Finite Group Databasebeta

← #19147509

Subgroups — #19147509

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#14583606C211yesmaximal, characteristic
3#14583306C212yesmaximal, complemented
4#14583302C211yesmaximal, characteristic, complemented
5#14583209C212yesmaximal, complemented
6#14583195C211yesmaximal, characteristic, complemented
7#14583177C212yesmaximal
8#14583026C211yesmaximal, characteristic, complemented
9#14582996C212yesmaximal
10C4×#10621883C211yesmaximal, characteristic
11C43×#476C211yesmaximal, characteristic
12C2×#10621883C2211yescharacteristic
13#13063325C2211yescharacteristic
14#13063324—21no—
15#13063324C2212yes—
16#13063323—22no—
17#13063316C2212yes—
18#13063304—21no—
19#13063302—22no—
20C4×Dic86C2211yescharacteristic
21C4×Dic86C2211yescharacteristic
22#13063290—21no—
23#13063290C2212yes—
24D4×Dic43C2212yes—
25C2×C4⋊Dic43—21no—
26#13063259C2212yes—
27#13063258C2212yes—
28#13063258C2212yes—
29#13063256C2211yescharacteristic
30Dic43⋊C8C2212yes—
31#13063250C2212yes—
32#13063248C2211yescharacteristic
33#13063246C2211yescharacteristic
34#13063235C2212yes—
35C4×C43⋊C8C2211yescharacteristic
36C4⋊Q8×C43C2211yescharacteristic
37C4×D4×C43C2211yescharacteristic
38#106×C43C2212yes—
39C4⋊C8×C43C2211yescharacteristic
40#102×C43C2212yes—
41C2×Q8×C43—21no—
42C2×D4×C43C2311yescharacteristic
43C22×C4×C43—21no—
44C22×Dic43—22no—
45C2×Dic86—21no—
46C2×Dic86—22no—
47C2×Dic86D411yescharacteristic
48C2×Dic86C2311yescharacteristic
49C2×C8×C43C2312yes—
50C4⋊C4×C43—21no—
51C4⋊C4×C43C2312yes—
52C4⋊C4×C43C2311yescharacteristic
53C22⋊C4×C43—21no—
54C42×C43C2311yescharacteristic
55C22⋊Dic43—22no—
56#10621883Q814yescomplemented
57C4⋊Dic43—21no—
58C4⋊Dic43—22no—
59C4⋊Dic43D411yescharacteristic
60C4⋊Dic43C2311yescharacteristic
61C4⋊Dic43C2312yes—
62Dic43⋊C4—21no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4D412yes—
67C4×Dic43—21no—
68C4×Dic43—22no—
69C4×Dic43C2312yes—
70C2×C43⋊C8C2311yescharacteristic
71C2×C43⋊C8C2311yescharacteristic
72C23×C43—21no—
73Q8×C43—81no—
74D4×C43—21no—
75D4×C43C2×Q812yes—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—42no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2411yescharacteristic
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—22no—
85C2×Dic43—82no—
86C2×Dic43C2×D412yes—
87C2×Dic43C2×D412yes—
88Dic86—22no—
89Dic86—21no—
90Dic86—82no—
91Dic86—81no—
92Dic86C2×Q812yes—
93C8×C43—22no—
94C43⋊C8—21no—
95C43⋊C8C2×Q812yes—
96C22×C43—22no—
97C22×C43—41no—
98C22×C43—41no—
99C22×C43C22×D411yescharacteristic
100C4×C43—21no—
101C4×C43—41no—
102C4×C43—42no—
103C4×C43#13712yes—
104C4×C43C22×Q811yescharacteristic
105C4×C432−1+411yescharacteristic
106Dic43—22no—
107Dic43—22no—
108Dic43—22no—
109Dic43—41no—
110Dic43—42no—
111#3385—431nomaximal, Sylow
112C2×C43—42no—
113C2×C43D4×Q811yescharacteristic
114C2×C43C2×#13711yescharacteristic
115C2×C43#57611yescharacteristic
116Q82—431no—
117#554—431no—
118#501—432no—
119#500—431no—
120#479—432no—
121#477—431no—
122#476D4311yescharacteristic
123#474—432no—
124#446—431no—
125#440—432no—
126C4×SD16—431no—
127C43#338511yescharacteristic, complemented, Sylow
128C2×SD16—431no—
129C4⋊Q8—432no—
130C4⋊Q8—431no—
131C4⋊Q8—861no—
132C4⋊Q8—862no—
133C4⋊Q8C2×D4311yescharacteristic
134#125—432no—
135C22⋊Q8—862no—
136C22⋊Q8—861no—
137C4×Q8—431no—
138C4×Q8—432no—
139C4×Q8—431no—
140C4×Q8—861no—
141C4×D4—432no—
142C4×D4C2×D4311yescharacteristic
143C2×C4⋊C4—861no—
144#107—432no—
145#107—432no—
146#107—432no—
147#106—431no—
148#106C2×D4312yes—
149C4⋊C8—432no—
150C4⋊C8C2×D4311yescharacteristic
151#103—432no—
152#103—431no—
153#102—431no—
154#102C2×D4312yes—
155#97—432no—
156C4×C8—431no—
157C2×Q8—21no—
158C2×Q8—431no—
159C2×Q8—431no—
160C2×Q8—862no—
161C2×Q8—861no—
162C2×D4C22×D4311yescharacteristic
163C22×C4—21no—
164C22×C4—862no—
165SD16—434no—
166C2×C8—431no—
167C2×C8—431no—
168C2×C8C22×D4312yes—
169C4⋊C4—21no—
170C4⋊C4—431no—
171C4⋊C4—432no—
172C4⋊C4—431no—
173C4⋊C4—432no—
174C4⋊C4—862no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—861no—
179C4⋊C4—861no—
180C4⋊C4C22×D4312yes—
181C4⋊C4C22×D4311yescharacteristic
182C22⋊C4—21no—
183C22⋊C4—862no—
184C42—432no—
185C42—862no—
186C42—861no—
187C42C22×D4311yescharacteristic
188C23—21no—
189Q8—81no—
190Q8—432no—
191Q8—862no—
192Q8—861no—
193Q8—3441no—
194Q8—3442no—
195D4—21no—
196D4Q8×D4312yes—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—432no—
201C2×C4—432no—
202C2×C4—861no—
203C2×C4—861no—
204C2×C4—862no—
205C2×C4—3442no—
206C2×C4D4×D4311yescharacteristic
207C2×C4D4×D4311yescharacteristic
208C2×C4C23×D4311yescharacteristic
209C8—22no—
210C8—432no—
211C8—861no—
212C22—22no—
213C22—41no—
214C22—41no—
215C22C2×D4×D4311yescharacteristic
216C4—21no—
217C4—41no—
218C4—42no—
219C4—862no—
220C4—862no—
221C4—862no—
222C4—1722no—
223C4—1721no—
224C4#1306335412yes—
225C4C2×Q8×D4311yescharacteristic
226C4#1306337211yescharacteristic
227C2—42no—
228C2#1458356211yescharacteristic
229C2C2×#1306335411yescharacteristic
230C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#476C2
socleC22×C43C22×D4
hypercenter#476D43
hypocenterC43#3385
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #14583629C2semidirect
3. #14583306C2semidirect
4. #14583302C2semidirect
5. #14583209C2semidirect
6. #14583195C2semidirect
8. #14583026C2semidirect
56. #10621883Q8semidirect
127. C43#3385semidirect