Finite Group Databasebeta

← #25009519

Subgroups — #25009519

Order 11008.

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

normal subgroups only

This group has 324 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#19142415C211yesmaximal, characteristic
2#19133637C211yesmaximal, characteristic
3#19133603C211yesmaximal, characteristic
4#19132621C211yesmaximal, characteristic
5#19132600C211yesmaximal, characteristic
6#19132541C211yesmaximal, characteristic
7C43×#2060C211yesmaximal, characteristic
8#14583232—21no—
9#14583227—21no—
10#14582838C2211yescharacteristic
11#14582837—21no—
12#14582837—21no—
13#14582829C2211yescharacteristic
14#14582785—21no—
15#14582785—21no—
16#14582783—21no—
17#14582780—21no—
18#14582636—21no—
19#14582636—21no—
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#428—21no—
24C43×#384C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#339—21no—
27C2×C4⋊Dic43D411yescharacteristic
28C2×C4⋊Dic43D411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×C4×Dic43—21no—
32#13063258—41no—
33#13063256—41no—
34#13063249—41no—
35#13063249—41no—
36C22⋊(C43⋊C8)—21no—
37C22⋊(C43⋊C8)—21no—
38C43⋊#95—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—
73M16×C43—22no—
74M16×C43—41no—
75C2×C8×C43—41no—
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—42no—
83C4⋊C4×C43—42no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C42×C43—21no—
88C42×C43—21no—
89C42×C43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92Dic43⋊C4—42no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95C4×Dic43—81no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C23×C43#12011yescharacteristic
99Q8×C43—81no—
100Q8×C43—81no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—22no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
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#13511yescharacteristic
116C2×C4×C43#13711yescharacteristic
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—42no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C8×C43—42no—
129C43⋊C8—81no—
130C43⋊C8—81no—
131#12236—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43#45211yescharacteristic
135C22×C43#45611yescharacteristic
136C22×C43B(4,𝔽2)11yescharacteristic
137C4×C43—21no—
138C4×C43—21no—
139C4×C43—42no—
140C4×C43—41no—
141C4×C43—41no—
142C4×C43—81no—
143C4×C43—81no—
144C4×C43—81no—
145Dic43—81no—
146Dic43—81no—
147Dic43—81no—
148Dic43—81no—
149#2794—431no—
150#2060D4311yescharacteristic
151#1617—431no—
152#1611—431no—
153#1353—431no—
154#1346—431no—
155#1325—431no—
156C2×C43—21no—
157C2×C43—21no—
158C2×C43#160311yescharacteristic
159C2×C43#219811yescharacteristic
160C2×C43#220311yescharacteristic
161#544C2×D4311yescharacteristic
162#484—861no—
163#483—861no—
164#428—21no—
165#400—431no—
166#400—861no—
167#400—861no—
168#398—431no—
169#387—861no—
170#387—861no—
171#387—861no—
172#387—861no—
173#384C2×D4311yescharacteristic
174#343C2×D4311yescharacteristic
175#339—21no—
176#328—861no—
177#328—861no—
178#324—431no—
179#324—431no—
180C43#1223611yescharacteristic, complemented, Sylow
181C2×M16—21no—
182C4⋊Q8—41no—
183#125—41no—
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186#117—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—431no—
190C2×C4⋊C4—431no—
191C2×C4⋊C4—861no—
192C2×C4⋊C4—861no—
193C2×C4⋊C4C22⋊D4311yescharacteristic
194C2×C4⋊C4C22×D4311yescharacteristic
195C2×C42—861no—
196C2×C42C22⋊D4311yescharacteristic
197#107—41no—
198#107—1721no—
199#106—41no—
200#106—1721no—
201#103—1721no—
202#103—1721no—
203C22⋊C8—861no—
204C22⋊C8—861no—
205#95—431no—
206#95—431no—
207#95—861no—
208#95—861no—
209#95—861no—
210#95—861no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216C2×Q8—21no—
217C2×Q8—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4D4×D4311yescharacteristic
225C22×C4D4×D4311yescharacteristic
226C22×C4C2×C22⋊D4311yescharacteristic
227M16—22no—
228M16—41no—
229C2×C8—41no—
230C2×C8—1721no—
231C2×C8—1721no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—1721no—
243C4⋊C4—1721no—
244C4⋊C4—1722no—
245C4⋊C4—1721no—
246C4⋊C4—1721no—
247C22⋊C4—41no—
248C42—21no—
249C42—21no—
250C42—41no—
251C42—3441no—
252C23#1306329311yescharacteristic
253Q8—81no—
254Q8—81no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1721no—
273C2×C4—1722no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4#1306334511yescharacteristic
281C2×C4#1306335611yescharacteristic
282C8—42no—
283C8—3441no—
284C8—3441no—
285C22—21no—
286C22—21no—
287C22#1458305911yescharacteristic
288C22#1458308111yescharacteristic
289C22#1458308511yescharacteristic
290C4—21no—
291C4—21no—
292C4—42no—
293C4—41no—
294C4—41no—
295C4—81no—
296C4—81no—
297C4—81no—
298C4—3441no—
299C4—3441no—
300C4—3441no—
301C4—3441no—
302C2—21no—
303C2—21no—
304C2#1913355611yescharacteristic
305C2#1913659011yescharacteristic
306C2#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#12236
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
180. C43#12236semidirect

Maximal subgroups

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

subgroupindex
#191424152
#191336372
#191336032
#191326212
#191326002
#191325412
C43×#20602
#1223643