Finite Group Databasebeta

← #19147510

Subgroups — #19147510

Order 5504.

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

normal subgroups only

This group has 340 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
1#14583629C211yesmaximal, characteristic, complemented
2#14583610C211yesmaximal, characteristic
3#14583307C212yesmaximal, complemented
4#14583205C212yesmaximal, complemented
5#14583191C211yesmaximal, characteristic, complemented
6#14583186C211yesmaximal, characteristic
7#14583178C212yesmaximal
8#14583029C211yesmaximal, characteristic, complemented
9#14582998C212yesmaximal
10C4×#10621873C211yesmaximal, characteristic
11C43×#500C211yesmaximal, characteristic, complemented
12C2×#10621873C2211yescharacteristic
13#13063324—21no—
14#13063324C2212yes—
15#13063323—22no—
16#13063316C2212yes—
17#13063305—21no—
18#13063301—22no—
19C4×Dic86C2211yescharacteristic
20C4×Dic86C2211yescharacteristic
21#13063290—21no—
22#13063290C2212yes—
23C4×D172C2211yescharacteristic
24#13063287C2212yes—
25C4⋊C4×D43—21no—
26#13063258C2212yes—
27#13063257C2211yescharacteristic
28#13063256C2212yes—
29C4⋊(C43⋊C8)C2211yescharacteristic
30Dic43⋊C8C2212yes—
31#13063250C2211yescharacteristic
32#13063248C2212yes—
33#13063247C2211yescharacteristic
34#13063245C2212yes—
35#13063235C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37C4⋊Q8×C43C2211yescharacteristic
38#107×C43C2212yes—
39#107×C43C2212yes—
40C4×C8×C43C2211yescharacteristic
41C2×Q8×C43—21no—
42C2×Q8×C43—21no—
43C2×D172C2311yescharacteristic
44C2×C4×D43—21no—
45C2×C4×D43—22no—
46C2×Dic86—22no—
47C2×Dic86D411yescharacteristic
48C2×Dic86C2311yescharacteristic
49C2×C8×C43C2311yescharacteristic
50C2×C8×C43C2311yescharacteristic
51C4⋊C4×C43—21no—
52C4⋊C4×C43—21no—
53C4⋊C4×C43C2312yes—
54C4⋊C4×C43C2312yes—
55C42×C43C2311yescharacteristic
56(C2×D43)⋊C4—21no—
57(C2×D43)⋊C4—22no—
58C4⋊Dic43—22no—
59C4⋊Dic43D411yescharacteristic
60C4⋊Dic43C2311yescharacteristic
61C4⋊Dic43C2311yescharacteristic
62Dic43⋊C4—21no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4D412yes—
67C4×Dic43—21no—
68C4×Dic43—22no—
69C4×Dic43C2312yes—
70C2×C43⋊C8C2312yes—
71#10621873Q814yescomplemented
72C22×D43—21no—
73Q8×C43—81no—
74Q8×C43—81no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2411yescharacteristic
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43C2×D412yes—
84C2×Dic43C2×D412yes—
85D172—21no—
86D172C2×Q812yes—
87C4×D43—42no—
88C4×D43—82no—
89Dic86—22no—
90Dic86—21no—
91Dic86—82no—
92Dic86C2×Q812yes—
93C8×C43—21no—
94C8×C43C2×Q812yes—
95C43⋊C8—22no—
96C22×C43C22×D411yescharacteristic
97C2×D43—22no—
98C2×D43—41no—
99C2×D43—41no—
100C4×C43—21no—
101C4×C43—42no—
102C4×C43—42no—
103C4×C43#13712yes—
104C4×C43C22×Q811yescharacteristic
105C4×C432−1+411yescharacteristic
106Dic43—22no—
107Dic43—22no—
108Dic43—22no—
109Dic43—41no—
110Dic43—41no—
111#3385—431nomaximal, Sylow
112C2×C43D4×Q811yescharacteristic
113C2×C43C2×#13711yescharacteristic
114C2×C43#57611yescharacteristic
115D43—42no—
116Q82—431no—
117#554—431no—
118#501—432no—
119#500D4311yescharacteristic, complemented
120#479—432no—
121#477—431no—
122#476—431no—
123#474—432no—
124#446—431no—
125#440—432no—
126C4×SD16—431no—
127C43#338511yescharacteristic, complemented, Sylow
128C2×SD16—431no—
129C4⋊Q8—432no—
130C4⋊Q8—861no—
131C4⋊Q8—862no—
132C4⋊Q8C2×D4311yescharacteristic
133C4⋊Q8C2×D4311yescharacteristic
134#125—432no—
135C22⋊Q8—861no—
136C22⋊Q8—862no—
137C4×Q8—431no—
138C4×Q8—432no—
139C4×Q8—431no—
140C4×Q8—861no—
141C4×D4—432no—
142C4×D4—431no—
143C2×C4⋊C4—861no—
144#107—432no—
145#107C2×D4312yes—
146#107C2×D4312yes—
147#106—431no—
148#106—432no—
149C4⋊C8—432no—
150C4⋊C8—431no—
151#103—431no—
152#103—432no—
153#102—431no—
154#102—432no—
155#97—432no—
156C4×C8C2×D4311yescharacteristic
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—431no—
160C2×Q8—431no—
161C2×Q8—862no—
162C2×D4—431no—
163C22×C4—862no—
164C22×C4—861no—
165SD16—434no—
166C2×C8—432no—
167C2×C8C22×D4311yescharacteristic
168C2×C8C22×D4311yescharacteristic
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—
181C4⋊C4C22×D4312yes—
182C22⋊C4—862no—
183C22⋊C4—861no—
184C42—432no—
185C42—862no—
186C42—861no—
187C42C22×D4311yescharacteristic
188C23—861no—
189Q8—81no—
190Q8—81no—
191Q8—432no—
192Q8—862no—
193Q8—861no—
194Q8—3442no—
195D4—432no—
196D4—861no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—432no—
200C2×C4—432no—
201C2×C4—861no—
202C2×C4—861no—
203C2×C4—861no—
204C2×C4—3442no—
205C2×C4—1722no—
206C2×C4D4×D4311yescharacteristic
207C2×C4D4×D4311yescharacteristic
208C2×C4C23×D4311yescharacteristic
209C8—21no—
210C8—862no—
211C8Q8×D4312yes—
212C22—862no—
213C22—1721no—
214C22—1721no—
215C22C2×D4×D4311yescharacteristic
216C4—21no—
217C4—42no—
218C4—42no—
219C4—862no—
220C4—862no—
221C4—862no—
222C4—1721no—
223C4—1721no—
224C4#1306335712yes—
225C4C2×Q8×D4311yescharacteristic
226C4#1306337311yescharacteristic
227C2—1722no—
228C2#1458356411yescharacteristic
229C2C2×#1306335711yescharacteristic
230C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#500C2
socleC22×C43C22×D4
hypercenter#500D43
hypocenterC43#3385
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #14583629C2semidirect
3. #14583307C2semidirect
4. #14583205C2semidirect
5. #14583191C2semidirect
8. #14583029C2semidirect
11. C43×#500C2semidirect
71. #10621873Q8semidirect
119. #500D43semidirect
127. C43#3385semidirect