Finite Group Databasebeta

← #21461103

Subgroups — #21461103

Order 7808.

214 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 58 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#16840782C211yesmaximal, characteristic, complemented
2#16840778C211yesmaximal, characteristic, complemented
3#16840607C212yesmaximal, complemented
4#16840606C212yesmaximal
5C2×#14519772C211yesmaximal, characteristic
6#14519844—21no—
7C4⋊#92420—21no—
8C22⋊#92420C2212yes—
9C22⋊#92420C2212yes—
10#14519832—21no—
11C4×#92420—21no—
12#14519772—21no—
13#14519772—21no—
14#14519772—21no—
15#14519772—21no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C411yescharacteristic
18C2×#11758198C411yescharacteristic
19C2×#11758198C411yescharacteristic
20C2×#11758198C2211yescharacteristic
21C2×C4×Dic61C2211yescharacteristic
22C2×C4⋊C4×C61C411yescharacteristic
23C23×D61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C22×C4×C61C2×C411yescharacteristic
27C22×Dic61C2×C411yescharacteristic
28C22×Dic61C2×C411yescharacteristic
29C22×Dic61C2311yescharacteristic
30C2×#92420—22no—
31C2×#92420—22no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34#11758198—21no—
35#11758198—21no—
36#11758198—21no—
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42#11758196—21no—
43#11758196—21no—
44C4×Dic61D411yescharacteristic
45C4×Dic61D411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C23×C61C22×C411yescharacteristic
49C22×D61—21no—
50C22×D61—22no—
51C22×D61—41no—
52C22×D61—41no—
53C2×C4×C61—22no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—22no—
57C2×C4×C61—41no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22⋊C411yescharacteristic
60C2×Dic61—21no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63C2×Dic61—41no—
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C2×D411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68#92420—42no—
69#92420—42no—
70C22×C61—21no—
71C22×C61—21no—
72C22×C61C2×C22⋊C411yescharacteristic
73C22×C61#13112yes—
74C2×D61—41no—
75C2×D61—41no—
76C2×D61—41no—
77C2×D61—82no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—41no—
81C4×C61—41no—
82Dic61—21no—
83Dic61—21no—
84Dic61—21no—
85Dic61—21no—
86Dic61—41no—
87#1473—611nomaximal, Sylow
88C2×C61—22no—
89C2×C61#40811yescharacteristic
90C2×C61#41011yescharacteristic
91C2×C61#41311yescharacteristic
92D61—81no—
93C2×#126—611no—
94#432—611no—
95#431—611no—
96#324—612no—
97#323—612no—
98C61#147311yescharacteristic, complemented, Sylow
99#126—1221no—
100#126—1221no—
101#126—1221no—
102#126—1221no—
103C2×C4⋊C4—611no—
104C2×C4⋊C4—611no—
105C2×C4⋊C4#692311yescharacteristic
106C2×C22⋊C4—611no—
107C2×C22⋊C4—611no—
108C2×C22⋊C4—611no—
109C2×C42—611no—
110C4⋊C8—1221no—
111C4⋊C8—1221no—
112C22⋊C8—612no—
113C22⋊C8—612no—
114#97—1221no—
115C4×C8—1221no—
116C24—611no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—611no—
120C22×C4C2×#692311yescharacteristic
121C22×C4C2×#692311yescharacteristic
122C22×C4C2×#692311yescharacteristic
123C2×C8—1222no—
124C2×C8—1222no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C22⋊C4—1221no—
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C22⋊C4—1221no—
137C42—611no—
138C42—611no—
139C42—611no—
140C42—611no—
141C23—1222no—
142C23—1221no—
143C23—2441no—
144C23—2441no—
145C23C22×#692311yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—611no—
152C2×C4—611no—
153C2×C4—611no—
154C2×C4—611no—
155C2×C4—1221no—
156C2×C4—2441no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4C22⋊#692311yescharacteristic
160C2×C4C22⋊#692311yescharacteristic
161C8—2442no—
162C8—2442no—
163C22—21no—
164C22—21no—
165C22—4882no—
166C22—2441no—
167C22—2441no—
168C22—2441no—
169C22C2×C22⋊#692311yescharacteristic
170C22#1451986412yes—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—1221no—
176C4—1221no—
177C4—1221no—
178C4—1221no—
179C4—2441no—
180C2—22no—
181C2—4881no—
182C2#1684073511yescharacteristic
183C2#1684074311yescharacteristic
184C2#1684074811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1473
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #16840782C2semidirect
2. #16840778C2semidirect
3. #16840607C2semidirect
98. C61#1473semidirect