Finite Group Databasebeta

← #21458472

Subgroups — #21458472

Order 7808.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840486C211yesmaximal, characteristic, complemented
2#16840469C211yesmaximal, characteristic, complemented
3#16840118C212yesmaximal, complemented
4#16840112C211yesmaximal, characteristic, complemented
5#16840067C212yesmaximal, complemented
6#16840053C211yesmaximal, characteristic, complemented
7#16839979C212yesmaximal
8#16839886C211yesmaximal, characteristic, complemented
9SD16×Dic61C212yesmaximal, complemented
10C4×#11758199C211yesmaximal, characteristic
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758199C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519772—22no—
15#14519768C2212yes—
16#14519766C2212yes—
17#14519757—21no—
18#14519756—21no—
19#14519754—22no—
20Q8×Dic61C2212yes—
21C4×Dic122C2211yescharacteristic
22C4×D244C2211yescharacteristic
23D4×Dic61C2212yes—
24#14519735—21no—
25C2×C4⋊Dic61—21no—
26#14519710C2211yescharacteristic
27#14519709C2212yes—
28#14519706C2212yes—
29#14519701C2212yes—
30#14519701C2212yes—
31#14519699C2212yes—
32#14519698C2211yescharacteristic
33#14519697C2211yescharacteristic
34C4×#92418C2211yescharacteristic
35C8×Dic61C2212yes—
36C2×SD16×C61C2212yes—
37C4⋊Q8×C61C2211yescharacteristic
38C4×D4×C61C2211yescharacteristic
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61C2312yes—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C22×Dic61—22no—
45C2×D244C2311yescharacteristic
46C2×C4×D61—21no—
47C2×Dic122—21no—
48C2×Dic122D411yescharacteristic
49SD16×C61—24no—
50C2×C8×C61C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61C2311yescharacteristic
54C22⋊C4×C61—21no—
55C42×C61C2311yescharacteristic
56C22⋊Dic61—22no—
57#11758199—22no—
58#11758198—21no—
59#11758198—22no—
60#11758198—22no—
61C4⋊Dic61—21no—
62C4⋊Dic61—22no—
63C4⋊Dic61—22no—
64C4⋊Dic61D411yescharacteristic
65C4⋊Dic61C2311yescharacteristic
66C4⋊Dic61C2312yes—
67#11758196—22no—
68#11758196D412yes—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2311yescharacteristic
72C2×#92418C2311yescharacteristic
73C23×C61—21no—
74C22×D61—21no—
75Q8×C61—22no—
76Q8×C61—22no—
77D4×C61—21no—
78D4×C61#4112yes—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61—42no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—82no—
88C2×Dic61C2×D412yes—
89C2×Dic61C2×D412yes—
90D244—21no—
91D244—21no—
92C4×D61—42no—
93Dic122—22no—
94Dic122—81no—
95C8×C61—22no—
96#92418—21no—
97#92418—21no—
98C22×C61—22no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61C22×D411yescharacteristic
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—41no—
105C4×C61—21no—
106C4×C61—42no—
107C4×C61—41no—
108C4×C61#13512yes—
109C4×C61C2×#4111yescharacteristic
110C4×C612−1+411yescharacteristic
111Dic61—22no—
112Dic61—22no—
113Dic61—41no—
114Dic61—42no—
115#3360—611nomaximal, Sylow
116C2×C61—42no—
117C2×C61#54811yescharacteristic
118C2×C61C2×#13511yescharacteristic
119C2×C61#57711yescharacteristic
120D61—81no—
121#556—611no—
122#554—611no—
123#488—612no—
124#487—611no—
125#479—612no—
126#476—611no—
127#463—612no—
128#461D6111yescharacteristic, complemented
129C8×Q8—611no—
130C4×SD16—612no—
131C4×D8—611no—
132C61#336011yescharacteristic, complemented, Sylow
133C2×SD16C2×D6112yes—
134C2×D8—611no—
135C4⋊Q8—611no—
136C4⋊Q8C2×D6111yescharacteristic
137#126—1222no—
138#125—612no—
139#124—612no—
140C22⋊Q8—1222no—
141C22⋊Q8—1221no—
142C22⋊Q8—1221no—
143C4×Q8—611no—
144C4×Q8—612no—
145C4×D4—612no—
146C4×D4—611no—
147C4×D4C2×D6111yescharacteristic
148#117—1221no—
149C2×C4⋊C4—1221no—
150#107—611no—
151#106—612no—
152C4⋊C8—612no—
153C4⋊C8C2×D6111yescharacteristic
154#103—612no—
155#103—612no—
156#103C2×D6112yes—
157#102—611no—
158#102—612no—
159#102—611no—
160C4×C8—612no—
161C4×C8—611no—
162C2×Q8—611no—
163C2×Q8—1221no—
164C2×Q8C22×D6112yes—
165C2×D4—611no—
166C2×D4C22×D6111yescharacteristic
167C22×C4—21no—
168C22×C4—1222no—
169C22×C4—1221no—
170SD16—24no—
171D8—1222no—
172C2×C8—611no—
173C2×C8—611no—
174C2×C8C22×D6112yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—611no—
178C4⋊C4—612no—
179C4⋊C4—612no—
180C4⋊C4—611no—
181C4⋊C4—1222no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C4⋊C4—1221no—
185C4⋊C4C22×D6111yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—1222no—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4—1221no—
191C42—612no—
192C42—1222no—
193C42C22×D6111yescharacteristic
194C23—21no—
195C23—1221no—
196Q8—22no—
197Q8—22no—
198Q8—1222no—
199Q8—4881no—
200D4—21no—
201D4—1221no—
202D4—1221no—
203D4#1175822412yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—612no—
208C2×C4—612no—
209C2×C4—1221no—
210C2×C4—1222no—
211C2×C4—4882no—
212C2×C4—2442no—
213C2×C4D4×D6111yescharacteristic
214C2×C4D4×D6111yescharacteristic
215C2×C4C23×D6111yescharacteristic
216C8—22no—
217C8—1221no—
218C8—1221no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—2441no—
223C22—2441no—
224C22—2441no—
225C22C2×D4×D6111yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—1222no—
230C4—1222no—
231C4—2441no—
232C4—2442no—
233C4#1451979812yes—
234C4C2×#1175822411yescharacteristic
235C4#1451982411yescharacteristic
236C2—42no—
237C2—4881no—
238C2#1684041811yescharacteristic
239C2C2×#1451979811yescharacteristic
240C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3360
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16840486C2semidirect
2. #16840469C2semidirect
3. #16840118C2semidirect
4. #16840112C2semidirect
5. #16840067C2semidirect
6. #16840053C2semidirect
8. #16839886C2semidirect
9. SD16×Dic61C2semidirect
11. C61×#461C2semidirect
128. #461D61semidirect
132. C61#3360semidirect