Finite Group Databasebeta

← C2×#14582812 #19137796

Subgroups — C2×#14582812 #19137796

Order 5504.

1036 conjugacy classes of subgroups; only the 253 normal subgroups are shown.

normal subgroups only

This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 253 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
1C23×Dic86C211yesmaximal, characteristic, complemented
2C22×(C2×D43)⋊C4C212yesmaximal
3C22×(C2×D43)⋊C4C211yesmaximal, characteristic
4#14582812C218yesmaximal, direct product factor
5C2×C43⋊#95C212yesmaximal, complemented
6C2×#95×C43C211yesmaximal, characteristic, complemented
7C24×D43C2211yescharacteristic
8C22×Dic86—24no—
9C22×Dic86—28no—
10C22×Dic86C2214yescomplemented
11C23×Dic43C2211yescharacteristic
12C23×Dic43C2212yes—
13C2×(C2×D43)⋊C4—24no—
14C2×(C2×D43)⋊C4—28no—
15C2×(C2×D43)⋊C4C2214yes—
16C2×(C2×D43)⋊C4C2218yes—
17C43⋊#95C2218yescomplemented
18C23×C4×C43C2212yes—
19C23×C4×C43C2211yescharacteristic
20#95×C43C2214yescomplemented
21C24×C43C2311yescharacteristic
22C23×D43—22no—
23C23×D43—24no—
24C23×D43—24no—
25C23×D43—22no—
26C23×D43Q814yescomplemented
27C23×D43C2312yes—
28C22×C4×C43—24no—
29C22×C4×C43—24no—
30C22×C4×C43—24no—
31C22×C4×C43—24no—
32C22×C4×C43D414yes—
33C22×C4×C43C2314yes—
34C22×C4×C43C2312yes—
35C22×Dic43—24no—
36C22×Dic43—24no—
37C22×Dic43—22no—
38C22×Dic43—24no—
39C22×Dic43D418yes—
40C22×Dic43C2312yes—
41C22×Dic43C2314yes—
42C2×Dic86—232no—
43C2×Dic86—28no—
44C2×Dic86—216no—
45(C2×D43)⋊C4—28no—
46(C2×D43)⋊C4—216no—
47C23×C43C2×D412yes—
48C23×C43C2×D414yes—
49C23×C43C2×Q812yes—
50C23×C43#4114yes—
51C23×C43#4112yes—
52C23×C43C2411yescharacteristic
53C22×D43—216no—
54C22×D43—28no—
55C22×D43—24no—
56C22×D43—22no—
57C22×D43—22no—
58C22×D43—24no—
59C22×D43—44no—
60C22×D43—48no—
61C22×D43—44no—
62C22×D43C2×Q814yescomplemented
63C2×C4×C43—28no—
64C2×C4×C43—24no—
65C2×C4×C43—24no—
66C2×C4×C43—24no—
67C2×C4×C43—24no—
68C2×C4×C43—48no—
69C2×C4×C43C2×D414yes—
70C2×Dic43—216no—
71C2×Dic43—24no—
72C2×Dic43—24no—
73C2×Dic43—22no—
74C2×Dic43—24no—
75C2×Dic43—44no—
76C2×Dic43C2×D418yes—
77Dic86—232no—
78C22×C43#12014yes—
79C22×C43C22⋊Q818yes—
80C22×C43C22⋊Q814yes—
81C22×C43#12418yes—
82C22×C43#12414yes—
83C22×C43C22×D412yes—
84C22×C43C22×D411yescharacteristic
85C22×C43C22×Q811yescharacteristic
86C22×C43C2×#4111yescharacteristic
87C22×C43C2×#4112yes—
88C2×D43—28no—
89C2×D43—24no—
90C2×D43—42no—
91C2×D43—44no—
92C2×D43—42no—
93C2×D43—416no—
94C4×C43—24no—
95C4×C43—44no—
96Dic43—28no—
97Dic43—42no—
98C2×#393—431nomaximal, Sylow
99C2×C43#39318yescomplemented
100C2×C43C2×#12011yescharacteristic
101C2×C43C2×C22⋊Q812yes—
102C2×C43C2×C22⋊Q811yescharacteristic
103C2×C43C2×#12412yes—
104C2×C43C2×#12411yescharacteristic
105D43—44no—
106C23×Q8—431no—
107C22×C22⋊C4—432no—
108C22×C22⋊C4—431no—
109#393—438no—
110C2×#95—432no—
111C2×#95D4311yescharacteristic, complemented
112C43C2×#39311yescharacteristic, complemented, Sylow
113C25—431no—
114C22×Q8—434no—
115C22×Q8—868no—
116C22×Q8—864no—
117C23×C4—432no—
118C23×C4—431no—
119C23×C4C2×D4312yes—
120C23×C4C2×D4311yescharacteristic
121C2×C22⋊C4—438no—
122C2×C22⋊C4—434no—
123C2×C22⋊C4—868no—
124C2×C22⋊C4—864no—
125#95—438no—
126#95C2×D4314yescomplemented
127C24—434no—
128C24—432no—
129C24—862no—
130C24—864no—
131C24—864no—
132C24—862no—
133C24C22×D4311yescharacteristic
134C2×Q8—8616no—
135C2×Q8—8632no—
136C2×Q8—868no—
137C22×C4—24no—
138C22×C4—24no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—438no—
142C22×C4—434no—
143C22×C4—432no—
144C22×C4—864no—
145C22×C4—864no—
146C22×C4—862no—
147C22×C4—864no—
148C22×C4D17214yes—
149C22×C4C22×D4314yes—
150C22×C4C22×D4312yes—
151C22⋊C4—8616no—
152C22⋊C4—868no—
153C23—434no—
154C23—8616no—
155C23—868no—
156C23—864no—
157C23—862no—
158C23—862no—
159C23—864no—
160C23—1724no—
161C23—1728no—
162C23—1724no—
163C23C2×D17212yes—
164C23#1062189814yes—
165C23D4×D4314yes—
166C23#1062190012yes—
167C23Q8×D4312yes—
168C23C23×D4311yescharacteristic
169Q8—8632no—
170C2×C4—28no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—48no—
176C2×C4—438no—
177C2×C4—8616no—
178C2×C4—864no—
179C2×C4—864no—
180C2×C4—862no—
181C2×C4—864no—
182C2×C4—1724no—
183C2×C4C2×D17214yes—
184C22—868no—
185C22—864no—
186C22—17216no—
187C22—1722no—
188C22—1724no—
189C22—1722no—
190C22#1306329514yes—
191C22#1306330318yes—
192C22#1306330514yes—
193C22#1306331118yes—
194C22#1306331314yes—
195C22C2×D4×D4312yes—
196C22C22×D17211yescharacteristic
197C22C2×Q8×D4311yescharacteristic
198C22C2×#1062190011yescharacteristic
199C22C2×#1062189812yes—
200C4—24no—
201C4—44no—
202C4—868no—
203C4—1722no—
204C2—1724no—
205C2#1458281218yesdirect product factor
206C2C2×#1306329511yescharacteristic
207C2C2×#1306330312yes—
208C2C2×#1306330511yescharacteristic
209C2C2×#1306331112yes—
210C2C2×#1306331311yescharacteristic
subgroupG/H
centerC24C22×D43
commutatorC23×C43C24
FrattiniC23C23×D43
FittingC2×#95×C43C2
socleC24×C43C23
hypercenterC2×#95D43
hypocenterC43C2×#393
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. C23×Dic86C2semidirect
4. #14582812C2direct (N × H)
5. C2×C43⋊#95C2semidirect
6. C2×#95×C43C2semidirect
10. C22×Dic86C22semidirect
17. C43⋊#95C22semidirect
20. #95×C43C22semidirect
26. C23×D43Q8semidirect
62. C22×D43C2×Q8semidirect
99. C2×C43#393semidirect
111. C2×#95D43semidirect
112. C43C2×#393semidirect
126. #95C2×D43semidirect
205. C2#14582812direct (N × H)