Finite Group Databasebeta

← #21456691

Subgroups — #21456691

Order 7808.

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

normal subgroups only

This group has 410 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#16840333C211yesmaximal, characteristic, complemented
2#16840103C212yesmaximal, complemented
3#16840083C212yesmaximal, complemented
4#16840006C212yesmaximal, complemented
5#16839989C212yesmaximal, complemented
6#16839913C212yesmaximal, complemented
7#16839900C212yesmaximal, complemented
8#16839729C211yesmaximal, characteristic, complemented
9C61×#535C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic, complemented
11C2×#11758200C2212yes—
12C2×#11758200C2212yes—
13C2×#11758194C2211yescharacteristic, complemented
14C22×#92418C2211yescharacteristic, complemented
15#14519775—21no—
16#14519764—21no—
17#14519758—21no—
18#14519758—21no—
19#14519756C2212yes—
20#14519756C2212yescomplemented
21#14519736C2211yescharacteristic, complemented
22#14519710C2212yescomplemented
23#14519708C2212yescomplemented
24#14519700C2212yescomplemented
25#14519700C2212yescomplemented
26#14519698C2212yes—
27#14519698C2212yes—
28C22⋊#92418C2212yes—
29C22⋊#92418C2212yescomplemented
30C2×#41×C61C2211yescharacteristic
31C22×D4×C61C2211yescharacteristic
32#127×C61—21no—
33#124×C61—21no—
34#121×C61C2212yes—
35#121×C61C2212yes—
36#120×C61—21no—
37#120×C61—21no—
38#117×C61C2211yescharacteristic
39C24×C61—21no—
40#41×C61—41no—
41#41×C61—41no—
42C2×Q8×C61D411yescharacteristic
43C2×D4×C61—22no—
44C2×D4×C61—22no—
45C2×D4×C61—21no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×D4×C61D411yescharacteristic
49C2×D4×C61D411yescharacteristic
50C2×D4×C61D411yescharacteristic
51C2×D4×C61C2312yes—
52C22×C4×C61C2311yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×Dic61—21no—
56C2×Dic122—21no—
57C2×Dic122—41no—
58C2×Dic122—41no—
59C2×Dic122C2312yes—
60C4⋊C4×C61C2312yes—
61C22⋊C4×C61—21no—
62C22⋊C4×C61—22no—
63C22⋊C4×C61—22no—
64C42×C61—21no—
65C22⋊Dic61—21no—
66C22⋊Dic61—22no—
67C22⋊Dic61—22no—
68#11758200—42no—
69#11758200—42no—
70C4⋊Dic61C2312yes—
71#11758196—22no—
72#11758196—22no—
73C4×Dic61—21no—
74#11758194—41no—
75C2×#92418—41no—
76C2×#92418C2312yes—
77C2×#92418C2312yes—
78C23×C61—22no—
79C23×C61—42no—
80C23×C61—82no—
81C23×C61C2×D411yescharacteristic
82C23×C61C2×D411yescharacteristic
83C23×C61C2×D411yescharacteristic
84Q8×C61—41no—
85D4×C61—22no—
86D4×C61—22no—
87D4×C61—41no—
88D4×C61—41no—
89D4×C61—41no—
90D4×C61—42no—
91D4×C61—82no—
92D4×C61—82no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2411yescharacteristic
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—42no—
107Dic122—22no—
108Dic122—22no—
109Dic122—42no—
110#92418—22no—
111#92418—22no—
112C22×C61—21no—
113C22×C61—21no—
114C22×C61—21no—
115C22×C61—22no—
116C22×C61—22no—
117C22×C61—22no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—84no—
122C22×C61C22×D411yescharacteristic
123C4×C61—21no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—42no—
127C4×C61H(5,𝔽2)11yescharacteristic
128C4×C61H(5,𝔽2)11yescharacteristic
129Dic61—42no—
130Dic61—42no—
131#3200—611nomaximal, Sylow
132C2×C61—41no—
133C2×C61—41no—
134C2×C61—41no—
135C2×C61—82no—
136C2×C61#53411yescharacteristic
137C2×C61#57712yes—
138#536—611no—
139#535D6111yescharacteristic
140#485—612no—
141#482—612no—
142#468—612no—
143#465—612no—
144#450—612no—
145#448—612no—
146#408—611no—
147C61#320011yescharacteristic, complemented, Sylow
148C2×#41C2×D6111yescharacteristic
149C22×Q8—611no—
150C22×D4C2×D6111yescharacteristic
151C2×SD16—612no—
152C2×SD16—612no—
153C2×M16—611no—
154C22×C8—611no—
155C4⋊Q8—1221no—
156#127—21no—
157#124—21no—
158#124—1221no—
159#123—1221no—
160#123—1221no—
161C22⋊Q8—612no—
162C22⋊Q8—612no—
163#121C2×D6112yes—
164#121C2×D6112yes—
165#120—21no—
166#120—21no—
167#117—611no—
168#117C2×D6111yescharacteristic
169#107—612no—
170#106—612no—
171#103—612no—
172#103—612no—
173#102—612no—
174#102—612no—
175C22⋊C8—612no—
176C22⋊C8—612no—
177C24—21no—
178#41—41no—
179#41—41no—
180C2×Q8—612no—
181C2×Q8—1221no—
182C2×Q8—2441no—
183C2×Q8—2441no—
184C2×Q8C22⋊D6111yescharacteristic
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4C22⋊D6111yescharacteristic
191C2×D4C22⋊D6111yescharacteristic
192C2×D4C22⋊D6111yescharacteristic
193C2×D4C22×D6112yes—
194C22×C4—1221no—
195C22×C4C22×D6111yescharacteristic
196C22×C4C22×D6111yescharacteristic
197C22×C4C22×D6111yescharacteristic
198SD16—2442no—
199SD16—2442no—
200M16—2441no—
201C2×C8—612no—
202C2×C8—612no—
203C2×C8—2441no—
204C4⋊C4—612no—
205C4⋊C4—1222no—
206C4⋊C4—1222no—
207C4⋊C4C22×D6112yes—
208C22⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—22no—
211C22⋊C4—1221no—
212C22⋊C4—1222no—
213C22⋊C4—1222no—
214C42—21no—
215C42—1221no—
216C23—22no—
217C23—42no—
218C23—82no—
219C23C2×C22⋊D6111yescharacteristic
220C23C2×C22⋊D6111yescharacteristic
221C23C2×C22⋊D6111yescharacteristic
222Q8—41no—
223Q8—1222no—
224Q8—1222no—
225Q8—2442no—
226D4—22no—
227D4—22no—
228D4—41no—
229D4—41no—
230D4—41no—
231D4—42no—
232D4—82no—
233D4—82no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—2442no—
244C2×C4C2×C22⋊D6111yescharacteristic
245C2×C4C2×C22⋊D6111yescharacteristic
246C2×C4C2×C22⋊D6111yescharacteristic
247C2×C4C23×D6111yescharacteristic
248C8—1222no—
249C8—1222no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—84no—
260C22C22×C22⋊D6111yescharacteristic
261C4—21no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—2442no—
266C4—2442no—
267C4#1451982211yescharacteristic
268C4#1451982211yescharacteristic
269C2—41no—
270C2—41no—
271C2—41no—
272C2—82no—
273C2#1684032111yescharacteristic
274C2#1684057312yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#535C2
socleC22×C61C22×D4
hypercenter#535D61
hypocenterC61#3200
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #16840333C2semidirect
2. #16840103C2semidirect
3. #16840083C2semidirect
4. #16840006C2semidirect
5. #16839989C2semidirect
6. #16839913C2semidirect
7. #16839900C2semidirect
8. #16839729C2semidirect
10. C22×Dic122C22semidirect
13. C2×#11758194C22semidirect
14. C22×#92418C22semidirect
20. #14519756C22semidirect
21. #14519736C22semidirect
22. #14519710C22semidirect
23. #14519708C22semidirect
24. #14519700C22semidirect
25. #14519700C22semidirect
29. C22⋊#92418C22semidirect
147. C61#3200semidirect