Finite Group Databasebeta

← #25009683

Subgroups — #25009683

Order 11008.

330 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 59 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#19142867C211yesmaximal, characteristic
2#19135945C211yesmaximal, characteristic
3#19133639C212yesmaximal
4#19132623C212yesmaximal
5C43×#1324C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7#14583235—22no—
8#14582939—21no—
9#14582841—22no—
10#14582838C2212yes—
11#14582820—22no—
12#14582819—21no—
13#14582765—21no—
14#14582668C2211yescharacteristic
15#14582659—21no—
16#14582637—22no—
17C43×#382C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86—21no—
20C2×#10621877—21no—
21#13063324—41no—
22#13063316—41no—
23#13063304—22no—
24#13063284—21no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43D412yes—
28C2×Dic43⋊C4—22no—
29#13063259—42no—
30#13063258—41no—
31#13063256—41no—
32#13063250—42no—
33C43⋊#95—21no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95D412yes—
38C2×C4⋊C4×C43D411yescharacteristic
39C2×C4⋊C4×C43C2311yescharacteristic
40C2×C42×C43D411yescharacteristic
41C22⋊C8×C43—22no—
42#95×C43—22no—
43C22×C4×C43—21no—
44C22×C4×C43—21no—
45C22×C4×C43C2×D411yescharacteristic
46C22×C4×C43C2×D412yes—
47C22×Dic43—22no—
48C22×Dic43—22no—
49C2×Dic86—22no—
50C2×Dic86—82no—
51C2×Dic86—81no—
52C2×C8×C43—42no—
53C4⋊C4×C43—41no—
54C4⋊C4×C43—41no—
55C42×C43—21no—
56C42×C43Q1612yes—
57C22⋊Dic43—41no—
58C4⋊Dic43—21no—
59C4⋊Dic43—21no—
60C4⋊Dic43—22no—
61C4⋊Dic43—42no—
62C4⋊Dic43—81no—
63C4⋊Dic43—81no—
64Dic43⋊C4—42no—
65Dic43⋊C4—82no—
66C4×Dic43—41no—
67#10621877—22no—
68#10621877—41no—
69C2×C43⋊C8—41no—
70C23×C43#12011yescharacteristic
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43—42no—
78C2×C4×C43—42no—
79C2×C4×C43—41no—
80C2×C4×C43C2×Q1611yescharacteristic
81C2×C4×C43#13711yescharacteristic
82C2×Dic43—42no—
83C2×Dic43—42no—
84C2×Dic43—42no—
85C2×Dic43—42no—
86C2×Dic43—42no—
87C2×Dic43—41no—
88C2×Dic43—41no—
89C2×Dic43—42no—
90Dic86—84no—
91Dic86—82no—
92C8×C43—82no—
93C43⋊C8—42no—
94#12261—431nomaximal, Sylow
95C22×C43—21no—
96C22×C43—21no—
97C22×C43#45111yescharacteristic
98C22×C43#45611yescharacteristic
99C22×C43B(4,𝔽2)11yescharacteristic
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—42no—
103C4×C43—42no—
104C4×C43—81no—
105Dic43—82no—
106Dic43—81no—
107Dic43—82no—
108Dic43—81no—
109#2844—431no—
110#2061—431no—
111#1617—432no—
112#1353—432no—
113#1324D4311yescharacteristic
114C2×C43—21no—
115C2×C43—21no—
116C2×C43#160511yescharacteristic
117C2×C43#220111yescharacteristic
118C2×C43#220211yescharacteristic
119#544—431no—
120#484—862no—
121#428—861no—
122#400—432no—
123#400—862no—
124#395—862no—
125#395—861no—
126#382—861no—
127#382C2×D4311yescharacteristic
128#343—431no—
129#339—861no—
130#328—862no—
131#324C2×D4312yes—
132C43#1226111yescharacteristic, complemented, Sylow
133C22×Q8—861no—
134C2×M16—861no—
135C4⋊Q8—1721no—
136#125—1721no—
137C22⋊Q8—862no—
138#117—861no—
139C2×C4⋊C4—432no—
140C2×C4⋊C4—862no—
141C2×C4⋊C4—861no—
142C2×C4⋊C4—861no—
143C2×C4⋊C4D17211yescharacteristic
144C2×C4⋊C4C22×D4311yescharacteristic
145C2×C42D17211yescharacteristic
146#107—1721no—
147#107—1722no—
148#106—1721no—
149#103—1722no—
150C22⋊C8—22no—
151#95—22no—
152#95—432no—
153#95—862no—
154#95—861no—
155#95—862no—
156#95—862no—
157C2×Q8—862no—
158C2×Q8—3442no—
159C2×Q8—3441no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—862no—
163C22×C4—862no—
164C22×C4C2×D17211yescharacteristic
165C22×C4D4×D4312yes—
166M16—862no—
167M16—1721no—
168C2×C8—42no—
169C2×C8—1721no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4—862no—
175C4⋊C4—3442no—
176C4⋊C4—3441no—
177C4⋊C4—3441no—
178C4⋊C4—1722no—
179C4⋊C4—1722no—
180C22⋊C4—1721no—
181C42—21no—
182C42—1721no—
183C42Dic17212yes—
184C23#1306329511yescharacteristic
185Q8—3442no—
186Q8—3444no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—1722no—
197C2×C4—1722no—
198C2×C4—1722no—
199C2×C4—1722no—
200C2×C4—1722no—
201C2×C4—1721no—
202C2×C4—1721no—
203C2×C4—1722no—
204C2×C4C2×Dic17211yescharacteristic
205C2×C4#1306335811yescharacteristic
206C8—82no—
207C8—1722no—
208C22—21no—
209C22—21no—
210C22#1458305711yescharacteristic
211C22#1458308411yescharacteristic
212C22#1458308711yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—81no—
218C4—3442no—
219C4—3441no—
220C4—3442no—
221C4—3441no—
222C2—21no—
223C2—21no—
224C2#1913357111yescharacteristic
225C2#1913661011yescharacteristic
226C2#1913661311yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1324C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1324D43
hypocenterC43#12261
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
132. C43#12261semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191428672
#191359452
#191336392
#191326232
C43×#13242
#1226143