Finite Group Databasebeta

← C2×#16840100 #21455708

Subgroups — C2×#16840100 #21455708

Order 7808.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519736C211yesmaximal, characteristic
2#16840100C218yesmaximal, direct product factor
3C2×#14519710C211yesmaximal, characteristic, complemented
4C2×#14519708C211yesmaximal, characteristic, complemented
5C2×#14519701C211yesmaximal, characteristic, complemented
6C2×#14519701C211yesmaximal, characteristic, complemented
7C2×C22⋊#92418C211yesmaximal, characteristic
8C2×C22⋊Q8×C61C211yesmaximal, characteristic
9C22×#92418C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11#14519736—22no—
12#14519736C2214yes—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C22⋊Dic61—21no—
16C2×C4×Dic61—21no—
17#14519710C2214yescomplemented
18#14519708C2214yescomplemented
19#14519701C2214yescomplemented
20#14519701C2214yescomplemented
21C22⋊#92418C2214yes—
22C22×Q8×C61C2211yescharacteristic
23C23×C4×C61C2211yescharacteristic
24C22⋊Q8×C61—22no—
25C22⋊Q8×C61C2214yes—
26C2×C4⋊C4×C61—21no—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61—21no—
29C24×C61D411yescharacteristic
30C2×Q8×C61—21no—
31C2×Q8×C61—22no—
32C2×Q8×C61—22no—
33C2×Q8×C61C2312yes—
34C22×C4×C61—22no—
35C22×C4×C61—22no—
36C22×C4×C61—21no—
37C22×C4×C61—21no—
38C22×C4×C61D411yescharacteristic
39C22×C4×C61D412yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×Dic61—21no—
43C22×Dic61—21no—
44C4⋊C4×C61—24no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61C2312yes—
47C22⋊C4×C61—24no—
48C22⋊Dic61—24no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61C2312yes—
52C4⋊Dic61C2312yes—
53C4×Dic61—24no—
54C2×#92418—22no—
55C2×#92418—22no—
56C2×#92418C2312yes—
57C2×#92418C2312yes—
58C23×C61—22no—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61C2×D412yes—
62C23×C61C2×D411yescharacteristic
63Q8×C61—22no—
64Q8×C61—22no—
65Q8×C61—42no—
66C2×C4×C61—22no—
67C2×C4×C61—24no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61#4112yes—
77C2×C4×C61#4112yes—
78C2×C4×C61C2411yescharacteristic
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83#92418—22no—
84#92418—22no—
85C22×C61—22no—
86C22×C61—22no—
87C22×C61—22no—
88C22×C61—44no—
89C22×C61#12312yes—
90C22×C61#13512yes—
91C22×C61#13712yes—
92C22×C61C22×D411yescharacteristic
93C4×C61—22no—
94C4×C61—42no—
95C4×C61—42no—
96C4×C61#12312yes—
97C4×C61C2×#4111yescharacteristic
98C4×C61C2×#4111yescharacteristic
99Dic61—42no—
100Dic61—42no—
101C2×#485—611nomaximal, Sylow
102C2×C61—42no—
103C2×C61#48514yescomplemented
104C2×C61C2×#12311yescharacteristic
105C2×C61C2×#13511yescharacteristic
106C2×C61C2×#13711yescharacteristic
107C2×C22⋊Q8D6111yescharacteristic
108C2×#117—611no—
109#485—618no—
110C2×#107—611no—
111C2×#106—611no—
112C2×#103—611no—
113C2×#103—611no—
114C2×C22⋊C8—611no—
115C61C2×#48511yescharacteristic, complemented, Sylow
116C22×Q8C2×D6111yescharacteristic
117C23×C4C2×D6111yescharacteristic
118C22×C8—611no—
119C22×C8—611no—
120C22⋊Q8—22no—
121C22⋊Q8C2×D6114yes—
122#117—614no—
123#117—1222no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—611no—
126C2×C4⋊C4—611no—
127C2×C4⋊C4C2×D6111yescharacteristic
128C2×C22⋊C4—21no—
129C2×C22⋊C4—1221no—
130C2×C42—1221no—
131#107—614no—
132#106—614no—
133#103—614no—
134#103—614no—
135C22⋊C8—614no—
136C24C22⋊D6111yescharacteristic
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8C22×D6112yes—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—1221no—
146C22×C4—1221no—
147C22×C4C22⋊D6112yes—
148C22×C4C22⋊D6111yescharacteristic
149C22×C4C22×D6112yes—
150C22×C4C22×D6111yescharacteristic
151C2×C8—612no—
152C2×C8—612no—
153C2×C8—1222no—
154C2×C8—1222no—
155C4⋊C4—24no—
156C4⋊C4—21no—
157C4⋊C4—612no—
158C4⋊C4—612no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C4⋊C4C22×D6112yes—
162C22⋊C4—24no—
163C22⋊C4—1224no—
164C42—1224no—
165C23—22no—
166C23—22no—
167C23—22no—
168C23C2×C22⋊D6112yes—
169C23C2×C22⋊D6111yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—42no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—2442no—
184C2×C4—2442no—
185C2×C4#1175822412yes—
186C2×C4#1175822412yes—
187C2×C4C2×C22⋊D6112yes—
188C2×C4C2×C22⋊D6111yescharacteristic
189C2×C4C23×D6111yescharacteristic
190C8—1222no—
191C8—1222no—
192C22—22no—
193C22—22no—
194C22—22no—
195C22—44no—
196C22#1451975812yes—
197C22#1451979712yes—
198C22#1451980812yes—
199C22C22×C22⋊D6111yescharacteristic
200C4—22no—
201C4—42no—
202C4—42no—
203C4—2442no—
204C4—2442no—
205C4#1451975812yes—
206C4C2×#1175822411yescharacteristic
207C4C2×#1175822411yescharacteristic
208C2—42no—
209C2#1684010014yesdirect product factor
210C2C2×#1451975811yescharacteristic
211C2C2×#1451979711yescharacteristic
212C2C2×#1451980811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C22⋊Q8×C61C2
socleC23×C61C2×D4
hypercenterC2×C22⋊Q8D61
hypocenterC61C2×#485
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16840100C2direct (N × H)
3. C2×#14519710C2semidirect
4. C2×#14519708C2semidirect
5. C2×#14519701C2semidirect
6. C2×#14519701C2semidirect
17. #14519710C22semidirect
18. #14519708C22semidirect
19. #14519701C22semidirect
20. #14519701C22semidirect
103. C2×C61#485semidirect
115. C61C2×#485semidirect
209. C2#16840100direct (N × H)