Finite Group Databasebeta

← #19147485

Subgroups — #19147485

Order 5504.

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

normal subgroups only

This group has 324 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#14583628C211yesmaximal, characteristic
2#14583624C211yesmaximal, characteristic
3#14583302C211yesmaximal, characteristic
4#14583299C212yesmaximal
5#14583209C212yesmaximal
6#14583204C212yesmaximal
7#14583185C211yesmaximal, characteristic
8#14583023C211yesmaximal, characteristic
9C4×#10621885C211yesmaximal, characteristic
10#14582991C212yesmaximal
11C43×#475C211yesmaximal, characteristic
12C2×#10621885C2211yescharacteristic
13#13063325—21no—
14#13063325C2211yescharacteristic
15#13063323—21no—
16#13063316—22no—
17#13063316C2212yes—
18#13063316C2212yes—
19#13063315—22no—
20Q8×Dic43—21no—
21Q8×Dic43C2212yes—
22C4×Dic86—21no—
23C4×Dic86C2211yescharacteristic
24C4×Dic86C2211yescharacteristic
25#13063290C2212yes—
26#13063258C2211yescharacteristic
27#13063258C2212yes—
28#13063258C2212yes—
29#13063257C2212yes—
30Dic43⋊C8C2212yes—
31#13063250C2212yes—
32#13063249C2211yescharacteristic
33#13063248C2211yescharacteristic
34C4×C43⋊C8C2211yescharacteristic
35C8×Dic43C2212yes—
36C4⋊Q8×C43C2211yescharacteristic
37C4×Q8×C43C2211yescharacteristic
38#106×C43C2212yes—
39C4⋊C8×C43C2211yescharacteristic
40#103×C43C2212yes—
41C2×Q8×C43—21no—
42C2×Q8×C43C2311yescharacteristic
43C2×Dic86—21no—
44C2×Dic86D411yescharacteristic
45C2×Dic86C2311yescharacteristic
46C2×C8×C43C2312yes—
47C4⋊C4×C43—21no—
48C4⋊C4×C43—21no—
49C4⋊C4×C43C2312yes—
50C4⋊C4×C43C2311yescharacteristic
51C42×C43—21no—
52C42×C43C2311yescharacteristic
53#10621885Q814yescomplemented
54C4⋊Dic43—21no—
55C4⋊Dic43—22no—
56C4⋊Dic43—22no—
57C4⋊Dic43—22no—
58C4⋊Dic43D411yescharacteristic
59C4⋊Dic43C2311yescharacteristic
60C4⋊Dic43C2312yes—
61Dic43⋊C4—21no—
62Dic43⋊C4—22no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65Dic43⋊C4D412yes—
66C4×Dic43—21no—
67C4×Dic43—22no—
68C4×Dic43—22no—
69C4×Dic43C2312yes—
70C2×C43⋊C8C2311yescharacteristic
71C2×C43⋊C8C2311yescharacteristic
72Q8×C43—21no—
73Q8×C43—42no—
74Q8×C43C2×Q812yes—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2411yescharacteristic
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43—22no—
84C2×Dic43C2×D412yes—
85C2×Dic43C2×D412yes—
86Dic86—22no—
87Dic86—21no—
88Dic86—42no—
89Dic86C2×Q812yes—
90C8×C43—22no—
91C43⋊C8—21no—
92C43⋊C8C2×Q812yes—
93C22×C43C22×D411yescharacteristic
94C4×C43—22no—
95C4×C43—21no—
96C4×C43—42no—
97C4×C43—41no—
98C4×C43#13512yes—
99C4×C43C22×Q811yescharacteristic
100C4×C432−1+411yescharacteristic
101Dic43—22no—
102Dic43—22no—
103Dic43—22no—
104Dic43—42no—
105Dic43—41no—
106#3383—431nomaximal, Sylow
107C2×C43D4×Q811yescharacteristic
108C2×C43C2×#13511yescharacteristic
109C2×C43#57811yescharacteristic
110#557—431no—
111#557—431no—
112#500—431no—
113#499—432no—
114#479—432no—
115#479—432no—
116#475—431no—
117#475D4311yescharacteristic
118C8×Q8—431no—
119C4×Q16—431no—
120C4×Q16—432no—
121C43#338311yescharacteristic, complemented, Sylow
122C2×Q16—431no—
123C4⋊Q8—431no—
124C4⋊Q8—861no—
125C4⋊Q8—861no—
126C4⋊Q8C2×D4311yescharacteristic
127#125—432no—
128#125—432no—
129#125—862no—
130#125—862no—
131C4×Q8—431no—
132C4×Q8—432no—
133C4×Q8—432no—
134C4×Q8—431no—
135C4×Q8—861no—
136C4×Q8—861no—
137C4×Q8C2×D4311yescharacteristic
138#107—431no—
139#107—432no—
140#107—432no—
141#106—432no—
142#106C2×D4312yes—
143C4⋊C8—432no—
144C4⋊C8C2×D4311yescharacteristic
145#103—431no—
146#103—432no—
147#103—431no—
148#103C2×D4312yes—
149C4×C8—432no—
150C4×C8—431no—
151C2×Q8—21no—
152C2×Q8—431no—
153C2×Q8—431no—
154C2×Q8—861no—
155C2×Q8C22×D4311yescharacteristic
156Q16—434no—
157C2×C8—431no—
158C2×C8—431no—
159C2×C8C22×D4312yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—431no—
163C4⋊C4—432no—
164C4⋊C4—431no—
165C4⋊C4—432no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C4⋊C4—862no—
169C4⋊C4—862no—
170C4⋊C4—862no—
171C4⋊C4—862no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4C22×D4311yescharacteristic
175C4⋊C4C22×D4312yes—
176C42—21no—
177C42—432no—
178C42—862no—
179C42—862no—
180C42—861no—
181C42C22×D4311yescharacteristic
182Q8—21no—
183Q8—42no—
184Q8—432no—
185Q8—862no—
186Q8—861no—
187Q8—1722no—
188Q8Q8×D4312yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—432no—
193C2×C4—432no—
194C2×C4—861no—
195C2×C4—861no—
196C2×C4—862no—
197C2×C4D4×D4311yescharacteristic
198C2×C4D4×D4311yescharacteristic
199C2×C4C23×D4311yescharacteristic
200C8—22no—
201C8—432no—
202C8—861no—
203C22C2×D4×D4311yescharacteristic
204C4—22no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—862no—
209C4—862no—
210C4—862no—
211C4—1722no—
212C4—1721no—
213C4#1306334612yes—
214C4C2×Q8×D4311yescharacteristic
215C4#1306337211yescharacteristic
216C2#1458356211yescharacteristic
217C2C2×#1306334611yescharacteristic
218C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#475C2
socleC22×C43C22×D4
hypercenter#475D43
hypocenterC43#3383
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
53. #10621885Q8semidirect
121. C43#3383semidirect