Finite Group Databasebeta

← C2×#16840665 #21462069

Subgroups — C2×#16840665 #21462069

Order 7808.

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

normal subgroups only

This group has 278 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
1C2×#14519837C211yesmaximal, characteristic
2C2×#14519835C211yesmaximal, characteristic
3#16840665C214yesmaximal, direct product factor
4C2×#14519761C211yesmaximal, characteristic
5C2×#11758217—21no—
6C2×C22⋊#6923—21no—
7#14519837—21no—
8#14519837C2212yes—
9#14519835—21no—
10#14519835C2212yes—
11C22×C22⋊D61C2211yescharacteristic
12C23×Dic61C411yescharacteristic, complemented
13#14519761—21no—
14#14519761—21no—
15#14519761C412yescomplemented
16#14519761C2212yes—
17C2×C4⋊Dic61—21no—
18C2×#11758198—21no—
19C2×C22⋊C4×C61C411yescharacteristic, complemented
20C24×C61C2×C411yescharacteristic
21C23×D61D411yescharacteristic
22C22×#6923—41no—
23C22×C4×C61—21no—
24C2×C22⋊D61—41no—
25C2×C22⋊D61—41no—
26C2×C22⋊D61C2×C411yescharacteristic
27C2×C22⋊D61D411yescharacteristic
28C2×C22⋊D61D411yescharacteristic
29C2×C22⋊D61C2311yescharacteristic
30C22×Dic61—21no—
31C22×Dic61—21no—
32C22×Dic61—41no—
33C22×Dic61—41no—
34C22×Dic61C2×C412yescomplemented
35C22×Dic61D411yescharacteristic
36C22⋊#6923—22no—
37C22⋊#6923—41no—
38#11758217—22no—
39#11758217—41no—
40C2×#92420—41no—
41C22⋊C4×C61—21no—
42C22⋊C4×C61C2×C412yescomplemented
43#11758198—22no—
44#11758198—22no—
45C4⋊Dic61—22no—
46C4⋊Dic61—22no—
47C23×C61—21no—
48C23×C61—21no—
49C23×C61—42no—
50C23×C61C22⋊C411yescharacteristic
51C23×C61C22⋊C411yescharacteristic
52C23×C61C22×C411yescharacteristic
53C22×D61—21no—
54C22×D61—21no—
55C22×D61—42no—
56C22×D61C22⋊C411yescharacteristic
57C22×D61C2×D411yescharacteristic
58C2×#6923—42no—
59C2×#6923—82no—
60C2×C4×C61—22no—
61C2×C4×C61—42no—
62C22⋊D61—41no—
63C22⋊D61—41no—
64C22⋊D61—41no—
65C22⋊D61—41no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—22no—
69C2×Dic61—42no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—42no—
73C2×Dic61C22⋊C411yescharacteristic
74C2×Dic61C2×D411yescharacteristic
75#92420—42no—
76C22×C61—22no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61—42no—
82C22×C61—42no—
83C22×C61#9911yescharacteristic
84C22×C61#9911yescharacteristic
85C22×C61C2×C22⋊C411yescharacteristic
86C2×D61—21no—
87C2×D61—21no—
88C2×D61—42no—
89C2×D61—41no—
90C2×D61—41no—
91C2×D61—81no—
92#6923—82no—
93C4×C61—42no—
94Dic61—21no—
95Dic61—21no—
96Dic61—42no—
97C2×#352—611nomaximal, Sylow
98C2×C61—21no—
99C2×C61—21no—
100C2×C61—41no—
101C2×C61—41no—
102C2×C61#35212yescomplemented
103C2×C61C2×#9911yescharacteristic
104D61—41no—
105D61—41no—
106C2×#123—611no—
107C2×#100—611no—
108C2×#99—611no—
109#352—614no—
110C61C2×#35211yescharacteristic, complemented, Sylow
111C22×D4—611no—
112C23×C4—611no—
113C2×M16—1221no—
114#123—612no—
115#123—612no—
116#123—1221no—
117#123—1221no—
118C2×C4⋊C4—1221no—
119C2×C22⋊C4—1221no—
120C2×C22⋊C4—1221no—
121C2×C22⋊C4#692311yescharacteristic, complemented
122#100—612no—
123#100—1221no—
124#99—612no—
125#99—1221no—
126C24—611no—
127C24C2×#692311yescharacteristic
128C2×D4—611no—
129C2×D4—611no—
130C2×D4—611no—
131C2×D4—611no—
132C2×D4—2441no—
133C2×D4—2441no—
134C22×C4—21no—
135C22×C4—611no—
136C22×C4—612no—
137C22×C4—1221no—
138C22×C4—1221no—
139C22×C4—2441no—
140C22×C4—2441no—
141C22×C4—2441no—
142M16—1222no—
143M16—2441no—
144C2×C8—2441no—
145C4⋊C4—1222no—
146C4⋊C4—1222no—
147C22⋊C4—21no—
148C22⋊C4—1222no—
149C22⋊C4—1222no—
150C22⋊C4—1222no—
151C22⋊C4—2441no—
152C22⋊C4C2×#692312yescomplemented
153C23—21no—
154C23—21no—
155C23—42no—
156C23—611no—
157C23—611no—
158C23—1221no—
159C23—1221no—
160C23—2442no—
161C23C22⋊#692311yescharacteristic
162C23C22⋊#692311yescharacteristic
163C23C22×#692311yescharacteristic
164D4—2441no—
165D4—2441no—
166D4—2441no—
167D4—2441no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—611no—
171C2×C4—611no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1222no—
175C2×C4—4882no—
176C2×C4—2442no—
177C2×C4—2442no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4—2442no—
181C8—2442no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—1221no—
190C22—1221no—
191C22—4881no—
192C22—2441no—
193C22—2441no—
194C22—2442no—
195C22#1451983611yescharacteristic
196C22#1451983611yescharacteristic
197C22C2×C22⋊#692311yescharacteristic
198C4—42no—
199C4—1221no—
200C4—1221no—
201C4—4882no—
202C4—2442no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—2441no—
208C2—2441no—
209C2#1684066512yesdirect product factor
210C2C2×#1451983611yescharacteristic
subgroupG/H
centerC22#14519836
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61#99
hypercenterC2×C22⋊C4#6923
hypocenterC61C2×#352
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #16840665C2direct (N × H)
12. C23×Dic61C4semidirect
15. #14519761C4semidirect
19. C2×C22⋊C4×C61C4semidirect
34. C22×Dic61C2×C4semidirect
42. C22⋊C4×C61C2×C4semidirect
102. C2×C61#352semidirect
110. C61C2×#352semidirect
121. C2×C22⋊C4#6923semidirect
152. C22⋊C4C2×#6923semidirect
209. C2#16840665direct (N × H)