Finite Group Databasebeta

← #21461288

Subgroups — #21461288

Order 7808.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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
2C2×#14519832C211yesmaximal, characteristic, complemented
3#16840618C212yesmaximal, complemented
4#16840617C212yesmaximal, complemented
5#16840308C211yesmaximal, characteristic
6C22×#92420—21no—
7#14519844—21no—
8C22⋊#92420—21no—
9#14519832—21no—
10#14519832C2212yes—
11#14519832C2212yes—
12C2×#11758222C411yescharacteristic
13#14519775C411yescharacteristic
14#14519773C411yescharacteristic
15#14519766C2211yescharacteristic
16#14519764C2211yescharacteristic
17#14519749—21no—
18#14519749—21no—
19C4×C22⋊D61—21no—
20C4×C22⋊D61—21no—
21C2×C4×Dic61C2211yescharacteristic
22C2×#41×C61C411yescharacteristic
23#41×C61—42no—
24C2×Q8×C61C2×C411yescharacteristic
25C2×D4×C61—21no—
26C2×D4×C61C2×C411yescharacteristic
27C22×C4×C61—21no—
28C22×C4×C61C2×C411yescharacteristic
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C22×Dic61D411yescharacteristic
33C22×Dic61D411yescharacteristic
34#11758222—42no—
35C2×D244C2×C411yescharacteristic
36C2×C4×D61—21no—
37C2×Dic122C2×C411yescharacteristic
38C2×#92420—24no—
39C2×#92420—22no—
40C2×#92420—22no—
41C22⋊Dic61—21no—
42C22⋊Dic61—21no—
43#11758198—21no—
44#11758198—21no—
45#11758196—21no—
46#11758196—21no—
47C4×Dic61C2×C411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61C2311yescharacteristic
51C23×C61—21no—
52C23×C61C22⋊C411yescharacteristic
53C22×D61—21no—
54Q8×C61—41no—
55D4×C61—41no—
56D4×C61—42no—
57C2×C4×C61—22no—
58C2×C4×C61—21no—
59C2×C4×C61—42no—
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22×C411yescharacteristic
62C22⋊D61—42no—
63C22⋊D61—42no—
64C22⋊D61—42no—
65C2×Dic61—22no—
66C2×Dic61—21no—
67C2×Dic61—41no—
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C2×D411yescharacteristic
71C2×Dic61C2×D411yescharacteristic
72D244—41no—
73C4×D61—42no—
74Dic122—41no—
75#92420—24no—
76#92420—42no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61—41no—
82C22×C61#10012yes—
83C22×C61C2×C22⋊C411yescharacteristic
84C2×D61—41no—
85C2×D61—41no—
86C2×D61—41no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—41no—
90Dic61—21no—
91Dic61—21no—
92Dic61—21no—
93Dic61—41no—
94Dic61#10412yes—
95#1530—611nomaximal, Sylow
96C2×C61—22no—
97C2×C61—81no—
98C2×C61C2×#10011yescharacteristic
99C2×C61C2×#10411yescharacteristic
100C2×C61#42111yescharacteristic
101D61—81no—
102#532—611no—
103#432—611no—
104C2×#97—611no—
105#329—612no—
106#329—612no—
107C61#153011yescharacteristic, complemented, Sylow
108C2×#41—611no—
109C2×#41#692311yescharacteristic
110C22×C8—1221no—
111C4⋊Q8—611no—
112#127—611no—
113#124—611no—
114#124—611no—
115#121—1221no—
116#121—1221no—
117C4×D4—1221no—
118C4×D4—1221no—
119C2×C42—611no—
120C4⋊C8—1221no—
121C22⋊C8—1221no—
122#97—612no—
123#97—612no—
124#97—1221no—
125#41—42no—
126#41—2442no—
127C2×Q8—611no—
128C2×Q8C2×#692311yescharacteristic
129C2×D4—21no—
130C2×D4—611no—
131C2×D4—1221no—
132C2×D4—1221no—
133C2×D4—1221no—
134C2×D4C2×#692311yescharacteristic
135C22×C4—21no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—1221no—
139C22×C4C2×#692311yescharacteristic
140C2×C8—1222no—
141C2×C8—1224no—
142C2×C8—1222no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C22⋊C4—1221no—
146C22⋊C4—1221no—
147C22⋊C4—1221no—
148C22⋊C4—1221no—
149C42—611no—
150C42—611no—
151C42—611no—
152C42—611no—
153C23—21no—
154C23—1221no—
155C23C22⋊#692311yescharacteristic
156Q8—41no—
157Q8—2441no—
158D4—41no—
159D4—42no—
160D4—2441no—
161D4—2442no—
162D4—2442no—
163D4—2442no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—42no—
167C2×C4—611no—
168C2×C4—611no—
169C2×C4—611no—
170C2×C4—611no—
171C2×C4—1222no—
172C2×C4—1221no—
173C2×C4—2442no—
174C2×C4—2441no—
175C2×C4C22⋊#692311yescharacteristic
176C2×C4C22×#692311yescharacteristic
177C8—1224no—
178C8—2442no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—2441no—
185C22—2441no—
186C22—2441no—
187C22#1451983712yes—
188C22C2×C22⋊#692311yescharacteristic
189C4—21no—
190C4—21no—
191C4—41no—
192C4—612no—
193C4—1221no—
194C4—1221no—
195C4—1221no—
196C4—2441no—
197C2—22no—
198C2—81no—
199C2—4881no—
200C2C2×#1451983711yescharacteristic
201C2D61⋊#10411yescharacteristic
202C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×#41×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×#41#6923
hypocenterC61#1530
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #16840782C2semidirect
2. C2×#14519832C2semidirect
3. #16840618C2semidirect
4. #16840617C2semidirect
107. C61#1530semidirect