Finite Group Databasebeta

← #25009527

Subgroups — #25009527

Order 11008.

334 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 55 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#19142357C211yesmaximal, characteristic
2#19135942C211yesmaximal, characteristic
3#19133603C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic
5#19132602C211yesmaximal, characteristic
6#19132538C211yesmaximal, characteristic
7C43×#1605C211yesmaximal, characteristic
8#14583227—21no—
9#14582942—21no—
10C43⋊#401—21no—
11#14582838—21no—
12#14582829C2211yescharacteristic
13#14582806—21no—
14#14582786—21no—
15#14582785—21no—
16#14582784—21no—
17#14582764C2211yescharacteristic
18#14582668C2211yescharacteristic
19#14582658—21no—
20#14582636—21no—
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#451—21no—
24C43×#395C2211yescharacteristic
25C43×#328—21no—
26C43×#324C2211yescharacteristic
27C2×#10621877—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43D411yescharacteristic
30C2×C4⋊Dic43D411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×C4×Dic43—21no—
33C2×C4×Dic43D411yescharacteristic
34#13063258—41no—
35#13063256—41no—
36#13063256—41no—
37#13063249—41no—
38C22⋊(C43⋊C8)—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95D411yescharacteristic
49C22×Q8×C43D411yescharacteristic
50C2×Q16×C43—41no—
51C4⋊Q8×C43—41no—
52#125×C43—41no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55#117×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43C2311yescharacteristic
58#103×C43—41no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62C2×Q8×C43—21no—
63C2×Q8×C43—21no—
64C2×Q8×C43—42no—
65C2×Q8×C43—41no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75Q16×C43—82no—
76C2×C8×C43—41no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—42no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C22⋊C4×C43—41no—
86C42×C43—41no—
87C4⋊Dic43—42no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92C4×Dic43—21no—
93C4×Dic43—21no—
94C4×Dic43—81no—
95#10621877—22no—
96#10621877—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C23×C43#12011yescharacteristic
100Q8×C43—42no—
101Q8×C43—81no—
102Q8×C43—81no—
103Q8×C43—81no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43#13511yescharacteristic
119C2×C4×C43#13711yescharacteristic
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—42no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C8×C43—81no—
132C43⋊C8—42no—
133C43⋊C8—81no—
134#12237—431nomaximal, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43#45211yescharacteristic
138C22×C43#45611yescharacteristic
139C22×C43B(4,𝔽2)11yescharacteristic
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—41no—
143C4×C43—41no—
144C4×C43—42no—
145C4×C43—81no—
146C4×C43—81no—
147C4×C43—81no—
148Dic43—81no—
149Dic43—81no—
150Dic43—81no—
151Dic43—81no—
152#2789—431no—
153#2061—431no—
154#1611—431no—
155#1605D4311yescharacteristic
156#1354—431no—
157#1346—431no—
158#1324—431no—
159C2×C43—21no—
160C2×C43—21no—
161C2×C43#160311yescharacteristic
162C2×C43#219711yescharacteristic
163C2×C43#220311yescharacteristic
164#544C2×D4311yescharacteristic
165#483—861no—
166#451—21no—
167#428—861no—
168#401—861no—
169#400—861no—
170#398—431no—
171#395C2×D4311yescharacteristic
172#391—861no—
173#387—861no—
174#387—861no—
175#387—861no—
176#382—431no—
177#343—431no—
178#339—861no—
179#328—21no—
180#328—861no—
181#324—431no—
182#324C2×D4311yescharacteristic
183C43#1223711yescharacteristic, complemented, Sylow
184C22×Q8C22⋊D4311yescharacteristic
185C2×Q16—41no—
186C2×M16—861no—
187C4⋊Q8—41no—
188#125—41no—
189C22⋊Q8—21no—
190C22⋊Q8—21no—
191#117—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—431no—
194C2×C4⋊C4—431no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4C22×D4311yescharacteristic
198C2×C42—431no—
199C2×C42—861no—
200#107—1721no—
201#106—1721no—
202#106—1721no—
203#103—41no—
204#103—1721no—
205C22⋊C8—21no—
206C22⋊C8—861no—
207#95—21no—
208#95—431no—
209#95—861no—
210#95—861no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—861no—
218#95C22⋊D4311yescharacteristic
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—42no—
222C2×Q8—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—861no—
226C22×C4—861no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4D4×D4311yescharacteristic
230C22×C4D4×D4311yescharacteristic
231C22×C4C2×C22⋊D4311yescharacteristic
232Q16—82no—
233M16—862no—
234M16—1721no—
235C2×C8—41no—
236C2×C8—1721no—
237C2×C8—1721no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—1721no—
247C4⋊C4—1721no—
248C4⋊C4—1722no—
249C4⋊C4—1721no—
250C4⋊C4—1721no—
251C22⋊C4—41no—
252C42—41no—
253C42—861no—
254C42—861no—
255C42—3441no—
256C23#1306329311yescharacteristic
257Q8—42no—
258Q8—81no—
259Q8—81no—
260Q8—81no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1722no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4#1306334811yescharacteristic
287C2×C4#1306335711yescharacteristic
288C8—81no—
289C8—3441no—
290C8—1722no—
291C22—21no—
292C22—21no—
293C22#1458306011yescharacteristic
294C22#1458308011yescharacteristic
295C22#1458308511yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—42no—
301C4—81no—
302C4—81no—
303C4—81no—
304C4—3441no—
305C4—3441no—
306C4—3441no—
307C4—3441no—
308C2—21no—
309C2—21no—
310C2#1913355711yescharacteristic
311C2#1913658311yescharacteristic
312C2#1913661411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1605C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1605D43
hypocenterC43#12237
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1605

Complements

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

NH ≅ G/Ntype
183. C43#12237semidirect

Maximal subgroups

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

subgroupindex
#191423572
#191359422
#191336032
#191326252
#191326022
#191325382
C43×#16052
#1223743