Finite Group Databasebeta

← #21456754

Subgroups — #21456754

Order 7808.

438 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840312C211yesmaximal, characteristic, complemented
2#16840312C211yesmaximal, characteristic, complemented
3#16840139C211yesmaximal, characteristic, complemented
4#16840135C211yesmaximal, characteristic, complemented
5#16840113C211yesmaximal, characteristic, complemented
6#16840109C211yesmaximal, characteristic, complemented
7#16839978C214yesmaximal, complemented
8#16839909C214yesmaximal, complemented
9C61×#431C211yesmaximal, characteristic, complemented
10C2×#11758222—21no—
11C2×#11758222C2212yes—
12C2×#11758190C2214yes—
13C2×D488C2214yes—
14#14519777C2211yescharacteristic
15#14519777C2211yescharacteristic
16#14519774C2211yescharacteristic
17#14519774C2211yescharacteristic
18#14519765—21no—
19#14519765C2212yes—
20#14519751—21no—
21#14519751—21no—
22#14519751—21no—
23#14519751C2212yes—
24C4×D244—21no—
25C4×D244—21no—
26C4×D244—21no—
27C4×D244C2212yes—
28#14519702C2214yes—
29#14519699C2214yes—
30C2×C42×C61C2211yescharacteristic
31C4⋊C8×C61C2212yes—
32C22⋊C8×C61C2212yes—
33C4×C8×C61C2211yescharacteristic
34C4×C8×C61C2211yescharacteristic
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—22no—
39C2×C22⋊D61—22no—
40#11758222—44no—
41#11758222—44no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244—21no—
45C2×D244—21no—
46C2×D244C2312yes—
47C2×D244C2312yes—
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×Dic122—21no—
51C2×Dic122C2312yes—
52C2×C8×C61C2312yes—
53C2×C8×C61C2312yes—
54C42×C61D411yescharacteristic
55C42×C61D411yescharacteristic
56C42×C61C2311yescharacteristic
57C42×C61C2311yescharacteristic
58#11758198—22no—
59#11758198—22no—
60#11758198—22no—
61#11758198—22no—
62C4⋊Dic61—21no—
63C4⋊Dic61—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61C2312yes—
66D488—44no—
67#11758190—44no—
68C23×C61C2×D411yescharacteristic
69C22×D61—22no—
70C22×D61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2411yescharacteristic
80C22⋊D61—44no—
81C22⋊D61—44no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84D244—24no—
85D244—24no—
86D244—42no—
87D244—42no—
88D244—42no—
89D244—42no—
90C4×D61—44no—
91C4×D61—44no—
92Dic122—24no—
93Dic122—42no—
94C8×C61—22no—
95C8×C61—22no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61C22×D411yescharacteristic
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—21no—
109C4×C61#13512yes—
110C4×C61AGL(1,ℤ/8)12yes—
111C4×C61H(5,𝔽2)12yes—
112Dic61—42no—
113Dic61—42no—
114#3207—611nomaximal, Sylow
115C2×C61—41no—
116C2×C61#53511yescharacteristic
117C2×C61C2×#13511yescharacteristic
118C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
119D61—82no—
120D61—82no—
121#532—611no—
122#532—611no—
123#493—611no—
124#492—611no—
125#487—611no—
126#486—611no—
127#463—614no—
128#449—614no—
129#431D6111yescharacteristic, complemented
130C61#320711yescharacteristic, complemented, Sylow
131C2×#41—612no—
132C2×#41—1221no—
133C2×SD16—614no—
134C2×D8—614no—
135C4⋊Q8—611no—
136C4⋊Q8—611no—
137#127—611no—
138#127—611no—
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×C42C2×D6111yescharacteristic
150C4⋊C8C2×D6112yes—
151#103—614no—
152#102—614no—
153C22⋊C8C2×D6112yes—
154C4×C8C2×D6111yescharacteristic
155C4×C8C2×D6111yescharacteristic
156#41—2444no—
157#41—2444no—
158C2×Q8—612no—
159C2×Q8—1221no—
160C2×D4—612no—
161C2×D4—612no—
162C2×D4—1222no—
163C2×D4—1222no—
164C2×D4—1221no—
165C2×D4—1221no—
166C2×D4—1221no—
167C2×D4—1221no—
168C22×C4—1222no—
169C22×C4—1222no—
170C22×C4D24411yescharacteristic
171C22×C4D24411yescharacteristic
172C22×C4C22×D6111yescharacteristic
173SD16—2444no—
174D8—2444no—
175C2×C8C22×D6112yes—
176C2×C8C22×D6112yes—
177C4⋊C4—612no—
178C4⋊C4—1221no—
179C4⋊C4—1221no—
180C4⋊C4—1221no—
181C22⋊C4—1222no—
182C22⋊C4—1222no—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C42D24411yescharacteristic
186C42D24411yescharacteristic
187C42C22×D6111yescharacteristic
188C42C22×D6111yescharacteristic
189C23—1222no—
190C23—1222no—
191C23C2×D24411yescharacteristic
192Q8—1224no—
193Q8—2442no—
194D4—1224no—
195D4—1224no—
196D4—2444no—
197D4—2444no—
198D4—2442no—
199D4—2442no—
200D4—2442no—
201D4—2442no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—2444no—
208C2×C4—2444no—
209C2×C4C2×D24411yescharacteristic
210C2×C4C2×D24411yescharacteristic
211C2×C4C2×D24411yescharacteristic
212C2×C4C2×D24411yescharacteristic
213C2×C4C2×D24411yescharacteristic
214C2×C4C23×D6111yescharacteristic
215C8—22no—
216C8—22no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—2442no—
221C22—2442no—
222C22—2442no—
223C22—2442no—
224C22—2442no—
225C22—2442no—
226C22C22×D24411yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—2442no—
231C4—2442no—
232C4#1451979912yes—
233C4#1451980512yes—
234C4#1451982312yes—
235C2—41no—
236C2—4882no—
237C2—4882no—
238C2#1684033111yescharacteristic
239C2C2×#1451979911yescharacteristic
240C2C2×#1451980511yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#431C2
socleC22×C61C22×D4
hypercenter#431D61
hypocenterC61#3207
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #16840312C2semidirect
2. #16840312C2semidirect
3. #16840139C2semidirect
4. #16840135C2semidirect
5. #16840113C2semidirect
6. #16840109C2semidirect
7. #16839978C2semidirect
8. #16839909C2semidirect
9. C61×#431C2semidirect
129. #431D61semidirect
130. C61#3207semidirect