Finite Group Databasebeta

← C2×#16840066 #21455593

Subgroups — C2×#16840066 #21455593

Order 7808.

384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4×Dic122C211yesmaximal, characteristic
2#16840066C218yesmaximal, direct product factor
3C2×#14519710C211yesmaximal, characteristic
4C2×#14519708C211yesmaximal, characteristic
5C2×C4⋊#92418C211yesmaximal, characteristic
6C2×#14519700C211yesmaximal, characteristic
7C2×#14519700C211yesmaximal, characteristic
8C2×#125×C61C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11C22×#92418C2211yescharacteristic
12C4×Dic122—22no—
13C4×Dic122C2214yes—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196—21no—
16C2×C4×Dic61—21no—
17#14519710C2214yes—
18#14519708C2214yes—
19C4⋊#92418C2214yes—
20#14519700C2214yes—
21#14519700C2214yes—
22#125×C61—22no—
23#125×C61C2214yes—
24C2×C4⋊C4×C61—21no—
25C2×C4⋊C4×C61—21no—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C42×C61C2211yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61—21no—
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—21no—
35C22×Dic61—21no—
36C2×Dic122—21no—
37C2×Dic122—22no—
38C2×Dic122Q814yes—
39C2×Dic122C2312yes—
40C4⋊C4×C61—24no—
41C4⋊C4×C61—24no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61—21no—
44C4⋊C4×C61C2312yes—
45C4⋊C4×C61C2312yes—
46C42×C61D412yes—
47C42×C61C2312yes—
48C4⋊Dic61—21no—
49C4⋊Dic61C2312yes—
50#11758196—24no—
51C4×Dic61—24no—
52C2×#92418—22no—
53C2×#92418—22no—
54C2×#92418C2312yes—
55C2×#92418C2312yes—
56C23×C61C2×D411yescharacteristic
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—42no—
62C2×C4×C61—42no—
63C2×C4×C61C2×D412yes—
64C2×C4×C61C2×D412yes—
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×Q812yes—
67C2×C4×C61#4112yes—
68C2×C4×C61C2411yescharacteristic
69C2×Dic61—24no—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—42no—
73Dic122—24no—
74Dic122—22no—
75Dic122C2×Q814yes—
76#92418—22no—
77#92418—22no—
78C22×C61C22⋊Q812yes—
79C22×C61#13512yes—
80C22×C61#13712yes—
81C22×C61C22×D411yescharacteristic
82C4×C61—22no—
83C4×C61—22no—
84C4×C61—42no—
85C4×C61—42no—
86C4×C61C22⋊Q812yes—
87C4×C61C22×Q811yescharacteristic
88C4×C61C2×#4111yescharacteristic
89Dic61—24no—
90Dic61—42no—
91C2×#479—611nomaximal, Sylow
92C2×C61#47914yescomplemented
93C2×C61C2×C22⋊Q811yescharacteristic
94C2×C61C2×#13511yescharacteristic
95C2×C61C2×#13711yescharacteristic
96C2×#125D6111yescharacteristic
97C2×C4×Q8—611no—
98#479—618no—
99C2×#107—611no—
100C2×#106—611no—
101C2×C4⋊C8—611no—
102C2×#103—611no—
103C2×#103—611no—
104C61C2×#47911yescharacteristic, complemented, Sylow
105C22×Q8—611no—
106C22×C8—611no—
107C22×C8—611no—
108#125—22no—
109#125C2×D6114yes—
110C4×Q8—614no—
111C4×Q8—1222no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—611no—
115C2×C4⋊C4—1221no—
116C2×C4⋊C4C2×D6111yescharacteristic
117C2×C4⋊C4C2×D6111yescharacteristic
118C2×C42—1221no—
119C2×C42C2×D6111yescharacteristic
120#107—614no—
121#106—614no—
122C4⋊C8—614no—
123#103—614no—
124#103—614no—
125C2×Q8—614no—
126C2×Q8—612no—
127C2×Q8—1222no—
128C2×Q8—1221no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—1221no—
132C22×C4—1221no—
133C22×C4C22⋊D6111yescharacteristic
134C22×C4C22⋊D6111yescharacteristic
135C22×C4C22×D6111yescharacteristic
136C2×C8—612no—
137C2×C8—612no—
138C2×C8—1222no—
139C2×C8—1222no—
140C4⋊C4—24no—
141C4⋊C4—24no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—612no—
145C4⋊C4—1221no—
146C4⋊C4—1224no—
147C4⋊C4C22×D6112yes—
148C4⋊C4C22×D6112yes—
149C42—1224no—
150C42C22⋊D6112yes—
151C42C22×D6112yes—
152C23C2×C22⋊D6111yescharacteristic
153Q8—614no—
154Q8—1222no—
155Q8—1224no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—1222no—
163C2×C4—1224no—
164C2×C4—1222no—
165C2×C4—2442no—
166C2×C4Q8×D6112yes—
167C2×C4#1175822612yes—
168C2×C4C2×C22⋊D6112yes—
169C2×C4C2×C22⋊D6112yes—
170C2×C4C2×C22⋊D6111yescharacteristic
171C2×C4C23×D6111yescharacteristic
172C8—1222no—
173C8—1222no—
174C22#1451975312yes—
175C22#1451979712yes—
176C22#1451980712yes—
177C22C22×C22⋊D6111yescharacteristic
178C4—22no—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—1224no—
183C4—2442no—
184C4#1451975312yes—
185C4C2×Q8×D6111yescharacteristic
186C4C2×#1175822611yescharacteristic
187C2#1684006614yesdirect product factor
188C2C2×#1451975311yescharacteristic
189C2C2×#1451979711yescharacteristic
190C2C2×#1451980711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#125×C61C2
socleC23×C61C2×D4
hypercenterC2×#125D61
hypocenterC61C2×#479
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #16840066C2direct (N × H)
92. C2×C61#479semidirect
104. C61C2×#479semidirect
187. C2#16840066direct (N × H)