Finite Group Databasebeta

← #21456885

Subgroups — #21456885

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#16840331C211yesmaximal, characteristic
2#16840154C211yesmaximal, characteristic, complemented
3#16840136C211yesmaximal, characteristic, complemented
4#16840128C211yesmaximal, characteristic, complemented
5#16840119C211yesmaximal, characteristic, complemented
6#16839984C212yesmaximal, complemented
7#16839962C212yesmaximal, complemented
8#16839922C212yesmaximal, complemented
9#16839912C212yesmaximal, complemented
10#16839823C211yesmaximal, characteristic, complemented
11C61×#541C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C2×#11758202C2212yescomplemented
15C2×#11758201C2212yes—
16C2×#11758201C2212yes—
17C2×#11758201C2212yescomplemented
18#14519774C2211yescharacteristic
19#14519774C2211yescharacteristic
20#14519765C2211yescharacteristic
21#14519765C2211yescharacteristic
22#14519752—22no—
23#14519747—22no—
24C4⋊#92418C2212yescomplemented
25#14519700C2212yescomplemented
26#14519697C2212yes—
27#14519697C2212yes—
28#14519697C2212yescomplemented
29C22⋊#92418C2212yes—
30#14519688C2211yescharacteristic, complemented
31C4×#92418C2211yescharacteristic, complemented
32C4⋊Q8×C61C2211yescharacteristic, complemented
33#126×C61—22no—
34#125×C61—22no—
35#125×C61C2211yescharacteristic, complemented
36C22⋊Q8×C61C2212yes—
37C4×Q8×C61C2212yescomplemented
38#117×C61C2211yescharacteristic
39C23×D61—21no—
40C2×Q8×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—21no—
43#11758222—42no—
44C2×D244—21no—
45C2×D244—22no—
46C2×D244—22no—
47C2×D244—42no—
48C2×D244C2311yescharacteristic
49C2×D244C2311yescharacteristic
50C2×D244C2311yescharacteristic
51C2×C4×D61—21no—
52C2×Dic122C2311yescharacteristic
53C4⋊C4×C61—22no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—22no—
57C4⋊C4×C61D412yes—
58C4⋊C4×C61C2312yes—
59C22⋊C4×C61—22no—
60C22⋊C4×C61D412yes—
61C42×C61—22no—
62C42×C61C2311yescharacteristic
63C42×C61C2311yescharacteristic
64#11758202—42no—
65#11758201—42no—
66#11758201—42no—
67#11758201—42no—
68#11758198—22no—
69#11758198—22no—
70C2×#92418C2312yes—
71C2×#92418C2312yes—
72C23×C61C2×D411yescharacteristic
73C22×D61—21no—
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—42no—
77C22×D61—82no—
78Q8×C61—22no—
79Q8×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D412yes—
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C22⋊D61—42no—
88C2×Dic61—21no—
89D244—22no—
90D244—22no—
91D244—22no—
92D244—42no—
93D244—82no—
94D244—82no—
95C4×D61—42no—
96Dic122—22no—
97#92418—22no—
98#92418—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×C61—42no—
113C4×C61—42no—
114C4×C61H(5,𝔽2)12yes—
115Dic61—41no—
116#3222—611nomaximal, Sylow
117C2×C61—41no—
118C2×C61#53511yescharacteristic
119C2×C61#57712yes—
120D61—81no—
121D61—81no—
122D61—81no—
123#541D6111yescharacteristic, complemented
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#433—611no—
134C61#322211yescharacteristic, complemented, Sylow
135C2×#41—611no—
136C22×D4—611no—
137C2×Q16—612no—
138C2×SD16—612no—
139C2×SD16—612no—
140C2×SD16—612no—
141C4⋊Q8C2×D6111yescharacteristic, complemented
142#127—611no—
143#127—611no—
144#126—22no—
145#125—22no—
146#125C2×D6111yescharacteristic, complemented
147#124—611no—
148#124—611no—
149C22⋊Q8C2×D6112yes—
150#121—1222no—
151#120—1222no—
152C4×Q8C2×D6112yescomplemented
153#117C2×D6111yescharacteristic
154C4⋊C8—612no—
155#103—612no—
156#102—612no—
157#102—612no—
158#102—612no—
159C22⋊C8—612no—
160#97—611no—
161C4×C8—611no—
162C24—1221no—
163#41—2442no—
164C2×Q8—611no—
165C2×Q8C22×D6112yes—
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×C8—612no—
181C2×C8—612no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4C22⋊D6112yes—
187C4⋊C4C22×D6112yes—
188C22⋊C4—22no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4C22⋊D6112yes—
192C42—22no—
193C42C22×D6111yescharacteristic
194C42C22×D6111yescharacteristic
195C23—1221no—
196C23—1221no—
197C23—1221no—
198C23—4882no—
199C23—2442no—
200C23C2×C22⋊D6111yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—1222no—
204D4—1222no—
205D4—1222no—
206D4—1222no—
207D4—4882no—
208D4—4882no—
209D4—2442no—
210D4—2442no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—1221no—
215C2×C4—2442no—
216C2×C4C2×C22⋊D6112yes—
217C2×C4C2×C22⋊D6112yes—
218C2×C4C2×C22⋊D6111yescharacteristic
219C2×C4C23×D6111yescharacteristic
220C8—1222no—
221C8—1222no—
222C22—22no—
223C22—21no—
224C22—4884no—
225C22—2442no—
226C22—2442no—
227C22—2442no—
228C22—2441no—
229C22—2441no—
230C22—2441no—
231C22C22×C22⋊D6111yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—42no—
236C4—42no—
237C4—2441no—
238C4#1451982312yes—
239C2—41no—
240C2—4881no—
241C2—4881no—
242C2—4881no—
243C2#1684032611yescharacteristic
244C2#1684057012yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#541C2
socleC22×C61C22×D4
hypercenter#541D61
hypocenterC61#3222
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #16840154C2semidirect
3. #16840136C2semidirect
4. #16840128C2semidirect
5. #16840119C2semidirect
6. #16839984C2semidirect
7. #16839962C2semidirect
8. #16839922C2semidirect
9. #16839912C2semidirect
10. #16839823C2semidirect
11. C61×#541C2semidirect
14. C2×#11758202C22semidirect
17. C2×#11758201C22semidirect
24. C4⋊#92418C22semidirect
25. #14519700C22semidirect
28. #14519697C22semidirect
30. #14519688C22semidirect
31. C4×#92418C22semidirect
32. C4⋊Q8×C61C22semidirect
35. #125×C61C22semidirect
37. C4×Q8×C61C22semidirect
123. #541D61semidirect
134. C61#3222semidirect
141. C4⋊Q8C2×D61semidirect
146. #125C2×D61semidirect
152. C4×Q8C2×D61semidirect