Finite Group Databasebeta

← C2×#16840105 #21455713

Subgroups — C2×#16840105 #21455713

Order 7808.

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×#14519757C211yesmaximal, characteristic
2C2×#14519735C211yesmaximal, characteristic
3#16840105C218yesmaximal, direct product factor
4C2×#14519708C211yesmaximal, characteristic, complemented
5C2×#14519702C211yesmaximal, characteristic, complemented
6C2×#14519700C211yesmaximal, characteristic, complemented
7C2×#14519689C211yesmaximal, characteristic
8C2×#107×C61C211yesmaximal, characteristic, complemented
9C22×Dic122C2211yescharacteristic
10C22×C4×D61C2211yescharacteristic
11C22×#92418C2211yescharacteristic
12#14519757—22no—
13#14519757C2214yes—
14#14519735—22no—
15#14519735C2214yes—
16C2×C4⋊Dic61—21no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758198—21no—
19C2×#11758198—21no—
20C2×C4×Dic61—21no—
21#14519708C2214yescomplemented
22#14519702C2214yescomplemented
23#14519700C2214yescomplemented
24#14519689C2214yes—
25C22×C8×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28#107×C61C2214yescomplemented
29C23×D61D411yescharacteristic
30C22×C4×C61—21no—
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C22×Dic61—21no—
34C22×Dic61—21no—
35C22×Dic61D411yescharacteristic
36C2×C4×D61—22no—
37C2×C4×D61—22no—
38C2×C4×D61D412yes—
39C2×C4×D61C2312yes—
40C2×Dic122—22no—
41C2×Dic122—22no—
42C2×Dic122—21no—
43C2×Dic122C2312yes—
44C2×C8×C61—22no—
45C2×C8×C61C2312yes—
46C4⋊C4×C61—21no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61C2312yes—
49C4⋊C4×C61C2312yes—
50#11758198—24no—
51#11758198—24no—
52C4⋊Dic61—21no—
53C4⋊Dic61—24no—
54C4⋊Dic61C2312yes—
55C4×Dic61—24no—
56C2×#92418—22no—
57C2×#92418C2312yes—
58C23×C61C2×D411yescharacteristic
59C22×D61—22no—
60C22×D61—22no—
61C22×D61—22no—
62C22×D61C2×D412yes—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61#4112yes—
69C2×C4×C61#4112yes—
70C2×C4×C61C2411yescharacteristic
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—42no—
75C2×Dic61—42no—
76C2×Dic61C2×D412yes—
77C4×D61—24no—
78C4×D61—22no—
79C4×D61—22no—
80Dic122—22no—
81Dic122—22no—
82Dic122—42no—
83C8×C61—22no—
84#92418—22no—
85C22×C61#12312yes—
86C22×C61#13512yes—
87C22×C61#13712yes—
88C22×C61C22×D411yescharacteristic
89C2×D61—22no—
90C2×D61—22no—
91C2×D61—22no—
92C2×D61—44no—
93C4×C61—42no—
94C4×C61—42no—
95C4×C61#12312yes—
96C4×C61C2×#4111yescharacteristic
97C4×C61C2×#4111yescharacteristic
98Dic61—22no—
99Dic61—42no—
100Dic61—42no—
101C2×#485—611nomaximal, Sylow
102C2×C61#48514yescomplemented
103C2×C61C2×#12311yescharacteristic
104C2×C61C2×#13511yescharacteristic
105C2×C61C2×#13711yescharacteristic
106D61—42no—
107C2×C22⋊Q8—611no—
108C2×#117—611no—
109#485—618no—
110C2×#107D6111yescharacteristic, complemented
111C2×#106—611no—
112C2×#103—611no—
113C2×#103—611no—
114C2×C22⋊C8—611no—
115C61C2×#48511yescharacteristic, complemented, Sylow
116C22×Q8—611no—
117C23×C4—611no—
118C22×C8—611no—
119C22×C8C2×D6111yescharacteristic
120C22⋊Q8—614no—
121C22⋊Q8—1222no—
122#117—614no—
123#117—1222no—
124C2×C4⋊C4—611no—
125C2×C4⋊C4—1221no—
126C2×C4⋊C4C2×D6111yescharacteristic
127C2×C4⋊C4C2×D6111yescharacteristic
128C2×C22⋊C4—1221no—
129C2×C22⋊C4—1221no—
130C2×C42—1221no—
131#107C2×D6114yescomplemented
132#106—614no—
133#103—614no—
134#103—614no—
135C22⋊C8—614no—
136C24—611no—
137C2×Q8—612no—
138C2×Q8—1221no—
139C2×Q8—1222no—
140C2×Q8—1222no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—611no—
144C22×C4—612no—
145C22×C4—612no—
146C22×C4—1222no—
147C22×C4—1222no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4C22×D6111yescharacteristic
151C2×C8—22no—
152C2×C8—612no—
153C2×C8—1222no—
154C2×C8C22×D6112yes—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—612no—
158C4⋊C4—1224no—
159C4⋊C4—1221no—
160C4⋊C4C22×D6112yes—
161C4⋊C4C22×D6112yes—
162C22⋊C4—1224no—
163C22⋊C4—1224no—
164C42—1224no—
165C23—612no—
166C23—1222no—
167C23—1222no—
168C23—1222no—
169C23D4×D6111yescharacteristic
170Q8—1222no—
171Q8—1222no—
172Q8—2442no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—612no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1224no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—2442no—
185C2×C4—2442no—
186C2×C4#1175822212yes—
187C2×C4D4×D6111yescharacteristic
188C2×C4#1175822612yes—
189C2×C4C23×D6111yescharacteristic
190C8—22no—
191C8—1222no—
192C22—1222no—
193C22—1222no—
194C22—1222no—
195C22—2444no—
196C22#1451976212yes—
197C22#1451979612yes—
198C22#1451980912yes—
199C22C2×D4×D6111yescharacteristic
200C4—42no—
201C4—42no—
202C4—1222no—
203C4—2442no—
204C4—2442no—
205C4#1451976212yes—
206C4C2×#1175822211yescharacteristic
207C4C2×#1175822611yescharacteristic
208C2—2442no—
209C2#1684010514yesdirect product factor
210C2C2×#1451976211yescharacteristic
211C2C2×#1451979611yescharacteristic
212C2C2×#1451980911yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#107×C61C2
socleC23×C61C2×D4
hypercenterC2×#107D61
hypocenterC61C2×#485
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #16840105C2direct (N × H)
4. C2×#14519708C2semidirect
5. C2×#14519702C2semidirect
6. C2×#14519700C2semidirect
8. C2×#107×C61C2semidirect
21. #14519708C22semidirect
22. #14519702C22semidirect
23. #14519700C22semidirect
28. #107×C61C22semidirect
102. C2×C61#485semidirect
110. C2×#107D61semidirect
115. C61C2×#485semidirect
131. #107C2×D61semidirect
209. C2#16840105direct (N × H)