Finite Group Databasebeta

← #19133587

Subgroups — #19133587

Order 5504.

228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#14583524C211yesmaximal, characteristic
2#14583230C211yesmaximal, characteristic, complemented
3#14583227C211yesmaximal, characteristic, complemented
4#14582826C211yesmaximal, characteristic
5#14582635C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic
7C43×#328C211yesmaximal, characteristic, complemented
8#13063305—21no—
9#13063304C2211yescharacteristic
10#13063303—21no—
11#13063303—21no—
12#13063302—21no—
13#13063301—21no—
14C2×C4⋊Dic43C2211yescharacteristic
15C2×(C2×D43)⋊C4—21no—
16C2×(C2×D43)⋊C4C2211yescharacteristic
17C22⋊C4×D43—21no—
18#13063257—21no—
19#13063256—21no—
20#13063250—21no—
21#13063249—21no—
22C22⋊(C43⋊C8)C2211yescharacteristic
23C43⋊#95—21no—
24C22⋊Q8×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28C2×Q8×C43D411yescharacteristic
29C22×C4×C43—21no—
30C22×C4×C43C2311yescharacteristic
31C22×Dic43—21no—
32C22×Dic43D411yescharacteristic
33C2×C4×D43—21no—
34C2×C4×D43—21no—
35C2×Dic86—21no—
36C2×Dic86D411yescharacteristic
37C2×C8×C43—21no—
38C4⋊C4×C43—21no—
39C4⋊C4×C43D411yescharacteristic
40C22⋊C4×C43—21no—
41C22⋊Dic43—21no—
42(C2×D43)⋊C4—21no—
43(C2×D43)⋊C4—21no—
44(C2×D43)⋊C4—21no—
45(C2×D43)⋊C4—21no—
46(C2×D43)⋊C4—42no—
47C4⋊Dic43—21no—
48C4⋊Dic43—21no—
49C4⋊Dic43—21no—
50C4⋊Dic43D411yescharacteristic
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54C2×C43⋊C8—21no—
55C23×C43C2×D411yescharacteristic
56C22×D43—21no—
57C22×D43—21no—
58C22×D43—41no—
59C22×D43—41no—
60C22×D43SD1612yes—
61Q8×C43—41no—
62C2×C4×C43—21no—
63C2×C4×C43—21no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×Dic43—21no—
71C2×Dic43—21no—
72C2×Dic43—21no—
73C2×Dic43—41no—
74C2×Dic43—41no—
75C2×Dic43—41no—
76C2×Dic43—41no—
77C4×D43—81no—
78C4×D43—81no—
79Dic86—41no—
80Dic86—81no—
81C8×C43—41no—
82C43⋊C8—41no—
83C22×C43—21no—
84C22×C43—21no—
85C22×C43#12011yescharacteristic
86C22×C43C2×SD1611yescharacteristic
87C22×C43#13711yescharacteristic
88C2×D43—22no—
89C2×D43—41no—
90C2×D43—41no—
91C2×D43—42no—
92C2×D43—81no—
93C4×C43—21no—
94C4×C43—21no—
95C4×C43—41no—
96C4×C43—41no—
97C4×C43—81no—
98Dic43—41no—
99Dic43—41no—
100Dic43—41no—
101Dic43—81no—
102#1608—431nomaximal, Sylow
103C2×C43—21no—
104C2×C43—21no—
105C2×C43#44811yescharacteristic
106C2×C43#45511yescharacteristic
107C2×C43#45811yescharacteristic
108D43—42no—
109#543—431no—
110#483—431no—
111#483—431no—
112#397—431no—
113#328—431no—
114#328D4311yescharacteristic, complemented
115#323—431no—
116C43#160811yescharacteristic, complemented, Sylow
117C22⋊Q8—431no—
118C22⋊Q8—861no—
119C22⋊Q8—861no—
120C22⋊Q8—861no—
121C22⋊Q8—861no—
122C22⋊Q8—861no—
123C22⋊Q8C2×D4311yescharacteristic
124C2×C4⋊C4—431no—
125C2×C22⋊C4—431no—
126C2×C22⋊C4—861no—
127C2×C22⋊C4—861no—
128#106—861no—
129#106—861no—
130#103—861no—
131#103—861no—
132C22⋊C8—431no—
133C22⋊C8C2×D4311yescharacteristic
134#95—861no—
135#95C2×D4311yescharacteristic
136C24—431no—
137C2×Q8—431no—
138C2×Q8—861no—
139C2×Q8D17211yescharacteristic
140C22×C4—21no—
141C22×C4—431no—
142C22×C4—861no—
143C22×C4—861no—
144C22×C4—861no—
145C22×C4C22×D4311yescharacteristic
146C2×C8—21no—
147C2×C8—861no—
148C4⋊C4—21no—
149C4⋊C4—431no—
150C4⋊C4—861no—
151C4⋊C4—861no—
152C4⋊C4—861no—
153C4⋊C4—861no—
154C4⋊C4—861no—
155C4⋊C4—861no—
156C4⋊C4D17211yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—861no—
159C22⋊C4—861no—
160C22⋊C4—861no—
161C22⋊C4—861no—
162C22⋊C4—861no—
163C22⋊C4—1722no—
164C23—432no—
165C23—861no—
166C23—861no—
167C23—1721no—
168C23—1721no—
169C23D4×D4311yescharacteristic
170Q8—41no—
171Q8—3441no—
172Q8—1721no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—861no—
180C2×C4—861no—
181C2×C4—861no—
182C2×C4—3441no—
183C2×C4—3441no—
184C2×C4—1721no—
185C2×C4—1721no—
186C2×C4—1721no—
187C2×C4—1721no—
188C2×C4C2×D17211yescharacteristic
189C2×C4D4×D4311yescharacteristic
190C8—41no—
191C8—1721no—
192C22—21no—
193C22—21no—
194C22—862no—
195C22—3441no—
196C22—1722no—
197C22—1721no—
198C22—1721no—
199C22#1306329511yescharacteristic
200C22SD16×D4311yescharacteristic
201C22#1306335711yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—3441no—
208C4—1721no—
209C4—1721no—
210C4—1721no—
211C2—21no—
212C2—21no—
213C2—1722no—
214C2#1458303911yescharacteristic
215C2#1458307811yescharacteristic
216C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43#120
hypercenter#328D43
hypocenterC43#1608
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #14583230C2semidirect
3. #14583227C2semidirect
5. #14582635C2semidirect
7. C43×#328C2semidirect
114. #328D43semidirect
116. C43#1608semidirect