Finite Group Databasebeta

← #19145827

Subgroups — #19145827

Order 5504.

362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#13063325C211yesmaximal, characteristic, complemented
2#14583433C211yesmaximal, characteristic
3#14583308C212yesmaximal, complemented
4#14583259C212yesmaximal, complemented
5#14583235C212yesmaximal, complemented
6#14583218C212yesmaximal
7#14583185C212yesmaximal, complemented
8#14583180C212yesmaximal, complemented
9C43×#432C211yesmaximal, characteristic, complemented
10C22×Dic86—21no—
11#13063325—21no—
12#13063325—21no—
13#13063325C2212yes—
14#13063325C2212yes—
15#13063319—21no—
16#13063317C2211yescharacteristic
17#13063313C2211yescharacteristic
18#13063308—21no—
19#13063304C2211yescharacteristic
20#13063299C2211yescharacteristic
21C4×Dic86C2211yescharacteristic
22C4×D172C2211yescharacteristic
23C4×C22⋊D43—21no—
24#13063282—21no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43C2212yes—
27#13063259C2214yes—
28#13063257C2214yes—
29#13063250C2214yes—
30#13063247C2214yes—
31C2×C42×C43C2211yescharacteristic
32C4⋊C8×C43C2212yes—
33C22⋊C8×C43C2212yes—
34#97×C43C2212yes—
35C22×C4×C43D411yescharacteristic
36C22×C4×C43D411yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—21no—
39C22×Dic43—22no—
40C2×D172C2311yescharacteristic
41C2×C4×D43—21no—
42C2×Dic86—22no—
43C2×Dic86—22no—
44C2×Dic86—44no—
45C2×Dic86C2311yescharacteristic
46C2×C8×C43C2314yes—
47C42×C43D411yescharacteristic
48C42×C43D411yescharacteristic
49C42×C43C2311yescharacteristic
50C42×C43C2311yescharacteristic
51C22⋊Dic43—21no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—21no—
56C4⋊Dic43—22no—
57C4⋊Dic43—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43C2314yes—
60C4⋊Dic43C2311yescharacteristic
61C4⋊Dic43C2311yescharacteristic
62Dic43⋊C4—21no—
63Dic43⋊C4—21no—
64Dic43⋊C4—21no—
65Dic43⋊C4—21no—
66C4×Dic43—21no—
67C23×C43C2×D411yescharacteristic
68C22×D43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2411yescharacteristic
78C22⋊D43—42no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—24no—
83C2×Dic43—44no—
84D172—22no—
85C4×D43—42no—
86Dic86—22no—
87Dic86—44no—
88Dic86—44no—
89C8×C43—24no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43#13712yes—
93C22×C43C22×D411yescharacteristic
94C2×D43—41no—
95C2×D43—41no—
96C2×D43—41no—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—21no—
101C4×C43AGL(1,ℤ/8)12yes—
102C4×C432−1+412yes—
103Dic43—41no—
104Dic43—44no—
105Dic43—41no—
106Dic43—41no—
107#3239—431nomaximal, Sylow
108C2×C43—22no—
109C2×C43#53611yescharacteristic
110C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C43C2×#13711yescharacteristic
112D43—81no—
113C2×C4⋊Q8—431no—
114#529—431no—
115#501—432no—
116#489—432no—
117#484—432no—
118#481—432no—
119#475—432no—
120#474—432no—
121#432D4311yescharacteristic, complemented
122C43#323911yescharacteristic, complemented, Sylow
123C22×Q8—861no—
124C4⋊Q8—432no—
125C4⋊Q8—432no—
126C4⋊Q8—861no—
127C4⋊Q8—861no—
128#126—861no—
129#125—431no—
130#124—431no—
131#123—861no—
132C22⋊Q8—431no—
133#121—431no—
134C4×Q8—431no—
135C4×D4—431no—
136C4×D4—861no—
137#117—861no—
138C2×C4⋊C4—432no—
139C2×C4⋊C4—861no—
140C2×C42C2×D4311yescharacteristic
141#107—434no—
142#106—434no—
143C4⋊C8C2×D4312yes—
144#103—434no—
145#102—434no—
146C22⋊C8C2×D4312yes—
147#97C2×D4312yes—
148C2×Q8—431no—
149C2×Q8—862no—
150C2×Q8—862no—
151C2×Q8—1724no—
152C2×D4—431no—
153C2×D4—861no—
154C22×C4—862no—
155C22×C4—861no—
156C22×C4D17211yescharacteristic
157C22×C4D17211yescharacteristic
158C22×C4C22×D4311yescharacteristic
159C2×C8C22×D4314yes—
160C4⋊C4—434no—
161C4⋊C4—431no—
162C4⋊C4—431no—
163C4⋊C4—862no—
164C4⋊C4—862no—
165C4⋊C4—862no—
166C4⋊C4—861no—
167C4⋊C4—861no—
168C4⋊C4—861no—
169C4⋊C4—861no—
170C22⋊C4—861no—
171C22⋊C4—861no—
172C22⋊C4—861no—
173C22⋊C4—861no—
174C22⋊C4—861no—
175C42—861no—
176C42D17211yescharacteristic
177C42D17211yescharacteristic
178C42C22×D4311yescharacteristic
179C42C22×D4311yescharacteristic
180C23—861no—
181C23C2×D17211yescharacteristic
182Q8—862no—
183Q8—1724no—
184Q8—1724no—
185D4—862no—
186D4—1722no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—861no—
193C2×C4—864no—
194C2×C4—1724no—
195C2×C4—1722no—
196C2×C4C2×D17211yescharacteristic
197C2×C4C2×D17211yescharacteristic
198C2×C4C2×D17211yescharacteristic
199C2×C4C2×D17211yescharacteristic
200C2×C4C2×D17211yescharacteristic
201C2×C4C23×D4311yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—1721no—
206C22—1721no—
207C22—1721no—
208C22#1306335812yes—
209C22C22×D17211yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—1724no—
215C4—1721no—
216C4—1721no—
217C4—1721no—
218C4#1306335312yes—
219C4#1306337212yes—
220C2—22no—
221C2—3441no—
222C2#1458347511yescharacteristic
223C2C2×#1306335311yescharacteristic
224C2C2×#1306335811yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#432C2
socleC22×C43C22×D4
hypercenter#432D43
hypocenterC43#3239
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. C2×#13063325C2semidirect
3. #14583308C2semidirect
4. #14583259C2semidirect
5. #14583235C2semidirect
7. #14583185C2semidirect
8. #14583180C2semidirect
9. C43×#432C2semidirect
121. #432D43semidirect
122. C43#3239semidirect