Finite Group Databasebeta

← #25009790

Subgroups — #25009790

Order 11008.

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

normal subgroups only

This group has 318 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#19142771C211yesmaximal, characteristic
2#19133637C211yesmaximal, characteristic
3#19133603C211yesmaximal, characteristic
4#19132621C211yesmaximal, characteristic
5#19132600C211yesmaximal, characteristic
6#19132529C211yesmaximal, characteristic
7C43×#2028C211yesmaximal, characteristic
8#14583232—21no—
9#14583227—21no—
10C43⋊#401—21no—
11#14582841—21no—
12#14582840—21no—
13#14582838C2211yescharacteristic
14#14582833—21no—
15#14582829C2211yescharacteristic
16#14582818—21no—
17#14582783—21no—
18#14582636—21no—
19#14582636—21no—
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#419—21no—
24C43×#391C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#339—21no—
27C2×C4⋊Dic43D411yescharacteristic
28C2×C4⋊Dic43D411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33#13063258—41no—
34#13063256—41no—
35#13063249—41no—
36#13063249—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
49C22×Q8×C43D411yescharacteristic
50C2×M16×C43—21no—
51C4⋊Q8×C43—41no—
52#125×C43—41no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55#117×C43—21no—
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C42×C43D411yescharacteristic
58#103×C43—41no—
59#103×C43—41no—
60#95×C43—21no—
61#95×C43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—21no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77M16×C43—41no—
78M16×C43—41no—
79C2×C8×C43—41no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C42×C43—41no—
89C42×C43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—81no—
95Dic43⋊C4—81no—
96Dic43⋊C4—81no—
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—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×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—81no—
133C43⋊C8—81no—
134#12277—431nomaximal, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43#45211yescharacteristic
138C22×C43#45511yescharacteristic
139C22×C43B(4,𝔽2)11yescharacteristic
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—41no—
143C4×C43—41no—
144C4×C43—81no—
145C4×C43—81no—
146C4×C43—81no—
147C4×C43—81no—
148Dic43—81no—
149Dic43—81no—
150Dic43—81no—
151Dic43—81no—
152#2833—431no—
153#2028D4311yescharacteristic
154#1617—431no—
155#1611—431no—
156#1353—431no—
157#1346—431no—
158#1319—431no—
159C2×C43—21no—
160C2×C43—21no—
161C2×C43#160611yescharacteristic
162C2×C43#220111yescharacteristic
163C2×C43#220311yescharacteristic
164#544C2×D4311yescharacteristic
165#484—861no—
166#483—861no—
167#419—21no—
168#401—861no—
169#400—431no—
170#400—861no—
171#400—861no—
172#398—431no—
173#398—861no—
174#395—861no—
175#391C2×D4311yescharacteristic
176#387—861no—
177#343C2×D4311yescharacteristic
178#339—21no—
179#328—861no—
180#328—861no—
181#324—431no—
182#324—431no—
183C43#1227711yescharacteristic, complemented, Sylow
184C22×Q8C22⋊D4311yescharacteristic
185C2×M16—21no—
186C4⋊Q8—41no—
187#125—41no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190#117—21no—
191C2×C4⋊C4—431no—
192C2×C4⋊C4—431no—
193C2×C4⋊C4—861no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4C22×D4311yescharacteristic
198C2×C42C22⋊D4311yescharacteristic
199#107—1721no—
200#106—1721no—
201#103—41no—
202#103—41no—
203#103—1721no—
204#103—1721no—
205C22⋊C8—861no—
206C22⋊C8—861no—
207#95—21no—
208#95—21no—
209#95—431no—
210#95—431no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—861no—
218#95—861no—
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—41no—
224C2×Q8—41no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4D4×D4311yescharacteristic
232C22×C4D4×D4311yescharacteristic
233C22×C4C2×C22⋊D4311yescharacteristic
234M16—41no—
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—3441no—
247C4⋊C4—3441no—
248C4⋊C4—3441no—
249C4⋊C4—1721no—
250C4⋊C4—1721no—
251C4⋊C4—1721no—
252C4⋊C4—1721no—
253C22⋊C4—41no—
254C42—41no—
255C42—41no—
256C23#1306329311yescharacteristic
257Q8—42no—
258Q8—81no—
259Q8—81no—
260Q8—81no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
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#1306334511yescharacteristic
287C2×C4#1306335611yescharacteristic
288C8—81no—
289C8—3441no—
290C8—3441no—
291C22—21no—
292C22—21no—
293C22#1458305911yescharacteristic
294C22#1458307611yescharacteristic
295C22#1458308511yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—81no—
301C4—81no—
302C4—81no—
303C4—81no—
304C4—3441no—
305C4—3441no—
306C4—3441no—
307C4—3441no—
308C2—21no—
309C2—21no—
310C2#1913357311yescharacteristic
311C2#1913660711yescharacteristic
312C2#1913661411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2028C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#2028D43
hypocenterC43#12277
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2028

Complements

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

NH ≅ G/Ntype
183. C43#12277semidirect

Maximal subgroups

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

subgroupindex
#191427712
#191336372
#191336032
#191326212
#191326002
#191325292
C43×#20282
#1227743