Finite Group Databasebeta

← #21455328

Subgroups — #21455328

Order 7808.

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

normal subgroups only

This group has 494 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
1C2×#14519803C211yesmaximal, characteristic
2#16840336C211yesmaximal, characteristic, complemented
3#16840237C211yesmaximal, characteristic, complemented
4#16839979C214yesmaximal, complemented
5#16839965C214yesmaximal, complemented
6#16839788C211yesmaximal, characteristic, complemented
7#16839771C211yesmaximal, characteristic, complemented
8#16839759C211yesmaximal, characteristic, complemented
9C22×SD16×C61C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11#14519803—24no—
12C2×#11758200C2212yes—
13C2×#11758199C2212yes—
14C2×#11758194C2211yescharacteristic
15#14519775C2212yescomplemented
16#14519766C2212yescomplemented
17#14519760—22no—
18#14519753—22no—
19D4×Dic61—22no—
20D4×Dic61C2214yes—
21#14519736C2211yescharacteristic
22#14519736C2211yescharacteristic
23C2×C22⋊Dic61—22no—
24#14519706C2214yescomplemented
25#14519702C2212yescomplemented
26#14519701C2214yescomplemented
27#14519699C2212yescomplemented
28C22×Q8×C61C2211yescharacteristic
29C22×D4×C61C2211yescharacteristic
30C2×SD16×C61—24no—
31C2×SD16×C61C2214yes—
32C22×C8×C61C2211yescharacteristic
33C24×C61—21no—
34C2×Q8×C61—21no—
35C2×Q8×C61—22no—
36C2×Q8×C61—22no—
37C2×Q8×C61C2312yes—
38C2×D4×C61—21no—
39C2×D4×C61—22no—
40C2×D4×C61D414yes—
41C2×D4×C61C2312yes—
42C22×C4×C61—21no—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—21no—
45C22×Dic61—24no—
46#11758222—22no—
47#11758222—22no—
48C2×D244C2311yescharacteristic
49C2×C4×D61—21no—
50C2×Dic122C2311yescharacteristic
51SD16×C61—28no—
52C2×C8×C61—22no—
53C2×C8×C61C2312yes—
54C22⋊Dic61—21no—
55C22⋊Dic61—24no—
56C22⋊Dic61D412yes—
57#11758200—24no—
58#11758199—24no—
59#11758198—24no—
60C4⋊Dic61D412yes—
61C4⋊Dic61C2312yes—
62#11758196—24no—
63C4×Dic61—21no—
64C4×Dic61C2312yes—
65#11758194—22no—
66C2×#92418C2312yes—
67C23×C61—22no—
68C23×C61—24no—
69C23×C61—82no—
70C23×C61C2×D411yescharacteristic
71C22×D61—21no—
72Q8×C61—22no—
73Q8×C61—22no—
74Q8×C61—42no—
75D4×C61—24no—
76D4×C61—22no—
77D4×C61C2×D414yes—
78C2×C4×C61—22no—
79C2×C4×C61—42no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D412yes—
82C2×C4×C61#4112yes—
83C2×C4×C61C2411yescharacteristic
84C22⋊D61—42no—
85C2×Dic61—22no—
86C2×Dic61—21no—
87C2×Dic61—84no—
88C2×Dic61C2×D414yes—
89D244—21no—
90D244—21no—
91C4×D61—42no—
92Dic122—21no—
93Dic122—21no—
94C8×C61—22no—
95#92418—22no—
96C22×C61—22no—
97C22×C61—24no—
98C22×C61—44no—
99C22×C61—84no—
100C22×C61#12112yes—
101C22×C61C22×D411yescharacteristic
102C2×D61—41no—
103C2×D61—42no—
104C4×C61—42no—
105C4×C61#12112yes—
106C4×C61C22×D411yescharacteristic
107C4×C61C2×#4111yescharacteristic
108Dic61—24no—
109Dic61—41no—
110Dic61—42no—
111#3042—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61—44no—
114C2×C61C2×#12111yescharacteristic
115C2×C61#57712yes—
116D61—81no—
117C2×AGL(1,ℤ/8)—611no—
118C22×SD16D6111yescharacteristic, complemented
119#536—611no—
120#518—611no—
121#463—614no—
122#461—614no—
123#424—611no—
124#419—611no—
125#416—611no—
126C61#304211yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C22×Q8C2×D6111yescharacteristic
129C22×D4C2×D6111yescharacteristic
130AGL(1,ℤ/8)—1224no—
131C2×SD16—24no—
132C2×SD16—612no—
133C2×SD16C2×D6114yes—
134C2×D8—612no—
135C2×M16—611no—
136C22×C8C2×D6111yescharacteristic
137C4⋊Q8—612no—
138#124—612no—
139#123—1222no—
140C22⋊Q8—1222no—
141C4×D4—614no—
142C4×D4—1222no—
143#117—611no—
144#117—611no—
145C2×C22⋊C4—1222no—
146C4⋊C8—614no—
147#103—614no—
148#103—612no—
149#102—612no—
150C24—21no—
151#41—1222no—
152#41—1222no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—611no—
157C2×Q8C22×D6112yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—611no—
161C2×D4—1221no—
162C2×D4C22⋊D6114yes—
163C2×D4C22×D6112yes—
164C22×C4—21no—
165C22×C4—1224no—
166C22×C4—1221no—
167C22×C4C22×D6111yescharacteristic
168SD16—28no—
169SD16—1224no—
170D8—1224no—
171M16—1222no—
172C2×C8—22no—
173C2×C8—612no—
174C2×C8C22×D6112yes—
175C4⋊C4—612no—
176C4⋊C4—612no—
177C4⋊C4—1224no—
178C22⋊C4—612no—
179C22⋊C4—1224no—
180C22⋊C4—1224no—
181C22⋊C4—1221no—
182C42—612no—
183C42—1221no—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—1221no—
188C23D4×D6111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—1221no—
193Q8—1221no—
194D4—22no—
195D4—24no—
196D4—1221no—
197D4—1221no—
198D4—2442no—
199D4C2×C22⋊D6114yes—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—614no—
203C2×C4—1222no—
204C2×C4—1221no—
205C2×C4—4884no—
206C2×C4—2442no—
207C2×C4D4×D6111yescharacteristic
208C2×C4#1175822412yes—
209C2×C4C2×C22⋊D6112yes—
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—1222no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—2441no—
218C22—2442no—
219C22#1451974912yes—
220C22C2×D4×D6111yescharacteristic
221C4—42no—
222C4—1224no—
223C4—2441no—
224C4—2442no—
225C4#1451974912yes—
226C4C22×C22⋊D6111yescharacteristic
227C4C2×#1175822411yescharacteristic
228C2—22no—
229C2—44no—
230C2—4881no—
231C2C2×#1451974911yescharacteristic
232C2#1684056812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC22×SD16×C61C2
socleC22×C61C22×D4
hypercenterC22×SD16D61
hypocenterC61#3042
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. #16840336C2semidirect
3. #16840237C2semidirect
4. #16839979C2semidirect
5. #16839965C2semidirect
6. #16839788C2semidirect
7. #16839771C2semidirect
8. #16839759C2semidirect
9. C22×SD16×C61C2semidirect
15. #14519775C22semidirect
16. #14519766C22semidirect
24. #14519706C22semidirect
25. #14519702C22semidirect
26. #14519701C22semidirect
27. #14519699C22semidirect
118. C22×SD16D61semidirect
126. C61#3042semidirect