Finite Group Databasebeta

← #24985853

Subgroups — #24985853

Order 11008.

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

normal subgroups only

This group has 422 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#19136123C211yesmaximal, characteristic
3#19136005C212yesmaximal, complemented
4#19132420C212yesmaximal, complemented
5C43×#1270C211yesmaximal, characteristic
6C2×#13063258—21no—
7C2×#13063250—22no—
8C2×#13063246—21no—
9#14582838—21no—
10#14582811—22no—
11#14582805C2212yes—
12#14582779—21no—
13#14582774—22no—
14#14582769C2211yescharacteristic
15#14582662—22no—
16#14582654C2211yescharacteristic
17C43×#390C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86D412yes—
20C23×Dic43—21no—
21C22×C43⋊C8—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43—22no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43D412yes—
26C2×C22⋊Dic43—21no—
27C2×C22⋊Dic43—22no—
28#13063258—42no—
29#13063250—44no—
30#13063246—42no—
31C43⋊#95—21no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C22×D4×C43D411yescharacteristic
36C22×C8×C43—22no—
37C2×C4⋊C4×C43D411yescharacteristic
38C2×C22⋊C4×C43—22no—
39C2×C42×C43C2311yescharacteristic
40C24×C43—21no—
41C2×D4×C43—21no—
42C2×D4×C43—41no—
43C2×D4×C43—41no—
44C2×D4×C43Q1612yes—
45C22×C4×C43—21no—
46C22×C4×C43C2×D411yescharacteristic
47C22×C4×C43C2×D412yes—
48C22×Dic43—22no—
49C22×Dic43—22no—
50C22×Dic43—41no—
51C22×Dic43—81no—
52C22×Dic43—82no—
53C2×Dic86—22no—
54C2×Dic86—22no—
55C2×Dic86—42no—
56C2×Dic86—42no—
57C2×C8×C43—42no—
58C2×C8×C43—42no—
59C2×C8×C43—42no—
60C4⋊C4×C43—41no—
61C22⋊C4×C43—42no—
62C22⋊C4×C43—42no—
63C42×C43—41no—
64C22⋊Dic43—82no—
65C22⋊Dic43—81no—
66C4⋊Dic43—42no—
67C4⋊Dic43—41no—
68C4⋊Dic43—41no—
69C4⋊Dic43—42no—
70C4⋊Dic43—42no—
71C4⋊Dic43—81no—
72C2×C43⋊C8—22no—
73C2×C43⋊C8—41no—
74C2×C43⋊C8—41no—
75C23×C43—22no—
76C23×C43—42no—
77C23×C43—41no—
78C23×C43—42no—
79C23×C43—41no—
80C23×C43#12011yescharacteristic
81D4×C43—42no—
82D4×C43—81no—
83C2×C4×C43—21no—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—42no—
88C2×C4×C43—41no—
89C2×C4×C43C2×Q1611yescharacteristic
90C2×C4×C43#13512yes—
91C2×C4×C43AGL(1,ℤ/8)12yes—
92C2×C4×C43#13711yescharacteristic
93C2×Dic43—42no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—42no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—84no—
100C2×Dic43—82no—
101C2×Dic43—81no—
102Dic86—44no—
103Dic86—82no—
104C8×C43—82no—
105C43⋊C8—42no—
106#7821—431nomaximal, Sylow
107C22×C43—42no—
108C22×C43—44no—
109C22×C43—82no—
110C22×C43—81no—
111C22×C43—81no—
112C22×C43#44912yes—
113C22×C43#45111yescharacteristic
114C22×C43#45311yescharacteristic
115C22×C43#45512yes—
116C22×C43#45811yescharacteristic
117C4×C43—22no—
118C4×C43—22no—
119C4×C43—21no—
120C4×C43—21no—
121C4×C43—81no—
122Dic43—82no—
123Dic43—82no—
124Dic43—161no—
125#2804—431no—
126#2093—431no—
127#2072—432no—
128#1272—432no—
129#1270D4311yescharacteristic
130C2×C43—82no—
131C2×C43#161212yes—
132C2×C43#161411yescharacteristic
133C2×C43#162011yescharacteristic
134C2×C43#164412yes—
135C2×C43#165911yescharacteristic
136C2×#107—861no—
137C2×#103—862no—
138C2×#102—861no—
139#400—861no—
140#393—862no—
141#391—432no—
142#390C2×D4311yescharacteristic
143#386—861no—
144#385—862no—
145#384—431no—
146#340—862no—
147#336—431no—
148#336C2×D4312yes—
149C43#782111yescharacteristic, complemented, Sylow
150C22×Q8—432no—
151C22×D4D17211yescharacteristic
152C23×C4—861no—
153C22×C8—22no—
154C22×C8—861no—
155C2×C4⋊C4—432no—
156C2×C4⋊C4—861no—
157C2×C4⋊C4—861no—
158C2×C4⋊C4—862no—
159C2×C4⋊C4D17211yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—862no—
162C2×C22⋊C4—861no—
163C2×C42C22×D4311yescharacteristic
164#107—1722no—
165#103—1724no—
166#102—1722no—
167#95—862no—
168#95—861no—
169#95—862no—
170#95—862no—
171C24—21no—
172C2×Q8—862no—
173C2×Q8—862no—
174C2×Q8—1722no—
175C2×Q8—1722no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4Dic17212yes—
180C22×C4—21no—
181C22×C4—862no—
182C22×C4—862no—
183C22×C4—3441no—
184C22×C4—3442no—
185C22×C4—1721no—
186C22×C4C2×D17211yescharacteristic
187C22×C4D4×D4312yes—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—862no—
192C2×C8—1721no—
193C2×C8—1721no—
194C4⋊C4—41no—
195C4⋊C4—3441no—
196C4⋊C4—1721no—
197C4⋊C4—1721no—
198C4⋊C4—1722no—
199C4⋊C4—1722no—
200C4⋊C4—1722no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—3442no—
204C22⋊C4—3441no—
205C42—41no—
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#1306329511yescharacteristic
212Q8—3442no—
213Q8—1724no—
214D4—42no—
215D4—81no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—3444no—
223C2×C4—3442no—
224C2×C4—3441no—
225C2×C4—1722no—
226C2×C4—1722no—
227C2×C4—1722no—
228C2×C4—1722no—
229C2×C4—1722no—
230C2×C4—1722no—
231C2×C4C2×Dic17211yescharacteristic
232C2×C4#1306334612yes—
233C2×C4#1306334912yes—
234C2×C4#1306335811yescharacteristic
235C8—82no—
236C8—1722no—
237C22—44no—
238C22—42no—
239C22—82no—
240C22—81no—
241C22—81no—
242C22#1458304512yes—
243C22#1458305711yescharacteristic
244C22#1458306911yescharacteristic
245C22#1458307812yes—
246C22#1458309011yescharacteristic
247C4—22no—
248C4—22no—
249C4—21no—
250C4—21no—
251C4—81no—
252C4—3442no—
253C4—3442no—
254C4—6881no—
255C2—82no—
256C2#1913361012yes—
257C2#1913362211yescharacteristic
258C2#1913365511yescharacteristic
259C2#1913381212yes—
260C2#1913390211yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#1270D43
hypocenterC43#7821
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
3. #19136005C2semidirect
4. #19132420C2semidirect
149. C43#7821semidirect

Maximal subgroups

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

subgroupindex
#191425412
#191361232
#191360052
#191324202
C43×#12702
#782143