Finite Group Databasebeta

← #21458616

Subgroups — #21458616

Order 7808.

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

normal subgroups only

This group has 384 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#16840498C211yesmaximal, characteristic, complemented
2#16840427C211yesmaximal, characteristic, complemented
3#16840120C212yesmaximal, complemented
4#16840050C212yesmaximal, complemented
5#16840044C211yesmaximal, characteristic, complemented
6#16839976C212yesmaximal, complemented
7#16839954C211yesmaximal, characteristic
8#16839892C211yesmaximal, characteristic, complemented
9#16839871C212yesmaximal, complemented
10C4×#11758190C211yesmaximal, characteristic, complemented
11C61×#486C211yesmaximal, characteristic, complemented
12C2×Q8×D61—21no—
13C2×#11758190C2211yescharacteristic
14C2×#11758199C2212yes—
15#14519776C2212yes—
16#14519764—21no—
17#14519764C2212yes—
18#14519758—22no—
19#14519755—22no—
20#14519753—21no—
21C4×Dic122C2211yescharacteristic
22C4×Dic122C2211yescharacteristic
23C4×D244C2211yescharacteristic
24D4×Dic61—21no—
25D4×Dic61C2212yes—
26#14519739C2212yes—
27#14519709C2211yescharacteristic
28#14519708C2212yes—
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519700C2212yes—
33#14519699C2211yescharacteristic
34#14519698C2212yes—
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—
45C22×Dic61—22no—
46Q8×D61—44no—
47C2×D244C2311yescharacteristic
48C2×C4×D61—21no—
49C2×C4×D61—22no—
50C2×Dic122—22no—
51C2×Dic122D411yescharacteristic
52C2×Dic122C2311yescharacteristic
53C2×C8×C61C2311yescharacteristic
54C2×C8×C61C2311yescharacteristic
55C4⋊C4×C61—21no—
56C4⋊C4×C61C2312yes—
57C42×C61C2311yescharacteristic
58C22⋊Dic61—22no—
59C22⋊Dic61—22no—
60C22⋊Dic61—22no—
61#11758199—24no—
62#11758198—21no—
63#11758198—22no—
64C4⋊Dic61D411yescharacteristic
65C4⋊Dic61C2311yescharacteristic
66C4⋊Dic61C2311yescharacteristic
67#11758196—21no—
68#11758196—22no—
69#11758196D412yes—
70C4×Dic61—21no—
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
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—82no—
89C2×Dic61C2×D412yes—
90C2×Dic61C2×D412yes—
91D244—21no—
92D244#4112yes—
93C4×D61—44no—
94C4×D61—42no—
95Dic122—22no—
96Dic122—21no—
97Dic122—21no—
98Dic122—44no—
99C8×C61—21no—
100C8×C61—21no—
101#92418—22no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61C22×D411yescharacteristic
106C2×D61—22no—
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—41no—
117Dic61—41no—
118Dic61—41no—
119#3373—611nomaximal, Sylow
120C2×C61—82no—
121C2×C61#54811yescharacteristic
122C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
123C2×C61#57711yescharacteristic
124D61—42no—
125#559—611no—
126D4×Q8—611no—
127#489—612no—
128#486D6111yescharacteristic, complemented
129#476—612no—
130#475—611no—
131#463—612no—
132#459—611no—
133#446—611no—
134#442—612no—
135C4×SD16—611no—
136C61#337311yescharacteristic, complemented, Sylow
137C22×Q8—1221no—
138C2×SD16—611no—
139C2×D8—612no—
140C4⋊Q8—612no—
141C4⋊Q8C2×D6111yescharacteristic
142#127C2×D6111yescharacteristic
143#124—612no—
144#124—1221no—
145#123—1222no—
146C22⋊Q8—1222no—
147C22⋊Q8—1221no—
148C4×Q8—611no—
149C4×Q8—611no—
150C4×D4—612no—
151C4×D4—612no—
152C4×D4—611no—
153C4×D4—1221no—
154#106—611no—
155#106—612no—
156C4⋊C8—612no—
157C4⋊C8—611no—
158#103—611no—
159#103—612no—
160#102—612no—
161#102—611no—
162#102C2×D6112yes—
163#102C2×D6112yes—
164#97—612no—
165C4×C8C2×D6111yescharacteristic
166C2×Q8—21no—
167C2×Q8—611no—
168C2×Q8—611no—
169C2×Q8—1222no—
170C2×Q8—2444no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—611no—
174C2×D4C22×D6112yes—
175C22×C4—1222no—
176C22×C4—1222no—
177C22×C4—1221no—
178SD16—1222no—
179D8—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—1221no—
190C4⋊C4C22×D6112yes—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C22⋊C4—1222no—
194C22⋊C4—1222no—
195C22⋊C4—1221no—
196C42—612no—
197C42—1221no—
198C42C22×D6111yescharacteristic
199C23—22no—
200C23—1221no—
201Q8—42no—
202Q8—1222no—
203Q8—1221no—
204Q8—1221no—
205Q8—2444no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—81no—
210D4—612no—
211D4—1221no—
212C2×C4—22no—
213C2×C4—612no—
214C2×C4—612no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—4882no—
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—1222no—
231C22—2441no—
232C22—2441no—
233C22C2×D4×D6111yescharacteristic
234C4—21no—
235C4—42no—
236C4—1222no—
237C4—1222no—
238C4—2441no—
239C4—2441no—
240C4—2441no—
241C4#1451980112yes—
242C4#41×D6111yescharacteristic
243C4#1451982411yescharacteristic
244C2—82no—
245C2—2442no—
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#3373
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. #16840498C2semidirect
2. #16840427C2semidirect
3. #16840120C2semidirect
4. #16840050C2semidirect
5. #16840044C2semidirect
6. #16839976C2semidirect
8. #16839892C2semidirect
9. #16839871C2semidirect
10. C4×#11758190C2semidirect
11. C61×#486C2semidirect
128. #486D61semidirect
136. C61#3373semidirect