Finite Group Databasebeta

← #19135973

Subgroups — #19135973

Order 5504.

248 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13063256C211yesmaximal, characteristic
2C2×C4⋊(C43⋊C8)C211yesmaximal, characteristic
3C2×#13063248C211yesmaximal, characteristic
4C2×#13063248C211yesmaximal, characteristic
5#14582805C211yesmaximal, characteristic
6#14582661C211yesmaximal, characteristic
7C43×#389C211yesmaximal, characteristic
8C22×Dic86C2211yescharacteristic
9C22×C43⋊C8C2211yescharacteristic
10C22×C43⋊C8C2211yescharacteristic
11C2×C4⋊Dic43C2211yescharacteristic
12#13063256—22no—
13C4⋊(C43⋊C8)—22no—
14#13063248—22no—
15#13063248—22no—
16C43⋊#95—21no—
17C43⋊#95—21no—
18C2×C4⋊C4×C43—21no—
19C2×C4⋊C4×C43C2211yescharacteristic
20C2×C4⋊C4×C43C2211yescharacteristic
21C2×C42×C43C2211yescharacteristic
22#95×C43—21no—
23C22×C4×C43—21no—
24C22×C4×C43—21no—
25C22×C4×C43D411yescharacteristic
26C22×C4×C43D411yescharacteristic
27C22×C4×C43C2311yescharacteristic
28C22×Dic43—21no—
29C22×Dic43—21no—
30C2×Dic86—21no—
31C2×Dic86—21no—
32C2×Dic86—21no—
33C2×Dic86—21no—
34C2×Dic86—21no—
35C2×Dic86Q812yes—
36C4⋊C4×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43—21no—
39C4⋊C4×C43—42no—
40C4⋊C4×C43D412yes—
41C42×C43—21no—
42C42×C43—21no—
43C4⋊Dic43—21no—
44C4⋊Dic43—21no—
45C2×C43⋊C8—21no—
46C2×C43⋊C8—21no—
47C2×C43⋊C8—21no—
48C2×C43⋊C8—21no—
49C2×C43⋊C8—21no—
50C2×C43⋊C8D412yes—
51C23×C43C2×D411yescharacteristic
52C2×C4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—21no—
55C2×C4×C43—22no—
56C2×C4×C43—21no—
57C2×C4×C43—21no—
58C2×C4×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43—41no—
61C2×C4×C43—41no—
62C2×C4×C43—41no—
63C2×C4×C43SD1612yes—
64C2×C4×C43C2×D411yescharacteristic
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×Q811yescharacteristic
67C2×C4×C43#4111yescharacteristic
68C2×C4×C43#4111yescharacteristic
69C2×C4×C43#4111yescharacteristic
70C2×Dic43—22no—
71C2×Dic43—41no—
72C2×Dic43—41no—
73C2×Dic43—41no—
74C2×Dic43—41no—
75C2×Dic43—41no—
76Dic86—22no—
77Dic86—22no—
78Dic86—41no—
79Dic86—41no—
80C43⋊C8—22no—
81C43⋊C8—41no—
82C22×C43#12111yescharacteristic
83C22×C43#12111yescharacteristic
84C22×C43C22⋊Q811yescharacteristic
85C22×C43C2×SD1611yescharacteristic
86C22×C43#13511yescharacteristic
87C22×C43#13711yescharacteristic
88C22×C43#13711yescharacteristic
89C4×C43—22no—
90C4×C43—42no—
91C4×C43—41no—
92C4×C43—81no—
93C4×C43#12111yescharacteristic
94C4×C43C22⋊Q811yescharacteristic
95C4×C43C22⋊Q811yescharacteristic
96C4×C43#12611yescharacteristic
97Dic43—42no—
98Dic43—81no—
99#2066—431nomaximal, Sylow
100C2×C43#39611yescharacteristic
101C2×C43#46111yescharacteristic
102C2×C43#46411yescharacteristic
103C2×C43#46511yescharacteristic
104C2×C43#47011yescharacteristic
105C2×C43#47511yescharacteristic
106C2×C43#47911yescharacteristic
107C2×#106—431no—
108C2×C4⋊C8—431no—
109C2×#103—431no—
110C2×#103—431no—
111#391—431no—
112#389D4311yescharacteristic
113#340—431no—
114C43#206611yescharacteristic, complemented, Sylow
115C22×Q8—431no—
116C22×C8—431no—
117C22×C8—431no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—431no—
120C2×C4⋊C4C2×D4311yescharacteristic
121C2×C4⋊C4C2×D4311yescharacteristic
122C2×C42C2×D4311yescharacteristic
123#106—862no—
124C4⋊C8—862no—
125#103—862no—
126#103—862no—
127#95—21no—
128#95—861no—
129#95—861no—
130C2×Q8—432no—
131C2×Q8—861no—
132C2×Q8—861no—
133C2×Q8—861no—
134C2×Q8—861no—
135C2×Q8—861no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—861no—
139C22×C4—861no—
140C22×C4C22⋊D4311yescharacteristic
141C22×C4C22⋊D4311yescharacteristic
142C22×C4C22×D4311yescharacteristic
143C2×C8—432no—
144C2×C8—861no—
145C2×C8—861no—
146C2×C8—861no—
147C2×C8—861no—
148C2×C8—861no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—42no—
153C4⋊C4—861no—
154C4⋊C4—861no—
155C4⋊C4D17212yes—
156C42—21no—
157C42—21no—
158C23C2×C22⋊D4311yescharacteristic
159Q8—862no—
160Q8—862no—
161Q8—1721no—
162Q8—1721no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—862no—
175C2×C4—1721no—
176C2×C4—1721no—
177C2×C4—1721no—
178C2×C4—1721no—
179C2×C4—1721no—
180C2×C4#1062188312yes—
181C2×C4C2×D17211yescharacteristic
182C2×C4#1062189811yescharacteristic
183C2×C4D4×D4311yescharacteristic
184C2×C4#1062190011yescharacteristic
185C2×C4Q8×D4311yescharacteristic
186C2×C4#1062190211yescharacteristic
187C8—862no—
188C8—1721no—
189C22#1306329711yescharacteristic
190C22#1306329911yescharacteristic
191C22#1306330111yescharacteristic
192C22C2×#1062188311yescharacteristic
193C22#1306334511yescharacteristic
194C22#1306335511yescharacteristic
195C22#1306335611yescharacteristic
196C4—22no—
197C4—42no—
198C4—41no—
199C4—81no—
200C4—3441no—
201C4—1722no—
202C4#1306330011yescharacteristic
203C4#1306330311yescharacteristic
204C4#1306330511yescharacteristic
205C4#1306332011yescharacteristic
206C2#1458282111yescharacteristic
207C2#1458310411yescharacteristic
208C2#1458312111yescharacteristic
209C2#1458312611yescharacteristic
210C2#1458315511yescharacteristic
211C2#1458318111yescharacteristic
212C2#1458320311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D43
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#389C2
socleC23×C43C2×D4
hypercenter#389D43
hypocenterC43#2066
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
114. C43#2066semidirect