Finite Group Databasebeta

← #21458446

Subgroups — #21458446

Order 7808.

354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840477C211yesmaximal, characteristic
2#16840469C211yesmaximal, characteristic, complemented
3#16840167C211yesmaximal, characteristic, complemented
4#16840104C212yesmaximal, complemented
5#16840076C212yesmaximal, complemented
6#16840058C211yesmaximal, characteristic, complemented
7#16840053C211yesmaximal, characteristic, complemented
8#16840008C212yesmaximal, complemented
9C4×#11758190C211yesmaximal, characteristic, complemented
10#16839804C212yesmaximal, complemented
11C61×#436C211yesmaximal, characteristic, complemented
12C2×#11758190C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519768—21no—
16#14519763—22no—
17#14519756C2212yes—
18#14519754—22no—
19#14519751C2212yes—
20#14519748—21no—
21C4×Dic122C2211yescharacteristic
22C4×D244C2211yescharacteristic
23D4×Dic61—21no—
24#14519736C2212yes—
25#14519735—21no—
26C2×C4⋊Dic61C2212yes—
27#14519711C2212yes—
28#14519711C2212yes—
29#14519711C2212yes—
30#14519709C2212yes—
31#14519709C2211yescharacteristic
32#14519702C2212yes—
33#14519702C2211yescharacteristic
34#14519699C2212yes—
35#14519699C2211yescharacteristic
36C2×M16×C61C2212yes—
37C4×D4×C61C2211yescharacteristic
38C4⋊C8×C61C2211yescharacteristic
39C22⋊C8×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×D4×C61D411yescharacteristic
42C22×C4×C61C2312yes—
43C2×C22⋊D61—22no—
44C22×Dic61—22no—
45C2×D244C2311yescharacteristic
46C2×C4×D61—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122C2311yescharacteristic
50M16×C61—24no—
51C2×C8×C61C2311yescharacteristic
52C2×C8×C61C2312yes—
53C2×C8×C61C2311yescharacteristic
54C4⋊C4×C61D411yescharacteristic
55C22⋊C4×C61D412yes—
56C42×C61C2311yescharacteristic
57C22⋊Dic61—22no—
58C22⋊Dic61—22no—
59#11758198—22no—
60#11758198—21no—
61C4⋊Dic61—22no—
62C4⋊Dic61—21no—
63C4⋊Dic61—21no—
64C4⋊Dic61C2311yescharacteristic
65C4⋊Dic61C2312yes—
66C4⋊Dic61C2311yescharacteristic
67C4⋊Dic61C2312yes—
68#11758196—21no—
69#11758196—22no—
70C4×Dic61—22no—
71C4×Dic61—21no—
72#11758190—22no—
73C23×C61C2×D412yes—
74C22×D61—21no—
75D4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C22⋊D61—82no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—82no—
89D244—21no—
90D244—21no—
91C4×D61—42no—
92Dic122—21no—
93Dic122—21no—
94Dic122—81no—
95Dic122—81no—
96C8×C61—22no—
97C8×C61—21no—
98C8×C61#4112yes—
99C22×C61—22no—
100C22×C61—22no—
101C22×C61—22no—
102C22×C61C22×D411yescharacteristic
103C2×D61—41no—
104C2×D61—41no—
105C2×D61—41no—
106C4×C61—22no—
107C4×C61—21no—
108C4×C61#13712yes—
109C4×C61C2×#4111yescharacteristic
110C4×C612−1+411yescharacteristic
111Dic61—41no—
112Dic61—41no—
113Dic61—42no—
114Dic61—42no—
115Dic61—41no—
116#3357—611nomaximal, Sylow
117C2×C61—42no—
118C2×C61#54711yescharacteristic
119C2×C61C2×#13711yescharacteristic
120C2×C61#57611yescharacteristic
121D61—81no—
122#555—611no—
123#554—611no—
124#500—611no—
125#485—612no—
126#480—612no—
127#477—611no—
128#476—611no—
129#468—612no—
130C4×SD16—611no—
131#436D6111yescharacteristic, complemented
132#428—612no—
133C61#335711yescharacteristic, complemented, Sylow
134C2×SD16—611no—
135C2×M16C2×D6112yes—
136C4⋊Q8—611no—
137C4⋊Q8—611no—
138#125—1221no—
139#124—1222no—
140C22⋊Q8—612no—
141C22⋊Q8—1222no—
142#121—612no—
143#121—1221no—
144C4×Q8—611no—
145C4×D4—611no—
146C4×D4—1221no—
147C4×D4C2×D6111yescharacteristic
148#117—612no—
149#117—1221no—
150C2×C4⋊C4—612no—
151#107—612no—
152#107—612no—
153#107—612no—
154#106—611no—
155#106—612no—
156C4⋊C8C2×D6111yescharacteristic
157#103—611no—
158#103—612no—
159#102—611no—
160#102—612no—
161C22⋊C8C2×D6112yes—
162C4×C8C2×D6111yescharacteristic
163C2×Q8—611no—
164C2×Q8—1221no—
165C2×Q8—1221no—
166C2×D4—611no—
167C2×D4—1222no—
168C2×D4D24411yescharacteristic
169C22×C4—1222no—
170C22×C4—1221no—
171C22×C4C22×D6112yes—
172SD16—1222no—
173M16—24no—
174C2×C8C22×D6111yescharacteristic
175C2×C8C22×D6112yes—
176C2×C8C22×D6111yescharacteristic
177C4⋊C4—611no—
178C4⋊C4—612no—
179C4⋊C4—611no—
180C4⋊C4—612no—
181C4⋊C4—1222no—
182C4⋊C4—1221no—
183C4⋊C4—1222no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4D24411yescharacteristic
187C22⋊C4—1222no—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4—1221no—
191C22⋊C4D24412yes—
192C42—1222no—
193C42—1221no—
194C42C22×D6111yescharacteristic
195C23—1221no—
196C23C2×D24412yes—
197Q8—1221no—
198Q8—1221no—
199Q8—4881no—
200Q8—4881no—
201D4—22no—
202D4—1221no—
203D4—1221no—
204D4—4882no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—1221no—
208C2×C4—1222no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1222no—
212C2×C4—4882no—
213C2×C4—2442no—
214C2×C4C2×D24412yes—
215C2×C4C2×D24411yescharacteristic
216C2×C4C2×D24411yescharacteristic
217C2×C4C23×D6111yescharacteristic
218C8—22no—
219C8—21no—
220C8#1175822412yes—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—2441no—
225C22—2441no—
226C22—2441no—
227C22C22×D24411yescharacteristic
228C4—21no—
229C4—22no—
230C4—2441no—
231C4—2441no—
232C4—2442no—
233C4—2442no—
234C4—2441no—
235C4#1451981012yes—
236C4C2×#1175822411yescharacteristic
237C4#1451982411yescharacteristic
238C2—42no—
239C2—4881no—
240C2#1684041611yescharacteristic
241C2C2×#1451981011yescharacteristic
242C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#436C2
socleC22×C61C22×D4
hypercenter#436D61
hypocenterC61#3357
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
2. #16840469C2semidirect
3. #16840167C2semidirect
4. #16840104C2semidirect
5. #16840076C2semidirect
6. #16840058C2semidirect
7. #16840053C2semidirect
8. #16840008C2semidirect
9. C4×#11758190C2semidirect
10. #16839804C2semidirect
11. C61×#436C2semidirect
131. #436D61semidirect
133. C61#3357semidirect