Finite Group Databasebeta

← #25009440

Subgroups — #25009440

Order 11008.

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

normal subgroups only

This group has 380 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#19135756C211yesmaximal, characteristic
2#19133568C212yesmaximal
3#19132625C212yesmaximal
4#19132529C211yesmaximal, characteristic
5C43×#2811C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7#14583055—22no—
8#14582908—21no—
9#14582668C2211yescharacteristic
10#14582659—21no—
11#14582635—22no—
12#14582625C2212yes—
13C43×#395—22no—
14C43×#395C2212yes—
15C43×#391—21no—
16C43×#391—21no—
17C43×#391—22no—
18C43×#391C2211yescharacteristic
19C2×#10621885—42no—
20C2×#10621877—21no—
21#13063324—41no—
22#13063316—41no—
23#13063304—22no—
24#13063284—21no—
25#13063249—42no—
26#13063249—41no—
27#13063249—41no—
28C22⋊(C43⋊C8)—22no—
29C22×Q8×C43—21no—
30C22×Q8×C43D411yescharacteristic
31C22×Q8×C43D412yes—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43C2311yescharacteristic
36C2×C42×C43—21no—
37C2×C42×C43D411yescharacteristic
38#95×C43—22no—
39#95×C43—22no—
40#95×C43—22no—
41#95×C43—22no—
42#95×C43D412yes—
43C2×Q8×C43—24no—
44C2×Q8×C43—21no—
45C2×Q8×C43—41no—
46C2×Q8×C43—41no—
47C2×Q8×C43—42no—
48C2×Q8×C43—82no—
49C2×Q8×C43—81no—
50C2×Q8×C43—81no—
51C2×Q8×C43Q1612yescomplemented
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D412yes—
58C2×Dic86—22no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—82no—
61C4⋊C4×C43—81no—
62C4⋊C4×C43—81no—
63C42×C43—41no—
64C42×C43—81no—
65C22⋊Dic43—41no—
66#10621885—84no—
67C4⋊Dic43—21no—
68C4⋊Dic43—21no—
69C4⋊Dic43—22no—
70Dic43⋊C4—42no—
71C4×Dic43—41no—
72#10621877—41no—
73#10621877—41no—
74C2×C43⋊C8—42no—
75C2×C43⋊C8—41no—
76C23×C43#12011yescharacteristic
77Q8×C43—42no—
78Q8×C43—44no—
79Q8×C43—81no—
80Q8×C43—84no—
81Q8×C43—82no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—22no—
85C2×C4×C43—24no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—41no—
89C2×C4×C43—42no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43—42no—
93C2×C4×C43—41no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43C2×Q1611yescharacteristic
99C2×C4×C43#13711yescharacteristic
100C2×Dic43—41no—
101C2×Dic43—41no—
102Dic86—82no—
103C43⋊C8—81no—
104C43⋊C8—82no—
105#12224—431nomaximal, Sylow
106C22×C43—21no—
107C22×C43—21no—
108C22×C43#45111yescharacteristic
109C22×C43#45511yescharacteristic
110C22×C43B(4,𝔽2)11yescharacteristic
111C4×C43—21no—
112C4×C43—21no—
113C4×C43—42no—
114C4×C43—44no—
115C4×C43—42no—
116C4×C43—42no—
117C4×C43—82no—
118Dic43—81no—
119Dic43—81no—
120#2811D4311yescharacteristic
121#2028—431no—
122#1605—432no—
123#1354—432no—
124#1319—431no—
125C2×C43—21no—
126C2×C43—21no—
127C2×C43#160211yescharacteristic
128C2×C43#219911yescharacteristic
129C2×C43#220511yescharacteristic
130#544—431no—
131#451—862no—
132#419—861no—
133#395—22no—
134#395C2×D4312yes—
135#391—21no—
136#391—21no—
137#391—22no—
138#391C2×D4311yescharacteristic
139#343—431no—
140#339—861no—
141#328—862no—
142#324—432no—
143C43#1222411yescharacteristic, complemented, Sylow
144C22×Q8—21no—
145C22×Q8C22⋊D4311yescharacteristic
146C22×Q8C22⋊D4312yes—
147C2×Q16—1722no—
148C2×M16—861no—
149C4⋊Q8—1721no—
150#125—1721no—
151C22⋊Q8—862no—
152#117—861no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4C22×D4311yescharacteristic
157C2×C42—21no—
158C2×C42C22⋊D4311yescharacteristic
159#103—1721no—
160#103—1721no—
161#103—1722no—
162C22⋊C8—862no—
163#95—22no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95C22⋊D4312yes—
168C2×Q8—24no—
169C2×Q8—21no—
170C2×Q8—41no—
171C2×Q8—42no—
172C2×Q8—41no—
173C2×Q8—82no—
174C2×Q8—81no—
175C2×Q8—81no—
176C2×Q8—862no—
177C2×Q8#1062188512yescomplemented
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C2×C22⋊D4311yescharacteristic
183C22×C4C2×C22⋊D4312yes—
184Q16—3444no—
185M16—1721no—
186M16—1721no—
187C2×C8—1722no—
188C2×C8—1721no—
189C4⋊C4—41no—
190C4⋊C4—82no—
191C4⋊C4—81no—
192C4⋊C4—81no—
193C4⋊C4—861no—
194C4⋊C4—861no—
195C4⋊C4—862no—
196C4⋊C4—1722no—
197C22⋊C4—1721no—
198C42—41no—
199C42—81no—
200C42—1721no—
201C23#1306329411yescharacteristic
202Q8—42no—
203Q8—44no—
204Q8—81no—
205Q8—84no—
206Q8—82no—
207Q8—3442no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—1721no—
225C2×C4—1721no—
226C2×C4C2×#1062188511yescharacteristic
227C2×C4#1306335611yescharacteristic
228C8—3441no—
229C8—3442no—
230C22—21no—
231C22—21no—
232C22#1458305511yescharacteristic
233C22#1458307711yescharacteristic
234C22#1458308611yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—44no—
239C4—42no—
240C4—42no—
241C4—82no—
242C4—3441no—
243C4—3441no—
244C2—21no—
245C2—21no—
246C2#1913355211yescharacteristic
247C2#1913659611yescharacteristic
248C2#1913662511yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2811C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#2811D43
hypocenterC43#12224
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2811

Complements

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

NH ≅ G/Ntype
51. C2×Q8×C43Q16semidirect
143. C43#12224semidirect
177. C2×Q8#10621885semidirect

Maximal subgroups

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

subgroupindex
#191357562
#191335682
#191326252
#191325292
C43×#28112
#1222443