Finite Group Databasebeta

← #21443817

Subgroups — #21443817

Order 7808.

222 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 35 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#16839671C211yesmaximal, characteristic
2#16839529C211yesmaximal, characteristic, complemented
3C61×#323C211yesmaximal, characteristic, complemented
4C22×D244C411yescharacteristic, complemented
5C22×C22⋊D61—21no—
6C2×C22⋊Dic61—21no—
7C2×#11758198—21no—
8#14519684C411yescharacteristic, complemented
9C2×C22⋊C4×C61C2211yescharacteristic
10C22⋊C8×C61—21no—
11C24×C61D411yescharacteristic
12C23×D61—21no—
13C22×C4×C61C2×C411yescharacteristic
14C22×C4×C61D411yescharacteristic
15C2×C22⋊D61—42no—
16C2×C22⋊D61—42no—
17C2×C22⋊D61—41no—
18C2×C22⋊D61—41no—
19C22×Dic61—21no—
20C22×Dic61—41no—
21C2×D244—41no—
22C2×D244—42no—
23C2×C8×C61—41no—
24C22⋊C4×C61—41no—
25C22⋊Dic61—22no—
26C22⋊Dic61—41no—
27#11758198—42no—
28C23×C61—21no—
29C23×C61—21no—
30C23×C61—41no—
31C23×C61—41no—
32C23×C61C22⋊C411yescharacteristic
33C23×C61D811yescharacteristic
34C23×C61SD1611yescharacteristic
35C22×D61—22no—
36C22×D61—41no—
37C22×D61—41no—
38C22×D61—41no—
39C22×D61—41no—
40C22×D61—41no—
41C22×D61—41no—
42C2×C4×C61—21no—
43C2×C4×C61—21no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C22⋊D61—44no—
47C22⋊D61—44no—
48C2×Dic61—22no—
49C2×Dic61—41no—
50C2×Dic61—41no—
51C2×Dic61—42no—
52C2×Dic61—81no—
53C2×Dic61—81no—
54D244—42no—
55D244—42no—
56C8×C61—81no—
57C22×C61—21no—
58C22×C61—21no—
59C22×C61—21no—
60C22×C61—21no—
61C22×C61—41no—
62C22×C61—41no—
63C22×C61—41no—
64C22×C61—41no—
65C22×C61—81no—
66C22×C61#9911yescharacteristic
67C22×C61#10211yescharacteristic
68C22×C61#10411yescharacteristic
69C2×D61—42no—
70C2×D61—42no—
71C2×D61—42no—
72C2×D61—81no—
73C2×D61—81no—
74C2×D61—81no—
75C2×D61—81no—
76C4×C61—41no—
77C4×C61—41no—
78Dic61—42no—
79Dic61—82no—
80#1343—611nomaximal, Sylow
81C2×C61—21no—
82C2×C61—21no—
83C2×C61—41no—
84C2×C61—41no—
85C2×C61#32711yescharacteristic
86C2×C61AΣL(1,𝔽16)11yescharacteristic
87C2×C61#35311yescharacteristic
88D61—82no—
89#392—611no—
90#342—611no—
91#323D6111yescharacteristic, complemented
92C61#134311yescharacteristic, complemented, Sylow
93C22×D4—611no—
94C22×D4—1221no—
95C2×C22⋊C4—1221no—
96C2×C22⋊C4—1221no—
97C2×C22⋊C4C2×D6111yescharacteristic
98C22⋊C8—21no—
99#95—611no—
100C24—1221no—
101C24D24411yescharacteristic
102C2×D4—2441no—
103C2×D4—2442no—
104C2×D4—2442no—
105C2×D4—2442no—
106C2×D4—2441no—
107C2×D4—2441no—
108C22×C4—1221no—
109C22×C4—2441no—
110C22×C4C4×D6111yescharacteristic
111C22×C4C22⋊D6111yescharacteristic
112C2×C8—41no—
113C22⋊C4—41no—
114C22⋊C4—1222no—
115C22⋊C4—2442no—
116C22⋊C4—2441no—
117C23—21no—
118C23—21no—
119C23—41no—
120C23—41no—
121C23—1222no—
122C23—2441no—
123C23—2441no—
124C23—2441no—
125C23—2441no—
126C23—2441no—
127C23—2441no—
128C23#1175819011yescharacteristic
129C23D48811yescharacteristic
130C23#1175819811yescharacteristic
131D4—2442no—
132D4—2442no—
133D4—2444no—
134D4—2444no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—1222no—
140C2×C4—4881no—
141C2×C4—4881no—
142C2×C4—2442no—
143C2×C4—2441no—
144C2×C4—2441no—
145C8—81no—
146C22—21no—
147C22—21no—
148C22—21no—
149C22—21no—
150C22—41no—
151C22—41no—
152C22—41no—
153C22—41no—
154C22—81no—
155C22—4881no—
156C22—4881no—
157C22—4881no—
158C22—4881no—
159C22—2442no—
160C22—2442no—
161C22—2442no—
162C22#1451969111yescharacteristic
163C22#1451969911yescharacteristic
164C22#1451970311yescharacteristic
165C4—41no—
166C4—41no—
167C4—4882no—
168C4—2442no—
169C2—21no—
170C2—21no—
171C2—41no—
172C2—41no—
173C2—4882no—
174C2#1683949711yescharacteristic
175C2#1683955011yescharacteristic
176C2#1683955411yescharacteristic
subgroupG/H
centerC22#14519691
commutatorC22×C4×C61C2×C4
FrattiniC2×C22⋊C4C2×D61
FittingC61×#323C2
socleC22×C61#99
hypercenter#323D61
hypocenterC61#1343
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #16839529C2semidirect
3. C61×#323C2semidirect
4. C22×D244C4semidirect
8. #14519684C4semidirect
91. #323D61semidirect
92. C61#1343semidirect