Finite Group Databasebeta

← C2×#16840046 #21455583

Subgroups — C2×#16840046 #21455583

Order 7808.

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

normal subgroups only

This group has 416 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×#14519776C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic
3#16840046C218yesmaximal, direct product factor
4C2×#14519708C211yesmaximal, characteristic
5C2×#14519706C211yesmaximal, characteristic
6C2×#14519702C211yesmaximal, characteristic
7C2×#14519700C211yesmaximal, characteristic
8C2×#106×C61C211yesmaximal, characteristic
9C22×Dic122—21no—
10C22×Dic122C2211yescharacteristic
11C22×#92418C2211yescharacteristic
12#14519776—22no—
13#14519776C2214yes—
14#14519742—22no—
15#14519742C2214yes—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196—21no—
18C2×#11758196—21no—
19C2×C4×Dic61—21no—
20C2×C4×Dic61C2211yescharacteristic
21#14519708C2214yes—
22#14519706C2214yes—
23#14519702C2214yes—
24#14519700C2214yes—
25C22×C8×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28#106×C61C2214yes—
29C22×C4×C61—21no—
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C22×Dic61—21no—
33C22×Dic61—21no—
34C22×Dic61D411yescharacteristic
35C22×Dic61D411yescharacteristic
36C2×Dic122—21no—
37C2×Dic122—22no—
38C2×Dic122—24no—
39C2×Dic122—44no—
40C2×Dic122Q814yescomplemented
41C2×Dic122C2312yes—
42C2×C8×C61—22no—
43C2×C8×C61C2312yes—
44C4⋊C4×C61—21no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61C2312yes—
47C4⋊C4×C61C2312yes—
48C4⋊Dic61—21no—
49C4⋊Dic61C2312yes—
50#11758196—24no—
51#11758196—24no—
52C4×Dic61—24no—
53C4×Dic61D412yes—
54C4×Dic61C2312yes—
55C2×#92418—22no—
56C2×#92418C2312yes—
57C23×C61C2×D411yescharacteristic
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—42no—
61C2×C4×C61—42no—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×Q812yes—
64C2×C4×C61#4112yes—
65C2×C4×C61C2411yescharacteristic
66C2×Dic61—24no—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—42no—
71C2×Dic61SD1614yes—
72C2×Dic61C2×D412yes—
73C2×Dic61C2×D412yes—
74Dic122—24no—
75Dic122—22no—
76Dic122—48no—
77Dic122C2×Q814yescomplemented
78C8×C61—22no—
79#92418—22no—
80C22×C61C22⋊Q812yes—
81C22×C61C2×SD1612yes—
82C22×C61#13712yes—
83C22×C61C22×D411yescharacteristic
84C4×C61—42no—
85C4×C61—42no—
86C4×C61C22⋊Q812yes—
87C4×C61C22×Q811yescharacteristic
88C4×C61C2×#4111yescharacteristic
89Dic61—24no—
90Dic61—22no—
91Dic61—42no—
92Dic61C2×SD1614yes—
93C2×#475—611nomaximal, Sylow
94C2×C61#47514yescomplemented
95C2×C61C2×C22⋊Q811yescharacteristic
96C2×C61C22×SD1611yescharacteristic
97C2×C61C2×#13711yescharacteristic
98C2×C4⋊Q8—611no—
99C2×C4×Q8—611no—
100#475—618no—
101C2×#106—611no—
102C2×#106D6111yescharacteristic
103C2×C4⋊C8—611no—
104C2×#103—611no—
105C2×#103—611no—
106C61C2×#47511yescharacteristic, complemented, Sylow
107C22×Q8—611no—
108C22×Q8—1221no—
109C22×C8—611no—
110C22×C8C2×D6111yescharacteristic
111C4⋊Q8—614no—
112C4⋊Q8—1222no—
113C4×Q8—614no—
114C4×Q8—1222no—
115C2×C4⋊C4—611no—
116C2×C4⋊C4—1221no—
117C2×C4⋊C4—1221no—
118C2×C4⋊C4C2×D6111yescharacteristic
119C2×C4⋊C4C2×D6111yescharacteristic
120C2×C42—611no—
121C2×C42—1221no—
122#106—614no—
123#106C2×D6114yes—
124C4⋊C8—614no—
125#103—614no—
126#103—614no—
127C2×Q8—614no—
128C2×Q8—612no—
129C2×Q8—1224no—
130C2×Q8—1222no—
131C2×Q8—1221no—
132C2×Q8—2444no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—1221no—
138C22×C4—1221no—
139C22×C4C22×D6111yescharacteristic
140C2×C8—22no—
141C2×C8—612no—
142C2×C8—1222no—
143C2×C8C22×D6112yes—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—612no—
147C4⋊C4—1224no—
148C4⋊C4—1224no—
149C4⋊C4—1221no—
150C4⋊C4C22×D6112yes—
151C4⋊C4C22×D6112yes—
152C42—612no—
153C42—612no—
154C42—1224no—
155C23D4×D6111yescharacteristic
156Q8—614no—
157Q8—1222no—
158Q8—1224no—
159Q8—2448no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—612no—
165C2×C4—614no—
166C2×C4—612no—
167C2×C4—1222no—
168C2×C4—1224no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—2442no—
172C2×C4#1175822212yes—
173C2×C4D4×D6111yescharacteristic
174C2×C4Q8×D6112yes—
175C2×C4C23×D6111yescharacteristic
176C8—22no—
177C8—1222no—
178C22#1451975512yes—
179C22SD16×D6112yes—
180C22#1451980612yes—
181C22C2×D4×D6111yescharacteristic
182C4—42no—
183C4—42no—
184C4—614no—
185C4—1224no—
186C4—1222no—
187C4—2442no—
188C4#1451975512yes—
189C4C2×Q8×D6111yescharacteristic
190C4C2×#1175822211yescharacteristic
191C2#1684004614yesdirect product factor
192C2C2×#1451975511yescharacteristic
193C2C2×SD16×D6111yescharacteristic
194C2C2×#1451980611yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#106×C61C2
socleC23×C61C2×D4
hypercenterC2×#106D61
hypocenterC61C2×#475
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #16840046C2direct (N × H)
40. C2×Dic122Q8semidirect
77. Dic122C2×Q8semidirect
94. C2×C61#475semidirect
106. C61C2×#475semidirect
191. C2#16840046direct (N × H)