Finite Group Databasebeta

← #21446206

Subgroups — #21446206

Order 7808.

360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14519765C211yesmaximal, characteristic
2#16840236C211yesmaximal, characteristic
3#16839772C211yesmaximal, characteristic, complemented
4#16839770C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic
6#16839522C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C22×D244C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519765—22no—
12#14519765C414yescomplemented
13C4×D244—22no—
14#14519739—22no—
15#14519736C2211yescharacteristic
16C2×#11758198—22no—
17C22⋊C4×D61—22no—
18#14519702—22no—
19#14519700—22no—
20#14519693—22no—
21C2×M16×C61C2211yescharacteristic
22#117×C61C2211yescharacteristic
23C2×C42×C61C2211yescharacteristic
24C23×D61D412yes—
25C22×C4×C61—21no—
26C22×C4×C61C2311yescharacteristic
27C22×Dic61—21no—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244C2×C412yes—
33C2×D244D412yes—
34C2×C4×D61—24no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122C2×C412yescomplemented
41M16×C61—21no—
42M16×C61—21no—
43C2×C8×C61—21no—
44C4⋊C4×C61D412yes—
45C22⋊C4×C61—21no—
46C42×C61—21no—
47C42×C61—21no—
48C42×C61C2×C412yescomplemented
49C22⋊Dic61—21no—
50#11758198—24no—
51#11758198—28no—
52C4⋊Dic61D412yes—
53C4×Dic61—21no—
54#11758194—21no—
55#11758194—21no—
56C2×#92418—21no—
57C23×C61C2×D411yescharacteristic
58C22×D61—22no—
59C22×D61—22no—
60C22×D61—44no—
61C22×D61C22⋊C414yes—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—42no—
65C2×C4×C61C22×C411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75D244—22no—
76D244—22no—
77D244—22no—
78D244—22no—
79C4×D61—84no—
80Dic122—22no—
81Dic122—22no—
82Dic122—41no—
83Dic122—41no—
84C8×C61—41no—
85#92418—41no—
86C22×C61—22no—
87C22×C61C2×C22⋊C411yescharacteristic
88C22×C61#12011yescharacteristic
89C22×C61#12311yescharacteristic
90C2×D61—24no—
91C2×D61—44no—
92C2×D61—44no—
93C2×D61—82no—
94C4×C61—42no—
95C4×C61—42no—
96C4×C61C4×D411yescharacteristic
97C4×C61C4×D411yescharacteristic
98C4×C61#12111yescharacteristic
99C4×C61#12111yescharacteristic
100Dic61—42no—
101Dic61—42no—
102#1885—611nomaximal, Sylow
103C2×C61—21no—
104C2×C61—21no—
105C2×C61#38611yescharacteristic
106C2×C61#45512yes—
107D61—44no—
108C2×#124—611no—
109#518—611no—
110#419—611no—
111#419—611no—
112C2×#100—611no—
113#339—611no—
114#339D6111yescharacteristic, complemented
115C61#188511yescharacteristic, complemented, Sylow
116C22×Q8—611no—
117C22×D4—611no—
118C2×M16—611no—
119C2×M16C2×D6111yescharacteristic
120#124—614no—
121#124—1222no—
122C4×D4—1222no—
123C4×D4—1222no—
124#117—611no—
125#117C2×D6111yescharacteristic
126C2×C22⋊C4—1222no—
127C2×C22⋊C4—1222no—
128C2×C42C2×D6111yescharacteristic
129#103—1222no—
130#103—1222no—
131#100—1222no—
132C24—612no—
133C2×Q8—612no—
134C2×Q8—1221no—
135C2×Q8—1221no—
136C2×Q8—1221no—
137C2×Q8—1221no—
138C2×Q8—1221no—
139C2×D4—612no—
140C2×D4—612no—
141C2×D4—1221no—
142C2×D4—1221no—
143C2×D4—1221no—
144C2×D4—1221no—
145C22×C4—21no—
146C22×C4—1224no—
147C22×C4—1221no—
148C22×C4C22×D6111yescharacteristic
149M16—21no—
150M16—21no—
151M16—1221no—
152M16—1221no—
153C2×C8—21no—
154C2×C8—1221no—
155C4⋊C4—612no—
156C4⋊C4D24412yes—
157C22⋊C4—21no—
158C22⋊C4—1228no—
159C22⋊C4—1224no—
160C22⋊C4—1221no—
161C42—21no—
162C42—21no—
163C42—1221no—
164C42C4×D6112yescomplemented
165C23—614no—
166C23—1222no—
167C23—1222no—
168C23—2444no—
169C23D4×D6111yescharacteristic
170Q8—1222no—
171Q8—1222no—
172Q8—2441no—
173Q8—2441no—
174D4—1222no—
175D4—1222no—
176D4—1222no—
177D4—1222no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—4884no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4C2×C4×D6111yescharacteristic
187C2×C4C2×D24411yescharacteristic
188C2×C4#1175822211yescharacteristic
189C2×C4D4×D6111yescharacteristic
190C2×C4D4×D6111yescharacteristic
191C2×C4#1175822611yescharacteristic
192C8—41no—
193C8—2441no—
194C22—22no—
195C22—1224no—
196C22—4882no—
197C22—2444no—
198C22—2444no—
199C22C22⋊C4×D6111yescharacteristic
200C22#1451974711yescharacteristic
201C22#1451976211yescharacteristic
202C4—42no—
203C4—42no—
204C4—2442no—
205C4—2442no—
206C4#1451973911yescharacteristic
207C4C4×D24411yescharacteristic
208C4#1451975011yescharacteristic
209C4#1451975211yescharacteristic
210C2—21no—
211C2—21no—
212C2—2444no—
213C2#1683964011yescharacteristic
214C2#1683994112yes—
subgroupG/H
centerC22#14519747
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61#120
hypercenter#339D61
hypocenterC61#1885
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
3. #16839772C2semidirect
4. #16839770C2semidirect
6. #16839522C2semidirect
7. C61×#339C2semidirect
12. #14519765C4semidirect
40. C2×Dic122C2×C4semidirect
48. C42×C61C2×C4semidirect
114. #339D61semidirect
115. C61#1885semidirect
164. C42C4×D61semidirect