Finite Group Databasebeta

← #19135926

Subgroups — #19135926

Order 5504.

282 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13063324C211yesmaximal, characteristic
2C2×#13063256C211yesmaximal, characteristic
3#14582795C211yesmaximal, characteristic
4#14582662C211yesmaximal, characteristic
5#14582661C211yesmaximal, characteristic
6#14582653C211yesmaximal, characteristic
7C2×#106×C43C211yesmaximal, characteristic
8C22×Dic86—21no—
9C22×C43⋊C8C2211yescharacteristic
10#13063324—22no—
11#13063324—22no—
12C2×C4⋊Dic43C2211yescharacteristic
13C2×C4⋊Dic43C2211yescharacteristic
14C2×Dic43⋊C4—21no—
15C2×Dic43⋊C4—21no—
16C2×C4×Dic43C2211yescharacteristic
17#13063256—22no—
18C43⋊#95—21no—
19C22×C8×C43C2211yescharacteristic
20C2×C4⋊C4×C43C2211yescharacteristic
21C2×C4⋊C4×C43C2211yescharacteristic
22#106×C43—22no—
23C22×C4×C43—21no—
24C22×C4×C43—21no—
25C22×C4×C43C2311yescharacteristic
26C22×Dic43—21no—
27C22×Dic43—21no—
28C22×Dic43D411yescharacteristic
29C22×Dic43D411yescharacteristic
30C2×Dic86—24no—
31C2×Dic86—42no—
32C2×Dic86—42no—
33C2×C8×C43—21no—
34C2×C8×C43—21no—
35C2×C8×C43Q812yescomplemented
36C4⋊C4×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43—21no—
39C4⋊C4×C43D412yes—
40C4⋊Dic43—21no—
41C4⋊Dic43—21no—
42C4⋊Dic43D412yes—
43C4⋊Dic43Q812yescomplemented
44Dic43⋊C4—24no—
45Dic43⋊C4—42no—
46C4×Dic43—21no—
47C4×Dic43—21no—
48C2×C43⋊C8—21no—
49C2×C43⋊C8—21no—
50C2×C43⋊C8Q812yescomplemented
51C23×C43C2×D411yescharacteristic
52C2×C4×C43—22no—
53C2×C4×C43—41no—
54C2×C4×C43—41no—
55C2×C4×C43—41no—
56C2×C4×C43—41no—
57C2×C4×C43—41no—
58C2×C4×C43C2×D411yescharacteristic
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×Q811yescharacteristic
61C2×C4×C43C2×Q811yescharacteristic
62C2×C4×C43C2×Q811yescharacteristic
63C2×C4×C43#4111yescharacteristic
64C2×Dic43—21no—
65C2×Dic43—21no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68C2×Dic43—22no—
69C2×Dic43—22no—
70C2×Dic43—41no—
71C2×Dic43—41no—
72C2×Dic43—41no—
73C2×Dic43—41no—
74C2×Dic43SD1612yes—
75C2×Dic43SD1612yes—
76Dic86—48no—
77C8×C43—22no—
78C43⋊C8—22no—
79C22×C43#12011yescharacteristic
80C22×C43C22⋊Q811yescharacteristic
81C22×C43C4⋊Q811yescharacteristic
82C22×C43C2×SD1611yescharacteristic
83C22×C43C2×SD1611yescharacteristic
84C22×C43AGL(1,ℤ/8)11yescharacteristic
85C22×C43#13711yescharacteristic
86C4×C43—42no—
87C4×C43—81no—
88C4×C43C22⋊Q811yescharacteristic
89C4×C43C22⋊Q811yescharacteristic
90C4×C43C4⋊Q811yescharacteristic
91C4×C43C4⋊Q811yescharacteristic
92Dic43—22no—
93Dic43—22no—
94Dic43—42no—
95Dic43—42no—
96#2058—431nomaximal, Sylow
97C2×C43#39511yescharacteristic
98C2×C43#44811yescharacteristic
99C2×C43#45011yescharacteristic
100C2×C43#47511yescharacteristic
101C2×C43#47611yescharacteristic
102C2×C43#49811yescharacteristic
103C2×C43#50111yescharacteristic
104C2×C4⋊Q8—431no—
105C2×#106—431no—
106C2×#106D4311yescharacteristic
107#389—431no—
108#340—431no—
109#340—431no—
110#336—431no—
111C43#205811yescharacteristic, complemented, Sylow
112C22×Q8—861no—
113C22×C8—431no—
114C22×C8C2×D4311yescharacteristic
115C4⋊Q8—862no—
116C4⋊Q8—862no—
117C2×C4⋊C4—431no—
118C2×C4⋊C4—431no—
119C2×C4⋊C4—861no—
120C2×C4⋊C4—861no—
121C2×C4⋊C4C2×D4311yescharacteristic
122C2×C4⋊C4C2×D4311yescharacteristic
123C2×C42—431no—
124#106—22no—
125#106—862no—
126#95—861no—
127C2×Q8—864no—
128C2×Q8—1722no—
129C2×Q8—1722no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—431no—
133C22×C4—431no—
134C22×C4—861no—
135C22×C4—861no—
136C22×C4C22×D4311yescharacteristic
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—432no—
140C2×C8—861no—
141C2×C8—861no—
142C2×C8Dic8612yescomplemented
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—432no—
147C4⋊C4—432no—
148C4⋊C4—864no—
149C4⋊C4—861no—
150C4⋊C4—861no—
151C4⋊C4—1722no—
152C4⋊C4C22⋊D4312yes—
153C42—861no—
154C42—861no—
155C23D4×D4311yescharacteristic
156Q8—1728no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—432no—
164C2×C4—432no—
165C2×C4—861no—
166C2×C4—861no—
167C2×C4—861no—
168C2×C4—861no—
169C2×C4—862no—
170C2×C4—862no—
171C2×C4—1721no—
172C2×C4—1721no—
173C2×C4—1721no—
174C2×C4—1721no—
175C2×C4C2×Dic8611yescharacteristic
176C2×C4#1062189811yescharacteristic
177C2×C4D4×D4311yescharacteristic
178C2×C4Q8×D4311yescharacteristic
179C2×C4Q8×D4311yescharacteristic
180C2×C4C2×C22⋊D4311yescharacteristic
181C8—22no—
182C8—862no—
183C22#1306329311yescharacteristic
184C22#1306330311yescharacteristic
185C22#1306332411yescharacteristic
186C22SD16×D4311yescharacteristic
187C22SD16×D4311yescharacteristic
188C22#1306335211yescharacteristic
189C22#1306335411yescharacteristic
190C4—42no—
191C4—81no—
192C4—862no—
193C4—862no—
194C4—1722no—
195C4—1722no—
196C4#1306330311yescharacteristic
197C4#1306330411yescharacteristic
198C4#1306332311yescharacteristic
199C4#1306332411yescharacteristic
200C2#1458281911yescharacteristic
201C2#1458303611yescharacteristic
202C2#1458304811yescharacteristic
203C2#1458318311yescharacteristic
204C2#1458318811yescharacteristic
205C2#1458329611yescharacteristic
206C2#1458330611yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC2×#106×C43C2
socleC23×C43C2×D4
hypercenterC2×#106D43
hypocenterC43#2058
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
35. C2×C8×C43Q8semidirect
43. C4⋊Dic43Q8semidirect
50. C2×C43⋊C8Q8semidirect
111. C43#2058semidirect
142. C2×C8Dic86semidirect