Finite Group Databasebeta

← #19145658

Subgroups — #19145658

Order 5504.

388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583504C211yesmaximal, characteristic, complemented
2#14583475C211yesmaximal, characteristic, complemented
3#14583288C211yesmaximal, characteristic, complemented
4#14583272C211yesmaximal, characteristic, complemented
5#14583268C211yesmaximal, characteristic, complemented
6#14583254C211yesmaximal, characteristic, complemented
7#14583115C212yesmaximal, complemented
8#14583105C212yesmaximal, complemented
9#14583046C212yesmaximal, complemented
10#14583040C212yesmaximal, complemented
11C43×#433C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×Dic86C2211yescharacteristic
14C2×#10621873C2212yes—
15C2×#10621873C2212yes—
16C2×#10621873C2212yes—
17C2×D344C2212yes—
18#13063325C2211yescharacteristic
19#13063325C2211yescharacteristic
20#13063322C2211yescharacteristic
21#13063317C2211yescharacteristic
22#13063313C2211yescharacteristic
23#13063313C2211yescharacteristic
24#13063310—22no—
25#13063309—22no—
26#13063305—22no—
27#13063299C2212yes—
28#13063298—22no—
29C4×D172C2212yes—
30#13063250C2212yes—
31#13063250C2212yes—
32#13063250C2212yes—
33#13063247C2212yes—
34#117×C43C2211yescharacteristic
35C4⋊C8×C43C2212yes—
36C22⋊C8×C43C2212yes—
37#97×C43C2211yescharacteristic
38C4×C8×C43C2211yescharacteristic
39C22×C4×C43C2311yescharacteristic
40C2×C22⋊D43—21no—
41C2×C22⋊D43—22no—
42C22×Dic43—21no—
43#10621898—42no—
44C2×D172—22no—
45C2×D172C2311yescharacteristic
46C2×D172C2312yes—
47C2×C4×D43—21no—
48C2×C4×D43—22no—
49C2×Dic86—21no—
50C2×Dic86—42no—
51C2×Dic86C2311yescharacteristic
52C2×Dic86C2311yescharacteristic
53C2×Dic86C2311yescharacteristic
54C2×C8×C43C2312yes—
55C2×C8×C43C2312yes—
56C4⋊C4×C43D412yes—
57C22⋊C4×C43D412yes—
58C42×C43C2311yescharacteristic
59C42×C43C2311yescharacteristic
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—22no—
63(C2×D43)⋊C4—22no—
64C4⋊Dic43—22no—
65C4⋊Dic43—22no—
66C4⋊Dic43C2312yes—
67Dic43⋊C4—22no—
68D344—42no—
69#10621873—42no—
70#10621873—42no—
71#10621873—42no—
72C23×C43C2×D411yescharacteristic
73C22×D43—21no—
74C22×D43—22no—
75C2×C4×C43—22no—
76C2×C4×C43C2×D412yes—
77C2×C4×C43C2×D412yes—
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2411yescharacteristic
80C22⋊D43—42no—
81C22⋊D43—82no—
82C2×Dic43—22no—
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—42no—
87D172—22no—
88D172—22no—
89D172—22no—
90D172—82no—
91C4×D43—42no—
92C4×D43—82no—
93Dic86—22no—
94Dic86—22no—
95Dic86—22no—
96Dic86—42no—
97C8×C43—22no—
98C8×C43—22no—
99C22×C43—21no—
100C22×C43—22no—
101C22×C43C22×D411yescharacteristic
102C2×D43—41no—
103C2×D43—42no—
104C2×D43—42no—
105C2×D43—42no—
106C2×D43—42no—
107C4×C43—21no—
108C4×C43—22no—
109C4×C43—22no—
110C4×C43H(5,𝔽2)12yes—
111Dic43—41no—
112Dic43—41no—
113Dic43—41no—
114Dic43—42no—
115#3221—431nomaximal, Sylow
116C2×C43—41no—
117C2×C43#53511yescharacteristic
118C2×C43#57712yes—
119D43—81no—
120D43—82no—
121#540—431no—
122#536—431no—
123#496—431no—
124#492—431no—
125#491—431no—
126#488—431no—
127#463—432no—
128#461—432no—
129#449—432no—
130#448—432no—
131#433D4311yescharacteristic, complemented
132C43#322111yescharacteristic, complemented, Sylow
133C2×#41—431no—
134C22×Q8—431no—
135C2×SD16—432no—
136C2×SD16—432no—
137C2×SD16—432no—
138C2×D8—432no—
139C4⋊Q8—431no—
140C4⋊Q8—431no—
141#127—431no—
142#125—431no—
143#124—431no—
144#124—431no—
145#123—862no—
146#123—862no—
147C22⋊Q8—862no—
148#121—432no—
149#121—862no—
150C4×D4—432no—
151#117C2×D4311yescharacteristic
152C4⋊C8C2×D4312yes—
153#103—432no—
154#103—432no—
155#103—432no—
156#102—432no—
157C22⋊C8C2×D4312yes—
158#97C2×D4311yescharacteristic
159C4×C8C2×D4311yescharacteristic
160#41—1722no—
161C2×Q8—431no—
162C2×Q8—431no—
163C2×Q8—431no—
164C2×Q8—861no—
165C2×Q8—1722no—
166C2×D4—431no—
167C2×D4—432no—
168C2×D4—862no—
169C2×D4—861no—
170C2×D4—862no—
171C22×C4—861no—
172C22×C4—862no—
173C22×C4—861no—
174C22×C4C22×D4311yescharacteristic
175SD16—1722no—
176SD16—1722no—
177SD16—1722no—
178D8—1722no—
179C2×C8C22×D4312yes—
180C2×C8C22×D4312yes—
181C4⋊C4—432no—
182C4⋊C4—862no—
183C4⋊C4—862no—
184C4⋊C4—862no—
185C4⋊C4D17212yes—
186C22⋊C4—862no—
187C22⋊C4—862no—
188C22⋊C4—862no—
189C22⋊C4—862no—
190C22⋊C4D17212yes—
191C42C22×D4311yescharacteristic
192C42C22×D4311yescharacteristic
193C23—861no—
194C23—862no—
195C23C2×D17211yescharacteristic
196Q8—862no—
197Q8—862no—
198Q8—862no—
199Q8—1722no—
200D4—862no—
201D4—862no—
202D4—862no—
203D4—3442no—
204D4—3442no—
205D4—1722no—
206C2×C4—22no—
207C2×C4—862no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—861no—
211C2×C4—3442no—
212C2×C4—1722no—
213C2×C4—1722no—
214C2×C4C2×D17212yes—
215C2×C4C2×D17212yes—
216C2×C4C2×D17211yescharacteristic
217C2×C4C23×D4311yescharacteristic
218C8—22no—
219C8—22no—
220C22—22no—
221C22—21no—
222C22—1722no—
223C22—1722no—
224C22—1722no—
225C22—1721no—
226C22—1722no—
227C22C22×D17211yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—1722no—
232C4—1721no—
233C4—1721no—
234C4—1721no—
235C4#1306337112yes—
236C2—41no—
237C2—3442no—
238C2—3441no—
239C2#1458346811yescharacteristic
240C2#1458371112yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#433C2
socleC22×C43C22×D4
hypercenter#433D43
hypocenterC43#3221
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14583504C2semidirect
2. #14583475C2semidirect
3. #14583288C2semidirect
4. #14583272C2semidirect
5. #14583268C2semidirect
6. #14583254C2semidirect
7. #14583115C2semidirect
8. #14583105C2semidirect
9. #14583046C2semidirect
10. #14583040C2semidirect
11. C43×#433C2semidirect
131. #433D43semidirect
132. C43#3221semidirect