Finite Group Databasebeta

← #19133553

Subgroups — #19133553

Order 5504.

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

normal subgroups only

This group has 256 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#14583057C211yesmaximal, characteristic, complemented
3#14583054C211yesmaximal, characteristic, complemented
4#14582812C211yesmaximal, characteristic
5#14582635C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic
7C43×#328C211yesmaximal, characteristic, complemented
8C22×Dic86C2211yescharacteristic
9C2×Dic172—21no—
10C2×#10621885—21no—
11#13063305—21no—
12#13063304C2211yescharacteristic
13#13063303—21no—
14#13063303—21no—
15#13063302—21no—
16#13063301—21no—
17C2×(C2×D43)⋊C4—21no—
18C2×(C2×D43)⋊C4C2211yescharacteristic
19C22⋊C4×D43—21no—
20#13063250—21no—
21#13063248—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×Dic86—21no—
37C2×Dic86—21no—
38C2×Dic86—42no—
39C2×Dic86D411yescharacteristic
40C2×C8×C43—21no—
41C4⋊C4×C43—21no—
42C4⋊C4×C43D411yescharacteristic
43C22⋊C4×C43—21no—
44C22⋊Dic43—21no—
45#10621885—42no—
46(C2×D43)⋊C4—21no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—42no—
51C4⋊Dic43—21no—
52C4⋊Dic43D411yescharacteristic
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56C2×C43⋊C8—21no—
57Dic172—42no—
58C23×C43C2×D411yescharacteristic
59C22×D43—21no—
60C22×D43—21no—
61C22×D43—41no—
62C22×D43—41no—
63C22×D43Q1612yescomplemented
64Q8×C43—41no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—41no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×Dic43—22no—
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—41no—
78C2×Dic43—41no—
79C2×Dic43—41no—
80C4×D43—81no—
81C4×D43—81no—
82Dic86—22no—
83Dic86—22no—
84Dic86—41no—
85Dic86—41no—
86Dic86—41no—
87Dic86—81no—
88C8×C43—41no—
89C43⋊C8—41no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43#12011yescharacteristic
93C22×C43C2×Q1611yescharacteristic
94C22×C43#13711yescharacteristic
95C2×D43—22no—
96C2×D43—41no—
97C2×D43—41no—
98C2×D43—42no—
99C2×D43—81no—
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—41no—
103C4×C43—41no—
104C4×C43—81no—
105Dic43—41no—
106Dic43—41no—
107Dic43—42no—
108Dic43—41no—
109#1602—431nomaximal, Sylow
110C2×C43—21no—
111C2×C43—21no—
112C2×C43#45111yescharacteristic
113C2×C43#45511yescharacteristic
114C2×C43B(4,𝔽2)11yescharacteristic
115D43—42no—
116#543—431no—
117#451—431no—
118#451—431no—
119#393—431no—
120#328—431no—
121#328D4311yescharacteristic, complemented
122#323—431no—
123C43#160211yescharacteristic, complemented, Sylow
124C22×Q8—431no—
125C2×Q16—861no—
126C2×Q16—861no—
127C22⋊Q8—431no—
128C22⋊Q8—861no—
129C22⋊Q8—861no—
130C22⋊Q8—861no—
131C22⋊Q8—861no—
132C22⋊Q8—861no—
133C22⋊Q8C2×D4311yescharacteristic
134C2×C22⋊C4—431no—
135C2×C22⋊C4—861no—
136C2×C22⋊C4—861no—
137#103—861no—
138#103—861no—
139C22⋊C8—431no—
140C22⋊C8C2×D4311yescharacteristic
141#95—861no—
142#95C2×D4311yescharacteristic
143C24—431no—
144C2×Q8—431no—
145C2×Q8—861no—
146C2×Q8—861no—
147C2×Q8—861no—
148C2×Q8—1722no—
149C2×Q8D17211yescharacteristic
150C22×C4—21no—
151C22×C4—431no—
152C22×C4—861no—
153C22×C4—861no—
154C22×C4—861no—
155C22×C4C22×D4311yescharacteristic
156Q16—1722no—
157Q16—1722no—
158C2×C8—21no—
159C2×C8—861no—
160C4⋊C4—21no—
161C4⋊C4—431no—
162C4⋊C4—861no—
163C4⋊C4—861no—
164C4⋊C4—861no—
165C4⋊C4—861no—
166C4⋊C4D17211yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—861no—
169C22⋊C4—861no—
170C22⋊C4—861no—
171C22⋊C4—861no—
172C22⋊C4—861no—
173C22⋊C4—1722no—
174C23—432no—
175C23—861no—
176C23—861no—
177C23—1721no—
178C23—1721no—
179C23D4×D4311yescharacteristic
180Q8—41no—
181Q8—862no—
182Q8—862no—
183Q8—3441no—
184Q8—1721no—
185Q8—1721no—
186Q8—1721no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—862no—
194C2×C4—861no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—3441no—
198C2×C4—3441no—
199C2×C4—1721no—
200C2×C4—1721no—
201C2×C4—1721no—
202C2×C4C2×D17211yescharacteristic
203C2×C4D4×D4311yescharacteristic
204C8—41no—
205C8—1721no—
206C22—21no—
207C22—21no—
208C22—862no—
209C22—3441no—
210C22—1722no—
211C22—1721no—
212C22—1721no—
213C22#1306329511yescharacteristic
214C22Q16×D4311yescharacteristic
215C22#1306335411yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—41no—
220C4—81no—
221C4—1721no—
222C4—1721no—
223C4—1721no—
224C4—1722no—
225C2—21no—
226C2—21no—
227C2—1722no—
228C2#1458305611yescharacteristic
229C2#1458307811yescharacteristic
230C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43#120
hypercenter#328D43
hypocenterC43#1602
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. #14583057C2semidirect
3. #14583054C2semidirect
5. #14582635C2semidirect
7. C43×#328C2semidirect
63. C22×D43Q16semidirect
121. #328D43semidirect
123. C43#1602semidirect