Finite Group Databasebeta

← #19147408

Subgroups — #19147408

Order 5504.

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

normal subgroups only

This group has 350 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#14583634C211yesmaximal, characteristic
2#14583629C211yesmaximal, characteristic, complemented
3#14583260C212yesmaximal, complemented
4#14583247C211yesmaximal, characteristic
5#14583178C212yesmaximal, complemented
6#14583124C212yesmaximal, complemented
7#14583100C211yesmaximal, characteristic
8#14583026C211yesmaximal, characteristic, complemented
9#14582998C212yesmaximal, complemented
10C4×#10621885C211yesmaximal, characteristic, complemented
11C43×#477C211yesmaximal, characteristic, complemented
12C2×#10621885C2211yescharacteristic
13C2×#10621873C2212yes—
14#13063324—21no—
15#13063324C2212yes—
16#13063323—22no—
17#13063322C2211yescharacteristic
18#13063314C2212yes—
19#13063313—21no—
20#13063310—22no—
21C4×Dic86C2211yescharacteristic
22C4×Dic86C2211yescharacteristic
23#13063290—21no—
24#13063290C2212yes—
25C4×D172—21no—
26#13063287C2212yes—
27#13063258C2211yescharacteristic
28Dic43⋊C8C2212yes—
29#13063249C2211yescharacteristic
30#13063248C2211yescharacteristic
31#13063247C2212yes—
32#13063245C2212yes—
33#13063245C2212yes—
34#13063235C2212yes—
35C4×C43⋊C8C2211yescharacteristic
36C4⋊Q8×C43C2211yescharacteristic
37C4×Q8×C43C2211yescharacteristic
38#107×C43C2212yes—
39C4⋊C8×C43C2211yescharacteristic
40#103×C43C2212yes—
41C2×Q8×C43—21no—
42C2×Q8×C43C2311yescharacteristic
43C2×D172—21no—
44C2×D172—21no—
45C2×D172C2312yes—
46C2×C4×D43—22no—
47C2×Dic86—22no—
48C2×Dic86D411yescharacteristic
49C2×Dic86C2311yescharacteristic
50C2×C8×C43C2312yes—
51C4⋊C4×C43—21no—
52C4⋊C4×C43—21no—
53C4⋊C4×C43C2312yes—
54C4⋊C4×C43C2311yescharacteristic
55C42×C43—21no—
56C42×C43C2311yescharacteristic
57#10621885—22no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61C4⋊Dic43D411yescharacteristic
62C4⋊Dic43C2311yescharacteristic
63Dic43⋊C4—21no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4D412yes—
67C4×Dic43—21no—
68C4×Dic43—22no—
69C4×Dic43C2312yes—
70C2×C43⋊C8C2311yescharacteristic
71C2×C43⋊C8C2311yescharacteristic
72#10621873—24no—
73C22×D43—22no—
74Q8×C43—21no—
75Q8×C43—21no—
76Q8×C43—81no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2411yescharacteristic
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43C2×D412yes—
86C2×Dic43C2×D412yes—
87D172—22no—
88D172—22no—
89D172—42no—
90D172—81no—
91C4×D43—82no—
92Dic86—22no—
93Dic86—21no—
94Dic86—82no—
95Dic86#4112yes—
96C8×C43—22no—
97C43⋊C8—21no—
98C43⋊C8—21no—
99C22×C43C22×D411yescharacteristic
100C2×D43—42no—
101C2×D43—42no—
102C2×D43—42no—
103C4×C43—21no—
104C4×C43—41no—
105C4×C43—42no—
106C4×C43—41no—
107C4×C43#13712yes—
108C4×C43C2×#4111yescharacteristic
109C4×C432−1+411yescharacteristic
110Dic43—22no—
111Dic43—22no—
112Dic43—22no—
113Dic43—41no—
114#3375—431nomaximal, Sylow
115C2×C43#54811yescharacteristic
116C2×C43C2×#13711yescharacteristic
117C2×C43#57611yescharacteristic
118D43—82no—
119#559—431no—
120Q82—431no—
121#489—432no—
122#486—431no—
123#477D4311yescharacteristic, complemented
124#474—432no—
125#464—432no—
126#460—431no—
127#446—431no—
128#440—432no—
129C4×Q16—431no—
130C43#337511yescharacteristic, complemented, Sylow
131C2×Q16—431no—
132C2×SD16—432no—
133C4⋊Q8—432no—
134C4⋊Q8—861no—
135C4⋊Q8—862no—
136C4⋊Q8C2×D4311yescharacteristic
137#127—431no—
138#124—432no—
139#124—861no—
140#123—862no—
141C4×Q8—431no—
142C4×Q8—432no—
143C4×Q8—431no—
144C4×Q8—861no—
145C4×Q8C2×D4311yescharacteristic
146C4×D4—432no—
147C4×D4—861no—
148#107—431no—
149#107C2×D4312yes—
150C4⋊C8—432no—
151C4⋊C8C2×D4311yescharacteristic
152#103—431no—
153#103—431no—
154#103C2×D4312yes—
155#102—432no—
156#102—432no—
157#102—432no—
158#97—432no—
159C4×C8—431no—
160C2×Q8—21no—
161C2×Q8—431no—
162C2×Q8—431no—
163C2×Q8—862no—
164C2×Q8C22×D4311yescharacteristic
165C2×D4—432no—
166C2×D4—861no—
167C2×D4—861no—
168C22×C4—862no—
169Q16—862no—
170SD16—864no—
171C2×C8—431no—
172C2×C8—431no—
173C2×C8C22×D4312yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—431no—
177C4⋊C4—432no—
178C4⋊C4—431no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4—861no—
182C4⋊C4C22×D4312yes—
183C4⋊C4C22×D4311yescharacteristic
184C22⋊C4—862no—
185C22⋊C4—862no—
186C22⋊C4—862no—
187C42—21no—
188C42—432no—
189C42—862no—
190C42—861no—
191C42C22×D4311yescharacteristic
192C23—862no—
193Q8—21no—
194Q8—21no—
195Q8—81no—
196Q8—432no—
197Q8—862no—
198Q8—861no—
199Q8—3442no—
200D4—862no—
201D4—862no—
202D4—3441no—
203D4—1722no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—432no—
208C2×C4—432no—
209C2×C4—861no—
210C2×C4—861no—
211C2×C4—3442no—
212C2×C4D4×D4311yescharacteristic
213C2×C4D4×D4311yescharacteristic
214C2×C4C23×D4311yescharacteristic
215C8—22no—
216C8—861no—
217C8—861no—
218C22—1722no—
219C22—1722no—
220C22—1722no—
221C22C2×D4×D4311yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—42no—
226C4—862no—
227C4—862no—
228C4—862no—
229C4—1721no—
230C4#1306335712yes—
231C4#41×D4311yescharacteristic
232C4#1306337311yescharacteristic
233C2—3442no—
234C2#1458355911yescharacteristic
235C2C2×#1306335711yescharacteristic
236C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#477C2
socleC22×C43C22×D4
hypercenter#477D43
hypocenterC43#3375
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #14583629C2semidirect
3. #14583260C2semidirect
5. #14583178C2semidirect
6. #14583124C2semidirect
8. #14583026C2semidirect
9. #14582998C2semidirect
10. C4×#10621885C2semidirect
11. C43×#477C2semidirect
123. #477D43semidirect
130. C43#3375semidirect