Finite Group Databasebeta

← #25010116

Subgroups — #25010116

Order 11008.

322 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 67 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#19147599C211yesmaximal, characteristic, complemented
2#19136632C211yesmaximal, characteristic
3#19133952C211yesmaximal, characteristic
4#19132644C211yesmaximal, characteristic, complemented
5#19132575C211yesmaximal, characteristic, complemented
6#19132560C211yesmaximal, characteristic, complemented
7C43×#2248C211yesmaximal, characteristic
8#14583624—21no—
9C2×#13063269—21no—
10#14583277—21no—
11#14583107—22no—
12#14583106—21no—
13#14583096—21no—
14C8×Dic86C2211yescharacteristic
15C4×Dic172C2211yescharacteristic
16Q16×Dic43—21no—
17C4⋊(C43⋊C16)C2211yescharacteristic
18#14582700—21no—
19#14582652C2211yescharacteristic
20#14582643—21no—
21C2×SD32×C43—22no—
22C43×#494C2211yescharacteristic
23C43×#493C2211yescharacteristic
24C4×C16×C43C2211yescharacteristic
25C2×Dic172D411yescharacteristic
26C2×#10621885—22no—
27C2×#10621883—41no—
28#13063323—22no—
29#13063316—41no—
30#13063315—42no—
31Q8×Dic43—22no—
32C4×Dic86—21no—
33C4×Dic86D411yescharacteristic
34#13063290—41no—
35#13063269—42no—
36C2×C43⋊C16—21no—
37#13063259D411yescharacteristic
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063250—21no—
42#13063249—22no—
43#13063246—41no—
44C8×Dic43—21no—
45C2×Q16×C43—21no—
46C2×Q16×C43D412yes—
47C2×D8×C43—21no—
48C2×D8×C43—21no—
49C4⋊Q8×C43—21no—
50#127×C43—21no—
51SD32×C43—44no—
52C2×C16×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—22no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43—41no—
58C2×Dic86—21no—
59C2×Dic86D811yescharacteristic
60Q16×C43—42no—
61Q16×C43—41no—
62Q16×C43—41no—
63D8×C43—42no—
64D8×C43—41no—
65D8×C43—41no—
66C2×C8×C43C2×D411yescharacteristic
67C2×C8×C43C2×D411yescharacteristic
68C4⋊C4×C43—41no—
69C4⋊C4×C43—41no—
70C42×C43C2×D411yescharacteristic
71#10621885—82no—
72#10621883—82no—
73C4⋊Dic43—21no—
74C4⋊Dic43—42no—
75C4⋊Dic43D811yescharacteristic
76Dic43⋊C4—21no—
77Dic43⋊C4—42no—
78Dic43⋊C4—42no—
79Dic43⋊C4—41no—
80C4×Dic43—21no—
81C4×Dic43—42no—
82C4×Dic43—41no—
83C2×C43⋊C8—21no—
84C2×C43⋊C8—41no—
85Dic172—21no—
86Dic172—21no—
87C16×C43—22no—
88C43⋊C16—41no—
89C23×C43—81no—
90Q8×C43—42no—
91Q8×C43—42no—
92D4×C43—81no—
93D4×C43—81no—
94D4×C43—81no—
95D4×C43—81no—
96D4×C43—161no—
97C2×C4×C43—42no—
98C2×C4×C43#12011yescharacteristic
99C2×C4×C43C2×D811yescharacteristic
100C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
101C2×Dic43—21no—
102C2×Dic43—21no—
103C2×Dic43—41no—
104C2×Dic43—41no—
105Dic86—21no—
106Dic86—41no—
107Dic86—41no—
108Dic86SD3212yescomplemented
109C8×C43—21no—
110C8×C43#13511yescharacteristic
111C8×C43AGL(1,ℤ/8)11yescharacteristic
112C43⋊C8—41no—
113C43⋊C8—81no—
114#12330—431nomaximal, Sylow
115C22×C43—161no—
116C22×C43—161no—
117C22×C43—161no—
118C22×C43#44711yescharacteristic
119C4×C43—21no—
120C4×C43—82no—
121C4×C43#44911yescharacteristic
122C4×C43#45311yescharacteristic
123C4×C43C2×SD3211yescharacteristic
124C4×C43#51011yescharacteristic
125Dic43—22no—
126Dic43—41no—
127Dic43—81no—
128Dic43—81no—
129#3395—431no—
130#2248D4311yescharacteristic
131#2207—431no—
132#1668—431no—
133#1362—431no—
134Q8⋊C16—431no—
135#1332—431no—
136C2×C43—321no—
137C2×C43#162111yescharacteristic
138C2×C43#218511yescharacteristic
139C2×C43#219311yescharacteristic
140#557—861no—
141C2×SD32—22no—
142C2×SD32—861no—
143#494—861no—
144#494C2×D4311yescharacteristic
145#493C2×D4311yescharacteristic
146#462—861no—
147#462—862no—
148#460—861no—
149C8×Q8—431no—
150C4×Q16—431no—
151C4×Q16—861no—
152C4⋊C16—431no—
153#357—861no—
154C4×C16C2×D4311yescharacteristic
155#335—431no—
156#331—861no—
157C43#1233011yescharacteristic, complemented, Sylow
158C2×Q16—21no—
159C2×Q16—431no—
160C2×Q16—862no—
161C2×Q16C22⋊D4312yes—
162C2×SD16—1721no—
163C2×D8—21no—
164C2×D8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—862no—
167#127—21no—
168#125—1721no—
169#125—1722no—
170C4×Q8—431no—
171C4×Q8—862no—
172C4×Q8—861no—
173C4×Q8—1721no—
174SD32—44no—
175SD32—1722no—
176C2×C16—21no—
177C2×C16—861no—
178#107—431no—
179C4⋊C8—431no—
180C4⋊C8—861no—
181C4⋊C8—861no—
182#103—862no—
183#103—861no—
184#102—1721no—
185C4×C8—861no—
186C4×C8C22×D4311yescharacteristic
187C2×Q8—22no—
188C2×Q8—431no—
189C2×Q8—861no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—41no—
193Q16—42no—
194Q16—41no—
195Q16—41no—
196Q16—861no—
197Q16—861no—
198Q16—3442no—
199SD16—3442no—
200D8—42no—
201D8—41no—
202D8—41no—
203C2×C8—861no—
204C2×C8—1721no—
205C2×C8D4×D4311yescharacteristic
206C2×C8C2×C22⋊D4311yescharacteristic
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—431no—
210C4⋊C4—861no—
211C4⋊C4—861no—
212C4⋊C4—1722no—
213C4⋊C4—1722no—
214C4⋊C4—1722no—
215C4⋊C4—1721no—
216C42—861no—
217C42—1722no—
218C42—1721no—
219C42D4×D4311yescharacteristic
220C16—22no—
221C16—1721no—
222C23—81no—
223Q8—42no—
224Q8—42no—
225Q8—432no—
226Q8—861no—
227Q8—1721no—
228Q8—1721no—
229D4—81no—
230D4—81no—
231D4—81no—
232D4—81no—
233D4—161no—
234C2×C4—42no—
235C2×C4—861no—
236C2×C4—861no—
237C2×C4—1721no—
238C2×C4—1721no—
239C2×C4#1306329311yescharacteristic
240C2×C4D8×D4311yescharacteristic
241C2×C4#1306334911yescharacteristic
242C8—21no—
243C8—3441no—
244C8—1721no—
245C8#1306334411yescharacteristic
246C8#1306334911yescharacteristic
247C22—161no—
248C22—161no—
249C22—161no—
250C22#1458303111yescharacteristic
251C4—21no—
252C4—82no—
253C4—862no—
254C4—3441no—
255C4—3441no—
256C4—1721no—
257C4#1458304111yescharacteristic
258C4#1458306611yescharacteristic
259C4SD32×D4311yescharacteristic
260C4#1458333811yescharacteristic
261C2—321no—
262C2#1913365711yescharacteristic
263C2#1913651011yescharacteristic
264C2#1913655811yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2248C2
socleC22×C43#447
prime radicalC43×#493C22
hypercenter#2248D43
hypocenterC43#12330
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #19147599C2semidirect
4. #19132644C2semidirect
5. #19132575C2semidirect
6. #19132560C2semidirect
108. Dic86SD32semidirect
157. C43#12330semidirect

Maximal subgroups

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

subgroupindex
#191475992
#191366322
#191339522
#191326442
#191325752
#191325602
C43×#22482
#1233043