Finite Group Databasebeta

← #19134954

Subgroups — #19134954

Order 5504.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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#14583665C211yesmaximal, characteristic, complemented
3#14582893C211yesmaximal, characteristic, complemented
4#14582866C211yesmaximal, characteristic, complemented
5#14582669C211yesmaximal, characteristic, complemented
6#14582663C211yesmaximal, characteristic, complemented
7C43×#421C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063356C412yescomplemented
10#13063355—21no—
11#13063351C412yescomplemented
12#13063350—21no—
13#13063345—22no—
14#13063333—22no—
15#13063331—22no—
16C2×#10621877C2211yescharacteristic
17C2×#10621877C2211yescharacteristic
18M16×D43—22no—
19C22×C43⋊C8C2211yescharacteristic
20#13063248—21no—
21#13063245—21no—
22C22⋊(C43⋊C8)—22no—
23C2×#41×C43C2211yescharacteristic
24C2×M16×C43C2211yescharacteristic
25#117×C43C2211yescharacteristic
26#104×C43—22no—
27#41×C43—21no—
28#41×C43—21no—
29#41×C43—21no—
30#41×C43—21no—
31C2×Q8×C43C2×C411yescharacteristic
32C2×D4×C43—21no—
33C2×D4×C43C2×C411yescharacteristic
34C22×C4×C43—21no—
35C22×C4×C43C2311yescharacteristic
36C2×C22⋊D43—21no—
37#10621898—21no—
38#10621898—21no—
39#10621898C2×C412yes—
40#10621898D412yes—
41C2×D172D411yescharacteristic
42C2×C4×D43—21no—
43C2×Dic86D411yescharacteristic
44M16×C43—21no—
45M16×C43D412yes—
46C2×C8×C43—21no—
47C4⋊C4×C43—21no—
48C22⋊C4×C43—21no—
49C42×C43—21no—
50#10621885—22no—
51#10621884—22no—
52#10621883—22no—
53#10621882—22no—
54#10621877—21no—
55#10621877—21no—
56#10621877—21no—
57#10621877C2×C412yes—
58C2×C43⋊C8—21no—
59C2×C43⋊C8—21no—
60C2×C43⋊C8—21no—
61C2×C43⋊C8—21no—
62C2×C43⋊C8D412yes—
63#10621872—24no—
64C8×D43—24no—
65C23×C43—21no—
66C23×C43#4111yescharacteristic
67C22×D43—21no—
68Q8×C43—21no—
69Q8×C43—21no—
70D4×C43—21no—
71D4×C43—21no—
72D4×C43—41no—
73D4×C43—41no—
74C2×C4×C43—21no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43C22×C411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43#4111yescharacteristic
84C22⋊D43—22no—
85C22⋊D43—22no—
86C2×Dic43—21no—
87D172—21no—
88D172C22⋊C412yes—
89C4×D43—22no—
90C4×D43—22no—
91Dic86—21no—
92Dic86C22⋊C412yes—
93C8×C43—22no—
94C43⋊C8—22no—
95C43⋊C8—22no—
96C43⋊C8—41no—
97C22×C43—41no—
98C22×C43—42no—
99C22×C43—41no—
100C22×C43C4×D411yescharacteristic
101C22×C43#12111yescharacteristic
102C22×C43#12311yescharacteristic
103C2×D43—22no—
104C2×D43—81no—
105C4×C43—41no—
106C4×C43—81no—
107C4×C43C2×C22⋊C411yescharacteristic
108C4×C43C4×D411yescharacteristic
109C4×C43#12011yescharacteristic
110C4×C43#12111yescharacteristic
111Dic43—22no—
112#1881—431nomaximal, Sylow
113C2×C43—21no—
114C2×C43—21no—
115C2×C43—21no—
116C2×C43—81no—
117C2×C43#38611yescharacteristic
118D43—42no—
119#575—431no—
120#568—431no—
121#421D4311yescharacteristic, complemented
122#416—431no—
123#408—431no—
124#344—431no—
125#341—431no—
126C43#188111yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C2×#41C2×D4311yescharacteristic
129#137—432no—
130#137—861no—
131AGL(1,ℤ/8)—432no—
132AGL(1,ℤ/8)—861no—
133#135—862no—
134#131—862no—
135#131—862no—
136C2×M16—431no—
137C2×M16—431no—
138C2×M16—862no—
139C2×M16C2×D4311yescharacteristic
140C22×C8—431no—
141#117C2×D4311yescharacteristic
142#104—22no—
143#103—861no—
144#102—861no—
145C22⋊C8—862no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—432no—
151#41—432no—
152#41—861no—
153#41—861no—
154C2×Q8—431no—
155C2×Q8C4×D4311yescharacteristic
156C2×D4—21no—
157C2×D4—431no—
158C2×D4—861no—
159C2×D4C4×D4311yescharacteristic
160C22×C4—21no—
161C22×C4—861no—
162C22×C4C22×D4311yescharacteristic
163Q16—862no—
164SD16—862no—
165SD16—862no—
166D8—862no—
167M16—21no—
168M16—432no—
169M16—864no—
170M16—861no—
171M16—861no—
172M16—861no—
173M16C22⋊D4312yes—
174C2×C8—21no—
175C2×C8—432no—
176C2×C8—864no—
177C2×C8—861no—
178C2×C8—861no—
179C2×C8—861no—
180C2×C8—861no—
181C4⋊C4—21no—
182C22⋊C4—21no—
183C42—21no—
184C23—21no—
185C23—861no—
186C23#1062190011yescharacteristic
187Q8—21no—
188Q8—21no—
189Q8—432no—
190Q8—861no—
191D4—21no—
192D4—21no—
193D4—41no—
194D4—41no—
195D4—432no—
196D4—862no—
197D4—862no—
198D4—861no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—861no—
204C2×C4—862no—
205C2×C4—862no—
206C2×C4C2×C4×D4311yescharacteristic
207C2×C4#1062189811yescharacteristic
208C2×C4D4×D4311yescharacteristic
209C2×C4D4×D4311yescharacteristic
210C2×C4D4×D4311yescharacteristic
211C2×C4C2×C22⋊D4311yescharacteristic
212C8—22no—
213C8—862no—
214C8—862no—
215C8—1721no—
216C22—41no—
217C22—42no—
218C22—41no—
219C22—862no—
220C22—3441no—
221C22(C22⋊D43)⋊C411yescharacteristic
222C22#1306329611yescharacteristic
223C22#1306330711yescharacteristic
224C4—41no—
225C4—81no—
226C4—862no—
227C4C22⋊C4×D4311yescharacteristic
228C4C4×C22⋊D4311yescharacteristic
229C4#1306329311yescharacteristic
230C4#1306329811yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—1722no—
236C2#1458277511yescharacteristic
subgroupG/H
centerC4#13063293
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#421C2
socleC2×C43#386
hypercenter#421D43
hypocenterC43#1881
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #14583665C2semidirect
3. #14582893C2semidirect
4. #14582866C2semidirect
5. #14582669C2semidirect
6. #14582663C2semidirect
7. C43×#421C2semidirect
9. #13063356C4semidirect
11. #13063351C4semidirect
121. #421D43semidirect
126. C43#1881semidirect