Finite Group Databasebeta

← #21456417

Subgroups — #21456417

Order 7808.

408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840291C211yesmaximal, characteristic, complemented
3#16840168C211yesmaximal, characteristic, complemented
4#16840152C211yesmaximal, characteristic, complemented
5#16840127C211yesmaximal, characteristic, complemented
6#16840014C212yesmaximal, complemented
7#16840011C212yesmaximal, complemented
8#16839847C212yesmaximal, complemented
9#16839842C212yesmaximal, complemented
10#16839714C211yesmaximal, characteristic, complemented
11C61×#489C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×#11758201C2212yes—
14C2×#11758199C2212yes—
15C2×#11758189C2212yes—
16#14519774C2211yescharacteristic
17#14519770—21no—
18#14519769C2211yescharacteristic
19#14519766—21no—
20#14519759—21no—
21#14519753C2211yescharacteristic
22#14519752—21no—
23#14519752C2212yes—
24#14519748C2211yescharacteristic
25Q8×Dic61C2211yescharacteristic
26D4×Dic61C2211yescharacteristic
27#14519739—21no—
28#14519739C2212yes—
29#14519737—21no—
30#14519733—21no—
31C42×D61C2211yescharacteristic
32#14519710C2212yes—
33#14519708C2212yes—
34#14519699C2212yes—
35#14519699C2212yes—
36#14519688C2211yescharacteristic
37C8×Dic61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39#124×C61C2211yescharacteristic
40#103×C61C2212yes—
41#102×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45C2×D4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C22×Dic61—21no—
48#11758226—44no—
49C2×D244—22no—
50C2×D244—21no—
51C2×D244—21no—
52C2×D244C2312yes—
53C2×C4×D61—22no—
54C2×C4×D61D411yescharacteristic
55C2×C4×D61D411yescharacteristic
56C2×C4×D61C2311yescharacteristic
57C2×C8×C61C2312yes—
58C4⋊C4×C61—21no—
59C4⋊C4×C61C2312yes—
60C22⋊C4×C61—21no—
61C22⋊C4×C61—21no—
62C42×C61C2311yescharacteristic
63C22⋊Dic61—21no—
64C22⋊Dic61—21no—
65#11758201—24no—
66#11758199—24no—
67#11758198—21no—
68#11758198—22no—
69#11758198—22no—
70C4⋊Dic61—21no—
71C4⋊Dic61C2311yescharacteristic
72C4⋊Dic61C2311yescharacteristic
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76C4×Dic61—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81#11758189—24no—
82C23×C61—21no—
83C22×D61—22no—
84C22×D61C2×D411yescharacteristic
85Q8×C61—22no—
86Q8×C61—42no—
87D4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—42no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—42no—
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100D244—22no—
101D244—22no—
102D244—42no—
103D244—42no—
104D244—44no—
105C4×D61—22no—
106C4×D61—22no—
107C4×D61—41no—
108C4×D61—44no—
109C8×C61—22no—
110#92418#4114yescomplemented
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61C22×D411yescharacteristic
115C2×D61—21no—
116C2×D61—21no—
117C2×D61—21no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—42no—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—41no—
124C4×C61—42no—
125C4×C61C2×#4112yes—
126Dic61—21no—
127Dic61—21no—
128Dic61—41no—
129Dic61—41no—
130Dic61AGL(1,ℤ/8)12yes—
131#3171—611nomaximal, Sylow
132C2×C61—81no—
133C2×C61#53211yescharacteristic
134C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
135C2×C61#57511yescharacteristic
136D61—41no—
137D61—82no—
138#532—611no—
139#529—611no—
140#501—611no—
141#496—611no—
142#490—611no—
143#489D6111yescharacteristic, complemented
144#469—612no—
145#468—612no—
146C4×SD16—612no—
147C4×D8—612no—
148C4×M16—611no—
149C61#317111yescharacteristic, complemented, Sylow
150C2×#41—1221no—
151C2×SD16—612no—
152C2×D8—612no—
153C2×M16—612no—
154C4⋊Q8C2×D6111yescharacteristic
155#127—611no—
156#126—1221no—
157#125—611no—
158#124—1221no—
159#124C2×D6111yescharacteristic
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#107—612no—
173#106—612no—
174#103C2×D6112yes—
175#102—612no—
176#102—612no—
177#102C2×D6112yes—
178#97—611no—
179#97C2×D6111yescharacteristic
180C4×C8—612no—
181#41—2444no—
182C2×Q8—21no—
183C2×Q8C22×D6111yescharacteristic
184C2×D4—612no—
185C2×D4—1222no—
186C2×D4—1221no—
187C2×D4—1221no—
188C2×D4—1221no—
189C2×D4C22×D6111yescharacteristic
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—1222no—
194C22×C4—1221no—
195SD16—1224no—
196D8—1224no—
197M16—1224no—
198C2×C8—612no—
199C2×C8C22×D6112yes—
200C4⋊C4—21no—
201C4⋊C4—611no—
202C4⋊C4—611no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4C22×D6112yes—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—1222no—
211C22⋊C4—1222no—
212C22⋊C4—1221no—
213C22⋊C4—1221no—
214C22⋊C4—1221no—
215C42—611no—
216C42—611no—
217C42—611no—
218C42—1221no—
219C42C22×D6111yescharacteristic
220C23—21no—
221C23—611no—
222C23—1222no—
223Q8—22no—
224Q8—42no—
225D4—22no—
226D4—1222no—
227D4—1222no—
228D4—2442no—
229D4—2442no—
230D4—2444no—
231D4—2442no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—2441no—
242C2×C4—2444no—
243C2×C4—2442no—
244C2×C4D4×D6111yescharacteristic
245C2×C4D4×D6111yescharacteristic
246C2×C4C23×D6111yescharacteristic
247C8—22no—
248C8—614no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—1221no—
253C22—1221no—
254C22—1221no—
255C22—2442no—
256C22—2442no—
257C22—2442no—
258C22C2×D4×D6111yescharacteristic
259C4—21no—
260C4—21no—
261C4—42no—
262C4—41no—
263C4—612no—
264C4—1221no—
265C4—1221no—
266C4—2441no—
267C4—2441no—
268C4#41×D6112yes—
269C2—81no—
270C2—4882no—
271C2—2441no—
272C2#1684031111yescharacteristic
273C2AGL(1,ℤ/8)×D6111yescharacteristic
274C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#489C2
socleC22×C61C22×D4
hypercenter#489D61
hypocenterC61#3171
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #16840291C2semidirect
3. #16840168C2semidirect
4. #16840152C2semidirect
5. #16840127C2semidirect
6. #16840014C2semidirect
7. #16840011C2semidirect
8. #16839847C2semidirect
9. #16839842C2semidirect
10. #16839714C2semidirect
11. C61×#489C2semidirect
110. #92418#41semidirect
143. #489D61semidirect
149. C61#3171semidirect