Finite Group Databasebeta

← #19139806

Subgroups — #19139806

Order 5504.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×#13063324C211yesmaximal, characteristic
2C2×#13063290C211yesmaximal, characteristic
3#14582839C211yesmaximal, characteristic
4#14582838C211yesmaximal, characteristic
5#14582837C211yesmaximal, characteristic
6#14582803C212yesmaximal
7#14582803C212yesmaximal
8#14582803C212yesmaximal
9#14582763C212yesmaximal
10#14582750C211yesmaximal, characteristic
11C43×#400C211yesmaximal, characteristic
12C22×Dic86C2212yes—
13C22×Dic86C2211yescharacteristic
14#13063324—24no—
15#13063290—24no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×C4×Dic43C2211yescharacteristic
22C2×C4×Dic43C2211yescharacteristic
23C2×C4×Dic43C2212yes—
24C2×C4×Dic43C2211yescharacteristic
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34#95×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C22×C4×C43C2312yes—
38C22×C4×C43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×Dic43C2312yes—
43C22×Dic43C2311yescharacteristic
44C22×Dic43C2312yes—
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×Dic86—22no—
49C2×Dic86—22no—
50C2×Dic86—24no—
51C2×Dic86—28no—
52C2×Dic86Q814yescomplemented
53C4⋊C4×C43—22no—
54C4⋊C4×C43—22no—
55C4⋊Dic43—22no—
56Dic43⋊C4—22no—
57Dic43⋊C4—22no—
58Dic43⋊C4—24no—
59Dic43⋊C4—24no—
60C4×Dic43—22no—
61C4×Dic43—22no—
62C4×Dic43—24no—
63C4×Dic43D414yes—
64C23×C43C2411yescharacteristic
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—22no—
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—24no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43C2×D412yes—
76C2×C4×C43C2×Q812yes—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—24no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43C2×D412yes—
87C2×Dic43C2×D412yes—
88C2×Dic43C2×Q812yes—
89C2×Dic43C2×Q812yes—
90C2×Dic43#4112yes—
91C2×Dic43#4114yes—
92Dic86—28no—
93Dic86—48no—
94C22×C43C22×D411yescharacteristic
95C22×C43C22×Q811yescharacteristic
96C22×C43C2×#4111yescharacteristic
97C22×C43C2×#4112yes—
98C22×C432−1+412yes—
99C4×C43—22no—
100C4×C43—22no—
101C4×C43—42no—
102C4×C43—41no—
103C4×C43—42no—
104Dic43—22no—
105Dic43—42no—
106Dic43—41no—
107Dic43—42no—
108Dic43C22⋊Q814yes—
109Dic43#12414yes—
110#2568—431nomaximal, Sylow
111C2×C43C2×C22⋊Q811yescharacteristic
112C2×C43C2×#12411yescharacteristic
113C2×C43#53611yescharacteristic
114C2×C43#55612yes—
115C2×C43#55712yes—
116C2×C4⋊Q8—431no—
117C2×C4×Q8—431no—
118#400—431no—
119#400—431no—
120#400—431no—
121#400D4311yescharacteristic
122#391—432no—
123#391—432no—
124#391—432no—
125#382—432no—
126C4×C4⋊C4—431no—
127C43#256811yescharacteristic, complemented, Sylow
128C22×Q8—431no—
129C22×Q8—432no—
130C4⋊Q8—864no—
131C4×Q8—864no—
132C2×C4⋊C4—431no—
133C2×C4⋊C4—431no—
134C2×C4⋊C4—432no—
135C2×C4⋊C4—431no—
136C2×C4⋊C4—432no—
137C2×C4⋊C4C2×D4311yescharacteristic
138C2×C4⋊C4C2×D4311yescharacteristic
139C2×C42—431no—
140C2×C42—431no—
141C2×C42—431no—
142C2×C42—432no—
143#95—431no—
144#95—432no—
145#95—432no—
146#95—432no—
147#95—432no—
148#95—432no—
149#95—432no—
150#95C2×D4311yescharacteristic
151#95C2×D4312yes—
152#95C2×D4312yes—
153C2×Q8—434no—
154C2×Q8—862no—
155C2×Q8—862no—
156C2×Q8—864no—
157C2×Q8—868no—
158C22×C4—431no—
159C22×C4—431no—
160C22×C4—431no—
161C22×C4—432no—
162C22×C4—431no—
163C22×C4—432no—
164C22×C4C22×D4312yes—
165C22×C4C22×D4311yescharacteristic
166C22×C4C22×D4312yes—
167C22×C4C22×D4311yescharacteristic
168C22×C4C22×D4311yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—862no—
172C4⋊C4—864no—
173C4⋊C4—864no—
174C4⋊C4—862no—
175C4⋊C4—862no—
176C42—434no—
177C42—862no—
178C42—862no—
179C42—864no—
180C23C23×D4311yescharacteristic
181Q8—868no—
182Q8—1728no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—432no—
194C2×C4—432no—
195C2×C4—432no—
196C2×C4—432no—
197C2×C4—434no—
198C2×C4—432no—
199C2×C4—861no—
200C2×C4—861no—
201C2×C4—861no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4—862no—
205C2×C4—864no—
206C2×C4—862no—
207C2×C4—862no—
208C2×C4D4×D4312yes—
209C2×C4Q8×D4312yes—
210C22C2×D4×D4311yescharacteristic
211C22C2×Q8×D4311yescharacteristic
212C22#41×D4311yescharacteristic
213C22#41×D4312yes—
214C22#1306337212yes—
215C4—22no—
216C4—22no—
217C4—42no—
218C4—42no—
219C4—41no—
220C4—434no—
221C4—434no—
222C4—862no—
223C4—1722no—
224C4—1722no—
225C4—1721no—
226C2C22⋊Q8×D4311yescharacteristic
227C2#124×D4311yescharacteristic
228C2#1458347111yescharacteristic
229C2#1458361612yes—
230C2#1458362612yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2568
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
52. C2×Dic86Q8semidirect
127. C43#2568semidirect