Finite Group Databasebeta

← #19135964

Subgroups — #19135964

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×Dic43⋊C8C211yesmaximal, characteristic, complemented
2C2×#13063247C211yesmaximal, characteristic
3C2×#13063245C211yesmaximal, characteristic
4#14582800C211yesmaximal, characteristic
5#14582798C211yesmaximal, characteristic, complemented
6#14582661C211yesmaximal, characteristic, complemented
7C2×#106×C43C211yesmaximal, characteristic, complemented
8C22×D172C2211yescharacteristic
9C22×C43⋊C8C2211yescharacteristic
10C2×C4⋊Dic43—21no—
11C2×C4⋊Dic43C2211yescharacteristic
12C2×(C2×D43)⋊C4—21no—
13C2×(C2×D43)⋊C4—21no—
14C2×C4×Dic43C2211yescharacteristic
15Dic43⋊C8—22no—
16#13063247—22no—
17#13063245—22no—
18C43⋊#95—21no—
19C22×C8×C43C2211yescharacteristic
20C2×C4⋊C4×C43C2211yescharacteristic
21C2×C4⋊C4×C43C2211yescharacteristic
22#106×C43—22no—
23C23×D43—21no—
24C22×C4×C43—21no—
25C22×C4×C43—21no—
26C22×C4×C43C2311yescharacteristic
27C22×Dic43—21no—
28C22×Dic43D411yescharacteristic
29C22×Dic43D411yescharacteristic
30C2×D172—21no—
31C2×D172—21no—
32C2×D172—21no—
33C2×D172—21no—
34C2×D172—21no—
35C2×D172Q812yes—
36C2×C8×C43—21no—
37C2×C8×C43—21no—
38C2×C8×C43D412yes—
39C4⋊C4×C43—21no—
40C4⋊C4×C43—21no—
41C4⋊C4×C43—21no—
42C4⋊C4×C43D412yes—
43(C2×D43)⋊C4—42no—
44(C2×D43)⋊C4—42no—
45C4⋊Dic43—21no—
46C4⋊Dic43—21no—
47C4⋊Dic43—42no—
48C4×Dic43—21no—
49C4×Dic43—21no—
50C2×C43⋊C8—21no—
51C2×C43⋊C8—21no—
52C2×C43⋊C8—21no—
53C23×C43C2×D411yescharacteristic
54C22×D43—22no—
55C22×D43—41no—
56C22×D43—41no—
57C22×D43—41no—
58C22×D43—41no—
59C22×D43—41no—
60C22×D43—41no—
61C2×C4×C43—22no—
62C2×C4×C43—41no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×Q811yescharacteristic
70C2×C4×C43#4111yescharacteristic
71C2×C4×C43#4111yescharacteristic
72C2×C4×C43#4111yescharacteristic
73C2×Dic43—21no—
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—41no—
79C2×Dic43—41no—
80C2×Dic43—41no—
81C2×Dic43SD1612yes—
82D172—22no—
83D172—22no—
84D172—41no—
85D172—41no—
86C8×C43—22no—
87C43⋊C8—41no—
88C22×C43#12111yescharacteristic
89C22×C43#12111yescharacteristic
90C22×C43C22⋊Q811yescharacteristic
91C22×C43C2×SD1611yescharacteristic
92C22×C43#13511yescharacteristic
93C22×C43AGL(1,ℤ/8)11yescharacteristic
94C22×C43AGL(1,ℤ/8)11yescharacteristic
95C2×D43—42no—
96C2×D43—42no—
97C2×D43—42no—
98C2×D43—81no—
99C2×D43—81no—
100C2×D43—81no—
101C2×D43—81no—
102C4×C43—42no—
103C4×C43—81no—
104C4×C43#12111yescharacteristic
105C4×C43C22⋊Q811yescharacteristic
106C4×C43C22⋊Q811yescharacteristic
107C4×C43#12611yescharacteristic
108Dic43—22no—
109Dic43—41no—
110Dic43—81no—
111#2065—431nomaximal, Sylow
112C2×C43#39611yescharacteristic
113C2×C43#46011yescharacteristic
114C2×C43#46311yescharacteristic
115C2×C43#46511yescharacteristic
116C2×C43#46911yescharacteristic
117C2×C43#47611yescharacteristic
118C2×C43#47811yescharacteristic
119D43—82no—
120C2×#106D4311yescharacteristic, complemented
121C2×C4⋊C8—431no—
122C2×#102—431no—
123C2×#102—431no—
124#390—431no—
125#389—431no—
126#340—431no—
127C43#206511yescharacteristic, complemented, Sylow
128C22×D4—431no—
129C22×C8—431no—
130C22×C8C2×D4311yescharacteristic
131C2×C4⋊C4—431no—
132C2×C4⋊C4—861no—
133C2×C4⋊C4C2×D4311yescharacteristic
134C2×C4⋊C4C2×D4311yescharacteristic
135C2×C22⋊C4—861no—
136C2×C22⋊C4—861no—
137C2×C42—431no—
138#106—22no—
139C4⋊C8—862no—
140#102—862no—
141#102—862no—
142#95—861no—
143C24—861no—
144C2×D4—432no—
145C2×D4—861no—
146C2×D4—861no—
147C2×D4—861no—
148C2×D4—861no—
149C2×D4—861no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—431no—
153C22×C4—431no—
154C22×C4—861no—
155C22×C4C22×D4311yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—861no—
159C2×C8—861no—
160C2×C8—861no—
161C2×C8D17212yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—861no—
166C4⋊C4—861no—
167C4⋊C4—1722no—
168C4⋊C4C22⋊D4312yes—
169C22⋊C4—1722no—
170C22⋊C4—1722no—
171C42—861no—
172C42—861no—
173C23—862no—
174C23—1721no—
175C23—1721no—
176C23—1721no—
177C23—1721no—
178C23—1721no—
179C23—1721no—
180C23D4×D4311yescharacteristic
181D4—862no—
182D4—862no—
183D4—1721no—
184D4—1721no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—432no—
192C2×C4—861no—
193C2×C4—861no—
194C2×C4—861no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—1721no—
198C2×C4—1721no—
199C2×C4—1721no—
200C2×C4C2×D17211yescharacteristic
201C2×C4#1062189811yescharacteristic
202C2×C4#1062190011yescharacteristic
203C2×C4Q8×D4311yescharacteristic
204C2×C4#1062190211yescharacteristic
205C2×C4C2×C22⋊D4311yescharacteristic
206C8—22no—
207C8—1721no—
208C22—3441no—
209C22—3441no—
210C22—3441no—
211C22—3441no—
212C22—1722no—
213C22—1722no—
214C22—1722no—
215C22#1306329711yescharacteristic
216C22#1306330011yescharacteristic
217C22#1306330311yescharacteristic
218C22SD16×D4311yescharacteristic
219C22#1306334611yescharacteristic
220C22#1306335211yescharacteristic
221C22#1306335211yescharacteristic
222C4—42no—
223C4—81no—
224C4—862no—
225C4—3441no—
226C4—1721no—
227C4#1306329911yescharacteristic
228C4#1306330111yescharacteristic
229C4#1306330511yescharacteristic
230C4#1306332011yescharacteristic
231C2—3442no—
232C2#1458282111yescharacteristic
233C2#1458309711yescharacteristic
234C2#1458311611yescharacteristic
235C2#1458312911yescharacteristic
236C2#1458315311yescharacteristic
237C2#1458318811yescharacteristic
238C2#1458319811yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC2×#106×C43C2
socleC23×C43C2×D4
hypercenterC2×#106D43
hypocenterC43#2065
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
1. C2×Dic43⋊C8C2semidirect
5. #14582798C2semidirect
6. #14582661C2semidirect
7. C2×#106×C43C2semidirect
120. C2×#106D43semidirect
127. C43#2065semidirect