Finite Group Databasebeta

← #20248599

Subgroups — #20248599

Order 6016.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#13094023C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic
3#15689063C211yesmaximal, characteristic
4#15689062C211yesmaximal, characteristic
5#15689061C211yesmaximal, characteristic
6#15689027C212yesmaximal
7#15689027C212yesmaximal
8#15689027C212yesmaximal
9#15688987C212yesmaximal
10#15688974C211yesmaximal, characteristic
11C47×#400C211yesmaximal, characteristic
12C22×Dic94C2212yes—
13C22×Dic94C2211yescharacteristic
14#13094023—24no—
15#13093989—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×C4×Dic47C2212yes—
22C2×C4×Dic47C2211yescharacteristic
23C2×C4×Dic47C2211yescharacteristic
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34#95×C47C2211yescharacteristic
35#95×C47C2212yes—
36#95×C47C2212yes—
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×Dic47C2312yes—
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2312yes—
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C2×Dic94—22no—
49C2×Dic94—22no—
50C2×Dic94—24no—
51C2×Dic94—28no—
52C2×Dic94Q814yescomplemented
53C4⋊C4×C47—22no—
54C4⋊C4×C47—22no—
55C4⋊Dic47—22no—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—24no—
59Dic47⋊C4—24no—
60C4×Dic47—22no—
61C4×Dic47—22no—
62C4×Dic47—24no—
63C4×Dic47D414yes—
64C23×C47C2411yescharacteristic
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—24no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×Q812yes—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—24no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47C2×D412yes—
87C2×Dic47C2×D412yes—
88C2×Dic47C2×Q812yes—
89C2×Dic47C2×Q812yes—
90C2×Dic47#4112yes—
91C2×Dic47#4114yes—
92Dic94—28no—
93Dic94—48no—
94C22×C47C22×D411yescharacteristic
95C22×C47C22×Q811yescharacteristic
96C22×C47C2×#4111yescharacteristic
97C22×C47C2×#4112yes—
98C22×C472−1+412yes—
99C4×C47—22no—
100C4×C47—22no—
101C4×C47—42no—
102C4×C47—41no—
103C4×C47—42no—
104Dic47—22no—
105Dic47—42no—
106Dic47—41no—
107Dic47—42no—
108Dic47C22⋊Q814yes—
109Dic47#12414yes—
110#2568—471nomaximal, Sylow
111C2×C47C2×C22⋊Q811yescharacteristic
112C2×C47C2×#12411yescharacteristic
113C2×C47#53611yescharacteristic
114C2×C47#55612yes—
115C2×C47#55712yes—
116C2×C4⋊Q8—471no—
117C2×C4×Q8—471no—
118#400—471no—
119#400—471no—
120#400—471no—
121#400D4711yescharacteristic
122#391—472no—
123#391—472no—
124#391—472no—
125#382—472no—
126C4×C4⋊C4—471no—
127C47#256811yescharacteristic, complemented, Sylow
128C22×Q8—471no—
129C22×Q8—472no—
130C4⋊Q8—944no—
131C4×Q8—944no—
132C2×C4⋊C4—471no—
133C2×C4⋊C4—471no—
134C2×C4⋊C4—472no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4—472no—
137C2×C4⋊C4C2×D4711yescharacteristic
138C2×C4⋊C4C2×D4711yescharacteristic
139C2×C42—471no—
140C2×C42—471no—
141C2×C42—471no—
142C2×C42—472no—
143#95—471no—
144#95—472no—
145#95—472no—
146#95—472no—
147#95—472no—
148#95—472no—
149#95—472no—
150#95C2×D4711yescharacteristic
151#95C2×D4712yes—
152#95C2×D4712yes—
153C2×Q8—474no—
154C2×Q8—942no—
155C2×Q8—942no—
156C2×Q8—944no—
157C2×Q8—948no—
158C22×C4—471no—
159C22×C4—471no—
160C22×C4—471no—
161C22×C4—472no—
162C22×C4—471no—
163C22×C4—472no—
164C22×C4C22×D4712yes—
165C22×C4C22×D4711yescharacteristic
166C22×C4C22×D4712yes—
167C22×C4C22×D4711yescharacteristic
168C22×C4C22×D4711yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—944no—
172C4⋊C4—942no—
173C4⋊C4—944no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C42—474no—
177C42—944no—
178C42—942no—
179C42—942no—
180C23C23×D4711yescharacteristic
181Q8—948no—
182Q8—1888no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—472no—
194C2×C4—472no—
195C2×C4—472no—
196C2×C4—472no—
197C2×C4—474no—
198C2×C4—472no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—944no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4D4×D4712yes—
209C2×C4Q8×D4712yes—
210C22C2×D4×D4711yescharacteristic
211C22C2×Q8×D4711yescharacteristic
212C22#41×D4711yescharacteristic
213C22#41×D4712yes—
214C22#1309407112yes—
215C4—22no—
216C4—22no—
217C4—42no—
218C4—42no—
219C4—41no—
220C4—474no—
221C4—474no—
222C4—942no—
223C4—1882no—
224C4—1882no—
225C4—1881no—
226C2C22⋊Q8×D4711yescharacteristic
227C2#124×D4711yescharacteristic
228C2#1568969511yescharacteristic
229C2#1568984012yes—
230C2#1568985012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2568
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
52. C2×Dic94Q8semidirect
127. C47#2568semidirect