Finite Group Databasebeta

← #25009676

Subgroups — #25009676

Order 11008.

342 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135945C211yesmaximal, characteristic
2#19133568C212yesmaximal
3#19132625C212yesmaximal
4#19132539C211yesmaximal, characteristic
5C43×#2844C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7#14583055—22no—
8#14582939—21no—
9#14582668C2211yescharacteristic
10#14582659—21no—
11#14582635—22no—
12#14582625C2212yes—
13C43×#400—21no—
14C43×#400—22no—
15C43×#395—22no—
16C43×#395C2212yes—
17C43×#382—21no—
18C43×#382C2211yescharacteristic
19C2×#10621885—42no—
20C2×#10621877—21no—
21#13063324—41no—
22#13063316—41no—
23#13063304—22no—
24#13063284—21no—
25#13063258—41no—
26#13063256—41no—
27#13063249—42no—
28C22⋊(C43⋊C8)—22no—
29C22×Q8×C43D412yes—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43D411yescharacteristic
35C2×C4⋊C4×C43C2311yescharacteristic
36C2×C42×C43D411yescharacteristic
37#95×C43—22no—
38#95×C43—22no—
39#95×C43—21no—
40#95×C43—22no—
41#95×C43—22no—
42#95×C43D412yes—
43C2×Q8×C43—42no—
44C2×Q8×C43—82no—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43—22no—
48C22×C4×C43—22no—
49C22×C4×C43C2×D411yescharacteristic
50C22×C4×C43C2×D412yes—
51C2×Dic86—22no—
52C4⋊C4×C43—41no—
53C4⋊C4×C43—41no—
54C4⋊C4×C43—81no—
55C4⋊C4×C43—81no—
56C4⋊C4×C43—82no—
57C4⋊C4×C43—81no—
58C42×C43—21no—
59C42×C43Q1612yescomplemented
60C22⋊Dic43—41no—
61#10621885—84no—
62C4⋊Dic43—22no—
63C4⋊Dic43—21no—
64C4⋊Dic43—21no—
65Dic43⋊C4—42no—
66C4×Dic43—41no—
67#10621877—22no—
68#10621877—41no—
69C2×C43⋊C8—41no—
70C2×C43⋊C8—42no—
71C23×C43#12011yescharacteristic
72Q8×C43—44no—
73Q8×C43—82no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43—42no—
81C2×C4×C43—42no—
82C2×C4×C43—42no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43—41no—
88C2×C4×C43—42no—
89C2×C4×C43C2×Q1611yescharacteristic
90C2×C4×C43#13711yescharacteristic
91C2×Dic43—41no—
92C2×Dic43—41no—
93Dic86—82no—
94C43⋊C8—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—82no—
107C4×C43—82no—
108C4×C43—81no—
109Dic43—81no—
110Dic43—81no—
111#2844D4311yescharacteristic
112#2061—431no—
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#544—431no—
122#451—862no—
123#428—861no—
124#400—21no—
125#400—22no—
126#395—22no—
127#395C2×D4312yes—
128#382—21no—
129#382C2×D4311yescharacteristic
130#343—431no—
131#339—861no—
132#328—862no—
133#324—432no—
134C43#1226011yescharacteristic, complemented, Sylow
135C22×Q8C22⋊D4312yes—
136C2×Q16—1722no—
137C2×M16—861no—
138C4⋊Q8—1721no—
139#125—1721no—
140C22⋊Q8—862no—
141#117—861no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4C22⋊D4311yescharacteristic
147C2×C4⋊C4C22×D4311yescharacteristic
148C2×C42C22⋊D4311yescharacteristic
149#107—1721no—
150#106—1721no—
151#103—1722no—
152C22⋊C8—862no—
153#95—22no—
154#95—22no—
155#95—21no—
156#95—22no—
157#95—22no—
158#95C22⋊D4312yes—
159C2×Q8—42no—
160C2×Q8—82no—
161C2×Q8—862no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4C2×C22⋊D4311yescharacteristic
167C22×C4C2×C22⋊D4312yes—
168Q16—3444no—
169M16—862no—
170M16—1721no—
171C2×C8—1722no—
172C2×C8—1721no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—81no—
176C4⋊C4—81no—
177C4⋊C4—82no—
178C4⋊C4—81no—
179C4⋊C4—862no—
180C4⋊C4—861no—
181C4⋊C4—861no—
182C4⋊C4—1722no—
183C22⋊C4—1721no—
184C42—21no—
185C42—1721no—
186C42#1062188512yescomplemented
187C23#1306329411yescharacteristic
188Q8—44no—
189Q8—82no—
190Q8—3442no—
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—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—1721no—
207C2×C4—1721no—
208C2×C4C2×#1062188511yescharacteristic
209C2×C4#1306335611yescharacteristic
210C8—3442no—
211C8—1722no—
212C22—21no—
213C22—21no—
214C22#1458305511yescharacteristic
215C22#1458308211yescharacteristic
216C22#1458308611yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—82no—
222C4—82no—
223C4—81no—
224C4—3441no—
225C4—3441no—
226C2—21no—
227C2—21no—
228C2#1913356911yescharacteristic
229C2#1913659611yescharacteristic
230C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2844C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#2844D43
hypocenterC43#12260
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2844

Complements

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

NH ≅ G/Ntype
59. 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
#191359452
#191335682
#191326252
#191325392
C43×#28442
#1226043