Finite Group Databasebeta

← #19135899

Subgroups — #19135899

Order 5504.

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

normal subgroups only

This group has 264 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#14582925C211yesmaximal, characteristic, complemented
3#14582896C211yesmaximal, characteristic, complemented
4#14582873C211yesmaximal, characteristic, complemented
5#14582872C211yesmaximal, characteristic, complemented
6#14582655C211yesmaximal, characteristic, complemented
7C43×#416C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063356—21no—
10#13063355—21no—
11#13063351—21no—
12#13063350—21no—
13#13063345—22no—
14C2×#10621877C2211yescharacteristic
15#13063284C2211yescharacteristic
16#13063284C2211yescharacteristic
17Dic43⋊C8—22no—
18#13063250—21no—
19#13063247—21no—
20#13063240—22no—
21#13063239—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×C43—21no—
30#41×C43—21no—
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×D172D411yescharacteristic
42C2×C4×D43—21no—
43C2×Dic86D411yescharacteristic
44C2×C8×C43—21no—
45C2×C8×C43—21no—
46C2×C8×C43—21no—
47C4⋊C4×C43—21no—
48C22⋊C4×C43—21no—
49C42×C43—21no—
50C22⋊Dic43—21no—
51C22⋊Dic43D412yes—
52#10621885—22no—
53#10621884—22no—
54#10621883—22no—
55#10621882—22no—
56C4⋊Dic43—21no—
57C4⋊Dic43—21no—
58C4×Dic43—21no—
59C4×Dic43—21no—
60#10621877—21no—
61#10621877—21no—
62C2×C43⋊C8D412yes—
63C23×C43—21no—
64C23×C43C2×D411yescharacteristic
65C22×D43—21no—
66Q8×C43—21no—
67Q8×C43—21no—
68D4×C43—21no—
69D4×C43—21no—
70D4×C43—41no—
71D4×C43—41no—
72C2×C4×C43—21no—
73C2×C4×C43—41no—
74C2×C4×C43—41no—
75C2×C4×C43—41no—
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43#4111yescharacteristic
80C2×C4×C43#4111yescharacteristic
81C2×C4×C43#4111yescharacteristic
82C22⋊D43—41no—
83C22⋊D43—41no—
84C2×Dic43—22no—
85C2×Dic43—21no—
86C2×Dic43—41no—
87D172—21no—
88D172—21no—
89C4×D43—41no—
90C4×D43—41no—
91Dic86—21no—
92Dic86—21no—
93C8×C43—41no—
94C43⋊C8—22no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43—81no—
98C22×C43#12111yescharacteristic
99C22×C43#12111yescharacteristic
100C22×C43#12111yescharacteristic
101C2×D43—41no—
102C2×D43—81no—
103C4×C43—41no—
104C4×C43—81no—
105C4×C43#12011yescharacteristic
106C4×C43#12311yescharacteristic
107C4×C43#12311yescharacteristic
108C4×C43#12411yescharacteristic
109Dic43—42no—
110Dic43—41no—
111Dic43—81no—
112#2053—431nomaximal, Sylow
113C2×C43—21no—
114C2×C43—21no—
115C2×C43—21no—
116C2×C43—81no—
117C2×C43#39411yescharacteristic
118D43—81no—
119#575—431no—
120#424—431no—
121#416—431no—
122#416D4311yescharacteristic, complemented
123#410—431no—
124#410—431no—
125H(3,ℤ/4)—431no—
126C43#205311yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C2×#41C2×D4311yescharacteristic
129#137—861no—
130#137—861no—
131AGL(1,ℤ/8)—861no—
132AGL(1,ℤ/8)—861no—
133#135—862no—
134C2×M16—431no—
135C22×C8C2×D4311yescharacteristic
136#117—431no—
137#117—431no—
138#117C2×D4311yescharacteristic
139C4⋊C8—862no—
140#103—21no—
141#103—861no—
142#102—21no—
143#102—861no—
144#99—862no—
145#99—862no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—861no—
151#41—861no—
152#41—861no—
153#41—861no—
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—861no—
168M16—861no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—432no—
173C4⋊C4—21no—
174C4⋊C4—861no—
175C4⋊C4—861no—
176C22⋊C4—21no—
177C22⋊C4—432no—
178C22⋊C4—861no—
179C42—21no—
180C42—861no—
181C42—861no—
182C23—21no—
183C23—861no—
184C23D4×D4311yescharacteristic
185Q8—21no—
186Q8—21no—
187Q8—861no—
188Q8—861no—
189D4—21no—
190D4—21no—
191D4—41no—
192D4—41no—
193D4—861no—
194D4—861no—
195D4—1721no—
196D4—1721no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—862no—
202C2×C4—861no—
203C2×C4—1721no—
204C2×C4—1721no—
205C2×C4—1721no—
206C2×C4#1062189811yescharacteristic
207C2×C4#1062189811yescharacteristic
208C2×C4D4×D4311yescharacteristic
209C2×C4D4×D4311yescharacteristic
210C2×C4#1062190011yescharacteristic
211C2×C4C2×C22⋊D4311yescharacteristic
212C8—41no—
213C8—862no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—3441no—
218C22—1721no—
219C22#1306329711yescharacteristic
220C22#1306329811yescharacteristic
221C22#1306329811yescharacteristic
222C4—41no—
223C4—81no—
224C4—3441no—
225C4—1722no—
226C4—1721no—
227C4#1306329311yescharacteristic
228C4#1306330711yescharacteristic
229C4#1306330811yescharacteristic
230C4#1306331111yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—3441no—
236C2#1458281411yescharacteristic
subgroupG/H
centerC4#13063311
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#416C2
socleC2×C43#394
hypercenter#416D43
hypocenterC43#2053
LCSG ▷ C22×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. #14582925C2semidirect
3. #14582896C2semidirect
4. #14582873C2semidirect
5. #14582872C2semidirect
6. #14582655C2semidirect
7. C43×#416C2semidirect
122. #416D43semidirect
126. C43#2053semidirect