Finite Group Databasebeta

← #21455343

Subgroups — #21455343

Order 7808.

490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519807C211yesmaximal, characteristic, complemented
2C22×#11758190C211yesmaximal, characteristic, complemented
3#16840326C211yesmaximal, characteristic
4#16840239C211yesmaximal, characteristic, complemented
5#16839987C214yesmaximal, complemented
6#16839961C214yesmaximal, complemented
7#16839788C211yesmaximal, characteristic, complemented
8#16839766C211yesmaximal, characteristic, complemented
9C61×#416C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12#14519807—24no—
13C2×#11758202C2212yescomplemented
14C2×#11758190—24no—
15C2×#11758190C2214yes—
16C2×#11758200C2212yescomplemented
17C2×#11758194C2211yescharacteristic
18#14519773C2212yes—
19#14519766C2212yes—
20#14519751—22no—
21#14519745—22no—
22C4×Dic122—22no—
23#14519742C2214yescomplemented
24#14519736C2211yescharacteristic
25#14519733—22no—
26#14519706C2214yescomplemented
27#14519697C2214yes—
28C2×#41×C61C2211yescharacteristic
29C22×C8×C61C2211yescharacteristic
30#117×C61C2211yescharacteristic
31#103×C61C2212yescomplemented
32#102×C61C2212yescomplemented
33C23×D61—21no—
34#41×C61—22no—
35#41×C61—22no—
36C2×Q8×C61C2311yescharacteristic
37C2×D4×C61—21no—
38C2×D4×C61C2311yescharacteristic
39C22×C4×C61—21no—
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61—24no—
42C22×Dic61—21no—
43C2×D244—22no—
44C2×D244—22no—
45C2×D244—21no—
46C2×D244C2312yes—
47C2×Dic122—21no—
48C2×Dic122—22no—
49C2×Dic122D414yescomplemented
50C2×Dic122C2312yes—
51C2×C8×C61—22no—
52C2×C8×C61C2312yes—
53C4⋊C4×C61C2312yes—
54C22⋊C4×C61—21no—
55C42×C61—21no—
56C22⋊Dic61D412yes—
57#11758202—24no—
58#11758200—24no—
59#11758198—24no—
60C4⋊Dic61D412yes—
61#11758196—24no—
62C4×Dic61—24no—
63C4×Dic61C2312yes—
64#11758194—22no—
65C2×#92418C2312yes—
66#11758190—28no—
67C23×C61—21no—
68C23×C61C2×D411yescharacteristic
69C22×D61—22no—
70C22×D61—42no—
71C22×D61—82no—
72Q8×C61—21no—
73Q8×C61—21no—
74D4×C61—21no—
75D4×C61—21no—
76D4×C61—42no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—42no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D412yes—
82C2×C4×C61#4112yes—
83C2×C4×C61C2411yescharacteristic
84C22⋊D61—84no—
85C2×Dic61—24no—
86C2×Dic61—22no—
87C2×Dic61C2×D414yes—
88D244—22no—
89D244—22no—
90D244—42no—
91Dic122—24no—
92Dic122—22no—
93Dic122C2×D414yes—
94C8×C61—22no—
95#92418—22no—
96C22×C61—22no—
97C22×C61—41no—
98C22×C61—42no—
99C22×C61#12112yes—
100C22×C61C22×D411yescharacteristic
101C2×D61—42no—
102C2×D61—44no—
103C2×D61—84no—
104C4×C61—41no—
105C4×C61—42no—
106C4×C61#12112yes—
107C4×C61C22×D411yescharacteristic
108C4×C61C2×#4111yescharacteristic
109Dic61—24no—
110Dic61—24no—
111#3043—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61—81no—
114C2×C61C2×#12111yescharacteristic
115C2×C61#57712yes—
116D61—82no—
117C2×#137—611no—
118C22×SD16—611no—
119#535—611no—
120#519—611no—
121#464—614no—
122#460—614no—
123#424—611no—
124#418—611no—
125#416D6111yescharacteristic, complemented
126C61#304311yescharacteristic, complemented, Sylow
127C2×#41C2×D6111yescharacteristic
128C22×Q8—611no—
129C22×D4—611no—
130#137—1224no—
131C2×Q16—612no—
132C2×SD16—612no—
133C2×SD16—614no—
134C2×SD16—1224no—
135C2×M16—611no—
136C22×C8C2×D6111yescharacteristic
137#127—612no—
138#124—612no—
139#121—1222no—
140#120—1222no—
141C4×Q8—614no—
142C4×Q8—1222no—
143#117—611no—
144#117—1222no—
145#117C2×D6111yescharacteristic
146C4⋊C8—614no—
147#103C2×D6112yescomplemented
148#102—614no—
149#102C2×D6112yescomplemented
150C24—1221no—
151#41—22no—
152#41—22no—
153C2×Q8—614no—
154C2×Q8—612no—
155C2×Q8—1222no—
156C2×Q8—1221no—
157C2×Q8C22×D6111yescharacteristic
158C2×D4—21no—
159C2×D4—612no—
160C2×D4—1224no—
161C2×D4—1222no—
162C2×D4—1222no—
163C2×D4—1221no—
164C2×D4C22×D6111yescharacteristic
165C22×C4—21no—
166C22×C4—1221no—
167C22×C4C22×D6111yescharacteristic
168Q16—1224no—
169SD16—1228no—
170SD16—1224no—
171M16—1222no—
172C2×C8—22no—
173C2×C8—612no—
174C2×C8C22×D6112yes—
175C4⋊C4—612no—
176C4⋊C4—1224no—
177C4⋊C4C22×D6112yes—
178C22⋊C4—21no—
179C22⋊C4—612no—
180C22⋊C4—1224no—
181C42—21no—
182C42—612no—
183C42—1224no—
184C23—21no—
185C23—1222no—
186C23—4882no—
187C23—2442no—
188C23D4×D6111yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—614no—
192Q8—1222no—
193Q8—1224no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—1222no—
198D4—1222no—
199D4—4884no—
200D4—2442no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—614no—
205C2×C4—1222no—
206C2×C4—1224no—
207C2×C4#1175822212yes—
208C2×C4D4×D6112yes—
209C2×C4D4×D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—1222no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—4884no—
217C22—2442no—
218C22—2444no—
219C22#1451975012yes—
220C22C2×D4×D6111yescharacteristic
221C4—41no—
222C4—42no—
223C4—1224no—
224C4—1224no—
225C4#1451975012yes—
226C4C2×D4×D6111yescharacteristic
227C4C2×#1175822211yescharacteristic
228C2—22no—
229C2—81no—
230C2—4882no—
231C2C2×#1451975011yescharacteristic
232C2#1684056912yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#416C2
socleC22×C61C22×D4
hypercenter#416D61
hypocenterC61#3043
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#14519807C2semidirect
2. C22×#11758190C2semidirect
4. #16840239C2semidirect
5. #16839987C2semidirect
6. #16839961C2semidirect
7. #16839788C2semidirect
8. #16839766C2semidirect
9. C61×#416C2semidirect
13. C2×#11758202C22semidirect
16. C2×#11758200C22semidirect
23. #14519742C22semidirect
26. #14519706C22semidirect
31. #103×C61C22semidirect
32. #102×C61C22semidirect
49. C2×Dic122D4semidirect
125. #416D61semidirect
126. C61#3043semidirect
147. #103C2×D61semidirect
149. #102C2×D61semidirect