Finite Group Databasebeta

← #24995926

Subgroups — #24995926

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135544C211yesmaximal, characteristic, complemented
2#19135523C211yesmaximal, characteristic
3#19134462C211yesmaximal, characteristic, complemented
4C2×#14582652C211yesmaximal, characteristic, complemented
5C2×#14582648C211yesmaximal, characteristic, complemented
6C2×#14582643C211yesmaximal, characteristic
7C2×C43×#486C211yesmaximal, characteristic
8C2×C4⋊(C43⋊C8)C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063246—22no—
12C2×#13063235—21no—
13C4×C4⋊Dic43C2211yescharacteristic
14#14582661—22no—
15#14582653—21no—
16#14582652—22no—
17#14582648—22no—
18#14582643—22no—
19C2×C4⋊Q8×C43C2211yescharacteristic
20C2×#127×C43C2211yescharacteristic
21C43×#486—22no—
22C43×#486C414yescomplemented
23C2×#102×C43—21no—
24C2×#102×C43—21no—
25C2×C4×C8×C43C2211yescharacteristic
26C22×C43⋊C8—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29C2×C4⋊Dic43D412yes—
30C2×C4×Dic43—21no—
31C4⋊(C43⋊C8)—21no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)D412yes—
37#13063246—44no—
38#13063235—42no—
39C43⋊#95—21no—
40C22×Q8×C43—21no—
41C22×D4×C43—21no—
42C22×D4×C43—21no—
43C22×D4×C43—21no—
44C22×C8×C43D411yescharacteristic
45C22×C8×C43D411yescharacteristic
46C4⋊Q8×C43—21no—
47C4⋊Q8×C43—21no—
48C4⋊Q8×C43—21no—
49C4⋊Q8×C43C2×C412yes—
50#127×C43—21no—
51#127×C43—21no—
52#127×C43—21no—
53#127×C43C2×C412yes—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C42×C43C2311yescharacteristic
57#102×C43—24no—
58#102×C43—24no—
59C4×C8×C43C2×C412yes—
60C4×C8×C43D412yes—
61C24×C43—41no—
62C2×Q8×C43—22no—
63C2×Q8×C43—41no—
64C2×Q8×C43—82no—
65C2×D4×C43—22no—
66C2×D4×C43—22no—
67C2×D4×C43—22no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—42no—
75C2×D4×C43—41no—
76C2×D4×C43—42no—
77C2×D4×C43—82no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C22×Dic43—22no—
83C2×C8×C43—21no—
84C2×C8×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43—21no—
87C2×C8×C43C22⋊C412yes—
88C2×C8×C43C22⋊C412yes—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C42×C43C22×C411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43#4111yescharacteristic
97C4⋊Dic43—22no—
98C4⋊Dic43—22no—
99C4×Dic43—41no—
100C4×Dic43—41no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—42no—
107C2×C43⋊C8—42no—
108C23×C43—42no—
109C23×C43—81no—
110C23×C43—81no—
111C23×C43—82no—
112C23×C43—82no—
113C23×C43#12111yescharacteristic
114Q8×C43—82no—
115Q8×C43—82no—
116D4×C43—42no—
117D4×C43—42no—
118D4×C43—44no—
119D4×C43—82no—
120D4×C43—82no—
121D4×C43—81no—
122D4×C43—81no—
123D4×C43—81no—
124D4×C43—81no—
125C2×C4×C43—22no—
126C2×C4×C43—42no—
127C2×C4×C43—82no—
128C2×C4×C43C2×C22⋊C411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12411yescharacteristic
133C2×C4×C43#12711yescharacteristic
134C2×C4×C43#13511yescharacteristic
135C2×C4×C43#13511yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)12yes—
138C2×C4×C43#13712yes—
139C2×C4×C43#13711yescharacteristic
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—42no—
143C8×C43—22no—
144C8×C43—22no—
145C43⋊C8—42no—
146C43⋊C8—81no—
147C43⋊C8—81no—
148#9747—431nomaximal, Sylow
149C22×C43—82no—
150C22×C43—82no—
151C22×C43—82no—
152C22×C43—162no—
153C22×C43—162no—
154C22×C43#39011yescharacteristic
155C22×C43#46311yescharacteristic
156C22×C43#46411yescharacteristic
157C22×C43#46812yes—
158C22×C43#47212yes—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—82no—
162C4×C43#41611yescharacteristic
163C4×C43#41711yescharacteristic
164C4×C43#44012yes—
165C4×C43#46311yescharacteristic
166C4×C43#46411yescharacteristic
167C4×C43#49611yescharacteristic
168C4×C43#49711yescharacteristic
169Dic43—82no—
170C2×#486D4311yescharacteristic
171#1987—431no—
172#1982—431no—
173#1770—431no—
174C2×#335—431no—
175C2×#333—431no—
176C2×#331—431no—
177C2×C43—162no—
178C2×C43#169712yes—
179C2×C43#169812yes—
180C2×C43#197311yescharacteristic
181C2×C43#197811yescharacteristic
182C2×C43#198311yescharacteristic
183C2×C4⋊Q8C2×D4311yescharacteristic
184C2×#127C2×D4311yescharacteristic
185#486—22no—
186#486Dic4314yescomplemented
187C2×C4⋊C8—431no—
188C2×C4⋊C8—431no—
189C2×C4⋊C8—431no—
190C2×#102—21no—
191C2×#102—21no—
192C2×#102—862no—
193C2×#97—861no—
194C2×C4×C8C2×D4311yescharacteristic
195C4×C4⋊C4—431no—
196#340—862no—
197#336—861no—
198#335—862no—
199#333—862no—
200#331—862no—
201C43#974711yescharacteristic, complemented, Sylow
202C22×Q8—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×C8—861no—
207C22×C8—861no—
208C22×C8—861no—
209C22×C8C22⋊D4311yescharacteristic
210C22×C8C22⋊D4311yescharacteristic
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8C2×Dic4312yes—
215#127—21no—
216#127—21no—
217#127—21no—
218#127C2×Dic4312yes—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—432no—
222C2×C42—861no—
223C2×C42C22×D4311yescharacteristic
224C4⋊C8—432no—
225C4⋊C8—861no—
226C4⋊C8—861no—
227C4⋊C8—861no—
228C4⋊C8—861no—
229C4⋊C8—861no—
230#102—24no—
231#102—24no—
232#102—1724no—
233#97—1722no—
234C4×C8C2×Dic4312yes—
235C4×C8C22⋊D4312yes—
236#95—861no—
237C24—41no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—82no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—41no—
253C2×D4—82no—
254C22×C4—41no—
255C22×C4—862no—
256C22×C4D4×D4311yescharacteristic
257C22×C4#1062190011yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—862no—
264C2×C8—1721no—
265C2×C8—1721no—
266C2×C8—1722no—
267C2×C8—1722no—
268C2×C8—1721no—
269C2×C8—1721no—
270C2×C8C22⋊Dic4312yes—
271C2×C8C22⋊Dic4312yes—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—862no—
277C4⋊C4—862no—
278C42—1721no—
279C42—1721no—
280C42D4×D4311yescharacteristic
281C42#1062190011yescharacteristic
282C42C22×Dic4311yescharacteristic
283C42C2×C22⋊D4311yescharacteristic
284C23—42no—
285C23—81no—
286C23—81no—
287C23—82no—
288C23—82no—
289C23#1306329611yescharacteristic
290Q8—82no—
291Q8—82no—
292D4—42no—
293D4—42no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—81no—
298D4—81no—
299D4—81no—
300D4—81no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—82no—
304C2×C4—1722no—
305C2×C4—1722no—
306C2×C4—1722no—
307C2×C4C2×C22⋊Dic4311yescharacteristic
308C2×C4D4×Dic4311yescharacteristic
309C2×C4D4×Dic4311yescharacteristic
310C2×C4#1306329611yescharacteristic
311C2×C4#1306331211yescharacteristic
312C2×C4#1306332111yescharacteristic
313C2×C4#1306334511yescharacteristic
314C2×C4#1306334511yescharacteristic
315C2×C4#1306335011yescharacteristic
316C2×C4#1306335212yes—
317C2×C4#1306335412yes—
318C2×C4#1306335511yescharacteristic
319C8—22no—
320C8—22no—
321C8—3441no—
322C8—3441no—
323C8—1722no—
324C22—82no—
325C22—82no—
326C22—82no—
327C22—162no—
328C22—162no—
329C22#1458280211yescharacteristic
330C22#1458311111yescharacteristic
331C22#1458311811yescharacteristic
332C22#1458314212yes—
333C22#1458316612yes—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—3442no—
338C4#1458289511yescharacteristic
339C4#1458290011yescharacteristic
340C4#1458300012yes—
341C4#1458311111yescharacteristic
342C4#1458311811yescharacteristic
343C4#1458328511yescharacteristic
344C4#1458329011yescharacteristic
345C2—162no—
346C2#1913412512yes—
347C2#1913413212yes—
348C2#1913547811yescharacteristic
349C2#1913550611yescharacteristic
350C2#1913552811yescharacteristic
subgroupG/H
centerC23#13063296
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#486C2
socleC23×C43#121
prime radicalC2×#127×C43C22
cosocleC2×C42×C43C23
hypercenterC2×#486D43
hypocenterC43#9747
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #19135544C2semidirect
3. #19134462C2semidirect
4. C2×#14582652C2semidirect
5. C2×#14582648C2semidirect
22. C43×#486C4semidirect
186. #486Dic43semidirect
201. C43#9747semidirect

Maximal subgroups

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

subgroupindex
#191355442
#191355232
#191344622
C2×#145826522
C2×#145826482
C2×#145826432
C2×C43×#4862
#974743