Finite Group Databasebeta

← #21461209

Subgroups — #21461209

Order 7808.

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

normal subgroups only

This group has 272 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#16840785C211yesmaximal, characteristic, complemented
2#16840698C211yesmaximal, characteristic, complemented
3#16840614C212yesmaximal, complemented
4#16840613C212yesmaximal, complemented
5#16840309C211yesmaximal, characteristic
6C2×C4×#6923—21no—
7#14519844—21no—
8#14519834C2212yes—
9#14519832—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×#6923—24no—
39C4⋊C4×C61C2×C411yescharacteristic
40C22⋊C4×C61—21no—
41C42×C61C2×C411yescharacteristic
42C22⋊Dic61—21no—
43#11758198—21no—
44#11758198—21no—
45C4⋊Dic61C2×C411yescharacteristic
46#11758196—21no—
47C4×Dic61C2×C411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C23×C61—21no—
51C22×D61—21no—
52C22×D61C2×D411yescharacteristic
53C2×#6923—24no—
54C2×#6923—42no—
55C2×#6923—42no—
56D4×C61—41no—
57C2×C4×C61—21no—
58C2×C4×C61—42no—
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22×C411yescharacteristic
62C22⋊D61—42no—
63C22⋊D61—42no—
64C22⋊D61—42no—
65C2×Dic61—21no—
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C2×D411yescharacteristic
69D244—41no—
70D244—42no—
71C4×D61—22no—
72C4×D61—22no—
73C4×D61—41no—
74C4×D61—42no—
75Dic122—42no—
76#92420—42no—
77C22×C61—41no—
78C22×C61—41no—
79C22×C61—41no—
80C22×C61C2×C22⋊C411yescharacteristic
81C2×D61—21no—
82C2×D61—21no—
83C2×D61—41no—
84C2×D61—41no—
85C2×D61—41no—
86C2×D61AGL(1,ℤ/8)12yes—
87#6923—44no—
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—41no—
92Dic61—21no—
93Dic61—21no—
94Dic61—41no—
95Dic61#10412yes—
96#1505—611nomaximal, Sylow
97C2×C61—81no—
98C2×C61#41011yescharacteristic
99C2×C61#41811yescharacteristic
100C2×C61C2×#10411yescharacteristic
101D61—22no—
102D61—81no—
103#532—611no—
104#432—611no—
105#376—611no—
106#327—612no—
107#327—612no—
108C61#150511yescharacteristic, complemented, Sylow
109C2×#41—1221no—
110C4⋊Q8—611no—
111#127—611no—
112#124—1221no—
113#121—611no—
114#121—611no—
115#121—1221no—
116C4×D4—611no—
117C4×D4—1221no—
118C4×D4#692311yescharacteristic, complemented
119C2×C42—611no—
120C2×C42—1221no—
121C4⋊C8—1221no—
122C22⋊C8—612no—
123#97—1221no—
124#95—612no—
125#95—1221no—
126#41—2444no—
127C2×Q8—1221no—
128C2×D4—611no—
129C2×D4—1221no—
130C2×D4—1221no—
131C2×D4—1221no—
132C2×D4—1221no—
133C2×D4C2×#692311yescharacteristic
134C22×C4—21no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—1222no—
139C22×C4—1221no—
140C2×C8—1222no—
141C4⋊C4—611no—
142C4⋊C4—1221no—
143C4⋊C4C2×#692311yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—1221no—
146C22⋊C4—1221no—
147C22⋊C4—1221no—
148C42—611no—
149C42—611no—
150C42—611no—
151C42—1224no—
152C42C2×#692311yescharacteristic
153C23—21no—
154C23—611no—
155C23—1221no—
156Q8—2442no—
157D4—41no—
158D4—2441no—
159D4—2442no—
160D4—2442no—
161D4—2442no—
162D4—2442no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—611no—
166C2×C4—611no—
167C2×C4—611no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—1224no—
171C2×C4—1221no—
172C2×C4—2441no—
173C2×C4—2442no—
174C2×C4—2442no—
175C2×C4—2442no—
176C2×C4C22⋊#692311yescharacteristic
177C2×C4C22⋊#692311yescharacteristic
178C2×C4C22×#692311yescharacteristic
179C8—2442no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—612no—
184C22—1221no—
185C22—1221no—
186C22—2441no—
187C22—2441no—
188C22—2441no—
189C22C2×C22⋊#692311yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—612no—
195C4—1221no—
196C4—1221no—
197C4—2444no—
198C4—2441no—
199C2—81no—
200C2—1222no—
201C2—4881no—
202C2#1684074111yescharacteristic
203C2#1684075411yescharacteristic
204C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1505
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. #16840785C2semidirect
2. #16840698C2semidirect
3. #16840614C2semidirect
4. #16840613C2semidirect
13. #14519776C4semidirect
14. #14519773C4semidirect
19. C4×D244C4semidirect
22. C4×D4×C61C4semidirect
108. C61#1505semidirect
118. C4×D4#6923semidirect