Finite Group Databasebeta

← #25009620

Subgroups — #25009620

Order 11008.

342 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 57 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#19142661C211yesmaximal, characteristic
2#19135946C211yesmaximal, characteristic
3#19133605C211yesmaximal, characteristic
4#19133602C211yesmaximal, characteristic
5#19132600C211yesmaximal, characteristic
6#19132538C211yesmaximal, characteristic
7C43×#1346C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9C2×#13063315—21no—
10#14583230—21no—
11#14583229—21no—
12#14582941—21no—
13#14582841—21no—
14#14582840—21no—
15#14582833—21no—
16#14582832—21no—
17#14582832—21no—
18#14582829C2211yescharacteristic
19#14582764C2211yescharacteristic
20#14582660—21no—
21#14582637—21no—
22#14582635—21no—
23#14582625C2211yescharacteristic
24C43×#398C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27#13063324—41no—
28#13063316—41no—
29#13063315—42no—
30#13063315—42no—
31#13063304—21no—
32#13063304—21no—
33#13063284—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×C4×Dic43D411yescharacteristic
43#13063259—41no—
44#13063257—41no—
45#13063257—41no—
46#13063256—41no—
47#13063250—41no—
48#13063248—41no—
49C22⋊(C43⋊C8)—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95D411yescharacteristic
57C2×M16×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43D411yescharacteristic
60C2×C4⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43D411yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C2×Dic86—21no—
74C2×Dic86—21no—
75M16×C43—22no—
76M16×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C22⋊Dic43—41no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—42no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91Dic43⋊C4—42no—
92Dic43⋊C4—42no—
93Dic43⋊C4—42no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—81no—
99C4×Dic43—21no—
100C4×Dic43—41no—
101C4×Dic43SD1612yes—
102C2×C43⋊C8—41no—
103C23×C43#12011yescharacteristic
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—41no—
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×C43C2×SD1611yescharacteristic
117C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
118C2×Dic43—22no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—42no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131Dic86—81no—
132Dic86—81no—
133C8×C43—42no—
134C8×C43—81no—
135C43⋊C8—81no—
136#12251—431nomaximal, Sylow
137C22×C43—21no—
138C22×C43—21no—
139C22×C43#45011yescharacteristic
140C22×C43#45611yescharacteristic
141C22×C43B(4,𝔽2)11yescharacteristic
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—41no—
145C4×C43—41no—
146C4×C43—81no—
147C4×C43—81no—
148Dic43—42no—
149Dic43—81no—
150Dic43—81no—
151Dic43—81no—
152Dic43—81no—
153Dic43—81no—
154#2822—431no—
155#2061—431no—
156#1611—431no—
157#1611—431no—
158#1346—431no—
159#1346D4311yescharacteristic
160#1324—431no—
161C2×C43—21no—
162C2×C43—21no—
163C2×C43#160411yescharacteristic
164C2×C43#220111yescharacteristic
165C2×C43#220311yescharacteristic
166#544—431no—
167C2×#125—861no—
168#483—861no—
169#483—861no—
170#428—861no—
171#400—861no—
172#400—861no—
173#398—431no—
174#398—861no—
175#398—861no—
176#398—861no—
177#398C2×D4311yescharacteristic
178#382—431no—
179#343C2×D4311yescharacteristic
180#339—861no—
181#328—861no—
182#328—861no—
183#324—431no—
184#324C2×D4311yescharacteristic
185C43#1225111yescharacteristic, complemented, Sylow
186C2×M16—21no—
187C4⋊Q8—1721no—
188#125—1722no—
189#125—1722no—
190#125—1721no—
191C22⋊Q8—861no—
192C22⋊Q8—861no—
193#117—861no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—431no—
196C2×C4⋊C4—431no—
197C2×C4⋊C4—861no—
198C2×C4⋊C4—861no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4—861no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4D17211yescharacteristic
204C2×C4⋊C4C22×D4311yescharacteristic
205C2×C42—431no—
206#107—1721no—
207#106—1721no—
208#106—1721no—
209#106—1721no—
210#103—1721no—
211#103—1721no—
212C22⋊C8—21no—
213C22⋊C8—861no—
214#95—21no—
215#95—431no—
216#95—861no—
217#95—861no—
218#95—861no—
219#95—861no—
220#95—861no—
221#95—861no—
222#95D17211yescharacteristic
223C2×Q8—861no—
224C2×Q8—861no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4C2×D17211yescharacteristic
232C22×C4D4×D4311yescharacteristic
233C22×C4D4×D4311yescharacteristic
234M16—22no—
235M16—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—1721no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—861no—
244C4⋊C4—861no—
245C4⋊C4—861no—
246C4⋊C4—861no—
247C4⋊C4—3441no—
248C4⋊C4—1721no—
249C4⋊C4—1721no—
250C4⋊C4—1721no—
251C4⋊C4—1721no—
252C4⋊C4—1722no—
253C4⋊C4—1722no—
254C4⋊C4—1722no—
255C4⋊C4—1722no—
256C4⋊C4—1721no—
257C4⋊C4—1721no—
258C22⋊C4—1721no—
259C42—432no—
260C42—861no—
261C42—1721no—
262C23#1306329511yescharacteristic
263Q8—3441no—
264Q8—3441no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—862no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4—1722no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4SD16×D4311yescharacteristic
291C2×C4#1306334911yescharacteristic
292C8—42no—
293C8—81no—
294C8—3441no—
295C22—21no—
296C22—21no—
297C22#1458305111yescharacteristic
298C22#1458308311yescharacteristic
299C22#1458308711yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—81no—
305C4—81no—
306C4—3441no—
307C4—3441no—
308C4—3441no—
309C4—3441no—
310C4—3441no—
311C4—1722no—
312C2—21no—
313C2—21no—
314C2#1913356511yescharacteristic
315C2#1913660911yescharacteristic
316C2#1913661711yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1346C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1346D43
hypocenterC43#12251
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
185. C43#12251semidirect

Maximal subgroups

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

subgroupindex
#191426612
#191359462
#191336052
#191336022
#191326002
#191325382
C43×#13462
#1225143