Finite Group Databasebeta

← #21456612

Subgroups — #21456612

Order 7808.

424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840273C212yesmaximal, complemented
2#16840104C212yesmaximal, complemented
3#16840087C212yesmaximal, complemented
4#16840003C211yesmaximal, characteristic, complemented
5#16839998C211yesmaximal, characteristic, complemented
6#16839991C212yesmaximal, complemented
7#16839926C212yesmaximal, complemented
8#16839909C212yesmaximal, complemented
9C2×C22⋊C8×C61C211yesmaximal, characteristic, complemented
10C2×#11758222C2212yes—
11C2×Dic244C2211yescharacteristic, complemented
12C2×#11758190C2212yescomplemented
13C2×D488C2211yescharacteristic, complemented
14#14519760—22no—
15#14519756C2212yes—
16#14519756C2212yes—
17#14519751C2212yes—
18#14519751C2212yes—
19#14519746—22no—
20C4×C22⋊D61—22no—
21C4×C22⋊D61—22no—
22#14519736C2212yes—
23#14519711C2211yescharacteristic, complemented
24#14519711C2211yescharacteristic, complemented
25#14519709C2212yescomplemented
26#14519702C2212yescomplemented
27#14519702C2212yescomplemented
28#14519699C2212yescomplemented
29#14519699C2212yescomplemented
30C23×C4×C61C2211yescharacteristic
31C22×C8×C61C2211yescharacteristic
32C22×C8×C61C2211yescharacteristic
33C22⋊C8×C61C2212yes—
34C22⋊C8×C61C2212yes—
35C24×C61D411yescharacteristic
36C22×C4×C61—41no—
37C22×C4×C61—41no—
38C22×C4×C61D411yescharacteristic
39C22×C4×C61D412yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—22no—
43C2×C22⋊D61—22no—
44C2×C22⋊D61—22no—
45#11758222—42no—
46#11758222—42no—
47C2×D244C2312yes—
48C2×C4×D61—22no—
49C2×Dic122C2312yes—
50C2×C8×C61—41no—
51C2×C8×C61—41no—
52C2×C8×C61C2311yescharacteristic
53C2×C8×C61C2312yes—
54C2×C8×C61C2311yescharacteristic
55C22⋊Dic61—22no—
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61C2312yes—
61C4⋊Dic61C2312yes—
62#11758196—22no—
63#11758196—22no—
64C4×Dic61—22no—
65Dic244—41no—
66D488—41no—
67#11758190—42no—
68C23×C61—22no—
69C23×C61—41no—
70C23×C61—41no—
71C23×C61C2×D412yes—
72C23×C61C2×D411yescharacteristic
73C22×D61—22no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—41no—
79C2×C4×C61—42no—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—44no—
84C22⋊D61—44no—
85C22⋊D61—44no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89D244—22no—
90D244—22no—
91C4×D61—44no—
92Dic122—22no—
93Dic122—22no—
94C8×C61—22no—
95C8×C61—21no—
96C8×C61—21no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61—22no—
100C22×C61—22no—
101C22×C61—22no—
102C22×C61—44no—
103C22×C61#13512yes—
104C22×C61C22×D411yescharacteristic
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C4×C61—22no—
109C4×C61—21no—
110C4×C61H(5,𝔽2)11yescharacteristic
111C4×C61H(5,𝔽2)11yescharacteristic
112Dic61—42no—
113Dic61—42no—
114Dic61—42no—
115#3191—611nomaximal, Sylow
116C2×C61—22no—
117C2×C61—42no—
118C2×C61#53411yescharacteristic
119C2×C61C2×#13511yescharacteristic
120C2×C61#57511yescharacteristic
121D61—82no—
122#525—612no—
123#485—612no—
124#482—612no—
125#467—611no—
126#466—611no—
127#465—612no—
128#452—612no—
129#449—612no—
130C2×C22⋊C8D6111yescharacteristic, complemented
131C61#319111yescharacteristic, complemented, Sylow
132C2×#41—612no—
133C23×C4C2×D6111yescharacteristic
134C2×Q16—611no—
135C2×SD16—612no—
136C2×D8—611no—
137C22×C8C2×D6111yescharacteristic
138C22×C8C2×D6111yescharacteristic
139#123—1222no—
140C22⋊Q8—612no—
141C22⋊Q8—612no—
142#121—612no—
143#121—612no—
144#120—1222no—
145C4×D4—1222no—
146C4×D4—1222no—
147#117—612no—
148#107—611no—
149#107—611no—
150#106—612no—
151#103—612no—
152#103—612no—
153#102—612no—
154#102—612no—
155C22⋊C8C2×D6112yes—
156C22⋊C8C2×D6112yes—
157C24D24411yescharacteristic
158#41—2442no—
159#41—2442no—
160C2×Q8—612no—
161C2×D4—612no—
162C2×D4—1222no—
163C2×D4—1222no—
164C2×D4—1222no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—1222no—
168C22×C4D24411yescharacteristic
169C22×C4D24412yes—
170C22×C4C22×D6112yes—
171C22×C4C22×D6111yescharacteristic
172Q16—2441no—
173SD16—2442no—
174D8—2441no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8C22×D6111yescharacteristic
178C2×C8C22×D6112yes—
179C2×C8C22×D6111yescharacteristic
180C4⋊C4—612no—
181C4⋊C4—612no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C22⋊C4—1222no—
187C22⋊C4—1222no—
188C22⋊C4—1222no—
189C42—1222no—
190C23—22no—
191C23—41no—
192C23—41no—
193C23—1222no—
194C23C2×D24412yes—
195C23C2×D24411yescharacteristic
196Q8—1222no—
197Q8—1222no—
198D4—1222no—
199D4—1222no—
200D4—2444no—
201D4—2444no—
202D4—2444no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—2444no—
213C2×C4C2×D24412yes—
214C2×C4C2×D24411yescharacteristic
215C2×C4C23×D6111yescharacteristic
216C8—21no—
217C8—22no—
218C8—21no—
219C22—21no—
220C22—21no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—44no—
225C22—2442no—
226C22—2442no—
227C22—2442no—
228C22#1451979912yes—
229C22C22×D24411yescharacteristic
230C4—22no—
231C4—21no—
232C4—2442no—
233C4—2442no—
234C4—2442no—
235C4#1451982211yescharacteristic
236C4#1451982211yescharacteristic
237C2—22no—
238C2—42no—
239C2—4882no—
240C2#1684032411yescharacteristic
241C2C2×#1451979911yescharacteristic
242C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C22⋊C8×C61C2
socleC22×C61C22×D4
hypercenterC2×C22⋊C8D61
hypocenterC61#3191
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #16840273C2semidirect
2. #16840104C2semidirect
3. #16840087C2semidirect
4. #16840003C2semidirect
5. #16839998C2semidirect
6. #16839991C2semidirect
7. #16839926C2semidirect
8. #16839909C2semidirect
9. C2×C22⋊C8×C61C2semidirect
11. C2×Dic244C22semidirect
12. C2×#11758190C22semidirect
13. C2×D488C22semidirect
23. #14519711C22semidirect
24. #14519711C22semidirect
25. #14519709C22semidirect
26. #14519702C22semidirect
27. #14519702C22semidirect
28. #14519699C22semidirect
29. #14519699C22semidirect
130. C2×C22⋊C8D61semidirect
131. C61#3191semidirect