Finite Group Databasebeta

← #21456613

Subgroups — #21456613

Order 7808.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840275C212yesmaximal, complemented
2#16840102C212yesmaximal, complemented
3#16840089C212yesmaximal, complemented
4#16839998C211yesmaximal, characteristic, complemented
5#16839993C212yesmaximal, complemented
6#16839923C212yesmaximal, complemented
7#16839910C212yesmaximal, complemented
8C2×#14519689C211yesmaximal, characteristic, complemented
9C61×#467C211yesmaximal, characteristic, complemented
10C2×#11758226C2212yes—
11C22×C4×D61C2211yescharacteristic
12C2×#11758201C2212yescomplemented
13C2×D488C2211yescharacteristic, complemented
14C22×#92418C2211yescharacteristic
15#14519762—22no—
16#14519753C2212yes—
17#14519752C2212yes—
18#14519751C2212yes—
19#14519747—22no—
20#14519739—22no—
21#14519737—22no—
22#14519735C2212yes—
23#14519711C2211yescharacteristic, complemented
24#14519708C2212yescomplemented
25#14519701C2212yescomplemented
26#14519699C2212yescomplemented
27#14519697C2212yescomplemented
28#14519689C2212yes—
29#14519689C2212yes—
30C2×Q16×C61C2211yescharacteristic, complemented
31C22×C8×C61C2211yescharacteristic
32C22⋊Q8×C61C2212yes—
33#107×C61C2211yescharacteristic, complemented
34#103×C61C2212yescomplemented
35C23×D61D411yescharacteristic
36C2×Q8×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—22no—
39C22×Dic61D411yescharacteristic
40#11758226—42no—
41#11758226—42no—
42C2×D244—22no—
43C2×D244—22no—
44C2×D244C2312yes—
45C2×C4×D61—22no—
46C2×C4×D61—41no—
47C2×C4×D61—41no—
48C2×C4×D61D412yes—
49C2×C4×D61C2312yes—
50Q16×C61—41no—
51C2×C8×C61—41no—
52C2×C8×C61C2311yescharacteristic
53C2×C8×C61C2311yescharacteristic
54C4⋊C4×C61—22no—
55C4⋊C4×C61C2312yes—
56C22⋊C4×C61—22no—
57#11758201—42no—
58#11758198—22no—
59#11758198—22no—
60#11758198—22no—
61#11758198—22no—
62C4⋊Dic61C2312yes—
63#11758196—22no—
64C4×Dic61—22no—
65C2×#92418—41no—
66C2×#92418C2312yes—
67D488—41no—
68C23×C61C2×D411yescharacteristic
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—41no—
72C22×D61—41no—
73C22×D61C2×D412yes—
74Q8×C61—22no—
75Q8×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C22⋊D61—44no—
83C2×Dic61—22no—
84C2×Dic61—41no—
85C2×Dic61C2×D412yes—
86D244—22no—
87D244—22no—
88D244—44no—
89D244—44no—
90C4×D61—22no—
91C4×D61—22no—
92C4×D61—42no—
93C4×D61—44no—
94C8×C61—21no—
95C8×C61—21no—
96#92418—22no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61#13512yes—
100C22×C61C22×D411yescharacteristic
101C2×D61—22no—
102C2×D61—22no—
103C2×D61—22no—
104C2×D61—44no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C4×C61—21no—
109C4×C61—42no—
110C4×C61—42no—
111C4×C61H(5,𝔽2)11yescharacteristic
112C4×C61H(5,𝔽2)11yescharacteristic
113Dic61—22no—
114Dic61—42no—
115#3191—611nomaximal, Sylow
116C2×C61—22no—
117C2×C61#53411yescharacteristic
118C2×C61C2×#13511yescharacteristic
119C2×C61#57511yescharacteristic
120D61—42no—
121D61—82no—
122#525—612no—
123#485—612no—
124#482—612no—
125#467D6111yescharacteristic, complemented
126#466—611no—
127#465—612no—
128#452—612no—
129#449—612no—
130C2×C22⋊C8—611no—
131C61#319111yescharacteristic, complemented, Sylow
132C2×#41—612no—
133C23×C4—611no—
134C2×Q16C2×D6111yescharacteristic, complemented
135C2×SD16—612no—
136C2×D8—611no—
137C22×C8—611no—
138C22×C8C2×D6111yescharacteristic
139#123—1222no—
140C22⋊Q8—612no—
141C22⋊Q8C2×D6112yes—
142#121—612no—
143#121—612no—
144#120—1222no—
145C4×D4—1222no—
146C4×D4—1222no—
147#117—612no—
148#107—611no—
149#107C2×D6111yescharacteristic, complemented
150#106—612no—
151#103—612no—
152#103C2×D6112yescomplemented
153#102—612no—
154#102—612no—
155C22⋊C8—612no—
156C22⋊C8—612no—
157C24—611no—
158#41—2442no—
159#41—2442no—
160C2×Q8C22×D6112yes—
161C2×D4—612no—
162C2×D4—1222no—
163C2×D4—1222no—
164C2×D4—1222no—
165C22×C4—611no—
166C22×C4—612no—
167C22×C4—612no—
168C22×C4—1222no—
169C22×C4—2441no—
170C22×C4—2441no—
171C22×C4C22×D6111yescharacteristic
172Q16—41no—
173SD16—2442no—
174D8—2441no—
175C2×C8—41no—
176C2×C8—612no—
177C2×C8—2441no—
178C2×C8C22×D6111yescharacteristic
179C2×C8C22×D6111yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—612no—
182C4⋊C4—1222no—
183C4⋊C4C22×D6112yes—
184C22⋊C4—22no—
185C22⋊C4—1222no—
186C22⋊C4—1222no—
187C22⋊C4—1222no—
188C22⋊C4—1222no—
189C42—1222no—
190C23—612no—
191C23—1222no—
192C23—1222no—
193C23—2441no—
194C23—2441no—
195C23D4×D6111yescharacteristic
196Q8—22no—
197Q8—22no—
198D4—1222no—
199D4—1222no—
200D4—2444no—
201D4—2444no—
202D4—2444no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—612no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—2442no—
212C2×C4—2444no—
213C2×C4—2441no—
214C2×C4D4×D6111yescharacteristic
215C2×C4C23×D6111yescharacteristic
216C8—21no—
217C8—21no—
218C8—1222no—
219C22—21no—
220C22—21no—
221C22—1222no—
222C22—1222no—
223C22—1222no—
224C22—2444no—
225C22—2442no—
226C22—2442no—
227C22—2442no—
228C22#1451980012yes—
229C22C2×D4×D6111yescharacteristic
230C4—21no—
231C4—42no—
232C4—42no—
233C4—1222no—
234C4—2442no—
235C4#1451982211yescharacteristic
236C4#1451982311yescharacteristic
237C2—22no—
238C2—4882no—
239C2—2442no—
240C2#1684032011yescharacteristic
241C2C2×#1451980011yescharacteristic
242C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#467C2
socleC22×C61C22×D4
hypercenter#467D61
hypocenterC61#3191
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #16840275C2semidirect
2. #16840102C2semidirect
3. #16840089C2semidirect
4. #16839998C2semidirect
5. #16839993C2semidirect
6. #16839923C2semidirect
7. #16839910C2semidirect
8. C2×#14519689C2semidirect
9. C61×#467C2semidirect
12. C2×#11758201C22semidirect
13. C2×D488C22semidirect
23. #14519711C22semidirect
24. #14519708C22semidirect
25. #14519701C22semidirect
26. #14519699C22semidirect
27. #14519697C22semidirect
30. C2×Q16×C61C22semidirect
33. #107×C61C22semidirect
34. #103×C61C22semidirect
125. #467D61semidirect
131. C61#3191semidirect
134. C2×Q16C2×D61semidirect
149. #107C2×D61semidirect
152. #103C2×D61semidirect