Finite Group Databasebeta

← #25010118

Subgroups — #25010118

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#19147600C211yesmaximal, characteristic, complemented
2#19136850C211yesmaximal, characteristic
3#19133952C211yesmaximal, characteristic
4#19132645C211yesmaximal, characteristic, complemented
5#19132573C211yesmaximal, characteristic, complemented
6#19132559C211yesmaximal, characteristic, complemented
7C43×#2207C211yesmaximal, characteristic
8#14583627—21no—
9C2×#13063269—22no—
10#14583279C2211yescharacteristic
11#14583277—21no—
12#14583109—21no—
13#14583108—22no—
14#14583096—21no—
15C8×Dic86C2211yescharacteristic
16#14582993—21no—
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582643—21no—
20C2×SD32×C43—21no—
21C43×#493C2211yescharacteristic
22C4×Q16×C43C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#357—21no—
25C2×Dic172—21no—
26C2×Dic172D412yes—
27C2×#10621885—22no—
28C2×#10621883—41no—
29#13063325—21no—
30#13063323—22no—
31#13063317—41no—
32#13063315—42no—
33C4×Dic86—41no—
34C4×Dic86D411yescharacteristic
35#13063290—22no—
36#13063269—44no—
37C2×C43⋊C16—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40Dic43⋊C8—21no—
41#13063248—22no—
42#13063246—41no—
43C8×Dic43—21no—
44C2×Q16×C43D411yescharacteristic
45C2×D8×C43—21no—
46C2×D8×C43—21no—
47#127×C43—21no—
48C4×Q8×C43—21no—
49SD32×C43—42no—
50C2×C16×C43—21no—
51#107×C43D411yescharacteristic
52#103×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—21no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43—41no—
58C2×Dic86—22no—
59C2×Dic86D811yescharacteristic
60Q16×C43—21no—
61Q16×C43—21no—
62D8×C43—42no—
63D8×C43—41no—
64D8×C43—41no—
65C2×C8×C43C2×D411yescharacteristic
66C2×C8×C43C2×D411yescharacteristic
67C4⋊C4×C43—21no—
68C4⋊C4×C43—41no—
69C42×C43—41no—
70C42×C43C2×D411yescharacteristic
71#10621885—82no—
72#10621883—82no—
73C4⋊Dic43—41no—
74C4⋊Dic43—41no—
75C4⋊Dic43D811yescharacteristic
76Dic43⋊C4—21no—
77Dic43⋊C4—42no—
78Dic43⋊C4—42no—
79Dic43⋊C4—42no—
80C4×Dic43—21no—
81C4×Dic43—42no—
82C2×C43⋊C8—21no—
83C2×C43⋊C8—41no—
84Dic172—42no—
85Dic172—41no—
86Dic172—41no—
87C16×C43—41no—
88C43⋊C16—22no—
89C23×C43—81no—
90Q8×C43—41no—
91Q8×C43—41no—
92D4×C43—81no—
93D4×C43—81no—
94D4×C43—81no—
95D4×C43—81no—
96D4×C43—161no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43#12011yescharacteristic
100C2×C4×C43C2×D811yescharacteristic
101C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
102C2×Dic43—21no—
103C2×Dic43—21no—
104C2×Dic43—42no—
105Dic86—21no—
106Dic86—42no—
107Dic86—42no—
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—81no—
121C4×C43—81no—
122C4×C43#44911yescharacteristic
123C4×C43#45311yescharacteristic
124C4×C43C2×SD3211yescharacteristic
125C4×C43#51011yescharacteristic
126Dic43—22no—
127Dic43—41no—
128Dic43—82no—
129#3395—431no—
130#2248—431no—
131#2207D4311yescharacteristic
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—21no—
142C2×SD32—862no—
143#494—431no—
144#494—861no—
145#493C2×D4311yescharacteristic
146#462—862no—
147#462—861no—
148#460—861no—
149C8×Q8—431no—
150C4×Q16—861no—
151C4×Q16C2×D4311yescharacteristic
152C4⋊C16C2×D4311yescharacteristic
153#357—21no—
154C4×C16—431no—
155#335—431no—
156#331—861no—
157C43#1233011yescharacteristic, complemented, Sylow
158C2×Q16—432no—
159C2×Q16—862no—
160C2×Q16—861no—
161C2×Q16C22⋊D4311yescharacteristic
162C2×SD16—1721no—
163C2×D8—21no—
164C2×D8—21no—
165C4⋊Q8—862no—
166C4⋊Q8—861no—
167#127—21no—
168#125—1721no—
169#125—1722no—
170C4×Q8—21no—
171C4×Q8—431no—
172C4×Q8—862no—
173C4×Q8—1721no—
174SD32—42no—
175SD32—1724no—
176C2×C16—21no—
177C2×C16—861no—
178#107C22⋊D4311yescharacteristic
179C4⋊C8—431no—
180C4⋊C8—861no—
181C4⋊C8—861no—
182#103—21no—
183#103—862no—
184#102—1721no—
185C4×C8—861no—
186C4×C8C22×D4311yescharacteristic
187C2×Q8—21no—
188C2×Q8—431no—
189C2×Q8—862no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—41no—
193Q16—21no—
194Q16—21no—
195Q16—3442no—
196Q16—1722no—
197Q16—1721no—
198Q16—1721no—
199SD16—3442no—
200D8—42no—
201D8—41no—
202D8—41no—
203C2×C8—861no—
204C2×C8—1721no—
205C2×C8D4×D4311yescharacteristic
206C2×C8C2×C22⋊D4311yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—431no—
210C4⋊C4—861no—
211C4⋊C4—1722no—
212C4⋊C4—1722no—
213C4⋊C4—1722no—
214C4⋊C4—1721no—
215C4⋊C4—1721no—
216C42—41no—
217C42—861no—
218C42—1722no—
219C42D4×D4311yescharacteristic
220C16—41no—
221C16—862no—
222C23—81no—
223Q8—41no—
224Q8—41no—
225Q8—432no—
226Q8—861no—
227Q8—1722no—
228Q8—1722no—
229D4—81no—
230D4—81no—
231D4—81no—
232D4—81no—
233D4—161no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—861no—
237C2×C4—861no—
238C2×C4—1722no—
239C2×C4#1306329311yescharacteristic
240C2×C4D8×D4311yescharacteristic
241C2×C4#1306334911yescharacteristic
242C8—21no—
243C8—3441no—
244C8—1721no—
245C8#1306334511yescharacteristic
246C8#1306335111yescharacteristic
247C22—161no—
248C22—161no—
249C22—161no—
250C22#1458303111yescharacteristic
251C4—21no—
252C4—81no—
253C4—81no—
254C4—862no—
255C4—3442no—
256C4—1721no—
257C4#1458304211yescharacteristic
258C4#1458306511yescharacteristic
259C4SD32×D4311yescharacteristic
260C4#1458333811yescharacteristic
261C2—321no—
262C2#1913365911yescharacteristic
263C2#1913651011yescharacteristic
264C2#1913655611yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2207C2
socleC22×C43#447
prime radicalC43×#493C22
hypercenter#2207D43
hypocenterC43#12330
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #19147600C2semidirect
4. #19132645C2semidirect
5. #19132573C2semidirect
6. #19132559C2semidirect
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
#191476002
#191368502
#191339522
#191326452
#191325732
#191325592
C43×#22072
#1233043