Finite Group Databasebeta

← #20255755

Subgroups — #20255755

Order 6016.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689811C212yesmaximal
2#15689467C212yesmaximal, complemented
3#15689455C212yesmaximal, complemented
4#15689427C212yesmaximal, complemented
5#15689365C211yesmaximal, characteristic, complemented
6#15689365C211yesmaximal, characteristic, complemented
7C4×Dic188C211yesmaximal, characteristic, complemented
8C8×D188C211yesmaximal, characteristic
9#15689160C211yesmaximal, characteristic, complemented
10#107×D47C211yesmaximal, characteristic, complemented
11C47×#499C211yesmaximal, characteristic, complemented
12C2×Dic188C2211yescharacteristic
13C2×C8×D47C2211yescharacteristic
14C2×C8×D47C2211yescharacteristic
15#13094019—22no—
16#13094015—22no—
17#13094009—22no—
18#13094004C2212yes—
19#13094004C2212yes—
20C4×Dic94C2212yes—
21C4×D188C2211yescharacteristic
22#13093982—22no—
23#13093982C2212yes—
24C4⋊C4×D47C2212yes—
25#13093958C2211yescharacteristic
26#13093957C2212yes—
27#13093955C2212yes—
28C4⋊(C47⋊C8)C2211yescharacteristic
29#13093949C2212yes—
30#13093947C2212yes—
31#13093947C2212yes—
32(C2×D47)⋊C8C2211yescharacteristic
33(C2×D47)⋊C8C2211yescharacteristic
34#125×C47C2212yes—
35#107×C47C2211yescharacteristic
36#107×C47C2211yescharacteristic
37#106×C47C2212yes—
38C4×C8×C47C2211yescharacteristic
39C2×D188D411yescharacteristic
40C2×C4×D47—22no—
41C2×C4×D47C2311yescharacteristic
42C2×C4×D47C2311yescharacteristic
43C2×Dic94C2312yes—
44C2×C8×C47C2311yescharacteristic
45C2×C8×C47C2311yescharacteristic
46C4⋊C4×C47—22no—
47C4⋊C4×C47—22no—
48C4⋊C4×C47C2312yes—
49C4⋊C4×C47C2312yes—
50C42×C47C2311yescharacteristic
51(C2×D47)⋊C4—22no—
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4D411yescharacteristic
55(C2×D47)⋊C4D411yescharacteristic
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47D411yescharacteristic
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C4×Dic47—22no—
64C2×C47⋊C8C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66Dic188—22no—
67C8×D47—22no—
68C8×D47—22no—
69C22×D47C2×D411yescharacteristic
70C22×D47C2×D411yescharacteristic
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2411yescharacteristic
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47C2×D411yescharacteristic
79C2×Dic47C2×D411yescharacteristic
80D188—22no—
81C4×D47—21no—
82C4×D47—21no—
83C4×D47—21no—
84C4×D47—21no—
85C4×D47—44no—
86Dic94—22no—
87Dic94—22no—
88C8×C47—21no—
89C8×C47#4112yes—
90C47⋊C8—21no—
91C47⋊C8—21no—
92C22×C47C22×D411yescharacteristic
93C2×D47—21no—
94C2×D47—21no—
95C2×D47—21no—
96C2×D47—21no—
97C2×D47—21no—
98C2×D47#13512yes—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—42no—
102C4×C47—42no—
103C4×C47C2×#4111yescharacteristic
104C4×C472−1+411yescharacteristic
105Dic47—21no—
106Dic47—21no—
107Dic47—42no—
108Dic47—42no—
109#3336—471nomaximal, Sylow
110C2×C47#54711yescharacteristic
111C2×C47C2×#13511yescharacteristic
112C2×C47#57811yescharacteristic
113D47—22no—
114D47—41no—
115#552—472no—
116#499D4711yescharacteristic, complemented
117#485—472no—
118#483—472no—
119#479—472no—
120#467—471no—
121#467—471no—
122C4×Q16—471no—
123C8×D4—471no—
124#427—471no—
125C2×#107—471no—
126C47#333611yescharacteristic, complemented, Sylow
127C2×Q16—471no—
128C22×C8—471no—
129C22×C8—471no—
130#126—942no—
131#125—942no—
132#125C2×D4712yes—
133#123—942no—
134C22⋊Q8—472no—
135C22⋊Q8—472no—
136C4×Q8—472no—
137C4×D4—471no—
138#117—472no—
139#117—942no—
140C2×C4⋊C4—472no—
141#107—471no—
142#107—472no—
143#107C2×D4711yescharacteristic
144#107C2×D4711yescharacteristic
145#106—472no—
146#106C2×D4712yes—
147C4⋊C8—471no—
148#103—472no—
149#103—472no—
150#103—472no—
151C22⋊C8—471no—
152C22⋊C8—471no—
153C4×C8C2×D4711yescharacteristic
154C2×Q8—472no—
155C2×D4—471no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—942no—
159Q16—942no—
160C2×C8—471no—
161C2×C8—471no—
162C2×C8—942no—
163C2×C8—942no—
164C2×C8C22×D4711yescharacteristic
165C2×C8C22×D4711yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—471no—
169C4⋊C4—472no—
170C4⋊C4—942no—
171C4⋊C4—942no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4C22×D4712yes—
175C4⋊C4C22×D4712yes—
176C22⋊C4—471no—
177C22⋊C4—471no—
178C22⋊C4—942no—
179C22⋊C4—942no—
180C22⋊C4—942no—
181C42—942no—
182C42—942no—
183C42C22×D4711yescharacteristic
184C23—471no—
185C23—471no—
186Q8—942no—
187Q8—942no—
188D4—942no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—471no—
192C2×C4—471no—
193C2×C4—941no—
194C2×C4—941no—
195C2×C4—941no—
196C2×C4—941no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—1884no—
200C2×C4D4×D4711yescharacteristic
201C2×C4D4×D4711yescharacteristic
202C2×C4C23×D4711yescharacteristic
203C8—21no—
204C8—941no—
205C8—941no—
206C8#1062535412yes—
207C22—472no—
208C22—941no—
209C22—941no—
210C22—941no—
211C22—941no—
212C22—941no—
213C22C2×D4×D4711yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—42no—
218C4—941no—
219C4—941no—
220C4—1882no—
221C4—1882no—
222C4C2×#1062535411yescharacteristic
223C4#1309407211yescharacteristic
224C2—942no—
225C2—1881no—
226C2#1568977611yescharacteristic
227C2#135×D4711yescharacteristic
228C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#499C2
socleC22×C47C22×D4
hypercenter#499D47
hypocenterC47#3336
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
2. #15689467C2semidirect
3. #15689455C2semidirect
4. #15689427C2semidirect
5. #15689365C2semidirect
6. #15689365C2semidirect
7. C4×Dic188C2semidirect
9. #15689160C2semidirect
10. #107×D47C2semidirect
11. C47×#499C2semidirect
116. #499D47semidirect
126. C47#3336semidirect