Finite Group Databasebeta

← #21458484

Subgroups — #21458484

Order 7808.

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

normal subgroups only

This group has 362 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#16840473C211yesmaximal, characteristic, complemented
3#16840115C212yesmaximal, complemented
4#16840064C212yesmaximal, complemented
5#16840054C211yesmaximal, characteristic, complemented
6#16839976C212yesmaximal, complemented
7#16839954C211yesmaximal, characteristic
8C8×Dic122C211yesmaximal, characteristic, complemented
9C4×#11758190C211yesmaximal, characteristic, complemented
10#16839842C212yesmaximal, complemented
11C61×#486C211yesmaximal, characteristic, complemented
12C2×#11758190C2211yescharacteristic
13C2×#11758199C2212yes—
14#14519768C2212yes—
15#14519764—21no—
16#14519764C2212yes—
17#14519758—22no—
18#14519757—21no—
19#14519753—22no—
20C4×Dic122C2211yescharacteristic
21C4×Dic122C2211yescharacteristic
22C4×D244C2211yescharacteristic
23D4×Dic61—21no—
24D4×Dic61C2212yes—
25#14519739C2212yes—
26C4⋊C4×D61—21no—
27#14519710C2212yes—
28#14519709C2211yescharacteristic
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519700C2212yes—
33#14519699C2211yescharacteristic
34#14519698C2212yes—
35C8×Dic61C2212yes—
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—
46C2×D244C2311yescharacteristic
47C2×C4×D61—21no—
48C2×C4×D61—22no—
49C2×Dic122D411yescharacteristic
50C2×Dic122C2311yescharacteristic
51C2×C8×C61C2311yescharacteristic
52C2×C8×C61C2311yescharacteristic
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2312yes—
55C42×C61C2311yescharacteristic
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58C22⋊Dic61—22no—
59#11758199—24no—
60#11758198—21no—
61#11758198—22no—
62C4⋊Dic61—22no—
63C4⋊Dic61D411yescharacteristic
64C4⋊Dic61C2311yescharacteristic
65C4⋊Dic61C2311yescharacteristic
66#11758196—21no—
67#11758196—22no—
68#11758196D412yes—
69C4×Dic61—21no—
70C4×Dic61C2312yes—
71C2×#92418C2312yes—
72#11758190—22no—
73C23×C61—22no—
74C22×D61—21no—
75Q8×C61—81no—
76D4×C61—22no—
77D4×C61—22no—
78D4×C61—42no—
79D4×C61—81no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2411yescharacteristic
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—82no—
88C2×Dic61C2×D412yes—
89C2×Dic61C2×D412yes—
90D244—21no—
91D244#4112yes—
92C4×D61—42no—
93C4×D61—82no—
94Dic122—22no—
95Dic122—21no—
96Dic122—21no—
97C8×C61—21no—
98C8×C61—21no—
99#92418—22no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61C22×D411yescharacteristic
104C2×D61—22no—
105C2×D61—41no—
106C2×D61—41no—
107C4×C61—21no—
108C4×C61—42no—
109C4×C61#13512yes—
110C4×C61C2×#4111yescharacteristic
111C4×C612−1+411yescharacteristic
112Dic61—22no—
113Dic61—22no—
114Dic61—41no—
115Dic61—41no—
116Dic61—41no—
117#3361—611nomaximal, Sylow
118C2×C61—82no—
119C2×C61#54811yescharacteristic
120C2×C61C2×#13511yescharacteristic
121C2×C61#57611yescharacteristic
122D61—42no—
123#559—611no—
124#554—611no—
125#488—612no—
126#486D6111yescharacteristic, complemented
127#478—612no—
128#477—611no—
129#463—612no—
130#459—611no—
131C8×Q8—611no—
132C4×SD16—611no—
133C4×D8—612no—
134C61#336111yescharacteristic, complemented, Sylow
135C2×SD16—611no—
136C2×D8—612no—
137C4⋊Q8C2×D6111yescharacteristic
138#127C2×D6111yescharacteristic
139#125—612no—
140#124—612no—
141#124—1221no—
142#123—1222no—
143C22⋊Q8—1221no—
144C22⋊Q8—1222no—
145C4×Q8—611no—
146C4×Q8—611no—
147C4×D4—612no—
148C4×D4—612no—
149C4×D4—611no—
150C4×D4—1221no—
151C2×C4⋊C4—1221no—
152#107—612no—
153#106—611no—
154C4⋊C8—612no—
155C4⋊C8—611no—
156#103—611no—
157#103—612no—
158#102—612no—
159#102—611no—
160#102C2×D6112yes—
161#102C2×D6112yes—
162C4×C8—612no—
163C4×C8C2×D6111yescharacteristic
164C2×Q8—21no—
165C2×Q8—611no—
166C2×Q8—611no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—611no—
170C2×D4C22×D6112yes—
171C22×C4—1222no—
172C22×C4—1222no—
173C22×C4—1221no—
174SD16—1222no—
175D8—1224no—
176C2×C8—612no—
177C2×C8C22×D6111yescharacteristic
178C2×C8C22×D6111yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—611no—
181C4⋊C4—612no—
182C4⋊C4—611no—
183C4⋊C4—611no—
184C4⋊C4—1222no—
185C4⋊C4—1222no—
186C4⋊C4—1221no—
187C4⋊C4C22×D6112yes—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4—1222no—
192C22⋊C4—1221no—
193C42—612no—
194C42—1221no—
195C42C22×D6111yescharacteristic
196C23—22no—
197C23—1221no—
198Q8—81no—
199Q8—1222no—
200Q8—1221no—
201Q8—1221no—
202D4—22no—
203D4—22no—
204D4—42no—
205D4—81no—
206D4—612no—
207D4—1221no—
208C2×C4—22no—
209C2×C4—612no—
210C2×C4—612no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—4882no—
215C2×C4—4882no—
216C2×C4—2442no—
217C2×C4D4×D6111yescharacteristic
218C2×C4D4×D6111yescharacteristic
219C2×C4C23×D6111yescharacteristic
220C8—21no—
221C8—21no—
222C8—1222no—
223C22—42no—
224C22—42no—
225C22—42no—
226C22—1222no—
227C22—2441no—
228C22—2441no—
229C22C2×D4×D6111yescharacteristic
230C4—21no—
231C4—42no—
232C4—1222no—
233C4—1222no—
234C4—2441no—
235C4—2441no—
236C4—2441no—
237C4#1451979812yes—
238C4#41×D6111yescharacteristic
239C4#1451982411yescharacteristic
240C2—82no—
241C2—2442no—
242C2#1684042011yescharacteristic
243C2C2×#1451979811yescharacteristic
244C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3361
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. #16840473C2semidirect
3. #16840115C2semidirect
4. #16840064C2semidirect
5. #16840054C2semidirect
6. #16839976C2semidirect
8. C8×Dic122C2semidirect
9. C4×#11758190C2semidirect
10. #16839842C2semidirect
11. C61×#486C2semidirect
126. #486D61semidirect
134. C61#3361semidirect