—1882no—
156#41—1882no—
157C2×Q8—472no—
158C2×Q8D18811yescharacteristic
159C2×D4—472no—
160C2×D4—942no—
161C2×D4—942no—
162C2×D4—942no—
163C2×D4D18811yescharacteristic
164C2×D4D18812yes—
165C22×C4—942no—
166C22×C4—942no—
167C22×C4C22×D4712yes—
168C22×C4C22×D4711yescharacteristic
169Q16—1881no—
170SD16—1882no—
171D8—1881no—
172M16—41no—
173C2×C8—41no—
174C2×C8C22×D4711yescharacteristic
175C2×C8C22×D4712yes—
176C2×C8C22×D4711yescharacteristic
177C4⋊C4—472no—
178C4⋊C4—472no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—942no—
182C22⋊C4—942no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C23—942no—
187C23C2×D18811yescharacteristic
188C23C2×D18812yes—
189Q8—41no—
190Q8—942no—
191Q8—942no—
192D4—42no—
193D4—41no—
194D4—942no—
195D4—942no—
196D4—3762no—
197D4—3762no—
198D4—1884no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—3762no—
207C2×C4—1884no—
208C2×C4C2×D18811yescharacteristic
209C2×C4C2×D18812yes—
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—21no—
213C8—21no—
214C22—22no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—21no—
219C22—1882no—
220C22—1882no—
221C22—1882no—
222C22C22×D18811yescharacteristic
223C4—22no—
224C4—21no—
225C4—1882no—
226C4—1882no—
227C4—1882no—
228C4#1309406911yescharacteristic
229C4#1309406911yescharacteristic
230C2—42no—
231C2—41no—
232C2—3762no—
233C2#1568968511yescharacteristic
234C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#408C2
socleC22×C47C22×D4
hypercenter#408D47
hypocenterC47#3204
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #15689701C2semidirect
2. #15689454C2semidirect
3. #15689442C2semidirect
4. #15689381C2semidirect
5. #15689376C2semidirect
6. #15689352C2semidirect
7. #15689287C2semidirect
8. #15689270C2semidirect
9. C47×#408C2semidirect
126. #408D47semidirect
127. C47#3204semidirect