Finite Group Databasebeta

← #24984680

Subgroups — #24984680

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137059C211yesmaximal, characteristic
2#19134738C211yesmaximal, characteristic, complemented
3#19132417C212yesmaximal, complemented
4#19132415C212yesmaximal
5C43×#1831C211yesmaximal, characteristic, complemented
6C2×C4×D172C411yescharacteristic
7C2×#13063282—21no—
8#14582801C411yescharacteristic
9#14582801C2211yescharacteristic
10#14582797C411yescharacteristic
11#14582797C2211yescharacteristic
12#14582790—21no—
13#14582790—21no—
14C4×C4⋊Dic43C411yescharacteristic
15C4×(C2×D43)⋊C4—21no—
16#14582654—21no—
17#14582654—21no—
18#14582654C2212yes—
19C2×C4⋊C8×C43—21no—
20C43×C43C2211yescharacteristic
21C43×#336—21no—
22C43×#336C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C4×D43—21no—
25C22×C43⋊C8—22no—
26C4×D172—22no—
27C4×D172C814yescomplemented
28#13063282—44no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×C4×Dic43—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C22×C8×C43—22no—
44C2×C42×C43C2×C411yescharacteristic
45C2×C42×C43C2×C411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C2×C42×C43D411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50C2×C42×C43C2311yescharacteristic
51C4⋊C8×C43—42no—
52C23×D43—21no—
53C22×C4×C43C22⋊C411yescharacteristic
54C22×C4×C43C22⋊C411yescharacteristic
55C22×C4×C43C22⋊C411yescharacteristic
56C22×C4×C43C22⋊C411yescharacteristic
57C22×C4×C43C22×C411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×Dic43—21no—
61C22×Dic43—21no—
62C22×Dic43—21no—
63C2×D172—21no—
64C2×D172—41no—
65C2×D172—41no—
66C2×D172C2×C812yes—
67C2×C4×D43—24no—
68C2×C4×D43—42no—
69C2×C4×D43—42no—
70C2×C8×C43—42no—
71C2×C8×C43—42no—
72C2×C8×C43—42no—
73C42×C43—21no—
74C42×C43—22no—
75C42×C43—21no—
76C42×C43—41no—
77C42×C43—41no—
78C42×C43—41no—
79C42×C43—41no—
80C42×C43C2×C812yes—
81C42×C43M1612yes—
82(C2×D43)⋊C4—24no—
83(C2×D43)⋊C4—42no—
84(C2×D43)⋊C4—42no—
85(C2×D43)⋊C4—41no—
86(C2×D43)⋊C4—42no—
87(C2×D43)⋊C4—41no—
88C4⋊Dic43—21no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43C2×C812yes—
92Dic43⋊C4—42no—
93Dic43⋊C4—42no—
94C4×Dic43—42no—
95C2×C43⋊C8—42no—
96C2×C43⋊C8—42no—
97C2×C43⋊C8—42no—
98C23×C43C2×C22⋊C411yescharacteristic
99C22×D43—22no—
100C22×D43—41no—
101C22×D43—41no—
102C22×D43—41no—
103C22×D43—41no—
104C22×D43—41no—
105C22×D43—41no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43C22⋊C812yes—
123C2×C4×C43C22⋊C812yes—
124C2×C4×C43C22×C811yescharacteristic
125C2×C4×C43C2×M1611yescharacteristic
126C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C43AGL(1,ℤ/8)12yes—
128C2×C4×C43#13711yescharacteristic
129C2×Dic43—22no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138D172—42no—
139D172—42no—
140C4×D43—48no—
141C8×C43—82no—
142C43⋊C8—82no—
143#7594—431nomaximal, Sylow
144C22×C43C2×C22⋊C811yescharacteristic
145C22×C43#41011yescharacteristic
146C22×C43#41311yescharacteristic
147C22×C43#41711yescharacteristic
148C22×C43#41811yescharacteristic
149C22×C43#42111yescharacteristic
150C22×C43#42111yescharacteristic
151C2×D43—42no—
152C2×D43—42no—
153C2×D43—42no—
154C2×D43—81no—
155C2×D43—81no—
156C2×D43—81no—
157C2×D43—81no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—22no—
161C4×C43—22no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—22no—
165C4×C43—41no—
166C4×C43—41no—
167Dic43—42no—
168Dic43—81no—
169Dic43—81no—
170#2293—431no—
171#1839—431no—
172#1831D4311yescharacteristic, complemented
173#1271—432no—
174#1270—432no—
175C2×C43#145811yescharacteristic
176C2×C43#147711yescharacteristic
177C2×C43#147811yescharacteristic
178C2×C43#151211yescharacteristic
179C2×C43#151411yescharacteristic
180C2×C43#153511yescharacteristic
181C2×C43#155711yescharacteristic
182D43—82no—
183C2×C4×D4—431no—
184C2×#117—861no—
185C2×C4⋊C8—21no—
186#390—431no—
187#390—431no—
188#389—431no—
189#389—431no—
190#388—861no—
191#388—861no—
192C4×C4⋊C4—431no—
193C4×C22⋊C4—861no—
194C43C2×D4311yescharacteristic
195#336—21no—
196#336—432no—
197#336—861no—
198#336—861no—
199#336C2×D4312yes—
200C43#759411yescharacteristic, complemented, Sylow
201C22×D4—431no—
202C23×C4—861no—
203C22×C8—22no—
204C22×C8—862no—
205C4×D4—434no—
206C4×D4—862no—
207#117—1724no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4—431no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C22⋊C4—861no—
214C2×C22⋊C4—861no—
215C2×C22⋊C4—861no—
216C2×C22⋊C4—861no—
217C2×C22⋊C4—861no—
218C2×C42—861no—
219C2×C42C4×D4311yescharacteristic
220C2×C42C4×D4311yescharacteristic
221C2×C42D17211yescharacteristic
222C2×C42D17211yescharacteristic
223C2×C42C22⋊D4311yescharacteristic
224C2×C42C22⋊D4311yescharacteristic
225C2×C42C22×D4311yescharacteristic
226C4⋊C8—42no—
227#95—861no—
228#95—861no—
229#95—861no—
230C24—861no—
231C2×D4—432no—
232C2×D4—861no—
233C2×D4—1721no—
234C2×D4—1721no—
235C22×C4—861no—
236C22×C4—864no—
237C22×C4—861no—
238C22×C4—861no—
239C22×C4—1722no—
240C22×C4—1722no—
241C22×C4(C2×D43)⋊C411yescharacteristic
242C22×C4(C2×D43)⋊C411yescharacteristic
243C22×C4(C2×D43)⋊C411yescharacteristic
244C22×C4(C2×D43)⋊C411yescharacteristic
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4C2×D17211yescharacteristic
247C22×C4C2×C22⋊D4311yescharacteristic
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—1722no—
252C2×C8—1722no—
253C2×C8—1722no—
254C4⋊C4—432no—
255C4⋊C4—861no—
256C4⋊C4—1721no—
257C4⋊C4—1721no—
258C4⋊C4—1722no—
259C4⋊C4—1722no—
260C22⋊C4—864no—
261C22⋊C4—1722no—
262C22⋊C4—1722no—
263C22⋊C4—1721no—
264C22⋊C4—1722no—
265C22⋊C4—1721no—
266C42—21no—
267C42—22no—
268C42—21no—
269C42—41no—
270C42—41no—
271C42—41no—
272C42—41no—
273C42—1722no—
274C42C8×D4312yes—
275C42#1062187212yes—
276C23—862no—
277C23—1721no—
278C23—1721no—
279C23—1721no—
280C23—1721no—
281C23—1721no—
282C23—1721no—
283C23C2×(C2×D43)⋊C411yescharacteristic
284D4—1722no—
285D4—1722no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—862no—
303C2×C4—1728no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4(C2×D43)⋊C812yes—
313C2×C4(C2×D43)⋊C812yes—
314C2×C4C2×C8×D4311yescharacteristic
315C2×C4C2×#1062187211yescharacteristic
316C2×C4#1306335111yescharacteristic
317C2×C4#1306335312yes—
318C2×C4#1306335611yescharacteristic
319C8—82no—
320C8—3442no—
321C22—3441no—
322C22—3441no—
323C22—3441no—
324C22—3441no—
325C22—1722no—
326C22—1722no—
327C22—1722no—
328C22C2×(C2×D43)⋊C811yescharacteristic
329C22#1458287211yescharacteristic
330C22#1458288111yescharacteristic
331C22#1458289811yescharacteristic
332C22#1458290511yescharacteristic
333C22#1458291511yescharacteristic
334C22#1458291711yescharacteristic
335C4—22no—
336C4—22no—
337C4—21no—
338C4—21no—
339C4—22no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—3441no—
345C4—3441no—
346C4—1722no—
347C2—3442no—
348C2#1913290711yescharacteristic
349C2#1913298011yescharacteristic
350C2#1913298711yescharacteristic
351C2#1913313111yescharacteristic
352C2#1913314311yescharacteristic
353C2#1913322411yescharacteristic
354C2#1913331511yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1831C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1831D43
hypocenterC43#7594
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
2. #19134738C2semidirect
3. #19132417C2semidirect
5. C43×#1831C2semidirect
27. C4×D172C8semidirect
172. #1831D43semidirect
200. C43#7594semidirect

Maximal subgroups

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

subgroupindex
#191370592
#191347382
#191324172
#191324152
C43×#18312
#759443