Finite Group Databasebeta

← #21455330

Subgroups — #21455330

Order 7808.

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

normal subgroups only

This group has 494 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×#14519805C211yesmaximal, characteristic
2C22×#11758201C211yesmaximal, characteristic, complemented
3#16840336C211yesmaximal, characteristic, complemented
4#16840236C211yesmaximal, characteristic, complemented
5#16839980C214yesmaximal, complemented
6#16839966C214yesmaximal, complemented
7#16839790C211yesmaximal, characteristic, complemented
8#16839756C211yesmaximal, characteristic, complemented
9C61×#419C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C22×D244C2211yescharacteristic
12#14519805—24no—
13C2×#11758190C2212yes—
14C2×#11758201—24no—
15C2×#11758201C2214yes—
16C2×D488C2212yes—
17C22×#92418C2211yescharacteristic
18#14519775C2212yescomplemented
19#14519766C2212yescomplemented
20#14519760—22no—
21#14519753—22no—
22C4×D244—22no—
23#14519739C2214yes—
24#14519736C2211yescharacteristic
25C22⋊C4×D61—22no—
26#14519706C2214yescomplemented
27#14519700C2212yescomplemented
28#14519697C2212yescomplemented
29C22×Q8×C61C2211yescharacteristic
30C2×M16×C61C2211yescharacteristic
31#117×C61C2211yescharacteristic
32#103×C61C2214yescomplemented
33C23×D61—21no—
34C2×Q8×C61—21no—
35C2×Q8×C61—22no—
36C2×Q8×C61—22no—
37C2×Q8×C61C2312yes—
38C22×C4×C61—21no—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—21no—
41#11758222—22no—
42#11758222—22no—
43C2×D244—21no—
44C2×D244—22no—
45C2×D244D414yes—
46C2×D244C2311yescharacteristic
47C2×D244C2312yes—
48C2×C4×D61—21no—
49C2×C4×D61—24no—
50C2×Dic122C2311yescharacteristic
51M16×C61—22no—
52C2×C8×C61C2312yes—
53C4⋊C4×C61C2312yes—
54C22⋊C4×C61—21no—
55C42×C61—21no—
56C22⋊Dic61D412yes—
57#11758201—28no—
58#11758198—24no—
59#11758198—24no—
60C4⋊Dic61D412yes—
61#11758196—24no—
62C4×Dic61C2312yes—
63C2×#92418—22no—
64C2×#92418C2312yes—
65D488—24no—
66#11758190—24no—
67C23×C61C2×D411yescharacteristic
68C22×D61—22no—
69C22×D61—24no—
70C22×D61—21no—
71C22×D61—82no—
72Q8×C61—22no—
73Q8×C61—22no—
74Q8×C61—42no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—42no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D412yes—
80C2×C4×C61#4112yes—
81C2×C4×C61C2411yescharacteristic
82C22⋊D61—42no—
83C2×Dic61—21no—
84C2×Dic61C2×D414yes—
85D244—24no—
86D244—21no—
87D244—22no—
88D244—21no—
89D244C2×D414yes—
90C4×D61—42no—
91C4×D61—84no—
92Dic122—21no—
93Dic122—21no—
94C8×C61—22no—
95#92418—22no—
96C22×C61—22no—
97C22×C61#12112yes—
98C22×C61C22×D411yescharacteristic
99C2×D61—24no—
100C2×D61—44no—
101C2×D61—41no—
102C2×D61—42no—
103C2×D61—84no—
104C4×C61—42no—
105C4×C61—42no—
106C4×C61#12112yes—
107C4×C61C22×D411yescharacteristic
108C4×C61C2×#4111yescharacteristic
109Dic61—24no—
110Dic61—41no—
111#3042—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61C2×#12111yescharacteristic
114C2×C61#57712yes—
115D61—44no—
116D61—81no—
117C2×AGL(1,ℤ/8)—611no—
118C22×SD16—611no—
119#536—611no—
120#518—611no—
121#463—614no—
122#461—614no—
123#424—611no—
124#419D6111yescharacteristic, complemented
125#416—611no—
126C61#304211yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C22×Q8C2×D6111yescharacteristic
129C22×D4—611no—
130AGL(1,ℤ/8)—1224no—
131C2×SD16—614no—
132C2×SD16—612no—
133C2×SD16—1224no—
134C2×D8—612no—
135C2×M16C2×D6111yescharacteristic
136C22×C8—611no—
137C4⋊Q8—612no—
138#124—612no—
139#123—1222no—
140C22⋊Q8—1222no—
141C4×D4—614no—
142C4×D4—1222no—
143#117—611no—
144#117C2×D6111yescharacteristic
145C2×C22⋊C4—1222no—
146C4⋊C8—614no—
147#103—612no—
148#103C2×D6114yescomplemented
149#102—612no—
150C24—1221no—
151#41—1222no—
152#41—1222no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—611no—
157C2×Q8C22×D6112yes—
158C2×D4—614no—
159C2×D4—612no—
160C2×D4—611no—
161C2×D4—1221no—
162C2×D4—1222no—
163C2×D4—1221no—
164C22×C4—21no—
165C22×C4—1224no—
166C22×C4—1221no—
167C22×C4C22×D6111yescharacteristic
168SD16—1224no—
169SD16—1228no—
170D8—1224no—
171M16—22no—
172C2×C8—612no—
173C2×C8—1222no—
174C2×C8C22×D6112yes—
175C4⋊C4—612no—
176C4⋊C4—1224no—
177C4⋊C4C22×D6112yes—
178C22⋊C4—21no—
179C22⋊C4—612no—
180C22⋊C4—1224no—
181C22⋊C4—1224no—
182C42—21no—
183C42—612no—
184C23—1224no—
185C23—1222no—
186C23—1221no—
187C23—4882no—
188C23D4×D6111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—1221no—
193Q8—1221no—
194D4—614no—
195D4—1221no—
196D4—1222no—
197D4—1221no—
198D4—1224no—
199D4—2442no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—614no—
204C2×C4—1221no—
205C2×C4—4884no—
206C2×C4—2442no—
207C2×C4#1175822212yes—
208C2×C4D4×D6112yes—
209C2×C4D4×D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—1222no—
213C22—22no—
214C22—1224no—
215C22—4884no—
216C22—2441no—
217C22—2442no—
218C22—2444no—
219C22#1451975012yes—
220C22C2×D4×D6111yescharacteristic
221C4—42no—
222C4—42no—
223C4—1224no—
224C4—2441no—
225C4#1451975012yes—
226C4C2×D4×D6111yescharacteristic
227C4C2×#1175822211yescharacteristic
228C2—22no—
229C2—4881no—
230C2—2444no—
231C2C2×#1451975011yescharacteristic
232C2#1684057112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#419C2
socleC22×C61C22×D4
hypercenter#419D61
hypocenterC61#3042
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C22×#11758201C2semidirect
3. #16840336C2semidirect
4. #16840236C2semidirect
5. #16839980C2semidirect
6. #16839966C2semidirect
7. #16839790C2semidirect
8. #16839756C2semidirect
9. C61×#419C2semidirect
18. #14519775C22semidirect
19. #14519766C22semidirect
26. #14519706C22semidirect
27. #14519700C22semidirect
28. #14519697C22semidirect
32. #103×C61C22semidirect
124. #419D61semidirect
126. C61#3042semidirect
148. #103C2×D61semidirect