Finite Group Databasebeta

← #25009345

Subgroups — #25009345

Order 11008.

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

normal subgroups only

This group has 388 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#19142632C211yesmaximal, characteristic
2#19135762C211yesmaximal, characteristic
3#19133588C212yesmaximal
4#19132596C212yesmaximal
5C43×#1317C211yesmaximal, characteristic
6#14583525C2211yescharacteristic
7C2×#13063304—21no—
8#14583230—22no—
9#14582839—22no—
10#14582824—21no—
11#14582824C2212yes—
12#14582820—22no—
13#14582762—21no—
14#14582666C2211yescharacteristic
15#14582665—21no—
16#14582637—22no—
17C43×#381C2211yescharacteristic
18C43×#323C2212yes—
19C22×Dic86—21no—
20#13063304—22no—
21#13063304—42no—
22#13063304—42no—
23#13063302—42no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43D412yes—
27C2×Dic43⋊C4—22no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—21no—
31#13063257—42no—
32#13063250—42no—
33C43⋊#95—22no—
34C43⋊#95—21no—
35C43⋊#95—22no—
36C43⋊#95—42no—
37C43⋊#95D412yes—
38C23×C4×C43D411yescharacteristic
39C2×C22⋊C4×C43D411yescharacteristic
40C2×C22⋊C4×C43C2311yescharacteristic
41C22⋊C8×C43—22no—
42#95×C43—22no—
43C24×C43C2×D411yescharacteristic
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43—41no—
48C22×C4×C43—41no—
49C22×C4×C43SD1612yes—
50C22×C4×C43C2×D412yes—
51C22×Dic43—22no—
52C22×Dic43—22no—
53C22×Dic43—22no—
54C22×Dic43—41no—
55C2×Dic86—22no—
56C2×Dic86—42no—
57C2×Dic86—81no—
58C2×Dic86—81no—
59C2×C8×C43—42no—
60C22⋊C4×C43—41no—
61C22⋊C4×C43—41no—
62C22⋊Dic43—41no—
63C22⋊Dic43—41no—
64C22⋊Dic43—41no—
65C22⋊Dic43—42no—
66C22⋊Dic43—42no—
67C22⋊Dic43—41no—
68C4⋊Dic43—22no—
69C4⋊Dic43—42no—
70C4⋊Dic43—42no—
71C4⋊Dic43—81no—
72Dic43⋊C4—44no—
73Dic43⋊C4—42no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43—42no—
77C23×C43#12011yescharacteristic
78C23×C43C2×SD1611yescharacteristic
79C23×C43AGL(1,ℤ/8)11yescharacteristic
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—41no—
83C2×C4×C43—41no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43—41no—
88C2×C4×C43—81no—
89C2×Dic43—44no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95C2×Dic43—82no—
96C2×Dic43—81no—
97C2×Dic43—82no—
98Dic86—84no—
99Dic86—82no—
100C8×C43—82no—
101#12207—431nomaximal, Sylow
102C22×C43—22no—
103C22×C43—21no—
104C22×C43—21no—
105C22×C43—41no—
106C22×C43—41no—
107C22×C43—42no—
108C22×C43—81no—
109C22×C43#45011yescharacteristic
110C22×C43#45511yescharacteristic
111C22×C43B(4,𝔽2)11yescharacteristic
112C4×C43—42no—
113C4×C43—42no—
114C4×C43—81no—
115Dic43—82no—
116Dic43—82no—
117Dic43—82no—
118Dic43—161no—
119#2817—431no—
120#2030—431no—
121#1608—432no—
122#1344—432no—
123#1317D4311yescharacteristic
124C2×C43—21no—
125C2×C43—21no—
126C2×C43—41no—
127C2×C43—41no—
128C2×C43#160111yescharacteristic
129C2×C43#220112yes—
130#543—431no—
131C2×C22⋊Q8—861no—
132#483—862no—
133#400—862no—
134#397—432no—
135#397—861no—
136#395—862no—
137#381—861no—
138#381C2×D4311yescharacteristic
139#342—431no—
140#342—861no—
141#328—862no—
142#323C2×D4312yes—
143C43#1220711yescharacteristic, complemented, Sylow
144C22×Q8—861no—
145C23×C4D17211yescharacteristic
146C22⋊Q8—862no—
147C22⋊Q8—1722no—
148C22⋊Q8—1722no—
149C22⋊Q8—1722no—
150C2×C4⋊C4—432no—
151C2×C4⋊C4—861no—
152C2×C4⋊C4—862no—
153C2×C4⋊C4—861no—
154C2×C22⋊C4—862no—
155C2×C22⋊C4—861no—
156C2×C22⋊C4—861no—
157C2×C22⋊C4D17211yescharacteristic
158C2×C22⋊C4C22×D4311yescharacteristic
159#106—1722no—
160#103—1722no—
161C22⋊C8—22no—
162#95—22no—
163#95—432no—
164#95—862no—
165#95—861no—
166#95—862no—
167#95—1722no—
168C24C2×D17211yescharacteristic
169C2×Q8—862no—
170C2×Q8—3441no—
171C2×Q8—3441no—
172C2×Q8—1722no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—862no—
179C22×C4—862no—
180C22×C4—862no—
181C22×C4—1721no—
182C22×C4#1062187312yes—
183C22×C4D4×D4312yes—
184C2×C8—42no—
185C4⋊C4—862no—
186C4⋊C4—3441no—
187C4⋊C4—1722no—
188C4⋊C4—1724no—
189C4⋊C4—1722no—
190C4⋊C4—1722no—
191C22⋊C4—41no—
192C22⋊C4—41no—
193C22⋊C4—1721no—
194C22⋊C4—1721no—
195C22⋊C4—1721no—
196C22⋊C4—1721no—
197C22⋊C4—1722no—
198C22⋊C4—1722no—
199C23—21no—
200C23—21no—
201C23—42no—
202C23#1306329511yescharacteristic
203C23C2×#1062187311yescharacteristic
204C23#1306335311yescharacteristic
205Q8—3442no—
206Q8—3444no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—81no—
216C2×C4—3442no—
217C2×C4—3441no—
218C2×C4—3442no—
219C2×C4—1724no—
220C2×C4—1722no—
221C2×C4—1722no—
222C2×C4—1722no—
223C2×C4—1722no—
224C2×C4—1722no—
225C8—82no—
226C22—22no—
227C22—21no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—81no—
233C22#1458305211yescharacteristic
234C22#1458307911yescharacteristic
235C22#1458308711yescharacteristic
236C4—42no—
237C4—42no—
238C4—81no—
239C4—3442no—
240C4—3442no—
241C4—3442no—
242C4—6881no—
243C2—21no—
244C2—21no—
245C2—41no—
246C2—41no—
247C2#1913354911yescharacteristic
248C2#1913660912yes—
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1317C2
socleC22×C43B(4,𝔽2)
prime radicalC24×C43C2×D4
hypercenter#1317D43
hypocenterC43#12207
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
143. C43#12207semidirect

Maximal subgroups

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

subgroupindex
#191426322
#191357622
#191335882
#191325962
C43×#13172
#1220743