Finite Group Databasebeta

← #21456893

Subgroups — #21456893

Order 7808.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840374C211yesmaximal, characteristic, complemented
2#16840331C211yesmaximal, characteristic
3#16840156C211yesmaximal, characteristic, complemented
4#16840135C211yesmaximal, characteristic, complemented
5#16840127C211yesmaximal, characteristic, complemented
6#16840117C211yesmaximal, characteristic, complemented
7#16839985C212yesmaximal, complemented
8#16839963C212yesmaximal, complemented
9#16839926C212yesmaximal, complemented
10#16839915C212yesmaximal, complemented
11C61×#433C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C2×Dic244C2212yescomplemented
15C2×#11758190C2212yes—
16C2×#11758190C2212yes—
17C2×#11758190C2212yescomplemented
18#14519777C2211yescharacteristic, complemented
19#14519774C2211yescharacteristic
20#14519774C2211yescharacteristic
21#14519770—22no—
22#14519769C2211yescharacteristic, complemented
23#14519767—22no—
24#14519765C2211yescharacteristic
25#14519765C2211yescharacteristic
26#14519756C2212yes—
27#14519752—22no—
28#14519747—22no—
29C4×Dic122C2212yescomplemented
30#14519702C2212yescomplemented
31#14519699C2212yes—
32#14519699C2212yes—
33#14519699C2212yescomplemented
34#117×C61C2211yescharacteristic
35C4⋊C8×C61C2212yescomplemented
36C22⋊C8×C61C2212yes—
37#97×C61C2211yescharacteristic, complemented
38C4×C8×C61C2211yescharacteristic, complemented
39C23×D61—21no—
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61—21no—
42#11758222—42no—
43C2×D244—21no—
44C2×D244—22no—
45C2×D244—22no—
46C2×D244—42no—
47C2×D244C2311yescharacteristic
48C2×D244C2311yescharacteristic
49C2×D244C2311yescharacteristic
50C2×C4×D61—21no—
51C2×Dic122C2311yescharacteristic
52C2×Dic122C2312yes—
53C2×C8×C61C2312yes—
54C2×C8×C61C2312yes—
55C4⋊C4×C61D412yes—
56C22⋊C4×C61D412yes—
57C42×C61C2311yescharacteristic
58C42×C61C2311yescharacteristic
59C22⋊Dic61—22no—
60#11758198—22no—
61#11758198—22no—
62C4⋊Dic61—22no—
63C4⋊Dic61C2312yes—
64#11758196—22no—
65#11758196—22no—
66#11758196—22no—
67C4×Dic61—22no—
68Dic244—42no—
69#11758190—42no—
70#11758190—42no—
71#11758190—42no—
72C23×C61C2×D411yescharacteristic
73C22×D61—21no—
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—42no—
77C22×D61—82no—
78C2×C4×C61—22no—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—42no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—21no—
87D244—22no—
88D244—22no—
89D244—22no—
90D244—42no—
91D244—82no—
92D244—82no—
93C4×D61—42no—
94Dic122—22no—
95Dic122—22no—
96Dic122—22no—
97C8×C61—22no—
98C8×C61—22no—
99C22×C61—21no—
100C22×C61—22no—
101C22×C61C22×D411yescharacteristic
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—41no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—84no—
109C4×C61—21no—
110C4×C61—22no—
111C4×C61—22no—
112C4×C61H(5,𝔽2)12yes—
113Dic61—41no—
114Dic61—42no—
115Dic61—42no—
116#3222—611nomaximal, Sylow
117C2×C61—41no—
118C2×C61#53511yescharacteristic
119C2×C61#57712yes—
120D61—81no—
121D61—81no—
122D61—81no—
123#541—611no—
124#535—611no—
125#497—611no—
126#492—611no—
127#490—611no—
128#488—611no—
129#464—612no—
130#460—612no—
131#452—612no—
132#450—612no—
133#433D6111yescharacteristic, complemented
134C61#322211yescharacteristic, complemented, Sylow
135C2×#41—611no—
136C22×D4—611no—
137C2×Q16—612no—
138C2×SD16—612no—
139C2×SD16—612no—
140C2×SD16—612no—
141C4⋊Q8—611no—
142#127—611no—
143#127—611no—
144#126—1222no—
145#125—611no—
146#125—1222no—
147#124—611no—
148#124—611no—
149C22⋊Q8—612no—
150#121—1222no—
151#120—1222no—
152C4×Q8—612no—
153#117C2×D6111yescharacteristic
154C4⋊C8C2×D6112yescomplemented
155#103—612no—
156#102—612no—
157#102—612no—
158#102—612no—
159C22⋊C8C2×D6112yes—
160#97C2×D6111yescharacteristic, complemented
161C4×C8C2×D6111yescharacteristic, complemented
162C24—1221no—
163#41—2442no—
164C2×Q8—611no—
165C2×Q8—612no—
166C2×D4—611no—
167C2×D4—611no—
168C2×D4—611no—
169C2×D4—1221no—
170C2×D4—1222no—
171C2×D4—1222no—
172C2×D4—1221no—
173C2×D4—2442no—
174C22×C4—1221no—
175C22×C4C22×D6111yescharacteristic
176Q16—2442no—
177SD16—2442no—
178SD16—2442no—
179SD16—2442no—
180C2×C8C22×D6112yes—
181C2×C8C22×D6112yes—
182C4⋊C4—612no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4D24412yes—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4D24412yes—
192C42—1222no—
193C42C22×D6111yescharacteristic
194C42C22×D6111yescharacteristic
195C23—1221no—
196C23—1221no—
197C23—1221no—
198C23—4882no—
199C23—2442no—
200C23C2×D24411yescharacteristic
201Q8—1222no—
202Q8—1222no—
203Q8—1222no—
204D4—1222no—
205D4—1222no—
206D4—1222no—
207D4—4882no—
208D4—4882no—
209D4—2442no—
210D4—2442no—
211C2×C4—22no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1221no—
215C2×C4—2442no—
216C2×C4C2×D24412yes—
217C2×C4C2×D24412yes—
218C2×C4C2×D24411yescharacteristic
219C2×C4C23×D6111yescharacteristic
220C8—22no—
221C8—22no—
222C22—22no—
223C22—21no—
224C22—4884no—
225C22—2442no—
226C22—2442no—
227C22—2442no—
228C22—2441no—
229C22—2441no—
230C22—2441no—
231C22C22×D24411yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—2442no—
236C4—2441no—
237C4—2442no—
238C4#1451982312yes—
239C2—41no—
240C2—4881no—
241C2—4881no—
242C2—4881no—
243C2#1684033111yescharacteristic
244C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3222
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16840374C2semidirect
3. #16840156C2semidirect
4. #16840135C2semidirect
5. #16840127C2semidirect
6. #16840117C2semidirect
7. #16839985C2semidirect
8. #16839963C2semidirect
9. #16839926C2semidirect
10. #16839915C2semidirect
11. C61×#433C2semidirect
14. C2×Dic244C22semidirect
17. C2×#11758190C22semidirect
18. #14519777C22semidirect
22. #14519769C22semidirect
29. C4×Dic122C22semidirect
30. #14519702C22semidirect
33. #14519699C22semidirect
35. C4⋊C8×C61C22semidirect
37. #97×C61C22semidirect
38. C4×C8×C61C22semidirect
133. #433D61semidirect
134. C61#3222semidirect
154. C4⋊C8C2×D61semidirect
160. #97C2×D61semidirect
161. C4×C8C2×D61semidirect