Finite Group Databasebeta

← #19147647

Subgroups — #19147647

Order 5504.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#14583635C211yesmaximal, characteristic
2#14583627C211yesmaximal, characteristic, complemented
3#14583290C212yesmaximal, complemented
4#14583271C211yesmaximal, characteristic
5#14583120C212yesmaximal, complemented
6#14583110C211yesmaximal, characteristic, complemented
7#14583102C212yesmaximal, complemented
8#14583026C211yesmaximal, characteristic, complemented
9#14582996C212yesmaximal, complemented
10C4×#10621885C211yesmaximal, characteristic, complemented
11C43×#460C211yesmaximal, characteristic
12C2×Dic172C2212yes—
13C2×#10621885C2211yescharacteristic
14C2×#10621883C2212yes—
15C2×#10621883C2212yes—
16#13063325C2211yescharacteristic
17#13063323C2212yes—
18#13063317—21no—
19#13063315—22no—
20#13063312—21no—
21#13063312C2212yes—
22#13063306—22no—
23C4×Dic86—21no—
24C4×Dic86C2211yescharacteristic
25C4×Dic86C2211yescharacteristic
26#13063290C2212yes—
27D4×Dic43—21no—
28D4×Dic43C2212yes—
29#13063258C2211yescharacteristic
30Dic43⋊C8C2212yes—
31#13063250C2212yes—
32#13063249C2211yescharacteristic
33#13063248C2211yescharacteristic
34#13063235C2212yes—
35C4×C43⋊C8C2211yescharacteristic
36C2×SD16×C43C2212yes—
37#127×C43C2211yescharacteristic
38C4×Q8×C43C2211yescharacteristic
39C4⋊C8×C43C2211yescharacteristic
40#102×C43C2212yes—
41C2×Q8×C43C2311yescharacteristic
42C2×D4×C43—21no—
43C2×D4×C43—21no—
44C2×D4×C43C2312yes—
45C22×Dic43—22no—
46C2×Dic86D411yescharacteristic
47C2×Dic86C2311yescharacteristic
48C2×Dic86C2312yes—
49SD16×C43—42no—
50C2×C8×C43C2312yes—
51C4⋊C4×C43—21no—
52C4⋊C4×C43C2311yescharacteristic
53C42×C43—21no—
54C42×C43C2311yescharacteristic
55C22⋊Dic43—22no—
56C22⋊Dic43—22no—
57C22⋊Dic43—22no—
58#10621885—22no—
59#10621883—24no—
60#10621883—42no—
61C4⋊Dic43—21no—
62C4⋊Dic43—21no—
63C4⋊Dic43D411yescharacteristic
64C4⋊Dic43C2311yescharacteristic
65Dic43⋊C4—21no—
66Dic43⋊C4—22no—
67Dic43⋊C4—22no—
68Dic43⋊C4—22no—
69Dic43⋊C4D412yes—
70C4×Dic43—21no—
71C4×Dic43—22no—
72C4×Dic43C2312yes—
73C2×C43⋊C8C2311yescharacteristic
74C2×C43⋊C8C2311yescharacteristic
75Dic172—42no—
76C23×C43—22no—
77Q8×C43—21no—
78Q8×C43—21no—
79D4×C43—22no—
80D4×C43—22no—
81D4×C43—42no—
82D4×C43—81no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43C2×D411yescharacteristic
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2411yescharacteristic
88C2×Dic43—22no—
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43—82no—
92C2×Dic43C2×D412yes—
93C2×Dic43C2×D412yes—
94Dic86—22no—
95Dic86—22no—
96Dic86—21no—
97Dic86—21no—
98Dic86—22no—
99C8×C43—22no—
100C43⋊C8—21no—
101C43⋊C8#4112yes—
102C22×C43—42no—
103C22×C43—42no—
104C22×C43—42no—
105C22×C43C22×D411yescharacteristic
106C4×C43—21no—
107C4×C43—41no—
108C4×C43—41no—
109C4×C43#13712yes—
110C4×C43C2×#4111yescharacteristic
111C4×C43H(5,𝔽2)11yescharacteristic
112Dic43—22no—
113Dic43—22no—
114Dic43—42no—
115Dic43—41no—
116Dic43—41no—
117#3400—431nomaximal, Sylow
118C2×C43—82no—
119C2×C43#55011yescharacteristic
120C2×C43C2×#13711yescharacteristic
121C2×C43#57711yescharacteristic
122#559—431no—
123#557—431no—
124#497—432no—
125#492—431no—
126#464—432no—
127#462—431no—
128#461—432no—
129#460D4311yescharacteristic
130#446—431no—
131#440—432no—
132C4×Q16—431no—
133C43#340011yescharacteristic, complemented, Sylow
134C2×Q16—431no—
135C2×Q16—432no—
136C2×SD16—432no—
137C2×SD16—432no—
138C2×SD16C2×D4312yes—
139C4⋊Q8—432no—
140C4⋊Q8—431no—
141#127C2×D4311yescharacteristic
142#125—861no—
143#125—862no—
144#124—432no—
145#124—861no—
146#123—862no—
147C4×Q8—431no—
148C4×Q8—432no—
149C4×Q8—431no—
150C4×Q8—861no—
151C4×Q8C2×D4311yescharacteristic
152C4×D4—432no—
153C4×D4—861no—
154#107—431no—
155C4⋊C8—432no—
156C4⋊C8C2×D4311yescharacteristic
157#103—431no—
158#103—432no—
159#103—431no—
160#102C2×D4312yes—
161#97—432no—
162C4×C8—431no—
163C2×Q8—431no—
164C2×Q8—431no—
165C2×Q8—432no—
166C2×Q8C22×D4311yescharacteristic
167C2×D4—21no—
168C2×D4—21no—
169C2×D4C22×D4312yes—
170C22×C4—862no—
171Q16—862no—
172Q16—1722no—
173SD16—42no—
174SD16—864no—
175SD16—1722no—
176C2×C8—431no—
177C2×C8—431no—
178C2×C8C22×D4312yes—
179C4⋊C4—21no—
180C4⋊C4—431no—
181C4⋊C4—432no—
182C4⋊C4—431no—
183C4⋊C4—862no—
184C4⋊C4—862no—
185C4⋊C4—862no—
186C4⋊C4—861no—
187C4⋊C4—861no—
188C4⋊C4—861no—
189C4⋊C4C22×D4311yescharacteristic
190C22⋊C4—862no—
191C22⋊C4—862no—
192C22⋊C4—862no—
193C42—21no—
194C42—432no—
195C42—862no—
196C42—861no—
197C42C22×D4311yescharacteristic
198C23—22no—
199Q8—21no—
200Q8—21no—
201Q8—862no—
202Q8—862no—
203Q8—861no—
204Q8—862no—
205Q8—861no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—81no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—432no—
213C2×C4—432no—
214C2×C4—861no—
215C2×C4—861no—
216C2×C4—862no—
217C2×C4—3442no—
218C2×C4D4×D4311yescharacteristic
219C2×C4D4×D4311yescharacteristic
220C2×C4C23×D4311yescharacteristic
221C8—22no—
222C8—432no—
223C8—861no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22C2×D4×D4311yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—862no—
232C4—862no—
233C4—1721no—
234C4—1722no—
235C4—1721no—
236C4#1306335412yes—
237C4#41×D4311yescharacteristic
238C4#1306337011yescharacteristic
239C2—82no—
240C2#1458356711yescharacteristic
241C2C2×#1306335411yescharacteristic
242C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#460C2
socleC22×C43C22×D4
hypercenter#460D43
hypocenterC43#3400
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #14583627C2semidirect
3. #14583290C2semidirect
5. #14583120C2semidirect
6. #14583110C2semidirect
7. #14583102C2semidirect
8. #14583026C2semidirect
9. #14582996C2semidirect
10. C4×#10621885C2semidirect
133. C43#3400semidirect