Finite Group Databasebeta

← #20255752

Subgroups — #20255752

Order 6016.

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

normal subgroups only

This group has 342 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#15689808C212yesmaximal
2#15689524C211yesmaximal, characteristic, complemented
3#15689466C212yesmaximal, complemented
4#15689453C212yesmaximal, complemented
5#15689429C212yesmaximal, complemented
6#15689365C211yesmaximal, characteristic, complemented
7#15689364C211yesmaximal, characteristic, complemented
8#15689217C211yesmaximal, characteristic, complemented
9C8×C22⋊D47C211yesmaximal, characteristic
10#15689160C211yesmaximal, characteristic, complemented
11C2×#107×C47C211yesmaximal, characteristic, complemented
12C2×Dic188C2211yescharacteristic
13C2×C8×D47C2211yescharacteristic
14#13094019—22no—
15#13094015C2212yes—
16#13094014—22no—
17#13094007—22no—
18#13094004C2212yes—
19#13094003C2212yes—
20#13093989C2212yes—
21C4×C22⋊D47C2211yescharacteristic
22#13093983—22no—
23#13093982C2212yes—
24#13093958C2211yescharacteristic
25#13093955C2212yes—
26#13093955C2212yes—
27Dic47⋊C8C2211yescharacteristic
28#13093949C2212yes—
29#13093947C2212yes—
30#13093947C2212yes—
31C22⋊(C47⋊C8)C2211yescharacteristic
32(C2×D47)⋊C8C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C22×C8×C47C2211yescharacteristic
35C2×C4⋊C4×C47C2212yes—
36#107×C47C2211yescharacteristic
37#107×C47C2211yescharacteristic
38#107×C47C2212yes—
39C22×C4×C47—22no—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47D411yescharacteristic
42C2×C4×D47C2311yescharacteristic
43C2×Dic94C2312yes—
44C2×C8×C47—22no—
45C2×C8×C47C2311yescharacteristic
46C2×C8×C47C2311yescharacteristic
47C4⋊C4×C47—22no—
48C4⋊C4×C47C2312yes—
49C4⋊C4×C47C2312yes—
50C22⋊Dic47—22no—
51C22⋊Dic47D411yescharacteristic
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4D411yescharacteristic
55C4⋊Dic47—22no—
56C4⋊Dic47—22no—
57C4⋊Dic47C2312yes—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4D411yescharacteristic
62C4×Dic47—22no—
63C4×Dic47—22no—
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66C2×C47⋊C8C2311yescharacteristic
67Dic188—22no—
68C8×D47—22no—
69C23×C47C2×D411yescharacteristic
70C22×D47C2×D411yescharacteristic
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—44no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47C2×D411yescharacteristic
82C2×Dic47C2×D411yescharacteristic
83C2×Dic47C2×D411yescharacteristic
84C4×D47—21no—
85C4×D47—21no—
86Dic94—22no—
87Dic94—22no—
88C8×C47—21no—
89C8×C47#4112yes—
90C47⋊C8—21no—
91C47⋊C8—21no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47#13512yes—
95C22×C47C22×D411yescharacteristic
96C2×D47—21no—
97C2×D47—21no—
98C2×D47—21no—
99C4×C47—21no—
100C4×C47—42no—
101C4×C47—42no—
102C4×C47C2×#4111yescharacteristic
103C4×C472−1+411yescharacteristic
104Dic47—21no—
105Dic47—21no—
106Dic47—21no—
107Dic47—42no—
108Dic47—42no—
109#3336—471nomaximal, Sylow
110C2×C47—22no—
111C2×C47#54711yescharacteristic
112C2×C47C2×#13511yescharacteristic
113C2×C47#57811yescharacteristic
114D47—41no—
115#552—472no—
116#499—471no—
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×#107D4711yescharacteristic, complemented
126C47#333611yescharacteristic, complemented, Sylow
127C2×Q16—471no—
128C22×C8—471no—
129C22×C8C2×D4711yescharacteristic
130#126—942no—
131#125—472no—
132#125—942no—
133#123—942no—
134C22⋊Q8—472no—
135C22⋊Q8—472no—
136C4×Q8—472no—
137C4×D4—471no—
138#117—472no—
139#117—942no—
140C2×C4⋊C4C2×D4712yes—
141#107—471no—
142#107C2×D4711yescharacteristic
143#107C2×D4711yescharacteristic
144#107C2×D4712yes—
145#106—472no—
146#106—472no—
147C4⋊C8—471no—
148#103—472no—
149#103—472no—
150#103—472no—
151C22⋊C8—471no—
152C22⋊C8—471no—
153C4×C8—471no—
154C2×Q8—472no—
155C2×D4—471no—
156C22×C4—22no—
157C22×C4—471no—
158C22×C4C22×D4711yescharacteristic
159Q16—942no—
160C2×C8—22no—
161C2×C8—471no—
162C2×C8—471no—
163C2×C8—942no—
164C2×C8C22×D4711yescharacteristic
165C2×C8C22×D4711yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—471no—
168C4⋊C4—472no—
169C4⋊C4—942no—
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—471no—
182C42—942no—
183C42—942no—
184C23—471no—
185C23D4×D4711yescharacteristic
186Q8—942no—
187Q8—942no—
188D4—942no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—44no—
194C2×C4—471no—
195C2×C4—471no—
196C2×C4—471no—
197C2×C4—941no—
198C2×C4—941no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4D4×D4711yescharacteristic
202C2×C4C23×D4711yescharacteristic
203C8—21no—
204C8—941no—
205C8—941no—
206C8#1062535012yes—
207C22—21no—
208C22—21no—
209C22—941no—
210C22—941no—
211C22—941no—
212C22#1309404312yes—
213C22C2×D4×D4711yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—941no—
218C4—941no—
219C4—941no—
220C4—1882no—
221C4—1882no—
222C4C2×#1062535011yescharacteristic
223C4#1309407211yescharacteristic
224C2—22no—
225C2—1881no—
226C2#1568977411yescharacteristic
227C2C2×#1309404311yescharacteristic
228C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#107×C47C2
socleC22×C47C22×D4
hypercenterC2×#107D47
hypocenterC47#3336
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #15689524C2semidirect
3. #15689466C2semidirect
4. #15689453C2semidirect
5. #15689429C2semidirect
6. #15689365C2semidirect
7. #15689364C2semidirect
8. #15689217C2semidirect
10. #15689160C2semidirect
11. C2×#107×C47C2semidirect
125. C2×#107D47semidirect
126. C47#3336semidirect