Finite Group Databasebeta

← #19147285

Subgroups — #19147285

Order 5504.

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

normal subgroups only

This group has 336 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#14583624C211yesmaximal, characteristic, complemented
2#14583623C211yesmaximal, characteristic
3#14583255C212yesmaximal
4#14583204C212yesmaximal, complemented
5#14583176C211yesmaximal, characteristic
6#14583124C212yesmaximal
7#14583106C211yesmaximal, characteristic, complemented
8C8×Dic86C211yesmaximal, characteristic, complemented
9#14582991C212yesmaximal, complemented
10C4×#10621873C211yesmaximal, characteristic
11C43×#487C211yesmaximal, characteristic, complemented
12C2×#10621885C2212yes—
13C2×#10621873C2211yescharacteristic
14#13063323—21no—
15#13063320—22no—
16#13063316C2212yes—
17#13063315—22no—
18#13063314C2212yes—
19#13063305—21no—
20Q8×Dic43—21no—
21Q8×Dic43C2212yes—
22C4×Dic86C2211yescharacteristic
23C4×Dic86C2211yescharacteristic
24#13063290C2212yes—
25C4×D172C2211yescharacteristic
26#13063283—21no—
27#13063258C2212yes—
28#13063257C2211yescharacteristic
29C4⋊(C43⋊C8)C2211yescharacteristic
30Dic43⋊C8C2212yes—
31#13063250C2211yescharacteristic
32#13063249C2212yes—
33#13063247C2211yescharacteristic
34#13063245C2212yes—
35C8×Dic43C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37C4⋊Q8×C43C2211yescharacteristic
38#103×C43C2212yes—
39#103×C43C2212yes—
40C4×C8×C43C2211yescharacteristic
41C2×Q8×C43—21no—
42C2×Q8×C43C2312yes—
43C2×D172C2311yescharacteristic
44C2×C4×D43—21no—
45C2×Dic86D411yescharacteristic
46C2×Dic86C2311yescharacteristic
47C2×C8×C43C2311yescharacteristic
48C2×C8×C43C2311yescharacteristic
49C4⋊C4×C43—21no—
50C4⋊C4×C43—21no—
51C4⋊C4×C43—21no—
52C4⋊C4×C43C2312yes—
53C42×C43C2311yescharacteristic
54#10621885—24no—
55(C2×D43)⋊C4—21no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43—22no—
60C4⋊Dic43D411yescharacteristic
61C4⋊Dic43C2311yescharacteristic
62C4⋊Dic43C2311yescharacteristic
63Dic43⋊C4—21no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4D412yes—
67C4×Dic43—21no—
68C4×Dic43—22no—
69C4×Dic43—22no—
70C4×Dic43C2312yes—
71C2×C43⋊C8C2312yes—
72#10621873—22no—
73C22×D43—21no—
74Q8×C43—22no—
75Q8×C43—22no—
76Q8×C43—42no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2411yescharacteristic
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43C2×D412yes—
86C2×Dic43C2×D412yes—
87D172—21no—
88D172—21no—
89C4×D43—42no—
90Dic86—22no—
91Dic86—21no—
92Dic86#4112yes—
93C8×C43—21no—
94C8×C43—21no—
95C43⋊C8—22no—
96C22×C43C22×D411yescharacteristic
97C2×D43—41no—
98C2×D43—41no—
99C2×D43—41no—
100C4×C43—21no—
101C4×C43—42no—
102C4×C43—42no—
103C4×C43#13512yes—
104C4×C43C2×#4111yescharacteristic
105C4×C432−1+411yescharacteristic
106Dic43—22no—
107Dic43—22no—
108Dic43—22no—
109Dic43—41no—
110Dic43—41no—
111#3364—431nomaximal, Sylow
112C2×C43#54811yescharacteristic
113C2×C43C2×#13511yescharacteristic
114C2×C43#57811yescharacteristic
115D43—81no—
116#557—431no—
117#556—431no—
118#488—432no—
119#487D4311yescharacteristic, complemented
120#479—432no—
121#474—431no—
122#464—432no—
123#462—431no—
124C8×Q8—431no—
125C4×Q16—432no—
126C4×SD16—431no—
127C43#336411yescharacteristic, complemented, Sylow
128C2×Q16—432no—
129C2×SD16—431no—
130C4⋊Q8—861no—
131C4⋊Q8C2×D4311yescharacteristic
132C4⋊Q8C2×D4311yescharacteristic
133#126—862no—
134#125—432no—
135#125—862no—
136#124—432no—
137C22⋊Q8—861no—
138C4×Q8—431no—
139C4×Q8—432no—
140C4×Q8—432no—
141C4×Q8—431no—
142C4×Q8—861no—
143C4×D4—431no—
144#117—861no—
145#107—432no—
146#106—431no—
147C4⋊C8—432no—
148C4⋊C8—431no—
149#103—432no—
150#103—431no—
151#103C2×D4312yes—
152#103C2×D4312yes—
153#102—431no—
154#102—432no—
155C4×C8—432no—
156C4×C8C2×D4311yescharacteristic
157C2×Q8—21no—
158C2×Q8—431no—
159C2×Q8—431no—
160C2×Q8C22×D4312yes—
161C2×D4—431no—
162C22×C4—861no—
163Q16—864no—
164SD16—862no—
165C2×C8—432no—
166C2×C8C22×D4311yescharacteristic
167C2×C8C22×D4311yescharacteristic
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—431no—
172C4⋊C4—432no—
173C4⋊C4—431no—
174C4⋊C4—431no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—861no—
180C4⋊C4C22×D4312yes—
181C22⋊C4—862no—
182C22⋊C4—862no—
183C22⋊C4—861no—
184C42—432no—
185C42—862no—
186C42—862no—
187C42—861no—
188C42C22×D4311yescharacteristic
189C23—861no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—432no—
194Q8—862no—
195Q8—861no—
196D4—861no—
197D4—861no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—432no—
201C2×C4—432no—
202C2×C4—861no—
203C2×C4—861no—
204C2×C4—861no—
205C2×C4—1722no—
206C2×C4D4×D4311yescharacteristic
207C2×C4D4×D4311yescharacteristic
208C2×C4C23×D4311yescharacteristic
209C8—21no—
210C8—21no—
211C8—862no—
212C22—1721no—
213C22—1721no—
214C22—1721no—
215C22C2×D4×D4311yescharacteristic
216C4—21no—
217C4—42no—
218C4—42no—
219C4—862no—
220C4—862no—
221C4—862no—
222C4—1721no—
223C4—1721no—
224C4#1306334612yes—
225C4#41×D4311yescharacteristic
226C4#1306337211yescharacteristic
227C2—3441no—
228C2#1458355711yescharacteristic
229C2C2×#1306334611yescharacteristic
230C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#487C2
socleC22×C43C22×D4
hypercenter#487D43
hypocenterC43#3364
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #14583624C2semidirect
4. #14583204C2semidirect
7. #14583106C2semidirect
8. C8×Dic86C2semidirect
9. #14582991C2semidirect
11. C43×#487C2semidirect
119. #487D43semidirect
127. C43#3364semidirect