Finite Group Databasebeta

← #21446887

Subgroups — #21446887

Order 7808.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#16840562C211yesmaximal, characteristic, complemented
2#16840274C212yesmaximal, complemented
3#16839780C212yesmaximal, complemented
4#16839725C211yesmaximal, characteristic, complemented
5C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
6C2×#11758222C2212yes—
7C22×C4×D61C2211yescharacteristic
8#14519810—22no—
9#14519805—22no—
10#14519799—22no—
11C2×#11758194C2211yescharacteristic
12#14519761—22no—
13#14519757—22no—
14#14519752—22no—
15#14519747—22no—
16C4×D244—24no—
17#14519705—24no—
18#14519689—22no—
19C2×M16×C61C2211yescharacteristic
20#117×C61C2212yes—
21C23×D61D411yescharacteristic
22C22×C4×C61C2311yescharacteristic
23C2×C22⋊D61—22no—
24C22×Dic61D411yescharacteristic
25#11758222—22no—
26#11758222—22no—
27#11758222—22no—
28#11758222—22no—
29C2×D244—24no—
30C2×D244D412yescomplemented
31C2×C4×D61—21no—
32C2×C4×D61—22no—
33C2×C4×D61—22no—
34C2×C4×D61—22no—
35C2×C4×D61—21no—
36C2×Dic122D412yescomplemented
37M16×C61—22no—
38C2×C8×C61D412yescomplemented
39C4⋊C4×C61—22no—
40C22⋊C4×C61—22no—
41C42×C61D414yescomplemented
42#11758198—24no—
43#11758198—24no—
44C4⋊Dic61—24no—
45#11758194—22no—
46C2×#92418—21no—
47Dic244—22no—
48D488—22no—
49#11758190—24no—
50C23×C61C2×D411yescharacteristic
51C22×D61—22no—
52C22×D61—21no—
53C22×D61—22no—
54C22×D61—42no—
55C2×C4×C61—24no—
56C2×C4×C61C2×D412yes—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D412yes—
59C2×C4×C61#4111yescharacteristic
60C22⋊D61—42no—
61C22⋊D61—42no—
62C2×Dic61—22no—
63C2×Dic61—22no—
64C2×Dic61—21no—
65D244—22no—
66D244—22no—
67D244—48no—
68C4×D61—41no—
69C4×D61—42no—
70C4×D61—42no—
71C4×D61—41no—
72C4×D61—42no—
73Dic122—22no—
74Dic122—22no—
75C8×C61—22no—
76#92418—41no—
77C22×C61—41no—
78C22×C61#12012yes—
79C22×C61#12111yescharacteristic
80C2×D61—24no—
81C2×D61—22no—
82C2×D61—42no—
83C2×D61—41no—
84C2×D61—41no—
85C2×D61—44no—
86C2×D61—42no—
87C4×C61—44no—
88C4×C61#12011yescharacteristic
89C4×C61#12112yes—
90C4×C61#12711yescharacteristic
91Dic61—42no—
92Dic61—41no—
93#2010—611nomaximal, Sylow
94C2×C61—22no—
95C2×C61—21no—
96C2×C61#39211yescharacteristic
97D61—42no—
98D61—82no—
99#575—611no—
100#525—612no—
101#421—612no—
102#407—611no—
103H(3,ℤ/4)D6111yescharacteristic, complemented
104C61#201011yescharacteristic, complemented, Sylow
105C2×#41—612no—
106C23×C4—611no—
107#137—1222no—
108AGL(1,ℤ/8)—1222no—
109#135—1222no—
110C2×M16—611no—
111C2×M16C2×D6111yescharacteristic
112#123—1222no—
113C22⋊Q8—1222no—
114#121—1222no—
115#120—1222no—
116C4×D4—1224no—
117#117C2×D6112yes—
118#104—1224no—
119C22⋊C8—1222no—
120C24—611no—
121#41—1222no—
122#41—1222no—
123#41—1222no—
124#41—1222no—
125C2×Q8—612no—
126C2×D4—612no—
127C2×D4—1224no—
128C2×D4—1222no—
129C22×C4—611no—
130C22×C4—1221no—
131C22×C4—1222no—
132C22×C4—1222no—
133C22×C4—1222no—
134C22×C4—1221no—
135C22×C4C22×D6111yescharacteristic
136Q16—1222no—
137SD16—1224no—
138D8—1222no—
139M16—22no—
140M16—1222no—
141C2×C8—1221no—
142C2×C8D24412yescomplemented
143C4⋊C4—22no—
144C4⋊C4—1224no—
145C22⋊C4—22no—
146C22⋊C4—1224no—
147C22⋊C4—1224no—
148C42D24414yescomplemented
149C23—1222no—
150C23—1221no—
151C23—1222no—
152C23—2442no—
153C23D4×D6111yescharacteristic
154Q8—1222no—
155Q8—1222no—
156D4—1222no—
157D4—1222no—
158D4—2448no—
159D4—2442no—
160D4—2442no—
161C2×C4—24no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4—1221no—
165C2×C4—2441no—
166C2×C4—2442no—
167C2×C4—2442no—
168C2×C4—2441no—
169C2×C4—2442no—
170C2×C4C2×D24411yescharacteristic
171C2×C4C2×D24412yes—
172C2×C4D4×D6112yes—
173C2×C4#1175822611yescharacteristic
174C8—22no—
175C8—2441no—
176C22—41no—
177C22—1224no—
178C22—1222no—
179C22—2444no—
180C22—2442no—
181C22—2441no—
182C22—2442no—
183C22—2441no—
184C22#1451974712yes—
185C22#1451975211yescharacteristic
186C4—44no—
187C4—2441no—
188C4—2442no—
189C4#1451974711yescharacteristic
190C4#1451975212yes—
191C4#1451977411yescharacteristic
192C2—22no—
193C2—21no—
194C2—4882no—
195C2—2442no—
196C2#1683967211yescharacteristic
subgroupG/H
centerC4#14519774
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×H(3,ℤ/4)C2
socleC2×C61#392
hypercenterH(3,ℤ/4)D61
hypocenterC61#2010
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #16840562C2semidirect
2. #16840274C2semidirect
3. #16839780C2semidirect
4. #16839725C2semidirect
5. C61×H(3,ℤ/4)C2semidirect
30. C2×D244D4semidirect
36. C2×Dic122D4semidirect
38. C2×C8×C61D4semidirect
41. C42×C61D4semidirect
103. H(3,ℤ/4)D61semidirect
104. C61#2010semidirect
142. C2×C8D244semidirect
148. C42D244semidirect