Finite Group Databasebeta

← #20248365

Subgroups — #20248365

Order 6016.

576 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13094013C211yesmaximal, characteristic
2C2×#13094013C211yesmaximal, characteristic
3C2×Q8×Dic47C211yesmaximal, characteristic, complemented
4#15689045C214yesmaximal, complemented
5#15689030C211yesmaximal, characteristic, complemented
6#15689025C211yesmaximal, characteristic
7#15689013C214yesmaximal, complemented
8C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11#13094013—24no—
12#13094013—24no—
13Q8×Dic47—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2214yes—
19C2×(C2×D47)⋊C4C2214yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×C4×Dic47C2211yescharacteristic
22C2×C4×Dic47C2212yes—
23C2×C4×Dic47C2211yescharacteristic
24C47⋊#95C2212yes—
25C47⋊#95C2214yes—
26C22×Q8×C47C2211yescharacteristic
27C22×Q8×C47C2211yescharacteristic
28C4⋊Q8×C47—24no—
29C2×C4⋊C4×C47C2214yes—
30C2×C42×C47C2211yescharacteristic
31C23×D47C2312yes—
32C2×Q8×C47—22no—
33C2×Q8×C47—22no—
34C2×Q8×C47—22no—
35C2×Q8×C47—22no—
36C2×Q8×C47—22no—
37C2×Q8×C47D414yes—
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2311yescharacteristic
46C2×D188—22no—
47C2×D188—22no—
48C2×D188—22no—
49C4⋊C4×C47—28no—
50C42×C47—22no—
51(C2×D47)⋊C4—28no—
52(C2×D47)⋊C4—28no—
53(C2×D47)⋊C4—24no—
54(C2×D47)⋊C4—24no—
55C4⋊Dic47—22no—
56C4⋊Dic47—24no—
57Dic47⋊C4—24no—
58C4×Dic47—22no—
59C4×Dic47—24no—
60C4×Dic47D414yes—
61C23×C47C2411yescharacteristic
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—24no—
65C22×D47—22no—
66C22×D47—24no—
67Q8×C47—28no—
68Q8×C47—44no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2×D414yes—
78C2×C4×C47C2×D412yes—
79C2×C4×C47#4112yes—
80C2×C4×C47#4114yes—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—24no—
87C2×Dic47—22no—
88C2×Dic47C2×D412yes—
89C2×Dic47C2×D412yes—
90D188—44no—
91C22×C47C22×D411yescharacteristic
92C22×C47C22×D411yescharacteristic
93C22×C47C2×#4111yescharacteristic
94C22×C47C2×#4112yes—
95C22×C472−1+412yes—
96C2×D47—42no—
97C2×D47—42no—
98C2×D47—42no—
99C2×D47—44no—
100C2×D47—44no—
101C4×C47—24no—
102C4×C47—24no—
103C4×C47—42no—
104C4×C47#12114yes—
105Dic47—22no—
106Dic47—22no—
107Dic47—42no—
108Dic47—42no—
109#2545—471nomaximal, Sylow
110C2×C47C2×#12111yescharacteristic
111C2×C47#53211yescharacteristic
112C2×C47#53611yescharacteristic
113C2×C47#54812yes—
114C2×C47#55612yes—
115D47—82no—
116C2×C4⋊Q8D4711yescharacteristic, complemented
117C2×#124—471no—
118C2×#124—471no—
119C2×C4×Q8—471no—
120#396—474no—
121#391—471no—
122#390—471no—
123#388—474no—
124C4×C4⋊C4—471no—
125C47#254511yescharacteristic, complemented, Sylow
126C22×Q8C2×D4711yescharacteristic
127C22×Q8C2×D4711yescharacteristic
128C22×D4—471no—
129C4⋊Q8—24no—
130#124—944no—
131#124—944no—
132C4×Q8—944no—
133C2×C4⋊C4—471no—
134C2×C4⋊C4—472no—
135C2×C4⋊C4—472no—
136C2×C4⋊C4C2×D4714yes—
137C2×C22⋊C4—472no—
138C2×C22⋊C4—474no—
139C2×C22⋊C4—472no—
140C2×C22⋊C4—474no—
141C2×C42—471no—
142C2×C42—472no—
143C2×C42—471no—
144C2×C42C2×D4711yescharacteristic
145#95—472no—
146#95—474no—
147C24—472no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8C22⋊D4714yes—
154C2×D4—942no—
155C2×D4—942no—
156C2×D4—942no—
157C22×C4—471no—
158C22×C4—471no—
159C22×C4—472no—
160C22×C4—472no—
161C22×C4C22×D4712yes—
162C22×C4C22×D4712yes—
163C22×C4C22×D4712yes—
164C22×C4C22×D4711yescharacteristic
165C4⋊C4—28no—
166C4⋊C4—944no—
167C4⋊C4—942no—
168C4⋊C4—944no—
169C22⋊C4—944no—
170C22⋊C4—944no—
171C22⋊C4—948no—
172C22⋊C4—948no—
173C42—22no—
174C42—474no—
175C42—944no—
176C42—942no—
177C23—942no—
178C23—942no—
179C23—942no—
180C23—944no—
181C23—944no—
182C23C23×D4711yescharacteristic
183Q8—28no—
184Q8—44no—
185D4—1884no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—472no—
194C2×C4—472no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—944no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4D4×D4712yes—
203C2×C4#1062535212yes—
204C2×C4#1062535414yes—
205C2×C4C2×C22⋊D4714yes—
206C2×C4C2×C22⋊D4712yes—
207C22—1884no—
208C22—1884no—
209C22—1882no—
210C22—1882no—
211C22—1882no—
212C22C2×D4×D4711yescharacteristic
213C22C22×C22⋊D4711yescharacteristic
214C22C2×#1062535211yescharacteristic
215C22C2×#1062535412yes—
216C22#1309407212yes—
217C4—24no—
218C4—24no—
219C4—42no—
220C4—942no—
221C4—942no—
222C4—1882no—
223C4—1882no—
224C4#1309399614yes—
225C2—3762no—
226C2C2×#1309399611yescharacteristic
227C2#1568967411yescharacteristic
228C2#1568969811yescharacteristic
229C2#1568978412yes—
230C2#1568984712yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4⋊Q8×C47C2
hypercenterC2×C4⋊Q8D47
hypocenterC47#2545
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×Q8×Dic47C2semidirect
4. #15689045C2semidirect
5. #15689030C2semidirect
7. #15689013C2semidirect
8. C4×Dic47⋊C4C2semidirect
9. C2×C4⋊Q8×C47C2semidirect
116. C2×C4⋊Q8D47semidirect
125. C47#2545semidirect