Finite Group Databasebeta

← C2×#16840069 #21455596

Subgroups — C2×#16840069 #21455596

Order 7808.

384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14519769C211yesmaximal, characteristic
2#16840069C218yesmaximal, direct product factor
3C2×#14519710C211yesmaximal, characteristic
4C2×#14519708C211yesmaximal, characteristic
5C2×C4⋊#92418C211yesmaximal, characteristic
6C2×#14519701C211yesmaximal, characteristic
7C2×#14519701C211yesmaximal, characteristic
8C2×C4×Q8×C61C211yesmaximal, characteristic
9C22×#92418C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11#14519769—22no—
12#14519769C2214yes—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196—21no—
16C2×#11758196—21no—
17#14519710C2214yes—
18#14519708C2214yes—
19C4⋊#92418C2214yes—
20#14519701C2214yes—
21#14519701C2214yes—
22C22×Q8×C61C2211yescharacteristic
23C4×Q8×C61—22no—
24C4×Q8×C61C2214yes—
25C2×C4⋊C4×C61—21no—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C42×C61—21no—
28C2×C42×C61C2211yescharacteristic
29C2×Q8×C61—21no—
30C2×Q8×C61—22no—
31C2×Q8×C61Q814yes—
32C2×Q8×C61C2312yes—
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61—21no—
39C22×Dic61—21no—
40C4⋊C4×C61—24no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61C2312yes—
43C42×C61—24no—
44C42×C61D412yes—
45C42×C61C2312yes—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61C2312yes—
49C4⋊Dic61C2312yes—
50#11758196—24no—
51#11758196—24no—
52C2×#92418—22no—
53C2×#92418—22no—
54C2×#92418C2312yes—
55C2×#92418C2312yes—
56C23×C61C2×D411yescharacteristic
57Q8×C61—24no—
58Q8×C61—22no—
59Q8×C61C2×Q814yes—
60C2×C4×C61—24no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—42no—
66C2×C4×C61C2×D412yes—
67C2×C4×C61C2×D412yes—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×Q812yes—
70C2×C4×C61#4112yes—
71C2×C4×C61C2411yescharacteristic
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—42no—
75C2×Dic61—42no—
76#92418—22no—
77#92418—22no—
78C22×C61C22⋊Q812yes—
79C22×C61#13512yes—
80C22×C61#13712yes—
81C22×C61C22×D411yescharacteristic
82C4×C61—24no—
83C4×C61—22no—
84C4×C61—22no—
85C4×C61—42no—
86C4×C61C22⋊Q812yes—
87C4×C61C22×Q811yescharacteristic
88C4×C61C2×#4111yescharacteristic
89Dic61—42no—
90Dic61—42no—
91C2×#479—611nomaximal, Sylow
92C2×C61#47914yescomplemented
93C2×C61C2×C22⋊Q811yescharacteristic
94C2×C61C2×#13511yescharacteristic
95C2×C61C2×#13711yescharacteristic
96C2×#125—611no—
97C2×C4×Q8D6111yescharacteristic
98#479—618no—
99C2×#107—611no—
100C2×#106—611no—
101C2×C4⋊C8—611no—
102C2×#103—611no—
103C2×#103—611no—
104C61C2×#47911yescharacteristic, complemented, Sylow
105C22×Q8C2×D6111yescharacteristic
106C22×C8—611no—
107C22×C8—611no—
108#125—614no—
109#125—1222no—
110C4×Q8—22no—
111C4×Q8C2×D6114yes—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—611no—
114C2×C4⋊C4—611no—
115C2×C4⋊C4—1221no—
116C2×C4⋊C4—1221no—
117C2×C4⋊C4C2×D6111yescharacteristic
118C2×C42—21no—
119C2×C42C2×D6111yescharacteristic
120#107—614no—
121#106—614no—
122C4⋊C8—614no—
123#103—614no—
124#103—614no—
125C2×Q8—22no—
126C2×Q8—21no—
127C2×Q8Dic12214yes—
128C2×Q8C22×D6112yes—
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—21no—
142C4⋊C4—612no—
143C4⋊C4—612no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C4⋊C4—1224no—
147C4⋊C4—1224no—
148C4⋊C4C22×D6112yes—
149C42—24no—
150C42C22⋊D6112yes—
151C42C22×D6112yes—
152C23C2×C22⋊D6111yescharacteristic
153Q8—22no—
154Q8—24no—
155Q8C2×Dic12214yes—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4—2442no—
165C2×C4—2442no—
166C2×C4C2×Dic12212yes—
167C2×C4#1175822212yes—
168C2×C4C2×C22⋊D6112yes—
169C2×C4C2×C22⋊D6112yes—
170C2×C4C2×C22⋊D6111yescharacteristic
171C2×C4C23×D6111yescharacteristic
172C8—1222no—
173C8—1222no—
174C22#1451975612yes—
175C22#1451979712yes—
176C22#1451980812yes—
177C22C22×C22⋊D6111yescharacteristic
178C4—24no—
179C4—22no—
180C4—22no—
181C4—42no—
182C4—2442no—
183C4—2442no—
184C4#1451975612yes—
185C4C22×Dic12211yescharacteristic
186C4C2×#1175822211yescharacteristic
187C2#1684006914yesdirect product factor
188C2C2×#1451975611yescharacteristic
189C2C2×#1451979711yescharacteristic
190C2C2×#1451980811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C4×Q8×C61C2
socleC23×C61C2×D4
hypercenterC2×C4×Q8D61
hypocenterC61C2×#479
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #16840069C2direct (N × H)
92. C2×C61#479semidirect
104. C61C2×#479semidirect
187. C2#16840069direct (N × H)