Finite Group Databasebeta

← #21456756

Subgroups — #21456756

Order 7808.

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

normal subgroups only

This group has 488 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#16840317C211yesmaximal, characteristic, complemented
2#127×D61C211yesmaximal, characteristic
3#16840136C211yesmaximal, characteristic, complemented
4#16840109C211yesmaximal, characteristic, complemented
5#16840108C211yesmaximal, characteristic, complemented
6#16839960C214yesmaximal, complemented
7#16839911C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic, complemented
9C61×#492C211yesmaximal, characteristic, complemented
10C2×D4×D61—21no—
11C2×D4×D61—21no—
12C2×D4×D61C2212yes—
13C2×#11758201C2214yescomplemented
14#14519777C2211yescharacteristic, complemented
15#14519774C2211yescharacteristic
16#14519773—21no—
17#14519773—21no—
18#14519773C2212yes—
19#14519768—21no—
20#14519757—21no—
21#14519753C2212yes—
22Q8×Dic61C2212yescomplemented
23#14519742—21no—
24#14519735—21no—
25C42×D61C2211yescharacteristic
26#14519706C2212yescomplemented
27#14519699C2214yescomplemented
28#14519698C2214yescomplemented
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic, complemented
31C2×SD16×C61C2214yescomplemented
32C4⋊Q8×C61C2211yescharacteristic, complemented
33#127×C61C2211yescharacteristic
34C4×C8×C61C2211yescharacteristic, complemented
35C23×D61—22no—
36C2×Q8×C61C2312yes—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61C2312yes—
40C2×C22⋊D61—22no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61—22no—
43D4×D61—44no—
44D4×D61—44no—
45D4×D61—44no—
46C2×D244—21no—
47C2×D244—21no—
48C2×D244C2312yes—
49C2×C4×D61D411yescharacteristic
50C2×C4×D61D411yescharacteristic
51C2×C4×D61C2311yescharacteristic
52C2×Dic122—21no—
53SD16×C61—44no—
54C2×C8×C61C2312yes—
55C4⋊C4×C61—21no—
56C4⋊C4×C61—21no—
57C42×C61C2311yescharacteristic
58#11758201—44no—
59#11758198—22no—
60C4⋊Dic61—21no—
61C4⋊Dic61—22no—
62C4⋊Dic61C2312yes—
63#11758196—22no—
64C4×Dic61—22no—
65C4×Dic61D411yescharacteristic
66C4×Dic61D411yescharacteristic
67C4×Dic61C2311yescharacteristic
68C2×#92418C2312yes—
69C23×C61—22no—
70C22×D61—22no—
71C22×D61—44no—
72C22×D61—44no—
73C22×D61—44no—
74C22×D61C2×D411yescharacteristic
75Q8×C61—24no—
76D4×C61—24no—
77D4×C61—42no—
78D4×C61—42no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—44no—
84C22⋊D61—44no—
85C22⋊D61—44no—
86C2×Dic61—22no—
87C2×Dic61C2×D411yescharacteristic
88C2×Dic61C2×D411yescharacteristic
89C2×Dic61C2×D411yescharacteristic
90D244—24no—
91D244—42no—
92D244—42no—
93C4×D61—22no—
94C4×D61—22no—
95C4×D61SD1614yescomplemented
96Dic122—42no—
97C8×C61—22no—
98#92418—22no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61C22×D411yescharacteristic
103C2×D61—21no—
104C2×D61—21no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—88no—
109C2×D61C2×SD1612yes—
110C4×C61—42no—
111C4×C61C2×SD1612yes—
112C4×C61AGL(1,ℤ/8)12yes—
113C4×C61H(5,𝔽2)12yes—
114Dic61—21no—
115Dic61—21no—
116Dic61—42no—
117Dic61C2×SD1612yes—
118#3208—611nomaximal, Sylow
119C2×C61—82no—
120C2×C61#53511yescharacteristic
121C2×C61C22×SD1611yescharacteristic
122C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
123D61—22no—
124D61—82no—
125#533—611no—
126C2×#127—611no—
127#492—611no—
128#492D6111yescharacteristic, complemented
129#486—611no—
130#486—611no—
131#460—614no—
132#450—614no—
133#431—611no—
134C61#320811yescharacteristic, complemented, Sylow
135C22×D4—612no—
136C22×D4—1221no—
137C22×D4—1221no—
138C2×SD16—614no—
139C2×SD16C2×D6114yescomplemented
140C4⋊Q8—611no—
141C4⋊Q8C2×D6111yescharacteristic, complemented
142#127—612no—
143#127—611no—
144#127—1221no—
145#127—1221no—
146#127C2×D6111yescharacteristic
147#125—1221no—
148C22⋊Q8—612no—
149C22⋊Q8—1221no—
150C4×Q8—612no—
151C4×Q8—1221no—
152#117—1221no—
153C2×C42—611no—
154C4⋊C8—612no—
155#102—614no—
156#102—614no—
157C22⋊C8—612no—
158C4×C8—611no—
159C4×C8C2×D6111yescharacteristic, complemented
160C24—1222no—
161C2×Q8—1221no—
162C2×Q8C22×D6112yes—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—612no—
166C2×D4—1222no—
167C2×D4—1222no—
168C2×D4—1222no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—2444no—
172C2×D4—2444no—
173C2×D4—2444no—
174C2×D4C22×D6112yes—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—611no—
178SD16—44no—
179SD16—2444no—
180C2×C8—612no—
181C2×C8C22×D6112yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—612no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1221no—
188C22⋊C4—1222no—
189C42—611no—
190C42—611no—
191C42—611no—
192C42—1222no—
193C42C22×D6111yescharacteristic
194C23—22no—
195C23—611no—
196C23—1222no—
197C23—2444no—
198C23—2444no—
199C23—2444no—
200Q8—24no—
201Q8—2442no—
202D4—24no—
203D4—42no—
204D4—42no—
205D4—1224no—
206D4—2444no—
207D4—2444no—
208D4—2444no—
209D4—2442no—
210D4—2442no—
211C2×C4—22no—
212C2×C4—611no—
213C2×C4—614no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4D4×D6111yescharacteristic
220C2×C4D4×D6111yescharacteristic
221C2×C4C23×D6111yescharacteristic
222C8—22no—
223C8—1222no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—612no—
228C22—1221no—
229C22—1221no—
230C22—4888no—
231C22—2442no—
232C22—2442no—
233C22—2442no—
234C22C2×D4×D6111yescharacteristic
235C4—42no—
236C4—612no—
237C4—1221no—
238C4—1221no—
239C4—2442no—
240C4SD16×D6112yes—
241C4#1451980412yes—
242C4#1451982212yes—
243C2—82no—
244C2—1222no—
245C2—4882no—
246C2#1684032511yescharacteristic
247C2C2×SD16×D6111yescharacteristic
248C2C2×#1451980411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#492C2
socleC22×C61C22×D4
hypercenter#492D61
hypocenterC61#3208
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840136C2semidirect
4. #16840109C2semidirect
5. #16840108C2semidirect
6. #16839960C2semidirect
7. #16839911C2semidirect
8. #16839813C2semidirect
9. C61×#492C2semidirect
13. C2×#11758201C22semidirect
14. #14519777C22semidirect
22. Q8×Dic61C22semidirect
26. #14519706C22semidirect
27. #14519699C22semidirect
28. #14519698C22semidirect
30. C4×#92418C22semidirect
31. C2×SD16×C61C22semidirect
32. C4⋊Q8×C61C22semidirect
34. C4×C8×C61C22semidirect
95. C4×D61SD16semidirect
128. #492D61semidirect
134. C61#3208semidirect
139. C2×SD16C2×D61semidirect
141. C4⋊Q8C2×D61semidirect
159. C4×C8C2×D61semidirect