Finite Group Databasebeta

← #24985414

Subgroups — #24985414

Order 11008.

480 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 83 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#19142541C211yesmaximal, characteristic
2#19135737C212yesmaximal, complemented
3#19135677C211yesmaximal, characteristic
4#19132420C212yesmaximal, complemented
5C43×#1270C211yesmaximal, characteristic
6C22×#10621883—21no—
7C2×#13063325C2211yescharacteristic
8C2×#13063250—22no—
9C2×#13063248—21no—
10#14582838—21no—
11#14582811—22no—
12#14582805C2212yes—
13#14582779—21no—
14#14582774—22no—
15#14582662—22no—
16#14582654C2211yescharacteristic
17C43×#390C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86—21no—
20C22×Dic86D412yes—
21C23×Dic43—21no—
22C2×#10621883—42no—
23C2×#10621883—42no—
24C2×#10621883—42no—
25C22×C43⋊C8—21no—
26#13063325—42no—
27C2×C4⋊Dic43—22no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43D412yes—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—22no—
32#13063250—44no—
33#13063248—42no—
34C43⋊#95—21no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C22×D4×C43D411yescharacteristic
39C22×C8×C43—22no—
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C22⋊C4×C43—22no—
42C2×C42×C43C2311yescharacteristic
43C24×C43—21no—
44C2×D4×C43—21no—
45C2×D4×C43—41no—
46C2×D4×C43—41no—
47C2×D4×C43SD1612yes—
48C22×C4×C43—21no—
49C22×C4×C43C2×D411yescharacteristic
50C22×C4×C43C2×D412yes—
51C22×Dic43—22no—
52C22×Dic43—22no—
53C22×Dic43—41no—
54C22×Dic43—81no—
55C22×Dic43—82no—
56C2×Dic86—22no—
57C2×Dic86—22no—
58C2×Dic86—22no—
59C2×Dic86—42no—
60C2×Dic86—42no—
61C2×Dic86—41no—
62C2×Dic86—41no—
63C2×Dic86—41no—
64C2×Dic86—41no—
65C2×Dic86—41no—
66C2×C8×C43—42no—
67C2×C8×C43—42no—
68C2×C8×C43—42no—
69C4⋊C4×C43—41no—
70C22⋊C4×C43—42no—
71C22⋊C4×C43—42no—
72C42×C43—41no—
73C22⋊Dic43—82no—
74C22⋊Dic43—81no—
75#10621883—48no—
76C4⋊Dic43—24no—
77C4⋊Dic43—42no—
78C4⋊Dic43—42no—
79C4⋊Dic43—81no—
80C2×C43⋊C8—22no—
81C2×C43⋊C8—41no—
82C2×C43⋊C8—41no—
83C23×C43—22no—
84C23×C43—42no—
85C23×C43—41no—
86C23×C43—42no—
87C23×C43—41no—
88C23×C43#12011yescharacteristic
89D4×C43—42no—
90D4×C43—81no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—42no—
96C2×C4×C43—41no—
97C2×C4×C43C2×SD1611yescharacteristic
98C2×C4×C43#13512yes—
99C2×C4×C43#13712yes—
100C2×C4×C43#13711yescharacteristic
101C2×Dic43—42no—
102C2×Dic43—42no—
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—84no—
109C2×Dic43—81no—
110C2×Dic43—81no—
111Dic86—42no—
112Dic86—42no—
113Dic86—44no—
114Dic86—81no—
115Dic86—81no—
116Dic86—82no—
117C8×C43—82no—
118C43⋊C8—42no—
119#7755—431nomaximal, Sylow
120C22×C43—42no—
121C22×C43—44no—
122C22×C43—82no—
123C22×C43—81no—
124C22×C43—81no—
125C22×C43#44811yescharacteristic
126C22×C43#45212yes—
127C22×C43#45311yescharacteristic
128C22×C43#45512yes—
129C22×C43B(4,𝔽2)11yescharacteristic
130C4×C43—21no—
131C4×C43—21no—
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—81no—
135Dic43—82no—
136Dic43—82no—
137Dic43—82no—
138#2804—431no—
139#2024—432no—
140#2013—431no—
141#1272—432no—
142#1270D4311yescharacteristic
143C2×C43—82no—
144C2×C43#159611yescharacteristic
145C2×C43#160612yes—
146C2×C43#163011yescharacteristic
147C2×C43#164312yes—
148C2×C43#165911yescharacteristic
149C22×SD16—861no—
150C2×C4⋊Q8—431no—
151C2×#103—862no—
152C2×#103—861no—
153#400—861no—
154#393—862no—
155#391—432no—
156#390C2×D4311yescharacteristic
157#386—861no—
158#385—862no—
159#340—862no—
160#336—431no—
161#336C2×D4312yes—
162C43#775511yescharacteristic, complemented, Sylow
163C22×Q8—432no—
164C22×Q8—861no—
165C22×D4D17211yescharacteristic
166C23×C4—861no—
167C2×SD16—1722no—
168C2×SD16—1722no—
169C2×SD16—1722no—
170C22×C8—22no—
171C22×C8—861no—
172C4⋊Q8—1722no—
173C2×C4⋊C4—432no—
174C2×C4⋊C4—862no—
175C2×C4⋊C4—861no—
176C2×C4⋊C4D17211yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—862no—
179C2×C22⋊C4—861no—
180C2×C42C22×D4311yescharacteristic
181#103—1722no—
182#103—1724no—
183#95—862no—
184#95—861no—
185#95—862no—
186#95—862no—
187C24—21no—
188C2×Q8—862no—
189C2×Q8—862no—
190C2×Q8—862no—
191C2×Q8—1721no—
192C2×Q8—1721no—
193C2×Q8—1721no—
194C2×Q8—1722no—
195C2×Q8—1722no—
196C2×Q8—1721no—
197C2×Q8—1721no—
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4#1062187312yes—
202C22×C4—21no—
203C22×C4—862no—
204C22×C4—862no—
205C22×C4—3441no—
206C22×C4—3442no—
207C22×C4—1721no—
208C22×C4C2×D17211yescharacteristic
209C22×C4D4×D4312yes—
210SD16—1728no—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—862no—
215C2×C8—1721no—
216C2×C8—1721no—
217C4⋊C4—41no—
218C4⋊C4—864no—
219C4⋊C4—3441no—
220C4⋊C4—1722no—
221C4⋊C4—1722no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—3442no—
225C22⋊C4—3441no—
226C42—41no—
227C23—22no—
228C23—42no—
229C23—41no—
230C23—42no—
231C23—41no—
232C23#1306329511yescharacteristic
233Q8—3442no—
234Q8—3441no—
235Q8—3441no—
236Q8—1722no—
237Q8—1722no—
238Q8—1724no—
239D4—42no—
240D4—81no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—3444no—
248C2×C4—3441no—
249C2×C4—3441no—
250C2×C4—1722no—
251C2×C4—1722no—
252C2×C4—1722no—
253C2×C4—1722no—
254C2×C4—1722no—
255C2×C4—1722no—
256C2×C4—1722no—
257C2×C4C2×#1062187311yescharacteristic
258C2×C4#1306334412yes—
259C2×C4#1306335412yes—
260C2×C4#1306335811yescharacteristic
261C8—82no—
262C8—1722no—
263C22—42no—
264C22—44no—
265C22—81no—
266C22—82no—
267C22—81no—
268C22#1458304011yescharacteristic
269C22#1458306212yes—
270C22#1458306911yescharacteristic
271C22#1458307812yes—
272C22#1458308711yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—81no—
278C4—3442no—
279C4—3442no—
280C4—3442no—
281C2—82no—
282C2#1913352011yescharacteristic
283C2#1913357612yes—
284C2#1913371711yescharacteristic
285C2#1913380412yes—
286C2#1913390211yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#1270D43
hypocenterC43#7755
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #19135737C2semidirect
4. #19132420C2semidirect
162. C43#7755semidirect

Maximal subgroups

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

subgroupindex
#191425412
#191357372
#191356772
#191324202
C43×#12702
#775543