Finite Group Databasebeta

← #19135880

Subgroups — #19135880

Order 5504.

266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 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#14583697C211yesmaximal, characteristic
2#14582922C211yesmaximal, characteristic, complemented
3C2×#13063252C211yesmaximal, characteristic, complemented
4C2×#13063251C211yesmaximal, characteristic, complemented
5#14582881C211yesmaximal, characteristic, complemented
6C43⋊#338C211yesmaximal, characteristic, complemented
7C43×#413C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063356—21no—
10#13063355—21no—
11#13063351—21no—
12#13063350—21no—
13#13063345—22no—
14C2×#10621877C2211yescharacteristic
15C2×#10621877C2211yescharacteristic
16C2×C4×Dic43C2211yescharacteristic
17Dic43⋊C8—22no—
18#13063252—21no—
19#13063252—21no—
20#13063251—21no—
21#13063251—21no—
22#13063243—21no—
23#13063241—21no—
24C2×#41×C43C2211yescharacteristic
25C2×M16×C43C2211yescharacteristic
26C2×M16×C43C2211yescharacteristic
27#101×C43—21no—
28#100×C43—21no—
29#41×C43—21no—
30#41×C43—21no—
31#41×C43—21no—
32#41×C43—21no—
33C2×Q8×C43D411yescharacteristic
34C2×D4×C43—21no—
35C2×D4×C43D411yescharacteristic
36C22×C4×C43—21no—
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—21no—
39C22×Dic43—21no—
40#10621898—21no—
41#10621898—21no—
42#10621898—21no—
43#10621898—21no—
44C2×D172D411yescharacteristic
45C2×C4×D43—21no—
46C2×Dic86D411yescharacteristic
47M16×C43—21no—
48M16×C43—21no—
49M16×C43—21no—
50M16×C43—21no—
51C2×C8×C43—21no—
52C2×C8×C43—21no—
53#10621885—22no—
54#10621884—22no—
55#10621883—22no—
56#10621882—22no—
57C4×Dic43—21no—
58C4×Dic43D411yescharacteristic
59C4×Dic43D411yescharacteristic
60#10621877—21no—
61#10621877—21no—
62#10621877—21no—
63#10621877—21no—
64C2×C43⋊C8—21no—
65C2×C43⋊C8D412yes—
66C23×C43—21no—
67C23×C43#4111yescharacteristic
68C22×D43—21no—
69Q8×C43—21no—
70Q8×C43—21no—
71D4×C43—21no—
72D4×C43—21no—
73D4×C43—41no—
74D4×C43—41no—
75C2×C4×C43—21no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43#4111yescharacteristic
83C2×C4×C43#4111yescharacteristic
84C22⋊D43—41no—
85C22⋊D43—41no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—42no—
90D172—21no—
91D172—21no—
92C4×D43—41no—
93C4×D43—41no—
94Dic86—21no—
95Dic86—21no—
96C8×C43—41no—
97C8×C43—41no—
98C43⋊C8—22no—
99C43⋊C8—41no—
100C22×C43—41no—
101C22×C43—41no—
102C22×C43—81no—
103C22×C43#12111yescharacteristic
104C22×C43#12311yescharacteristic
105C22×C43#12311yescharacteristic
106C2×D43—41no—
107C2×D43—81no—
108C4×C43—41no—
109C4×C43#12011yescharacteristic
110C4×C43#12111yescharacteristic
111C4×C43#12111yescharacteristic
112C4×C43#12411yescharacteristic
113Dic43—22no—
114Dic43—41no—
115Dic43—41no—
116#2050—431nomaximal, Sylow
117C2×C43—21no—
118C2×C43—21no—
119C2×C43—21no—
120C2×C43—81no—
121C2×C43#39411yescharacteristic
122D43—81no—
123#575—431no—
124#423—431no—
125C2×#104—431no—
126C2×#104—431no—
127#413—431no—
128#413D4311yescharacteristic, complemented
129#338—431no—
130C43#205011yescharacteristic, complemented, Sylow
131C2×#41—431no—
132C2×#41C2×D4311yescharacteristic
133#137—861no—
134#137—861no—
135AGL(1,ℤ/8)—861no—
136AGL(1,ℤ/8)—861no—
137#135—862no—
138C2×M16—431no—
139C2×M16—431no—
140C2×M16C2×D4311yescharacteristic
141C2×M16C2×D4311yescharacteristic
142C2×C42—431no—
143C4⋊C8—862no—
144#104—861no—
145#104—861no—
146#104—861no—
147#104—861no—
148#101—21no—
149#101—861no—
150#100—21no—
151#100—861no—
152#41—21no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—861no—
157#41—861no—
158#41—861no—
159#41—861no—
160C2×Q8—431no—
161C2×Q8C22⋊D4311yescharacteristic
162C2×D4—21no—
163C2×D4—431no—
164C2×D4—861no—
165C2×D4C22⋊D4311yescharacteristic
166C22×C4—21no—
167C22×C4—861no—
168C22×C4—861no—
169C22×C4C22×D4311yescharacteristic
170Q16—862no—
171SD16—862no—
172SD16—862no—
173D8—862no—
174M16—21no—
175M16—21no—
176M16—21no—
177M16—21no—
178M16—861no—
179M16—861no—
180M16—861no—
181M16—861no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—432no—
185C2×C8—861no—
186C42—431no—
187C42—431no—
188C42—861no—
189C23—21no—
190C23—861no—
191C23#1062189811yescharacteristic
192Q8—21no—
193Q8—21no—
194Q8—861no—
195Q8—861no—
196D4—21no—
197D4—21no—
198D4—41no—
199D4—41no—
200D4—861no—
201D4—861no—
202D4—1721no—
203D4—1721no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—861no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—1722no—
211C2×C4—1721no—
212C2×C4—1721no—
213C2×C4#1062189811yescharacteristic
214C2×C4D4×D4311yescharacteristic
215C2×C4D4×D4311yescharacteristic
216C2×C4D4×D4311yescharacteristic
217C2×C4#1062190011yescharacteristic
218C2×C4C2×C22⋊D4311yescharacteristic
219C8—41no—
220C8—41no—
221C8—862no—
222C8—1721no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—3441no—
227C22—1721no—
228C22#1306329811yescharacteristic
229C22#1306330711yescharacteristic
230C22#1306330811yescharacteristic
231C4—41no—
232C4—862no—
233C4—1721no—
234C4—1721no—
235C4#1306329311yescharacteristic
236C4#1306329711yescharacteristic
237C4#1306329811yescharacteristic
238C4#1306331111yescharacteristic
239C2—21no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—3441no—
244C2#1458281411yescharacteristic
subgroupG/H
centerC4#13063311
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#413C2
socleC2×C43#394
hypercenter#413D43
hypocenterC43#2050
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #14582922C2semidirect
3. C2×#13063252C2semidirect
4. C2×#13063251C2semidirect
5. #14582881C2semidirect
6. C43⋊#338C2semidirect
7. C43×#413C2semidirect
128. #413D43semidirect
130. C43#2050semidirect