Finite Group Databasebeta

← #21458553

Subgroups — #21458553

Order 7808.

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

normal subgroups only

This group has 382 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#16840487C211yesmaximal, characteristic, complemented
2#16840432C211yesmaximal, characteristic
3#16840125C212yesmaximal, complemented
4#16840064C212yesmaximal, complemented
5#16840039C211yesmaximal, characteristic, complemented
6#16839961C212yesmaximal, complemented
7#16839959C211yesmaximal, characteristic, complemented
8#16839892C211yesmaximal, characteristic, complemented
9#16839859C212yesmaximal, complemented
10C4×#11758190C211yesmaximal, characteristic, complemented
11C61×#486C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C2×#11758190C2211yescharacteristic
14C2×#11758200C2212yes—
15#14519775—21no—
16#14519773C2212yes—
17#14519768C2212yes—
18#14519767—22no—
19#14519749—22no—
20#14519748—21no—
21Q8×Dic61—21no—
22C4×Dic122C2211yescharacteristic
23C4×Dic122C2211yescharacteristic
24#14519742C2212yes—
25C4×D244C2211yescharacteristic
26D4×Dic61C2212yes—
27#14519710C2212yes—
28#14519709C2211yescharacteristic
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519699C2211yescharacteristic
33#14519698C2212yes—
34#14519697C2212yes—
35#14519687C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37#127×C61C2211yescharacteristic
38#102×C61C2212yes—
39#102×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61C2312yes—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C22×Dic61—22no—
48#11758224—44no—
49C2×D244C2311yescharacteristic
50C2×C4×D61—21no—
51C2×Dic122D411yescharacteristic
52C2×Dic122C2311yescharacteristic
53C2×C8×C61C2311yescharacteristic
54C2×C8×C61C2311yescharacteristic
55C4⋊C4×C61—21no—
56C4⋊C4×C61C2312yes—
57C42×C61C2311yescharacteristic
58C22⋊Dic61—22no—
59#11758200—24no—
60#11758198—21no—
61C4⋊Dic61—22no—
62C4⋊Dic61D411yescharacteristic
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2311yescharacteristic
65#11758196—21no—
66#11758196—22no—
67#11758196—22no—
68#11758196D412yes—
69C4×Dic61—21no—
70C4×Dic61—22no—
71C4×Dic61C2312yes—
72C2×#92418C2312yes—
73#11758190—22no—
74C23×C61—22no—
75C22×D61—21no—
76Q8×C61—42no—
77D4×C61—22no—
78D4×C61—22no—
79D4×C61—42no—
80D4×C61—81no—
81C2×C4×C61—22no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C22⋊D61—44no—
86C22⋊D61—82no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—44no—
91C2×Dic61C2×D412yes—
92C2×Dic61C2×D412yes—
93D244—21no—
94D244—21no—
95C4×D61—42no—
96Dic122—22no—
97Dic122—21no—
98Dic122#4112yescomplemented
99C8×C61—21no—
100C8×C61—21no—
101#92418—22no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61C22×D411yescharacteristic
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—41no—
109C4×C61—21no—
110C4×C61—42no—
111C4×C61AGL(1,ℤ/8)12yes—
112C4×C61C2×#4111yescharacteristic
113C4×C612−1+411yescharacteristic
114Dic61—22no—
115Dic61—22no—
116Dic61—22no—
117Dic61—41no—
118Dic61—41no—
119#3368—611nomaximal, Sylow
120C2×C61—82no—
121C2×C61#54811yescharacteristic
122C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
123C2×C61#57711yescharacteristic
124D61—81no—
125#557—611no—
126#550—611no—
127#490—612no—
128#486D6111yescharacteristic, complemented
129#478—612no—
130#474—611no—
131#460—611no—
132#460—612no—
133#446—611no—
134#440—612no—
135C4×SD16—611no—
136C61#336811yescharacteristic, complemented, Sylow
137C2×#41—1221no—
138C2×SD16—612no—
139C2×SD16—611no—
140C4⋊Q8—1221no—
141C4⋊Q8C2×D6111yescharacteristic
142#127—612no—
143#127C2×D6111yescharacteristic
144#125—612no—
145#125—1222no—
146#121—1221no—
147#121—1222no—
148C4×Q8—611no—
149C4×Q8—612no—
150C4×Q8—611no—
151C4×Q8—1221no—
152C4×D4—612no—
153C4×D4—611no—
154#107—612no—
155#106—611no—
156C4⋊C8—612no—
157C4⋊C8—611no—
158#103—611no—
159#102—612no—
160#102—611no—
161#102—612no—
162#102C2×D6112yes—
163#102C2×D6112yes—
164#97—612no—
165C4×C8C2×D6111yescharacteristic
166#41—2444no—
167C2×Q8—21no—
168C2×Q8—611no—
169C2×Q8—611no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—611no—
173C2×D4—1222no—
174C2×D4—1222no—
175C2×D4C22×D6112yes—
176C22×C4—1222no—
177C22×C4—1221no—
178SD16—1222no—
179SD16—1224no—
180C2×C8—612no—
181C2×C8C22×D6111yescharacteristic
182C2×C8C22×D6111yescharacteristic
183C4⋊C4—21no—
184C4⋊C4—612no—
185C4⋊C4—611no—
186C4⋊C4—611no—
187C4⋊C4—611no—
188C4⋊C4—1222no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1221no—
192C4⋊C4C22×D6112yes—
193C22⋊C4—1222no—
194C22⋊C4—1221no—
195C42—612no—
196C42—1222no—
197C42—1221no—
198C42C22×D6111yescharacteristic
199C23—22no—
200C23—1221no—
201Q8—42no—
202Q8—612no—
203Q8—1221no—
204Q8—1222no—
205D4—22no—
206D4—22no—
207D4—42no—
208D4—81no—
209D4—1221no—
210D4—1221no—
211D4—4882no—
212D4—2444no—
213C2×C4—22no—
214C2×C4—612no—
215C2×C4—612no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—2444no—
220C2×C4—2442no—
221C2×C4D4×D6111yescharacteristic
222C2×C4D4×D6111yescharacteristic
223C2×C4C23×D6111yescharacteristic
224C8—21no—
225C8—21no—
226C8—1222no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—2441no—
231C22—2441no—
232C22—2441no—
233C22C2×D4×D6111yescharacteristic
234C4—21no—
235C4—42no—
236C4—1222no—
237C4—1222no—
238C4—1222no—
239C4—2441no—
240C4—2441no—
241C4#1451980112yes—
242C4#41×D6111yescharacteristic
243C4#1451982411yescharacteristic
244C2—82no—
245C2—4881no—
246C2#1684042011yescharacteristic
247C2C2×#1451980111yescharacteristic
248C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3368
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16840487C2semidirect
3. #16840125C2semidirect
4. #16840064C2semidirect
5. #16840039C2semidirect
6. #16839961C2semidirect
7. #16839959C2semidirect
8. #16839892C2semidirect
9. #16839859C2semidirect
10. C4×#11758190C2semidirect
11. C61×#486C2semidirect
98. Dic122#41semidirect
128. #486D61semidirect
136. C61#3368semidirect