Finite Group Databasebeta

← #21456753

Subgroups — #21456753

Order 7808.

438 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#16840313C211yesmaximal, characteristic, complemented
2#16840310C211yesmaximal, characteristic, complemented
3#16840138C211yesmaximal, characteristic, complemented
4#16840135C211yesmaximal, characteristic, complemented
5#16840114C211yesmaximal, characteristic, complemented
6#16839976C214yesmaximal, complemented
7#16839908C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic, complemented
9C61×#486C211yesmaximal, characteristic, complemented
10C2×#11758226—21no—
11C2×#11758224C2212yes—
12C2×#11758190C2214yes—
13C2×#11758199C2214yes—
14#14519777C2211yescharacteristic
15#14519774C2211yescharacteristic
16#14519766—21no—
17#14519764C2212yes—
18#14519752—21no—
19#14519752C2212yes—
20#14519748—21no—
21#14519748—21no—
22D4×Dic61—21no—
23D4×Dic61—21no—
24#14519739—21no—
25#14519739C2212yes—
26C42×D61C2211yescharacteristic
27#14519706C2212yes—
28#14519700C2214yes—
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic
31C4⋊Q8×C61C2211yescharacteristic
32#127×C61C2211yescharacteristic
33#102×C61C2214yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61C2312yes—
39C2×C22⋊D61—22no—
40C22×Dic61—22no—
41#11758226—44no—
42#11758224—44no—
43C2×D244—22no—
44C2×D244—21no—
45C2×D244—21no—
46C2×D244C2312yes—
47C2×C4×D61—22no—
48C2×C4×D61D411yescharacteristic
49C2×C4×D61D411yescharacteristic
50C2×C4×D61C2311yescharacteristic
51C2×Dic122C2312yes—
52C2×C8×C61C2312yes—
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2312yes—
55C42×C61C2311yescharacteristic
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58#11758199—44no—
59#11758198—22no—
60#11758198—22no—
61C4⋊Dic61—21no—
62C4⋊Dic61—21no—
63C4×Dic61D411yescharacteristic
64C4×Dic61D411yescharacteristic
65C4×Dic61C2311yescharacteristic
66C2×#92418C2312yes—
67#11758190—44no—
68C23×C61—22no—
69C22×D61—22no—
70C22×D61C2×D411yescharacteristic
71Q8×C61—42no—
72D4×C61—24no—
73D4×C61—42no—
74D4×C61—42no—
75C2×C4×C61—22no—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2411yescharacteristic
79C22⋊D61—44no—
80C2×Dic61—22no—
81C2×Dic61—44no—
82C2×Dic61C2×D411yescharacteristic
83C2×Dic61C2×D411yescharacteristic
84C2×Dic61C2×D411yescharacteristic
85D244—24no—
86D244—44no—
87D244—42no—
88D244—42no—
89C4×D61—22no—
90C4×D61—22no—
91C4×D61—22no—
92C4×D61—44no—
93Dic122—24no—
94C8×C61—22no—
95#92418—22no—
96C22×C61—42no—
97C22×C61—42no—
98C22×C61—42no—
99C22×C61C22×D411yescharacteristic
100C2×D61—21no—
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C4×C61—42no—
107C4×C61#13512yes—
108C4×C61AGL(1,ℤ/8)12yes—
109C4×C61H(5,𝔽2)12yes—
110Dic61—21no—
111Dic61—21no—
112Dic61—21no—
113Dic61—42no—
114#3207—611nomaximal, Sylow
115C2×C61—82no—
116C2×C61#53511yescharacteristic
117C2×C61C2×#13511yescharacteristic
118C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
119D61—41no—
120D61—82no—
121#532—611no—
122#532—611no—
123#493—611no—
124#492—611no—
125#487—611no—
126#486D6111yescharacteristic, complemented
127#463—614no—
128#449—614no—
129#431—611no—
130C61#320711yescharacteristic, complemented, Sylow
131C2×#41—612no—
132C2×#41—1221no—
133C2×SD16—614no—
134C2×D8—614no—
135C4⋊Q8—611no—
136C4⋊Q8C2×D6111yescharacteristic
137#127—611no—
138#127C2×D6111yescharacteristic
139#124—612no—
140#124—1221no—
141#121—612no—
142#121—1221no—
143#121—1221no—
144#121—1221no—
145C4×D4—612no—
146C4×D4—1221no—
147C4×D4—1221no—
148C4×D4—1221no—
149C2×C42—611no—
150C4⋊C8—612no—
151#103—614no—
152#102C2×D6114yes—
153C22⋊C8—612no—
154C4×C8—611no—
155C4×C8C2×D6111yescharacteristic
156#41—2444no—
157#41—2444no—
158C2×Q8—21no—
159C2×Q8—612no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—612no—
163C2×D4—1222no—
164C2×D4—1222no—
165C2×D4—1221no—
166C2×D4—1221no—
167C2×D4C22×D6112yes—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—1222no—
172C22×C4—1222no—
173SD16—2444no—
174D8—2444no—
175C2×C8—612no—
176C2×C8C22×D6112yes—
177C4⋊C4—21no—
178C4⋊C4—1221no—
179C4⋊C4—1221no—
180C4⋊C4C22×D6112yes—
181C22⋊C4—1222no—
182C22⋊C4—1222no—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C42—611no—
186C42—611no—
187C42—611no—
188C42C22×D6111yescharacteristic
189C23—22no—
190C23—611no—
191C23—1222no—
192Q8—42no—
193Q8—1224no—
194D4—24no—
195D4—42no—
196D4—42no—
197D4—1224no—
198D4—2444no—
199D4—2444no—
200D4—2442no—
201D4—2442no—
202C2×C4—22no—
203C2×C4—611no—
204C2×C4—611no—
205C2×C4—611no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—2444no—
211C2×C4—2444no—
212C2×C4D4×D6111yescharacteristic
213C2×C4D4×D6111yescharacteristic
214C2×C4C23×D6111yescharacteristic
215C8—22no—
216C8—1222no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—1221no—
221C22—1221no—
222C22—1221no—
223C22—2442no—
224C22—2442no—
225C22—2442no—
226C22C2×D4×D6111yescharacteristic
227C4—42no—
228C4—1221no—
229C4—1221no—
230C4—1221no—
231C4—2442no—
232C4#1451979812yes—
233C4#1451980112yes—
234C4#1451982312yes—
235C2—82no—
236C2—4882no—
237C2—2441no—
238C2#1684033011yescharacteristic
239C2C2×#1451979811yescharacteristic
240C2C2×#1451980111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3207
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #16840310C2semidirect
3. #16840138C2semidirect
4. #16840135C2semidirect
5. #16840114C2semidirect
6. #16839976C2semidirect
7. #16839908C2semidirect
8. #16839813C2semidirect
9. C61×#486C2semidirect
126. #486D61semidirect
130. C61#3207semidirect