Finite Group Databasebeta

← #21456872

Subgroups — #21456872

Order 7808.

420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840368C211yesmaximal, characteristic, complemented
2#16840330C211yesmaximal, characteristic, complemented
3#16840152C211yesmaximal, characteristic, complemented
4#16840139C211yesmaximal, characteristic, complemented
5#16840128C211yesmaximal, characteristic, complemented
6#16839980C212yesmaximal, complemented
7#16839956C212yesmaximal, complemented
8#16839910C212yesmaximal, complemented
9#16839897C212yesmaximal, complemented
10#16839821C211yesmaximal, characteristic, complemented
11C61×#488C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic
13C2×D4×D61C2211yescharacteristic
14C2×#11758201C2212yescomplemented
15C2×D488C2212yes—
16C2×D488C2212yescomplemented
17C2×#11758199C2212yes—
18#14519774C2211yescharacteristic
19#14519774C2211yescharacteristic, complemented
20#14519773C2211yescharacteristic
21#14519766C2211yescharacteristic
22#14519762—22no—
23#14519752—22no—
24#14519752C2212yes—
25#14519750—22no—
26#14519747—22no—
27#14519739C2212yescomplemented
28#14519734C2211yescharacteristic
29#14519706C2212yescomplemented
30#14519697C2212yes—
31#14519697C2212yescomplemented
32#14519689C2212yes—
33#14519688C2211yescharacteristic, complemented
34#125×C61C2211yescharacteristic, complemented
35#124×C61C2211yescharacteristic
36#103×C61C2212yescomplemented
37#102×C61C2212yes—
38C4×C8×C61C2211yescharacteristic, complemented
39C23×D61—21no—
40C2×Q8×C61C2311yescharacteristic
41C2×D4×C61C2311yescharacteristic
42C2×C22⋊D61—21no—
43C2×C22⋊D61—22no—
44#11758226—42no—
45D4×D61—42no—
46C2×D244—21no—
47C2×D244—22no—
48C2×D244—22no—
49C2×D244—22no—
50C2×D244C2311yescharacteristic
51C2×D244C2311yescharacteristic
52C2×D244C2312yes—
53C2×C4×D61—21no—
54C2×C4×D61—22no—
55C2×C4×D61C2311yescharacteristic
56C2×C8×C61C2312yes—
57C4⋊C4×C61—22no—
58C4⋊C4×C61C2312yes—
59C22⋊C4×C61—22no—
60C42×C61C2311yescharacteristic
61#11758201—42no—
62#11758199—42no—
63#11758198—22no—
64#11758198—22no—
65#11758198—22no—
66#11758198D412yes—
67#11758196D412yes—
68C4×Dic61C2311yescharacteristic
69C2×#92418C2312yes—
70D488—42no—
71D488—42no—
72C23×C61—21no—
73C22×D61—22no—
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—42no—
77C22×D61—82no—
78C22×D61C2×D411yescharacteristic
79Q8×C61—22no—
80D4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D412yes—
84C2×C4×C61C2411yescharacteristic
85C22⋊D61—42no—
86C22⋊D61—82no—
87C2×Dic61C2×D412yes—
88C2×Dic61C2×D411yescharacteristic
89D244—22no—
90D244—22no—
91D244—22no—
92D244—22no—
93D244—42no—
94D244—82no—
95D244—82no—
96D244—82no—
97C4×D61—22no—
98C4×D61—42no—
99C4×D61—82no—
100C8×C61—22no—
101#92418—22no—
102C22×C61—41no—
103C22×C61—42no—
104C22×C61C22×D411yescharacteristic
105C2×D61—21no—
106C2×D61—22no—
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—84no—
115C4×C61—22no—
116C4×C61—41no—
117C4×C61—42no—
118C4×C61H(5,𝔽2)12yes—
119Dic61—21no—
120Dic61—22no—
121#3220—611nomaximal, Sylow
122C2×C61—81no—
123C2×C61#53511yescharacteristic
124C2×C61#57612yes—
125D61—41no—
126D61—81no—
127D61—82no—
128D61—81no—
129#540—611no—
130#535—611no—
131#496—611no—
132#493—611no—
133#490—611no—
134#488D6111yescharacteristic, complemented
135#463—612no—
136#459—612no—
137#449—612no—
138#447—612no—
139#433—611no—
140C61#322011yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C22×D4—611no—
143C2×SD16—612no—
144C2×D8—612no—
145C2×D8—612no—
146C2×D8—612no—
147#127—611no—
148#127—611no—
149#127—611no—
150#125C2×D6111yescharacteristic, complemented
151#124—611no—
152#124C2×D6111yescharacteristic
153#123—1222no—
154#121—612no—
155#121—1222no—
156#121—1222no—
157#120—1222no—
158C4×D4—612no—
159#117—611no—
160C4⋊C8—612no—
161#103C2×D6112yescomplemented
162#102—612no—
163#102—612no—
164#102C2×D6112yes—
165C22⋊C8—612no—
166#97—611no—
167C4×C8C2×D6111yescharacteristic, complemented
168C24—1221no—
169#41—2442no—
170C2×Q8C22×D6111yescharacteristic
171C2×D4—611no—
172C2×D4—611no—
173C2×D4—612no—
174C2×D4—1222no—
175C2×D4—1221no—
176C2×D4—1222no—
177C2×D4—1221no—
178C2×D4—1222no—
179C2×D4—1222no—
180C2×D4—2442no—
181C2×D4C22×D6111yescharacteristic
182C22×C4—611no—
183C22×C4—1222no—
184C22×C4—1221no—
185SD16—2442no—
186D8—2442no—
187D8—2442no—
188D8—2442no—
189C2×C8—612no—
190C2×C8C22×D6112yes—
191C4⋊C4—22no—
192C4⋊C4—612no—
193C4⋊C4C22×D6112yes—
194C22⋊C4—22no—
195C22⋊C4—612no—
196C22⋊C4—1222no—
197C22⋊C4—1222no—
198C22⋊C4—1222no—
199C42—611no—
200C42C22×D6111yescharacteristic
201C23—21no—
202C23—611no—
203C23—1222no—
204C23—1221no—
205C23—1221no—
206C23—4882no—
207C23—2442no—
208Q8—22no—
209D4—22no—
210D4—1222no—
211D4—1222no—
212D4—1222no—
213D4—1222no—
214D4—4882no—
215D4—4882no—
216D4—4882no—
217D4—4882no—
218D4—2442no—
219D4—2442no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—612no—
223C2×C4—611no—
224C2×C4—1222no—
225C2×C4—4882no—
226C2×C4—2442no—
227C2×C4D4×D6112yes—
228C2×C4C23×D6111yescharacteristic
229C8—22no—
230C8—1222no—
231C22—42no—
232C22—41no—
233C22—1222no—
234C22—1221no—
235C22—4884no—
236C22—2442no—
237C22—2442no—
238C22—2442no—
239C22—2442no—
240C22—2441no—
241C22—2441no—
242C22—2442no—
243C22C2×D4×D6111yescharacteristic
244C4—22no—
245C4—42no—
246C4—41no—
247C4—1222no—
248C4—1221no—
249C4#1451982312yes—
250C2—81no—
251C2—4881no—
252C2—4882no—
253C2—4881no—
254C2—2441no—
255C2#1684033011yescharacteristic
256C2#1684056412yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#488C2
socleC22×C61C22×D4
hypercenter#488D61
hypocenterC61#3220
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #16840368C2semidirect
2. #16840330C2semidirect
3. #16840152C2semidirect
4. #16840139C2semidirect
5. #16840128C2semidirect
6. #16839980C2semidirect
7. #16839956C2semidirect
8. #16839910C2semidirect
9. #16839897C2semidirect
10. #16839821C2semidirect
11. C61×#488C2semidirect
14. C2×#11758201C22semidirect
16. C2×D488C22semidirect
19. #14519774C22semidirect
27. #14519739C22semidirect
29. #14519706C22semidirect
31. #14519697C22semidirect
33. #14519688C22semidirect
34. #125×C61C22semidirect
36. #103×C61C22semidirect
38. C4×C8×C61C22semidirect
134. #488D61semidirect
140. C61#3220semidirect
150. #125C2×D61semidirect
161. #103C2×D61semidirect
167. C4×C8C2×D61semidirect