Finite Group Databasebeta

← #19135931

Subgroups — #19135931

Order 5504.

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

normal subgroups only

This group has 250 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×#13063316C211yesmaximal, characteristic
2C2×#13063256C211yesmaximal, characteristic
3#14582795C211yesmaximal, characteristic
4#14582662C211yesmaximal, characteristic
5#14582661C211yesmaximal, characteristic
6#14582653C211yesmaximal, characteristic
7C2×#107×C43C211yesmaximal, characteristic
8C22×C43⋊C8C2211yescharacteristic
9#13063316—22no—
10#13063316—22no—
11C2×C4⋊Dic43—21no—
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#107×C43—22no—
23C22×C4×C43—21no—
24C22×C4×C43—21no—
25C22×C4×C43C2311yescharacteristic
26C22×Dic43—21no—
27C22×Dic43—21no—
28C22×Dic43D411yescharacteristic
29C22×Dic43D411yescharacteristic
30C2×C8×C43—21no—
31C2×C8×C43—21no—
32C2×C8×C43Q812yes—
33C4⋊C4×C43—21no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43D412yes—
37C4⋊Dic43—24no—
38C4⋊Dic43—21no—
39C4⋊Dic43—21no—
40C4⋊Dic43D412yes—
41C4⋊Dic43Q812yes—
42Dic43⋊C4—24no—
43Dic43⋊C4—42no—
44C4×Dic43—21no—
45C4×Dic43—21no—
46C2×C43⋊C8—21no—
47C2×C43⋊C8—21no—
48C2×C43⋊C8Q812yes—
49C23×C43C2×D411yescharacteristic
50C2×C4×C43—22no—
51C2×C4×C43—41no—
52C2×C4×C43—41no—
53C2×C4×C43—41no—
54C2×C4×C43—41no—
55C2×C4×C43—41no—
56C2×C4×C43C2×D411yescharacteristic
57C2×C4×C43C2×D411yescharacteristic
58C2×C4×C43C2×Q811yescharacteristic
59C2×C4×C43C2×Q811yescharacteristic
60C2×C4×C43C2×Q811yescharacteristic
61C2×C4×C43#4111yescharacteristic
62C2×Dic43—21no—
63C2×Dic43—21no—
64C2×Dic43—22no—
65C2×Dic43—22no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68C2×Dic43—21no—
69C2×Dic43—21no—
70C2×Dic43—41no—
71C2×Dic43—41no—
72C2×Dic43—41no—
73C2×Dic43—41no—
74C8×C43—22no—
75C43⋊C8—22no—
76C22×C43#12011yescharacteristic
77C22×C43C22⋊Q811yescharacteristic
78C22×C43C4⋊Q811yescharacteristic
79C22×C43#13511yescharacteristic
80C22×C43#13511yescharacteristic
81C22×C43AGL(1,ℤ/8)11yescharacteristic
82C22×C43#13711yescharacteristic
83C4×C43—42no—
84C4×C43—81no—
85C4×C43C22⋊Q811yescharacteristic
86C4×C43C22⋊Q811yescharacteristic
87C4×C43C4⋊Q811yescharacteristic
88C4×C43C4⋊Q811yescharacteristic
89Dic43—41no—
90Dic43—41no—
91Dic43—42no—
92Dic43—42no—
93#2059—431nomaximal, Sylow
94C2×C43#39511yescharacteristic
95C2×C43#44911yescharacteristic
96C2×C43#45211yescharacteristic
97C2×C43#47811yescharacteristic
98C2×C43#47911yescharacteristic
99C2×C43#49911yescharacteristic
100C2×C43#50111yescharacteristic
101C2×#125—431no—
102C2×#107D4311yescharacteristic
103C2×#106—431no—
104#389—431no—
105#340—431no—
106#340—431no—
107#336—431no—
108C43#205911yescharacteristic, complemented, Sylow
109C22×C8—431no—
110C22×C8C2×D4311yescharacteristic
111#125—862no—
112#125—862no—
113C2×C4⋊C4—431no—
114C2×C4⋊C4—431no—
115C2×C4⋊C4—861no—
116C2×C4⋊C4—861no—
117C2×C4⋊C4—861no—
118C2×C4⋊C4C2×D4311yescharacteristic
119C2×C4⋊C4C2×D4311yescharacteristic
120C2×C42—431no—
121#107—22no—
122#106—862no—
123#95—861no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—431no—
127C22×C4—431no—
128C22×C4—861no—
129C22×C4—861no—
130C22×C4C22×D4311yescharacteristic
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—432no—
134C2×C8—861no—
135C2×C8—861no—
136C2×C8Dic8612yes—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—432no—
141C4⋊C4—432no—
142C4⋊C4—864no—
143C4⋊C4—864no—
144C4⋊C4—861no—
145C4⋊C4—861no—
146C4⋊C4—1722no—
147C4⋊C4C22⋊D4312yes—
148C42—861no—
149C42—861no—
150C23D4×D4311yescharacteristic
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—861no—
158C2×C4—861no—
159C2×C4—862no—
160C2×C4—862no—
161C2×C4—861no—
162C2×C4—861no—
163C2×C4—861no—
164C2×C4—861no—
165C2×C4—1721no—
166C2×C4—1721no—
167C2×C4—1721no—
168C2×C4—1721no—
169C2×C4C2×Dic8611yescharacteristic
170C2×C4#1062189811yescharacteristic
171C2×C4D4×D4311yescharacteristic
172C2×C4Q8×D4311yescharacteristic
173C2×C4Q8×D4311yescharacteristic
174C2×C4C2×C22⋊D4311yescharacteristic
175C8—22no—
176C8—862no—
177C22#1306329311yescharacteristic
178C22#1306330311yescharacteristic
179C22#1306332411yescharacteristic
180C22#1306334411yescharacteristic
181C22#1306334811yescharacteristic
182C22#1306334911yescharacteristic
183C22#1306335711yescharacteristic
184C4—42no—
185C4—81no—
186C4—1721no—
187C4—1721no—
188C4—1722no—
189C4—1722no—
190C4#1306330311yescharacteristic
191C4#1306330411yescharacteristic
192C4#1306332311yescharacteristic
193C4#1306332411yescharacteristic
194C2#1458281911yescharacteristic
195C2#1458304111yescharacteristic
196C2#1458306011yescharacteristic
197C2#1458320211yescharacteristic
198C2#1458320511yescharacteristic
199C2#1458330011yescharacteristic
200C2#1458330711yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC2×#107×C43C2
socleC23×C43C2×D4
hypercenterC2×#107D43
hypocenterC43#2059
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
108. C43#2059semidirect