Finite Group Databasebeta

← #19135967

Subgroups — #19135967

Order 5504.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13063257C211yesmaximal, characteristic, complemented
2C2×Dic43⋊C8C211yesmaximal, characteristic, complemented
3C2×#13063246C211yesmaximal, characteristic
4#14582802C211yesmaximal, characteristic
5#14582795C211yesmaximal, characteristic, complemented
6#14582661C211yesmaximal, characteristic, complemented
7C2×#102×C43C211yesmaximal, characteristic
8C22×C43⋊C8C2211yescharacteristic
9C2×C4⋊Dic43C2211yescharacteristic
10C2×C4⋊Dic43C2211yescharacteristic
11C2×Dic43⋊C4—21no—
12C2×C22⋊Dic43—21no—
13C2×C22⋊Dic43—21no—
14C2×C4×Dic43C2211yescharacteristic
15#13063257—22no—
16Dic43⋊C8—22no—
17#13063246—22no—
18C43⋊#95—21no—
19C22×D4×C43C2211yescharacteristic
20C22×C8×C43C2211yescharacteristic
21C2×C4⋊C4×C43C2211yescharacteristic
22#102×C43—22no—
23C24×C43—21no—
24C2×D4×C43—21no—
25C2×D4×C43—21no—
26C2×D4×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43—21no—
29C2×D4×C43Q812yes—
30C22×C4×C43—21no—
31C22×C4×C43C2311yescharacteristic
32C22×Dic43—21no—
33C22×Dic43—21no—
34C22×Dic43D411yescharacteristic
35C22×Dic43D411yescharacteristic
36C2×C8×C43—21no—
37C2×C8×C43—21no—
38C2×C8×C43D412yes—
39C4⋊C4×C43—21no—
40C4⋊C4×C43—21no—
41C22⋊Dic43—42no—
42C22⋊Dic43—42no—
43C4⋊Dic43—21no—
44C4⋊Dic43—21no—
45C4⋊Dic43—21no—
46C4⋊Dic43D412yes—
47Dic43⋊C4—42no—
48C4×Dic43—21no—
49C4×Dic43—21no—
50C2×C43⋊C8—21no—
51C2×C43⋊C8—21no—
52C2×C43⋊C8—21no—
53C23×C43—22no—
54C23×C43—41no—
55C23×C43—41no—
56C23×C43—41no—
57C23×C43—41no—
58C23×C43—41no—
59C23×C43—41no—
60C23×C43C2×D411yescharacteristic
61D4×C43—22no—
62D4×C43—22no—
63D4×C43—41no—
64D4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×Q811yescharacteristic
71C2×C4×C43#4111yescharacteristic
72C2×C4×C43#4111yescharacteristic
73C2×C4×C43#4111yescharacteristic
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—22no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—41no—
81C2×Dic43—41no—
82C2×Dic43—41no—
83C2×Dic43—41no—
84C2×Dic43—41no—
85C2×Dic43SD1612yes—
86C8×C43—22no—
87C43⋊C8—41no—
88C22×C43—42no—
89C22×C43—42no—
90C22×C43—42no—
91C22×C43—81no—
92C22×C43—81no—
93C22×C43—81no—
94C22×C43—81no—
95C22×C43#12111yescharacteristic
96C22×C43#12111yescharacteristic
97C22×C43C22⋊Q811yescharacteristic
98C22×C43C2×SD1611yescharacteristic
99C22×C43#13511yescharacteristic
100C22×C43AGL(1,ℤ/8)11yescharacteristic
101C22×C43AGL(1,ℤ/8)11yescharacteristic
102C4×C43—81no—
103C4×C43#12111yescharacteristic
104C4×C43C22⋊Q811yescharacteristic
105C4×C43C22⋊Q811yescharacteristic
106C4×C43#12611yescharacteristic
107Dic43—22no—
108Dic43—42no—
109Dic43—41no—
110Dic43—81no—
111#2065—431nomaximal, Sylow
112C2×C43—82no—
113C2×C43#39611yescharacteristic
114C2×C43#46011yescharacteristic
115C2×C43#46311yescharacteristic
116C2×C43#46511yescharacteristic
117C2×C43#46911yescharacteristic
118C2×C43#47611yescharacteristic
119C2×C43#47811yescharacteristic
120C2×#106—431no—
121C2×C4⋊C8—431no—
122C2×#102—431no—
123C2×#102D4311yescharacteristic
124#390—431no—
125#389—431no—
126#340—431no—
127C43#206511yescharacteristic, complemented, Sylow
128C22×D4C2×D4311yescharacteristic
129C22×C8—431no—
130C22×C8C2×D4311yescharacteristic
131C2×C4⋊C4—431no—
132C2×C4⋊C4—431no—
133C2×C4⋊C4—861no—
134C2×C4⋊C4C2×D4311yescharacteristic
135C2×C22⋊C4—861no—
136C2×C22⋊C4—861no—
137C2×C42—431no—
138#106—862no—
139C4⋊C8—862no—
140#102—22no—
141#102—862no—
142#95—861no—
143C24—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4Dic8612yes—
150C22×C4—21no—
151C22×C4—431no—
152C22×C4—431no—
153C22×C4—861no—
154C22×C4—861no—
155C22×C4C22×D4311yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—861no—
159C2×C8—861no—
160C2×C8—861no—
161C2×C8C22⋊D4312yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—432no—
165C4⋊C4—861no—
166C4⋊C4—861no—
167C4⋊C4—861no—
168C4⋊C4—1722no—
169C22⋊C4—1722no—
170C22⋊C4—1722no—
171C42—861no—
172C42—861no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23D4×D4311yescharacteristic
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—432no—
189C2×C4—861no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—862no—
193C2×C4—861no—
194C2×C4—861no—
195C2×C4—1721no—
196C2×C4—1721no—
197C2×C4—1721no—
198C2×C4—1721no—
199C2×C4—1721no—
200C2×C4C2×Dic8611yescharacteristic
201C2×C4#1062189811yescharacteristic
202C2×C4D4×D4311yescharacteristic
203C2×C4#1062190011yescharacteristic
204C2×C4#1062190011yescharacteristic
205C2×C4C2×C22⋊D4311yescharacteristic
206C8—22no—
207C8—1721no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22—81no—
215C22#1306329611yescharacteristic
216C22#1306329811yescharacteristic
217C22#1306330211yescharacteristic
218C22SD16×D4311yescharacteristic
219C22#1306334611yescharacteristic
220C22#1306334911yescharacteristic
221C22#1306334911yescharacteristic
222C4—81no—
223C4—862no—
224C4—3441no—
225C4—1722no—
226C4—1721no—
227C4#1306329711yescharacteristic
228C4#1306330211yescharacteristic
229C4#1306330411yescharacteristic
230C4#1306331811yescharacteristic
231C2—82no—
232C2#1458282211yescharacteristic
233C2#1458309811yescharacteristic
234C2#1458311311yescharacteristic
235C2#1458312511yescharacteristic
236C2#1458314911yescharacteristic
237C2#1458318711yescharacteristic
238C2#1458320111yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC2×#102×C43C2
socleC23×C43C2×D4
hypercenterC2×#102D43
hypocenterC43#2065
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#13063257C2semidirect
2. C2×Dic43⋊C8C2semidirect
5. #14582795C2semidirect
6. #14582661C2semidirect
127. C43#2065semidirect