Finite Group Databasebeta

← #20253230

Subgroups — #20253230

Order 6016.

362 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 149 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#15689751C211yesmaximal, characteristic
2#15689430C212yesmaximal, complemented
3#15689430C212yesmaximal, complemented
4#15689418C212yesmaximal, complemented
5#15689408C212yesmaximal, complemented
6#15689166C211yesmaximal, characteristic
7#15689159C211yesmaximal, characteristic
8#15689150C211yesmaximal, characteristic
9#15689132C211yesmaximal, characteristic
10C2×#13093948C211yesmaximal, characteristic
11C47×#519C211yesmaximal, characteristic
12C2×#10625329C2211yescharacteristic
13C22×C47⋊C8C2211yescharacteristic
14#13094024C2212yes—
15#13094023—21no—
16#13094016C2212yes—
17#13094015—21no—
18#13094001—22no—
19#13093983C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21#13093957C2211yescharacteristic
22#13093957C2211yescharacteristic
23#13093957C2212yes—
24#13093955C2211yescharacteristic
25#13093955C2212yes—
26#13093955C2211yescharacteristic
27C4⋊(C47⋊C8)C2212yes—
28C4⋊(C47⋊C8)C2212yes—
29#13093948C2212yes—
30#13093948C2212yes—
31#13093948C2212yes—
32#13093948C2212yes—
33C22×Q8×C47C2211yescharacteristic
34C4×Q8×C47—21no—
35C4×Q8×C47—21no—
36C4×Q8×C47C2212yes—
37C4×Q8×C47C2212yes—
38#117×C47—22no—
39#117×C47C2211yescharacteristic
40#117×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47—22no—
43C2×Q8×C47Q814yescomplemented
44C2×Q8×C47C2312yes—
45C22×C4×C47—21no—
46C22×C4×C47C2311yescharacteristic
47C22×Dic47—21no—
48C2×Dic94—22no—
49C4⋊C4×C47—22no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47D411yescharacteristic
52C4⋊C4×C47D411yescharacteristic
53C4⋊C4×C47C2311yescharacteristic
54C4⋊C4×C47C2311yescharacteristic
55C22⋊C4×C47—21no—
56C22⋊C4×C47D412yes—
57C42×C47—22no—
58C42×C47—22no—
59C42×C47—21no—
60C42×C47C2312yes—
61C22⋊Dic47—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47—22no—
64C4⋊Dic47C2312yes—
65C4⋊Dic47C2311yescharacteristic
66C4⋊Dic47C2311yescharacteristic
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69C4×Dic47—21no—
70#10625329—22no—
71C2×C47⋊C8—22no—
72C2×C47⋊C8C2311yescharacteristic
73C2×C47⋊C8C2312yes—
74C2×C47⋊C8C2311yescharacteristic
75C23×C47C2×D411yescharacteristic
76Q8×C47—24no—
77Q8×C47—22no—
78Q8×C47C2×Q814yes—
79C2×C4×C47—24no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47C2×D412yes—
84C2×C4×C47C2×D412yes—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×Q812yes—
87C2×C4×C47#4112yes—
88C2×C4×C47C2411yescharacteristic
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—22no—
92C2×Dic47—81no—
93Dic94—82no—
94C47⋊C8—21no—
95C47⋊C8—21no—
96C47⋊C8—22no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47C22⋊Q812yes—
100C22×C47C22×D411yescharacteristic
101C4×C47—24no—
102C4×C47—22no—
103C4×C47—22no—
104C4×C47—41no—
105C4×C47—41no—
106C4×C47C22⋊Q812yes—
107C4×C47C22×Q811yescharacteristic
108C4×C47C2×#4111yescharacteristic
109Dic47—41no—
110Dic47—42no—
111Dic47—41no—
112#3082—471nomaximal, Sylow
113C2×C47—22no—
114C2×C47C2×C22⋊Q811yescharacteristic
115C2×C47#57711yescharacteristic
116C2×C47#57811yescharacteristic
117#544—471no—
118#519D4711yescharacteristic
119#479—472no—
120#479—472no—
121#477—472no—
122#475—472no—
123#428—471no—
124#427—471no—
125#424—471no—
126#419—471no—
127C2×#103—471no—
128C47#308211yescharacteristic, complemented, Sylow
129C22×Q8C2×D4711yescharacteristic
130C2×M16—471no—
131C22×C8—471no—
132C4⋊Q8—472no—
133C4⋊Q8—941no—
134#125—472no—
135#125—941no—
136C22⋊Q8—942no—
137C4×Q8—21no—
138C4×Q8—21no—
139C4×Q8C2×D4712yes—
140C4×Q8C2×D4712yes—
141#117—22no—
142#117—471no—
143#117C2×D4711yescharacteristic
144#117C2×D4711yescharacteristic
145C2×C4⋊C4—471no—
146#107—471no—
147#107—471no—
148#107—472no—
149#106—471no—
150#106—471no—
151#106—472no—
152C4⋊C8—472no—
153C4⋊C8—472no—
154#103—472no—
155#103—472no—
156#103—472no—
157#103—472no—
158C2×Q8—22no—
159C2×Q8—21no—
160C2×Q8—942no—
161C2×Q8Dic9414yescomplemented
162C2×Q8C22×D4712yes—
163C22×C4—21no—
164C22×C4—941no—
165C22×C4C22×D4711yescharacteristic
166M16—942no—
167C2×C8—471no—
168C2×C8—472no—
169C2×C8—471no—
170C2×C8—942no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—472no—
174C4⋊C4—471no—
175C4⋊C4—471no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—941no—
179C4⋊C4—942no—
180C4⋊C4C22⋊D4711yescharacteristic
181C4⋊C4C22⋊D4711yescharacteristic
182C4⋊C4C22×D4711yescharacteristic
183C4⋊C4C22×D4711yescharacteristic
184C22⋊C4—21no—
185C22⋊C4—941no—
186C22⋊C4C22⋊D4712yes—
187C42—22no—
188C42—22no—
189C42—21no—
190C42—941no—
191C42C22×D4712yes—
192C23C2×C22⋊D4711yescharacteristic
193Q8—24no—
194Q8—22no—
195Q8—3762no—
196Q8C2×Dic9414yes—
197C2×C4—24no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—941no—
202C2×C4—941no—
203C2×C4—942no—
204C2×C4—3761no—
205C2×C4C2×Dic9412yes—
206C2×C4#1062535012yes—
207C2×C4C2×C22⋊D4712yes—
208C2×C4C2×C22⋊D4712yes—
209C2×C4C2×C22⋊D4711yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—941no—
212C8—941no—
213C8—942no—
214C22—21no—
215C22—21no—
216C22#1309400312yes—
217C22C22×C22⋊D4711yescharacteristic
218C4—24no—
219C4—22no—
220C4—22no—
221C4—41no—
222C4—41no—
223C4—1882no—
224C4—1881no—
225C4—1881no—
226C4#1309400312yes—
227C4C22×Dic9411yescharacteristic
228C4C2×#1062535011yescharacteristic
229C2—22no—
230C2C2×#1309400311yescharacteristic
231C2#1568993111yescharacteristic
232C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#519C2
socleC22×C47C22×D4
hypercenter#519D47
hypocenterC47#3082
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #15689430C2semidirect
3. #15689430C2semidirect
4. #15689418C2semidirect
5. #15689408C2semidirect
43. C2×Q8×C47Q8semidirect
128. C47#3082semidirect
161. C2×Q8Dic94semidirect