Finite Group Databasebeta

← C2×#14583108 #19144032

Subgroups — C2×#14583108 #19144032

Order 5504.

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

normal subgroups only

This group has 480 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
1C22×Dic172C211yesmaximal, characteristic
2C22×#10621885C211yesmaximal, characteristic
3C2×#13063323C211yesmaximal, characteristic
4C2×#13063290C211yesmaximal, characteristic
5#14583108C218yesmaximal, direct product factor
6C2×Dic43⋊C8C211yesmaximal, characteristic
7C2×#13063248C211yesmaximal, characteristic
8C2×#103×C43C211yesmaximal, characteristic
9C22×Dic86C2211yescharacteristic
10C22×Dic86C2211yescharacteristic
11C2×Dic172—24no—
12C2×Dic172C2214yes—
13C2×#10621885—24no—
14C2×#10621885C2214yes—
15C22×C43⋊C8C2211yescharacteristic
16#13063323—22no—
17#13063323C2214yes—
18#13063290—22no—
19#13063290C2214yes—
20C2×Dic43⋊C4—21no—
21C2×Dic43⋊C4—21no—
22C2×Dic43⋊C4—21no—
23C2×C4×Dic43—21no—
24C2×C4×Dic43C2211yescharacteristic
25Dic43⋊C8C2214yes—
26#13063248C2214yes—
27C22×Q8×C43C2211yescharacteristic
28C22×C8×C43C2211yescharacteristic
29C2×C4⋊C4×C43C2211yescharacteristic
30#103×C43C2214yes—
31C2×Q8×C43—21no—
32C2×Q8×C43—22no—
33C2×Q8×C43—22no—
34C2×Q8×C43C2312yes—
35C22×C4×C43—21no—
36C22×C4×C43—21no—
37C22×C4×C43C2311yescharacteristic
38C22×Dic43—21no—
39C22×Dic43—21no—
40C22×Dic43D411yescharacteristic
41C22×Dic43D411yescharacteristic
42C2×Dic86—21no—
43C2×Dic86—22no—
44C2×Dic86—22no—
45C2×Dic86—22no—
46C2×Dic86—21no—
47C2×Dic86D414yes—
48C2×Dic86C2312yes—
49C2×Dic86C2312yes—
50C2×C8×C43—22no—
51C2×C8×C43C2312yes—
52C4⋊C4×C43—21no—
53C4⋊C4×C43C2312yes—
54#10621885—28no—
55Dic43⋊C4—24no—
56Dic43⋊C4—24no—
57Dic43⋊C4—24no—
58C4×Dic43—24no—
59C4×Dic43D412yes—
60C4×Dic43C2312yes—
61C2×C43⋊C8—22no—
62C2×C43⋊C8C2312yes—
63Dic172—28no—
64C23×C43C2×D411yescharacteristic
65Q8×C43—22no—
66Q8×C43—22no—
67Q8×C43—42no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—42no—
71C2×C4×C43—42no—
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D412yes—
74C2×C4×C43#4112yes—
75C2×C4×C43C2411yescharacteristic
76C2×Dic43—24no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—42no—
81C2×Dic43Q1614yescomplemented
82C2×Dic43C2×D412yes—
83C2×Dic43C2×D412yes—
84Dic86—24no—
85Dic86—22no—
86Dic86—22no—
87Dic86—22no—
88Dic86—42no—
89Dic86C2×D414yes—
90C8×C43—22no—
91C43⋊C8—22no—
92C22×C43#12112yes—
93C22×C43C2×Q1612yes—
94C22×C43#13712yes—
95C22×C43C22×D411yescharacteristic
96C4×C43—42no—
97C4×C43—42no—
98C4×C43#12112yes—
99C4×C43C22×D411yescharacteristic
100C4×C43C2×#4111yescharacteristic
101Dic43—24no—
102Dic43—22no—
103Dic43—42no—
104Dic43C2×Q1614yescomplemented
105C2×#462—431nomaximal, Sylow
106C2×C43#46214yescomplemented
107C2×C43C2×#12111yescharacteristic
108C2×C43C22×Q1611yescharacteristic
109C2×C43C2×#13711yescharacteristic
110C22×Q16—431no—
111C22×Q16—431no—
112C2×C4⋊Q8—431no—
113C2×C4×Q8—431no—
114#462—438no—
115C2×C4⋊C8—431no—
116C2×#103—431no—
117C2×#103D4311yescharacteristic
118C43C2×#46211yescharacteristic, complemented, Sylow
119C22×Q8—431no—
120C22×Q8—431no—
121C22×Q8C2×D4311yescharacteristic
122C2×Q16—434no—
123C2×Q16—434no—
124C2×Q16—864no—
125C2×Q16—864no—
126C22×C8—431no—
127C22×C8C2×D4311yescharacteristic
128C4⋊Q8—434no—
129C4⋊Q8—862no—
130C4×Q8—434no—
131C4×Q8—862no—
132C2×C4⋊C4—861no—
133C2×C4⋊C4—861no—
134C2×C4⋊C4—861no—
135C2×C4⋊C4C2×D4311yescharacteristic
136C2×C42—431no—
137C2×C42—861no—
138C4⋊C8—434no—
139#103—434no—
140#103C2×D4314yes—
141C2×Q8—21no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—434no—
145C2×Q8—432no—
146C2×Q8—432no—
147C2×Q8—862no—
148C2×Q8—861no—
149C2×Q8—861no—
150C2×Q8—862no—
151C2×Q8—862no—
152C2×Q8C22×D4312yes—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—431no—
156C22×C4—431no—
157C22×C4—861no—
158C22×C4—861no—
159C22×C4C22×D4311yescharacteristic
160Q16—868no—
161Q16—868no—
162C2×C8—22no—
163C2×C8—432no—
164C2×C8—862no—
165C2×C8C22×D4312yes—
166C4⋊C4—21no—
167C4⋊C4—864no—
168C4⋊C4—864no—
169C4⋊C4—864no—
170C4⋊C4C22×D4312yes—
171C42—432no—
172C42—432no—
173C42—864no—
174C23D4×D4311yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—42no—
178Q8—434no—
179Q8—864no—
180Q8—862no—
181Q8—862no—
182Q8—862no—
183Q8—1722no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—434no—
189C2×C4—432no—
190C2×C4—432no—
191C2×C4—864no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—862no—
195C2×C4—1722no—
196C2×C4#1062189812yes—
197C2×C4D4×D4311yescharacteristic
198C2×C4D4×D4312yes—
199C2×C4C23×D4311yescharacteristic
200C8—22no—
201C8—862no—
202C22#1306329812yes—
203C22Q16×D4312yes—
204C22#1306335412yes—
205C22C2×D4×D4311yescharacteristic
206C4—42no—
207C4—42no—
208C4—434no—
209C4—864no—
210C4—862no—
211C4—1722no—
212C4#1306329812yes—
213C4C2×D4×D4311yescharacteristic
214C4C2×#1062189811yescharacteristic
215C2#1458310814yesdirect product factor
216C2C2×#1306329811yescharacteristic
217C2C2×Q16×D4311yescharacteristic
218C2C2×#1306335411yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#103×C43C2
socleC23×C43C2×D4
hypercenterC2×#103D43
hypocenterC43C2×#462
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
5. #14583108C2direct (N × H)
81. C2×Dic43Q16semidirect
104. Dic43C2×Q16semidirect
106. C2×C43#462semidirect
118. C43C2×#462semidirect
215. C2#14583108direct (N × H)