Finite Group Databasebeta

← C2×#16810966 #20284609

Subgroups — C2×#16810966 #20284609

Order 6784.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13133197C211yesmaximal, characteristic
2C2×#13133175C211yesmaximal, characteristic
3#16810966C218yesmaximal, direct product factor
4C2×#13133148C211yesmaximal, characteristic, complemented
5C2×#13133142C211yesmaximal, characteristic, complemented
6C2×#13133140C211yesmaximal, characteristic, complemented
7C2×#13133129C211yesmaximal, characteristic
8C2×#107×C53C211yesmaximal, characteristic, complemented
9C22×Dic106C2211yescharacteristic
10C22×C4×D53C2211yescharacteristic
11C22×#88322C2211yescharacteristic
12#13133197—22no—
13#13133197C2214yes—
14#13133175—22no—
15#13133175C2214yes—
16C2×C4⋊Dic53—21no—
17C2×C4⋊Dic53C2211yescharacteristic
18C2×#11719921—21no—
19C2×#11719921—21no—
20C2×C4×Dic53—21no—
21#13133148C2214yescomplemented
22#13133142C2214yescomplemented
23#13133140C2214yescomplemented
24#13133129C2214yes—
25C22×C8×C53C2211yescharacteristic
26C2×C4⋊C4×C53C2211yescharacteristic
27C2×C4⋊C4×C53C2211yescharacteristic
28#107×C53C2214yescomplemented
29C23×D53D411yescharacteristic
30C22×C4×C53—21no—
31C22×C4×C53—21no—
32C22×C4×C53C2311yescharacteristic
33C22×Dic53—21no—
34C22×Dic53—21no—
35C22×Dic53D411yescharacteristic
36C2×C4×D53—22no—
37C2×C4×D53—22no—
38C2×C4×D53D412yes—
39C2×C4×D53C2312yes—
40C2×Dic106—22no—
41C2×Dic106—22no—
42C2×Dic106—21no—
43C2×Dic106C2312yes—
44C2×C8×C53—22no—
45C2×C8×C53C2312yes—
46C4⋊C4×C53—21no—
47C4⋊C4×C53—21no—
48C4⋊C4×C53C2312yes—
49C4⋊C4×C53C2312yes—
50#11719921—24no—
51#11719921—24no—
52C4⋊Dic53—21no—
53C4⋊Dic53—24no—
54C4⋊Dic53C2312yes—
55C4×Dic53—24no—
56C2×#88322—22no—
57C2×#88322C2312yes—
58C23×C53C2×D411yescharacteristic
59C22×D53—22no—
60C22×D53—22no—
61C22×D53—22no—
62C22×D53C2×D412yes—
63C2×C4×C53—22no—
64C2×C4×C53—22no—
65C2×C4×C53—42no—
66C2×C4×C53—42no—
67C2×C4×C53C2×D411yescharacteristic
68C2×C4×C53#4112yes—
69C2×C4×C53#4112yes—
70C2×C4×C53C2411yescharacteristic
71C2×Dic53—22no—
72C2×Dic53—22no—
73C2×Dic53—22no—
74C2×Dic53—42no—
75C2×Dic53—42no—
76C2×Dic53C2×D412yes—
77C4×D53—24no—
78C4×D53—22no—
79C4×D53—22no—
80Dic106—22no—
81Dic106—22no—
82Dic106—42no—
83C8×C53—22no—
84#88322—22no—
85C22×C53#12312yes—
86C22×C53#13512yes—
87C22×C53#13712yes—
88C22×C53C22×D411yescharacteristic
89C2×D53—22no—
90C2×D53—22no—
91C2×D53—22no—
92C2×D53—44no—
93C4×C53—42no—
94C4×C53—42no—
95C4×C53#12312yes—
96C4×C53C2×#4111yescharacteristic
97C4×C53C2×#4111yescharacteristic
98Dic53—22no—
99Dic53—42no—
100Dic53—42no—
101C2×#485—531nomaximal, Sylow
102C2×C53#48514yescomplemented
103C2×C53C2×#12311yescharacteristic
104C2×C53C2×#13511yescharacteristic
105C2×C53C2×#13711yescharacteristic
106D53—42no—
107C2×C22⋊Q8—531no—
108C2×#117—531no—
109#485—538no—
110C2×#107D5311yescharacteristic, complemented
111C2×#106—531no—
112C2×#103—531no—
113C2×#103—531no—
114C2×C22⋊C8—531no—
115C53C2×#48511yescharacteristic, complemented, Sylow
116C22×Q8—531no—
117C23×C4—531no—
118C22×C8—531no—
119C22×C8C2×D5311yescharacteristic
120C22⋊Q8—534no—
121C22⋊Q8—1062no—
122#117—534no—
123#117—1062no—
124C2×C4⋊C4—531no—
125C2×C4⋊C4—1061no—
126C2×C4⋊C4C2×D5311yescharacteristic
127C2×C4⋊C4C2×D5311yescharacteristic
128C2×C22⋊C4—1061no—
129C2×C22⋊C4—1061no—
130C2×C42—1061no—
131#107C2×D5314yescomplemented
132#106—534no—
133#103—534no—
134#103—534no—
135C22⋊C8—534no—
136C24—531no—
137C2×Q8—532no—
138C2×Q8—1061no—
139C2×Q8—1062no—
140C2×Q8—1062no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—531no—
144C22×C4—532no—
145C22×C4—532no—
146C22×C4—1062no—
147C22×C4—1062no—
148C22×C4—1061no—
149C22×C4—1061no—
150C22×C4C22×D5311yescharacteristic
151C2×C8—22no—
152C2×C8—532no—
153C2×C8—1062no—
154C2×C8C22×D5312yes—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—532no—
158C4⋊C4—1064no—
159C4⋊C4—1061no—
160C4⋊C4C22×D5312yes—
161C4⋊C4C22×D5312yes—
162C22⋊C4—1064no—
163C22⋊C4—1064no—
164C42—1064no—
165C23—532no—
166C23—1062no—
167C23—1062no—
168C23—1062no—
169C23D4×D5311yescharacteristic
170Q8—1062no—
171Q8—1062no—
172Q8—2122no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—532no—
178C2×C4—1062no—
179C2×C4—1064no—
180C2×C4—1062no—
181C2×C4—1062no—
182C2×C4—1062no—
183C2×C4—1062no—
184C2×C4—2122no—
185C2×C4—2122no—
186C2×C4#1171994512yes—
187C2×C4D4×D5311yescharacteristic
188C2×C4#1171994912yes—
189C2×C4C23×D5311yescharacteristic
190C8—22no—
191C8—1062no—
192C22—1062no—
193C22—1062no—
194C22—1062no—
195C22—2124no—
196C22#1313320212yes—
197C22#1313323612yes—
198C22#1313324912yes—
199C22C2×D4×D5311yescharacteristic
200C4—42no—
201C4—42no—
202C4—1062no—
203C4—2122no—
204C4—2122no—
205C4#1313320212yes—
206C4C2×#1171994511yescharacteristic
207C4C2×#1171994911yescharacteristic
208C2—2122no—
209C2#1681096614yesdirect product factor
210C2C2×#1313320211yescharacteristic
211C2C2×#1313323611yescharacteristic
212C2C2×#1313324911yescharacteristic
subgroupG/H
centerC23D4×D53
commutatorC2×C4×C53C24
FrattiniC2×C4C23×D53
FittingC2×#107×C53C2
socleC23×C53C2×D4
hypercenterC2×#107D53
hypocenterC53C2×#485
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #16810966C2direct (N × H)
4. C2×#13133148C2semidirect
5. C2×#13133142C2semidirect
6. C2×#13133140C2semidirect
8. C2×#107×C53C2semidirect
21. #13133148C22semidirect
22. #13133142C22semidirect
23. #13133140C22semidirect
28. #107×C53C22semidirect
102. C2×C53#485semidirect
110. C2×#107D53semidirect
115. C53C2×#485semidirect
131. #107C2×D53semidirect
209. C2#16810966direct (N × H)