Finite Group Databasebeta

← #19135840

Subgroups — #19135840

Order 5504.

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

normal subgroups only

This group has 298 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×#13063323C211yesmaximal, characteristic
2C2×#13063250C211yesmaximal, characteristic
3C2×#13063249C211yesmaximal, characteristic
4C2×#13063248C211yesmaximal, characteristic
5#14582798C211yesmaximal, characteristic
6#14582653C211yesmaximal, characteristic
7C2×#103×C43C211yesmaximal, characteristic
8C22×Dic86C2211yescharacteristic
9C22×C43⋊C8C2211yescharacteristic
10#13063323—22no—
11#13063323—22no—
12C2×C4⋊Dic43—21no—
13C2×C4⋊Dic43C2211yescharacteristic
14C2×Dic43⋊C4—21no—
15C2×Dic43⋊C4—21no—
16C2×C4×Dic43C2211yescharacteristic
17#13063250—22no—
18#13063249—22no—
19#13063248—22no—
20C43⋊#95—21no—
21C22×Q8×C43C2211yescharacteristic
22C22×C8×C43C2211yescharacteristic
23C2×C4⋊C4×C43C2211yescharacteristic
24#103×C43—22no—
25C2×Q8×C43—21no—
26C2×Q8×C43—21no—
27C2×Q8×C43—21no—
28C2×Q8×C43—21no—
29C2×Q8×C43—21no—
30C2×Q8×C43D412yes—
31C22×C4×C43—21no—
32C22×C4×C43—21no—
33C22×C4×C43C2311yescharacteristic
34C22×Dic43—21no—
35C22×Dic43—21no—
36C22×Dic43D411yescharacteristic
37C22×Dic43D411yescharacteristic
38C2×Dic86—21no—
39C2×Dic86—21no—
40C2×Dic86—21no—
41C2×Dic86—21no—
42C2×Dic86—21no—
43C2×Dic86D412yes—
44C2×C8×C43—21no—
45C2×C8×C43—21no—
46C2×C8×C43—21no—
47C4⋊C4×C43—21no—
48C4⋊C4×C43D412yes—
49C4⋊Dic43—21no—
50C4⋊Dic43—21no—
51C4⋊Dic43—42no—
52Dic43⋊C4—24no—
53Dic43⋊C4—24no—
54C4×Dic43—21no—
55C4×Dic43—21no—
56C2×C43⋊C8—21no—
57C2×C43⋊C8—21no—
58C2×C43⋊C8—21no—
59C23×C43C2×D411yescharacteristic
60Q8×C43—22no—
61Q8×C43—22no—
62Q8×C43—41no—
63Q8×C43—41no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43#4111yescharacteristic
74C2×C4×C43#4111yescharacteristic
75C2×C4×C43#4111yescharacteristic
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—22no—
81C2×Dic43—41no—
82C2×Dic43—41no—
83C2×Dic43—41no—
84C2×Dic43—41no—
85C2×Dic43—41no—
86C2×Dic43SD1612yes—
87C2×Dic43Q1612yes—
88Dic86—22no—
89Dic86—22no—
90Dic86—41no—
91Dic86—41no—
92C8×C43—41no—
93C43⋊C8—41no—
94C22×C43#12011yescharacteristic
95C22×C43#12111yescharacteristic
96C22×C43#12411yescharacteristic
97C22×C43C2×SD1611yescharacteristic
98C22×C43C2×Q1611yescharacteristic
99C22×C43#13711yescharacteristic
100C22×C43#13711yescharacteristic
101C4×C43—42no—
102C4×C43—42no—
103C4×C43#12111yescharacteristic
104C4×C43#12111yescharacteristic
105C4×C43#12311yescharacteristic
106C4×C43#12311yescharacteristic
107Dic43—22no—
108Dic43—22no—
109Dic43—42no—
110Dic43—81no—
111#2043—431nomaximal, Sylow
112C2×C43#39411yescharacteristic
113C2×C43#44811yescharacteristic
114C2×C43#45111yescharacteristic
115C2×C43#46111yescharacteristic
116C2×C43#46211yescharacteristic
117C2×C43#48711yescharacteristic
118C2×C43#49111yescharacteristic
119C2×C4⋊Q8—431no—
120C2×#103—431no—
121C2×#103—431no—
122C2×#103—431no—
123C2×#103D4311yescharacteristic
124#389—431no—
125#336—431no—
126C43#204311yescharacteristic, complemented, Sylow
127C22×Q8—431no—
128C22×Q8C2×D4311yescharacteristic
129C22×C8—431no—
130C22×C8C2×D4311yescharacteristic
131C4⋊Q8—862no—
132C4⋊Q8—862no—
133C2×C4⋊C4—431no—
134C2×C4⋊C4—861no—
135C2×C4⋊C4—861no—
136C2×C4⋊C4—861no—
137C2×C4⋊C4C2×D4311yescharacteristic
138C2×C42—431no—
139#103—22no—
140#103—862no—
141#103—862no—
142#103—862no—
143#95—861no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—432no—
150C2×Q8—861no—
151C2×Q8—861no—
152C2×Q8—861no—
153C2×Q8—861no—
154C2×Q8—861no—
155C2×Q8D17212yes—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—431no—
159C22×C4—431no—
160C22×C4—861no—
161C22×C4—861no—
162C22×C4C22×D4311yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—861no—
167C2×C8—861no—
168C2×C8—861no—
169C4⋊C4—21no—
170C4⋊C4—864no—
171C4⋊C4—864no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4—1722no—
175C4⋊C4C22⋊D4312yes—
176C42—861no—
177C42—861no—
178C23D4×D4311yescharacteristic
179Q8—22no—
180Q8—22no—
181Q8—41no—
182Q8—41no—
183Q8—862no—
184Q8—862no—
185Q8—1721no—
186Q8—1721no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—432no—
194C2×C4—432no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—861no—
198C2×C4—861no—
199C2×C4—862no—
200C2×C4—1721no—
201C2×C4—1721no—
202C2×C4—1721no—
203C2×C4—1721no—
204C2×C4—1721no—
205C2×C4C2×D17211yescharacteristic
206C2×C4#1062189811yescharacteristic
207C2×C4D4×D4311yescharacteristic
208C2×C4#1062190011yescharacteristic
209C2×C4#1062190011yescharacteristic
210C2×C4C2×C22⋊D4311yescharacteristic
211C8—41no—
212C8—1721no—
213C22#1306329511yescharacteristic
214C22#1306329711yescharacteristic
215C22#1306331111yescharacteristic
216C22SD16×D4311yescharacteristic
217C22Q16×D4311yescharacteristic
218C22#1306335411yescharacteristic
219C22#1306335711yescharacteristic
220C4—42no—
221C4—42no—
222C4—862no—
223C4—862no—
224C4—3441no—
225C4—1722no—
226C4#1306329611yescharacteristic
227C4#1306329911yescharacteristic
228C4#1306330711yescharacteristic
229C4#1306330911yescharacteristic
230C2#1458281511yescharacteristic
231C2#1458303911yescharacteristic
232C2#1458305611yescharacteristic
233C2#1458310211yescharacteristic
234C2#1458310711yescharacteristic
235C2#1458324811yescharacteristic
236C2#1458326611yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC2×#103×C43C2
socleC23×C43C2×D4
hypercenterC2×#103D43
hypocenterC43#2043
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
126. C43#2043semidirect