Finite Group Databasebeta

← #19134808

Subgroups — #19134808

Order 5504.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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
1#14583376C211yesmaximal, characteristic
2#14582939C211yesmaximal, characteristic
3C2×#13063243C211yesmaximal, characteristic
4#14582804C211yesmaximal, characteristic
5#14582660C211yesmaximal, characteristic
6#14582658C211yesmaximal, characteristic
7C43×#428C211yesmaximal, characteristic
8C22×Dic86C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10C4×Dic86—21no—
11C4×Dic86—21no—
12#13063290—21no—
13#13063290—21no—
14#13063284C2211yescharacteristic
15#13063281—22no—
16C2×C4×Dic43C2211yescharacteristic
17#13063258—21no—
18#13063256—21no—
19#13063243C414yescomplemented
20C43⋊#95—22no—
21C2×M16×C43C2211yescharacteristic
22#117×C43C2211yescharacteristic
23C2×C4⋊C4×C43C2211yescharacteristic
24#107×C43—21no—
25#106×C43—21no—
26C22×C4×C43—21no—
27C22×C4×C43C2311yescharacteristic
28C22×Dic43—21no—
29C22×Dic43D412yes—
30C2×Dic86—21no—
31C2×Dic86—21no—
32C2×Dic86—21no—
33C2×Dic86—21no—
34C2×Dic86C2×C412yes—
35C2×Dic86Q812yes—
36M16×C43—21no—
37M16×C43C2×C412yes—
38C2×C8×C43—21no—
39C4⋊C4×C43—21no—
40C4⋊C4×C43—21no—
41C4⋊C4×C43D411yescharacteristic
42C4⋊C4×C43D411yescharacteristic
43C22⋊C4×C43—21no—
44C42×C43—21no—
45C22⋊Dic43—21no—
46C4⋊Dic43D411yescharacteristic
47C4⋊Dic43D411yescharacteristic
48Dic43⋊C4—22no—
49Dic43⋊C4—22no—
50C4×Dic43—22no—
51C4×Dic43—22no—
52C4×Dic43—21no—
53C4×Dic43—21no—
54C4×Dic43—21no—
55#10621877—21no—
56#10621877C2×C412yes—
57C2×C43⋊C8—21no—
58C23×C43C2×D411yescharacteristic
59C2×C4×C43—21no—
60C2×C4×C43—21no—
61C2×C4×C43—42no—
62C2×C4×C43—41no—
63C2×C4×C43C22×C411yescharacteristic
64C2×C4×C43C2×D411yescharacteristic
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×Q811yescharacteristic
67C2×C4×C43#4111yescharacteristic
68C2×C4×C43#4111yescharacteristic
69C2×Dic43—22no—
70C2×Dic43—22no—
71C2×Dic43—22no—
72C2×Dic43—21no—
73C2×Dic43—21no—
74C2×Dic43—41no—
75C2×Dic43—41no—
76C2×Dic43C4⋊C414yes—
77Dic86—22no—
78Dic86—22no—
79Dic86—22no—
80Dic86—22no—
81C8×C43—22no—
82C43⋊C8—22no—
83C22×C43—21no—
84C22×C43—21no—
85C22×C43C2×C4⋊C411yescharacteristic
86C22×C43#12011yescharacteristic
87C22×C43#12311yescharacteristic
88C4×C43—41no—
89C4×C43—41no—
90C4×C43—81no—
91C4×C43C4×D411yescharacteristic
92C4×C43C4×D411yescharacteristic
93C4×C43C22⋊Q811yescharacteristic
94C4×C43C22⋊Q811yescharacteristic
95Dic43—24no—
96Dic43—42no—
97Dic43—41no—
98Dic43—41no—
99#1857—431nomaximal, Sylow
100C2×C43—21no—
101C2×C43—21no—
102C2×C43#38511yescharacteristic
103C2×C43#45411yescharacteristic
104C2×C43#45611yescharacteristic
105#519—431no—
106#428—431no—
107#428D4311yescharacteristic
108C2×#101—431no—
109#391—431no—
110#339—431no—
111#339—431no—
112C43#185711yescharacteristic, complemented, Sylow
113C22×Q8—431no—
114C2×M16—431no—
115C2×M16C2×D4311yescharacteristic
116C4×Q8—861no—
117C4×Q8—861no—
118C4×Q8—861no—
119C4×Q8—861no—
120#117—431no—
121#117—862no—
122#117C2×D4311yescharacteristic
123C2×C4⋊C4C2×D4311yescharacteristic
124C2×C42—431no—
125#107—21no—
126#107—861no—
127#106—21no—
128#106—861no—
129#101—434no—
130#95—862no—
131C2×Q8—432no—
132C2×Q8—432no—
133C2×Q8—861no—
134C2×Q8—861no—
135C2×Q8—861no—
136C2×Q8—861no—
137C22×C4—21no—
138C22×C4—432no—
139C22×C4—861no—
140C22×C4C22×D4311yescharacteristic
141M16—21no—
142M16—432no—
143M16—861no—
144M16C4×D4312yes—
145C2×C8—21no—
146C2×C8—861no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—431no—
150C4⋊C4—431no—
151C4⋊C4—862no—
152C4⋊C4—862no—
153C4⋊C4C22⋊D4311yescharacteristic
154C4⋊C4C22⋊D4311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—861no—
157C42—21no—
158C42—862no—
159C42—862no—
160C42—861no—
161C42—861no—
162C42—861no—
163C23D4×D4311yescharacteristic
164Q8—862no—
165Q8—862no—
166Q8—862no—
167Q8—862no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—434no—
173C2×C4—862no—
174C2×C4—862no—
175C2×C4—862no—
176C2×C4—861no—
177C2×C4—861no—
178C2×C4—1721no—
179C2×C4—1721no—
180C2×C4C2×C4×D4311yescharacteristic
181C2×C4#1062189811yescharacteristic
182C2×C4D4×D4311yescharacteristic
183C2×C4Q8×D4311yescharacteristic
184C2×C4#1062190211yescharacteristic
185C2×C4C2×C22⋊D4311yescharacteristic
186C8—22no—
187C8—862no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D4311yescharacteristic
191C22#1306329311yescharacteristic
192C22#1306331011yescharacteristic
193C4—41no—
194C4—41no—
195C4—81no—
196C4—864no—
197C4—1722no—
198C4—1721no—
199C4—1721no—
200C4C4×C22⋊D4311yescharacteristic
201C4#1306328711yescharacteristic
202C4#1306330111yescharacteristic
203C4#1306330311yescharacteristic
204C2—21no—
205C2—21no—
206C2#1458277011yescharacteristic
207C2#1458307011yescharacteristic
208C2#1458308011yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#428C2
socleC22×C43#120
hypercenter#428D43
hypocenterC43#1857
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
19. #13063243C4semidirect
112. C43#1857semidirect