Finite Group Databasebeta

← #19134955

Subgroups — #19134955

Order 5504.

310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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#14583666C211yesmaximal, characteristic, complemented
3#14582917C211yesmaximal, characteristic, complemented
4#14582865C211yesmaximal, characteristic, complemented
5#14582669C211yesmaximal, characteristic, complemented
6#14582664C211yesmaximal, characteristic, complemented
7C43×#416C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063356—21no—
10#13063355C412yescomplemented
11#13063351—21no—
12#13063350C412yescomplemented
13#13063345—22no—
14#13063332—22no—
15#13063332—22no—
16C2×#10621877—22no—
17C2×#10621877C2211yescharacteristic
18C2×#10621877C2211yescharacteristic
19C2×#10621877C2211yescharacteristic
20#13063253—22no—
21(C2×D43)⋊C8—22no—
22C2×#41×C43C2211yescharacteristic
23C22×C8×C43C2211yescharacteristic
24#117×C43C2211yescharacteristic
25#103×C43—21no—
26#102×C43—21no—
27#41×C43—21no—
28#41×C43—21no—
29#41×C43C2×C412yes—
30#41×C43D412yes—
31C2×Q8×C43D411yescharacteristic
32C2×D4×C43—21no—
33C2×D4×C43D411yescharacteristic
34C22×C4×C43—21no—
35C22×C4×C43C2311yescharacteristic
36C2×C22⋊D43—21no—
37#10621898—21no—
38#10621898—21no—
39#10621898—21no—
40#10621898—21no—
41C2×D172C2×C411yescharacteristic
42C2×C4×D43—21no—
43C2×Dic86C2×C411yescharacteristic
44C2×C8×C43—21no—
45C2×C8×C43—21no—
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—24no—
55#10621877—21no—
56#10621877—21no—
57#10621877—21no—
58#10621877—21no—
59#10621877C2×C412yes—
60#10621877D412yes—
61C2×C43⋊C8—24no—
62C2×C43⋊C8—21no—
63C2×C43⋊C8—21no—
64C2×C43⋊C8D412yes—
65C23×C43—21no—
66C23×C43#4111yescharacteristic
67C22×D43—21no—
68Q8×C43—21no—
69Q8×C43C22⋊C412yes—
70D4×C43—22no—
71D4×C43—22no—
72D4×C43—21no—
73D4×C43C22⋊C412yes—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
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—41no—
85C22⋊D43—41no—
86C2×Dic43—21no—
87D172—21no—
88D172—21no—
89C4×D43—41no—
90C4×D43—41no—
91Dic86—21no—
92Dic86—21no—
93C8×C43—41no—
94C43⋊C8—22no—
95C43⋊C8—22no—
96C43⋊C8—22no—
97C22×C43—22no—
98C22×C43—41no—
99C22×C43—81no—
100C22×C43C4×D411yescharacteristic
101C22×C43#12111yescharacteristic
102C22×C43#12311yescharacteristic
103C2×D43—42no—
104C2×D43—41no—
105C4×C43—22no—
106C4×C43—81no—
107C4×C43C2×C22⋊C411yescharacteristic
108C4×C43C4×D411yescharacteristic
109C4×C43#12011yescharacteristic
110C4×C43#12111yescharacteristic
111Dic43—41no—
112#1881—431nomaximal, Sylow
113C2×C43—21no—
114C2×C43—21no—
115C2×C43—21no—
116C2×C43—42no—
117C2×C43#38611yescharacteristic
118D43—81no—
119#575—431no—
120#568—431no—
121#421—431no—
122#416D4311yescharacteristic, complemented
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—431no—
139C2×M16—862no—
140C22×C8C2×D4311yescharacteristic
141#117C2×D4311yescharacteristic
142#104—862no—
143#103—21no—
144#102—21no—
145C22⋊C8—862no—
146#41—21no—
147#41—21no—
148#41—861no—
149#41—861no—
150#41—861no—
151#41—861no—
152#41C4×D4312yes—
153#41D17212yes—
154C2×Q8—431no—
155C2×Q8C22⋊D4311yescharacteristic
156C2×D4—21no—
157C2×D4—431no—
158C2×D4—861no—
159C2×D4C22⋊D4311yescharacteristic
160C22×C4—21no—
161C22×C4—861no—
162C22×C4C22×D4311yescharacteristic
163Q16—862no—
164SD16—862no—
165SD16—862no—
166D8—862no—
167M16—432no—
168M16—432no—
169M16—864no—
170M16—861no—
171M16—861no—
172M16—861no—
173M16—861no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—432no—
178C2×C8—864no—
179C2×C8—861no—
180C2×C8—861no—
181C4⋊C4—21no—
182C22⋊C4—21no—
183C42—21no—
184C23—21no—
185C23—861no—
186C23#1062190011yescharacteristic
187Q8—21no—
188Q8—861no—
189Q8—861no—
190Q8(C2×D43)⋊C412yes—
191D4—22no—
192D4—22no—
193D4—21no—
194D4—861no—
195D4—861no—
196D4—1721no—
197D4—1721no—
198D4(C2×D43)⋊C412yes—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—861no—
204C2×C4—1721no—
205C2×C4—1721no—
206C2×C4C2×C4×D4311yescharacteristic
207C2×C4C2×D17211yescharacteristic
208C2×C4D4×D4311yescharacteristic
209C2×C4D4×D4311yescharacteristic
210C2×C4#1062190011yescharacteristic
211C2×C4C2×C22⋊D4311yescharacteristic
212C8—41no—
213C8—862no—
214C8—862no—
215C8—862no—
216C22—22no—
217C22—41no—
218C22—81no—
219C22—1722no—
220C22—1721no—
221C22(C22⋊D43)⋊C411yescharacteristic
222C22#1306329711yescharacteristic
223C22#1306330911yescharacteristic
224C4—22no—
225C4—81no—
226C4—1721no—
227C4C2×(C2×D43)⋊C411yescharacteristic
228C4(C22⋊D43)⋊C411yescharacteristic
229C4#1306329511yescharacteristic
230C4#1306329711yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—42no—
235C2—3441no—
236C2#1458277611yescharacteristic
subgroupG/H
centerC4#13063295
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#416C2
socleC2×C43#386
hypercenter#416D43
hypocenterC43#1881
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #14583666C2semidirect
3. #14582917C2semidirect
4. #14582865C2semidirect
5. #14582669C2semidirect
6. #14582664C2semidirect
7. C43×#416C2semidirect
10. #13063355C4semidirect
12. #13063350C4semidirect
122. #416D43semidirect
126. C43#1881semidirect