Finite Group Databasebeta

← #20253224

Subgroups — #20253224

Order 6016.

362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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#15689600C211yesmaximal, characteristic
2#15689427C212yesmaximal, complemented
3#15689427C212yesmaximal, complemented
4#15689415C212yesmaximal, complemented
5#15689405C212yesmaximal, complemented
6#15689163C211yesmaximal, characteristic
7#15689159C211yesmaximal, characteristic
8#15689150C211yesmaximal, characteristic
9#15689131C211yesmaximal, characteristic
10C2×#13093947C211yesmaximal, characteristic
11C47×#544C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14C22×C47⋊C8C2211yescharacteristic
15C4×Dic94C2212yes—
16C4×Dic94C2212yes—
17#13093989—21no—
18#13093989—21no—
19#13093983C2211yescharacteristic
20#13093980—22no—
21#13093957C2211yescharacteristic
22#13093957C2211yescharacteristic
23#13093957C2212yes—
24#13093955C2211yescharacteristic
25#13093955C2212yes—
26#13093955C2211yescharacteristic
27C4⋊(C47⋊C8)C2212yes—
28C4⋊(C47⋊C8)C2212yes—
29#13093947C2212yes—
30#13093947C2212yes—
31#13093947C2212yes—
32#13093947C2212yes—
33C4⋊Q8×C47—21no—
34C4⋊Q8×C47C2212yes—
35#125×C47—21no—
36#125×C47C2212yes—
37C22⋊Q8×C47—22no—
38#117×C47C2211yescharacteristic
39#117×C47C2211yescharacteristic
40C2×C4⋊C4×C47C2211yescharacteristic
41C2×Q8×C47—22no—
42C22×C4×C47—21no—
43C22×C4×C47C2311yescharacteristic
44C22×Dic47—21no—
45C2×Dic94—21no—
46C2×Dic94—22no—
47C2×Dic94Q814yescomplemented
48C2×Dic94C2312yes—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47—22no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47D411yescharacteristic
54C4⋊C4×C47D411yescharacteristic
55C4⋊C4×C47C2312yes—
56C4⋊C4×C47C2311yescharacteristic
57C4⋊C4×C47C2311yescharacteristic
58C22⋊C4×C47—21no—
59C22⋊C4×C47D412yes—
60C42×C47—21no—
61C42×C47C2312yes—
62C22⋊Dic47—21no—
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67C4×Dic47—22no—
68C4×Dic47—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—82no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—81no—
81C2×C4×C47C2×D412yes—
82C2×C4×C47C2×D412yes—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×Q812yes—
85C2×C4×C47#4112yes—
86C2×C4×C47C2411yescharacteristic
87C2×Dic47—24no—
88C2×Dic47—22no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91Dic94—24no—
92Dic94—22no—
93Dic94C2×Q814yes—
94C47⋊C8—21no—
95C47⋊C8—21no—
96C47⋊C8—22no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47C22⋊Q812yes—
100C22×C47C22×D411yescharacteristic
101C4×C47—22no—
102C4×C47—22no—
103C4×C47—42no—
104C4×C47—41no—
105C4×C47—41no—
106C4×C47C22⋊Q812yes—
107C4×C47C22×Q811yescharacteristic
108C4×C47C2×#4111yescharacteristic
109Dic47—24no—
110Dic47—41no—
111Dic47—41no—
112#3082—471nomaximal, Sylow
113C2×C47—22no—
114C2×C47C2×C22⋊Q811yescharacteristic
115C2×C47#57711yescharacteristic
116C2×C47#57811yescharacteristic
117#544D4711yescharacteristic
118#519—471no—
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×Q8—471no—
130C2×M16—471no—
131C22×C8—471no—
132C4⋊Q8—21no—
133C4⋊Q8C2×D4712yes—
134#125—21no—
135#125C2×D4712yes—
136C22⋊Q8—22no—
137C4×Q8—472no—
138C4×Q8—472no—
139C4×Q8—941no—
140C4×Q8—941no—
141#117—471no—
142#117—942no—
143#117C2×D4711yescharacteristic
144#117C2×D4711yescharacteristic
145C2×C4⋊C4C2×D4711yescharacteristic
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—474no—
160C2×Q8—472no—
161C2×Q8—942no—
162C2×Q8—941no—
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—21no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—471no—
176C4⋊C4—471no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4C22⋊D4711yescharacteristic
180C4⋊C4C22⋊D4711yescharacteristic
181C4⋊C4C22×D4712yes—
182C4⋊C4C22×D4711yescharacteristic
183C4⋊C4C22×D4711yescharacteristic
184C22⋊C4—21no—
185C22⋊C4—941no—
186C22⋊C4C22⋊D4712yes—
187C42—21no—
188C42—941no—
189C42—942no—
190C42—942no—
191C42C22×D4712yes—
192C23C2×C22⋊D4711yescharacteristic
193Q8—82no—
194Q8—474no—
195Q8—944no—
196Q8—942no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—81no—
201C2×C4—944no—
202C2×C4—942no—
203C2×C4—941no—
204C2×C4—941no—
205C2×C4Q8×D4712yes—
206C2×C4#1062535412yes—
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#1309400012yes—
217C22C22×C22⋊D4711yescharacteristic
218C4—22no—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—944no—
224C4—1881no—
225C4—1881no—
226C4#1309400012yes—
227C4C2×Q8×D4711yescharacteristic
228C4C2×#1062535411yescharacteristic
229C2—22no—
230C2C2×#1309400011yescharacteristic
231C2#1568993411yescharacteristic
232C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#544C2
socleC22×C47C22×D4
hypercenter#544D47
hypocenterC47#3082
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
2. #15689427C2semidirect
3. #15689427C2semidirect
4. #15689415C2semidirect
5. #15689405C2semidirect
47. C2×Dic94Q8semidirect
128. C47#3082semidirect