Finite Group Databasebeta

← #21456519

Subgroups — #21456519

Order 7808.

410 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 119 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#16840313C211yesmaximal, characteristic, complemented
2#16840297C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840128C211yesmaximal, characteristic, complemented
5#16840124C211yesmaximal, characteristic, complemented
6#16839999C212yesmaximal, complemented
7#16839992C212yesmaximal, complemented
8#16839873C212yesmaximal, complemented
9#16839861C212yesmaximal, complemented
10#97×D61C211yesmaximal, characteristic, complemented
11C61×#501C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×#11758190C2212yes—
14C2×D488C2212yes—
15C2×C8×D61C2212yes—
16#14519774C2211yescharacteristic
17#14519772—21no—
18#14519766—21no—
19#14519765C2211yescharacteristic
20#14519762—21no—
21#14519757C2211yescharacteristic
22#14519752—21no—
23#14519752C2212yes—
24#14519752C2211yescharacteristic
25#14519742C2211yescharacteristic
26#14519739—21no—
27#14519739—21no—
28#14519739C2211yescharacteristic
29#14519739C2212yes—
30#14519735—21no—
31C42×D61C2211yescharacteristic
32#14519700C2212yes—
33#14519697C2212yes—
34#14519697C2212yes—
35#14519697C2212yes—
36#14519688C2211yescharacteristic
37#14519687C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39#125×C61C2211yescharacteristic
40#107×C61C2212yes—
41#106×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44#11758226—44no—
45C2×D244—22no—
46C2×D244—21no—
47C2×D244—21no—
48C2×D244—21no—
49C2×D244C2311yescharacteristic
50C2×D244C2312yes—
51C2×C4×D61—22no—
52C2×C4×D61—21no—
53C2×C4×D61D411yescharacteristic
54C2×C4×D61D411yescharacteristic
55C2×C4×D61C2311yescharacteristic
56C2×Dic122C2311yescharacteristic
57C2×C8×C61C2312yes—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61—21no—
61C4⋊C4×C61C2311yescharacteristic
62C4⋊C4×C61C2312yes—
63C4⋊C4×C61C2311yescharacteristic
64C42×C61C2311yescharacteristic
65#11758198—21no—
66#11758198—21no—
67#11758198—21no—
68#11758198—21no—
69#11758198—22no—
70#11758198—22no—
71#11758198—21no—
72C4⋊Dic61—21no—
73#11758196—21no—
74C4×Dic61—21no—
75C4×Dic61D411yescharacteristic
76C4×Dic61D411yescharacteristic
77C4×Dic61C2311yescharacteristic
78C2×#92418C2312yes—
79D488—24no—
80#11758190—24no—
81C8×D61—24no—
82C22×D61—21no—
83C22×D61—22no—
84C22×D61C2×D411yescharacteristic
85Q8×C61—42no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2411yescharacteristic
92C2×Dic61—21no—
93C2×Dic61C2×D411yescharacteristic
94C2×Dic61C2×D411yescharacteristic
95C2×Dic61C2×D411yescharacteristic
96D244—22no—
97D244—22no—
98D244—22no—
99D244—42no—
100D244—42no—
101D244—42no—
102D244—44no—
103C4×D61—22no—
104C4×D61—22no—
105C4×D61—41no—
106C4×D61—42no—
107C4×D61—44no—
108Dic122—22no—
109C8×C61#4114yescomplemented
110#92418—22no—
111C22×C61C22×D411yescharacteristic
112C2×D61—21no—
113C2×D61—21no—
114C2×D61—42no—
115C2×D61—41no—
116C2×D61—42no—
117C2×D61—41no—
118C2×D61—41no—
119C2×D61—42no—
120C2×D61AGL(1,ℤ/8)12yes—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—42no—
124C4×C61—41no—
125C4×C61—41no—
126C4×C61C2×#4112yes—
127Dic61—21no—
128Dic61—21no—
129Dic61—21no—
130Dic61—41no—
131#3180—611nomaximal, Sylow
132C2×C61#53211yescharacteristic
133C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
134C2×C61#57511yescharacteristic
135D61—22no—
136D61—82no—
137D61—81no—
138#532—611no—
139#529—611no—
140#501D6111yescharacteristic, complemented
141#496—611no—
142#490—611no—
143#489—611no—
144#466—612no—
145#465—612no—
146#442—612no—
147#440—612no—
148C2×#97—611no—
149C61#318011yescharacteristic, complemented, Sylow
150C2×#41—1221no—
151C2×SD16—612no—
152C2×D8—612no—
153C22×C8—612no—
154C4⋊Q8C2×D6111yescharacteristic
155#127—611no—
156#126—1221no—
157#125C2×D6111yescharacteristic
158#124—611no—
159#124—1221no—
160#123—1221no—
161C22⋊Q8—611no—
162#121—611no—
163#121—612no—
164#121—1221no—
165C4×Q8—611no—
166C4×D4—611no—
167C4×D4—612no—
168C4×D4—1221no—
169C4×D4—1221no—
170#117—1221no—
171C2×C42—611no—
172#107C2×D6112yes—
173#106C2×D6112yes—
174#103—612no—
175#102—612no—
176#102—612no—
177#102—612no—
178#97—612no—
179#97—611no—
180#97C2×D6111yescharacteristic
181#41—2444no—
182C2×Q8—21no—
183C2×Q8—611no—
184C2×D4—611no—
185C2×D4—612no—
186C2×D4—1221no—
187C2×D4—1222no—
188C2×D4—1221no—
189C2×D4—1221no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—1221no—
194C22×C4—1222no—
195SD16—1224no—
196D8—1224no—
197C2×C8—612no—
198C2×C8—1224no—
199C2×C8C22×D6112yes—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4C22×D6111yescharacteristic
206C4⋊C4C22×D6111yescharacteristic
207C4⋊C4C22×D6112yes—
208C22⋊C4—1221no—
209C22⋊C4—1222no—
210C22⋊C4—1221no—
211C22⋊C4—1222no—
212C22⋊C4—1221no—
213C22⋊C4—1221no—
214C22⋊C4—1221no—
215C42—611no—
216C42—611no—
217C42—611no—
218C42—1221no—
219C42C22×D6111yescharacteristic
220C23—611no—
221C23—1221no—
222C23—1222no—
223Q8—42no—
224Q8—1222no—
225D4—1222no—
226D4—1222no—
227D4—1222no—
228D4—2442no—
229D4—2442no—
230D4—2442no—
231D4—2444no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1221no—
241C2×C4—2441no—
242C2×C4—2442no—
243C2×C4—2444no—
244C2×C4D4×D6111yescharacteristic
245C2×C4D4×D6111yescharacteristic
246C2×C4C23×D6111yescharacteristic
247C8—1222no—
248C8#1175822614yescomplemented
249C22—612no—
250C22—1221no—
251C22—1221no—
252C22—2442no—
253C22—2441no—
254C22—2441no—
255C22—2442no—
256C22—2441no—
257C22—2442no—
258C22C2×D4×D6111yescharacteristic
259C4—21no—
260C4—21no—
261C4—42no—
262C4—41no—
263C4—41no—
264C4—1221no—
265C4—1221no—
266C4—1221no—
267C4—2441no—
268C4C2×#1175822612yes—
269C2—1222no—
270C2—4882no—
271C2—4881no—
272C2#1684031311yescharacteristic
273C2AGL(1,ℤ/8)×D6111yescharacteristic
274C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#501C2
socleC22×C61C22×D4
hypercenter#501D61
hypocenterC61#3180
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #16840297C2semidirect
3. #16840151C2semidirect
4. #16840128C2semidirect
5. #16840124C2semidirect
6. #16839999C2semidirect
7. #16839992C2semidirect
8. #16839873C2semidirect
9. #16839861C2semidirect
10. #97×D61C2semidirect
11. C61×#501C2semidirect
109. C8×C61#41semidirect
140. #501D61semidirect
149. C61#3180semidirect
248. C8#11758226semidirect