Finite Group Databasebeta

← #21461238

Subgroups — #21461238

Order 7808.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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#16840784C211yesmaximal, characteristic, complemented
2#16840707C211yesmaximal, characteristic, complemented
3#16840614C212yesmaximal, complemented
4#16840613C212yesmaximal, complemented
5#16840309C211yesmaximal, characteristic
6C4⋊#92420—21no—
7#14519834C2212yes—
8#14519832—21no—
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yes—
12C2×#11758222—21no—
13#14519776C411yescharacteristic, complemented
14#14519773C411yescharacteristic, complemented
15#14519763—21no—
16#14519752C2211yescharacteristic
17#14519750—21no—
18#14519748C2211yescharacteristic
19C4×D244C411yescharacteristic, complemented
20C4×C22⋊D61—21no—
21C42×D61C2211yescharacteristic
22C4×D4×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×D4×C61C2×C411yescharacteristic
25C22×C4×C61—21no—
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28C2×C22⋊D61—21no—
29#11758222—44no—
30C2×D244—21no—
31C2×D244C2×C411yescharacteristic
32C2×C4×D61—21no—
33C2×C4×D61D411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×C4×D61C2311yescharacteristic
36C2×Dic122—21no—
37C2×#92420—22no—
38C4⋊C4×C61C2×C411yescharacteristic
39C22⋊C4×C61—21no—
40C42×C61C2×C411yescharacteristic
41C22⋊Dic61—21no—
42#11758198—21no—
43#11758198—21no—
44C4⋊Dic61C2×C411yescharacteristic
45#11758196—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C23×C61—21no—
50C22×D61—21no—
51C22×D61C2×D411yescharacteristic
52C2×#6923—42no—
53C2×#6923—42no—
54C2×#6923—42no—
55D4×C61—41no—
56C2×C4×C61—21no—
57C2×C4×C61—42no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22×C411yescharacteristic
61C22⋊D61—42no—
62C22⋊D61—42no—
63C22⋊D61—42no—
64C2×Dic61—21no—
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68D244—41no—
69D244—42no—
70C4×D61—22no—
71C4×D61—41no—
72C4×D61—41no—
73C4×D61—42no—
74Dic122—42no—
75#92420—42no—
76C22×C61—41no—
77C22×C61—41no—
78C22×C61—41no—
79C22×C61C2×C22⋊C411yescharacteristic
80C2×D61—21no—
81C2×D61—21no—
82C2×D61—41no—
83C2×D61—41no—
84C2×D61—41no—
85C2×D61AGL(1,ℤ/8)12yes—
86#6923—82no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—41no—
91Dic61—21no—
92Dic61—21no—
93Dic61—21no—
94Dic61—41no—
95#1514—611nomaximal, Sylow
96C2×C61—81no—
97C2×C61#41011yescharacteristic
98C2×C61#41811yescharacteristic
99C2×C61#42111yescharacteristic
100D61—22no—
101D61—81no—
102#532—611no—
103#432—611no—
104#383—611no—
105#327—612no—
106#327—612no—
107C61#151411yescharacteristic, complemented, Sylow
108C2×#41—1221no—
109C4⋊Q8—611no—
110#127—611no—
111#124—1221no—
112#121—611no—
113#121—611no—
114#121—1221no—
115C4×D4—611no—
116C4×D4—1221no—
117C4×D4#692311yescharacteristic, complemented
118C2×C42—611no—
119C4⋊C8—1221no—
120C22⋊C8—612no—
121#97—1221no—
122#95—612no—
123#95—1221no—
124#95—1221no—
125#41—2444no—
126C2×Q8—1221no—
127C2×D4—611no—
128C2×D4—1221no—
129C2×D4—1221no—
130C2×D4—1221no—
131C2×D4—1221no—
132C2×D4C2×#692311yescharacteristic
133C22×C4—21no—
134C22×C4—611no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—1221no—
138C22×C4—1222no—
139C2×C8—1222no—
140C4⋊C4—611no—
141C4⋊C4—1221no—
142C4⋊C4C2×#692311yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—1221no—
145C22⋊C4—1221no—
146C22⋊C4—1221no—
147C42—611no—
148C42—611no—
149C42—611no—
150C42C2×#692311yescharacteristic
151C23—21no—
152C23—611no—
153C23—1221no—
154Q8—2442no—
155D4—41no—
156D4—2441no—
157D4—2442no—
158D4—2442no—
159D4—2442no—
160D4—2442no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—611no—
164C2×C4—611no—
165C2×C4—611no—
166C2×C4—1222no—
167C2×C4—1221no—
168C2×C4—2441no—
169C2×C4—2441no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4—2442no—
173C2×C4—2442no—
174C2×C4C22⋊#692311yescharacteristic
175C2×C4C22⋊#692311yescharacteristic
176C2×C4C22×#692311yescharacteristic
177C8—2442no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—612no—
182C22—1221no—
183C22—1221no—
184C22—2441no—
185C22—2441no—
186C22—2441no—
187C22C2×C22⋊#692311yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—41no—
192C4—1221no—
193C4—1221no—
194C4—1221no—
195C4—4882no—
196C4—2441no—
197C2—81no—
198C2—1222no—
199C2—4881no—
200C2#1684074111yescharacteristic
201C2#1684075411yescharacteristic
202C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1514
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #16840784C2semidirect
2. #16840707C2semidirect
3. #16840614C2semidirect
4. #16840613C2semidirect
13. #14519776C4semidirect
14. #14519773C4semidirect
19. C4×D244C4semidirect
22. C4×D4×C61C4semidirect
107. C61#1514semidirect
117. C4×D4#6923semidirect