Finite Group Databasebeta

← #25009668

Subgroups — #25009668

Order 11008.

332 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 59 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#19142864C211yesmaximal, characteristic
2#19133637C211yesmaximal, characteristic
3#19133569C211yesmaximal, characteristic
4#19132624C211yesmaximal, characteristic
5#19132621C211yesmaximal, characteristic
6#19132541C211yesmaximal, characteristic
7C43×#2060C211yesmaximal, characteristic
8#14583232—21no—
9#14583054—21no—
10#14582838—21no—
11#14582838C2211yescharacteristic
12#14582832—21no—
13#14582832—21no—
14#14582832—21no—
15#14582819—21no—
16#14582819C2211yescharacteristic
17#14582767—21no—
18#14582636—21no—
19#14582636—21no—
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#428—21no—
24C43×#384C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#339—21no—
27C22×Dic86D411yescharacteristic
28C2×#10621885—41no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43D411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34#13063258—41no—
35#13063249—41no—
36#13063248—41no—
37C22⋊(C43⋊C8)—21no—
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⋊#95D411yescharacteristic
48C43⋊#95D411yescharacteristic
49C2×M16×C43—21no—
50C4⋊Q8×C43—41no—
51#125×C43—41no—
52C22⋊Q8×C43—21no—
53C22⋊Q8×C43—21no—
54#117×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C4⋊C4×C43C2311yescharacteristic
59C2×C42×C43D411yescharacteristic
60#107×C43—41no—
61#106×C43—41no—
62C2×Q8×C43—21no—
63C2×Q8×C43—21no—
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—41no—
74C2×Dic86—81no—
75M16×C43—22no—
76M16×C43—41no—
77C2×C8×C43—41no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—81no—
87C4⋊C4×C43—81no—
88C22⋊C4×C43—41no—
89C42×C43—21no—
90C42×C43—41no—
91C42×C43Q1612yescomplemented
92#10621885—82no—
93C4⋊Dic43—41no—
94C4⋊Dic43—81no—
95Dic43⋊C4—81no—
96Dic43⋊C4—81no—
97Dic43⋊C4—81no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C23×C43#12011yescharacteristic
101Q8×C43—81no—
102Q8×C43—81no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
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×C43—41no—
117C2×C4×C43C2×Q1611yescharacteristic
118C2×C4×C43#13711yescharacteristic
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—42no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130Dic86—42no—
131Dic86—81no—
132C8×C43—42no—
133C43⋊C8—81no—
134C43⋊C8—81no—
135#12259—431nomaximal, Sylow
136C22×C43—21no—
137C22×C43—21no—
138C22×C43#45111yescharacteristic
139C22×C43#45611yescharacteristic
140C22×C43B(4,𝔽2)11yescharacteristic
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—42no—
144C4×C43—41no—
145C4×C43—41no—
146C4×C43—81no—
147C4×C43—81no—
148C4×C43—81no—
149Dic43—81no—
150Dic43—81no—
151Dic43—81no—
152Dic43—81no—
153#2843—431no—
154#2060D4311yescharacteristic
155#1617—431no—
156#1605—431no—
157#1354—431no—
158#1353—431no—
159#1325—431no—
160C2×C43—21no—
161C2×C43—21no—
162C2×C43#160511yescharacteristic
163C2×C43#220011yescharacteristic
164C2×C43#220311yescharacteristic
165#544C2×D4311yescharacteristic
166#484—861no—
167#451—861no—
168#428—21no—
169#400—431no—
170#400—861no—
171#398—861no—
172#398—861no—
173#398—861no—
174#395—431no—
175#395—861no—
176#384C2×D4311yescharacteristic
177#383—861no—
178#343C2×D4311yescharacteristic
179#339—21no—
180#328—861no—
181#328—861no—
182#324—431no—
183#324—431no—
184C43#1225911yescharacteristic, complemented, Sylow
185C22×Q8—431no—
186C2×Q16—1721no—
187C2×M16—21no—
188C4⋊Q8—41no—
189#125—41no—
190C22⋊Q8—21no—
191C22⋊Q8—21no—
192#117—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—431no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4—861no—
198C2×C4⋊C4—861no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4C22⋊D4311yescharacteristic
201C2×C4⋊C4C22×D4311yescharacteristic
202C2×C42C22⋊D4311yescharacteristic
203#107—41no—
204#107—1721no—
205#106—41no—
206#103—1721no—
207#103—1721no—
208C22⋊C8—861no—
209C22⋊C8—861no—
210#95—431no—
211#95—431no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—861no—
218#95—861no—
219#95—861no—
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—3441no—
223C2×Q8—1721no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—861no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4D4×D4311yescharacteristic
231C22×C4D4×D4311yescharacteristic
232C22×C4C2×C22⋊D4311yescharacteristic
233Q16—3442no—
234M16—22no—
235M16—41no—
236C2×C8—41no—
237C2×C8—1721no—
238C2×C8—1721no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—81no—
248C4⋊C4—81no—
249C4⋊C4—3441no—
250C4⋊C4—3441no—
251C4⋊C4—3441no—
252C4⋊C4—3441no—
253C4⋊C4—1721no—
254C22⋊C4—41no—
255C42—21no—
256C42—41no—
257C42#1062188512yescomplemented
258C23#1306329311yescharacteristic
259Q8—81no—
260Q8—81no—
261Q8—3441no—
262Q8—1722no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
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—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1722no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4C2×#1062188511yescharacteristic
289C2×C4#1306335511yescharacteristic
290C8—42no—
291C8—3441no—
292C8—3441no—
293C22—21no—
294C22—21no—
295C22#1458305411yescharacteristic
296C22#1458308111yescharacteristic
297C22#1458308511yescharacteristic
298C4—21no—
299C4—21no—
300C4—42no—
301C4—41no—
302C4—41no—
303C4—81no—
304C4—81no—
305C4—81no—
306C4—3441no—
307C4—3441no—
308C4—3441no—
309C4—3441no—
310C2—21no—
311C2—21no—
312C2#1913356811yescharacteristic
313C2#1913660111yescharacteristic
314C2#1913661411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2060C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#2060D43
hypocenterC43#12259
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
91. C42×C43Q16semidirect
184. C43#12259semidirect
257. C42#10621885semidirect

Maximal subgroups

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

subgroupindex
#191428642
#191336372
#191335692
#191326242
#191326212
#191325412
C43×#20602
#1225943