Finite Group Databasebeta

← #25009675

Subgroups — #25009675

Order 11008.

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

normal subgroups only

This group has 342 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#19133569C212yesmaximal
3#19132624C212yesmaximal
4#19132539C211yesmaximal, characteristic
5C43×#2061C211yesmaximal, characteristic
6#14583054—22no—
7#14582841—22no—
8#14582838—21no—
9#14582820—22no—
10#14582819C2212yes—
11#14582765—21no—
12#14582636—22no—
13#14582625C2212yes—
14C43×#544C2211yescharacteristic
15C43×#428—21no—
16C43×#382C2211yescharacteristic
17C43×#343C2211yescharacteristic
18C43×#339—21no—
19C22×Dic86D412yes—
20C2×#10621885—42no—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—21no—
24C2×Dic43⋊C4—22no—
25#13063248—42no—
26C22⋊(C43⋊C8)—22no—
27C43⋊#95—22no—
28C43⋊#95—22no—
29C43⋊#95—21no—
30C43⋊#95—22no—
31C43⋊#95D412yes—
32C2×M16×C43—21no—
33C4⋊Q8×C43—41no—
34#125×C43—41no—
35C22⋊Q8×C43—22no—
36#117×C43—21no—
37C2×C4⋊C4×C43D411yescharacteristic
38C2×C4⋊C4×C43C2311yescharacteristic
39C2×C42×C43D411yescharacteristic
40#107×C43—41no—
41#106×C43—41no—
42#95×C43—22no—
43C2×Q8×C43—22no—
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43C2×D412yes—
47C22×C4×C43C2×D411yescharacteristic
48C22×Dic43—22no—
49C22×Dic43—22no—
50C2×Dic86—42no—
51C2×Dic86—82no—
52M16×C43—22no—
53M16×C43—41no—
54C2×C8×C43—41no—
55C4⋊C4×C43—21no—
56C4⋊C4×C43—21no—
57C4⋊C4×C43—22no—
58C4⋊C4×C43—41no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—42no—
61C22⋊C4×C43—41no—
62C42×C43—21no—
63C42×C43—41no—
64C42×C43Q1612yescomplemented
65#10621885—84no—
66C4⋊Dic43—81no—
67C4⋊Dic43—81no—
68C4⋊Dic43—81no—
69Dic43⋊C4—82no—
70C2×C43⋊C8—42no—
71C23×C43#12011yescharacteristic
72Q8×C43—82no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43—42no—
80C2×C4×C43—42no—
81C2×C4×C43—41no—
82C2×C4×C43—41no—
83C2×C4×C43—41no—
84C2×C4×C43C2×Q1611yescharacteristic
85C2×C4×C43#13711yescharacteristic
86C2×Dic43—42no—
87C2×Dic43—42no—
88C2×Dic43—42no—
89C2×Dic43—42no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92Dic86—44no—
93Dic86—82no—
94C8×C43—42no—
95C43⋊C8—82no—
96#12260—431nomaximal, Sylow
97C22×C43—21no—
98C22×C43—21no—
99C22×C43#45111yescharacteristic
100C22×C43#45611yescharacteristic
101C22×C43B(4,𝔽2)11yescharacteristic
102C4×C43—21no—
103C4×C43—21no—
104C4×C43—42no—
105C4×C43—42no—
106C4×C43—81no—
107C4×C43—81no—
108C4×C43—81no—
109Dic43—82no—
110Dic43—82no—
111#2844—431no—
112#2061D4311yescharacteristic
113#1605—432no—
114#1354—432no—
115#1324—431no—
116C2×C43—21no—
117C2×C43—21no—
118C2×C43#160511yescharacteristic
119C2×C43#219911yescharacteristic
120C2×C43#220311yescharacteristic
121#544C2×D4311yescharacteristic
122#451—862no—
123#428—21no—
124#400—862no—
125#400—861no—
126#395—432no—
127#395—862no—
128#382—861no—
129#382C2×D4311yescharacteristic
130#343C2×D4311yescharacteristic
131#339—21no—
132#328—862no—
133#324—432no—
134C43#1226011yescharacteristic, complemented, Sylow
135C22×Q8—432no—
136C2×Q16—1722no—
137C2×M16—21no—
138C4⋊Q8—41no—
139#125—41no—
140C22⋊Q8—22no—
141#117—21no—
142C2×C4⋊C4—861no—
143C2×C4⋊C4—861no—
144C2×C4⋊C4—861no—
145C2×C4⋊C4—862no—
146C2×C4⋊C4C22⋊D4311yescharacteristic
147C2×C4⋊C4C22×D4311yescharacteristic
148C2×C42C22⋊D4311yescharacteristic
149#107—41no—
150#106—41no—
151#103—1722no—
152C22⋊C8—862no—
153#95—22no—
154#95—432no—
155#95—862no—
156#95—862no—
157#95—861no—
158#95—862no—
159C2×Q8—22no—
160C2×Q8—3442no—
161C2×Q8—1722no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—862no—
165C22×C4—862no—
166C22×C4D4×D4312yes—
167C22×C4C2×C22⋊D4311yescharacteristic
168Q16—3444no—
169M16—22no—
170M16—41no—
171C2×C8—41no—
172C2×C8—1722no—
173C4⋊C4—22no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C4⋊C4—3442no—
180C4⋊C4—3441no—
181C4⋊C4—3441no—
182C4⋊C4—3441no—
183C22⋊C4—41no—
184C42—21no—
185C42—41no—
186C42#1062188512yescomplemented
187C23#1306329311yescharacteristic
188Q8—82no—
189Q8—3442no—
190Q8—1724no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—1722no—
203C2×C4—1722no—
204C2×C4—1722no—
205C2×C4—1722no—
206C2×C4—1722no—
207C2×C4—1722no—
208C2×C4C2×#1062188511yescharacteristic
209C2×C4#1306335511yescharacteristic
210C8—42no—
211C8—3442no—
212C22—21no—
213C22—21no—
214C22#1458305411yescharacteristic
215C22#1458308111yescharacteristic
216C22#1458308511yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—81no—
222C4—81no—
223C4—81no—
224C4—3442no—
225C4—3442no—
226C2—21no—
227C2—21no—
228C2#1913356811yescharacteristic
229C2#1913659511yescharacteristic
230C2#1913661511yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2061C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#2061D43
hypocenterC43#12260
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2061

Complements

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

NH ≅ G/Ntype
64. C42×C43Q16semidirect
134. C43#12260semidirect
186. C42#10621885semidirect

Maximal subgroups

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

subgroupindex
#191428672
#191335692
#191326242
#191325392
C43×#20612
#1226043